Fracture characterization by hybrid enumerative search and Gauss-Newton least-squares inversion methods

NASA Astrophysics Data System (ADS)

Alkharji, Mohammed N.

Most fracture characterization methods provide a general description of the fracture parameters as part of the reservoirs parameters; the fracture interaction and geometry within the reservoir is given less attention. T-Matrix and Linear Slip effective medium fracture models are implemented to invert the elastic tensor for the parameters and geometries of the fractures within the reservoir. The fracture inverse problem has an ill-posed, overdetermined, underconstrained rank-deficit system of equations. Least-squares inverse methods are used to solve the problem. A good starting initial model for the parameters is a key factor in the reliability of the inversion. Most methods assume that the starting parameters are close to the solution to avoid inaccurate local minimum solutions. The prior knowledge of the fracture parameters and their geometry is not available. We develop a hybrid, enumerative and Gauss-Newton, method that estimates the fracture parameters and geometry from the elastic tensor with no prior knowledge of the initial parameter values. The fracture parameters are separated into two groups. The first group contains the fracture parameters with no prior information, and the second group contains the parameters with known prior information. Different models are generated from the first group parameters by sampling the solution space over a predefined range of possible solutions for each parameter. Each model generated by the first group is fixed and used as a starting model to invert for the second group of parameters using the Gauss-Newton method. The least-squares residual between the observed elastic tensor and the estimated elastic tensor is calculated for each model. The model parameters that yield the least-squares residual corresponds to the correct fracture reservoir parameters and geometry. Two synthetic examples of fractured reservoirs with oil and gas saturations were inverted with no prior information about the fracture properties. The results showed that the hybrid algorithm successfully predicted the fracture parametrization, geometry, and the fluid content within the modeled reservoir. The method was also applied on an elastic tensor extracted from the Weyburn field in Saskatchewan, Canada. The solution suggested no presence of fractures but only a VTI system caused by the shale layering in the targeted reservoir, this interpretation is supported by other Weyburn field data.

Moment Tensor Inversion of the 1998 Aiquile Earthquake Using Long-period surface waves

NASA Astrophysics Data System (ADS)

Wang, H.

2016-12-01

On 22nd May 1998 at 04:49(GMT), an earthquake of magnitude Mw = 6.6 struck the Aiquile region of Bolivia, causing 105 deaths and significant damage to the nearby towns of Hoyadas and Pampa Grande. This was the largest shallow earthquake (15 km depth) in Bolivia in over 50 years, and was felt as far Sucre, approximately 100 km away. In this report, a centroid moment tensor (CMT) inversion is carried using body waves and surface waves from 1998 Aiquile earthquake with 1-D and 3-D earth models to obtain the source model parameters and moment tensor, which are the values will be subsequently compared against the Global Centroid Moment Tensor Catalog(GCMT). Also, the excitation kernels could be gained and synthetic data can be created with different earth models. The two method for calculating synthetic seismograms are SPECFEM3D Globe which is based on shear wave mantle model S40RTS and crustal model CRUST 2.0, and AxiSEM which is based on PREM 1-D earth Model. Within the report, the theory behind the CMT inversion was explained and the source parameters gained from the inversion can be used to reveal the tectonics of the source of this earthquake, these information could be helpful in assessing seismic hazard and overall tectonic regime of this region. Furthermore, results of synthetic seismograms and the solution of inversion are going to be used to assess two models.

Moment tensor inversions using strong motion waveforms of Taiwan TSMIP data, 1993–2009

USGS Publications Warehouse

Chang, Kaiwen; Chi, Wu-Cheng; Gung, Yuancheng; Dreger, Douglas; Lee, William H K.; Chiu, Hung-Chie

2011-01-01

Earthquake source parameters are important for earthquake studies and seismic hazard assessment. Moment tensors are among the most important earthquake source parameters, and are now routinely derived using modern broadband seismic networks around the world. Similar waveform inversion techniques can also apply to other available data, including strong-motion seismograms. Strong-motion waveforms are also broadband, and recorded in many regions since the 1980s. Thus, strong-motion data can be used to augment moment tensor catalogs with a much larger dataset than that available from the high-gain, broadband seismic networks. However, a systematic comparison between the moment tensors derived from strong motion waveforms and high-gain broadband waveforms has not been available. In this study, we inverted the source mechanisms of Taiwan earthquakes between 1993 and 2009 by using the regional moment tensor inversion method using digital data from several hundred stations in the Taiwan Strong Motion Instrumentation Program (TSMIP). By testing different velocity models and filter passbands, we were able to successfully derive moment tensor solutions for 107 earthquakes of Mw >= 4.8. The solutions for large events agree well with other available moment tensor catalogs derived from local and global broadband networks. However, for Mw = 5.0 or smaller events, we consistently over estimated the moment magnitudes by 0.5 to 1.0. We have tested accelerograms, and velocity waveforms integrated from accelerograms for the inversions, and found the results are similar. In addition, we used part of the catalogs to study important seismogenic structures in the area near Meishan Taiwan which was the site of a very damaging earthquake a century ago, and found that the structures were dominated by events with complex right-lateral strike-slip faulting during the recent decade. The procedures developed from this study may be applied to other strong-motion datasets to compliment or fill gaps in catalogs from regional broadband networks and teleseismic networks.

New Methods For Interpretation Of Magnetic Gradient Tensor Data Using Eigenalysis And The Normalized Source Strength

NASA Astrophysics Data System (ADS)

Clark, D.

2012-12-01

In the future, acquisition of magnetic gradient tensor data is likely to become routine. New methods developed for analysis of magnetic gradient tensor data can also be applied to high quality conventional TMI surveys that have been processed using Fourier filtering techniques, or otherwise, to calculate magnetic vector and tensor components. This approach is, in fact, the only practical way at present to analyze vector component data, as measurements of vector components are seriously afflicted by motion noise, which is not as serious a problem for gradient components. In many circumstances, an optimal approach to extracting maximum information from magnetic surveys would be to combine analysis of measured gradient tensor data with vector components calculated from TMI measurements. New methods for inverting gradient tensor surveys to obtain source parameters have been developed for a number of elementary, but useful, models. These include point dipole (sphere), vertical line of dipoles (narrow vertical pipe), line of dipoles (horizontal cylinder), thin dipping sheet, horizontal line current and contact models. A key simplification is the use of eigenvalues and associated eigenvectors of the tensor. The normalized source strength (NSS), calculated from the eigenvalues, is a particularly useful rotational invariant that peaks directly over 3D compact sources, 2D compact sources, thin sheets and contacts, and is independent of magnetization direction for these sources (and only very weakly dependent on magnetization direction in general). In combination the NSS and its vector gradient enable estimation of the Euler structural index, thereby constraining source geometry, and determine source locations uniquely. NSS analysis can be extended to other useful models, such as vertical pipes, by calculating eigenvalues of the vertical derivative of the gradient tensor. Once source locations are determined, information of source magnetizations can be obtained by simple linear inversion of measured or calculated vector and/or tensor data. Inversions based on the vector gradient of the NSS over the Tallawang magnetite deposit in central New South Wales obtained good agreement between the inferred geometry of the tabular magnetite skarn body and drill hole intersections. Inverted magnetizations are consistent with magnetic property measurements on drill core samples from this deposit. Similarly, inversions of calculated tensor data over the Mount Leyshold gold-mineralized porphyry system in Queensland yield good estimates of the centroid location, total magnetic moment and magnetization direction of the magnetite-bearing potassic alteration zone that are consistent with geological and petrophysical information.

anisotropic microseismic focal mechanism inversion by waveform imaging matching

NASA Astrophysics Data System (ADS)

Wang, L.; Chang, X.; Wang, Y.; Xue, Z.

2016-12-01

The focal mechanism is one of the most important parameters in source inversion, for both natural earthquakes and human-induced seismic events. It has been reported to be useful for understanding stress distribution and evaluating the fracturing effect. The conventional focal mechanism inversion method picks the first arrival waveform of P wave. This method assumes the source as a Double Couple (DC) type and the media isotropic, which is usually not the case for induced seismic focal mechanism inversion. For induced seismic events, the inappropriate source and media model in inversion processing, by introducing ambiguity or strong simulation errors, will seriously reduce the inversion effectiveness. First, the focal mechanism contains significant non-DC source type. Generally, the source contains three components: DC, isotropic (ISO) and the compensated linear vector dipole (CLVD), which makes focal mechanisms more complicated. Second, the anisotropy of media will affect travel time and waveform to generate inversion bias. The common way to describe focal mechanism inversion is based on moment tensor (MT) inversion which can be decomposed into the combination of DC, ISO and CLVD components. There are two ways to achieve MT inversion. The wave-field migration method is applied to achieve moment tensor imaging. This method can construct elements imaging of MT in 3D space without picking the first arrival, but the retrieved MT value is influenced by imaging resolution. The full waveform inversion is employed to retrieve MT. In this method, the source position and MT can be reconstructed simultaneously. However, this method needs vast numerical calculation. Moreover, the source position and MT also influence each other in the inversion process. In this paper, the waveform imaging matching (WIM) method is proposed, which combines source imaging with waveform inversion for seismic focal mechanism inversion. Our method uses the 3D tilted transverse isotropic (TTI) elastic wave equation to approximate wave propagating in anisotropic media. First, a source imaging procedure is employed to obtain the source position. Second, we refine a waveform inversion algorithm to retrieve MT. We also use a microseismic data set recorded in surface acquisition to test our method.

Rethinking moment tensor inversion methods to retrieve the source mechanisms of low-frequency seismic events

NASA Astrophysics Data System (ADS)

Karl, S.; Neuberg, J.

2011-12-01

Volcanoes exhibit a variety of seismic signals. One specific type, the so-called long-period (LP) or low-frequency event, has proven to be crucial for understanding the internal dynamics of the volcanic system. These long period (LP) seismic events have been observed at many volcanoes around the world, and are thought to be associated with resonating fluid-filled conduits or fluid movements (Chouet, 1996; Neuberg et al., 2006). While the seismic wavefield is well established, the actual trigger mechanism of these events is still poorly understood. Neuberg et al. (2006) proposed a conceptual model for the trigger of LP events at Montserrat involving the brittle failure of magma in the glass transition in response to the upwards movement of magma. In an attempt to gain a better quantitative understanding of the driving forces of LPs, inversions for the physical source mechanisms have become increasingly common. Previous studies have assumed a point source for waveform inversion. Knowing that applying a point source model to synthetic seismograms representing an extended source process does not yield the real source mechanism, it can, however, still lead to apparent moment tensor elements which then can be compared to previous results in the literature. Therefore, this study follows the proposed concepts of Neuberg et al. (2006), modelling the extended LP source as an octagonal arrangement of double couples approximating a circular ringfault bounding the circumference of the volcanic conduit. Synthetic seismograms were inverted for the physical source mechanisms of LPs using the moment tensor inversion code TDMTISO_INVC by Dreger (2003). Here, we will present the effects of changing the source parameters on the apparent moment tensor elements. First results show that, due to negative interference, the amplitude of the seismic signals of a ringfault structure is greatly reduced when compared to a single double couple source. Furthermore, best inversion results yield a solution comprised of positive isotropic and compensated linear vector dipole components. Thus, the physical source mechanisms of volcano seismic signals may be misinterpreted as opening shear or tensile cracks when wrongly assuming a point source. In order to approach the real physical sources with our models, inversions based on higher-order tensors might have to be considered in the future. An inversion technique where the point source is replaced by a so-called moment tensor density would allow inversions of volcano seismic signals for sources that can then be temporally and spatially extended.

Damped regional-scale stress inversions: Methodology and examples for southern California and the Coalinga aftershock sequence

USGS Publications Warehouse

Hardebeck, J.L.; Michael, A.J.

2006-01-01

We present a new focal mechanism stress inversion technique to produce regional-scale models of stress orientation containing the minimum complexity necessary to fit the data. Current practice is to divide a region into small subareas and to independently fit a stress tensor to the focal mechanisms of each subarea. This procedure may lead to apparent spatial variability that is actually an artifact of overfitting noisy data or nonuniquely fitting data that does not completely constrain the stress tensor. To remove these artifacts while retaining any stress variations that are strongly required by the data, we devise a damped inversion method to simultaneously invert for stress in all subareas while minimizing the difference in stress between adjacent subareas. This method is conceptually similar to other geophysical inverse techniques that incorporate damping, such as seismic tomography. In checkerboard tests, the damped inversion removes the stress rotation artifacts exhibited by an undamped inversion, while resolving sharper true stress rotations than a simple smoothed model or a moving-window inversion. We show an example of a spatially damped stress field for southern California. The methodology can also be used to study temporal stress changes, and an example for the Coalinga, California, aftershock sequence is shown. We recommend use of the damped inversion technique for any study examining spatial or temporal variations in the stress field.

A moment-tensor catalog for intermediate magnitude earthquakes in Mexico

NASA Astrophysics Data System (ADS)

Rodríguez Cardozo, Félix; Hjörleifsdóttir, Vala; Martínez-Peláez, Liliana; Franco, Sara; Iglesias Mendoza, Arturo

2016-04-01

Located among five tectonic plates, Mexico is one of the world's most seismically active regions. The earthquake focal mechanisms provide important information on the active tectonics. A widespread technique for estimating the earthquake magnitud and focal mechanism is the inversion for the moment tensor, obtained by minimizing a misfit function that estimates the difference between synthetic and observed seismograms. An important element in the estimation of the moment tensor is an appropriate velocity model, which allows for the calculation of accurate Green's Functions so that the differences between observed and synthetics seismograms are due to the source of the earthquake rather than the velocity model. However, calculating accurate synthetic seismograms gets progressively more difficult as the magnitude of the earthquakes decreases. Large earthquakes (M>5.0) excite waves of longer periods that interact weakly with lateral heterogeneities in the crust. For these events, using 1D velocity models to compute Greens functions works well and they are well characterized by seismic moment tensors reported in global catalogs (eg. USGS fast moment tensor solutions and GCMT). The opposite occurs for small and intermediate sized events, where the relatively shorter periods excited interact strongly with lateral heterogeneities in the crust and upper mantle. To accurately model the Green's functions for the smaller events in a large heterogeneous area, requires 3D or regionalized 1D models. To obtain a rapid estimate of earthquake magnitude, the National Seismological Survey in Mexico (Servicio Sismológico Nacional, SSN) automatically calculates seismic moment tensors for events in the Mexican Territory (Franco et al., 2002; Nolasco-Carteño, 2006). However, for intermediate-magnitude and small earthquakes the signal-to-noise ratio could is low for many of the seismic stations, and without careful selection and filtering of the data, obtaining a stable focal mechanism is difficult. The selection of data windows and filter parameters is tedious without a tool that allows easy viewing of the data prior to the inversion. Therefore, we developed a graphical user interface (GUI), based on Python and the python library ObsPy, that processes in a iterative and interactive way observed and synthetic seismograms prior to the inversion. The processing includes filtering, choosing and discarding traces and manual adjustment of time windows in which synthetics and observed seismograms will be compared. We calculate the Green Functions using the SPECFEM3D_GLOBE algorithm (Komatitsch et al.,2004) which employs a velocity model that is composed of a mantle and a crustal model, S362ANI (Kustowski et al., 2008) and CRUST2.0 (Bassin et al., 2000), respectively. We invert the observed seismograms for the seismic moment tensor using a method developed for earthquakes in California (Liu et al., 2004) and implemented for earthquakes in Mexico (De la Vega, 2014). In this work, we introduce the GUI, the inversion method and the results from the moment-tensor inversions obtained for intermediate-magnitude earthquakes (4.5

Bayesian ISOLA: new tool for automated centroid moment tensor inversion

NASA Astrophysics Data System (ADS)

Vackář, Jiří; Burjánek, Jan; Gallovič, František; Zahradník, Jiří; Clinton, John

2017-08-01

We have developed a new, fully automated tool for the centroid moment tensor (CMT) inversion in a Bayesian framework. It includes automated data retrieval, data selection where station components with various instrumental disturbances are rejected and full-waveform inversion in a space-time grid around a provided hypocentre. A data covariance matrix calculated from pre-event noise yields an automated weighting of the station recordings according to their noise levels and also serves as an automated frequency filter suppressing noisy frequency ranges. The method is tested on synthetic and observed data. It is applied on a data set from the Swiss seismic network and the results are compared with the existing high-quality MT catalogue. The software package programmed in Python is designed to be as versatile as possible in order to be applicable in various networks ranging from local to regional. The method can be applied either to the everyday network data flow, or to process large pre-existing earthquake catalogues and data sets.

Ferrotoroidial propertiesof Non-Crystallographic Pointgroups

NASA Astrophysics Data System (ADS)

Sireesha, G.; Devi, S. Uma; Yamini Sankar, CH.

2017-08-01

Primary ferroic crystals are the crystals with domain states that are distinguished by properties like spontaneous magnetization, strain, or polarisation. Secondary ferroic crystals are the crystals with domain states that are distinguished by piezoelectric tensor and they are named as Ferromagnetotoroidic (eV2), Ferromagnetoelastic (aeV [V2]) crystals respectively. Here “e” denotes zero rank tensor that changes under spatial inversion, “a” denotes zero rank tensor that changes under time inversion, and “V” denotes a polar vector. Recent observations (Van Aken et al., 2007) identified the fourth type of primary ferroic crystals, a ferrotoroidic crystal with domains distinguished by a toroidial moment. The number of independent constants of quasi crystals is theoretically derived by Wenge Yang et al., (1995). He also formulated the number of independent components of any physical property tensor of quasi crystals using group representation theory. This paper accounts the effect of symmetry on some ferrotoroidial properties of quasi Crystals with 5-fold, 8-fold, 10-fold and 12-fold symmetries using group theoretical methods. Also the number of independent constants is calculated and tabulated that helps in describing the ferrotoroidial properties.

Inversion of gravity gradient tensor data: does it provide better resolution?

NASA Astrophysics Data System (ADS)

Paoletti, V.; Fedi, M.; Italiano, F.; Florio, G.; Ialongo, S.

2016-04-01

The gravity gradient tensor (GGT) has been increasingly used in practical applications, but the advantages and the disadvantages of the analysis of GGT components versus the analysis of the vertical component of the gravity field are still debated. We analyse the performance of joint inversion of GGT components versus separate inversion of the gravity field alone, or of one tensor component. We perform our analysis by inspection of the Picard Plot, a Singular Value Decomposition tool, and analyse both synthetic data and gradiometer measurements carried out at the Vredefort structure, South Africa. We show that the main factors controlling the reliability of the inversion are algebraic ambiguity (the difference between the number of unknowns and the number of available data points) and signal-to-noise ratio. Provided that algebraic ambiguity is kept low and the noise level is small enough so that a sufficient number of SVD components can be included in the regularized solution, we find that: (i) the choice of tensor components involved in the inversion is not crucial to the overall reliability of the reconstructions; (ii) GGT inversion can yield the same resolution as inversion with a denser distribution of gravity data points, but with the advantage of using fewer measurement stations.

Full-wave Moment Tensor and Tomographic Inversions Based on 3D Strain Green Tensor

DTIC Science & Technology

2010-01-31

propagation in three-dimensional (3D) earth, linearizes the inverse problem by iteratively updating the earth model , and provides an accurate way to...self-consistent FD-SGT databases constructed from finite-difference simulations of wave propagation in full-wave tomographic models can be used to...determine the moment tensors within minutes after a seismic event, making it possible for real time monitoring using 3D models . 15. SUBJECT TERMS

A framework for fast probabilistic centroid-moment-tensor determination—inversion of regional static displacement measurements

NASA Astrophysics Data System (ADS)

Käufl, Paul; Valentine, Andrew P.; O'Toole, Thomas B.; Trampert, Jeannot

2014-03-01

The determination of earthquake source parameters is an important task in seismology. For many applications, it is also valuable to understand the uncertainties associated with these determinations, and this is particularly true in the context of earthquake early warning (EEW) and hazard mitigation. In this paper, we develop a framework for probabilistic moment tensor point source inversions in near real time. Our methodology allows us to find an approximation to p(m|d), the conditional probability of source models (m) given observations (d). This is obtained by smoothly interpolating a set of random prior samples, using Mixture Density Networks (MDNs)-a class of neural networks which output the parameters of a Gaussian mixture model. By combining multiple networks as `committees', we are able to obtain a significant improvement in performance over that of a single MDN. Once a committee has been constructed, new observations can be inverted within milliseconds on a standard desktop computer. The method is therefore well suited for use in situations such as EEW, where inversions must be performed routinely and rapidly for a fixed station geometry. To demonstrate the method, we invert regional static GPS displacement data for the 2010 MW 7.2 El Mayor Cucapah earthquake in Baja California to obtain estimates of magnitude, centroid location and depth and focal mechanism. We investigate the extent to which we can constrain moment tensor point sources with static displacement observations under realistic conditions. Our inversion results agree well with published point source solutions for this event, once the uncertainty bounds of each are taken into account.

A high-order strong stability preserving Runge-Kutta method for three-dimensional full waveform modeling and inversion of anelastic models

NASA Astrophysics Data System (ADS)

Wang, N.; Shen, Y.; Yang, D.; Bao, X.; Li, J.; Zhang, W.

2017-12-01

Accurate and efficient forward modeling methods are important for high resolution full waveform inversion. Compared with the elastic case, solving anelastic wave equation requires more computational time, because of the need to compute additional material-independent anelastic functions. A numerical scheme with a large Courant-Friedrichs-Lewy (CFL) condition number enables us to use a large time step to simulate wave propagation, which improves computational efficiency. In this work, we apply the fourth-order strong stability preserving Runge-Kutta method with an optimal CFL coeffiecient to solve the anelastic wave equation. We use a fourth order DRP/opt MacCormack scheme for the spatial discretization, and we approximate the rheological behaviors of the Earth by using the generalized Maxwell body model. With a larger CFL condition number, we find that the computational efficient is significantly improved compared with the traditional fourth-order Runge-Kutta method. Then, we apply the scattering-integral method for calculating travel time and amplitude sensitivity kernels with respect to velocity and attenuation structures. For each source, we carry out one forward simulation and save the time-dependent strain tensor. For each station, we carry out three `backward' simulations for the three components and save the corresponding strain tensors. The sensitivity kernels at each point in the medium are the convolution of the two sets of the strain tensors. Finally, we show several synthetic tests to verify the effectiveness of the strong stability preserving Runge-Kutta method in generating accurate synthetics in full waveform modeling, and in generating accurate strain tensors for calculating sensitivity kernels at regional and global scales.

Full paleostress tensor reconstruction using quartz veins of Panasqueira Mine, central Portugal; part I: Paleopressure determination

NASA Astrophysics Data System (ADS)

Jaques, Luís; Pascal, Christophe

2017-09-01

Paleostress tensor restoration methods are traditionally limited to reconstructing geometrical parameters and are unable to resolve stress magnitudes. Based on previous studies we further developed a methodology to restore full paleostress tensors. We concentrated on inversion of Mode I fractures and acquired data in Panasqueira Mine, Portugal, where optimal exposures of mineralized quartz veins can be found. To carry out full paleostress restoration we needed to determine (1) pore (paleo)pressure and (2) vein attitudes. The present contribution focuses specifically on the determination of pore pressure. To these aims we conducted an extensive fluid inclusion study to derive fluid isochores from the quartz of the studied veins. To constrain P-T conditions, we combined these isochores with crystallisation temperatures derived from geochemical analyses of coeval arsenopyrite. We also applied the sphalerite geobarometer and considered two other independent pressure indicators. Our results point to pore pressures of ∼300 MPa and formation depths of ∼10 km. Such formation depths are in good agreement with the regional geological evolution. The obtained pore pressure will be merged with vein inversion results, in order to achieve full paleostress tensor restoration, in a forthcoming companion paper.

A 3D generic inverse dynamic method using wrench notation and quaternion algebra.

PubMed

Dumas, R; Aissaoui, R; de Guise, J A

2004-06-01

In the literature, conventional 3D inverse dynamic models are limited in three aspects related to inverse dynamic notation, body segment parameters and kinematic formalism. First, conventional notation yields separate computations of the forces and moments with successive coordinate system transformations. Secondly, the way conventional body segment parameters are defined is based on the assumption that the inertia tensor is principal and the centre of mass is located between the proximal and distal ends. Thirdly, the conventional kinematic formalism uses Euler or Cardanic angles that are sequence-dependent and suffer from singularities. In order to overcome these limitations, this paper presents a new generic method for inverse dynamics. This generic method is based on wrench notation for inverse dynamics, a general definition of body segment parameters and quaternion algebra for the kinematic formalism.

Seismic moment tensor inversion using 3D velocity model and its application to the 2013 Lushan earthquake sequence

NASA Astrophysics Data System (ADS)

Zhu, Lupei; Zhou, Xiaofeng

2016-10-01

Source inversion of small-magnitude events such as aftershocks or mine collapses requires use of relatively high frequency seismic waveforms which are strongly affected by small-scale heterogeneities in the crust. In this study, we developed a new inversion method called gCAP3D for determining general moment tensor of a seismic source using Green's functions of 3D models. It inherits the advantageous features of the ;Cut-and-Paste; (CAP) method to break a full seismogram into the Pnl and surface-wave segments and to allow time shift between observed and predicted waveforms. It uses grid search for 5 source parameters (relative strengths of the isotropic and compensated-linear-vector-dipole components and the strike, dip, and rake of the double-couple component) that minimize the waveform misfit. The scalar moment is estimated using the ratio of L2 norms of the data and synthetics. Focal depth can also be determined by repeating the inversion at different depths. We applied gCAP3D to the 2013 Ms 7.0 Lushan earthquake and its aftershocks using a 3D crustal-upper mantle velocity model derived from ambient noise tomography in the region. We first relocated the events using the double-difference method. We then used the finite-differences method and reciprocity principle to calculate Green's functions of the 3D model for 20 permanent broadband seismic stations within 200 km from the source region. We obtained moment tensors of the mainshock and 74 aftershocks ranging from Mw 5.2 to 3.4. The results show that the Lushan earthquake is a reverse faulting at a depth of 13-15 km on a plane dipping 40-47° to N46° W. Most of the aftershocks occurred off the main rupture plane and have similar focal mechanisms to the mainshock's, except in the proximity of the mainshock where the aftershocks' focal mechanisms display some variations.

Waveform inversion of oscillatory signatures in long-period events beneath volcanoes

USGS Publications Warehouse

Kumagai, H.; Chouet, B.A.; Nakano, M.

2002-01-01

The source mechanism of long-period (LP) events is examined using synthetic waveforms generated by the acoustic resonance of a fluid-filled crack. We perform a series of numerical tests in which the oscillatory signatures of synthetic LP waveforms are used to determine the source time functions of the six moment tensor components from waveform inversions assuming a point source. The results indicate that the moment tensor representation is valid for the odd modes of crack resonance with wavelengths 2L/n, 2W/n, n = 3, 5, 7, ..., where L and W are the crack length and width, respectively. For the even modes with wavelengths 2L/n, 2W/n, n = 2, 4, 6,..., a generalized source representation using higher-order tensors is required, although the efficiency of seismic waves radiated by the even modes is expected to be small. We apply the moment tensor inversion to the oscillatory signatures of an LP event observed at Kusatsu-Shirane Volcano, central Japan. Our results point to the resonance of a subhorizontal crack located a few hundred meters beneath the summit crater lakes. The present approach may be useful to quantify the source location, geometry, and force system of LP events, and opens the way for moment tensor inversions of tremor.

Computing the Sensitivity Kernels for 2.5-D Seismic Waveform Inversion in Heterogeneous, Anisotropic Media

NASA Astrophysics Data System (ADS)

Zhou, Bing; Greenhalgh, S. A.

2011-10-01

2.5-D modeling and inversion techniques are much closer to reality than the simple and traditional 2-D seismic wave modeling and inversion. The sensitivity kernels required in full waveform seismic tomographic inversion are the Fréchet derivatives of the displacement vector with respect to the independent anisotropic model parameters of the subsurface. They give the sensitivity of the seismograms to changes in the model parameters. This paper applies two methods, called `the perturbation method' and `the matrix method', to derive the sensitivity kernels for 2.5-D seismic waveform inversion. We show that the two methods yield the same explicit expressions for the Fréchet derivatives using a constant-block model parameterization, and are available for both the line-source (2-D) and the point-source (2.5-D) cases. The method involves two Green's function vectors and their gradients, as well as the derivatives of the elastic modulus tensor with respect to the independent model parameters. The two Green's function vectors are the responses of the displacement vector to the two directed unit vectors located at the source and geophone positions, respectively; they can be generally obtained by numerical methods. The gradients of the Green's function vectors may be approximated in the same manner as the differential computations in the forward modeling. The derivatives of the elastic modulus tensor with respect to the independent model parameters can be obtained analytically, dependent on the class of medium anisotropy. Explicit expressions are given for two special cases—isotropic and tilted transversely isotropic (TTI) media. Numerical examples are given for the latter case, which involves five independent elastic moduli (or Thomsen parameters) plus one angle defining the symmetry axis.

Combined Tensor Fitting and TV Regularization in Diffusion Tensor Imaging Based on a Riemannian Manifold Approach.

PubMed

Baust, Maximilian; Weinmann, Andreas; Wieczorek, Matthias; Lasser, Tobias; Storath, Martin; Navab, Nassir

2016-08-01

In this paper, we consider combined TV denoising and diffusion tensor fitting in DTI using the affine-invariant Riemannian metric on the space of diffusion tensors. Instead of first fitting the diffusion tensors, and then denoising them, we define a suitable TV type energy functional which incorporates the measured DWIs (using an inverse problem setup) and which measures the nearness of neighboring tensors in the manifold. To approach this functional, we propose generalized forward- backward splitting algorithms which combine an explicit and several implicit steps performed on a decomposition of the functional. We validate the performance of the derived algorithms on synthetic and real DTI data. In particular, we work on real 3D data. To our knowledge, the present paper describes the first approach to TV regularization in a combined manifold and inverse problem setup.

Global moment tensor computation at GFZ Potsdam

NASA Astrophysics Data System (ADS)

Saul, J.; Becker, J.; Hanka, W.

2011-12-01

As part of its earthquake information service, GFZ Potsdam has started to provide seismic moment tensor solutions for significant earthquakes world-wide. The software used to compute the moment tensors is a GFZ-Potsdam in-house development, which uses the framework of the software SeisComP 3 (Hanka et al., 2010). SeisComP 3 (SC3) is a software package for seismological data acquisition, archival, quality control and analysis. SC3 is developed by GFZ Potsdam with significant contributions from its user community. The moment tensor inversion technique uses a combination of several wave types, time windows and frequency bands depending on magnitude and station distance. Wave types include body, surface and mantle waves as well as the so-called 'W-Phase' (Kanamori and Rivera, 2008). The inversion is currently performed in the time domain only. An iterative centroid search can be performed independently both horizontally and in depth. Moment tensors are currently computed in a semi-automatic fashion. This involves inversions that are performed automatically in near-real time, followed by analyst review prior to publication. The automatic results are quite often good enough to be published without further improvements, sometimes in less than 30 minutes from origin time. In those cases where a manual interaction is still required, the automatic inversion usually does a good job at pre-selecting those traces that are the most relevant for the inversion, keeping the work required for the analyst at a minimum. Our published moment tensors are generally in good agreement with those published by the Global Centroid-Moment-Tensor (GCMT) project for earthquakes above a magnitude of about Mw 5. Additionally we provide solutions for smaller earthquakes above about Mw 4 in Europe, which are normally not analyzed by the GCMT project. We find that for earthquakes above Mw 6, the most robust automatic inversions can usually be obtained using the W-Phase time window. The GFZ earthquake bulletin is located at http://geofon.gfz-potsdam.de/eqinfo For more information on the SeisComP 3 software visit http://www.seiscomp3.org

Characterizing crustal and uppermost mantle anisotropy with a depth-dependent tilted hexagonally symmetric elastic tensor: theory and examples

NASA Astrophysics Data System (ADS)

Feng, L.; Xie, J.; Ritzwoller, M. H.

2017-12-01

Two major types of surface wave anisotropy are commonly observed by seismologists but are only rarely interpreted jointly: apparent radial anisotropy, which is the difference in propagation speed between horizontally and vertically polarized waves inferred from Love and Rayleigh waves, and apparent azimuthal anisotropy, which is the directional dependence of surface wave speeds (usually Rayleigh waves). We describe a method of inversion that interprets simultaneous observations of radial and azimuthal anisotropy under the assumption of a hexagonally symmetric elastic tensor with a tilted symmetry axis defined by dip and strike angles. With a full-waveform numerical solver based on the spectral element method (SEM), we verify the validity of the forward theory used for the inversion. We also present two examples, in the US and Tibet, in which we have successfully applied the tomographic method to demonstrate that the two types of apparent anisotropy can be interpreted jointly as a tilted hexagonally symmetric medium.

SORTAN: a Unix program for calculation and graphical presentation of fault slip as induced by stresses

NASA Astrophysics Data System (ADS)

Pascal, Christophe

2004-04-01

Stress inversion programs are nowadays frequently used in tectonic analysis. The purpose of this family of programs is to reconstruct the stress tensor characteristics from fault slip data acquired in the field or derived from earthquake focal mechanisms (i.e. inverse methods). Until now, little attention has been paid to direct methods (i.e. to determine fault slip directions from an inferred stress tensor). During the 1990s, the fast increase in resolution in 3D seismic reflection techniques made it possible to determine the geometry of subsurface faults with a satisfactory accuracy but not to determine precisely their kinematics. This recent improvement allows the use of direct methods. A computer program, namely SORTAN, is introduced. The program is highly portable on Unix platforms, straightforward to install and user-friendly. The computation is based on classical stress-fault slip relationships and allows for fast treatment of a set of faults and graphical presentation of the results (i.e. slip directions). In addition, the SORTAN program permits one to test the sensitivity of the results to input uncertainties. It is a complementary tool to classical stress inversion methods and can be used to check the mechanical consistency and the limits of structural interpretations based upon 3D seismic reflection surveys.

Inversion of calcite twin data for paleostress (1) : improved Etchecopar technique tested on numerically-generated and natural data

NASA Astrophysics Data System (ADS)

Parlangeau, Camille; Lacombe, Olivier; Daniel, Jean-Marc; Schueller, Sylvie

2015-04-01

Inversion of calcite twin data are known to be a powerful tool to reconstruct the past-state of stress in carbonate rocks of the crust, especially in fold-and-thrust belts and sedimentary basins. This is of key importance to constrain results of geomechanical modelling. Without proposing a new inversion scheme, this contribution reports some recent improvements of the most efficient stress inversion technique to date (Etchecopar, 1984) that allows to reconstruct the 5 parameters of the deviatoric paleostress tensors (principal stress orientations and differential stress magnitudes) from monophase and polyphase twin data sets. The improvements consist in the search of the possible tensors that account for the twin data (twinned and untwinned planes) and the aid to the user to define the best stress tensor solution, among others. We perform a systematic exploration of an hypersphere in 4 dimensions by varying different parameters, Euler's angles and the stress ratio. We first record all tensors with a minimum penalization function accounting for 20% of the twinned planes. We then define clusters of tensors following a dissimilarity criterion based on the stress distance between the 4 parameters of the reduced stress tensors and a degree of disjunction of the related sets of twinned planes. The percentage of twinned data to be explained by each tensor is then progressively increased and tested using the standard Etchecopar procedure until the best solution that explains the maximum number of twinned planes and the whole set of untwinned planes is reached. This new inversion procedure is tested on monophase and polyphase numerically-generated as well as natural calcite twin data in order to more accurately define the ability of the technique to separate more or less similar deviatoric stress tensors applied in sequence on the samples, to test the impact of strain hardening through the change of the critical resolved shear stress for twinning as well as to evaluate the possible bias due to measurement uncertainties or clustering of grain optical axes in the samples.

Resistivity Image from 2D Inversion of Magnetotelluric Data in the Northern Cascadia Subduction Zone (United States)

NASA Astrophysics Data System (ADS)

Gultom, F. B.; Niasari, S. W.; Hartantyo, E.

2018-04-01

Cascadia Subduction Zone (CSZ) lies between Pacific margin and North America plate. The purpose of this research is to identify the CSZ along Oregon, Idaho, Wyoming from conductivity (σ) contrast in the subsurface by using the magnetotelluric (MT) method. MT is an electromagnetic method that use frequency between 10-4 Hz and 104 Hz. We obtained the MT data from the EarthScope USArray in the form of EDI-File (five components of the electromagnetic field). We analyzed the MT data using phase tensor and modeled the data using 2D inversion. From the phase tensor analysis, the 3D data dominated the eastern regions. Global data misfit is 6,88, where WYI18 (close to Yellowstone) contributes misfit of 29,3. This means that the model response does not fit the data, which implies the data is not fully 2D. The 2D inversion results are found high resistivity anomalies (more than 500 ohm.m) at shallow depth beneath Oregon and Wyoming, which coresspond to high density anomalies. This high resistivity anomalies might correspond to the north American plate. Thus, it can be concluded that 2D inversion model can be used for most 3D MT data to illustrate the resistivity distribution in the Cascadia Subduction Zone.

Application of a moment tensor inversion code developed for mining-induced seismicity to fracture monitoring of civil engineering materials

NASA Astrophysics Data System (ADS)

Linzer, Lindsay; Mhamdi, Lassaad; Schumacher, Thomas

2015-01-01

A moment tensor inversion (MTI) code originally developed to compute source mechanisms from mining-induced seismicity data is now being used in the laboratory in a civil engineering research environment. Quantitative seismology methods designed for geological environments are being tested with the aim of developing techniques to assess and monitor fracture processes in structural concrete members such as bridge girders. In this paper, we highlight aspects of the MTI_Toolbox programme that make it applicable to performing inversions on acoustic emission (AE) data recorded by networks of uniaxial sensors. The influence of the configuration of a seismic network on the conditioning of the least-squares system and subsequent moment tensor results for a real, 3-D network are compared to a hypothetical 2-D version of the same network. This comparative analysis is undertaken for different cases: for networks consisting entirely of triaxial or uniaxial sensors; for both P and S-waves, and for P-waves only. The aim is to guide the optimal design of sensor configurations where only uniaxial sensors can be installed. Finally, the findings of recent laboratory experiments where the MTI_Toolbox has been applied to a concrete beam test are presented and discussed.

Full paleostress tensor reconstruction: case study of the Panasqueira Mine, Portugal.

NASA Astrophysics Data System (ADS)

Pascal, C.; Jaques Ribeiro, L. M.

2017-12-01

Paleostress tensor restoration methods are traditionally limited to reconstructing geometrical parameters and are unable to resolve stress magnitudes. Based on previous studies we further developed a methodology to restore full paleostress tensors. We concentrated on inversion of Mode I fractures and acquired data in Panasqueira Mine, Portugal, where optimal 3D exposures of mineralised quartz veins can be found. To carry out full paleostress restoration we needed to determine (1) pore (paleo)pressure and (2) vein attitudes. To these aims we conducted an extensive fluid inclusion study to derive fluid isochores from the quartz of the studied veins. To further constrain P-T conditions, we combined these isochores with crystallisation temperatures derived from geochemical analyses of coeval arsenopyrite. We also applied the sphalerite geobarometer and considered two other independent pressure indicators. Our results point to pore pressures of 300 MPa and formation depths of 10 km. As a second step, we measured 600 subhorizontal quartz veins in all the levels of the mine. The inversion of the attitudes of the veins allowed for reconstructing the orientations of the principal axes of stress, the unscaled Mohr circle and the relative pore pressure. After merging these results with the previously obtained absolute pore pressure we reconstructed the six parameters of the paleostress tensor.

A 2D forward and inverse code for streaming potential problems

NASA Astrophysics Data System (ADS)

Soueid Ahmed, A.; Jardani, A.; Revil, A.

2013-12-01

The self-potential method corresponds to the passive measurement of the electrical field in response to the occurrence of natural sources of current in the ground. One of these sources corresponds to the streaming current associated with the flow of the groundwater. We can therefore apply the self- potential method to recover non-intrusively some information regarding the groundwater flow. We first solve the forward problem starting with the solution of the groundwater flow problem, then computing the source current density, and finally solving a Poisson equation for the electrical potential. We use the finite-element method to solve the relevant partial differential equations. In order to reduce the number of (petrophysical) model parameters required to solve the forward problem, we introduced an effective charge density tensor of the pore water, which can be determined directly from the permeability tensor for neutral pore waters. The second aspect of our work concerns the inversion of the self-potential data using Tikhonov regularization with smoothness and weighting depth constraints. This approach accounts for the distribution of the electrical resistivity, which can be independently and approximately determined from electrical resistivity tomography. A numerical code, SP2DINV, has been implemented in Matlab to perform both the forward and inverse modeling. Three synthetic case studies are discussed.

Investigating source processes of isotropic events

NASA Astrophysics Data System (ADS)

Chiang, Andrea

This dissertation demonstrates the utility of the complete waveform regional moment tensor inversion for nuclear event discrimination. I explore the source processes and associated uncertainties for explosions and earthquakes under the effects of limited station coverage, compound seismic sources, assumptions in velocity models and the corresponding Green's functions, and the effects of shallow source depth and free-surface conditions. The motivation to develop better techniques to obtain reliable source mechanism and assess uncertainties is not limited to nuclear monitoring, but they also provide quantitative information about the characteristics of seismic hazards, local and regional tectonics and in-situ stress fields of the region . This dissertation begins with the analysis of three sparsely recorded events: the 14 September 1988 US-Soviet Joint Verification Experiment (JVE) nuclear test at the Semipalatinsk test site in Eastern Kazakhstan, and two nuclear explosions at the Chinese Lop Nor test site. We utilize a regional distance seismic waveform method fitting long-period, complete, three-component waveforms jointly with first-motion observations from regional stations and teleseismic arrays. The combination of long period waveforms and first motion observations provides unique discrimination of these sparsely recorded events in the context of the Hudson et al. (1989) source-type diagram. We examine the effects of the free surface on the moment tensor via synthetic testing, and apply the moment tensor based discrimination method to well-recorded chemical explosions. These shallow chemical explosions represent rather severe source-station geometry in terms of the vanishing traction issues. We show that the combined waveform and first motion method enables the unique discrimination of these events, even though the data include unmodeled single force components resulting from the collapse and blowout of the quarry face immediately following the initial explosion. In contrast, recovering the announced explosive yield using seismic moment estimates from moment tensor inversion remains challenging but we can begin to put error bounds on our moment estimates using the NSS technique. The estimation of seismic source parameters is dependent upon having a well-calibrated velocity model to compute the Green's functions for the inverse problem. Ideally, seismic velocity models are calibrated through broadband waveform modeling, however in regions of low seismicity velocity models derived from body or surface wave tomography may be employed. Whether a velocity model is 1D or 3D, or based on broadband seismic waveform modeling or the various tomographic techniques, the uncertainty in the velocity model can be the greatest source of error in moment tensor inversion. These errors have not been fully investigated for the nuclear discrimination problem. To study the effects of unmodeled structures on the moment tensor inversion, we set up a synthetic experiment where we produce synthetic seismograms for a 3D model (Moschetti et al., 2010) and invert these data using Green's functions computed with a 1D velocity mode (Song et al., 1996) to evaluate the recoverability of input solutions, paying particular attention to biases in the isotropic component. The synthetic experiment results indicate that the 1D model assumption is valid for moment tensor inversions at periods as short as 10 seconds for the 1D western U.S. model (Song et al., 1996). The correct earthquake mechanisms and source depth are recovered with statistically insignificant isotropic components as determined by the F-test. Shallow explosions are biased by the theoretical ISO-CLVD tradeoff but the tectonic release component remains low, and the tradeoff can be eliminated with constraints from P wave first motion. Path-calibration to the 1D model can reduce non-double-couple components in earthquakes, non-isotropic components in explosions and composite sources and improve the fit to the data. When we apply the 3D model to real data, at long periods (20-50 seconds), we see good agreement in the solutions between the 1D and 3D models and slight improvement in waveform fits when using the 3D velocity model Green's functions. (Abstract shortened by ProQuest.).

Moment tensor analysis of very shallow sources

DOE PAGES

Chiang, Andrea; Dreger, Douglas S.; Ford, Sean R.; ...

2016-10-11

An issue for moment tensor (MT) inversion of shallow seismic sources is that some components of the Green’s functions have vanishing amplitudes at the free surface, which can result in bias in the MT solution. The effects of the free surface on the stability of the MT method become important as we continue to investigate and improve the capabilities of regional full MT inversion for source–type identification and discrimination. It is important to understand free–surface effects on discriminating shallow explosive sources for nuclear monitoring purposes. It may also be important in natural systems that have very shallow seismicity, such asmore » volcanic and geothermal systems. We examine the effects of the free surface on the MT via synthetic testing and apply the MT–based discrimination method to three quarry blasts from the HUMMING ALBATROSS experiment. These shallow chemical explosions at ~10 m depth and recorded up to several kilometers distance represent rather severe source–station geometry in terms of free–surface effects. We show that the method is capable of recovering a predominantly explosive source mechanism, and the combined waveform and first–motion method enables the unique discrimination of these events. Furthermore, recovering the design yield using seismic moment estimates from MT inversion remains challenging, but we can begin to put error bounds on our moment estimates using the network sensitivity solution technique.« less

The magnetotelluric phase tensor analysis of the Sembalun-Propok area, West Nusa Tenggara, Indonesia

NASA Astrophysics Data System (ADS)

Febriani, F.; Widarto, D. S.; Gaffar, E.; Nasution, A.; Grandis, H.

2017-04-01

The subsurface structure of the Sembalun-Propok area, NTB, Indonesia, has been investigated using magnetotelluric method (MT). To obtain the information of the dimensionality of the regional structure and determine the regional strike of the study area, the phase tensor analysis has been performed in this study. The results show that most of the skew angle values (β) are distributed within ± 5°. It indicates that the regional structure of the study area can be assumed as two dimensional. In addition, to determine the regional strike of the study area, we also calculated the major axes of the phase tensor. The result presents that the regional strike of the study area is about N330°E. According to the results of the phase tensor analysis, we rotated the impedance tensor to N330°E and performed 2-D inversion modeling. The result presents that the substructure model suits with the geological background of the study area.

3D tensor-based blind multispectral image decomposition for tumor demarcation

NASA Astrophysics Data System (ADS)

Kopriva, Ivica; Peršin, Antun

2010-03-01

Blind decomposition of multi-spectral fluorescent image for tumor demarcation is formulated exploiting tensorial structure of the image. First contribution of the paper is identification of the matrix of spectral responses and 3D tensor of spatial distributions of the materials present in the image from Tucker3 or PARAFAC models of 3D image tensor. Second contribution of the paper is clustering based estimation of the number of the materials present in the image as well as matrix of their spectral profiles. 3D tensor of the spatial distributions of the materials is recovered through 3-mode multiplication of the multi-spectral image tensor and inverse of the matrix of spectral profiles. Tensor representation of the multi-spectral image preserves its local spatial structure that is lost, due to vectorization process, when matrix factorization-based decomposition methods (such as non-negative matrix factorization and independent component analysis) are used. Superior performance of the tensor-based image decomposition over matrix factorization-based decompositions is demonstrated on experimental red-green-blue (RGB) image with known ground truth as well as on RGB fluorescent images of the skin tumor (basal cell carcinoma).

Towards adjoint-based inversion for rheological parameters in nonlinear viscous mantle flow

NASA Astrophysics Data System (ADS)

Worthen, Jennifer; Stadler, Georg; Petra, Noemi; Gurnis, Michael; Ghattas, Omar

2014-09-01

We address the problem of inferring mantle rheological parameter fields from surface velocity observations and instantaneous nonlinear mantle flow models. We formulate this inverse problem as an infinite-dimensional nonlinear least squares optimization problem governed by nonlinear Stokes equations. We provide expressions for the gradient of the cost functional of this optimization problem with respect to two spatially-varying rheological parameter fields: the viscosity prefactor and the exponent of the second invariant of the strain rate tensor. Adjoint (linearized) Stokes equations, which are characterized by a 4th order anisotropic viscosity tensor, facilitates efficient computation of the gradient. A quasi-Newton method for the solution of this optimization problem is presented, which requires the repeated solution of both nonlinear forward Stokes and linearized adjoint Stokes equations. For the solution of the nonlinear Stokes equations, we find that Newton’s method is significantly more efficient than a Picard fixed point method. Spectral analysis of the inverse operator given by the Hessian of the optimization problem reveals that the numerical eigenvalues collapse rapidly to zero, suggesting a high degree of ill-posedness of the inverse problem. To overcome this ill-posedness, we employ Tikhonov regularization (favoring smooth parameter fields) or total variation (TV) regularization (favoring piecewise-smooth parameter fields). Solution of two- and three-dimensional finite element-based model inverse problems show that a constant parameter in the constitutive law can be recovered well from surface velocity observations. Inverting for a spatially-varying parameter field leads to its reasonable recovery, in particular close to the surface. When inferring two spatially varying parameter fields, only an effective viscosity field and the total viscous dissipation are recoverable. Finally, a model of a subducting plate shows that a localized weak zone at the plate boundary can be partially recovered, especially with TV regularization.

Finite-frequency structural sensitivities of short-period compressional body waves

NASA Astrophysics Data System (ADS)

Fuji, Nobuaki; Chevrot, Sébastien; Zhao, Li; Geller, Robert J.; Kawai, Kenji

2012-07-01

We present an extension of the method recently introduced by Zhao & Chevrot for calculating Fréchet kernels from a precomputed database of strain Green's tensors by normal mode summation. The extension involves two aspects: (1) we compute the strain Green's tensors using the Direct Solution Method, which allows us to go up to frequencies as high as 1 Hz; and (2) we develop a spatial interpolation scheme so that the Green's tensors can be computed with a relatively coarse grid, thus improving the efficiency in the computation of the sensitivity kernels. The only requirement is that the Green's tensors be computed with a fine enough spatial sampling rate to avoid spatial aliasing. The Green's tensors can then be interpolated to any location inside the Earth, avoiding the need to store and retrieve strain Green's tensors for a fine sampling grid. The interpolation scheme not only significantly reduces the CPU time required to calculate the Green's tensor database and the disk space to store it, but also enhances the efficiency in computing the kernels by reducing the number of I/O operations needed to retrieve the Green's tensors. Our new implementation allows us to calculate sensitivity kernels for high-frequency teleseismic body waves with very modest computational resources such as a laptop. We illustrate the potential of our approach for seismic tomography by computing traveltime and amplitude sensitivity kernels for high frequency P, PKP and Pdiff phases. A comparison of our PKP kernels with those computed by asymptotic ray theory clearly shows the limits of the latter. With ray theory, it is not possible to model waves diffracted by internal discontinuities such as the core-mantle boundary, and it is also difficult to compute amplitudes for paths close to the B-caustic of the PKP phase. We also compute waveform partial derivatives for different parts of the seismic wavefield, a key ingredient for high resolution imaging by waveform inversion. Our computations of partial derivatives in the time window where PcP precursors are commonly observed show that the distribution of sensitivity is complex and counter-intuitive, with a large contribution from the mid-mantle region. This clearly emphasizes the need to use accurate and complete partial derivatives in waveform inversion.

Detailed fault structure of the 2000 Western Tottori, Japan, earthquake sequence

USGS Publications Warehouse

Fukuyama, E.; Ellsworth, W.L.; Waldhauser, F.; Kubo, A.

2003-01-01

We investigate the faulting process of the aftershock region of the 2000 western Tottori earthquake (Mw 6.6) by combining aftershock hypocenters and moment tensor solutions. Aftershock locations were precisely determined by the double difference method using P- and S-phase arrival data of the Japan Meteorological Agency unified catalog. By combining the relocated hypocenters and moment tensor solutions of aftershocks by broadband waveform inversion of FREESIA (F-net), we successfully resolved very detailed fault structures activated by the mainshock. The estimated fault model resolves 15 individual fault segments that are consistent with both aftershock distribution and focal mechanism solutions. Rupture in the mainshock was principally confined to the three fault elements in the southern half of the zone, which is also where the earliest aftershocks concentrate. With time, the northern part of the zone becomes activated, which is also reflected in the postseismic deformation field. From the stress tensor analysis of aftershock focal mechanisms, we found a rather uniform stress field in the aftershock region, although fault strikes were scattered. The maximum stress direction is N107??E, which is consistent with the tectonic stress field in this region. In the northern part of the fault, where no slip occurred during the mainshock but postseismic slip was observed, the maximum stress direction of N130??E was possible as an alternative solution of stress tensor inversion.

Sampling-free Bayesian inversion with adaptive hierarchical tensor representations

NASA Astrophysics Data System (ADS)

Eigel, Martin; Marschall, Manuel; Schneider, Reinhold

2018-03-01

A sampling-free approach to Bayesian inversion with an explicit polynomial representation of the parameter densities is developed, based on an affine-parametric representation of a linear forward model. This becomes feasible due to the complete treatment in function spaces, which requires an efficient model reduction technique for numerical computations. The advocated perspective yields the crucial benefit that error bounds can be derived for all occuring approximations, leading to provable convergence subject to the discretization parameters. Moreover, it enables a fully adaptive a posteriori control with automatic problem-dependent adjustments of the employed discretizations. The method is discussed in the context of modern hierarchical tensor representations, which are used for the evaluation of a random PDE (the forward model) and the subsequent high-dimensional quadrature of the log-likelihood, alleviating the ‘curse of dimensionality’. Numerical experiments demonstrate the performance and confirm the theoretical results.

Inversion of magnetotelluric data using integral equation approach with variable sensitivity domain: Application to EarthScope MT data

NASA Astrophysics Data System (ADS)

Čuma, Martin; Gribenko, Alexander; Zhdanov, Michael S.

2017-09-01

We have developed a multi-level parallel magnetotelluric (MT) integral equation based inversion program which uses variable sensitivity domain. The limited sensitivity of the data, which decreases with increasing frequency, is exploited by a receiver sensitivity domain, which also varies with frequency. We assess the effect of inverting principal impedances, full impedance tensor, and full tensor jointly with magnetovariational data (tipper). We first apply this method to several models and then invert the EarthScope MT data. We recover well the prominent features in the area including resistive structure associated with the Juan de Fuca slab subducting beneath the northwestern United States, the conductive zone of partially melted material above the subducting slab at the Cascade volcanic arc, conductive features in the Great Basin and in the area of Yellowstone associated with the hot spot, and resistive areas to the east corresponding to the older and more stable cratons.

Crustal velocity structure and earthquake processes of Garhwal-Kumaun Himalaya: Constraints from regional waveform inversion and array beam modeling

NASA Astrophysics Data System (ADS)

Negi, Sanjay S.; Paul, Ajay; Cesca, Simone; Kamal; Kriegerowski, Marius; Mahesh, P.; Gupta, Sandeep

2017-08-01

In order to understand present day earthquake kinematics at the Indian plate boundary, we analyse seismic broadband data recorded between 2007 and 2015 by the regional network in the Garhwal-Kumaun region, northwest Himalaya. We first estimate a local 1-D velocity model for the computation of reliable Green's functions, based on 2837 P-wave and 2680 S-wave arrivals from 251 well located earthquakes. The resulting 1-D crustal structure yields a 4-layer velocity model down to the depths of 20 km. A fifth homogeneous layer extends down to 46 km, constraining the Moho using travel-time distance curve method. We then employ a multistep moment tensor (MT) inversion algorithm to infer seismic moment tensors of 11 moderate earthquakes with Mw magnitude in the range 4.0-5.0. The method provides a fast MT inversion for future monitoring of local seismicity, since Green's functions database has been prepared. To further support the moment tensor solutions, we additionally model P phase beams at seismic arrays at teleseismic distances. The MT inversion result reveals the presence of dominant thrust fault kinematics persisting along the Himalayan belt. Shallow low and high angle thrust faulting is the dominating mechanism in the Garhwal-Kumaun Himalaya. The centroid depths for these moderate earthquakes are shallow between 1 and 12 km. The beam modeling result confirm hypocentral depth estimates between 1 and 7 km. The updated seismicity, constrained source mechanism and depth results indicate typical setting of duplexes above the mid crustal ramp where slip is confirmed along out-of-sequence thrusting. The involvement of Tons thrust sheet in out-of-sequence thrusting indicate Tons thrust to be the principal active thrust at shallow depth in the Himalayan region. Our results thus support the critical taper wedge theory, where we infer the microseismicity cluster as a result of intense activity within the Lesser Himalayan Duplex (LHD) system.

Obtaining orthotropic elasticity tensor using entries zeroing method.

NASA Astrophysics Data System (ADS)

Gierlach, Bartosz; Danek, Tomasz

2017-04-01

A generally anisotropic elasticity tensor obtained from measurements can be represented by a tensor belonging to one of eight material symmetry classes. Knowledge of symmetry class and orientation is helpful for describing physical properties of a medium. For each non-trivial symmetry class except isotropic this problem is nonlinear. A common method of obtaining effective tensor is a choosing its non-trivial symmetry class and minimizing Frobenius norm between measured and effective tensor in the same coordinate system. Global optimization algorithm has to be used to determine the best rotation of a tensor. In this contribution, we propose a new approach to obtain optimal tensor, with the assumption that it is orthotropic (or at least has a similar shape to the orthotropic one). In orthotropic form tensor 24 out of 36 entries are zeros. The idea is to minimize the sum of squared entries which are supposed to be equal to zero through rotation calculated with optimization algorithm - in this case Particle Swarm Optimization (PSO) algorithm. Quaternions were used to parametrize rotations in 3D space to improve computational efficiency. In order to avoid a choice of local minima we apply PSO several times and only if we obtain similar results for the third time we consider it as a correct value and finish computations. To analyze obtained results Monte-Carlo method was used. After thousands of single runs of PSO optimization, we obtained values of quaternion parts and plot them. Points concentrate in several points of the graph following the regular pattern. It suggests the existence of more complex symmetry in the analyzed tensor. Then thousands of realizations of generally anisotropic tensor were generated - each tensor entry was replaced with a random value drawn from normal distribution having a mean equal to measured tensor entry and standard deviation of the measurement. Each of these tensors was subject of PSO based optimization delivering quaternion for optimal rotation. Computations were parallelized with OpenMP to decrease computational time what enables different tensors to be processed by different threads. As a result the distributions of rotated tensor entries values were obtained. For the entries which were to be zeroed we can observe almost normal distributions having mean equal to zero or sum of two normal distributions having inverse means. Non-zero entries represent different distributions with two or three maxima. Analysis of obtained results shows that described method produces consistent values of quaternions used to rotate tensors. Despite of less complex target function in a process of optimization in comparison to common approach, entries zeroing method provides results which can be applied to obtain an orthotropic tensor with good reliability. Modification of the method can produce also a tool for obtaining effective tensors belonging to another symmetry classes. This research was supported by the Polish National Science Center under contract No. DEC-2013/11/B/ST10/0472.

Divergence correction schemes in finite difference method for 3D tensor CSAMT in axial anisotropic media

NASA Astrophysics Data System (ADS)

Wang, Kunpeng; Tan, Handong; Zhang, Zhiyong; Li, Zhiqiang; Cao, Meng

2017-05-01

Resistivity anisotropy and full-tensor controlled-source audio-frequency magnetotellurics (CSAMT) have gradually become hot research topics. However, much of the current anisotropy research for tensor CSAMT only focuses on the one-dimensional (1D) solution. As the subsurface is rarely 1D, it is necessary to study three-dimensional (3D) model response. The staggered-grid finite difference method is an effective simulation method for 3D electromagnetic forward modelling. Previous studies have suggested using the divergence correction to constrain the iterative process when using a staggered-grid finite difference model so as to accelerate the 3D forward speed and enhance the computational accuracy. However, the traditional divergence correction method was developed assuming an isotropic medium. This paper improves the traditional isotropic divergence correction method and derivation process to meet the tensor CSAMT requirements for anisotropy using the volume integral of the divergence equation. This method is more intuitive, enabling a simple derivation of a discrete equation and then calculation of coefficients related to the anisotropic divergence correction equation. We validate the result of our 3D computational results by comparing them to the results computed using an anisotropic, controlled-source 2.5D program. The 3D resistivity anisotropy model allows us to evaluate the consequences of using the divergence correction at different frequencies and for two orthogonal finite length sources. Our results show that the divergence correction plays an important role in 3D tensor CSAMT resistivity anisotropy research and offers a solid foundation for inversion of CSAMT data collected over an anisotropic body.

Extraction of remanent magnetization from magnetization vector inversions of airborne full tensor magnetic gradiometry data

NASA Astrophysics Data System (ADS)

Queitsch, M.; Schiffler, M.; Stolz, R.; Meyer, M.; Kukowski, N.

2017-12-01

Measurements of the Earth's magnetic field are one of the most used methods in geophysical exploration. The ambiguity of the method, especially during modeling and inversion of magnetic field data sets, is one of its biggest challenges. Additional directional information, e.g. gathered by gradiometer systems based on Superconducting Quantum Interference Devices (SQUIDs), will positively influence the inversion results and will thus lead to better subsurface magnetization models. This is especially beneficial, regarding the shape and direction of magnetized structures, especially when a significant remanent magnetization of the underlying sources is present. The possibility to separate induced and remanent contributions to the total magnetization may in future also open up advanced ways for geological interpretation of the data, e.g. a first estimation of diagenesis processes. In this study we present the results of airborne full tensor magnetic gradiometry (FTMG) surveys conducted over a dolerite intrusion in central Germany and the results of two magnetization vector inversions (MVI) of the FTMG and a conventional total field anomaly data set. A separation of the two main contributions of the acquired total magnetization will be compared with information of the rock magnetization measured on orientated rock samples. The FTMG inversion results show a much better agreement in direction and strength of both total and remanent magnetization compared to the inversion using only total field anomaly data. To enhance the separation process, the application of additional geophysical methods, i.e. frequency domain electromagnetics (FDEM), in order to gather spatial information of subsurface rock susceptibility will also be discussed. In this approach, we try to extract not only information on subsurface conductivity but also the induced magnetization. Using the total magnetization from the FTMG data and the induced magnetization from the FDEM data, the full separation of induced and remanent magnetization should be enabled. First results this approach will be shown and discussed.

New methods for interpretation of magnetic vector and gradient tensor data I: eigenvector analysis and the normalised source strength

NASA Astrophysics Data System (ADS)

Clark, David A.

2012-09-01

Acquisition of magnetic gradient tensor data is likely to become routine in the near future. New methods for inverting gradient tensor surveys to obtain source parameters have been developed for several elementary, but useful, models. These include point dipole (sphere), vertical line of dipoles (narrow vertical pipe), line of dipoles (horizontal cylinder), thin dipping sheet, and contact models. A key simplification is the use of eigenvalues and associated eigenvectors of the tensor. The normalised source strength (NSS), calculated from the eigenvalues, is a particularly useful rotational invariant that peaks directly over 3D compact sources, 2D compact sources, thin sheets and contacts, and is independent of magnetisation direction. In combination the NSS and its vector gradient determine source locations uniquely. NSS analysis can be extended to other useful models, such as vertical pipes, by calculating eigenvalues of the vertical derivative of the gradient tensor. Inversion based on the vector gradient of the NSS over the Tallawang magnetite deposit obtained good agreement between the inferred geometry of the tabular magnetite skarn body and drill hole intersections. Besides the geological applications, the algorithms for the dipole model are readily applicable to the detection, location and characterisation (DLC) of magnetic objects, such as naval mines, unexploded ordnance, shipwrecks, archaeological artefacts, and buried drums.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dreger, Douglas S.; Ford, Sean R.; Walter, William R.

Research was carried out investigating the feasibility of using a regional distance seismic waveform moment tensor inverse procedure to estimate source parameters of nuclear explosions and to use the source inversion results to develop a source-type discrimination capability. The results of the research indicate that it is possible to robustly determine the seismic moment tensor of nuclear explosions, and when compared to natural seismicity in the context of the a Hudson et al. (1989) source-type diagram they are found to separate from populations of earthquakes and underground cavity collapse seismic sources.

Tensor methodology and computational geometry in direct computational experiments in fluid mechanics

NASA Astrophysics Data System (ADS)

Degtyarev, Alexander; Khramushin, Vasily; Shichkina, Julia

2017-07-01

The paper considers a generalized functional and algorithmic construction of direct computational experiments in fluid dynamics. Notation of tensor mathematics is naturally embedded in the finite - element operation in the construction of numerical schemes. Large fluid particle, which have a finite size, its own weight, internal displacement and deformation is considered as an elementary computing object. Tensor representation of computational objects becomes strait linear and uniquely approximation of elementary volumes and fluid particles inside them. The proposed approach allows the use of explicit numerical scheme, which is an important condition for increasing the efficiency of the algorithms developed by numerical procedures with natural parallelism. It is shown that advantages of the proposed approach are achieved among them by considering representation of large particles of a continuous medium motion in dual coordinate systems and computing operations in the projections of these two coordinate systems with direct and inverse transformations. So new method for mathematical representation and synthesis of computational experiment based on large particle method is proposed.

Moment tensor clustering: a tool to monitor mining induced seismicity

NASA Astrophysics Data System (ADS)

Cesca, Simone; Dahm, Torsten; Tolga Sen, Ali

2013-04-01

Automated moment tensor inversion routines have been setup in the last decades for the analysis of global and regional seismicity. Recent developments could be used to analyse smaller events and larger datasets. In particular, applications to microseismicity, e.g. in mining environments, have then led to the generation of large moment tensor catalogues. Moment tensor catalogues provide a valuable information about the earthquake source and details of rupturing processes taking place in the seismogenic region. Earthquake focal mechanisms can be used to discuss the local stress field, possible orientations of the fault system or to evaluate the presence of shear and/or tensile cracks. Focal mechanism and moment tensor solutions are typically analysed for selected events, and quick and robust tools for the automated analysis of larger catalogues are needed. We propose here a method to perform cluster analysis for large moment tensor catalogues and identify families of events which characterize the studied microseismicity. Clusters include events with similar focal mechanisms, first requiring the definition of distance between focal mechanisms. Different metrics are here proposed, both for the case of pure double couple, constrained moment tensor and full moment tensor catalogues. Different clustering approaches are implemented and discussed. The method is here applied to synthetic and real datasets from mining environments to demonstrate its potential: the proposed cluserting techniques prove to be able to automatically recognise major clusters. An important application for mining monitoring concerns the early identification of anomalous rupture processes, which is relevant for the hazard assessment. This study is funded by the project MINE, which is part of the R&D-Programme GEOTECHNOLOGIEN. The project MINE is funded by the German Ministry of Education and Research (BMBF), Grant of project BMBF03G0737.

Theory of electromagnetic wave propagation in ferromagnetic Rashba conductor

NASA Astrophysics Data System (ADS)

Shibata, Junya; Takeuchi, Akihito; Kohno, Hiroshi; Tatara, Gen

2018-02-01

We present a comprehensive study of various electromagnetic wave propagation phenomena in a ferromagnetic bulk Rashba conductor from the perspective of quantum mechanical transport. In this system, both the space inversion and time reversal symmetries are broken, as characterized by the Rashba field α and magnetization M, respectively. First, we present a general phenomenological analysis of electromagnetic wave propagation in media with broken space inversion and time reversal symmetries based on the dielectric tensor. The dependence of the dielectric tensor on the wave vector q and M is retained to first order. Then, we calculate the microscopic electromagnetic response of the current and spin of conduction electrons subjected to α and M, based on linear response theory and the Green's function method; the results are used to study the system optical properties. First, it is found that a large α enhances the anisotropic properties of the system and enlarges the frequency range in which the electromagnetic waves have hyperbolic dispersion surfaces and exhibit unusual propagations known as negative refraction and backward waves. Second, we consider the electromagnetic cross-correlation effects (direct and inverse Edelstein effects) on the wave propagation. These effects stem from the lack of space inversion symmetry and yield q-linear off-diagonal components in the dielectric tensor. This induces a Rashba-induced birefringence, in which the polarization vector rotates around the vector (α ×q ) . In the presence of M, which breaks time reversal symmetry, there arises an anomalous Hall effect and the dielectric tensor acquires off-diagonal components linear in M. For α ∥M , these components yield the Faraday effect for the Faraday configuration q ∥M and the Cotton-Mouton effect for the Voigt configuration ( q ⊥M ). When α and M are noncollinear, M- and q-induced optical phenomena are possible, which include nonreciprocal directional dichroism in the Voigt configuration. In these nonreciprocal optical phenomena, a "toroidal moment," α ×M , and a "quadrupole moment," αiMj+Miαj , play central roles. These phenomena are strongly enhanced at the spin-split transition edge in the electron band.

Complex brittle deformation pattern along the Southern Patagonian Andes (Argentina)

NASA Astrophysics Data System (ADS)

Barberón, Vanesa; Sue, Christian; Ronda, Gonzalo; Ghiglione, Matías

2016-04-01

The Southern Patagonian Andes is located in the southern extreme of the Pacific subduction zone, where the Antartic oceanic plate sinks underneath South America. The history of the area begins with compression during Paleozoic, Jurassic extension associated to the rift and opening of the South Atlantic Ocean, then a sag stage in the Lower Cretaceous followed by a foreland phase as a result of plate tectonics (Ghiglione et al., 2016). The kinematic study is concentrated in the Argentinean foothills, between 46°40' and 48° SL. We measured around 800 fault planes and their striaes with the sense of movement in order to characterize the stress field. The software used to make the stress inversion were Tensor (Delvaux, 2011) and Multiple Inverse Method MIM (Yamaji et al., 2011). The stress field map was built with the results of the MIM. We present new data from 48 sites located in the northern sector of the Southern Patagonian Andes. The measurements were made in several rocks from Paleozoic to Lower Cretaceous, even though most were taken in pyroclastic jurassic rocks from El Quemado Complex. Paleostress tensors obtained are mostly strike-slip, although a 25% is normal and there are a few compresional. The pattern of faults found is complex. In some sites the tensor can be locally linked to satellite images and observations from the field or be related to a major thrust front. There is no clear correlation between the age and/or lithology with the tensor since the youngest rocks measured are Lower Cretaceous. Probably there are several generations of family faults connected to different and recent tectonic phases then the paleostress tensors might correspond to the latest tectonic events.

Trans-dimensional and hierarchical Bayesian approaches toward rigorous estimation of seismic sources and structures in the Northeast Asia

NASA Astrophysics Data System (ADS)

Kim, Seongryong; Tkalčić, Hrvoje; Mustać, Marija; Rhie, Junkee; Ford, Sean

2016-04-01

A framework is presented within which we provide rigorous estimations for seismic sources and structures in the Northeast Asia. We use Bayesian inversion methods, which enable statistical estimations of models and their uncertainties based on data information. Ambiguities in error statistics and model parameterizations are addressed by hierarchical and trans-dimensional (trans-D) techniques, which can be inherently implemented in the Bayesian inversions. Hence reliable estimation of model parameters and their uncertainties is possible, thus avoiding arbitrary regularizations and parameterizations. Hierarchical and trans-D inversions are performed to develop a three-dimensional velocity model using ambient noise data. To further improve the model, we perform joint inversions with receiver function data using a newly developed Bayesian method. For the source estimation, a novel moment tensor inversion method is presented and applied to regional waveform data of the North Korean nuclear explosion tests. By the combination of new Bayesian techniques and the structural model, coupled with meaningful uncertainties related to each of the processes, more quantitative monitoring and discrimination of seismic events is possible.

Use of non-fault fractures in stress tensor reconstruction using the Mohr Circle with the Win-tensor program

NASA Astrophysics Data System (ADS)

Delvaux, Damien

2016-04-01

Paleostress inversion of geological fault-slip data is usually done using the directional part of the applied stress tensor on a slip plane and comparing it with the observed slip lines. However, this method do not fully exploit the brittle data sets as those are composed of shear and tension fractures, in addition to faults. Brittle deformation can be decomposed in two steps. An initial fracture/failure in previously intact rock generate extension/tensile fractures or shear fractures, both without visible opening or displacement. This first step may or not be followed by fracture opening to form tension joints, frictional shearing to form shear faults, or a combination of opening and shearing which produces hybrid fractures. Fractured rock outcrop contain information of the stress conditions that acted during both brittle deformation steps. The purpose here is to investigate how the fracture pattern generated during the initial fracture/failure step might be used in paleostress reconstruction. Each fracture is represented on the Mohr Circle by its resolved normal and shear stress magnitudes. We consider the typical domains on the Mohr circle where the different types de fractures nucleate (tension, hybrid, shear and compression fractures), as well the domain which contain reactivated fractures (faults reactivating an initial fracture plane). In function of the fracture type defined in the field, a "distance" is computed on the Mohr circle between each point and its expected corresponding nucleation/reactivation domain. This "Mohr Distance" is then used as function to minimize during the inversion. We implemented this new function in the Win-Tensor program, and tested it with natural and synthetic data sets from different stress regimes. It can be used alone using only the Mohr Distance on each plane (function F10), or combined with the angular misfit between observed striae and resolved shear directions (composite function F11). When used alone (F10), only the 3 stress axes can be determined and the stress ratio R (sigma 2-3)/sigma1-3) has to be pre-determined. With the combined function (F11), it provide an additional constrain to the classical angular misfit. With data sets composed of a majority of neoformed fractures, stress inversion using the Mohr Distance F10 function provide a good approximation of the 3 stress axes (using only the fracture data) as compared with the results of the F11 composite function (using also the observed slip lines). Tensor program is available at (http://www.damiendelvaux.be/Tensor/tensor-index.html).

The puzzle of the 1996 Bárdarbunga, Iceland, earthquake: no volumetric component in the source mechanism

USGS Publications Warehouse

Tkalcic, Hrvoje; Dreger, Douglas S.; Foulger, Gillian R.; Julian, Bruce R.

2009-01-01

A volcanic earthquake with Mw 5.6 occurred beneath the Bárdarbunga caldera in Iceland on 29 September 1996. This earthquake is one of a decade-long sequence of  events at Bárdarbunga with non-double-couple mechanisms in the Global Centroid Moment Tensor catalog. Fortunately, it was recorded well by the regional-scale Iceland Hotspot Project seismic experiment. We investigated the event with a complete moment tensor inversion method using regional long-period seismic waveforms and a composite structural model. The moment tensor inversion using data from stations of the Iceland Hotspot Project yields a non-double-couple solution with a 67% vertically oriented compensated linear vector dipole component, a 32% double-couple component, and a statistically insignificant (2%) volumetric (isotropic) contraction. This indicates the absence of a net volumetric component, which is puzzling in the case of a large volcanic earthquake that apparently is not explained by shear slip on a planar fault. A possible volcanic mechanism that can produce an earthquake without a volumetric component involves two offset sources with similar but opposite volume changes. We show that although such a model cannot be ruled out, the circumstances under which it could happen are rare.

Inversion of airborne tensor VLF data using integral equations

NASA Astrophysics Data System (ADS)

Kamm, Jochen; Pedersen, Laust B.

2014-08-01

The Geological Survey of Sweden has been collecting airborne tensor very low frequency data (VLF) over several decades, covering large parts of the country. The data has been an invaluable source of information for identifying conductive structures that can among other things be related to water-filled fault zones, wet sediments that fill valleys or ore mineralizations. Because the method only uses two differently polarized plane waves of very similar frequency, vertical resolution is low and interpretation is in most cases limited to maps that are directly derived from the data. Occasionally, 2-D inversion is carried out along selected profiles. In this paper, we present for the first time a 3-D inversion for tensor VLF data in order to further increase the usefulness of the data set. The inversion is performed using a non-linear conjugate gradient scheme (Polak-Ribière) with an inexact line-search. The gradient is obtained by an algebraic adjoint method that requires one additional forward calculation involving the adjoint system matrix. The forward modelling is based on integral equations with an analytic formulation of the half-space Green's tensor. It avoids typically required Hankel transforms and is particularly amenable to singularity removal prior to the numerical integration over the volume elements. The system is solved iteratively, thus avoiding construction and storage of the dense system matrix. By using fast 3-D Fourier transforms on nested grids, subsequently farther away interactions are represented with less detail and therefore with less computational effort, enabling us to bridge the gap between the relatively short wavelengths of the fields (tens of metres) and the large model dimensions (several square kilometres). We find that the approximation of the fields can be off by several per cent, yet the transfer functions in the air are practically unaffected. We verify our code using synthetic calculations from well-established 2-D methods, and trade modelling accuracy off against computational effort in order to keep the inversion feasible in both respects. Our compromise is to limit the permissible resistivity to not fall below 100 Ωm to maintain computational domains as large as 10 × 10 km2 and computation times on the order of a few hours on standard PCs. We investigate the effect of possible local violations of these limits. Even though the conductivity magnitude can then not be recovered correctly, we do not observe any structural artefacts related to this in our tests. We invert a data set from northern Sweden, where we find an excellent agreement of known geological features, such as contacts or fault zones, with elongated conductive structures, while high resistivity is encountered in probably less disturbed geology, often related to topographic highs, which have survived predominantly glacial erosion processes. As expected from synthetic studies, the resolution is laterally high, but vertically limited down to the top of conductive structures.

Wavefield simulations of earthquakes in Alaska for tomographic inversion

NASA Astrophysics Data System (ADS)

Silwal, V.; Tape, C.; Casarotti, E.

2017-12-01

We assemble a catalog of moment tensors and a three-dimensional seismic velocity model for mainland Alaska, in preparation for an iterative tomographic inversion using spectral-element and adjoint methods. The catalog contains approximately 200 earthquakes with Mw ≥ 4.0 that generate good long-period (≥6 s) signals for stations at distances up to approximately 500 km. To maximize the fraction of usable stations per earthquake, we divide our model into three subregions for simulations: south-central Alaska, central Alaska, and eastern Alaska. The primary geometrical interfaces in the model are the Moho surface, the basement surface of major sedimentary basins, and the topographic surface. The crustal and upper mantle tomographic model is from Eberhart-Phillips et al. (2006), but modified by removing the uppermost slow layer, then embedding sedimentary basin models for Cook Inlet basin, Susitna basin, and Nenana basin. We compute 3D synthetic seismograms using the spectral-element method. We demonstrate the accuracy of the initial three-dimensional reference model in each subregion by comparing 3D synthetics with observed data for several earthquakes originating in the crust and underlying subducting slab. Full waveform similarity between data and synthetics over the period range 6 s to 30 s provides a basis for an iterative inversion. The target resolution of the crustal structure is 4 km vertically and 20 km laterally. We use surface wave and body wave measurements from local earthquakes to obtain moment tensors that will be used within our tomographic inversion. Local slab events down to 180 km depth, in additional to pervasive crustal seismicity, should enhance resolution.

Moment Tensor Descriptions for Simulated Explosions of the Source Physics Experiment (SPE)

NASA Astrophysics Data System (ADS)

Yang, X.; Rougier, E.; Knight, E. E.; Patton, H. J.

2014-12-01

In this research we seek to understand damage mechanisms governing the behavior of geo-materials in the explosion source region, and the role they play in seismic-wave generation. Numerical modeling tools can be used to describe these mechanisms through the development and implementation of appropriate material models. Researchers at Los Alamos National Laboratory (LANL) have been working on a novel continuum-based-viscoplastic strain-rate-dependent fracture material model, AZ_Frac, in an effort to improve the description of these damage sources. AZ_Frac has the ability to describe continuum fracture processes, and at the same time, to handle pre-existing anisotropic material characteristics. The introduction of fractures within the material generates further anisotropic behavior that is also accounted for within the model. The material model has been calibrated to a granitic medium and has been applied in a number of modeling efforts under the SPE project. In our modeling, we use a 2D, axisymmetric layered earth model of the SPE site consisting of a weathered layer on top of a half-space. We couple the hydrodynamic simulation code with a seismic simulation code and propagate the signals to distances of up to 2 km. The signals are inverted for time-dependent moment tensors using a modified inversion scheme that accounts for multiple sources at different depths. The inversion scheme is evaluated for its resolving power to determine a centroid depth and a moment tensor description of the damage source. The capabilities of the inversion method to retrieve such information from waveforms recorded on three SPE tests conducted to date are also being assessed.

Moment-Tensor Spectra of Source Physics Experiments (SPE) Explosions in Granite

NASA Astrophysics Data System (ADS)

Yang, X.; Cleveland, M.

2016-12-01

We perform frequency-domain moment tensor inversions of Source Physics Experiments (SPE) explosions conducted in granite during Phase I of the experiment. We test the sensitivity of source moment-tensor spectra to factors such as the velocity model, selected dataset and smoothing and damping parameters used in the inversion to constrain the error bound of inverted source spectra. Using source moments and corner frequencies measured from inverted source spectra of these explosions, we develop a new explosion P-wave source model that better describes observed source spectra of these small and over-buried chemical explosions detonated in granite than classical explosion source models derived mainly from nuclear-explosion data. In addition to source moment and corner frequency, we analyze other features in the source spectra to investigate their physical causes.

Source spectra of the first four Source Physics Experiments (SPE) explosions from the frequency-domain moment-tensor inversion

DOE PAGES

Yang, Xiaoning

2016-08-01

In this study, I used seismic waveforms recorded within 2 km from the epicenter of the first four Source Physics Experiments (SPE) explosions to invert for the moment-tensor spectra of these explosions. I employed a one-dimensional (1D) Earth model for Green's function calculations. The model was developed from P- and R g-wave travel times and amplitudes. I selected data for the inversion based on the criterion that they had consistent travel times and amplitude behavior as those predicted by the 1D model. Due to limited azimuthal coverage of the sources and the mostly vertical-component-only nature of the dataset, only long-period,more » volumetric components of the moment-tensor spectra were well constrained.« less

Toward an efficient inverse characterization of the viscoelastic properties of anisotropic media based on the ultrasonic polar scan

NASA Astrophysics Data System (ADS)

Martens, A.; Kersemans, M.; Daemen, J.; Verboven, E.; Van Paepegem, W.; Degrieck, J.; Delrue, S.; Van Den Abeele, K.

2018-04-01

Composite materials (e.g., carbon fiber reinforced plastics (CFRP)) are increasingly used for critical components in several industrial sectors (e.g. aerospace, automotive). Their anisotropic nature makes it difficult to accurately determine material properties or to assess internal damages. To resolve these challenges, the Ultrasonic Polar Scan (UPS) technique has been introduced. In a UPS experiment, a fixed material spot is insonified at a multitude of incidence angles Ψ(θ,φ) for which the transmission amplitude as well as the associated arrival time (time-of-flight) are measured. Mapping these quantities on a polar diagram represents a fingerprint of the local viscoelasticity of the investigated material. In the present study, we propose a novel two-stage inversion scheme that is able to infer both the elastic and the viscous properties. In the first step, we solve the inverse problem of determining the elastic constants from time-of-flight UPS recordings. The second stage handles a similar inverse problem, but now operates on the amplitude landscape of a UPS experiment for determining the viscous part of the viscoelastic tensor. This two-stage procedure thus yields the viscoelastic tensor of the insonified material spot. The developed characterization scheme has been employed on both virtual (numerical) UPS recordings, to test the effectiveness of the method, and experimental UPS recordings of unidirectional C/E plates.

Moment Tensor Inversions of the M1.7+ Earthquakes in Basel. Switzerland Reveal Predominant Shear Dislocations

NASA Astrophysics Data System (ADS)

Guilhem, A.; Walter, F. T.

2013-12-01

We investigate moment tensor solutions of nearly 30 magnitude (M) 1.7+ earthquakes that occurred in Basel, Switzerland during and after the simulation of the geothermal enhanced system between December 2nd and 8th 2006. In 2009, Deichmann and Ernst determined the focal mechanisms for these events using P-wave first-motions. They found clear evidence for double-couple mechanisms with no indications for substantial volumetric changes. This differs from evidences of composite type ruptures (i.e., shearing with isotropic motion) observed in other geothermal environments. Here, we use a similar approach for the computation of the moment tensor inversions to the one used by Guilhem et al. (2012) for M3 earthquakes in Geysers. We use a dataset from strong-motion stations located within 7 km from the epicenters, with data filtered between 0.5 and 3 Hz and integrated twice to displacement. The waveforms are inverted for both deviatoric and full moment tensor solutions. In addition, we perform a network sensitivity test (NSS) by computing 100 million random moment tensors for each event thus testing the sensitivity of the moment tensor solutions. Finally, because the injection of fluids in the ground can promote crack growth generating seismic events, we also compute a crack + double-couple inversion (Minson et al., 2007) for each of the studied earthquakes between December 2006 and May 2007. From this extensive search we find that the results of our different techniques converge. Moment tensor solutions are very similar to the first-motion focal mechanisms of Deichmann and Ernst (2009) and accordingly do not exhibit dominant volumetric changes except for a subset of events, which we discuss in some detail. References: Deichmann, N. and Ernst, J. (2009), Swiss J. Geosc. Guilhem, A., Dreger, D.S., Hutchings, L. J., and Johnson, L. (2012), AGU Fall meeting Minson, S. E., Dreger, D. S., Bürgmann, R., Kanamori, H., Larson, K. M. (2007), J. Geophys. Res.

Identification of complex stiffness tensor from waveform reconstruction

NASA Astrophysics Data System (ADS)

Leymarie, N.; Aristégui, C.; Audoin, B.; Baste, S.

2002-03-01

An inverse method is proposed in order to determine the viscoelastic properties of composite-material plates from the plane-wave transmitted acoustic field. Analytical formulations of both the plate transmission coefficient and its first and second derivatives are established, and included in a two-step inversion scheme. Two objective functions to be minimized are then designed by considering the well-known maximum-likelihood principle and by using an analytic signal formulation. Through these innovative objective functions, the robustness of the inversion process against high level of noise in waveforms is improved and the method can be applied to a very thin specimen. The suitability of the inversion process for viscoelastic property identification is demonstrated using simulated data for composite materials with different anisotropy and damping degrees. A study of the effect of the rheologic model choice on the elastic property identification emphasizes the relevance of using a phenomenological description considering viscosity. Experimental characterizations show then the good reliability of the proposed approach. Difficulties arise experimentally for particular anisotropic media.

Full moment tensor and source location inversion based on full waveform adjoint method

NASA Astrophysics Data System (ADS)

Morency, C.

2012-12-01

The development of high-performance computing and numerical techniques enabled global and regional tomography to reach high levels of precision, and seismic adjoint tomography has become a state-of-the-art tomographic technique. The method was successfully used for crustal tomography of Southern California (Tape et al., 2009) and Europe (Zhu et al., 2012). Here, I will focus on the determination of source parameters (full moment tensor and location) based on the same approach (Kim et al, 2011). The method relies on full wave simulations and takes advantage of the misfit between observed and synthetic seismograms. An adjoint wavefield is calculated by back-propagating the difference between observed and synthetics from the receivers to the source. The interaction between this adjoint wavefield and the regular forward wavefield helps define Frechet derivatives of the source parameters, that is, the sensitivity of the misfit with respect to the source parameters. Source parameters are then recovered by minimizing the misfit based on a conjugate gradient algorithm using the Frechet derivatives. First, I will demonstrate the method on synthetic cases before tackling events recorded at the Geysers. The velocity model used at the Geysers is based on the USGS 3D velocity model. Waveform datasets come from the Northern California Earthquake Data Center. Finally, I will discuss strategies to ultimately use this method to characterize smaller events for microseismic and induced seismicity monitoring. References: - Tape, C., Q. Liu, A. Maggi, and J. Tromp, 2009, Adjoint tomography of the Southern California crust: Science, 325, 988992. - Zhu, H., Bozdag, E., Peter, D., and Tromp, J., 2012, Structure of the European upper mantle revealed by adjoint method: Nature Geoscience, 5, 493-498. - Kim, Y., Q. Liu, and J. Tromp, 2011, Adjoint centroid-moment tensor inversions: Geophys. J. Int., 186, 264278. Prepared by LLNL under Contract DE-AC52-07NA27344.

Moment tensor solutions estimated using optimal filter theory for 51 selected earthquakes, 1980-1984

USGS Publications Warehouse

Sipkin, S.A.

1987-01-01

The 51 global events that occurred from January 1980 to March 1984, which were chosen by the convenors of the Symposium on Seismological Theory and Practice, have been analyzed using a moment tensor inversion algorithm (Sipkin). Many of the events were routinely analyzed as part of the National Earthquake Information Center's (NEIC) efforts to publish moment tensor and first-motion fault-plane solutions for all moderate- to large-sized (mb>5.7) earthquakes. In routine use only long-period P-waves are used and the source-time function is constrained to be a step-function at the source (??-function in the far-field). Four of the events were of special interest, and long-period P, SH-wave solutions were obtained. For three of these events, an unconstrained inversion was performed. The resulting time-dependent solutions indicated that, for many cases, departures of the solutions from pure double-couples are caused by source complexity that has not been adequately modeled. These solutions also indicate that source complexity of moderate-sized events can be determined from long-period data. Finally, for one of the events of special interest, an inversion of the broadband P-waveforms was also performed, demonstrating the potential for using broadband waveform data in inversion procedures. ?? 1987.

Seismic source inversion using Green's reciprocity and a 3-D structural model for the Japanese Islands

NASA Astrophysics Data System (ADS)

Simutė, S.; Fichtner, A.

2015-12-01

We present a feasibility study for seismic source inversions using a 3-D velocity model for the Japanese Islands. The approach involves numerically calculating 3-D Green's tensors, which is made efficient by exploiting Green's reciprocity. The rationale for 3-D seismic source inversion has several aspects. For structurally complex regions, such as the Japan area, it is necessary to account for 3-D Earth heterogeneities to prevent unknown structure polluting source solutions. In addition, earthquake source characterisation can serve as a means to delineate existing faults. Source parameters obtained for more realistic Earth models can then facilitate improvements in seismic tomography and early warning systems, which are particularly important for seismically active areas, such as Japan. We have created a database of numerically computed 3-D Green's reciprocals for a 40°× 40°× 600 km size area around the Japanese Archipelago for >150 broadband stations. For this we used a regional 3-D velocity model, recently obtained from full waveform inversion. The model includes attenuation and radial anisotropy and explains seismic waveform data for periods between 10 - 80 s generally well. The aim is to perform source inversions using the database of 3-D Green's tensors. As preliminary steps, we present initial concepts to address issues that are at the basis of our approach. We first investigate to which extent Green's reciprocity works in a discrete domain. Considering substantial amounts of computed Green's tensors we address storage requirements and file formatting. We discuss the importance of the initial source model, as an intelligent choice can substantially reduce the search volume. Possibilities to perform a Bayesian inversion and ways to move to finite source inversion are also explored.

Description and Features of UX-Analyze

DTIC Science & Technology

2009-02-01

POB model and GUI for EM63 Inversion The full Pasion -Oldenburg-Billings (POB) analysis assumes an axially symmetric (axial and transverse) tensor...output from the EM63 inversion. 1 Pasion , L.R., and Oldenburg, D.W., 2001, Locating and

Improved preconditioned conjugate gradient algorithm and application in 3D inversion of gravity-gradiometry data

NASA Astrophysics Data System (ADS)

Wang, Tai-Han; Huang, Da-Nian; Ma, Guo-Qing; Meng, Zhao-Hai; Li, Ye

2017-06-01

With the continuous development of full tensor gradiometer (FTG) measurement techniques, three-dimensional (3D) inversion of FTG data is becoming increasingly used in oil and gas exploration. In the fast processing and interpretation of large-scale high-precision data, the use of the graphics processing unit process unit (GPU) and preconditioning methods are very important in the data inversion. In this paper, an improved preconditioned conjugate gradient algorithm is proposed by combining the symmetric successive over-relaxation (SSOR) technique and the incomplete Choleksy decomposition conjugate gradient algorithm (ICCG). Since preparing the preconditioner requires extra time, a parallel implement based on GPU is proposed. The improved method is then applied in the inversion of noisecontaminated synthetic data to prove its adaptability in the inversion of 3D FTG data. Results show that the parallel SSOR-ICCG algorithm based on NVIDIA Tesla C2050 GPU achieves a speedup of approximately 25 times that of a serial program using a 2.0 GHz Central Processing Unit (CPU). Real airborne gravity-gradiometry data from Vinton salt dome (southwest Louisiana, USA) are also considered. Good results are obtained, which verifies the efficiency and feasibility of the proposed parallel method in fast inversion of 3D FTG data.

Three-dimensional forward modeling and inversion of marine CSEM data in anisotropic conductivity structures

NASA Astrophysics Data System (ADS)

Han, B.; Li, Y.

2016-12-01

We present a three-dimensional (3D) forward and inverse modeling code for marine controlled-source electromagnetic (CSEM) surveys in anisotropic media. The forward solution is based on a primary/secondary field approach, in which secondary fields are solved using a staggered finite-volume (FV) method and primary fields are solved for 1D isotropic background models analytically. It is shown that it is rather straightforward to extend the isotopic 3D FV algorithm to a triaxial anisotropic one, while additional coefficients are required to account for full tensor conductivity. To solve the linear system resulting from FV discretization of Maxwell' s equations, both iterative Krylov solvers (e.g. BiCGSTAB) and direct solvers (e.g. MUMPS) have been implemented, makes the code flexible for different computing platforms and different problems. For iterative soloutions, the linear system in terms of electromagnetic potentials (A-Phi) is used to precondition the original linear system, transforming the discretized Curl-Curl equations to discretized Laplace-like equations, thus much more favorable numerical properties can be obtained. Numerical experiments suggest that this A-Phi preconditioner can dramatically improve the convergence rate of an iterative solver and high accuracy can be achieved without divergence correction even for low frequencies. To efficiently calculate the sensitivities, i.e. the derivatives of CSEM data with respect to tensor conductivity, the adjoint method is employed. For inverse modeling, triaxial anisotropy is taken into account. Since the number of model parameters to be resolved of triaxial anisotropic medias is twice or thrice that of isotropic medias, the data-space version of the Gauss-Newton (GN) minimization method is preferred due to its lower computational cost compared with the traditional model-space GN method. We demonstrate the effectiveness of the code with synthetic examples.

Resolving Isotropic Components from Regional Waves using Grid Search and Moment Tensor Inversion Methods

NASA Astrophysics Data System (ADS)

Ichinose, G. A.; Saikia, C. K.

2007-12-01

We applied the moment tensor (MT) analysis scheme to identify seismic sources using regional seismograms based on the representation theorem for the elastic wave displacement field. This method is applied to estimate the isotropic (ISO) and deviatoric MT components of earthquake, volcanic, and isotropic sources within the Basin and Range Province (BRP) and western US. The ISO components from Hoya, Bexar, Montello and Junction were compared to recently well recorded recent earthquakes near Little Skull Mountain, Scotty's Junction, Eureka Valley, and Fish Lake Valley within southern Nevada. We also examined "dilatational" sources near Mammoth Lakes Caldera and two mine collapses including the August 2007 event in Utah recorded by US Array. Using our formulation we have first implemented the full MT inversion method on long period filtered regional data. We also applied a grid-search technique to solve for the percent deviatoric and %ISO moments. By using the grid-search technique, high-frequency waveforms are used with calibrated velocity models. We modeled the ISO and deviatoric components (spall and tectonic release) as separate events delayed in time or offset in space. Calibrated velocity models helped the resolution of the ISO components and decrease the variance over the average, initial or background velocity models. The centroid location and time shifts are velocity model dependent. Models can be improved as was done in previously published work in which we used an iterative waveform inversion method with regional seismograms from four well recorded and constrained earthquakes. The resulting velocity models reduced the variance between predicted synthetics by about 50 to 80% for frequencies up to 0.5 Hz. Tests indicate that the individual path-specific models perform better at recovering the earthquake MT solutions even after using a sparser distribution of stations than the average or initial models.

An Improved Method for Seismic Event Depth and Moment Tensor Determination: CTBT Related Application

NASA Astrophysics Data System (ADS)

Stachnik, J.; Rozhkov, M.; Baker, B.

2016-12-01

According to the Protocol to CTBT, International Data Center is required to conduct expert technical analysis and special studies to improve event parameters and assist State Parties in identifying the source of specific event. Determination of seismic event source mechanism and its depth is a part of these tasks. It is typically done through a strategic linearized inversion of the waveforms for a complete or subset of source parameters, or similarly defined grid search through precomputed Greens Functions created for particular source models. We show preliminary results using the latter approach from an improved software design and applied on a moderately powered computer. In this development we tried to be compliant with different modes of CTBT monitoring regime and cover wide range of source-receiver distances (regional to teleseismic), resolve shallow source depths, provide full moment tensor solution based on body and surface waves recordings, be fast to satisfy both on-demand studies and automatic processing and properly incorporate observed waveforms and any uncertainties a priori as well as accurately estimate posteriori uncertainties. Implemented HDF5 based Green's Functions pre-packaging allows much greater flexibility in utilizing different software packages and methods for computation. Further additions will have the rapid use of Instaseis/AXISEM full waveform synthetics added to a pre-computed GF archive. Along with traditional post processing analysis of waveform misfits through several objective functions and variance reduction, we follow a probabilistic approach to assess the robustness of moment tensor solution. In a course of this project full moment tensor and depth estimates are determined for DPRK 2009, 2013 and 2016 events and shallow earthquakes using a new implementation of waveform fitting of teleseismic P waves. A full grid search over the entire moment tensor space is used to appropriately sample all possible solutions. A recent method by Tape & Tape (2012) to discretize the complete moment tensor space from a geometric perspective is used. Moment tensors for DPRK events show isotropic percentages greater than 50%. Depth estimates for the DPRK events range from 1.0-1.4 km. Probabilistic uncertainty estimates on the moment tensor parameters provide robustness to solution.

Moment tensor inversion of the 2016 southeast offshore Mie earthquake in the Tonankai region using a three-dimensional velocity structure model: effects of the accretionary prism and subducting oceanic plate

NASA Astrophysics Data System (ADS)

Takemura, Shunsuke; Kimura, Takeshi; Saito, Tatsuhiko; Kubo, Hisahiko; Shiomi, Katsuhiko

2018-03-01

The southeast offshore Mie earthquake occurred on April 1, 2016 near the rupture area of the 1944 Tonankai earthquake, where seismicity around the interface of the Philippine Sea plate had been very low until this earthquake. Since this earthquake occurred outside of seismic arrays, the focal mechanism and depth were not precisely constrained using a one-dimensional velocity model, as in a conventional approach. We conducted a moment tensor inversion of this earthquake by using a three-dimensional velocity structure model. Before the analysis of observed data, we investigated the effects of offshore heterogeneous structures such as the seawater, accretionary prism, and subducting oceanic plate by using synthetic seismograms in a full three-dimensional model and simpler models. The accretionary prism and subducting oceanic plate play important roles in the moment tensor inversion for offshore earthquakes in the subduction zone. Particularly, the accretionary prism, which controls the excitation and propagation of long-period surface waves around the offshore region, provides better estimations of the centroid depths and focal mechanisms of earthquakes around the Nankai subduction zone. The result of moment tensor inversion for the 2016 southeast offshore Mie earthquake revealed low-angle thrust faulting with a moment magnitude of 5.6. According to geophysical surveys in the Nankai Trough, our results suggest that the rupture of this earthquake occurred on the interface of the Philippine Sea plate, rather than on a mega-splay fault. Detailed comparisons of first-motion polarizations provided additional constraints of the rupture that occurred on the interface of the Philippine Sea plate.

Simplified moment tensor analysis and unified decomposition of acoustic emission source: Application to in situ hydrofracturing test

NASA Astrophysics Data System (ADS)

Ohtsu, Masayasu

1991-04-01

An application of a moment tensor analysis to acoustic emission (AE) is studied to elucidate crack types and orientations of AE sources. In the analysis, simplified treatment is desirable, because hundreds of AE records are obtained from just one experiment and thus sophisticated treatment is realistically cumbersome. Consequently, a moment tensor inversion based on P wave amplitude is employed to determine six independent tensor components. Selecting only P wave portion from the full-space Green's function of homogeneous and isotropic material, a computer code named SiGMA (simplified Green's functions for the moment tensor analysis) is developed for the AE inversion analysis. To classify crack type and to determine crack orientation from moment tensor components, a unified decomposition of eigenvalues into a double-couple (DC) part, a compensated linear vector dipole (CLVD) part, and an isotropic part is proposed. The aim of the decomposition is to determine the proportion of shear contribution (DC) and tensile contribution (CLVD + isotropic) on AE sources and to classify cracks into a crack type of the dominant motion. Crack orientations determined from eigenvectors are presented as crack-opening vectors for tensile cracks and fault motion vectors for shear cracks, instead of stereonets. The SiGMA inversion and the unified decomposition are applied to synthetic data and AE waveforms detected during an in situ hydrofracturing test. To check the accuracy of the procedure, numerical experiments are performed on the synthetic waveforms, including cases with 10% random noise added. Results show reasonable agreement with assumed crack configurations. Although the maximum error is approximately 10% with respect to the ratios, the differences on crack orientations are less than 7°. AE waveforms detected by eight accelerometers deployed during the hydrofracturing test are analyzed. Crack types and orientations determined are in reasonable agreement with a predicted failure plane from borehole TV observation. The results suggest that tensile cracks are generated first at weak seams and then shear cracks follow on the opened joints.

Near real-time estimation of the seismic source parameters in a compressed domain

NASA Astrophysics Data System (ADS)

Rodriguez, Ismael A. Vera

Seismic events can be characterized by its origin time, location and moment tensor. Fast estimations of these source parameters are important in areas of geophysics like earthquake seismology, and the monitoring of seismic activity produced by volcanoes, mining operations and hydraulic injections in geothermal and oil and gas reservoirs. Most available monitoring systems estimate the source parameters in a sequential procedure: first determining origin time and location (e.g., epicentre, hypocentre or centroid of the stress glut density), and then using this information to initialize the evaluation of the moment tensor. A more efficient estimation of the source parameters requires a concurrent evaluation of the three variables. The main objective of the present thesis is to address the simultaneous estimation of origin time, location and moment tensor of seismic events. The proposed method displays the benefits of being: 1) automatic, 2) continuous and, depending on the scale of application, 3) of providing results in real-time or near real-time. The inversion algorithm is based on theoretical results from sparse representation theory and compressive sensing. The feasibility of implementation is determined through the analysis of synthetic and real data examples. The numerical experiments focus on the microseismic monitoring of hydraulic fractures in oil and gas wells, however, an example using real earthquake data is also presented for validation. The thesis is complemented with a resolvability analysis of the moment tensor. The analysis targets common monitoring geometries employed in hydraulic fracturing in oil wells. Additionally, it is presented an application of sparse representation theory for the denoising of one-component and three-component microseismicity records, and an algorithm for improved automatic time-picking using non-linear inversion constraints.

Moment tensor inversion of ground motion from mining-induced earthquakes, Trail Mountain, Utah

USGS Publications Warehouse

Fletcher, Joe B.; McGarr, A.

2005-01-01

A seismic network was operated in the vicinity of the Trail Mountain mine, central Utah, from the summer of 2000 to the spring of 2001 to investigate the seismic hazard to a local dam from mining-induced events that we expect to be triggered by future coal mining in this area. In support of efforts to develop groundmotion prediction relations for this situation, we inverted ground-motion recordings for six mining-induced events to determine seismic moment tensors and then to estimate moment magnitudes M for comparison with the network coda magnitudes Mc. Six components of the tensor were determined, for an assumed point source, following the inversion method of McGarr (1992a), which uses key measurements of amplitude from obvious features of the displacement waveforms. When the resulting moment tensors were decomposed into implosive and deviatoric components, we found that four of the six events showed a substantial volume reduction, presumably due to coseismic closure of the adjacent mine openings. For these four events, the volume reduction ranges from 27% to 55% of the shear component (fault area times average slip). Radiated seismic energy, computed from attenuation-corrected body-wave spectra, ranged from 2.4 ?? 105 to 2.4 ?? 106 J for events with M from 1.3 to 1.8, yielding apparent stresses from 0.02 to 0.06 MPa. The energy released for each event, approximated as the product of volume reduction and overburden stress, when compared with the corresponding seismic energies, revealed seismic efficiencies ranging from 0.5% to 7%. The low apparent stresses are consistent with the shallow focal depths of 0.2 to 0.6 km and rupture in a low stress/low strength regime compared with typical earthquake source regions at midcrustal depths.

Quantification of Uncertainty in Full-Waveform Moment Tensor Inversion for Regional Seismicity

NASA Astrophysics Data System (ADS)

Jian, P.; Hung, S.; Tseng, T.

2013-12-01

Routinely and instantaneously determined moment tensor solutions deliver basic information for investigating faulting nature of earthquakes and regional tectonic structure. The accuracy of full-waveform moment tensor inversion mostly relies on azimuthal coverage of stations, data quality and previously known earth's structure (i.e., impulse responses or Green's functions). However, intrinsically imperfect station distribution, noise-contaminated waveform records and uncertain earth structure can often result in large deviations of the retrieved source parameters from the true ones, which prohibits the use of routinely reported earthquake catalogs for further structural and tectonic interferences. Duputel et al. (2012) first systematically addressed the significance of statistical uncertainty estimation in earthquake source inversion and exemplified that the data covariance matrix, if prescribed properly to account for data dependence and uncertainty due to incomplete and erroneous data and hypocenter mislocation, cannot only be mapped onto the uncertainty estimate of resulting source parameters, but it also aids obtaining more stable and reliable results. Over the past decade, BATS (Broadband Array in Taiwan for Seismology) has steadily devoted to building up a database of good-quality centroid moment tensor (CMT) solutions for moderate to large magnitude earthquakes that occurred in Taiwan area. Because of the lack of the uncertainty quantification and reliability analysis, it remains controversial to use the reported CMT catalog directly for further investigation of regional tectonics, near-source strong ground motions, and seismic hazard assessment. In this study, we develop a statistical procedure to make quantitative and reliable estimates of uncertainty in regional full-waveform CMT inversion. The linearized inversion scheme adapting efficient estimation of the covariance matrices associated with oversampled noisy waveform data and errors of biased centroid positions is implemented and inspected for improving source parameter determination of regional seismicity in Taiwan. Synthetic inversion tests demonstrate the resolved moment tensors would better match the hypothetical CMT solutions, and tend to suppress unreal non-double-couple components and reduce the trade-off between focal mechanism and centroid depth if individual signal-to-noise ratios and correlation lengths for 3-component seismograms at each station and mislocation uncertainties are properly taken into account. We further testify the capability of our scheme in retrieving the robust CMT information for mid-sized (Mw~3.5) and offshore earthquakes in Taiwan, which offers immediate and broad applications in detailed modelling of regional stress field and deformation pattern and mapping of subsurface velocity structures.

Determination of source parameters of the 2017 Mount Agung volcanic earthquake from moment-tensor inversion method using local broadband seismic waveforms

NASA Astrophysics Data System (ADS)

Madlazim; Prastowo, T.; Supardiyono; Hardy, T.

2018-03-01

Monitoring of volcanoes has been an important issue for many purposes, particularly hazard mitigation. With regard to this, the aims of the present work are to estimate and analyse source parameters of a volcanic earthquake driven by recent magmatic events of Mount Agung in Bali island that occurred on September 28, 2017. The broadband seismogram data consisting of 3 local component waveforms were recorded by the IA network of 5 seismic stations: SRBI, DNP, BYJI, JAGI, and TWSI (managed by BMKG). These land-based observatories covered a full 4-quadrant region surrounding the epicenter. The methods used in the present study were seismic moment-tensor inversions, where the data were all analyzed to extract the parameters, namely moment magnitude, type of a volcanic earthquake indicated by percentages of seismic components: compensated linear vector dipole (CLVD), isotropic (ISO), double-couple (DC), and source depth. The results are given in the forms of variance reduction of 65%, a magnitude of M W 3.6, a CLVD of 40%, an ISO of 33%, a DC of 27% and a centroid-depth of 9.7 km. These suggest that the unusual earthquake was dominated by a vertical CLVD component, implying the dominance of uplift motion of magmatic fluid flow inside the volcano.

Towards real-time regional earthquake simulation I: real-time moment tensor monitoring (RMT) for regional events in Taiwan

NASA Astrophysics Data System (ADS)

Lee, Shiann-Jong; Liang, Wen-Tzong; Cheng, Hui-Wen; Tu, Feng-Shan; Ma, Kuo-Fong; Tsuruoka, Hiroshi; Kawakatsu, Hitoshi; Huang, Bor-Shouh; Liu, Chun-Chi

2014-01-01

We have developed a real-time moment tensor monitoring system (RMT) which takes advantage of a grid-based moment tensor inversion technique and real-time broad-band seismic recordings to automatically monitor earthquake activities in the vicinity of Taiwan. The centroid moment tensor (CMT) inversion technique and a grid search scheme are applied to obtain the information of earthquake source parameters, including the event origin time, hypocentral location, moment magnitude and focal mechanism. All of these source parameters can be determined simultaneously within 117 s after the occurrence of an earthquake. The monitoring area involves the entire Taiwan Island and the offshore region, which covers the area of 119.3°E to 123.0°E and 21.0°N to 26.0°N, with a depth from 6 to 136 km. A 3-D grid system is implemented in the monitoring area with a uniform horizontal interval of 0.1° and a vertical interval of 10 km. The inversion procedure is based on a 1-D Green's function database calculated by the frequency-wavenumber (fk) method. We compare our results with the Central Weather Bureau (CWB) catalogue data for earthquakes occurred between 2010 and 2012. The average differences between event origin time and hypocentral location are less than 2 s and 10 km, respectively. The focal mechanisms determined by RMT are also comparable with the Broadband Array in Taiwan for Seismology (BATS) CMT solutions. These results indicate that the RMT system is realizable and efficient to monitor local seismic activities. In addition, the time needed to obtain all the point source parameters is reduced substantially compared to routine earthquake reports. By connecting RMT with a real-time online earthquake simulation (ROS) system, all the source parameters will be forwarded to the ROS to make the real-time earthquake simulation feasible. The RMT has operated offline (2010-2011) and online (since January 2012 to present) at the Institute of Earth Sciences (IES), Academia Sinica (http://rmt.earth.sinica.edu.tw). The long-term goal of this system is to provide real-time source information for rapid seismic hazard assessment during large earthquakes.

Methods for determining remanent and total magnetisations of magnetic sources - a review

NASA Astrophysics Data System (ADS)

Clark, David A.

2014-07-01

Assuming without evidence that magnetic sources are magnetised parallel to the geomagnetic field can seriously mislead interpretation and can result in drill holes missing their targets. This article reviews methods that are available for estimating, directly or indirectly, the natural remanent magnetisation (NRM) and total magnetisation of magnetic sources, noting the strengths and weaknesses of each approach. These methods are: (i) magnetic property measurements of samples; (ii) borehole magnetic measurements; (iii) inference of properties from petrographic/petrological information, supplemented by palaeomagnetic databases; (iv) constrained modelling/inversion of magnetic sources; (v) direct inversions of measured or calculated vector and gradient tensor data for simple sources; (vi) retrospective inference of magnetisation of a mined deposit by comparing magnetic data acquired pre- and post-mining; (vii) combined analysis of magnetic and gravity anomalies using Poisson's theorem; (viii) using a controlled magnetic source to probe the susceptibility distribution of the subsurface; (ix) Helbig-type analysis of gridded vector components, gradient tensor elements, and tensor invariants; (x) methods based on reduction to the pole and related transforms; and (xi) remote in situ determination of NRM direction, total magnetisation direction and Koenigsberger ratio by deploying dual vector magnetometers or a single combined gradiometer/magnetometer to monitor local perturbation of natural geomagnetic variations, operating in base station mode within a magnetic anomaly of interest. Characterising the total and remanent magnetisations of sources is important for several reasons. Knowledge of total magnetisation is often critical for accurate determination of source geometry and position. Knowledge of magnetic properties such as magnetisation intensity and Koenigsberger ratio constrains the likely magnetic mineralogy (composition and grain size) of a source, which gives an indication of its geological nature. Determining the direction of a stable ancient remanence gives an indication of the age of magnetisation, which provides useful information about the geological history of the source and its environs.

Multi-GPU parallel algorithm design and analysis for improved inversion of probability tomography with gravity gradiometry data

NASA Astrophysics Data System (ADS)

Hou, Zhenlong; Huang, Danian

2017-09-01

In this paper, we make a study on the inversion of probability tomography (IPT) with gravity gradiometry data at first. The space resolution of the results is improved by multi-tensor joint inversion, depth weighting matrix and the other methods. Aiming at solving the problems brought by the big data in the exploration, we present the parallel algorithm and the performance analysis combining Compute Unified Device Architecture (CUDA) with Open Multi-Processing (OpenMP) based on Graphics Processing Unit (GPU) accelerating. In the test of the synthetic model and real data from Vinton Dome, we get the improved results. It is also proved that the improved inversion algorithm is effective and feasible. The performance of parallel algorithm we designed is better than the other ones with CUDA. The maximum speedup could be more than 200. In the performance analysis, multi-GPU speedup and multi-GPU efficiency are applied to analyze the scalability of the multi-GPU programs. The designed parallel algorithm is demonstrated to be able to process larger scale of data and the new analysis method is practical.

A cut-&-paste strategy for the 3-D inversion of helicopter-borne electromagnetic data - I. 3-D inversion using the explicit Jacobian and a tensor-based formulation

NASA Astrophysics Data System (ADS)

Scheunert, M.; Ullmann, A.; Afanasjew, M.; Börner, R.-U.; Siemon, B.; Spitzer, K.

2016-06-01

We present an inversion concept for helicopter-borne frequency-domain electromagnetic (HEM) data capable of reconstructing 3-D conductivity structures in the subsurface. Standard interpretation procedures often involve laterally constrained stitched 1-D inversion techniques to create pseudo-3-D models that are largely representative for smoothly varying conductivity distributions in the subsurface. Pronounced lateral conductivity changes may, however, produce significant artifacts that can lead to serious misinterpretation. Still, 3-D inversions of entire survey data sets are numerically very expensive. Our approach is therefore based on a cut-&-paste strategy whereupon the full 3-D inversion needs to be applied only to those parts of the survey where the 1-D inversion actually fails. The introduced 3-D Gauss-Newton inversion scheme exploits information given by a state-of-the-art (laterally constrained) 1-D inversion. For a typical HEM measurement, an explicit representation of the Jacobian matrix is inevitable which is caused by the unique transmitter-receiver relation. We introduce tensor quantities which facilitate the matrix assembly of the forward operator as well as the efficient calculation of the Jacobian. The finite difference forward operator incorporates the displacement currents because they may seriously affect the electromagnetic response at frequencies above 100. Finally, we deliver the proof of concept for the inversion using a synthetic data set with a noise level of up to 5%.

Randomized interpolative decomposition of separated representations

NASA Astrophysics Data System (ADS)

Biagioni, David J.; Beylkin, Daniel; Beylkin, Gregory

2015-01-01

We introduce an algorithm to compute tensor interpolative decomposition (dubbed CTD-ID) for the reduction of the separation rank of Canonical Tensor Decompositions (CTDs). Tensor ID selects, for a user-defined accuracy ɛ, a near optimal subset of terms of a CTD to represent the remaining terms via a linear combination of the selected terms. CTD-ID can be used as an alternative to or in combination with the Alternating Least Squares (ALS) algorithm. We present examples of its use within a convergent iteration to compute inverse operators in high dimensions. We also briefly discuss the spectral norm as a computational alternative to the Frobenius norm in estimating approximation errors of tensor ID. We reduce the problem of finding tensor IDs to that of constructing interpolative decompositions of certain matrices. These matrices are generated via randomized projection of the terms of the given tensor. We provide cost estimates and several examples of the new approach to the reduction of separation rank.

Source-Type Identification Analysis Using Regional Seismic Moment Tensors

NASA Astrophysics Data System (ADS)

Chiang, A.; Dreger, D. S.; Ford, S. R.; Walter, W. R.

2012-12-01

Waveform inversion to determine the seismic moment tensor is a standard approach in determining the source mechanism of natural and manmade seismicity, and may be used to identify, or discriminate different types of seismic sources. The successful applications of the regional moment tensor method at the Nevada Test Site (NTS) and the 2006 and 2009 North Korean nuclear tests (Ford et al., 2009a, 2009b, 2010) show that the method is robust and capable for source-type discrimination at regional distances. The well-separated populations of explosions, earthquakes and collapses on a Hudson et al., (1989) source-type diagram enables source-type discrimination; however the question remains whether or not the separation of events is universal in other regions, where we have limited station coverage and knowledge of Earth structure. Ford et al., (2012) have shown that combining regional waveform data and P-wave first motions removes the CLVD-isotropic tradeoff and uniquely discriminating the 2009 North Korean test as an explosion. Therefore, including additional constraints from regional and teleseismic P-wave first motions enables source-type discrimination at regions with limited station coverage. We present moment tensor analysis of earthquakes and explosions (M6) from Lop Nor and Semipalatinsk test sites for station paths crossing Kazakhstan and Western China. We also present analyses of smaller events from industrial sites. In these sparse coverage situations we combine regional long-period waveforms, and high-frequency P-wave polarity from the same stations, as well as from teleseismic arrays to constrain the source type. Discrimination capability with respect to velocity model and station coverage is examined, and additionally we investigate the velocity model dependence of vanishing free-surface traction effects on seismic moment tensor inversion of shallow sources and recovery of explosive scalar moment. Our synthetic data tests indicate that biases in scalar seismic moment and discrimination for shallow sources are small and can be understood in a systematic manner. We are presently investigating the frequency dependence of vanishing traction of a very shallow (10m depth) M2+ chemical explosion recorded at several kilometer distances, and preliminary results indicate at the typical frequency passband we employ the bias does not affect our ability to retrieve the correct source mechanism but may affect the retrieval of the correct scalar seismic moment. Finally, we assess discrimination capability in a composite P-value statistical framework.

Earthquake source parameters from GPS-measured static displacements with potential for real-time application

NASA Astrophysics Data System (ADS)

O'Toole, Thomas B.; Valentine, Andrew P.; Woodhouse, John H.

2013-01-01

We describe a method for determining an optimal centroid-moment tensor solution of an earthquake from a set of static displacements measured using a network of Global Positioning System receivers. Using static displacements observed after the 4 April 2010, MW 7.2 El Mayor-Cucapah, Mexico, earthquake, we perform an iterative inversion to obtain the source mechanism and location, which minimize the least-squares difference between data and synthetics. The efficiency of our algorithm for forward modeling static displacements in a layered elastic medium allows the inversion to be performed in real-time on a single processor without the need for precomputed libraries of excitation kernels; we present simulated real-time results for the El Mayor-Cucapah earthquake. The only a priori information that our inversion scheme needs is a crustal model and approximate source location, so the method proposed here may represent an improvement on existing early warning approaches that rely on foreknowledge of fault locations and geometries.

Determination of focal mechanisms of intermediate-magnitude earthquakes in Mexico, based on Greens functions calculated for a 3D Earth model

NASA Astrophysics Data System (ADS)

Rodrigo Rodríguez Cardozo, Félix; Hjörleifsdóttir, Vala

2015-04-01

One important ingredient in the study of the complex active tectonics in Mexico is the analysis of earthquake focal mechanisms, or the seismic moment tensor. They can be determined trough the calculation of Green functions and subsequent inversion for moment-tensor parameters. However, this calculation is gets progressively more difficult as the magnitude of the earthquakes decreases. Large earthquakes excite waves of longer periods that interact weakly with laterally heterogeneities in the crust. For these earthquakes, using 1D velocity models to compute the Greens fucntions works well. The opposite occurs for smaller and intermediate sized events, where the relatively shorter periods excited interact strongly with lateral heterogeneities in the crust and upper mantle and requires more specific or regional 3D models. In this study, we calculate Greens functions for earthquakes in Mexico using a laterally heterogeneous seismic wave speed model, comprised of mantle model S362ANI (Kustowski et al 2008) and crustal model CRUST 2.0 (Bassin et al 1990). Subsequently, we invert the observed seismograms for the seismic moment tensor using a method developed by Liu et al (2004) an implemented by Óscar de La Vega (2014) for earthquakes in Mexico. By following a brute force approach, in which we include all observed Rayleigh and Love waves of the Mexican National Seismic Network (Servicio Sismológico Naciona, SSN), we obtain reliable focal mechanisms for events that excite a considerable amount of low frequency waves (Mw > 4.8). However, we are not able to consistently estimate focal mechanisms for smaller events using this method, due to high noise levels in many of the records. Excluding the noisy records, or noisy parts of the records manually, requires interactive edition of the data, using an efficient tool for the editing. Therefore, we developed a graphical user interface (GUI), based on python and the python library ObsPy, that allows the edition of observed and synthetic seismograms data such as signal filtering, choosing and disregarding traces and manual adjustment of time windows, to only include segments where the noise are excluded as much as possible. Subsequently, we invert for the seismic moment tensor of events of variable magnitude in the Mexican territory and compare the results to those obtained by other methods. In this presentation we introduce the software and present the results from the moment-tensor inversions.

Introducing Python tools for magnetotellurics: MTpy

NASA Astrophysics Data System (ADS)

Krieger, L.; Peacock, J.; Inverarity, K.; Thiel, S.; Robertson, K.

2013-12-01

Within the framework of geophysical exploration techniques, the magnetotelluric method (MT) is relatively immature: It is still not as widely spread as other geophysical methods like seismology, and its processing schemes and data formats are not thoroughly standardized. As a result, the file handling and processing software within the academic community is mainly based on a loose collection of codes, which are sometimes highly adapted to the respective local specifications. Although tools for the estimation of the frequency dependent MT transfer function, as well as inversion and modelling codes, are available, the standards and software for handling MT data are generally not unified throughout the community. To overcome problems that arise from missing standards, and to simplify the general handling of MT data, we have developed the software package "MTpy", which allows the handling, processing, and imaging of magnetotelluric data sets. It is written in Python and the code is open-source. The setup of this package follows the modular approach of successful software packages like GMT or Obspy. It contains sub-packages and modules for various tasks within the standard MT data processing and handling scheme. Besides pure Python classes and functions, MTpy provides wrappers and convenience scripts to call external software, e.g. modelling and inversion codes. Even though still under development, MTpy already contains ca. 250 functions that work on raw and preprocessed data. However, as our aim is not to produce a static collection of software, we rather introduce MTpy as a flexible framework, which will be dynamically extended in the future. It then has the potential to help standardise processing procedures and at same time be a versatile supplement for existing algorithms. We introduce the concept and structure of MTpy, and we illustrate the workflow of MT data processing utilising MTpy on an example data set collected over a geothermal exploration site in South Australia. Workflow of MT data processing. Within the structural diagram, the MTpy sub-packages are shown in red (time series data processing), green (handling of EDI files and impedance tensor data), yellow (connection to modelling/inversion algorithms), black (impedance tensor interpretation, e.g. by Phase Tensor calculations), and blue (generation of visual representations, e.g pseudo sections or resistivity models).

Seismic data interpolation and denoising by learning a tensor tight frame

NASA Astrophysics Data System (ADS)

Liu, Lina; Plonka, Gerlind; Ma, Jianwei

2017-10-01

Seismic data interpolation and denoising plays a key role in seismic data processing. These problems can be understood as sparse inverse problems, where the desired data are assumed to be sparsely representable within a suitable dictionary. In this paper, we present a new method based on a data-driven tight frame (DDTF) of Kronecker type (KronTF) that avoids the vectorization step and considers the multidimensional structure of data in a tensor-product way. It takes advantage of the structure contained in all different modes (dimensions) simultaneously. In order to overcome the limitations of a usual tensor-product approach we also incorporate data-driven directionality. The complete method is formulated as a sparsity-promoting minimization problem. It includes two main steps. In the first step, a hard thresholding algorithm is used to update the frame coefficients of the data in the dictionary; in the second step, an iterative alternating method is used to update the tight frame (dictionary) in each different mode. The dictionary that is learned in this way contains the principal components in each mode. Furthermore, we apply the proposed KronTF to seismic interpolation and denoising. Examples with synthetic and real seismic data show that the proposed method achieves better results than the traditional projection onto convex sets method based on the Fourier transform and the previous vectorized DDTF methods. In particular, the simple structure of the new frame construction makes it essentially more efficient.

Centroid moment tensor catalogue using a 3-D continental scale Earth model: Application to earthquakes in Papua New Guinea and the Solomon Islands

NASA Astrophysics Data System (ADS)

Hejrani, Babak; Tkalčić, Hrvoje; Fichtner, Andreas

2017-07-01

Although both earthquake mechanism and 3-D Earth structure contribute to the seismic wavefield, the latter is usually assumed to be layered in source studies, which may limit the quality of the source estimate. To overcome this limitation, we implement a method that takes advantage of a 3-D heterogeneous Earth model, recently developed for the Australasian region. We calculate centroid moment tensors (CMTs) for earthquakes in Papua New Guinea (PNG) and the Solomon Islands. Our method is based on a library of Green's functions for each source-station pair for selected Geoscience Australia and Global Seismic Network stations in the region, and distributed on a 3-D grid covering the seismicity down to 50 km depth. For the calculation of Green's functions, we utilize a spectral-element method for the solution of the seismic wave equation. Seismic moment tensors were calculated using least squares inversion, and the 3-D location of the centroid is found by grid search. Through several synthetic tests, we confirm a trade-off between the location and the correct input moment tensor components when using a 1-D Earth model to invert synthetics produced in a 3-D heterogeneous Earth. Our CMT catalogue for PNG in comparison to the global CMT shows a meaningful increase in the double-couple percentage (up to 70%). Another significant difference that we observe is in the mechanism of events with depth shallower then 15 km and Mw < 6, which contributes to accurate tectonic interpretation of the region.

Long-Lived Inverse Chirp Signals from Core-Collapse in Massive Scalar-Tensor Gravity

NASA Astrophysics Data System (ADS)

Sperhake, Ulrich; Moore, Christopher J.; Rosca, Roxana; Agathos, Michalis; Gerosa, Davide; Ott, Christian D.

2017-11-01

This Letter considers stellar core collapse in massive scalar-tensor theories of gravity. The presence of a mass term for the scalar field allows for dramatic increases in the radiated gravitational wave signal. There are several potential smoking gun signatures of a departure from general relativity associated with this process. These signatures could show up within existing LIGO-Virgo searches.

Analysis of seismicity and stress before and after the Mw 8.1 Pisagua, Chile, 2014 earthquake

NASA Astrophysics Data System (ADS)

Grigoli, F.; Cesca, S.; Dahm, T.; Hainzl, S.

2014-12-01

On April 1st, 2014 at 23:46:50 UTC, a powerful earthquake of magnitude Mw 8.1 occurred offshore the Northern Chile in the region of the North Chilean seismic gap. The epicenter of the earthquake was approximately 50 km offshore the Chilean coast, near the town of Pisagua. Two days after the main event a Mw 7.6 aftershock struck approximately the same area. In order to identify spatio-temporal changes of source parameters and stress before and after the mainshock, we analyzed in detail the local seismicity above magnitude Mw 3.0 within the time period 01/01/2013-30/04/2014 and estimated long term trends in b-values and earthquake productivity. We used data from the IPOC (Integrated Plate boundary Observatory Chile) regional seismic network, consisting of 20 "in land" broadband station deployed and managed by the GFZ-Potsdam. The recorded earthquake catalog shows an intense foreshock activity consisting of more than 1000 M3+ events in the source region. Full waveform techniques are used to derive both locations and focal mechanisms of about 435 seismic events. The location process has been performed by using a waveform stacking method (Grigoli et al 2013, 2014) with a layered velocity model based on CRUST 2.0 (see the attached figure for the location results of one of these events). Moment tensor inversion has been performed by using the KIWI tool software (Cesca et al. 2010), which is based on a two-step inversion approach. The first step consists in the inversion of the amplitude spectra to retrieve the best fitting focal planes, while the second inversion step is carried out in time domain to solve the focal mechanism polarity and to obtain the centroid location and time. Both location and moment tensor inversion resulted in agreement with the geodynamical settings of the region. Mapping the b-value reveals a spatiotemporal anomaly of low b-values characterizing the frequency-magnitude distribution of the foreshocks in the source area of the mainshock. Finally, clustering analysis of the retrieved focal mechanism and a stress tensor inversion has been performed in order to analyze the spatio-temporal evolution of the stress, before and after the mainshock. This work has been funded by the German BMBF "Geothecnologien" project MINE (BMBF03G0737A) and by Hazard and Risk Team (HART) and PBO-Chile of GFZ.

Comparison of the Cut-and-Paste and Full Moment Tensor Methods for Estimating Earthquake Source Parameters

NASA Astrophysics Data System (ADS)

Templeton, D.; Rodgers, A.; Helmberger, D.; Dreger, D.

2008-12-01

Earthquake source parameters (seismic moment, focal mechanism and depth) are now routinely reported by various institutions and network operators. These parameters are important for seismotectonic and earthquake ground motion studies as well as calibration of moment magnitude scales and model-based earthquake-explosion discrimination. Source parameters are often estimated from long-period three- component waveforms at regional distances using waveform modeling techniques with Green's functions computed for an average plane-layered models. One widely used method is waveform inversion for the full moment tensor (Dreger and Helmberger, 1993). This method (TDMT) solves for the moment tensor elements by performing a linearized inversion in the time-domain that minimizes the difference between the observed and synthetic waveforms. Errors in the seismic velocity structure inevitably arise due to either differences in the true average plane-layered structure or laterally varying structure. The TDMT method can account for errors in the velocity model by applying a single time shift at each station to the observed waveforms to best match the synthetics. Another method for estimating source parameters is the Cut-and-Paste (CAP) method. This method breaks the three-component regional waveforms into five windows: vertical and radial component Pnl; vertical and radial component Rayleigh wave; and transverse component Love waves. The CAP method performs a grid search over double-couple mechanisms and allows the synthetic waveforms for each phase (Pnl, Rayleigh and Love) to shift in time to account for errors in the Green's functions. Different filtering and weighting of the Pnl segment relative to surface wave segments enhances sensitivity to source parameters, however, some bias may be introduced. This study will compare the TDMT and CAP methods in two different regions in order to better understand the advantages and limitations of each method. Firstly, we will consider the northeastern China/Korean Peninsula region where average plane-layered structure is well known and relatively laterally homogenous. Secondly, we will consider the Middle East where crustal and upper mantle structure is laterally heterogeneous due to recent and ongoing tectonism. If time allows we will investigate the efficacy of each method for retrieving source parameters from synthetic data generated using a three-dimensional model of seismic structure of the Middle East, where phase delays are known to arise from path-dependent structure.

Identifying isotropic events using a regional moment tensor inversion

DOE PAGES

Ford, Sean R.; Dreger, Douglas S.; Walter, William R.

2009-01-17

We calculate the deviatoric and isotropic source components for 17 explosions at the Nevada Test Site, as well as 12 earthquakes and 3 collapses in the surrounding region of the western United States, using a regional time domain full waveform inversion for the complete moment tensor. The events separate into specific populations according to their deviation from a pure double-couple and ratio of isotropic to deviatoric energy. The separation allows for anomalous event identification and discrimination between explosions, earthquakes, and collapses. Confidence regions of the model parameters are estimated from the data misfit by assuming normally distributed parameter values. Wemore » investigate the sensitivity of the resolved parameters of an explosion to imperfect Earth models, inaccurate event depths, and data with low signal-to-noise ratio (SNR) assuming a reasonable azimuthal distribution of stations. In the band of interest (0.02–0.10 Hz) the source-type calculated from complete moment tensor inversion is insensitive to velocity model perturbations that cause less than a half-cycle shift (<5 s) in arrival time error if shifting of the waveforms is allowed. The explosion source-type is insensitive to an incorrect depth assumption (for a true depth of 1 km), and the goodness of fit of the inversion result cannot be used to resolve the true depth of the explosion. Noise degrades the explosive character of the result, and a good fit and accurate result are obtained when the signal-to-noise ratio is greater than 5. We assess the depth and frequency dependence upon the resolved explosive moment. As the depth decreases from 1 km to 200 m, the isotropic moment is no longer accurately resolved and is in error between 50 and 200%. Furthermore, even at the most shallow depth the resultant moment tensor is dominated by the explosive component when the data have a good SNR.« less

Bianisotropic metamaterial

DOEpatents

El-Kady, Ihab F.; Reinke, Charles M.

2017-07-18

The topology of the elements of a metamaterial can be engineered from its desired electromagnetic constitutive tensor using an inverse group theory method. Therefore, given a desired electromagnetic response and a generic metamaterial elemental design, group theory is applied to predict the various ways that the element can be arranged in three dimensions to produce the desired functionality. An optimizer can then be applied to an electromagnetic modeling tool to fine tune the values of the electromagnetic properties of the resulting metamaterial topology.

Three-dimensional inversion of magnetotelluric data for mineral exploration: An example from the McArthur River uranium deposit, Saskatchewan, Canada

NASA Astrophysics Data System (ADS)

Farquharson, Colin G.; Craven, James A.

2009-08-01

Shallow exploration targets are becoming scarce, meaning interest is turning towards deeper targets. The magnetotelluric method has the necessary depth capability, unlike many of the controlled-source electromagnetic prospecting techniques traditionally used. The geological setting of ore deposits is usually complex, requiring three-dimensional Earth models for their representation. An example of the applicability of three-dimensional inversion of magnetotelluric data to mineral exploration is presented here. Inversions of an audio-magnetotelluric data-set from the McArthur River uranium mine in the Athabasca Basin were carried out. A sub-set comprising data from eleven frequencies distributed over almost three decades was inverted. The form of the data used in the inversion was impedance. All four elements of the tensor were included. No decompositions of the data were done, nor rotation to a preferred strike direction, nor correction for static shifts. The inversions were successful: the observations were adequately reproduced and the main features in the conductivity model corresponded to known geological features. These included the graphitic basement fault along which the McArthur River uranium deposit is located.

In situ seismic anisotropy around deep earthquakes in Japan subduction slabs using Japan Meteorological Agency moment tensors

NASA Astrophysics Data System (ADS)

Li, J.; Zheng, Y.; Thomsen, L.

2017-12-01

Knowing the in situ seismic anisotropy around deep earthquakes in slabs is important in understanding deep-earthquake mechanism as it may provide critically needed information about the rock fabric where deep earthquakes occur. It has been recognized for about 50 years that many deep earthquakes are not double-couple (DC) events. Previously we showed that in situ anisotropy around deep earthquakes could explain such observed non-DC events. Traditionally, the shear wave splitting method has been used to infer such anisotropy around deep earthquakes but this is challenging because it will need many crossing ray paths for the method to localize the anisotropic region (Long 2013). In this abstract, we adopt the same procedure to obtain anisotropy in the Pacific slab under Japan using moment tensors provided by the Japan Meteorological Agency using the F-net data. We directly probe the in situ anisotropy within the subducting slabs using the radiation patterns (represented by the moment tensors) of deep earthquakes (with depth greater than 60 km). By assuming a group of shear dislocation events embedded in a common tilted transversely isotropic (TTI) medium, we used the moment tensors as our input data to invert for the anisotropy in Mariana-Japan-Kuril subducting zone. The TTI medium is characterized by the P and S wave velocities along the symmetry axis (described by two free angles) and three Thomsen parameters. We divided the deep earthquake events into 9 groups by their spatial proximity using the k-means clustering method (Hartigan and Wong 1979). These 9 groups include 2 intermediate-depth groups (depth from 60 km to 300 km) and 7 deep-focus groups (depth greater than 300 km). Our inversion results show that the inverted TTI symmetry axes are perpendicular to the slab interface for two intermediate-depth groups (consistent with dehydration metamorphic reactions) and parallel to the slab interface for 7 deep-focus group. The shear wave anisotropy is best resolved by our inversion algorithm with a typical value of around 28% (ranging from 25% to 41%). Our inverted anisotropy provides direct information of stress and rock fabric inside the subducting slab and may help explain the mechanisms of deep earthquakes.

3D electromagnetic modelling of a TTI medium and TTI effects in inversion

NASA Astrophysics Data System (ADS)

Jaysaval, Piyoosh; Shantsev, Daniil; de la Kethulle de Ryhove, Sébastien

2016-04-01

We present a numerical algorithm for 3D electromagnetic (EM) forward modelling in conducting media with general electric anisotropy. The algorithm is based on the finite-difference discretization of frequency-domain Maxwell's equations on a Lebedev grid, in which all components of the electric field are collocated but half a spatial step staggered with respect to the magnetic field components, which also are collocated. This leads to a system of linear equations that is solved using a stabilized biconjugate gradient method with a multigrid preconditioner. We validate the accuracy of the numerical results for layered and 3D tilted transverse isotropic (TTI) earth models representing typical scenarios used in the marine controlled-source EM method. It is then demonstrated that not taking into account the full anisotropy of the conductivity tensor can lead to misleading inversion results. For simulation data corresponding to a 3D model with a TTI anticlinal structure, a standard vertical transverse isotropic inversion is not able to image a resistor, while for a 3D model with a TTI synclinal structure the inversion produces a false resistive anomaly. If inversion uses the proposed forward solver that can handle TTI anisotropy, it produces resistivity images consistent with the true models.

Scalar and tensor perturbations in loop quantum cosmology: high-order corrections

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhu, Tao; Wang, Anzhong; Wu, Qiang

2015-10-01

Loop quantum cosmology (LQC) provides promising resolutions to the trans-Planckian issue and initial singularity arising in the inflationary models of general relativity. In general, due to different quantization approaches, LQC involves two types of quantum corrections, the holonomy and inverse-volume, to both of the cosmological background evolution and perturbations. In this paper, using the third-order uniform asymptotic approximations, we derive explicitly the observational quantities of the slow-roll inflation in the framework of LQC with these quantum corrections. We calculate the power spectra, spectral indices, and running of the spectral indices for both scalar and tensor perturbations, whereby the tensor-to-scalar ratiomore » is obtained. We expand all the observables at the time when the inflationary mode crosses the Hubble horizon. As the upper error bounds for the uniform asymptotic approximation at the third-order are ∼< 0.15%, these results represent the most accurate results obtained so far in the literature. It is also shown that with the inverse-volume corrections, both scalar and tensor spectra exhibit a deviation from the usual shape at large scales. Then, using the Planck, BAO and SN data we obtain new constraints on quantum gravitational effects from LQC corrections, and find that such effects could be within the detection of the forthcoming experiments.« less

Microseismic Full Waveform Modeling in Anisotropic Media with Moment Tensor Implementation

NASA Astrophysics Data System (ADS)

Shi, Peidong; Angus, Doug; Nowacki, Andy; Yuan, Sanyi; Wang, Yanyan

2018-03-01

Seismic anisotropy which is common in shale and fractured rocks will cause travel-time and amplitude discrepancy in different propagation directions. For microseismic monitoring which is often implemented in shale or fractured rocks, seismic anisotropy needs to be carefully accounted for in source location and mechanism determination. We have developed an efficient finite-difference full waveform modeling tool with an arbitrary moment tensor source. The modeling tool is suitable for simulating wave propagation in anisotropic media for microseismic monitoring. As both dislocation and non-double-couple source are often observed in microseismic monitoring, an arbitrary moment tensor source is implemented in our forward modeling tool. The increments of shear stress are equally distributed on the staggered grid to implement an accurate and symmetric moment tensor source. Our modeling tool provides an efficient way to obtain the Green's function in anisotropic media, which is the key of anisotropic moment tensor inversion and source mechanism characterization in microseismic monitoring. In our research, wavefields in anisotropic media have been carefully simulated and analyzed in both surface array and downhole array. The variation characteristics of travel-time and amplitude of direct P- and S-wave in vertical transverse isotropic media and horizontal transverse isotropic media are distinct, thus providing a feasible way to distinguish and identify the anisotropic type of the subsurface. Analyzing the travel-times and amplitudes of the microseismic data is a feasible way to estimate the orientation and density of the induced cracks in hydraulic fracturing. Our anisotropic modeling tool can be used to generate and analyze microseismic full wavefield with full moment tensor source in anisotropic media, which can help promote the anisotropic interpretation and inversion of field data.

Microseismic Full Waveform Modeling in Anisotropic Media with Moment Tensor Implementation

NASA Astrophysics Data System (ADS)

Shi, Peidong; Angus, Doug; Nowacki, Andy; Yuan, Sanyi; Wang, Yanyan

2018-07-01

Seismic anisotropy which is common in shale and fractured rocks will cause travel-time and amplitude discrepancy in different propagation directions. For microseismic monitoring which is often implemented in shale or fractured rocks, seismic anisotropy needs to be carefully accounted for in source location and mechanism determination. We have developed an efficient finite-difference full waveform modeling tool with an arbitrary moment tensor source. The modeling tool is suitable for simulating wave propagation in anisotropic media for microseismic monitoring. As both dislocation and non-double-couple source are often observed in microseismic monitoring, an arbitrary moment tensor source is implemented in our forward modeling tool. The increments of shear stress are equally distributed on the staggered grid to implement an accurate and symmetric moment tensor source. Our modeling tool provides an efficient way to obtain the Green's function in anisotropic media, which is the key of anisotropic moment tensor inversion and source mechanism characterization in microseismic monitoring. In our research, wavefields in anisotropic media have been carefully simulated and analyzed in both surface array and downhole array. The variation characteristics of travel-time and amplitude of direct P- and S-wave in vertical transverse isotropic media and horizontal transverse isotropic media are distinct, thus providing a feasible way to distinguish and identify the anisotropic type of the subsurface. Analyzing the travel-times and amplitudes of the microseismic data is a feasible way to estimate the orientation and density of the induced cracks in hydraulic fracturing. Our anisotropic modeling tool can be used to generate and analyze microseismic full wavefield with full moment tensor source in anisotropic media, which can help promote the anisotropic interpretation and inversion of field data.

Uncertainty estimations for moment tensor inversions: the issue of the 2012 May 20 Emilia earthquake

NASA Astrophysics Data System (ADS)

Scognamiglio, Laura; Magnoni, Federica; Tinti, Elisa; Casarotti, Emanuele

2016-08-01

Seismic moment tensor is one of the most important source parameters defining the earthquake dimension and style of the activated fault. Geoscientists ordinarily use moment tensor catalogues, however, few attempts have been done to assess possible impacts of moment magnitude uncertainties upon their analysis. The 2012 May 20 Emilia main shock is a representative event since it is defined in literature with a moment magnitude value (Mw) spanning between 5.63 and 6.12. A variability of ˜0.5 units in magnitude leads to a controversial knowledge of the real size of the event and reveals how the solutions could be poorly constrained. In this work, we investigate the stability of the moment tensor solution for this earthquake, studying the effect of five different 1-D velocity models, the number and the distribution of the stations used in the inversion procedure. We also introduce a 3-D velocity model to account for structural heterogeneity. We finally estimate the uncertainties associated to the computed focal planes and the obtained Mw. We conclude that our reliable source solutions provide a moment magnitude that ranges from 5.87, 1-D model, to 5.96, 3-D model, reducing the variability of the literature to ˜0.1. We endorse that the estimate of seismic moment from moment tensor solutions, as well as the estimate of the other kinematic source parameters, requires coming out with disclosed assumptions and explicit processing workflows. Finally and, probably more important, when moment tensor solution is used for secondary analyses it has to be combined with the same main boundary conditions (e.g. wave-velocity propagation model) to avoid conflicting results.

Subsurface structure imaging of the Sembalun-Propok area, West Nusa Tenggara, Indonesia by using the audio-frequency magnetotelluric data

NASA Astrophysics Data System (ADS)

Febriani, F.; Widarto, D. S.; Gaffar, E.; Nasution, A.; Grandis, H.

2017-07-01

We have investigated the subsurface structure of the Sembalun-Propok Area, West Nusa Tenggara, by using the audio-frequency magnetotelluric (AMT) method. This area is one of the geothermal prospect areas in eastern Indonesia. There are 38 AMT observation points, which were deployed along three profiles. We applied the phase tensor analysis on all observation points to determine both the dimensionality of and the regional strike of the study area. The results of the phase tensor analysis show that the study area can be assumed as 2-D and the regional strike of the study area is about N330°E. Then, after rotating the impedance tensor data to the regional strike, we carried out the 2-D inversion modeling to know more detail the subsurface structure of the study area. The results of the 2-D MT inversion are consistent with the geology of the study area. The near surface along all profiles is dominated by the higher resistivity layer (> 500 Ωm). It is highly associated with the surface geology of the study area which is characterized by the volcanic rock and mostly consist of andesitic to dacitic rocks of a calc-alkaline suite. Below the resistive layer at the near surface, the modelings show the layer which has the lower-moderate resistivity layer. It is possibly a cap rock layer of geothermal system of the Sembalun-Propok area. Lastly, the third layer is the very conductive layer and possibly associated with the presence of thermal fluids in the study area.

A Tensor-Train accelerated solver for integral equations in complex geometries

NASA Astrophysics Data System (ADS)

Corona, Eduardo; Rahimian, Abtin; Zorin, Denis

2017-04-01

We present a framework using the Quantized Tensor Train (QTT) decomposition to accurately and efficiently solve volume and boundary integral equations in three dimensions. We describe how the QTT decomposition can be used as a hierarchical compression and inversion scheme for matrices arising from the discretization of integral equations. For a broad range of problems, computational and storage costs of the inversion scheme are extremely modest O (log ⁡ N) and once the inverse is computed, it can be applied in O (Nlog ⁡ N) . We analyze the QTT ranks for hierarchically low rank matrices and discuss its relationship to commonly used hierarchical compression techniques such as FMM and HSS. We prove that the QTT ranks are bounded for translation-invariant systems and argue that this behavior extends to non-translation invariant volume and boundary integrals. For volume integrals, the QTT decomposition provides an efficient direct solver requiring significantly less memory compared to other fast direct solvers. We present results demonstrating the remarkable performance of the QTT-based solver when applied to both translation and non-translation invariant volume integrals in 3D. For boundary integral equations, we demonstrate that using a QTT decomposition to construct preconditioners for a Krylov subspace method leads to an efficient and robust solver with a small memory footprint. We test the QTT preconditioners in the iterative solution of an exterior elliptic boundary value problem (Laplace) formulated as a boundary integral equation in complex, multiply connected geometries.

Simulations of Ground Motion in Southern California based upon the Spectral-Element Method

NASA Astrophysics Data System (ADS)

Tromp, J.; Komatitsch, D.; Liu, Q.

2003-12-01

We use the spectral-element method to simulate ground motion generated by recent well-recorded small earthquakes in Southern California. Simulations are performed using a new sedimentary basin model that is constrained by hundreds of petroleum industry well logs and more than twenty thousand kilometers of seismic reflection profiles. The numerical simulations account for 3D variations of seismic wave speeds and density, topography and bathymetry, and attenuation. Simulations for several small recent events demonstrate that the combination of a detailed sedimentary basin model and an accurate numerical technique facilitates the simulation of ground motion at periods of 2 seconds and longer inside the Los Angeles basin and 6 seconds and longer elsewhere. Peak ground displacement, velocity and acceleration maps illustrate that significant amplification occurs in the basin. Centroid-Moment Tensor mechanisms are obtained based upon Pnl and surface waveforms and numerically calculated 3D Frechet derivatives. We use a combination of waveform and waveform-envelope misfit criteria, and facilitate pure double-couple or zero-trace moment-tensor inversions.

Inversion of calcite twin data for paleostress orientations and magnitudes: A new technique tested and calibrated on numerically-generated and natural data

NASA Astrophysics Data System (ADS)

Parlangeau, Camille; Lacombe, Olivier; Schueller, Sylvie; Daniel, Jean-Marc

2018-01-01

The inversion of calcite twin data is a powerful tool to reconstruct paleostresses sustained by carbonate rocks during their geological history. Following Etchecopar's (1984) pioneering work, this study presents a new technique for the inversion of calcite twin data that reconstructs the 5 parameters of the deviatoric stress tensors from both monophase and polyphase twin datasets. The uncertainties in the parameters of the stress tensors reconstructed by this new technique are evaluated on numerically-generated datasets. The technique not only reliably defines the 5 parameters of the deviatoric stress tensor, but also reliably separates very close superimposed stress tensors (30° of difference in maximum principal stress orientation or switch between σ3 and σ2 axes). The technique is further shown to be robust to sampling bias and to slight variability in the critical resolved shear stress. Due to our still incomplete knowledge of the evolution of the critical resolved shear stress with grain size, our results show that it is recommended to analyze twin data subsets of homogeneous grain size to minimize possible errors, mainly those concerning differential stress values. The methodological uncertainty in principal stress orientations is about ± 10°; it is about ± 0.1 for the stress ratio. For differential stresses, the uncertainty is lower than ± 30%. Applying the technique to vein samples within Mesozoic limestones from the Monte Nero anticline (northern Apennines, Italy) demonstrates its ability to reliably detect and separate tectonically significant paleostress orientations and magnitudes from naturally deformed polyphase samples, hence to fingerprint the regional paleostresses of interest in tectonic studies.

Three-dimensional inversion of multisource array electromagnetic data

NASA Astrophysics Data System (ADS)

Tartaras, Efthimios

Three-dimensional (3-D) inversion is increasingly important for the correct interpretation of geophysical data sets in complex environments. To this effect, several approximate solutions have been developed that allow the construction of relatively fast inversion schemes. One such method that is fast and provides satisfactory accuracy is the quasi-linear (QL) approximation. It has, however, the drawback that it is source-dependent and, therefore, impractical in situations where multiple transmitters in different positions are employed. I have, therefore, developed a localized form of the QL approximation that is source-independent. This so-called localized quasi-linear (LQL) approximation can have a scalar, a diagonal, or a full tensor form. Numerical examples of its comparison with the full integral equation solution, the Born approximation, and the original QL approximation are given. The objective behind developing this approximation is to use it in a fast 3-D inversion scheme appropriate for multisource array data such as those collected in airborne surveys, cross-well logging, and other similar geophysical applications. I have developed such an inversion scheme using the scalar and diagonal LQL approximation. It reduces the original nonlinear inverse electromagnetic (EM) problem to three linear inverse problems. The first of these problems is solved using a weighted regularized linear conjugate gradient method, whereas the last two are solved in the least squares sense. The algorithm I developed provides the option of obtaining either smooth or focused inversion images. I have applied the 3-D LQL inversion to synthetic 3-D EM data that simulate a helicopter-borne survey over different earth models. The results demonstrate the stability and efficiency of the method and show that the LQL approximation can be a practical solution to the problem of 3-D inversion of multisource array frequency-domain EM data. I have also applied the method to helicopter-borne EM data collected by INCO Exploration over the Voisey's Bay area in Labrador, Canada. The results of the 3-D inversion successfully delineate the shallow massive sulfides and show that the method can produce reasonable results even in areas of complex geology and large resistivity contrasts.

Hamiltonian Monte Carlo Inversion of Seismic Sources in Complex Media

NASA Astrophysics Data System (ADS)

Fichtner, A.; Simutė, S.

2017-12-01

We present a probabilistic seismic source inversion method that properly accounts for 3D heterogeneous Earth structure and provides full uncertainty information on the timing, location and mechanism of the event. Our method rests on two essential elements: (1) reciprocity and spectral-element simulations in complex media, and (2) Hamiltonian Monte Carlo sampling that requires only a small amount of test models. Using spectral-element simulations of 3D, visco-elastic, anisotropic wave propagation, we precompute a data base of the strain tensor in time and space by placing sources at the positions of receivers. Exploiting reciprocity, this receiver-side strain data base can be used to promptly compute synthetic seismograms at the receiver locations for any hypothetical source within the volume of interest. The rapid solution of the forward problem enables a Bayesian solution of the inverse problem. For this, we developed a variant of Hamiltonian Monte Carlo (HMC) sampling. Taking advantage of easily computable derivatives, HMC converges to the posterior probability density with orders of magnitude less samples than derivative-free Monte Carlo methods. (Exact numbers depend on observational errors and the quality of the prior). We apply our method to the Japanese Islands region where we previously constrained 3D structure of the crust and upper mantle using full-waveform inversion with a minimum period of around 15 s.

Three-dimensional magnetotelluric inversion in practice—the electrical conductivity structure of the San Andreas Fault in Central California

NASA Astrophysics Data System (ADS)

Tietze, Kristina; Ritter, Oliver

2013-10-01

3-D inversion techniques have become a widely used tool in magnetotelluric (MT) data interpretation. However, with real data sets, many of the controlling factors for the outcome of 3-D inversion are little explored, such as alignment of the coordinate system, handling and influence of data errors and model regularization. Here we present 3-D inversion results of 169 MT sites from the central San Andreas Fault in California. Previous extensive 2-D inversion and 3-D forward modelling of the data set revealed significant along-strike variation of the electrical conductivity structure. 3-D inversion can recover these features but only if the inversion parameters are tuned in accordance with the particularities of the data set. Based on synthetic 3-D data we explore the model space and test the impacts of a wide range of inversion settings. The tests showed that the recovery of a pronounced regional 2-D structure in inversion of the complete impedance tensor depends on the coordinate system. As interdependencies between data components are not considered in standard 3-D MT inversion codes, 2-D subsurface structures can vanish if data are not aligned with the regional strike direction. A priori models and data weighting, that is, how strongly individual components of the impedance tensor and/or vertical magnetic field transfer functions dominate the solution, are crucial controls for the outcome of 3-D inversion. If deviations from a prior model are heavily penalized, regularization is prone to result in erroneous and misleading 3-D inversion models, particularly in the presence of strong conductivity contrasts. A `good' overall rms misfit is often meaningless or misleading as a huge range of 3-D inversion results exist, all with similarly `acceptable' misfits but producing significantly differing images of the conductivity structures. Reliable and meaningful 3-D inversion models can only be recovered if data misfit is assessed systematically in the frequency-space domain.

Low-frequency centroid-moment-tensor inversion from superconducting-gravimeter data: The effect of seismic attenuation

NASA Astrophysics Data System (ADS)

Zábranová, Eliška; Matyska, Ctirad

2014-10-01

After the 2010 Maule and 2011 Tohoku earthquakes the spheroidal modes up to 1 mHz were clearly registered by the Global Geodynamic Project (GGP) network of superconducting gravimeters (SG). Fundamental parameters in synthetic calculations of the signals are the quality factors of the modes. We study the role of their uncertainties in the centroid-moment-tensor (CMT) inversions. First, we have inverted the SG data from selected GGP stations to jointly determine the quality factors of these normal modes and the three low-frequency CMT components, Mrr,(Mϑϑ-Mφφ)/2 and Mϑφ, that generate the observed SG signal. We have used several-days-long records to minimize the trade-off between the quality factors and the CMT but it was not eliminated completely. We have also inverted each record separately to get error estimates of the obtained parameters. Consequently, we have employed the GGP records of 60-h lengths for several published modal-quality-factor sets and inverted only the same three CMT components. The obtained CMT tensors are close to the solution from the joint Q-CMT inversion of longer records and resulting variability of the CMT components is smaller than differences among routine agency solutions. Reliable low-frequency CMT components can thus be obtained for any quality factors from the studied sets.

Full-Wave Tomographic and Moment Tensor Inversion Based on 3D Multigrid Strain Green’s Tensor Databases

DTIC Science & Technology

2014-04-30

grade metamorphic rocks on the southern slope of the Himalaya is imaged as a band of high velocity anomaly...velocity structures closely follow the geological features. As an indication of resolution, the ductile extrusion of high-grade metamorphic rocks on...MATERIEL COMMAND KIRTLAND AIR FORCE BASE, NM 87117-5776 DTIC COPY NOTICE AND SIGNATURE PAGE Using Government drawings, specifications, or other data

Traumatic Brain Injury: Hope Through Research

MedlinePlus

... last decade to image milder TBI damage. For example, diffusion tensor imaging (DTI) can image white matter tracts, more sensitive tests like fluid-attenuated inversion recovery (FLAIR) can detect ...

A fast and robust method for moment tensor and depth determination of shallow seismic events in CTBT related studies.

NASA Astrophysics Data System (ADS)

Baker, Ben; Stachnik, Joshua; Rozhkov, Mikhail

2017-04-01

International Data Center is required to conduct expert technical analysis and special studies to improve event parameters and assist State Parties in identifying the source of specific event according to the protocol to the Protocol to the Comprehensive Nuclear Test Ban Treaty. Determination of seismic event source mechanism and its depth is closely related to these tasks. It is typically done through a strategic linearized inversion of the waveforms for a complete or subset of source parameters, or similarly defined grid search through precomputed Greens Functions created for particular source models. In this presentation we demonstrate preliminary results obtained with the latter approach from an improved software design. In this development we tried to be compliant with different modes of CTBT monitoring regime and cover wide range of source-receiver distances (regional to teleseismic), resolve shallow source depths, provide full moment tensor solution based on body and surface waves recordings, be fast to satisfy both on-demand studies and automatic processing and properly incorporate observed waveforms and any uncertainties a priori as well as accurately estimate posteriori uncertainties. Posterior distributions of moment tensor parameters show narrow peaks where a significant number of reliable surface wave observations are available. For earthquake examples, fault orientation (strike, dip, and rake) posterior distributions also provide results consistent with published catalogues. Inclusion of observations on horizontal components will provide further constraints. In addition, the calculation of teleseismic P wave Green's Functions are improved through prior analysis to determine an appropriate attenuation parameter for each source-receiver path. Implemented HDF5 based Green's Functions pre-packaging allows much greater flexibility in utilizing different software packages and methods for computation. Further additions will have the rapid use of Instaseis/AXISEM full waveform synthetics added to a pre-computed GF archive. Along with traditional post processing analysis of waveform misfits through several objective functions and variance reduction, we follow a probabilistic approach to assess the robustness of moment tensor solution. In a course of this project full moment tensor and depth estimates are determined for DPRK events and shallow earthquakes using a new implementation of teleseismic P waves waveform fitting. A full grid search over the entire moment tensor space is used to appropriately sample all possible solutions. A recent method by Tape & Tape (2012) to discretize the complete moment tensor space from a geometric perspective is used. Probabilistic uncertainty estimates on the moment tensor parameters provide robustness to solution.

Surface topography estimated by inversion of satellite gravity gradiometry observations

NASA Astrophysics Data System (ADS)

Ramillien, Guillaume

2015-04-01

An integration of mass elements is presented for evaluating the six components of the 2-order gravity tensor (i.e., second derivatives of the Newtonian mass integral for the gravitational potential) created by an uneven sphere topography consisting of juxtaposed vertical prisms. The method is based on Legendre polynomial series with the originality of taking elastic compensation of the topography by the Earth's surface into account. The speed of computation of the polynomial series increases logically with the observing altitude from the source of anomaly. Such a forward modelling can be easily used for reduction of observed gravity gradient anomalies by the effects of any spherical interface of density. Moreover, an iterative least-square inversion of the observed gravity tensor values Γαβ is proposed to estimate a regional set of topographic heights. Several tests of recovery have been made by considering simulated gradiometry anomaly data, and for varying satellite altitudes and a priori levels of accuracy. In the case of GOCE-type gradiometry anomalies measured at an altitude of ~300 km, the search converges down to a stable and smooth topography after 20-30 iterations while the final r.m.s. error is ~100 m. The possibility of cumulating satellite information from different orbit geometries is also examined for improving the prediction.

Affine theory of gravitation

NASA Astrophysics Data System (ADS)

Popławski, Nikodem

2014-01-01

We propose a theory of gravitation, in which the affine connection is the only dynamical variable describing the gravitational field. We construct a simple dynamical Lagrangian density that is entirely composed from the connection, via its curvature and torsion, and is a polynomial function of its derivatives. It is given by the contraction of the Ricci tensor with a tensor which is inverse to the symmetric, contracted square of the torsion tensor, . We vary the total action for the gravitational field and matter with respect to the affine connection, assuming that the matter fields couple to the connection only through . We derive the resulting field equations and show that they are identical with the Einstein equations of general relativity with a nonzero cosmological constant if the tensor is regarded as proportional to the metric tensor. The cosmological constant is simply a constant of proportionality between the two tensors, which together with and provides a natural system of units in gravitational physics. This theory therefore provides a physical construction of the metric as a polynomial function of the connection, and explains dark energy as an intrinsic property of spacetime.

The Riemannian geometry is not sufficient for the geometrization of the Maxwell's equations

NASA Astrophysics Data System (ADS)

Kulyabov, Dmitry S.; Korolkova, Anna V.; Velieva, Tatyana R.

2018-04-01

The transformation optics uses geometrized Maxwell's constitutive equations to solve the inverse problem of optics, namely to solve the problem of finding the parameters of the medium along the paths of propagation of the electromagnetic field. For the geometrization of Maxwell's constitutive equations, the quadratic Riemannian geometry is usually used. This is due to the use of the approaches of the general relativity. However, there arises the question of the insufficiency of the Riemannian structure for describing the constitutive tensor of the Maxwell's equations. The authors analyze the structure of the constitutive tensor and correlate it with the structure of the metric tensor of Riemannian geometry. It is concluded that the use of the quadratic metric for the geometrization of Maxwell's equations is insufficient, since the number of components of the metric tensor is less than the number of components of the constitutive tensor. A possible solution to this problem may be a transition to Finslerian geometry, in particular, the use of the Berwald-Moor metric to establish the structural correspondence between the field tensors of the electromagnetic field.

The genetic algorithm: A robust method for stress inversion

NASA Astrophysics Data System (ADS)

Thakur, Prithvi; Srivastava, Deepak C.; Gupta, Pravin K.

2017-01-01

The stress inversion of geological or geophysical observations is a nonlinear problem. In most existing methods, it is solved by linearization, under certain assumptions. These linear algorithms not only oversimplify the problem but also are vulnerable to entrapment of the solution in a local optimum. We propose the use of a nonlinear heuristic technique, the genetic algorithm, which searches the global optimum without making any linearizing assumption or simplification. The algorithm mimics the natural evolutionary processes of selection, crossover and mutation and, minimizes a composite misfit function for searching the global optimum, the fittest stress tensor. The validity and efficacy of the algorithm are demonstrated by a series of tests on synthetic and natural fault-slip observations in different tectonic settings and also in situations where the observations are noisy. It is shown that the genetic algorithm is superior to other commonly practised methods, in particular, in those tectonic settings where none of the principal stresses is directed vertically and/or the given data set is noisy.

Overcoming the sign problem at finite temperature: Quantum tensor network for the orbital eg model on an infinite square lattice

NASA Astrophysics Data System (ADS)

Czarnik, Piotr; Dziarmaga, Jacek; Oleś, Andrzej M.

2017-07-01

The variational tensor network renormalization approach to two-dimensional (2D) quantum systems at finite temperature is applied to a model suffering the notorious quantum Monte Carlo sign problem—the orbital eg model with spatially highly anisotropic orbital interactions. Coarse graining of the tensor network along the inverse temperature β yields a numerically tractable 2D tensor network representing the Gibbs state. Its bond dimension D —limiting the amount of entanglement—is a natural refinement parameter. Increasing D we obtain a converged order parameter and its linear susceptibility close to the critical point. They confirm the existence of finite order parameter below the critical temperature Tc, provide a numerically exact estimate of Tc, and give the critical exponents within 1 % of the 2D Ising universality class.

[An Improved Spectral Quaternion Interpolation Method of Diffusion Tensor Imaging].

PubMed

Xu, Yonghong; Gao, Shangce; Hao, Xiaofei

2016-04-01

Diffusion tensor imaging(DTI)is a rapid development technology in recent years of magnetic resonance imaging.The diffusion tensor interpolation is a very important procedure in DTI image processing.The traditional spectral quaternion interpolation method revises the direction of the interpolation tensor and can preserve tensors anisotropy,but the method does not revise the size of tensors.The present study puts forward an improved spectral quaternion interpolation method on the basis of traditional spectral quaternion interpolation.Firstly,we decomposed diffusion tensors with the direction of tensors being represented by quaternion.Then we revised the size and direction of the tensor respectively according to different situations.Finally,we acquired the tensor of interpolation point by calculating the weighted average.We compared the improved method with the spectral quaternion method and the Log-Euclidean method by the simulation data and the real data.The results showed that the improved method could not only keep the monotonicity of the fractional anisotropy(FA)and the determinant of tensors,but also preserve the tensor anisotropy at the same time.In conclusion,the improved method provides a kind of important interpolation method for diffusion tensor image processing.

Focal mechanism determination of induced micro-earthquakes in reservoir by non linear inversion of amplitudes

NASA Astrophysics Data System (ADS)

Godano, M.; Regnier, M.; Deschamps, A.; Bardainne, T.

2009-04-01

Since these last years, the feasibility of CO2 storage in geological reservoir is carefully investigated. The monitoring of the seismicity (natural or induced by the gas injection) in the reservoir area is crucial for safety concerns. The location of the seismic events provide an imaging of the active structures which can be a potential leakage paths. Besides, the focal mechanism is an other important seismic attribute providing direct informations about the rock fracturing, and indirect information about the state of stress in the reservoir. We address the problem of focal mechanism determination for the micro-earthquakes induced in reservoirs with a potential application to the sites of CO2 storage. We developed a non linear inversion method of P, SV and SH direct waves amplitudes. To solve the inverse problem, we perfected our own simulated annealing algorithm. Our method allows simply determining the fault plane solution (strike, dip and rake of the fault plane) in the case of a double-couple source assumption. More generally, our method allows also determining the full moment tensor in case of non-purely shear source assumption. We searched to quantify the uncertainty associated to the obtained focal mechanisms. We defined three uncertainty causes. The first is related to the convergence process of the inversion, the second is related the amplitude picking error caused by the noise level and the third is related to the event location uncertainty. We performed a series of tests on synthetic data generated in reservoir configuration in order to validate our inversion method.

Complete Moment Tensor Determination of Induced Seismicity in Unconventional and Conventional Oil/Gas Fields

NASA Astrophysics Data System (ADS)

Gu, C.; Li, J.; Toksoz, M. N.

2013-12-01

Induced seismicity occurs both in conventional oil/gas fields due to production and water injection and in unconventional oil/gas fields due to hydraulic fracturing. Source mechanisms of these induced earthquakes are of great importance for understanding their causes and the physics of the seismic processes in reservoirs. Previous research on the analysis of induced seismic events in conventional oil/gas fields assumed a double couple (DC) source mechanism. However, recent studies have shown a non-negligible percentage of a non-double-couple (non-DC) component of source moment tensor in hydraulic fracturing events (Šílený et al., 2009; Warpinski and Du, 2010; Song and Toksöz, 2011). In this study, we determine the full moment tensor of the induced seismicity data in a conventional oil/gas field and for hydrofrac events in an unconventional oil/gas field. Song and Toksöz (2011) developed a full waveform based complete moment tensor inversion method to investigate a non-DC source mechanism. We apply this approach to the induced seismicity data from a conventional gas field in Oman. In addition, this approach is also applied to hydrofrac microseismicity data monitored by downhole geophones in four wells in US. We compare the source mechanisms of induced seismicity in the two different types of gas fields and explain the differences in terms of physical processes.

Characterizing heterogeneous properties of cerebral aneurysms with unknown stress-free geometry: a precursor to in vivo identification.

PubMed

Zhao, Xuefeng; Raghavan, Madhavan L; Lu, Jia

2011-05-01

Knowledge of elastic properties of cerebral aneurysms is crucial for understanding the biomechanical behavior of the lesion. However, characterizing tissue properties using in vivo motion data presents a tremendous challenge. Aside from the limitation of data accuracy, a pressing issue is that the in vivo motion does not expose the stress-free geometry. This is compounded by the nonlinearity, anisotropy, and heterogeneity of the tissue behavior. This article introduces a method for identifying the heterogeneous properties of aneurysm wall tissue under unknown stress-free configuration. In the proposed approach, an accessible configuration is taken as the reference; the unknown stress-free configuration is represented locally by a metric tensor describing the prestrain from the stress-free configuration to the reference configuration. Material parameters are identified together with the metric tensor pointwisely. The paradigm is tested numerically using a forward-inverse analysis loop. An image-derived sac is considered. The aneurysm tissue is modeled as an eightply laminate whose constitutive behavior is described by an anisotropic hyperelastic strain-energy function containing four material parameters. The parameters are assumed to vary continuously in two assigned patterns to represent two types of material heterogeneity. Nine configurations between the diastolic and systolic pressures are generated by forward quasi-static finite element analyses. These configurations are fed to the inverse analysis to delineate the material parameters and the metric tensor. The recovered and the assigned distributions are in good agreement. A forward verification is conducted by comparing the displacement solutions obtained from the recovered and the assigned material parameters at a different pressure. The nodal displacements are found in excellent agreement.

Fast estimation of diffusion tensors under Rician noise by the EM algorithm.

PubMed

Liu, Jia; Gasbarra, Dario; Railavo, Juha

2016-01-15

Diffusion tensor imaging (DTI) is widely used to characterize, in vivo, the white matter of the central nerve system (CNS). This biological tissue contains much anatomic, structural and orientational information of fibers in human brain. Spectral data from the displacement distribution of water molecules located in the brain tissue are collected by a magnetic resonance scanner and acquired in the Fourier domain. After the Fourier inversion, the noise distribution is Gaussian in both real and imaginary parts and, as a consequence, the recorded magnitude data are corrupted by Rician noise. Statistical estimation of diffusion leads a non-linear regression problem. In this paper, we present a fast computational method for maximum likelihood estimation (MLE) of diffusivities under the Rician noise model based on the expectation maximization (EM) algorithm. By using data augmentation, we are able to transform a non-linear regression problem into the generalized linear modeling framework, reducing dramatically the computational cost. The Fisher-scoring method is used for achieving fast convergence of the tensor parameter. The new method is implemented and applied using both synthetic and real data in a wide range of b-amplitudes up to 14,000s/mm(2). Higher accuracy and precision of the Rician estimates are achieved compared with other log-normal based methods. In addition, we extend the maximum likelihood (ML) framework to the maximum a posteriori (MAP) estimation in DTI under the aforementioned scheme by specifying the priors. We will describe how close numerically are the estimators of model parameters obtained through MLE and MAP estimation. Copyright © 2015 Elsevier B.V. All rights reserved.

Fluid moments of the nonlinear Landau collision operator

DOE PAGES

Hirvijoki, E.; Lingam, M.; Pfefferle, D.; ...

2016-08-09

An important problem in plasma physics is the lack of an accurate and complete description of Coulomb collisions in associated fluid models. To shed light on the problem, this Letter introduces an integral identity involving the multivariate Hermite tensor polynomials and presents a method for computing exact expressions for the fluid moments of the nonlinear Landau collision operator. In conclusion, the proposed methodology provides a systematic and rigorous means of extending the validity of fluid models that have an underlying inverse-square force particle dynamics to arbitrary collisionality and flow.

Progress report on lithium-related geologic investigations in Bolivia

USGS Publications Warehouse

Davis, J.R.; Howard, K.A.; Rettig, S.L.; Smith, R.L.; Ericksen, G.E.; Risacher, Francois; Alarcon, Hugo; Morales, Ricardo

1982-01-01

The September 1, 1981, Samoa Islands Region earthquake occurred at the extreme northern end of the Tonga arc in a region where the Pacific plate may be disjointed along a hinge fault. In the last 50 years, magnitude 7 or greater earthquakes have occurred in this region on the average of once every six years, but four 7+ events have now occurred within the last six years. The mainshock was preceded about two hours earlier by a foreshock that was used as a calibration event for the Joint Epicenter Determination relocation of the mainshock and nearby seismicity occurring within a period seven months prior to and one week after the mainshock. The foreshock, better-located events of the prior seismicity, and most aftershocks are concentrated in a group near the mainshock epicenter, but several more distant aftershocks suggest that the aftershock zone may have been as large as 125 km in length and trended about S35?E. Identification of depth phases from a full suite of broadband records gives source depths of 25-3km for the mainshock and 29.5?3 km for the foreshock using a JB earth model. Source parameters were determined for the mainshock utilizing WWSSN analog and GDSN digital data. The preferred fault plane solution based on P-wave first motion data is a south by southwesterly steeply dipping normal fault, remarkably similar to the mechanism reported by Johnson and Molnar (1972) for the nearby earthquake of April 20, 196B. A waveform inversion technique described by Sipkin (1982), when applied to long-period P waveforms, gives an 'average' point source solution for a purely deviatoric moment rate tensor at a preferred source depth of 22 km. Very similar results were obtained from long-period GDSN body-wave and mantle-wave data using a centroid-moment tensor inversion technique described in Dziewonski, and others (1981). Both techniques provide solutions very close to a double couple source with a south by southwesterly shallow-dipping normal fault mechanism. To obtain the scalar mantle wave moment, GDSN vertical and transverse records 20,000 see in length were processed as described by Buland and Taggart (1981). Averaging all the data from Rayleigh and Love waves yields an estimate of 3.8 x 10^27 dyne-cm (as compared to about 1.9 x 10^27 from body-wave moment tensor inversions) or a moment magnitude (Mr) of 7.6. For the portion of the waveform analysed (50-5B sec), the body-wave inversion performed by Sipkin gives a source time function of duration approximately 28 sec with two peaks in activity. Simultaneous analysis of short-period records, and broadband ground displacements and velocities, a method described by Harvey and Choy (1982) and Choy and Boatwright (1981) revealed a complex rupture consisting of two subevents, of about the same moment, separated in time by about 25 sec, and with durations of about 25 sec each. The two peaks in activity resolved by the body-wave moment tensor inversion correspond to the first of these subevents.

Electrical impedance tomography in anisotropic media with known eigenvectors

NASA Astrophysics Data System (ADS)

Abascal, Juan-Felipe P. J.; Lionheart, William R. B.; Arridge, Simon R.; Schweiger, Martin; Atkinson, David; Holder, David S.

2011-06-01

Electrical impedance tomography is an imaging method, with which volumetric images of conductivity are produced by injecting electrical current and measuring boundary voltages. It has the potential to become a portable non-invasive medical imaging technique. Until now, most implementations have neglected anisotropy even though human tissues like bone, muscle and brain white matter are markedly anisotropic. The recovery of an anisotropic conductivity tensor is uniquely determined by boundary measurements only up to a diffeomorphism that fixes the boundary. Nevertheless, uniqueness can be restored by providing information about the diffeomorphism. There are uniqueness results for two constraints: one eigenvalue and a multiple scalar of a general tensor. A useable constraint for medical applications is when the eigenvectors of the underlying tissue are known, which can be approximated from MRI or estimated from DT-MRI, although the eigenvalues are unknown. However there is no known theoretical result guaranteeing uniqueness for this constraint. In fact, only a few previous inversion studies have attempted to recover one or more eigenvalues assuming certain symmetries while ignoring nonuniqueness. In this work, the aim was to undertake a numerical study of the feasibility of the recovery of a piecewise linear finite element conductivity tensor in anisotropic media with known eigenvectors from the complete boundary data. The work suggests that uniqueness holds for this constraint, in addition to proposing a methodology for the incorporation of this prior for general conductivity tensors. This was carried out by performing an analysis of the Jacobian rank and by reconstructing four conductivity distributions: two diagonal tensors whose eigenvalues were linear and sinusoidal functions, and two general tensors whose eigenvectors resembled physiological tissue, one with eigenvectors spherically orientated like a spherical layered structure, and a sample of DT-MRI data of brain white matter. The Jacobian with respect to three eigenvalues was full-rank and it was possible to recover three eigenvalues for the four simulated distributions. This encourages further theoretical study of the uniqueness for this constraint and supports the use of this as a relevant usable method for medical applications.

3D joint inversion of gravity-gradient and borehole gravity data

NASA Astrophysics Data System (ADS)

Geng, Meixia; Yang, Qingjie; Huang, Danian

2017-12-01

Borehole gravity is increasingly used in mineral exploration due to the advent of slim-hole gravimeters. Given the full-tensor gradiometry data available nowadays, joint inversion of surface and borehole data is a logical next step. Here, we base our inversions on cokriging, which is a geostatistical method of estimation where the error variance is minimised by applying cross-correlation between several variables. In this study, the density estimates are derived using gravity-gradient data, borehole gravity and known densities along the borehole as a secondary variable and the density as the primary variable. Cokriging is non-iterative and therefore is computationally efficient. In addition, cokriging inversion provides estimates of the error variance for each model, which allows direct assessment of the inverse model. Examples are shown involving data from a single borehole, from multiple boreholes, and combinations of borehole gravity and gravity-gradient data. The results clearly show that the depth resolution of gravity-gradient inversion can be improved significantly by including borehole data in addition to gravity-gradient data. However, the resolution of borehole data falls off rapidly as the distance between the borehole and the feature of interest increases. In the case where the borehole is far away from the target of interest, the inverted result can be improved by incorporating gravity-gradient data, especially all five independent components for inversion.

A real-time moment-tensor inversion system (GRiD-MT-3D) using 3-D Green's functions

NASA Astrophysics Data System (ADS)

Nagao, A.; Furumura, T.; Tsuruoka, H.

2016-12-01

We developed a real-time moment-tensor inversion system using 3-D Green's functions (GRiD-MT-3D) by improving the current system (GRiD-MT; Tsuruoka et al., 2009), which uses 1-D Green's functions for longer periods than 20 s. Our moment-tensor inversion is applied to the real-time monitoring of earthquakes occurring beneath Kanto basin area. The basin, which is constituted of thick sediment layers, lies on the complex subduction of the Philippine-Sea Plate and the Pacific Plate that can significantly affect the seismic wave propagation. We compute 3-D Green's functions using finite-difference-method (FDM) simulations considering a 3-D velocity model, which is based on the Japan Integrated Velocity Structure Model (Koketsu et al., 2012), that includes crust, mantle, and subducting plates. The 3-D FDM simulations are computed over a volume of 468 km by 432 km by 120 km in the EW, NS, and depth directions, respectively, that is discretized into 0.25 km grids. Considering that the minimum S wave velocity of the sedimentary layer is 0.5 km/s, simulations can compute seismograms up to 0.5 Hz. We calculate Green's functions between 24,700 sources, which are distributed every 0.1° in the horizontal direction and every 9 km in depth direction, and 13 F-net stations. To compute this large number of Green's functions, we used the EIC parallel computer of ERI. The reciprocity theory, which switches the source and station positions, is used to reduce total computation costs. It took 156 hours to compute all the Green's functions. Results show that at long-periods (T>15 s), only small differences are observed between the 3-D and 1-D Green's functions as indicated by high correlation coefficients of 0.9 between the waveforms. However, at shorter periods (T<10 s), the differences become larger and the correlation coefficients drop to 0.5. The effect of the 3-D heterogeneous structure especially affects the Green's functions for the ray paths that across complex geological structures, such as the sedimentary basin or the subducting plates. After incorporation of the 3-D Green's functions in the GRiD-MT-3D system, we compare the results to the former GRiD-MT system to demonstrate the effectiveness of the new system in terms of variance reduction and accuracy of the moment-tensor estimation for much smaller events than the current one.

Stress regimes in the northwest of Iran from stress inversion of earthquake focal mechanisms

NASA Astrophysics Data System (ADS)

Afra, Mahsa; Moradi, Ali; Pakzad, Mehrdad

2017-11-01

Northwestern Iran is one of the seismically active regions with a high seismic risk in the world. This area is a part of the complex tectonic system due to the interaction between Arabia, Anatolia and Eurasia. The purpose of this study is to deduce the stress regimes in the northwestern Iran and surrounding regions from stress inversion of earthquake focal mechanisms. We compile 92 focal mechanisms data from the Global CMT catalogue and other sources and also determine the focal mechanisms of 14 earthquakes applying the moment tensor inversion. We divide the studied region into 9 zones using similarity of the horizontal GPS velocities and existing focal mechanisms. We implement two stress inversion methods, Multiple Inverse Method and Iterative Joint Inversion Method, which provide comparable results in terms of orientations of maximum horizontal stress axes SHmax. The similar results of the two methods should make us more confident about the interpretations. We consider zones of exclusion surrounding all the earthquakes according to independent focal mechanisms hypothesis. The hypothesis says that the inversion should involve events that are far enough from each other in order that any previous event doesn't affect the stress field near the earthquake under consideration. Accordingly we deal with the matter by considering zones of exclusion around all the events. The result of exclusion is only significant for eastern Anatolia. The stress regime in this region changes from oblique to strike slip faulting because of the exclusion. In eastern Anatolia, the direction of maximum horizontal stress is nearly north-south. The direction alters to east-west in Talesh region. Errors of σ1 are lower in all zones comparing with errors of σ2 and σ3 and there is a trade-off between data resolution and covariance of the model. The results substantiate the strike-slip and thrust faulting stress regimes in the northwest of Iran.

Tensor Factorization for Low-Rank Tensor Completion.

PubMed

Zhou, Pan; Lu, Canyi; Lin, Zhouchen; Zhang, Chao

2018-03-01

Recently, a tensor nuclear norm (TNN) based method was proposed to solve the tensor completion problem, which has achieved state-of-the-art performance on image and video inpainting tasks. However, it requires computing tensor singular value decomposition (t-SVD), which costs much computation and thus cannot efficiently handle tensor data, due to its natural large scale. Motivated by TNN, we propose a novel low-rank tensor factorization method for efficiently solving the 3-way tensor completion problem. Our method preserves the low-rank structure of a tensor by factorizing it into the product of two tensors of smaller sizes. In the optimization process, our method only needs to update two smaller tensors, which can be more efficiently conducted than computing t-SVD. Furthermore, we prove that the proposed alternating minimization algorithm can converge to a Karush-Kuhn-Tucker point. Experimental results on the synthetic data recovery, image and video inpainting tasks clearly demonstrate the superior performance and efficiency of our developed method over state-of-the-arts including the TNN and matricization methods.

Tensor-GMRES method for large sparse systems of nonlinear equations

NASA Technical Reports Server (NTRS)

Feng, Dan; Pulliam, Thomas H.

1994-01-01

This paper introduces a tensor-Krylov method, the tensor-GMRES method, for large sparse systems of nonlinear equations. This method is a coupling of tensor model formation and solution techniques for nonlinear equations with Krylov subspace projection techniques for unsymmetric systems of linear equations. Traditional tensor methods for nonlinear equations are based on a quadratic model of the nonlinear function, a standard linear model augmented by a simple second order term. These methods are shown to be significantly more efficient than standard methods both on nonsingular problems and on problems where the Jacobian matrix at the solution is singular. A major disadvantage of the traditional tensor methods is that the solution of the tensor model requires the factorization of the Jacobian matrix, which may not be suitable for problems where the Jacobian matrix is large and has a 'bad' sparsity structure for an efficient factorization. We overcome this difficulty by forming and solving the tensor model using an extension of a Newton-GMRES scheme. Like traditional tensor methods, we show that the new tensor method has significant computational advantages over the analogous Newton counterpart. Consistent with Krylov subspace based methods, the new tensor method does not depend on the factorization of the Jacobian matrix. As a matter of fact, the Jacobian matrix is never needed explicitly.

Volume in moment tensor space in terms of distance

NASA Astrophysics Data System (ADS)

Tape, Walter; Tape, Carl

2017-07-01

Suppose that we want to assess the extent to which some large collection of moment tensors is concentrated near a fixed moment tensor m. We are naturally led to consider the distribution of the distances of the moment tensors from m. This distribution, however, can only be judged in conjunction with the distribution of distances from m for randomly chosen moment tensors. In cumulative form, the latter distribution is the same as the fractional volume \\hat{V}(ω ) of the set of all moment tensors that are within distance ω of m. This definition of \\hat{V}(ω ) assumes that a reasonable universe {M} of moment tensors has been specified at the outset and that it includes the original collection as a subset. Our main goal in this article is to derive a formula for \\hat{V}(ω ) when {M} is the set [Λ]_{U} of all moment tensors having a specified eigenvalue triple Λ. We find that \\hat{V}(ω ) depends strongly on Λ, and we illustrate the dependence by plotting the derivative curves \\hat{V}^' }(ω ) for various seismologically relevant Λs. The exotic and unguessable shapes of these curves underscores the futility of interpreting the distribution of distances for the original moment tensors without knowing \\hat{V}(ω ) or \\hat{V}^' }(ω ). The derivation of the formula for \\hat{V}(ω ) relies on a certain ϕ σz coordinate system for [Λ]_{U}, which we treat in detail. Our underlying motivation for the paper is the estimation of uncertainties in moment tensor inversion.

3-D minimum-structure inversion of magnetotelluric data using the finite-element method and tetrahedral grids

NASA Astrophysics Data System (ADS)

Jahandari, H.; Farquharson, C. G.

2017-11-01

Unstructured grids enable representing arbitrary structures more accurately and with fewer cells compared to regular structured grids. These grids also allow more efficient refinements compared to rectilinear meshes. In this study, tetrahedral grids are used for the inversion of magnetotelluric (MT) data, which allows for the direct inclusion of topography in the model, for constraining an inversion using a wireframe-based geological model and for local refinement at the observation stations. A minimum-structure method with an iterative model-space Gauss-Newton algorithm for optimization is used. An iterative solver is employed for solving the normal system of equations at each Gauss-Newton step and the sensitivity matrix-vector products that are required by this solver are calculated using pseudo-forward problems. This method alleviates the need to explicitly form the Hessian or Jacobian matrices which significantly reduces the required computation memory. Forward problems are formulated using an edge-based finite-element approach and a sparse direct solver is used for the solutions. This solver allows saving and re-using the factorization of matrices for similar pseudo-forward problems within a Gauss-Newton iteration which greatly minimizes the computation time. Two examples are presented to show the capability of the algorithm: the first example uses a benchmark model while the second example represents a realistic geological setting with topography and a sulphide deposit. The data that are inverted are the full-tensor impedance and the magnetic transfer function vector. The inversions sufficiently recovered the models and reproduced the data, which shows the effectiveness of unstructured grids for complex and realistic MT inversion scenarios. The first example is also used to demonstrate the computational efficiency of the presented model-space method by comparison with its data-space counterpart.

Moment-tensor inversion for offshore earthquakes east of Taiwan and their implications to regional collision

NASA Astrophysics Data System (ADS)

Kao, Honn; Jian, Pei-Ru; Ma, Kuo-Fong; Huang, Bor-Shouh; Liu, Chun-Chi

Reliable determination of source parameters for offshore earthquakes east of Taiwan with mb<5.5 was a difficult task because of the poor azimuthal coverage by local network and the lack of signals at teleseismic distances. We take advantage of the recently established “Broadband Array in Taiwan for Seismology” (BATS) to invert seismic moment tensors for 7 such events occurred in 1996. To cope with different patterns of background noise and unknown structural details, we utilize variable frequency bands in the inversion and adapt a two-step procedure to select best velocity models for individual epicenter-station paths. Our results are consistent with the overall patterns of regional collision and indicate that the resulting compressive stress has caused significant intraplate deformation within the Philippine Sea plate. Simulation of the region's geological evolution and orogenic processes should take this factor into account and allow the Philippine Sea plate to deform internally.

Tensor non-Gaussianity from axion-gauge-fields dynamics: parameter search

NASA Astrophysics Data System (ADS)

Agrawal, Aniket; Fujita, Tomohiro; Komatsu, Eiichiro

2018-06-01

We calculate the bispectrum of scale-invariant tensor modes sourced by spectator SU(2) gauge fields during inflation in a model containing a scalar inflaton, a pseudoscalar axion and SU(2) gauge fields. A large bispectrum is generated in this model at tree-level as the gauge fields contain a tensor degree of freedom, and its production is dominated by self-coupling of the gauge fields. This is a unique feature of non-Abelian gauge theory. The shape of the tensor bispectrum is approximately an equilateral shape for 3lesssim mQlesssim 4, where mQ is an effective dimensionless mass of the SU(2) field normalised by the Hubble expansion rate during inflation. The amplitude of non-Gaussianity of the tensor modes, characterised by the ratio Bh/P2h, is inversely proportional to the energy density fraction of the gauge field. This ratio can be much greater than unity, whereas the ratio from the vacuum fluctuation of the metric is of order unity. The bispectrum is effective at constraining large mQ regions of the parameter space, whereas the power spectrum constrains small mQ regions.

An efficient and general approach for implementing thermodynamic phase equilibria information in geophysical and geodynamic studies

NASA Astrophysics Data System (ADS)

Afonso, Juan Carlos; Zlotnik, Sergio; Díez, Pedro

2015-10-01

We present a flexible, general, and efficient approach for implementing thermodynamic phase equilibria information (in the form of sets of physical parameters) into geophysical and geodynamic studies. The approach is based on Tensor Rank Decomposition methods, which transform the original multidimensional discrete information into a separated representation that contains significantly fewer terms, thus drastically reducing the amount of information to be stored in memory during a numerical simulation or geophysical inversion. Accordingly, the amount and resolution of the thermodynamic information that can be used in a simulation or inversion increases substantially. In addition, the method is independent of the actual software used to obtain the primary thermodynamic information, and therefore, it can be used in conjunction with any thermodynamic modeling program and/or database. Also, the errors associated with the decomposition procedure are readily controlled by the user, depending on her/his actual needs (e.g., preliminary runs versus full resolution runs). We illustrate the benefits, generality, and applicability of our approach with several examples of practical interest for both geodynamic modeling and geophysical inversion/modeling. Our results demonstrate that the proposed method is a competitive and attractive candidate for implementing thermodynamic constraints into a broad range of geophysical and geodynamic studies. MATLAB implementations of the method and examples are provided as supporting information and can be downloaded from the journal's website.

MT2D Inversion to Image the Gorda Plate Subduction Zone

NASA Astrophysics Data System (ADS)

Lubis, Y. K.; Niasari, S. W.; Hartantyo, E.

2018-04-01

The magnetotelluric method is applicable for studying complicated geological structures because the subsurface electrical properties are strongly influenced by the electric and magnetic fields. This research located in the Gorda subduction zone beneath the North American continental plate. Magnetotelluric 2D inversion was used to image the variation of subsurface resistivity although the phase tensor analysis shows that the majority of dimensionality data is 3D. 19 MT sites were acquired from EarthScope/USArray Project. Wepresent the image of MT 2D inversion to exhibit conductivity distribution from the middle crust to uppermost asthenosphere at a depth of 120 kilometers. Based on the inversion, the overall data misfit value is 3.89. The Gorda plate subduction appears as a high resistive zone beneath the California. Local conductive features are found in the middle crust downward Klamath Mountain, Bonneville Lake, and below the eastern of Utah. Furthermore, mid-crustal is characterized by moderately resistive. Below the extensional Basin and Range province was related to highly resistive. The middle crust to the uppermost asthenosphere becomes moderately resistive. We conclude that the electrical parameters and the dimensionality of datain the shallow depth(about 22.319 km) beneath the North American platein accordance with surface geological features.

Kubo formulas for the shear and bulk viscosity relaxation times and the scalar field theory shear τπ calculation

NASA Astrophysics Data System (ADS)

Czajka, Alina; Jeon, Sangyong

2017-06-01

In this paper we provide a quantum field theoretical study on the shear and bulk relaxation times. First, we find Kubo formulas for the shear and the bulk relaxation times, respectively. They are found by examining response functions of the stress-energy tensor. We use general properties of correlation functions and the gravitational Ward identity to parametrize analytical structures of the Green functions describing both sound and diffusion mode. We find that the hydrodynamic limits of the real parts of the respective energy-momentum tensor correlation functions provide us with the method of computing both the shear and bulk viscosity relaxation times. Next, we calculate the shear viscosity relaxation time using the diagrammatic approach in the Keldysh basis for the massless λ ϕ4 theory. We derive a respective integral equation which enables us to compute η τπ and then we extract the shear relaxation time. The relaxation time is shown to be inversely related to the thermal width as it should be.

Virtual Seismometers for Induced Seismicity Monitoring and Full Moment Tensor Inversion

NASA Astrophysics Data System (ADS)

Morency, C.; Matzel, E.

2016-12-01

Induced seismicity is associated with subsurface fluid injection, and puts at risk efforts to develop geologic carbon sequestration and enhanced geothermal systems. We are developing methods to monitor the microseismically active zone so that we can ultimately identify faults at risk of slipping. The virtual seismometer method (VSM) is an interferometric technique that is very sensitive to the source parameters (location, mechanism and magnitude) and to the Earth structure in the source region. VSM works by virtually placing seismometers inside a micro events cloud, where we can focus on properties directly between induced micro events, and effectively replacing each earthquake with a virtual seismometer recording all the others. Here, we show that the cross-correlated signals from seismic wavefields triggered by two events and recorded at the surface are a combination of the strain field between these two sources times a moment tensor. Based on this relationship, we demonstrate how we can use these measured cross-correlated signals to invert for full moment tensor. The advantage of VSM is to allow to considerably reduce the modeled numerical domain to the region directly around the micro events cloud, which lowers computational cost, permits to reach higher frequency resolution, and suppresses the impact of the Earth structural model uncertainties outside the micro events cloud. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

Molecular orbital analysis of the inverse halogen dependence of nuclear magnetic shielding in LaX₃, X = F, Cl, Br, I.

PubMed

Moncho, Salvador; Autschbach, Jochen

2010-12-01

The NMR nuclear shielding tensors for the series LaX(3), with X = F, Cl, Br and I, have been computed using two-component relativistic density functional theory based on the zeroth-order regular approximation (ZORA). A detailed analysis of the inverse halogen dependence (IHD) of the La shielding was performed via decomposition of the shielding tensor elements into contributions from localized and delocalized molecular orbitals. Both spin-orbit and paramagnetic shielding terms are important, with the paramagnetic terms being dominant. Major contributions to the IHD can be attributed to the La-X bonding orbitals, as well as to trends associated with the La core and halogen lone pair orbitals, the latter being related to X-La π donation. An 'orbital rotation' model for the in-plane π acceptor f orbital of La helps to rationalize the significant magnitude of deshielding associated with the in-plane π donation. The IHD goes along with a large increase in the shielding tensor anisotropy as X becomes heavier, which can be associated with trends for the covalency of the La-X bonds, with a particularly effective transfer of spin-orbit coupling induced spin density from iodine to La in LaI(3). Copyright © 2010 John Wiley & Sons, Ltd.

Moment tensor inversion of tremor events at Arenal Volcano (Costa Rica)

NASA Astrophysics Data System (ADS)

Davi, Rosalia; O'Brien, Gareth; Lokmer, Ivan; Bean, Christopher; Lesage, Philippe; de Barros, Louis

2010-05-01

Arenal is a small, andesitic stratovolcano located in north-western Costa Rica, 97 km from the capital San Josè. Arenal's explosive activity is preceded, and accompanied, by different types of seismic events such as long period events, explosions, tremor and sporadic tectonic swarms. Tremor is the most common type of event recorded at Arenal with durations of up to several hours. Both spasmodic (1-6 Hz) and harmonic (0.9-2 Hz) tremor are observed with no clear difference in the genesis of each; the former can progressively evolve into the latter and vice-versa. However, the origin of the tremor is, at present, not fully understood. In order to retrieve the source mechanism generating these types of events, a moment tensor inversion is performed. A dataset recorded on the volcano, during a seismic experiment carried out in 2005, is used for the inversion. This dataset consists of ten days of data, from which two main groups of tremor at different frequencies (group one at 0.8-1.5 Hz and group two at 1.8-2.5 Hz) have been selected. A major difficulty in any inversion of tremor is that a clear onset can rarely be determined and hence retrieving the direct arrivals from the source is impossible. Usually, these arrivals are heavily contaminated by scattered waves. On Arenal the initial part of the tremor bands can be isolated, therefore offering a good opportunity to invert tremor for the source mechanism. The Green's functions used in the inversion were calculated using 3D numerical simulations including the real topography of the volcano and the best estimation of the velocity model available for Arenal. This velocity model was retrieved from seismic refraction experiments and sounding using the SPAC method. For each day, different tremor starting bands have been selected and divided into the groups mentioned above. For each band a source location is determined by performing a grid search through a volume of 4735 possible source points located under the crater summit. From the evaluation of the misfit values, a common source location is determined. The source appears to be located in shallow position, (less than 200 meters deep) under the crater summit. The source mechanisms for each tremor bands are retrieved for each day using the inversion procedure.

Observational constraints on loop quantum cosmology.

PubMed

Bojowald, Martin; Calcagni, Gianluca; Tsujikawa, Shinji

2011-11-18

In the inflationary scenario of loop quantum cosmology in the presence of inverse-volume corrections, we give analytic formulas for the power spectra of scalar and tensor perturbations convenient to compare with observations. Since inverse-volume corrections can provide strong contributions to the running spectral indices, inclusion of terms higher than the second-order runnings in the power spectra is crucially important. Using the recent data of cosmic microwave background and other cosmological experiments, we place bounds on the quantum corrections.

Sparse alignment for robust tensor learning.

PubMed

Lai, Zhihui; Wong, Wai Keung; Xu, Yong; Zhao, Cairong; Sun, Mingming

2014-10-01

Multilinear/tensor extensions of manifold learning based algorithms have been widely used in computer vision and pattern recognition. This paper first provides a systematic analysis of the multilinear extensions for the most popular methods by using alignment techniques, thereby obtaining a general tensor alignment framework. From this framework, it is easy to show that the manifold learning based tensor learning methods are intrinsically different from the alignment techniques. Based on the alignment framework, a robust tensor learning method called sparse tensor alignment (STA) is then proposed for unsupervised tensor feature extraction. Different from the existing tensor learning methods, L1- and L2-norms are introduced to enhance the robustness in the alignment step of the STA. The advantage of the proposed technique is that the difficulty in selecting the size of the local neighborhood can be avoided in the manifold learning based tensor feature extraction algorithms. Although STA is an unsupervised learning method, the sparsity encodes the discriminative information in the alignment step and provides the robustness of STA. Extensive experiments on the well-known image databases as well as action and hand gesture databases by encoding object images as tensors demonstrate that the proposed STA algorithm gives the most competitive performance when compared with the tensor-based unsupervised learning methods.

Relationship between suicidality and impulsivity in bipolar I disorder: a diffusion tensor imaging study

PubMed Central

Mahon, Katie; Burdick, Katherine E; Wu, Jinghui; Ardekani, Babak A; Szeszko, Philip R

2012-01-01

Background Impulsivity is characteristic of individuals with bipolar disorder and may be a contributing factor to the high rate of suicide in patients with this disorder. Although white matter abnormalities have been implicated in the pathophysiology of bipolar disorder, their relationship to impulsivity and suicidality in this disorder has not been well-investigated. Methods Diffusion tensor imaging scans were acquired in 14 bipolar disorder patients with a prior suicide attempt, 15 bipolar disorder patients with no prior suicide attempt, and 15 healthy volunteers. Bipolar disorder patients received clinical assessments including measures of impulsivity, depression, mania, and anxiety. Images were processed using the Tract-Based Spatial Statistics method in the FSL software package. Results Bipolar disorder patients with a prior suicide attempt had lower fractional anisotropy (FA) within the left orbital frontal white matter (p < 0.05, corrected) and higher overall impulsivity compared to patients without a previous suicide attempt. Among patients with a prior suicide attempt, FA in the orbital frontal white matter region correlated inversely with motor impulsivity. Conclusions Abnormal orbital frontal white matter may play a role in impulsive and suicidal behavior among patients with bipolar disorder. PMID:22329475

Moment Inversion of the DPRK Nuclear Tests Using Finite-Difference Three-dimensional Strain Green's Tensors

NASA Astrophysics Data System (ADS)

Bao, X.; Shen, Y.; Wang, N.

2017-12-01

Accurate estimation of the source moment is important for discriminating underground explosions from earthquakes and other seismic sources. In this study, we invert for the full moment tensors of the recent seismic events (since 2016) at the Democratic People's Republic of Korea (PRRK) Punggye-ri test site. We use waveform data from broadband seismic stations located in China, Korea, and Japan in the inversion. Using a non-staggered-grid, finite-difference algorithm, we calculate the strain Green's tensors (SGT) based on one-dimensional (1D) and three-dimensional (3D) Earth models. Taking advantage of the source-receiver reciprocity, a SGT database pre-calculated and stored for the Punggye-ri test site is used in inversion for the source mechanism of each event. With the source locations estimated from cross-correlation using regional Pn and Pn-coda waveforms, we obtain the optimal source mechanism that best fits synthetics to the observed waveforms of both body and surface waves. The moment solutions of the first three events (2016-01-06, 2016-09-09, and 2017-09-03) show dominant isotropic components, as expected from explosions, though there are also notable non-isotropic components. The last event ( 8 minutes after the mb6.3 explosion in 2017) contained mainly implosive component, suggesting a collapse following the explosion. The solutions from the 3D model can better fit observed waveforms than the corresponding solutions from the 1D model. The uncertainty in the resulting moment solution is influenced by heterogeneities not resolved by the Earth model according to the waveform misfit. Using the moment solutions, we predict the peak ground acceleration at the Punggye-ri test site and compare the prediction with corresponding InSAR and other satellite images.

Design and Implementation of a Numerical Technique to Inform Anisotropic Hyperelastic Finite Element Models using Diffusion-Weighted Imaging

DTIC Science & Technology

2011-10-01

the deviatoric part of a tensor in the reference configuration and p = −∂Ψ ∂J is the hydrostatic pressure. Using the chain 4 rule, equation 13 can be...Kirchoff stress tensor S to the current configuration, and a scaling with the inverse of the volume ratio, transforms equation 16 to the Cauchy stress ...a characteristic of most soft tissues. Then, similar to equation 13, the second Piola-Kirchoff stress is given by: S = 2J−2/3DEV [ ∂Ψisoc ( C ) ∂C

A Bootstrap-Based Probabilistic Optimization Method to Explore and Efficiently Converge in Solution Spaces of Earthquake Source Parameter Estimation Problems: Application to Volcanic and Tectonic Earthquakes

NASA Astrophysics Data System (ADS)

Dahm, T.; Heimann, S.; Isken, M.; Vasyura-Bathke, H.; Kühn, D.; Sudhaus, H.; Kriegerowski, M.; Daout, S.; Steinberg, A.; Cesca, S.

2017-12-01

Seismic source and moment tensor waveform inversion is often ill-posed or non-unique if station coverage is poor or signals are weak. Therefore, the interpretation of moment tensors can become difficult, if not the full model space is explored, including all its trade-offs and uncertainties. This is especially true for non-double couple components of weak or shallow earthquakes, as for instance found in volcanic, geothermal or mining environments.We developed a bootstrap-based probabilistic optimization scheme (Grond), which is based on pre-calculated Greens function full waveform databases (e.g. fomosto tool, doi.org/10.5880/GFZ.2.1.2017.001). Grond is able to efficiently explore the full model space, the trade-offs and the uncertainties of source parameters. The program is highly flexible with respect to the adaption to specific problems, the design of objective functions, and the diversity of empirical datasets.It uses an integrated, robust waveform data processing based on a newly developed Python toolbox for seismology (Pyrocko, see Heimann et al., 2017, http://doi.org/10.5880/GFZ.2.1.2017.001), and allows for visual inspection of many aspects of the optimization problem. Grond has been applied to the CMT moment tensor inversion using W-phases, to nuclear explosions in Korea, to meteorite atmospheric explosions, to volcano-tectonic events during caldera collapse and to intra-plate volcanic and tectonic crustal events.Grond can be used to optimize simultaneously seismological waveforms, amplitude spectra and static displacements of geodetic data as InSAR and GPS (e.g. KITE, Isken et al., 2017, http://doi.org/10.5880/GFZ.2.1.2017.002). We present examples of Grond optimizations to demonstrate the advantage of a full exploration of source parameter uncertainties for interpretation.

Focal mechanisms and tidal modulation for tectonic tremors in Taiwan

NASA Astrophysics Data System (ADS)

Ide, S.; Yabe, S.; Tai, H. J.; Chen, K. H.

2015-12-01

Tectonic tremors in Taiwan have been discovered beneath the southern Central Range, but their hosting structure has been unknown. Here we constrain the focal mechanism of underground deformation related to tremors, using moment tensor inversion in the very low frequency band and tidal stress analysis. Three types of seismic data are used for two analysis steps: detection of tremors and the moment tensor inversion. Short-period seismograms from CWBSN are used for tremor detection. Broadband seismograms from BATS and the TAIGER project are used for both steps. About 1000 tremors were detected using an envelope correlation method in the high frequency band (2-8 Hz). Broadband seismograms are stacked relative to the tremor timing, and inverted for a moment tensor in the low frequency band (0.02-0.05 Hz). The best solution was obtained at 32 km depth, as a double-couple consistent with a low-angle thrust fault dipping to the east-southeast, or a high-angle thrust with a south-southwest strike. Almost all tremors occur when tidal shear stress is positive and normal stress is negative (clamping). Since the clamping stress is high for a high-angle thrust fault, the low-angle thrust fault is more likely to be the fault plane. Tremor rate increases non-linearly with increasing shear stress, suggesting a velocity strengthening friction law. The high tidal sensitivity is inconsistent with horizontal slip motion suggested by previous studies, and normal faults that dominates regional shallow earthquakes. Our results favor thrust slip on a low-angle fault dipping to the east-southeast, consistent with the subduction of the Eurasian plate. The tremor region is characterized by a deep thermal anomaly with decrease normal stress. This region has also experienced enough subduction to produce metamorphic fluids. A large amount of fluid and low vertical stress may explain the high tidal sensitivity.

Moment tensor and location of seismic events in the 2017 DPRK test

NASA Astrophysics Data System (ADS)

Wei, S.; Shi, Q.; Chen, Q. F.; Wang, T.

2017-12-01

The main seismic event in the 2017 DPRK test was followed by a secondary event about eight minutes later. We conducted waveform analysis on the regional broadband waveform data to better constrain the moment tensor and location of these two events, to further understand their relations. In the first place, we applied the generalized Cut-And-Paste (gCAP) method to the regional data to invert the full moment tensor solutions of the two events. Our long period (0.02-0.08 Hz for Pnl, 0.02-0.055 Hz for surface waves) inversions show that the main event was composed of large positive ISO component ( 90% of the total moment) and has a moment magnitude of 5.4. In contrast, the second event shows large negative ISO component ( 50% of the total moment) with a moment magnitude of 4.5. Although there are trade-offs between the CLVD and the ISO component for the second event, chiefly caused by the coda waves from the first event, the result is more robust if we force a small CVLD component in the inversion. We also relocated the epicenter of the second event using P-wave first arrival picks, relative to the location of the first event, which has been accurately determined from the high-resolution geodetic data. The calibration from the first event allows us to precisely locate the second event, which shows an almost identical location to the first event. After a polarity correction, their high-frequency ( 0.25 - 0.9 Hz) regional surface waves also display high similarity, supporting the similar location but opposite ISO polarity of the two events. Our results suggest that the second event was likely to be caused by the collapsing after the main event, in agreement with the surface displacement derived from geodetic observation and modeling results.

Network sensitivity solutions for regional moment-tensor inversions

DOE PAGES

Ford, Sean R.; Dreger, Douglas S.; Walter, William R.

2010-09-20

Well-resolved moment-tensor solutions reveal information about the sources of seismic waves. In this paper,we introduce a newly of assessing confidence in the regional full moment-tensor inversion via the introduction of the network sensitivity solution (NSS). The NSS takes into account the unique station distribution, frequency band, and signal-to-noise ratio of a given event scenario. The NSS compares both a hypothetical pure source (for example, an explosion or an earthquake) and the actual data with several thousand sets of synthetic data from a uniform distribution of all possible sources. The comparison with a hypothetical pure source provides the theoretically best-constrained source-typemore » distribution for a given set of stations; and with it, one can determine whether further analysis with the data is warranted. The NSS that employs the actual data gives a direct comparison of all other source types with the best fit source. In this way, one can choose a threshold level of fit in which the solution is comfortably constrained. The method is tested for the well-recorded nuclear test, JUNCTION, at the Nevada Test Site. Sources that fit comparably well to a hypothetical pure explosion recorded with no noise at the JUNCTION data stations have a large volumetric component and are not described well by a double-couple (DC) source. The NSS using the real data from JUNCTION is even more tightly constrained to an explosion because the data contain some energy that precludes fitting with any type of deviator source. We also calculate the NSS for the October 2006 North Korea test and a nearby earthquake, where the station coverage is poor and the event magnitude is small. As a result, the earthquake solution is very well fit by a DC source, and the best-fit solution to the nuclear test (M w 4.1) is dominantly explosion.« less

Demonstration of improved seismic source inversion method of tele-seismic body wave

NASA Astrophysics Data System (ADS)

Yagi, Y.; Okuwaki, R.

2017-12-01

Seismic rupture inversion of tele-seismic body wave has been widely applied to studies of large earthquakes. In general, tele-seismic body wave contains information of overall rupture process of large earthquake, while the tele-seismic body wave is inappropriate for analyzing a detailed rupture process of M6 7 class earthquake. Recently, the quality and quantity of tele-seismic data and the inversion method has been greatly improved. Improved data and method enable us to study a detailed rupture process of M6 7 class earthquake even if we use only tele-seismic body wave. In this study, we demonstrate the ability of the improved data and method through analyses of the 2016 Rieti, Italy earthquake (Mw 6.2) and the 2016 Kumamoto, Japan earthquake (Mw 7.0) that have been well investigated by using the InSAR data set and the field observations. We assumed the rupture occurring on a single fault plane model inferred from the moment tensor solutions and the aftershock distribution. We constructed spatiotemporal discretized slip-rate functions with patches arranged as closely as possible. We performed inversions using several fault models and found that the spatiotemporal location of large slip-rate area was robust. In the 2016 Kumamoto, Japan earthquake, the slip-rate distribution shows that the rupture propagated to southwest during the first 5 s. At 5 s after the origin time, the main rupture started to propagate toward northeast. First episode and second episode correspond to rupture propagation along the Hinagu fault and the Futagawa fault, respectively. In the 2016 Rieti, Italy earthquake, the slip-rate distribution shows that the rupture propagated to up-dip direction during the first 2 s, and then rupture propagated toward northwest. From both analyses, we propose that the spatiotemporal slip-rate distribution estimated by improved inversion method of tele-seismic body wave has enough information to study a detailed rupture process of M6 7 class earthquake.

Adjoint tomography of Europe

NASA Astrophysics Data System (ADS)

Zhu, H.; Bozdag, E.; Peter, D. B.; Tromp, J.

2010-12-01

We use spectral-element and adjoint methods to image crustal and upper mantle heterogeneity in Europe. The study area involves the convergent boundaries of the Eurasian, African and Arabian plates and the divergent boundary between the Eurasian and North American plates, making the tectonic structure of this region complex. Our goal is to iteratively fit observed seismograms and improve crustal and upper mantle images by taking advantage of 3D forward and inverse modeling techniques. We use data from 200 earthquakes with magnitudes between 5 and 6 recorded by 262 stations provided by ORFEUS. Crustal model Crust2.0 combined with mantle model S362ANI comprise the initial 3D model. Before the iterative adjoint inversion, we determine earthquake source parameters in the initial 3D model by using 3D Green functions and their Fréchet derivatives with respect to the source parameters (i.e., centroid moment tensor and location). The updated catalog is used in the subsequent structural inversion. Since we concentrate on upper mantle structures which involve anisotropy, transversely isotropic (frequency-dependent) traveltime sensitivity kernels are used in the iterative inversion. Taking advantage of the adjoint method, we use as many measurements as can obtain based on comparisons between observed and synthetic seismograms. FLEXWIN (Maggi et al., 2009) is used to automatically select measurement windows which are analyzed based on a multitaper technique. The bandpass ranges from 15 second to 150 second. Long-period surface waves and short-period body waves are combined in source relocations and structural inversions. A statistical assessments of traveltime anomalies and logarithmic waveform differences is used to characterize the inverted sources and structure.

Using Directional Diffusion Coefficients for Nonlinear Diffusion Acceleration of the First Order SN Equations in Near-Void Regions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schunert, Sebastian; Hammer, Hans; Lou, Jijie

2016-11-01

The common definition of the diffusion coeffcient as the inverse of three times the transport cross section is not compat- ible with voids. Morel introduced a non-local tensor diffusion coeffcient that remains finite in voids[1]. It can be obtained by solving an auxiliary transport problem without scattering or fission. Larsen and Trahan successfully applied this diffusion coeffcient for enhancing the accuracy of diffusion solutions of very high temperature reactor (VHTR) problems that feature large, optically thin channels in the z-direction [2]. It is demonstrated that a significant reduction of error can be achieved in particular in the optically thin region.more » Along the same line of thought, non-local diffusion tensors are applied modeling the TREAT reactor confirming the findings of Larsen and Trahan [3]. Previous work of the authors have introduced a flexible Nonlinear-Diffusion Acceleration (NDA) method for the first order S N equations discretized with the discontinuous finite element method (DFEM), [4], [5], [6]. This NDA method uses a scalar diffusion coeffcient in the low-order system that is obtained as the flux weighted average of the inverse transport cross section. Hence, it su?ers from very large and potentially unbounded diffusion coeffcients in the low order problem. However, it was noted that the choice of the diffusion coeffcient does not influence consistency of the method at convergence and hence the di?usion coeffcient is essentially a free parameter. The choice of the di?usion coeffcient does, however, affect the convergence behavior of the nonlinear di?usion iterations. Within this work we use Morel’s non-local di?usion coef- ficient in the aforementioned NDA formulation in lieu of the flux weighted inverse of three times the transport cross section. The goal of this paper is to demonstrate that significant en- hancement of the spectral properties of NDA can be achieved in near void regions. For testing the spectral properties of the NDA with non-local diffusion coeffcients, the periodical horizontal interface problem is used [7]. This problem consists of alternating stripes of optically thin and thick materials both of which feature scattering ratios close to unity.« less

Waveform inversion in the frequency domain for the simultaneous determination of earthquake source mechanism and moment function

NASA Astrophysics Data System (ADS)

Nakano, M.; Kumagai, H.; Inoue, H.

2008-06-01

We propose a method of waveform inversion to rapidly and routinely estimate both the moment function and the centroid moment tensor (CMT) of an earthquake. In this method, waveform inversion is carried out in the frequency domain to obtain the moment function more rapidly than when solved in the time domain. We assume a pure double-couple source mechanism in order to stabilize the solution when using data from a small number of seismic stations. The fault and slip orientations are estimated by a grid search with respect to the strike, dip and rake angles. The moment function in the time domain is obtained from the inverse Fourier transform of the frequency components determined by the inversion. Since observed waveforms used for the inversion are limited in a particular frequency band, the estimated moment function is a bandpassed form. We develop a practical approach to estimate the deconvolved form of the moment function, from which we can reconstruct detailed rupture history and the seismic moment. The source location is determined by a spatial grid search using adaptive grid spacings, which are gradually decreased in each step of the search. We apply this method to two events that occurred in Indonesia by using data from a broad-band seismic network in Indonesia (JISNET): one northeast of Sulawesi (Mw = 7.5) on 2007 January 21, and the other south of Java (Mw = 7.5) on 2006 July 17. The source centroid locations and mechanisms we estimated for both events are consistent with those determined by the Global CMT Project and the National Earthquake Information Center of the U.S. Geological Survey. The estimated rupture duration of the Sulawesi event is 16 s, which is comparable to a typical duration for earthquakes of this magnitude, while that of the Java event is anomalously long (176 s), suggesting that this event was a tsunami earthquake. Our application demonstrates that this inversion method has great potential for rapid and routine estimations of both the CMT and the moment function, and may be useful for identification of tsunami earthquakes.

Automatic deformable diffusion tensor registration for fiber population analysis.

PubMed

Irfanoglu, M O; Machiraju, R; Sammet, S; Pierpaoli, C; Knopp, M V

2008-01-01

In this work, we propose a novel method for deformable tensor-to-tensor registration of Diffusion Tensor Images. Our registration method models the distances in between the tensors with Geode-sic-Loxodromes and employs a version of Multi-Dimensional Scaling (MDS) algorithm to unfold the manifold described with this metric. Defining the same shape properties as tensors, the vector images obtained through MDS are fed into a multi-step vector-image registration scheme and the resulting deformation fields are used to reorient the tensor fields. Results on brain DTI indicate that the proposed method is very suitable for deformable fiber-to-fiber correspondence and DTI-atlas construction.

Evaluation of an Eulerian multi-material mixture formulation based on a single inverse deformation gradient tensor field

DOE PAGES

Ghaisas, N. S.; Subramaniam, A.; Lele, S. K.; ...

2017-12-31

We report high energy-density solids undergoing elastic-plastic deformations coupled to compressible fluids are a common occurrence in engineering applications. Examples include problems involving high-velocity impact and penetration, cavitation, and several manufacturing processes, such as cold forming. Numerical simulations of such phenomena require the ability to handle the interaction of shock waves with multi-material interfaces that can undergo large deformations and severe distortions. As opposed to Lagrangian (Benson 1992) and arbitrary Lagrangian-Eulerian (ALE) methods (Donea et al. 2004), fully Eulerian methods use grids that do not change in time. Consequently, Eulerian methods do not suffer from difficulties on account of meshmore » entanglement, and do not require periodic, expensive, remap operations.« less

Evaluation of an Eulerian multi-material mixture formulation based on a single inverse deformation gradient tensor field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghaisas, N. S.; Subramaniam, A.; Lele, S. K.

We report high energy-density solids undergoing elastic-plastic deformations coupled to compressible fluids are a common occurrence in engineering applications. Examples include problems involving high-velocity impact and penetration, cavitation, and several manufacturing processes, such as cold forming. Numerical simulations of such phenomena require the ability to handle the interaction of shock waves with multi-material interfaces that can undergo large deformations and severe distortions. As opposed to Lagrangian (Benson 1992) and arbitrary Lagrangian-Eulerian (ALE) methods (Donea et al. 2004), fully Eulerian methods use grids that do not change in time. Consequently, Eulerian methods do not suffer from difficulties on account of meshmore » entanglement, and do not require periodic, expensive, remap operations.« less

Comparative study of methods for recognition of an unknown person's action from a video sequence

NASA Astrophysics Data System (ADS)

Hori, Takayuki; Ohya, Jun; Kurumisawa, Jun

2009-02-01

This paper proposes a Tensor Decomposition Based method that can recognize an unknown person's action from a video sequence, where the unknown person is not included in the database (tensor) used for the recognition. The tensor consists of persons, actions and time-series image features. For the observed unknown person's action, one of the actions stored in the tensor is assumed. Using the motion signature obtained from the assumption, the unknown person's actions are synthesized. The actions of one of the persons in the tensor are replaced by the synthesized actions. Then, the core tensor for the replaced tensor is computed. This process is repeated for the actions and persons. For each iteration, the difference between the replaced and original core tensors is computed. The assumption that gives the minimal difference is the action recognition result. For the time-series image features to be stored in the tensor and to be extracted from the observed video sequence, the human body silhouette's contour shape based feature is used. To show the validity of our proposed method, our proposed method is experimentally compared with Nearest Neighbor rule and Principal Component analysis based method. Experiments using 33 persons' seven kinds of action show that our proposed method achieves better recognition accuracies for the seven actions than the other methods.

Waveform inversion of very long period impulsive signals associated with magmatic injection beneath Kilauea Volcano, Hawaii

USGS Publications Warehouse

Ohminato, T.; Chouet, B.A.; Dawson, P.; Kedar, S.

1998-01-01

We use data from broadband seismometers deployed around the summit of Kilauea Volcano to quantify the mechanism associated with a transient in the flow of magma feeding the east rift eruption of the volcano. The transient is marked by rapid inflation of the Kilauea summit peaking at 22 ??rad 4.5 hours after the event onset, followed by slow deflation over a period of 3 days. Superimposed on the summit inflation is a series of sawtooth displacement pulses, each characterized by a sudden drop in amplitude lasting 5-10 s followed by an exponential recovery lasting 1-3 min. The sawtooth waveforms display almost identical shapes, suggesting a process involving the repeated activation of a fixed source. The particle motion associated with each sawtooth is almost linear, and its major swing shows compressional motion at all stations. Analyses of semblance and particle motion are consistent with a point source located 1 km beneath the northeast edge of the Halemaumau pit crater. To estimate the source mechanism, we apply a moment tensor inversion to the waveform data, assuming a point source embedded in a homogeneous half-space with compressional and shear wave velocities representative of the average medium properties at shallow depth under Kilauea. Synthetic waveforms are constructed by a superposition of impulse responses for six moment tensor components and three single force components. The origin times of individual impulses are distributed along the time axis at appropriately small, equal intervals, and their amplitudes are determined by least squares. In this inversion, the source time functions of the six tensor and three force components are determined simultaneously. We confirm the accuracy of the inversion method through a series of numerical tests. The results from the inversion show that the waveform data are well explained by a pulsating transport mechanism operating on a subhorizontal crack linking the summit reservoir to the east rift of Kilauea. The crack acts like a buffer in which a batch of fluid (magma and/or gas) accumulates over a period of 1-3 min before being rapidly injected into a larger reservoir (possibly the east rift) over a timescale of 5-10 s. The seismic moment and volume change associated with a typical batch of fluid are approximately 1014 N m and 3000 m3, respectively. Our results also point to the existence of a single force component with amplitude of 109 N, which may be explained as the drag force generated by the flow of viscous magma through a narrow constriction in the flow path. The total volume of magma associated with the 4.5-hour-long activation of the pulsating source is roughly 500,000 m3 in good agreement with the integrated volume flow rate of magma estimated near the eruptive site.

White Matter Integrity, Creativity, and Psychopathology: Disentangling Constructs with Diffusion Tensor Imaging

PubMed Central

Jung, Rex E.; Grazioplene, Rachael; Caprihan, Arvind; Chavez, Robert S.; Haier, Richard J.

2010-01-01

That creativity and psychopathology are somehow linked remains a popular but controversial idea in neuroscience research. Brain regions implicated in both psychosis-proneness and creative cognition include frontal projection zones and association fibers. In normal subjects, we have previously demonstrated that a composite measure of divergent thinking (DT) ability exhibited significant inverse relationships in frontal lobe areas with both cortical thickness and metabolite concentration of N-acetyl-aspartate (NAA). These findings support the idea that creativity may reside upon a continuum with psychopathology. Here we examine whether white matter integrity, assessed by Fractional Anisotropy (FA), is related to two measures of creativity (Divergent Thinking and Openness to Experience). Based on previous findings, we hypothesize inverse correlations within fronto-striatal circuits. Seventy-two healthy, young adult (18–29 years) subjects were scanned on a 3 Tesla scanner with Diffusion Tensor Imaging. DT measures were scored by four raters (α = .81) using the Consensual Assessment Technique, from which a composite creativity index (CCI) was derived. We found that the CCI was significantly inversely related to FA within the left inferior frontal white matter (t = 5.36, p = .01), and Openness was inversely related to FA within the right inferior frontal white matter (t = 4.61, p = .04). These findings demonstrate an apparent overlap in specific white matter architecture underlying the normal variance of divergent thinking, openness, and psychotic-spectrum traits, consistent with the idea of a continuum. PMID:20339554

Killing-Yano tensors in spaces admitting a hypersurface orthogonal Killing vector

NASA Astrophysics Data System (ADS)

Garfinkle, David; Glass, E. N.

2013-03-01

Methods are presented for finding Killing-Yano tensors, conformal Killing-Yano tensors, and conformal Killing vectors in spacetimes with a hypersurface orthogonal Killing vector. These methods are similar to a method developed by the authors for finding Killing tensors. In all cases one decomposes both the tensor and the equation it satisfies into pieces along the Killing vector and pieces orthogonal to the Killing vector. Solving the separate equations that result from this decomposition requires less computing than integrating the original equation. In each case, examples are given to illustrate the method.

Effective material parameter retrieval of anisotropic elastic metamaterials with inherent nonlocality

NASA Astrophysics Data System (ADS)

Lee, Hyung Jin; Lee, Heung Son; Ma, Pyung Sik; Kim, Yoon Young

2016-09-01

In this paper, the scattering (S-) parameter retrieval method is presented specifically for anisotropic elastic metamaterials; so far, no retrieval has been accomplished when elastic metamaterials exhibit fully anisotropic behavior. Complex constitutive property and intrinsic scattering behavior of elastic metamaterials make their characterization far more complicated than that for acoustic and electromagnetic metamaterials. In particular, elastic metamaterials generally exhibit anisotropic scattering behavior due to higher scattering modes associated with shear deformation. They also exhibit nonlocal responses to some degrees, which originate from strong multiple scattering interactions even in the long wavelength limit. Accordingly, the conventional S-parameter retrieval methods cannot be directly used for elastic metamaterials, because they determine only the diagonal components in effective tensor property. Also, the conventional methods simply use the analytic inversion formulae for the material characterization so that inherent nonlocality cannot be taken into account. To establish a retrieval method applicable to anisotropic elastic metamaterials, we propose an alternative S-parameter method to deal with full anisotropy of elastic metamaterials. To retrieve the whole effective anisotropic parameter, we utilize not only normal but also oblique wave incidences. For the retrieval, we first retrieve the ratio of the effective stiffness tensor to effective density and then determine the effective density. The proposed retrieval method is validated by characterizing the effective material parameters of various types of non-resonant anisotropic metamaterials. It is found that the whole effective parameters are retrieved consistently regardless of used retrieval conditions in spite of inherent nonlocality.

Using Perturbation Theory to Reduce Noise in Diffusion Tensor Fields

PubMed Central

Bansal, Ravi; Staib, Lawrence H.; Xu, Dongrong; Laine, Andrew F.; Liu, Jun; Peterson, Bradley S.

2009-01-01

We propose the use of Perturbation theory to reduce noise in Diffusion Tensor (DT) fields. Diffusion Tensor Imaging (DTI) encodes the diffusion of water molecules along different spatial directions in a positive-definite, 3 × 3 symmetric tensor. Eigenvectors and eigenvalues of DTs allow the in vivo visualization and quantitative analysis of white matter fiber bundles across the brain. The validity and reliability of these analyses are limited, however, by the low spatial resolution and low Signal-to-Noise Ratio (SNR) in DTI datasets. Our procedures can be applied to improve the validity and reliability of these quantitative analyses by reducing noise in the tensor fields. We model a tensor field as a three-dimensional Markov Random Field and then compute the likelihood and the prior terms of this model using Perturbation theory. The prior term constrains the tensor field to be smooth, whereas the likelihood term constrains the smoothed tensor field to be similar to the original field. Thus, the proposed method generates a smoothed field that is close in structure to the original tensor field. We evaluate the performance of our method both visually and quantitatively using synthetic and real-world datasets. We quantitatively assess the performance of our method by computing the SNR for eigenvalues and the coherence measures for eigenvectors of DTs across tensor fields. In addition, we quantitatively compare the performance of our procedures with the performance of one method that uses a Riemannian distance to compute the similarity between two tensors, and with another method that reduces noise in tensor fields by anisotropically filtering the diffusion weighted images that are used to estimate diffusion tensors. These experiments demonstrate that our method significantly increases the coherence of the eigenvectors and the SNR of the eigenvalues, while simultaneously preserving the fine structure and boundaries between homogeneous regions, in the smoothed tensor field. PMID:19540791

A Guided Tour of Mathematical Methods for the Physical Sciences

NASA Astrophysics Data System (ADS)

Snieder, Roel; van Wijk, Kasper

2015-05-01

1. Introduction; 2. Dimensional analysis; 3. Power series; 4. Spherical and cylindrical coordinates; 5. Gradient; 6. Divergence of a vector field; 7. Curl of a vector field; 8. Theorem of Gauss; 9. Theorem of Stokes; 10. The Laplacian; 11. Scale analysis; 12. Linear algebra; 13. Dirac delta function; 14. Fourier analysis; 15. Analytic functions; 16. Complex integration; 17. Green's functions: principles; 18. Green's functions: examples; 19. Normal modes; 20. Potential-field theory; 21. Probability and statistics; 22. Inverse problems; 23. Perturbation theory; 24. Asymptotic evaluation of integrals; 25. Conservation laws; 26. Cartesian tensors; 27. Variational calculus; 28. Epilogue on power and knowledge.

Generalized Higher Order Orthogonal Iteration for Tensor Learning and Decomposition.

PubMed

Liu, Yuanyuan; Shang, Fanhua; Fan, Wei; Cheng, James; Cheng, Hong

2016-12-01

Low-rank tensor completion (LRTC) has successfully been applied to a wide range of real-world problems. Despite the broad, successful applications, existing LRTC methods may become very slow or even not applicable for large-scale problems. To address this issue, a novel core tensor trace-norm minimization (CTNM) method is proposed for simultaneous tensor learning and decomposition, and has a much lower computational complexity. In our solution, first, the equivalence relation of trace norm of a low-rank tensor and its core tensor is induced. Second, the trace norm of the core tensor is used to replace that of the whole tensor, which leads to two much smaller scale matrix TNM problems. Finally, an efficient alternating direction augmented Lagrangian method is developed to solve our problems. Our CTNM formulation needs only O((R N +NRI)log(√{I N })) observations to reliably recover an N th-order I×I×…×I tensor of n -rank (r,r,…,r) , compared with O(rI N-1 ) observations required by those tensor TNM methods ( I > R ≥ r ). Extensive experimental results show that CTNM is usually more accurate than them, and is orders of magnitude faster.

Vector and tensor contributions to the curvature perturbation at second order

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carrilho, Pedro; Malik, Karim A., E-mail: p.gregoriocarrilho@qmul.ac.uk, E-mail: k.malik@qmul.ac.uk

2016-02-01

We derive the evolution equation for the second order curvature perturbation using standard techniques of cosmological perturbation theory. We do this for different definitions of the gauge invariant curvature perturbation, arising from different splits of the spatial metric, and compare the expressions. The results are valid at all scales and include all contributions from scalar, vector and tensor perturbations, as well as anisotropic stress, with all our results written purely in terms of gauge invariant quantities. Taking the large-scale approximation, we find that a conserved quantity exists only if, in addition to the non-adiabatic pressure, the transverse traceless part ofmore » the anisotropic stress tensor is also negligible. We also find that the version of the gauge invariant curvature perturbation which is exactly conserved is the one defined with the determinant of the spatial part of the inverse metric.« less

Relativistic analysis of stochastic kinematics

NASA Astrophysics Data System (ADS)

Giona, Massimiliano

2017-10-01

The relativistic analysis of stochastic kinematics is developed in order to determine the transformation of the effective diffusivity tensor in inertial frames. Poisson-Kac stochastic processes are initially considered. For one-dimensional spatial models, the effective diffusion coefficient measured in a frame Σ moving with velocity w with respect to the rest frame of the stochastic process is inversely proportional to the third power of the Lorentz factor γ (w ) =(1-w2/c2) -1 /2 . Subsequently, higher-dimensional processes are analyzed and it is shown that the diffusivity tensor in a moving frame becomes nonisotropic: The diffusivities parallel and orthogonal to the velocity of the moving frame scale differently with respect to γ (w ) . The analysis of discrete space-time diffusion processes permits one to obtain a general transformation theory of the tensor diffusivity, confirmed by several different simulation experiments. Several implications of the theory are also addressed and discussed.

Tensor-based Dictionary Learning for Spectral CT Reconstruction

PubMed Central

Zhang, Yanbo; Wang, Ge

2016-01-01

Spectral computed tomography (CT) produces an energy-discriminative attenuation map of an object, extending a conventional image volume with a spectral dimension. In spectral CT, an image can be sparsely represented in each of multiple energy channels, and are highly correlated among energy channels. According to this characteristics, we propose a tensor-based dictionary learning method for spectral CT reconstruction. In our method, tensor patches are extracted from an image tensor, which is reconstructed using the filtered backprojection (FBP), to form a training dataset. With the Candecomp/Parafac decomposition, a tensor-based dictionary is trained, in which each atom is a rank-one tensor. Then, the trained dictionary is used to sparsely represent image tensor patches during an iterative reconstruction process, and the alternating minimization scheme is adapted for optimization. The effectiveness of our proposed method is validated with both numerically simulated and real preclinical mouse datasets. The results demonstrate that the proposed tensor-based method generally produces superior image quality, and leads to more accurate material decomposition than the currently popular popular methods. PMID:27541628

Relations between positivity, localization and degrees of freedom: The Weinberg-Witten theorem and the van Dam-Veltman-Zakharov discontinuity

NASA Astrophysics Data System (ADS)

Mund, Jens; Rehren, Karl-Henning; Schroer, Bert

2017-10-01

The problem of accounting for the quantum degrees of freedom in passing from massive higher-spin potentials to massless ones, and the inverse problem of "fattening" massless tensor potentials of helicity ±h to their massive s = | h | counterparts, are solved - in a perfectly ghost-free approach - using "string-localized fields". This approach allows to overcome the Weinberg-Witten impediment against the existence of massless | h | ≥ 2 energy-momentum tensors, and to qualitatively and quantitatively resolve the van Dam-Veltman-Zakharov discontinuity concerning, e.g., very light gravitons, in the limit m → 0.

The Application of COMSOL Multiphysics Package on the Modelling of Complex 3-D Lithospheric Electrical Resistivity Structures - A Case Study from the Proterozoic Orogenic belt within the North China Craton

NASA Astrophysics Data System (ADS)

Guo, L.; Yin, Y.; Deng, M.; Guo, L.; Yan, J.

2017-12-01

At present, most magnetotelluric (MT) forward modelling and inversion codes are based on finite difference method. But its structured mesh gridding cannot be well adapted for the conditions with arbitrary topography or complex tectonic structures. By contrast, the finite element method is more accurate in calculating complex and irregular 3-D region and has lower requirement of function smoothness. However, the complexity of mesh gridding and limitation of computer capacity has been affecting its application. COMSOL Multiphysics is a cross-platform finite element analysis, solver and multiphysics full-coupling simulation software. It achieves highly accurate numerical simulations with high computational performance and outstanding multi-field bi-directional coupling analysis capability. In addition, its AC/DC and RF module can be used to easily calculate the electromagnetic responses of complex geological structures. Using the adaptive unstructured grid, the calculation is much faster. In order to improve the discretization technique of computing area, we use the combination of Matlab and COMSOL Multiphysics to establish a general procedure for calculating the MT responses for arbitrary resistivity models. The calculated responses include the surface electric and magnetic field components, impedance components, magnetic transfer functions and phase tensors. Then, the reliability of this procedure is certificated by 1-D, 2-D and 3-D and anisotropic forward modeling tests. Finally, we establish the 3-D lithospheric resistivity model for the Proterozoic Wutai-Hengshan Mts. within the North China Craton by fitting the real MT data collected there. The reliability of the model is also verified by induced vectors and phase tensors. Our model shows more details and better resolution, compared with the previously published 3-D model based on the finite difference method. In conclusion, COMSOL Multiphysics package is suitable for modeling the 3-D lithospheric resistivity structures under complex tectonic deformation backgrounds, which could be a good complement to the existing finite-difference inversion algorithms.

Stress field estimation based on focal mechanisms and back projected imaging in the Eastern Llanos Basin (Colombia)

NASA Astrophysics Data System (ADS)

Gómez-Alba, Sebastián; Fajardo-Zarate, Carlos Eduardo; Vargas, Carlos Alberto

2016-11-01

At least 156 earthquakes (Mw 2.8-4.4) were detected in Puerto Gaitán, Colombia (Eastern Llanos Basin) between April 2013 and December 2014. Out of context, this figure is not surprising. However, from its inception in 1993, the Colombian National Seismological Network (CNSN) found no evidence of significant seismic events in this region. In this study, we used CNSN data to model the rupture front and orientation of the highest-energy events. For these earthquakes, we relied on a joint inversion method to estimate focal mechanisms and, in turn, determine the area's fault trends and stress tensor. While the stress tensor defines maximum stress with normal tendency, focal mechanisms generally represent normal faults with NW orientation, an orientation which lines up with the tracking rupture achieved via Back Projection Imaging for the study area. We ought to bear in mind that this anomalous earthquake activity has taken place within oil fields. In short, the present paper argues that, based on the spatiotemporal distribution of seismic events, hydrocarbon operations may induce the study area's seismicity.

Progression of White Matter Hyperintensities Preceded by Heterogeneous Decline of Microstructural Integrity.

PubMed

van Leijsen, Esther M C; Bergkamp, Mayra I; van Uden, Ingeborg W M; Ghafoorian, Mohsen; van der Holst, Helena M; Norris, David G; Platel, Bram; Tuladhar, Anil M; de Leeuw, Frank-Erik

2018-05-03

White matter hyperintensities (WMH) are frequently seen on neuroimaging of elderly and are associated with cognitive decline and the development of dementia. Yet, the temporal dynamics of conversion of normal-appearing white matter (NAWM) into WMH remains unknown. We examined whether and when progression of WMH was preceded by changes in fluid-attenuated inversion recovery and diffusion tensor imaging values, thereby taking into account differences between participants with mild versus severe baseline WMH. From 266 participants of the RUN DMC study (Radboud University Nijmegen Diffusion Tensor and Magnetic Resonance Imaging Cohort), we semiautomatically segmented WMH at 3 time points for 9 years. Images were registered to standard space through a subject template. We analyzed differences in baseline fluid-attenuated inversion recovery, fractional anisotropy, and mean diffusivity (MD) values and changes in MD values over time between 4 regions: (1) remaining NAWM, (2) NAWM converting into WMH in the second follow-up period, (3) NAWM converting into WMH in the first follow-up period, and (4) WMH. NAWM converting into WMH in the first or second time interval showed higher fluid-attenuated inversion recovery and MD values than remaining NAWM. MD values in NAWM converting into WMH in the first time interval were similar to MD values in WMH. When stratified by baseline WMH severity, participants with severe WMH had higher fluid-attenuated inversion recovery and MD and lower fractional anisotropy values than participants with mild WMH, in all areas including the NAWM. MD values in WMH and in NAWM that converted into WMH continuously increased over time. Impaired microstructural integrity preceded conversion into WMH and continuously declined over time, suggesting a continuous disease process of white matter integrity loss that can be detected using diffusion tensor imaging even years before WMH become visible on conventional neuroimaging. Differences in microstructural integrity between participants with mild versus severe WMH suggest heterogeneity of both NAWM and WMH, which might explain the clinical variability observed in patients with similar small vessel disease severity. © 2018 American Heart Association, Inc.

Diffusion tensor eigenvector directional color imaging patterns in the evaluation of cerebral white matter tracts altered by tumor.

PubMed

Field, Aaron S; Alexander, Andrew L; Wu, Yu-Chien; Hasan, Khader M; Witwer, Brian; Badie, Behnam

2004-10-01

To categorize the varied appearances of tumor-altered white matter (WM) tracts on diffusion tensor eigenvector directional color maps. Diffusion tensor imaging (DTI) was obtained preoperatively in 13 patients with brain tumors ranging from benign to high-grade malignant, including primary and metastatic lesions, and maps of apparent diffusion coefficient (ADC), fractional anisotropy (FA), and major eigenvector direction were generated. Regions of interest (ROIs) were drawn within identifiable WM tracts affected by tumor, avoiding grossly cystic and necrotic regions, known fiber crossings, and gray matter. Patterns of WM tract alteration were categorized on the basis of qualitative analysis of directional color maps and correlation analysis of ADC and FA. Four basic patterns of WM alteration were identified: 1) normal or nearly normal FA and ADC, with abnormal tract location or tensor directions attributable to bulk mass displacement, 2) moderately decreased FA and increased ADC with normal tract locations and tensor directions, 3) moderately decreased FA and increased ADC with abnormal tensor directions, and 4) near isotropy. FA and ADC were inversely correlated for Patterns 1-3 but did not discriminate edema from infiltrating tumor. However, in the absence of mass displacement, infiltrating tumor was found to produce tensor directional changes that were not observed with vasogenic edema, suggesting the possibility of discrimination on the basis of directional statistics. Tumor alteration of WM tracts tends to produce one of four patterns on FA and directional color maps. Clinical application of these patterns must await further study. Copyright 2004 Wiley-Liss, Inc.

Hydraulic Fracturing Induced Seismicity at Preese Hall, UK: Moment Tensors, Uncertainties and Implications for Microseismic Monitoring Strategies

NASA Astrophysics Data System (ADS)

O'toole, T. B.; Woodhouse, J. H.; Verdon, J.; Kendall, J.

2012-12-01

Hydraulic fracturing operations carried out in April and May 2011 by Cuadrilla Resources Ltd. during the exploration of a shale gas reservoir at Preese Hall, near Blackpool, UK, induced a series of microseismic events. The largest of these, with magnitude ML = 2.3, was felt at the surface and recorded by the British Geological Survey regional seismic network. Subsequently, two local seismic stations were installed, which continued to detect seismicity with ML ≤ 1.5 until the hydraulic fracture treatment was suspended due to the anomalously large magnitudes of the induced earthquakes. Here, we present the results of moment tensor inversions of seismic waveforms recorded by these two near-field stations. We determine the best point source description of an event by minimising the least-squares difference between observed and synthetic waveforms. In contrast to source mechanisms obtained from body wave polarity and amplitude picks, which require a good sampling of the focal sphere and typically assume a pure double-couple mechanism, using the whole waveform allows us to place good constraints on the moment tensor even when only a few seismograms are available, and also enables the investigation of possible non-double-couple components and volume changes associated with a source. We discuss our results in the context of the studies commissioned by Cuadrilla after the suspension of hydraulic fracturing operations at Preese Hall. Using synthetic waveform data, we investigate how different monitoring geometries can be used to reduce uncertainties in source parameters of induced microseisms. While our focus is on the monitoring of hydraulic fracturing operations, the methods developed here are general and could equally be applied to determine moment tensors from surface and borehole observations of seismicity induced by other activities.

Efficient Tensor Completion for Color Image and Video Recovery: Low-Rank Tensor Train.

PubMed

Bengua, Johann A; Phien, Ho N; Tuan, Hoang Duong; Do, Minh N

2017-05-01

This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks to its definition from a well-balanced matricization scheme. Accordingly, new optimization formulations for tensor completion are proposed as well as two new algorithms for their solution. The first one called simple low-rank tensor completion via TT (SiLRTC-TT) is intimately related to minimizing a nuclear norm based on TT rank. The second one is from a multilinear matrix factorization model to approximate the TT rank of a tensor, and is called tensor completion by parallel matrix factorization via TT (TMac-TT). A tensor augmentation scheme of transforming a low-order tensor to higher orders is also proposed to enhance the effectiveness of SiLRTC-TT and TMac-TT. Simulation results for color image and video recovery show the clear advantage of our method over all other methods.

Real-time object recognition in multidimensional images based on joined extended structural tensor and higher-order tensor decomposition methods

NASA Astrophysics Data System (ADS)

Cyganek, Boguslaw; Smolka, Bogdan

2015-02-01

In this paper a system for real-time recognition of objects in multidimensional video signals is proposed. Object recognition is done by pattern projection into the tensor subspaces obtained from the factorization of the signal tensors representing the input signal. However, instead of taking only the intensity signal the novelty of this paper is first to build the Extended Structural Tensor representation from the intensity signal that conveys information on signal intensities, as well as on higher-order statistics of the input signals. This way the higher-order input pattern tensors are built from the training samples. Then, the tensor subspaces are built based on the Higher-Order Singular Value Decomposition of the prototype pattern tensors. Finally, recognition relies on measurements of the distance of a test pattern projected into the tensor subspaces obtained from the training tensors. Due to high-dimensionality of the input data, tensor based methods require high memory and computational resources. However, recent achievements in the technology of the multi-core microprocessors and graphic cards allows real-time operation of the multidimensional methods as is shown and analyzed in this paper based on real examples of object detection in digital images.

Frequency domain and full waveform time domain inversion of ground based magnetometer, electrometer and incoherent scattering radar arrays to image strongly heterogenous 3-D Earth structure, ionospheric structure, and to predict the intensity of GICs in the power grid

NASA Astrophysics Data System (ADS)

Schultz, A.; Imamura, N.; Bonner, L. R., IV; Cosgrove, R. B.

2016-12-01

Ground-based magnetometer and electrometer arrays provide the means to probe the structure of the Earth's interior, the interactions of space weather with the ionosphere, and to anticipate the intensity of geomagnetically induced currents (GICs) in power grids. We present a local-to-continental scale view of a heterogeneous 3-D crust and mantle as determined from magnetotelluric (MT) observations across arrays of ground-based electric and magnetic field sensors. MT impedance tensors describe the relationship between electric and magnetic fields at a given site, thus implicitly they contain all known information on the 3-D electrical resistivity structure beneath and surrounding that site. By using multivariate transfer functions to project real-time magnetic observatory network data to areas surrounding electric power grids, and by projecting those magnetic fields through MT impedance tensors, the projected magnetic field can be transformed into predictions of electric fields along the path of the transmission lines, an essential element of predicting the intensity of GICs in the grid. Finally, we explore GICs, i.e. Earth-ionosphere coupling directly in the time-domain. We consider the fully coupled EM system, where we allow for a non-stationary ionospheric source field of arbitrary complexity above a 3-D Earth. We solve the simultaneous inverse problem for 3-D Earth conductivity and source field structure directly in the time domain. In the present work, we apply this method to magnetotelluric data obtained from a synchronously operating array of 25 MT stations that collected continuous MT waveform data in the interior of Alaska during the autumn and winter of 2015 under the footprint of the Poker Flat (Alaska) Incoherent Scattering Radar (PFISR). PFISR data yield functionals of the ionospheric electric field and ionospheric conductivity that constrain the MT source field. We show that in this region conventional robust MT processing methods struggle to produce reliable MT response functions at periods much greater than about 2,000 s, a consequence, we believe, of the complexity of the ionospheric source fields in this high latitude setting. This provides impetus for direct waveform inversion methods that dispense with typical parametric assumptions made about the MT source fields.

A Genetic Algorithm Method for Direct estimation of paleostress states from heterogeneous fault-slip observations

NASA Astrophysics Data System (ADS)

Srivastava, D. C.

2016-12-01

A Genetic Algorithm Method for Direct estimation of paleostress states from heterogeneous fault-slip observationsDeepak C. Srivastava, Prithvi Thakur and Pravin K. GuptaDepartment of Earth Sciences, Indian Institute of Technology Roorkee, Roorkee 247667, India. Abstract Paleostress estimation from a group of heterogeneous fault-slip observations entails first the classification of the observations into homogeneous fault sets and then a separate inversion of each homogeneous set. This study combines these two issues into a nonlinear inverse problem and proposes a heuristic search method that inverts the heterogeneous fault-slip observations. The method estimates different paleostress states in a group of heterogeneous fault-slip observations and classifies it into homogeneous sets as a byproduct. It uses the genetic algorithm operators, elitism, selection, encoding, crossover and mutation. These processes translate into a guided search that finds successively fitter solutions and operate iteratively until the termination criteria is met and the globally fittest stress tensors are obtained. We explain the basic steps of the algorithm on a working example and demonstrate validity of the method on several synthetic and a natural group of heterogeneous fault-slip observations. The method is independent of any user-defined bias or any entrapment of solution in a local optimum. It succeeds even in the difficult situations where other classification methods are found to fail.

Identifying the stored energy of a hyperelastic structure by using an attenuated Landweber method

NASA Astrophysics Data System (ADS)

Seydel, Julia; Schuster, Thomas

2017-12-01

We consider the nonlinear inverse problem of identifying the stored energy function of a hyperelastic material from full knowledge of the displacement field as well as from surface sensor measurements. The displacement field is represented as a solution of Cauchy’s equation of motion, which is a nonlinear elastic wave equation. Hyperelasticity means that the first Piola-Kirchhoff stress tensor is given as the gradient of the stored energy function. We assume that a dictionary of suitable functions is available. The aim is to recover the stored energy with respect to this dictionary. The considered inverse problem is of vital interest for the development of structural health monitoring systems which are constructed to detect defects in elastic materials from boundary measurements of the displacement field, since the stored energy encodes the mechanical properties of the underlying structure. In this article we develop a numerical solver using the attenuated Landweber method. We show that the parameter-to-solution map satisfies the local tangential cone condition. This result can be used to prove local convergence of the attenuated Landweber method in the case that the full displacement field is measured. In our numerical experiments we demonstrate how to construct an appropriate dictionary and show that our method is well suited to localize damages in various situations.

Anisotropy and phonon modes from analysis of the dielectric function tensor and the inverse dielectric function tensor of monoclinic yttrium orthosilicate

NASA Astrophysics Data System (ADS)

Mock, A.; Korlacki, R.; Knight, S.; Schubert, M.

2018-04-01

We determine the frequency dependence of the four independent Cartesian tensor elements of the dielectric function for monoclinic symmetry Y2SiO5 using generalized spectroscopic ellipsometry from 40-1200 cm-1. Three different crystal cuts, each perpendicular to a principle axis, are investigated. We apply our recently described augmentation of lattice anharmonicity onto the eigendielectric displacement vector summation approach [A. Mock et al., Phys. Rev. B 95, 165202 (2017), 10.1103/PhysRevB.95.165202], and we present and demonstrate the application of an eigendielectric displacement loss vector summation approach with anharmonic broadening. We obtain an excellent match between all measured and model-calculated dielectric function tensor elements and all dielectric loss function tensor elements. We obtain 23 Au and 22 Bu symmetry long-wavelength active transverse and longitudinal optical mode parameters including their eigenvector orientation within the monoclinic lattice. We perform density functional theory calculations and obtain 23 Au symmetry and 22 Bu transverse and longitudinal optical mode parameters and their orientation within the monoclinic lattice. We compare our results from ellipsometry and density functional theory and find excellent agreement. We also determine the static and above reststrahlen spectral range dielectric tensor values and find a recently derived generalization of the Lyddane-Sachs-Teller relation for polar phonons in monoclinic symmetry materials satisfied [M. Schubert, Phys Rev. Lett. 117, 215502 (2016), 10.1103/PhysRevLett.117.215502].

A Tensor-Based Subspace Approach for Bistatic MIMO Radar in Spatial Colored Noise

PubMed Central

Wang, Xianpeng; Wang, Wei; Li, Xin; Wang, Junxiang

2014-01-01

In this paper, a new tensor-based subspace approach is proposed to estimate the direction of departure (DOD) and the direction of arrival (DOA) for bistatic multiple-input multiple-output (MIMO) radar in the presence of spatial colored noise. Firstly, the received signals can be packed into a third-order measurement tensor by exploiting the inherent structure of the matched filter. Then, the measurement tensor can be divided into two sub-tensors, and a cross-covariance tensor is formulated to eliminate the spatial colored noise. Finally, the signal subspace is constructed by utilizing the higher-order singular value decomposition (HOSVD) of the cross-covariance tensor, and the DOD and DOA can be obtained through the estimation of signal parameters via rotational invariance technique (ESPRIT) algorithm, which are paired automatically. Since the multidimensional inherent structure and the cross-covariance tensor technique are used, the proposed method provides better angle estimation performance than Chen's method, the ESPRIT algorithm and the multi-SVD method. Simulation results confirm the effectiveness and the advantage of the proposed method. PMID:24573313

A tensor-based subspace approach for bistatic MIMO radar in spatial colored noise.

PubMed

Wang, Xianpeng; Wang, Wei; Li, Xin; Wang, Junxiang

2014-02-25

In this paper, a new tensor-based subspace approach is proposed to estimate the direction of departure (DOD) and the direction of arrival (DOA) for bistatic multiple-input multiple-output (MIMO) radar in the presence of spatial colored noise. Firstly, the received signals can be packed into a third-order measurement tensor by exploiting the inherent structure of the matched filter. Then, the measurement tensor can be divided into two sub-tensors, and a cross-covariance tensor is formulated to eliminate the spatial colored noise. Finally, the signal subspace is constructed by utilizing the higher-order singular value decomposition (HOSVD) of the cross-covariance tensor, and the DOD and DOA can be obtained through the estimation of signal parameters via rotational invariance technique (ESPRIT) algorithm, which are paired automatically. Since the multidimensional inherent structure and the cross-covariance tensor technique are used, the proposed method provides better angle estimation performance than Chen's method, the ESPRIT algorithm and the multi-SVD method. Simulation results confirm the effectiveness and the advantage of the proposed method.

Tensor-based spatiotemporal saliency detection

NASA Astrophysics Data System (ADS)

Dou, Hao; Li, Bin; Deng, Qianqian; Zhang, LiRui; Pan, Zhihong; Tian, Jinwen

2018-03-01

This paper proposes an effective tensor-based spatiotemporal saliency computation model for saliency detection in videos. First, we construct the tensor representation of video frames. Then, the spatiotemporal saliency can be directly computed by the tensor distance between different tensors, which can preserve the complete temporal and spatial structure information of object in the spatiotemporal domain. Experimental results demonstrate that our method can achieve encouraging performance in comparison with the state-of-the-art methods.

Normal-faulting stress state associated with low differential stress in an overriding plate in northeast Japan prior to the 2011 Mw 9.0 Tohoku earthquake

NASA Astrophysics Data System (ADS)

Otsubo, Makoto; Miyakawa, Ayumu; Imanishi, Kazutoshi

2018-03-01

Spatial and temporal variations in inland crustal stress prior to the 2011 Mw 9.0 Tohoku earthquake are investigated using focal mechanism solutions for shallow seismicity in Iwaki City, Japan. The multiple inverse method of stress tensor inversion detected two normal-faulting stress states that dominate in different regions. The stress field around Iwaki City changed from a NNW-SSE-trending triaxial extensional stress (stress regime A) to a NW-SE-trending axial tension (stress regime B) between 2005 and 2008. These stress changes may be the result of accumulated extensional stress associated with co- and post-seismic deformation due to the M7 class earthquakes. In this study we suggest that the stress state around Iwaki City prior to the 2011 Tohoku earthquake may have been extensional with a low differential stress. High pore pressure is required to cause earthquakes under such small differential stresses.

Fully anisotropic 3-D EM modelling on a Lebedev grid with a multigrid pre-conditioner

NASA Astrophysics Data System (ADS)

Jaysaval, Piyoosh; Shantsev, Daniil V.; de la Kethulle de Ryhove, Sébastien; Bratteland, Tarjei

2016-12-01

We present a numerical algorithm for 3-D electromagnetic (EM) simulations in conducting media with general electric anisotropy. The algorithm is based on the finite-difference discretization of frequency-domain Maxwell's equations on a Lebedev grid, in which all components of the electric field are collocated but half a spatial step staggered with respect to the magnetic field components, which also are collocated. This leads to a system of linear equations that is solved using a stabilized biconjugate gradient method with a multigrid preconditioner. We validate the accuracy of the numerical results for layered and 3-D tilted transverse isotropic (TTI) earth models representing typical scenarios used in the marine controlled-source EM method. It is then demonstrated that not taking into account the full anisotropy of the conductivity tensor can lead to misleading inversion results. For synthetic data corresponding to a 3-D model with a TTI anticlinal structure, a standard vertical transverse isotropic (VTI) inversion is not able to image a resistor, while for a 3-D model with a TTI synclinal structure it produces a false resistive anomaly. However, if the VTI forward solver used in the inversion is replaced by the proposed TTI solver with perfect knowledge of the strike and dip of the dipping structures, the resulting resistivity images become consistent with the true models.

Multi-Grid and Resolution Full-Wave Tomography and Moment Tensor Inversion (Postprint)

DTIC Science & Technology

2012-06-04

Denver: University of Colorado. Chen, P., L. Zhao, and T.H. Jordan (2007). Full 3D tomography for crustal structure of the Los Angeles Region, Bull...M.J.R. Wortel, and W. Spakman (2006). Subduction history of the Tethyan region derived from seismic tomography and tectonic reconstructions, J. Geophys

The excitation of long period seismic waves by a source spanning a structural discontinuity

NASA Astrophysics Data System (ADS)

Woodhouse, J. H.

Simple theoretical results are obtained for the excitation of seismic waves by an indigenous seismic source in the case that the source volume is intersected by a structural discontinuity. In the long wavelength approximation the seismic radiation is identical to that of a point source placed on one side of the discontinuity or of a different point source placed on the other side. The moment tensors of these two equivalent sources are related by a specific linear transformation and may differ appreciably both in magnitude and geometry. Either of these sources could be obtained by linear inversion of seismic data but the physical interpretation is more complicated than in the usual case. A source which involved no volume change would, for example, yield an isotropic component if, during inversion, it were assumed to lie on the wrong side of the discontinuity. The problem of determining the true moment tensor of the source is indeterminate unless further assumptions are made about the stress glut distribution; one way to resolve this indeterminancy is to assume proportionality between the integrated stress glut on each side of the discontinuity.

Growth patterns for shape-shifting elastic bilayers.

PubMed

van Rees, Wim M; Vouga, Etienne; Mahadevan, L

2017-10-31

Inspired by the differential-growth-driven morphogenesis of leaves, flowers, and other tissues, there is increasing interest in artificial analogs of these shape-shifting thin sheets made of active materials that respond to environmental stimuli such as heat, light, and humidity. But how can we determine the growth patterns to achieve a given shape from another shape? We solve this geometric inverse problem of determining the growth factors and directions (the metric tensors) for a given isotropic elastic bilayer to grow into a target shape by posing and solving an elastic energy minimization problem. A mathematical equivalence between bilayers and curved monolayers simplifies the inverse problem considerably by providing algebraic expressions for the growth metric tensors in terms of those of the final shape. This approach also allows us to prove that we can grow any target surface from any reference surface using orthotropically growing bilayers. We demonstrate this by numerically simulating the growth of a flat sheet into a face, a cylindrical sheet into a flower, and a flat sheet into a complex canyon-like structure.

Growth patterns for shape-shifting elastic bilayers

PubMed Central

van Rees, Wim M.; Vouga, Etienne; Mahadevan, L.

2017-01-01

Inspired by the differential-growth-driven morphogenesis of leaves, flowers, and other tissues, there is increasing interest in artificial analogs of these shape-shifting thin sheets made of active materials that respond to environmental stimuli such as heat, light, and humidity. But how can we determine the growth patterns to achieve a given shape from another shape? We solve this geometric inverse problem of determining the growth factors and directions (the metric tensors) for a given isotropic elastic bilayer to grow into a target shape by posing and solving an elastic energy minimization problem. A mathematical equivalence between bilayers and curved monolayers simplifies the inverse problem considerably by providing algebraic expressions for the growth metric tensors in terms of those of the final shape. This approach also allows us to prove that we can grow any target surface from any reference surface using orthotropically growing bilayers. We demonstrate this by numerically simulating the growth of a flat sheet into a face, a cylindrical sheet into a flower, and a flat sheet into a complex canyon-like structure. PMID:29078336

Polarization effects in the reactions p + 3 He → π+ + 4 He, π+ + 4 He → p + 3 He and quantum character of spin correlations in the final (p, 3 He) system

NASA Astrophysics Data System (ADS)

Lyuboshitz, Valery V.; Lyuboshitz, Vladimir L.

2017-12-01

The general consequences of T invariance for the direct and inverse binary reactions a + b → c + d, c + d → a + b with spin-1/2 particles a, b and unpolarized particles c, d are considered. Using the formalism of helicity amplitudes, the polarization effects are studied in the reaction p + 3 He → π+ + 4 He and in the inverse process π+ + 4 He → p + 3 He. It is shown that in the reaction π + + 4 He → p + 3 He the spins of the final proton and 3 He nucleus are strongly correlated. A structural expression through helicity amplitudes, corresponding to arbitrary emission angles, is obtained for the correlation tensor. It is established that in the reaction π + + 4 He → p + 3 He one of the “classical” incoherence inequalities of the Bell type for diagonal components of the correlation tensor is necessarily violated and, thus, the spin correlations of the final particles have the strongly pronounced quantum character.

The source mechanisms of low frequency events in volcanoes - a comparison of synthetic and real seismic data on Soufriere Hills Volcano, Montserrat

NASA Astrophysics Data System (ADS)

Karl, S.; Neuberg, J. W.

2012-04-01

Low frequency seismic signals are one class of volcano seismic earthquakes that have been observed at many volcanoes around the world, and are thought to be associated with resonating fluid-filled conduits or fluid movements. Amongst others, Neuberg et al. (2006) proposed a conceptual model for the trigger of low frequency events at Montserrat involving the brittle failure of magma in the glass transition in response to high shear stresses during the upwards movement of magma in the volcanic edifice. For this study, synthetic seismograms were generated following the proposed concept of Neuberg et al. (2006) by using an extended source modelled as an octagonal arrangement of double couples approximating a circular ringfault. For comparison, synthetic seismograms were generated using single forces only. For both scenarios, synthetic seismograms were generated using a seismic station distribution as encountered on Soufriere Hills Volcano, Montserrat. To gain a better quantitative understanding of the driving forces of low frequency events, inversions for the physical source mechanisms have become increasingly common. Therefore, we perform moment tensor inversions (Dreger, 2003) using the synthetic data as well as a chosen set of seismograms recorded on Soufriere Hills Volcano. The inversions are carried out under the (wrong) assumption to have an underlying point source rather than an extended source as the trigger mechanism of the low frequency seismic events. We will discuss differences between inversion results, and how to interpret the moment tensor components (double couple, isotropic, or CLVD), which were based on a point source, in terms of an extended source.

Point-source inversion techniques

NASA Astrophysics Data System (ADS)

Langston, Charles A.; Barker, Jeffrey S.; Pavlin, Gregory B.

1982-11-01

A variety of approaches for obtaining source parameters from waveform data using moment-tensor or dislocation point source models have been investigated and applied to long-period body and surface waves from several earthquakes. Generalized inversion techniques have been applied to data for long-period teleseismic body waves to obtain the orientation, time function and depth of the 1978 Thessaloniki, Greece, event, of the 1971 San Fernando event, and of several events associated with the 1963 induced seismicity sequence at Kariba, Africa. The generalized inversion technique and a systematic grid testing technique have also been used to place meaningful constraints on mechanisms determined from very sparse data sets; a single station with high-quality three-component waveform data is often sufficient to discriminate faulting type (e.g., strike-slip, etc.). Sparse data sets for several recent California earthquakes, for a small regional event associated with the Koyna, India, reservoir, and for several events at the Kariba reservoir have been investigated in this way. Although linearized inversion techniques using the moment-tensor model are often robust, even for sparse data sets, there are instances where the simplifying assumption of a single point source is inadequate to model the data successfully. Numerical experiments utilizing synthetic data and actual data for the 1971 San Fernando earthquake graphically demonstrate that severe problems may be encountered if source finiteness effects are ignored. These techniques are generally applicable to on-line processing of high-quality digital data, but source complexity and inadequacy of the assumed Green's functions are major problems which are yet to be fully addressed.

Possibilities of inversion of satellite third-order gravitational tensor onto gravity anomalies: a case study for central Europe

NASA Astrophysics Data System (ADS)

Pitoňák, Martin; Šprlák, Michal; Tenzer, Robert

2017-05-01

We investigate a numerical performance of four different schemes applied to a regional recovery of the gravity anomalies from the third-order gravitational tensor components (assumed to be observable in the future) synthetized at the satellite altitude of 200 km above the mean sphere. The first approach is based on applying a regional inversion without modelling the far-zone contribution or long-wavelength support. In the second approach we separate integral formulas into two parts, that is, the effects of the third-order disturbing tensor data within near and far zones. Whereas the far-zone contribution is evaluated by using existing global geopotential model (GGM) with spectral weights given by truncation error coefficients, the near-zone contribution is solved by applying a regional inversion. We then extend this approach for a smoothing procedure, in which we remove the gravitational contributions of the topographic-isostatic and atmospheric masses. Finally, we apply the remove-compute-restore (r-c-r) scheme in order to reduce the far-zone contribution by subtracting the reference (long-wavelength) gravity field, which is computed for maximum degree 80. We apply these four numerical schemes to a regional recovery of the gravity anomalies from individual components of the third-order gravitational tensor as well as from their combinations, while applying two different levels of a white noise. We validated our results with respect to gravity anomalies evaluated at the mean sphere from EGM2008 up to the degree 250. Not surprisingly, better fit in terms of standard deviation (STD) was attained using lower level of noise. The worst results were gained applying classical approach, STD values of our solution from Tzzz are 1.705 mGal (noise value with a standard deviation 0.01 × 10 - 15m - 1s - 2) and 2.005 mGal (noise value with a standard deviation 0.05 × 10 - 15m - 1s - 2), while the superior from r-c-r up to the degree 80, STD fit of gravity anomalies from Tzzz with respect to the same counterpart from EGM2008 is 0.510 mGal (noise value with a standard deviation 0.01 × 10 - 15m - 1s - 2) and 1.190 mGal (noise value with a standard deviation 0.05 × 10 - 15m - 1s - 2).

A Local Fast Marching-Based Diffusion Tensor Image Registration Algorithm by Simultaneously Considering Spatial Deformation and Tensor Orientation

PubMed Central

Xue, Zhong; Li, Hai; Guo, Lei; Wong, Stephen T.C.

2010-01-01

It is a key step to spatially align diffusion tensor images (DTI) to quantitatively compare neural images obtained from different subjects or the same subject at different timepoints. Different from traditional scalar or multi-channel image registration methods, tensor orientation should be considered in DTI registration. Recently, several DTI registration methods have been proposed in the literature, but deformation fields are purely dependent on the tensor features not the whole tensor information. Other methods, such as the piece-wise affine transformation and the diffeomorphic non-linear registration algorithms, use analytical gradients of the registration objective functions by simultaneously considering the reorientation and deformation of tensors during the registration. However, only relatively local tensor information such as voxel-wise tensor-similarity, is utilized. This paper proposes a new DTI image registration algorithm, called local fast marching (FM)-based simultaneous registration. The algorithm not only considers the orientation of tensors during registration but also utilizes the neighborhood tensor information of each voxel to drive the deformation, and such neighborhood tensor information is extracted from a local fast marching algorithm around the voxels of interest. These local fast marching-based tensor features efficiently reflect the diffusion patterns around each voxel within a spherical neighborhood and can capture relatively distinctive features of the anatomical structures. Using simulated and real DTI human brain data the experimental results show that the proposed algorithm is more accurate compared with the FA-based registration and is more efficient than its counterpart, the neighborhood tensor similarity-based registration. PMID:20382233

Source Parameters from Full Moment Tensor Inversions of Potentially Induced Earthquakes in Western Canada

NASA Astrophysics Data System (ADS)

Wang, R.; Gu, Y. J.; Schultz, R.; Kim, A.; Chen, Y.

2015-12-01

During the past four years, the number of earthquakes with magnitudes greater than three has substantially increased in the southern section of Western Canada Sedimentary Basin (WCSB). While some of these events are likely associated with tectonic forces, especially along the foothills of the Canadian Rockies, a significant fraction occurred in previously quiescent regions and has been linked to waste water disposal or hydraulic fracturing. A proper assessment of the origin and source properties of these 'induced earthquakes' requires careful analyses and modeling of regional broadband data, which steadily improved during the past 8 years due to recent establishments of regional broadband seismic networks such as CRANE, RAVEN and TD. Several earthquakes, especially those close to fracking activities (e.g. Fox creek town, Alberta) are analyzed. Our preliminary full moment tensor inversion results show maximum horizontal compressional orientations (P-axis) along the northeast-southwest orientation, which agree with the regional stress directions from borehole breakout data and the P-axis of historical events. The decomposition of those moment tensors shows evidence of strike-slip mechanism with near vertical fault plane solutions, which are comparable to the focal mechanisms of injection induced earthquakes in Oklahoma. Minimal isotropic components have been observed, while a modest percentage of compensated-linear-vector-dipole (CLVD) components, which have been linked to fluid migraition, may be required to match the waveforms. To further evaluate the non-double-couple components, we compare the outcomes of full, deviatoric and pure double couple (DC) inversions using multiple frequency ranges and phases. Improved location and depth information from a novel grid search greatly assists the identification and classification of earthquakes in potential connection with fluid injection or extraction. Overall, a systematic comparison of the source attributes of intermediate-sized earthquakes present a new window into the nature of potentially induced earthquakes in the WCSB.

Tensor-based dynamic reconstruction method for electrical capacitance tomography

NASA Astrophysics Data System (ADS)

Lei, J.; Mu, H. P.; Liu, Q. B.; Li, Z. H.; Liu, S.; Wang, X. Y.

2017-03-01

Electrical capacitance tomography (ECT) is an attractive visualization measurement method, in which the acquisition of high-quality images is beneficial for the understanding of the underlying physical or chemical mechanisms of the dynamic behaviors of the measurement objects. In real-world measurement environments, imaging objects are often in a dynamic process, and the exploitation of the spatial-temporal correlations related to the dynamic nature will contribute to improving the imaging quality. Different from existing imaging methods that are often used in ECT measurements, in this paper a dynamic image sequence is stacked into a third-order tensor that consists of a low rank tensor and a sparse tensor within the framework of the multiple measurement vectors model and the multi-way data analysis method. The low rank tensor models the similar spatial distribution information among frames, which is slowly changing over time, and the sparse tensor captures the perturbations or differences introduced in each frame, which is rapidly changing over time. With the assistance of the Tikhonov regularization theory and the tensor-based multi-way data analysis method, a new cost function, with the considerations of the multi-frames measurement data, the dynamic evolution information of a time-varying imaging object and the characteristics of the low rank tensor and the sparse tensor, is proposed to convert the imaging task in the ECT measurement into a reconstruction problem of a third-order image tensor. An effective algorithm is developed to search for the optimal solution of the proposed cost function, and the images are reconstructed via a batching pattern. The feasibility and effectiveness of the developed reconstruction method are numerically validated.

A contour for the entanglement entropies in harmonic lattices

NASA Astrophysics Data System (ADS)

Coser, Andrea; De Nobili, Cristiano; Tonni, Erik

2017-08-01

We construct a contour function for the entanglement entropies in generic harmonic lattices. In one spatial dimension, numerical analysis are performed by considering harmonic chains with either periodic or Dirichlet boundary conditions. In the massless regime and for some configurations where the subsystem is a single interval, the numerical results for the contour function are compared to the inverse of the local weight function which multiplies the energy-momentum tensor in the corresponding entanglement hamiltonian, found through conformal field theory methods, and a good agreement is observed. A numerical analysis of the contour function for the entanglement entropy is performed also in a massless harmonic chain for a subsystem made by two disjoint intervals.

Tensor Toolbox for MATLAB v. 3.0

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kola, Tamara; Bader, Brett W.; Acar Ataman, Evrim NMN

Tensors (also known as multidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to network analysis. The Tensor Toolbox provides classes for manipulating dense, sparse, and structured tensors using MATLAB's object-oriented features. It also provides algorithms for tensor decomposition and factorization, algorithms for computing tensor eigenvalues, and methods for visualization of results.

Spin and Pseudospin Symmetries of Hellmann Potential with Three Tensor Interactions Using Nikiforov-Uvarov Method

NASA Astrophysics Data System (ADS)

Akpan, N. Ikot; Hassan, Hassanabadi; Tamunoimi, M. Abbey

2015-12-01

The Dirac equation with Hellmann potential is presented in the presence of Coulomb-like tensor (CLT), Yukawa-like tensor (YLT), and Hulthen-type tensor (HLT) interactions by using Nikiforov-Uvarov method. The bound state energy spectra and the radial wave functions are obtained approximately within the framework of spin and pseudospin symmetries limit. We have also reported some numerical results and figures to show the effects of the tensor interactions. Special cases of the potential are also discussed.

Retrospective Correction of Physiological Noise in DTI Using an Extended Tensor Model and Peripheral Measurements

PubMed Central

Mohammadi, Siawoosh; Hutton, Chloe; Nagy, Zoltan; Josephs, Oliver; Weiskopf, Nikolaus

2013-01-01

Diffusion tensor imaging is widely used in research and clinical applications, but this modality is highly sensitive to artefacts. We developed an easy-to-implement extension of the original diffusion tensor model to account for physiological noise in diffusion tensor imaging using measures of peripheral physiology (pulse and respiration), the so-called extended tensor model. Within the framework of the extended tensor model two types of regressors, which respectively modeled small (linear) and strong (nonlinear) variations in the diffusion signal, were derived from peripheral measures. We tested the performance of four extended tensor models with different physiological noise regressors on nongated and gated diffusion tensor imaging data, and compared it to an established data-driven robust fitting method. In the brainstem and cerebellum the extended tensor models reduced the noise in the tensor-fit by up to 23% in accordance with previous studies on physiological noise. The extended tensor model addresses both large-amplitude outliers and small-amplitude signal-changes. The framework of the extended tensor model also facilitates further investigation into physiological noise in diffusion tensor imaging. The proposed extended tensor model can be readily combined with other artefact correction methods such as robust fitting and eddy current correction. PMID:22936599

Seismic moment tensor for anisotropic media: implication for Non-double-couple earthquakes

NASA Astrophysics Data System (ADS)

Cai, X.; Chen, X.; Chen, Y.; Cai, M.

2008-12-01

It is often found that the inversion results of seismic moment tensor from real seismic recorded data show the trace of seismic moment tensor M is not zero, a phenomenon called non-double-couple earthquake sources mechanism. Recently we have derived the analytical expressions of M in transversely isotropic media with the titled axis of symmetry and the results shows even only pure shear-motion of fault can lead to the implosive components determined by several combined anisotropic elastic constants. Many non-double-couple earthquakes from observations often appear in volcanic and geothermal areas (Julian, 1998), where there exist a mount of stress-aligned fluid-saturated parallel vertical micro-cracks identical to transversely isotropic media (Crampin, 2008), this stress-aligned crack will modify the seismic moment tensor. In another word, non-double-couple earthquakes don't mean to have a seismic failure movement perpendicular to the fault plane, while traditional research of seismic moment tensor focus on the case of isotropy, which cannot provide correct interpretation of seismic source mechanism. Reference: Julian, B.R., Miller, A.D. and Foulger, G.R., 1998. Non-double-couple earthquakes,1. Theory, Rev. Geophys., 36, 525¨C549. Crampin,S., Peacock,S., 2008, A review of the current understanding of seismic shear-wave splitting in the Earth's crust and common fallacies in interpretation, wave motion, 45,675-722

Finite Moment Tensors of Southern California Earthquakes

NASA Astrophysics Data System (ADS)

Jordan, T. H.; Chen, P.; Zhao, L.

2003-12-01

We have developed procedures for inverting broadband waveforms for the finite moment tensors (FMTs) of regional earthquakes. The FMT is defined in terms of second-order polynomial moments of the source space-time function and provides the lowest order representation of a finite fault rupture; it removes the fault-plane ambiguity of the centroid moment tensor (CMT) and yields several additional parameters of seismological interest: the characteristic length L{c}, width W{c}, and duration T{c} of the faulting, as well as the directivity vector {v}{d} of the fault slip. To formulate the inverse problem, we follow and extend the methods of McGuire et al. [2001, 2002], who have successfully recovered the second-order moments of large earthquakes using low-frequency teleseismic data. We express the Fourier spectra of a synthetic point-source waveform in its exponential (Rytov) form and represent the observed waveform relative to the synthetic in terms two frequency-dependent differential times, a phase delay δ τ {p}(ω ) and an amplitude-reduction time δ τ {q}(ω ), which we measure using Gee and Jordan's [1992] isolation-filter technique. We numerically calculate the FMT partial derivatives in terms of second-order spatiotemporal gradients, which allows us to use 3D finite-difference seismograms as our isolation filters. We have applied our methodology to a set of small to medium-sized earthquakes in Southern California. The errors in anelastic structure introduced perturbations larger than the signal level caused by finite source effect. We have therefore employed a joint inversion technique that recovers the CMT parameters of the aftershocks, as well as the CMT and FMT parameters of the mainshock, under the assumption that the source finiteness of the aftershocks can be ignored. The joint system of equations relating the δ τ {p} and δ τ {q} data to the source parameters of the mainshock-aftershock cluster is denuisanced for path anomalies in both observables; this projection operation effectively corrects the mainshock data for path-related amplitude anomalies in a way similar to, but more flexible than, empirical Green function (EGF) techniques.

Focal Mechanisms From Moment Tensor Solutions and First Motion Polarities of Shallow to Deep Local Earthquakes in Eastern Nepal and Southern Tibet

NASA Astrophysics Data System (ADS)

de La Torre, T. L.; Sheehan, A. F.; Monsalve, G.; Wu, F.

2004-12-01

We determined focal mechanisms using waveforms and first motion polarities from local earthquakes recorded during the Himalayan Nepal Tibet Seismic Experiment (HIMNT). The HIMNT experiment included the deployment of 28 broad band seismometers in eastern Nepal and southern Tibet from September 2001 to April 2003. Using a regional moment tensor method (Ammon and Randall, 2001) and first motion polarities for displaying double-couple focal mechanisms (Snokes, 2003), we analyzed the fault plane solutions at three distinct zones of seismicity. Characteristic focal mechanisms in seismically concentrated areas may indicate the presence of fault ramps or a decollement in the Himalayan collision zone. Previous studies of focal mechanisms on the Tibetan Plateau predominantly indicate east-west extension and shallow thrusting at the Himalayan collision zone for shallow to intermediate earthquakes (Ni and Barazangi, 1984; Molnar and Lyon-Caen, 1989; Randall et al., 1995) and east-west extension for intermediate to deep earthquakes (Zhu and Helmberger, 1996; Chen and Yang, 2004). The first zone in southeast Nepal between the Main Boundary and Main Frontal faults consist of earthquakes < Mw 4.0 at depths 40 - 60 km near the epicenter of the 1988 Udaypur earthquake, Mb 6.1, depth 57 km. The second zone north of the Main Central Thrust outcrop in eastern Nepal consists of 14 earthquakes 3.0 - 5.0 Mw at depths < 30 km that indicate north-south strike normal faulting and east-west strike thrust faulting. The third zone is an arc parallel to the Himalayas in southern Tibet and a cluster in northeast Nepal. This zone consists of 45 earthquakes < 4.0 Mw at depths > 50 km. Four earthquakes indicate northwest-southeast compression resulting in northeast strike strike-slip faulting while one earthquake in the northeast cluster indicates east-west compression at a source depth below the crust-mantle boundary. Focal mechanisms from full waveform moment tensor inversions are cross checked with first motion solutions for selected events. Source depths as determined from normalized error of the sum of the squared differences between the data and synthetic seismogram coincide with the source depths determined from the travel time residual inversion.

Surface‐wave Green’s tensors in the near field

USGS Publications Warehouse

Haney, Matt; Nakahara, Hisashi

2014-01-01

We demonstrate the connection between theoretical expressions for the correlation of ambient noise Rayleigh and Love waves and the exact surface‐wave Green’s tensors for a point force. The surface‐wave Green’s tensors are well known in the far‐field limit. On the other hand, the imaginary part of the exact Green’s tensors, including near‐field effects, arises in correlation techniques such as the spatial autocorrelation (SPAC) method. Using the imaginary part of the exact Green’s tensors from the SPAC method, we find the associated real part using the Kramers–Kronig relations. The application of the Kramers–Kronig relations is not straightforward, however, because the causality properties of the different tensor components vary. In addition to the Green’s tensors for a point force, we also derive expressions for a general point moment tensor source.

Tensor-Train Split-Operator Fourier Transform (TT-SOFT) Method: Multidimensional Nonadiabatic Quantum Dynamics.

PubMed

Greene, Samuel M; Batista, Victor S

2017-09-12

We introduce the "tensor-train split-operator Fourier transform" (TT-SOFT) method for simulations of multidimensional nonadiabatic quantum dynamics. TT-SOFT is essentially the grid-based SOFT method implemented in dynamically adaptive tensor-train representations. In the same spirit of all matrix product states, the tensor-train format enables the representation, propagation, and computation of observables of multidimensional wave functions in terms of the grid-based wavepacket tensor components, bypassing the need of actually computing the wave function in its full-rank tensor product grid space. We demonstrate the accuracy and efficiency of the TT-SOFT method as applied to propagation of 24-dimensional wave packets, describing the S 1 /S 2 interconversion dynamics of pyrazine after UV photoexcitation to the S 2 state. Our results show that the TT-SOFT method is a powerful computational approach for simulations of quantum dynamics of polyatomic systems since it avoids the exponential scaling problem of full-rank grid-based representations.

TNSPackage: A Fortran2003 library designed for tensor network state methods

NASA Astrophysics Data System (ADS)

Dong, Shao-Jun; Liu, Wen-Yuan; Wang, Chao; Han, Yongjian; Guo, G.-C.; He, Lixin

2018-07-01

Recently, the tensor network states (TNS) methods have proven to be very powerful tools to investigate the strongly correlated many-particle physics in one and two dimensions. The implementation of TNS methods depends heavily on the operations of tensors, including contraction, permutation, reshaping tensors, SVD and so on. Unfortunately, the most popular computer languages for scientific computation, such as Fortran and C/C++ do not have a standard library for such operations, and therefore make the coding of TNS very tedious. We develop a Fortran2003 package that includes all kinds of basic tensor operations designed for TNS. It is user-friendly and flexible for different forms of TNS, and therefore greatly simplifies the coding work for the TNS methods.

Filtering techniques for efficient inversion of two-dimensional Nuclear Magnetic Resonance data

NASA Astrophysics Data System (ADS)

Bortolotti, V.; Brizi, L.; Fantazzini, P.; Landi, G.; Zama, F.

2017-10-01

The inversion of two-dimensional Nuclear Magnetic Resonance (NMR) data requires the solution of a first kind Fredholm integral equation with a two-dimensional tensor product kernel and lower bound constraints. For the solution of this ill-posed inverse problem, the recently presented 2DUPEN algorithm [V. Bortolotti et al., Inverse Problems, 33(1), 2016] uses multiparameter Tikhonov regularization with automatic choice of the regularization parameters. In this work, I2DUPEN, an improved version of 2DUPEN that implements Mean Windowing and Singular Value Decomposition filters, is deeply tested. The reconstruction problem with filtered data is formulated as a compressed weighted least squares problem with multi-parameter Tikhonov regularization. Results on synthetic and real 2D NMR data are presented with the main purpose to deeper analyze the separate and combined effects of these filtering techniques on the reconstructed 2D distribution.

Tensor Fukunaga-Koontz transform for small target detection in infrared images

NASA Astrophysics Data System (ADS)

Liu, Ruiming; Wang, Jingzhuo; Yang, Huizhen; Gong, Chenglong; Zhou, Yuanshen; Liu, Lipeng; Zhang, Zhen; Shen, Shuli

2016-09-01

Infrared small targets detection plays a crucial role in warning and tracking systems. Some novel methods based on pattern recognition technology catch much attention from researchers. However, those classic methods must reshape images into vectors with the high dimensionality. Moreover, vectorizing breaks the natural structure and correlations in the image data. Image representation based on tensor treats images as matrices and can hold the natural structure and correlation information. So tensor algorithms have better classification performance than vector algorithms. Fukunaga-Koontz transform is one of classification algorithms and it is a vector version method with the disadvantage of all vector algorithms. In this paper, we first extended the Fukunaga-Koontz transform into its tensor version, tensor Fukunaga-Koontz transform. Then we designed a method based on tensor Fukunaga-Koontz transform for detecting targets and used it to detect small targets in infrared images. The experimental results, comparison through signal-to-clutter, signal-to-clutter gain and background suppression factor, have validated the advantage of the target detection based on the tensor Fukunaga-Koontz transform over that based on the Fukunaga-Koontz transform.

Seismotectonics and crustal stress across the northern Arabian plate

NASA Astrophysics Data System (ADS)

yassminh, R.; Gomez, F. G.; Sandvol, E. A.; Ghalib, H. A.; Daoud, M.

2013-12-01

The region encompassing the collision of northern Arabia with Eurasia is a tectonically heterogeneous region of distributed deformation. The northern Arabia plate is bounded to the west by the subducting Sinai plate and the left-lateral Dead Sea transform. This complexity suggests that there are, multiple competing processes that may influence regional tectonics in northern Arabia and adjacent areas. Earthquake mechanisms provide insight into crustal kinematics and stress; however, reliable determination of earthquake source parameters can be challenging in a complex geological region, such as the continental collision zone between the Arabian and Eurasian plates. The goal of this study is to investigate spatial patterns of the crustal stress in the northern Arabian plate and surrounding area. The focal mechanisms used in this study are based on (1) first-motion polarities for earthquakes recorded by Syrian earthquake center during 2000-2011, and (2) regional moment tensors from broadband seismic data, from Turkey and Iraq. First motion focal mechanisms were assigned quality classifications based on the variation of both nodal planes. Regional moment tensor analysis can be significantly influenced by seismic velocity structure; thus, we have divided the study area into regions based on tectonic units. For each region, a specific velocity model is defined using waveform-modeling technique prior to the regional moment tensor inversion. The resulting focal mechanisms, combined with other previously published focal mechanisms for the study area, provide a basis for stress inversion analysis. The resulting deviatoric stress tensors show the spatial distribution of the maximum horizontal stress varies from NW-SE along the Dead Sea Fault to the N-S toward the east. We interpret this to reflect the eastward change from the transform to collision processes in northern Arabia. Along the Dead Sea Fault, transposition of the sigma-1 and sigma-2 to vertical and horizontal, respectively, may relate to influences from the subducted part of the Sinai plate. This change in regional stress is also consistent with extensional strains observed from GPS velocities.

Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies.

PubMed

Khoromskaia, Venera; Khoromskij, Boris N

2015-12-21

We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and integral operators, first appeared as an accurate tensor calculus for the 3D Hartree potential using 1D complexity operations, and have evolved to entirely grid-based tensor-structured 3D Hartree-Fock eigenvalue solver. It benefits from tensor calculation of the core Hamiltonian and two-electron integrals (TEI) in O(n log n) complexity using the rank-structured approximation of basis functions, electron densities and convolution integral operators all represented on 3D n × n × n Cartesian grids. The algorithm for calculating TEI tensor in a form of the Cholesky decomposition is based on multiple factorizations using algebraic 1D "density fitting" scheme, which yield an almost irreducible number of product basis functions involved in the 3D convolution integrals, depending on a threshold ε > 0. The basis functions are not restricted to separable Gaussians, since the analytical integration is substituted by high-precision tensor-structured numerical quadratures. The tensor approaches to post-Hartree-Fock calculations for the MP2 energy correction and for the Bethe-Salpeter excitation energies, based on using low-rank factorizations and the reduced basis method, were recently introduced. Another direction is towards the tensor-based Hartree-Fock numerical scheme for finite lattices, where one of the numerical challenges is the summation of electrostatic potentials of a large number of nuclei. The 3D grid-based tensor method for calculation of a potential sum on a L × L × L lattice manifests the linear in L computational work, O(L), instead of the usual O(L(3) log L) scaling by the Ewald-type approaches.

Inference of segmented color and texture description by tensor voting.

PubMed

Jia, Jiaya; Tang, Chi-Keung

2004-06-01

A robust synthesis method is proposed to automatically infer missing color and texture information from a damaged 2D image by (N)D tensor voting (N > 3). The same approach is generalized to range and 3D data in the presence of occlusion, missing data and noise. Our method translates texture information into an adaptive (N)D tensor, followed by a voting process that infers noniteratively the optimal color values in the (N)D texture space. A two-step method is proposed. First, we perform segmentation based on insufficient geometry, color, and texture information in the input, and extrapolate partitioning boundaries by either 2D or 3D tensor voting to generate a complete segmentation for the input. Missing colors are synthesized using (N)D tensor voting in each segment. Different feature scales in the input are automatically adapted by our tensor scale analysis. Results on a variety of difficult inputs demonstrate the effectiveness of our tensor voting approach.

Groupwise Registration and Atlas Construction of 4th-Order Tensor Fields Using the ℝ+ Riemannian Metric*

PubMed Central

Barmpoutis, Angelos

2010-01-01

Registration of Diffusion-Weighted MR Images (DW-MRI) can be achieved by registering the corresponding 2nd-order Diffusion Tensor Images (DTI). However, it has been shown that higher-order diffusion tensors (e.g. order-4) outperform the traditional DTI in approximating complex fiber structures such as fiber crossings. In this paper we present a novel method for unbiased group-wise non-rigid registration and atlas construction of 4th-order diffusion tensor fields. To the best of our knowledge there is no other existing method to achieve this task. First we define a metric on the space of positive-valued functions based on the Riemannian metric of real positive numbers (denoted by ℝ+). Then, we use this metric in a novel functional minimization method for non-rigid 4th-order tensor field registration. We define a cost function that accounts for the 4th-order tensor re-orientation during the registration process and has analytic derivatives with respect to the transformation parameters. Finally, the tensor field atlas is computed as the minimizer of the variance defined using the Riemannian metric. We quantitatively compare the proposed method with other techniques that register scalar-valued or diffusion tensor (rank-2) representations of the DWMRI. PMID:20436782

Yang-Baxter maps, discrete integrable equations and quantum groups

NASA Astrophysics Data System (ADS)

Bazhanov, Vladimir V.; Sergeev, Sergey M.

2018-01-01

For every quantized Lie algebra there exists a map from the tensor square of the algebra to itself, which by construction satisfies the set-theoretic Yang-Baxter equation. This map allows one to define an integrable discrete quantum evolution system on quadrilateral lattices, where local degrees of freedom (dynamical variables) take values in a tensor power of the quantized Lie algebra. The corresponding equations of motion admit the zero curvature representation. The commuting Integrals of Motion are defined in the standard way via the Quantum Inverse Problem Method, utilizing Baxter's famous commuting transfer matrix approach. All elements of the above construction have a meaningful quasi-classical limit. As a result one obtains an integrable discrete Hamiltonian evolution system, where the local equation of motion are determined by a classical Yang-Baxter map and the action functional is determined by the quasi-classical asymptotics of the universal R-matrix of the underlying quantum algebra. In this paper we present detailed considerations of the above scheme on the example of the algebra Uq (sl (2)) leading to discrete Liouville equations, however the approach is rather general and can be applied to any quantized Lie algebra.

Stress pattern of the Shanxi rift system, North China, inferred from the inversion of new focal mechanisms

NASA Astrophysics Data System (ADS)

Li, Bin; Atakan, Kuvvet; Sørensen, Mathilde Bøttger; Havskov, Jens

2015-05-01

Earthquake focal mechanisms of the Shanxi rift system, North China, are investigated for the time period 1965-April 2014. A total of 143 focal mechanisms of ML ≥ 3.0 earthquakes were compiled. Among them, 105 solutions are newly determined in this study by combining the P-wave first motions and full waveform inversion, and 38 solutions are from available published data. Stress tensor inversion was then performed based on the new database. The results show that most solutions in the Shanxi rift system exhibit normal or strike-slip faulting, and the regional stress field is transtensional and dominated by NNW-SSE extension. This correlates well with results from GPS data, geological field observations and levelling measurements across the faults. Heterogeneity exists in the regional stress field, as indicated by individual stress tensor inversions conducted for five subzones. While the minimum stress axis (σ3) appears to be consistent and stable, the orientations, especially the plunges, of the maximum and intermediate stresses (σ1 and σ2) vary significantly along the strike of the different subzones. Based on our results and combining multidisciplinary observations from geological surveys, GPS and cross-fault monitoring, a kinematic model is proposed for the Shanxi rift system, in which the rift is situated between two opposite rotating crustal blocks, exhibiting a transtensional stress regimes. This model illustrates the present-day stress field and its correlation to the regional tectonics, as well as the current crustal deformation of the Shanxi rift system. Results obtained in this study, may help to understand the geodynamics, neotectonic activity, active seismicity and potential seismic hazard in this region.

Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. I. An efficient and simple linear scaling local MP2 method that uses an intermediate basis of pair natural orbitals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pinski, Peter; Riplinger, Christoph; Neese, Frank, E-mail: evaleev@vt.edu, E-mail: frank.neese@cec.mpg.de

2015-07-21

In this work, a systematic infrastructure is described that formalizes concepts implicit in previous work and greatly simplifies computer implementation of reduced-scaling electronic structure methods. The key concept is sparse representation of tensors using chains of sparse maps between two index sets. Sparse map representation can be viewed as a generalization of compressed sparse row, a common representation of a sparse matrix, to tensor data. By combining few elementary operations on sparse maps (inversion, chaining, intersection, etc.), complex algorithms can be developed, illustrated here by a linear-scaling transformation of three-center Coulomb integrals based on our compact code library that implementsmore » sparse maps and operations on them. The sparsity of the three-center integrals arises from spatial locality of the basis functions and domain density fitting approximation. A novel feature of our approach is the use of differential overlap integrals computed in linear-scaling fashion for screening products of basis functions. Finally, a robust linear scaling domain based local pair natural orbital second-order Möller-Plesset (DLPNO-MP2) method is described based on the sparse map infrastructure that only depends on a minimal number of cutoff parameters that can be systematically tightened to approach 100% of the canonical MP2 correlation energy. With default truncation thresholds, DLPNO-MP2 recovers more than 99.9% of the canonical resolution of the identity MP2 (RI-MP2) energy while still showing a very early crossover with respect to the computational effort. Based on extensive benchmark calculations, relative energies are reproduced with an error of typically <0.2 kcal/mol. The efficiency of the local MP2 (LMP2) method can be drastically improved by carrying out the LMP2 iterations in a basis of pair natural orbitals. While the present work focuses on local electron correlation, it is of much broader applicability to computation with sparse tensors in quantum chemistry and beyond.« less

A trial of reliable estimation of non-double-couple component of microearthquakes

NASA Astrophysics Data System (ADS)

Imanishi, K.; Uchide, T.

2017-12-01

Although most tectonic earthquakes are caused by shear failure, it has been reported that injection-induced seismicity and earthquakes occurring in volcanoes and geothermal areas contain non double couple (non-DC) components (e.g, Dreger et al., 2000). Also in the tectonic earthquakes, small non-DC components are beginning to be detected (e.g, Ross et al., 2015). However, it is generally limited to relatively large earthquakes that the non-DC component can be estimated with sufficient accuracy. In order to gain further understanding of fluid-driven earthquakes and fault zone properties, it is important to estimate full moment tensor of many microearthquakes with high precision. In the last AGU meeting, we proposed a method that iteratively applies the relative moment tensor inversion (RMTI) (Dahm, 1996) to source clusters improving each moment tensor as well as their relative accuracy. This new method overcomes the problem of RMTI that errors in the mechanism of reference events lead to biased solutions for other events, while taking advantage of RMTI that the source mechanisms can be determined without a computation of Green's function. The procedure is briefly summarized as follows: (1) Sample co-located multiple earthquakes with focal mechanisms, as initial solutions, determined by an ordinary method. (2) Apply the RMTI to estimate the source mechanism of each event relative to those of the other events. (3) Repeat the step 2 for the modified source mechanisms until the reduction of total residual converges. In order to confirm whether the method can resolve non-DC components, we conducted numerical tests on synthetic data. Amplitudes were computed assuming non-DC sources, amplifying by factor between 0.2 and 4 as site effects, and adding 10% random noise. As initial solutions in the step 1, we gave DC sources with arbitrary strike, dip and rake angle. In a test with eight sources at 12 stations, for example, all solutions were successively improved by iteration. Non-DC components were successfully resolved in spite of the fact that we gave DC sources as initial solutions. The application of the method to microearthquakes in geothermal area in Japan will be presented.

Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. I. An efficient and simple linear scaling local MP2 method that uses an intermediate basis of pair natural orbitals.

PubMed

Pinski, Peter; Riplinger, Christoph; Valeev, Edward F; Neese, Frank

2015-07-21

In this work, a systematic infrastructure is described that formalizes concepts implicit in previous work and greatly simplifies computer implementation of reduced-scaling electronic structure methods. The key concept is sparse representation of tensors using chains of sparse maps between two index sets. Sparse map representation can be viewed as a generalization of compressed sparse row, a common representation of a sparse matrix, to tensor data. By combining few elementary operations on sparse maps (inversion, chaining, intersection, etc.), complex algorithms can be developed, illustrated here by a linear-scaling transformation of three-center Coulomb integrals based on our compact code library that implements sparse maps and operations on them. The sparsity of the three-center integrals arises from spatial locality of the basis functions and domain density fitting approximation. A novel feature of our approach is the use of differential overlap integrals computed in linear-scaling fashion for screening products of basis functions. Finally, a robust linear scaling domain based local pair natural orbital second-order Möller-Plesset (DLPNO-MP2) method is described based on the sparse map infrastructure that only depends on a minimal number of cutoff parameters that can be systematically tightened to approach 100% of the canonical MP2 correlation energy. With default truncation thresholds, DLPNO-MP2 recovers more than 99.9% of the canonical resolution of the identity MP2 (RI-MP2) energy while still showing a very early crossover with respect to the computational effort. Based on extensive benchmark calculations, relative energies are reproduced with an error of typically <0.2 kcal/mol. The efficiency of the local MP2 (LMP2) method can be drastically improved by carrying out the LMP2 iterations in a basis of pair natural orbitals. While the present work focuses on local electron correlation, it is of much broader applicability to computation with sparse tensors in quantum chemistry and beyond.

Velocity model calibration as a tool to improve regional wave moment tensors: Application to the Basin and Range Province

NASA Astrophysics Data System (ADS)

Ichinose, G. A.

2006-12-01

Many scientific issues for the Basin and Range Province (BRP) remain unsettled including structural evolution, strain rates, slip partitioning and earthquake source physics. A catalog of earthquake source parameters including locations and moment tensors is the basis for tectonic and geophysical study. New instrumentation from the Advance National Seismic System, EarthScope Plate Boundary Observatory, Bigfoot and US-Array brings the opportunity for high quality research; therefore, a catalog is an underlying foundation for examining the BRP. We are continuing to generate a moment tensor catalog for the BRP (Mw<3.5) using long-period regional waves spanning back to 1990. Iterative waveform inversion method (e.g., Nolet et al., 1986, Randell, 1994) is used to calibrate the BRP velocity and density structure using two northern and southern BRP earthquakes. The calibrated models generate realistic synthetics for (f<0.5Hz) with ~50-80% variance reduction. We averaged all path specific models to construct a 1-D BRP community background model. The crust is relatively simple between 5-20km (~6.12km/s) and there is a strong velocity gradient in the upper 5- km. There are lower velocities in the upper crust but higher velocities in the mid-crust for the Sierra Nevada paths relative to BRP. There is also a lower crust high-velocity anomaly near Battle Mountain and Elko that is faster by ~5% and may indicate a wider area of under-plating by basaltic magmas. There are significant low velocity zones in the upper and mid crust mainly across the Walker Lane Belt that may indicate the presence of fluids. We are continuing to work on assessing the performance of these newly calibrated models in improving the estimation of moment tensors down to lower magnitudes and mapping out holes in the seismic network which can be filled to improve moment tensor catalog. We also are looking at how these models work at locating earthquakes and comparing synthetics with those computed from models constrained from different data including refraction, surface wave dispersion, and travel-time tomography.

Recent achievements in real-time computational seismology in Taiwan

NASA Astrophysics Data System (ADS)

Lee, S.; Liang, W.; Huang, B.

2012-12-01

Real-time computational seismology is currently possible to be achieved which needs highly connection between seismic database and high performance computing. We have developed a real-time moment tensor monitoring system (RMT) by using continuous BATS records and moment tensor inversion (CMT) technique. The real-time online earthquake simulation service is also ready to open for researchers and public earthquake science education (ROS). Combine RMT with ROS, the earthquake report based on computational seismology can provide within 5 minutes after an earthquake occurred (RMT obtains point source information < 120 sec; ROS completes a 3D simulation < 3 minutes). All of these computational results are posted on the internet in real-time now. For more information, welcome to visit real-time computational seismology earthquake report webpage (RCS).

Iterative joint inversion of in-situ stress state along Simeulue-Nias Island

NASA Astrophysics Data System (ADS)

Agustina, Anisa; Sahara, David P.; Nugraha, Andri Dian

2017-07-01

In-situ stress inversion from focal mechanisms requires knowledge of which of the two nodal planes is the fault. This is challenging, in particular, because of the inherent ambiguity of focal mechanisms the fault and the auxiliary nodal plane could not be distinguished. A relatively new inversion technique for estimating both stress and fault plane is developed by Vavryĉuk in 2014. The fault orientations are determined by applying the fault instability constraint, and the stress is calculated in iterations. In this study, this method is applied to a high-density earthquake regions, Simeulue-Batu Island. This area is interesting to be investigated because of the occurrence of the two large earthquakes, i.e. Aceh 2004 and Nias 2005 earthquake. The inversion was done based on 343 focal mechanisms data with Magnitude ≥5.5 Mw between 25th Mei 1977- 25th August 2015 from Harvard and Global Centroid Moment Tensor (GCMT) catalog. The area is divided into some grids, in which the analysis of stress orientation variation and its shape ratio is done for each grid. Stress inversion results show that there are three segments along Simeulue-Batu Island based on the variation of orientation stress σ1. The stress characteristics of each segments are discussed, i.e. shape ratio, principal stress orientation and subduction angle. Interestingly, the highest value of shape ratio is 0.93 and its association with the large earthquake Aceh 2004. This suggest that the zonation obtained in this study could also be used as a proxy for the hazard map.

Electric and magnetic galvanic distortion decomposition of tensor CSAMT data. Application to data from the Buchans Mine (Newfoundland, Canada)

NASA Astrophysics Data System (ADS)

Garcia, Xavier; Boerner, David; Pedersen, Laust B.

2003-09-01

We have developed a Marquardt-Levenberg inversion algorithm incorporating the effects of near-surface galvanic distortion into the electromagnetic (EM) response of a layered earth model. Different tests on synthetic model responses suggest that for the grounded source method, the magnetic distortion does not vanish for low frequencies. Including this effect is important, although to date it has been neglected. We have inverted 10 stations of controlled-source audio-magnetotellurics (CSAMT) data recorded near the Buchans Mine, Newfoundland, Canada. The Buchans Mine was one of the richest massive sulphide deposits in the world, and is situated in a highly resistive volcanogenic environment, substantially modified by thrust faulting. Preliminary work in the area demonstrated that the EM fields observed at adjacent stations show large differences due to the existence of mineralized fracture zones and variable overburden thickness. Our inversion results suggest a three-layered model that is appropriate for the Buchans Mine. The resistivity model correlates with the seismic reflection interpretation that documents the existence of two thrust packages. The distortion parameters obtained from the inversion concur with the synthetic studies that galvanic magnetic distortion is required to interpret the Buchans data since the magnetic component of the galvanic distortion does not vanish at low frequency.

Determination of the rotational diffusion tensor of macromolecules in solution from nmr relaxation data with a combination of exact and approximate methods--application to the determination of interdomain orientation in multidomain proteins.

PubMed

Ghose, R; Fushman, D; Cowburn, D

2001-04-01

In this paper we present a method for determining the rotational diffusion tensor from NMR relaxation data using a combination of approximate and exact methods. The approximate method, which is computationally less intensive, computes values of the principal components of the diffusion tensor and estimates the Euler angles, which relate the principal axis frame of the diffusion tensor to the molecular frame. The approximate values of the principal components are then used as starting points for an exact calculation by a downhill simplex search for the principal components of the tensor over a grid of the space of Euler angles relating the diffusion tensor frame to the molecular frame. The search space of Euler angles is restricted using the tensor orientations calculated using the approximate method. The utility of this approach is demonstrated using both simulated and experimental relaxation data. A quality factor that determines the extent of the agreement between the measured and predicted relaxation data is provided. This approach is then used to estimate the relative orientation of SH3 and SH2 domains in the SH(32) dual-domain construct of Abelson kinase complexed with a consolidated ligand. Copyright 2001 Academic Press.

Broadband waveform inversion of moderate earthquakes in the Messina Straits, southern Italy

NASA Astrophysics Data System (ADS)

D'Amico, Sebastiano; Orecchio, Barbara; Presti, Debora; Zhu, Lupei; Herrmann, Robert B.; Neri, Giancarlo

2010-04-01

We report the first application of the Cut and Paste (CAP) method to compute earthquake focal mechanisms in the Messina Straits area by waveform inversion of Pnl and surface wave segments. This application of CAP has furnished new knowledge about low-magnitude earthquake mechanics that will be useful for improved understanding of the local geodynamics. This is possible because the CAP inversion technique can be applied to small earthquakes, for which traditional moment tensor inversion methods are not appropriate and P-onset focal mechanisms in the study area fail because of a lack of sufficient observations. We estimate the focal mechanisms of 23 earthquakes with local magnitudes in the range of 3-4 occurring in the 2004-2008 time period, and recorded by the broadband stations of the Italian National Seismic Network and the Mediterranean Very Broadband Seismographic Network (MedNet) run by the Istituto Nazionale di Geofisica e Vulcanologia (INGV). The solutions show that normal faulting is the prevailing style of seismic deformation in the northern part of the study area while co-existence of normal faulting and strike-slip has been detected in the southern part. In the whole area of investigation the T-axes of focal mechanisms display a preferential northwest-southeast direction of extension. Combined with the findings of previous investigations, this improved database of focal mechanisms allows us to better detail the transitional area between the extensional domain related to subduction trench retreat (southern Calabria) and the compressional one associated with continental collision (western-central Sicily). The observed spatial change of seismic deformation regime offers new data to current seismotectonic and seismic hazard investigations in the area of Messina Straits where a magnitude 7.2 earthquake caused more than 60,000 casualties on 28 December 1908.

Stimulated echo diffusion tensor imaging and SPAIR T2-weighted imaging in Chronic Exertional Compartment Syndrome of the lower leg muscles

PubMed Central

Sigmund, Eric E.; Sui, Dabang; Ukpebor, Obehi; Baete, Steven; Fieremans, Els; Babb, James S.; Mechlin, Michael; Liu, Kecheng; Kwon, Jane; Mcgorty, KellyAnne; Hodnett, Phil; Bencardino, Jenny

2013-01-01

Purpose To evaluate the performance of diffusion tensor imaging (DTI) in the evaluation of chronic exertional compartment syndrome (CECS) as compared to T2-weighted imaging. Materials and Methods Using an IRB-approved HIPAA-compliant protocol, spectral adiabatic inversion recovery (SPAIR) T2-weighted imaging (T2w) and stimulated echo DTI were applied to 8 healthy volunteers and 14 suspected CECS patients before and after exertion. Longitudinal and transverse diffusion eigenvalues, mean diffusivity (MD), and fractional anisotropy (FA) were measured in 7 calf muscle compartments, which in patients were classified by their response on T2w: normal (<20% change), and CECS (>20% change). Mixed model analysis of variance compared subject groups and compartments in terms of response factors (post-/pre-exercise ratios) of DTI parameters. Results All diffusivities significantly increased (p<0.0001) and FA decreased (p=.0014) with exercise. Longitudinal diffusion responses were significantly smaller than transversal diffusion responses (p<0.0001). 19 of 98 patient compartments were classified as CECS on T2w. MD increased by 3.8±3.4% (volunteer), 7.4±4.2 % (normal), and 9.1±7.0% (CECS) with exercise. Conclusion DTI shows promise as an ancillary imaging method in the diagnosis and understanding of the pathophysiology in CECS. Future studies may explore its utility in predicting response to treatment. PMID:23440764

Research on the forward modeling of controlled-source audio-frequency magnetotellurics in three-dimensional axial anisotropic media

NASA Astrophysics Data System (ADS)

Wang, Kunpeng; Tan, Handong

2017-11-01

Controlled-source audio-frequency magnetotellurics (CSAMT) has developed rapidly in recent years and are widely used in the area of mineral and oil resource exploration as well as other fields. The current theory, numerical simulation, and inversion research are based on the assumption that the underground media have resistivity isotropy. However a large number of rock and mineral physical property tests show the resistivity of underground media is generally anisotropic. With the increasing application of CSAMT, the demand for probe accuracy of practical exploration to complex targets continues to increase. The question of how to evaluate the influence of anisotropic resistivity to CSAMT response is becoming important. To meet the demand for CSAMT response research of resistivity anisotropic media, this paper examines the CSAMT electric equations, derives and realizes a three-dimensional (3D) staggered-grid finite difference numerical simulation method of CSAMT resistivity axial anisotropy. Through building a two-dimensional (2D) resistivity anisotropy geoelectric model, we validate the 3D computation result by comparing it to the result of controlled-source electromagnetic method (CSEM) resistivity anisotropy 2D finite element program. Through simulating a 3D resistivity axial anisotropy geoelectric model, we compare and analyze the responses of equatorial configuration, axial configuration, two oblique sources and tensor source. The research shows that the tensor source is suitable for CSAMT to recognize the anisotropic effect of underground structure.

Full magnetic gradient tensor from triaxial aeromagnetic gradient measurements: Calculation and application

NASA Astrophysics Data System (ADS)

Luo, Yao; Wu, Mei-Ping; Wang, Ping; Duan, Shu-Ling; Liu, Hao-Jun; Wang, Jin-Long; An, Zhan-Feng

2015-09-01

The full magnetic gradient tensor (MGT) refers to the spatial change rate of the three field components of the geomagnetic field vector along three mutually orthogonal axes. The tensor is of use to geological mapping, resources exploration, magnetic navigation, and others. However, it is very difficult to measure the full magnetic tensor gradient using existing engineering technology. We present a method to use triaxial aeromagnetic gradient measurements for deriving the full MGT. The method uses the triaxial gradient data and makes full use of the variation of the magnetic anomaly modulus in three dimensions to obtain a self-consistent magnetic tensor gradient. Numerical simulations show that the full MGT data obtained with the proposed method are of high precision and satisfy the requirements of data processing. We selected triaxial aeromagnetic gradient data from the Hebei Province for calculating the full MGT. Data processing shows that using triaxial tensor gradient data allows to take advantage of the spatial rate of change of the total field in three dimensions and suppresses part of the independent noise in the aeromagnetic gradient. The calculated tensor components have improved resolution, and the transformed full tensor gradient satisfies the requirement of geological mapping and interpretation.

Inflationary spectra with inverse-volume corrections in loop quantum cosmology and their observational constraints from Planck 2015 data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhu, Tao; Wang, Anzhong; Wu, Qiang

We first derive the primordial power spectra, spectral indices and runnings of both scalar and tensor perturbations of a flat inflationary universe to the second-order approximations of the slow-roll parameters, in the framework of loop quantum cosmology with the inverse-volume quantum corrections. This represents an extension of our previous work in which the parameter σ was assumed to be an integer, where σ characterizes the quantum corrections and in general can take any of values from the range σ  element of  (0, 6]. Restricting to the first-order approximations of the slow-roll parameters, we find corrections to the results obtained previously inmore » the literature, and point out the causes for such errors. To our best knowledge, these represent the most accurate calculations of scalar and tensor perturbations given so far in the literature. Then, fitting the perturbations to the recently released data by Planck (2015), we obtain the most severe constraints for various values of σ. Using these constraints as our referring point, we discuss whether these quantum gravitational corrections can lead to measurable signatures in the future cosmological observations. We show that, depending on the value of σ, the scale-dependent contributions to the relativistic inflationary spectra due to the inverse-volume corrections could be well within the range of the detectability of the forthcoming generations of experiments, such as the Stage IV experiments.« less

Traffic speed data imputation method based on tensor completion.

PubMed

Ran, Bin; Tan, Huachun; Feng, Jianshuai; Liu, Ying; Wang, Wuhong

2015-01-01

Traffic speed data plays a key role in Intelligent Transportation Systems (ITS); however, missing traffic data would affect the performance of ITS as well as Advanced Traveler Information Systems (ATIS). In this paper, we handle this issue by a novel tensor-based imputation approach. Specifically, tensor pattern is adopted for modeling traffic speed data and then High accurate Low Rank Tensor Completion (HaLRTC), an efficient tensor completion method, is employed to estimate the missing traffic speed data. This proposed method is able to recover missing entries from given entries, which may be noisy, considering severe fluctuation of traffic speed data compared with traffic volume. The proposed method is evaluated on Performance Measurement System (PeMS) database, and the experimental results show the superiority of the proposed approach over state-of-the-art baseline approaches.

Traffic Speed Data Imputation Method Based on Tensor Completion

PubMed Central

Ran, Bin; Feng, Jianshuai; Liu, Ying; Wang, Wuhong

2015-01-01

Traffic speed data plays a key role in Intelligent Transportation Systems (ITS); however, missing traffic data would affect the performance of ITS as well as Advanced Traveler Information Systems (ATIS). In this paper, we handle this issue by a novel tensor-based imputation approach. Specifically, tensor pattern is adopted for modeling traffic speed data and then High accurate Low Rank Tensor Completion (HaLRTC), an efficient tensor completion method, is employed to estimate the missing traffic speed data. This proposed method is able to recover missing entries from given entries, which may be noisy, considering severe fluctuation of traffic speed data compared with traffic volume. The proposed method is evaluated on Performance Measurement System (PeMS) database, and the experimental results show the superiority of the proposed approach over state-of-the-art baseline approaches. PMID:25866501

Compartmentalization of the Coso East Flank geothermal field imaged by 3-D full-tensor MT inversion

USGS Publications Warehouse

Lindsey, Nathaniel J.; Kaven, Joern; Davatzes, Nicholas C.; Newman, Gregory A.

2017-01-01

Previous magnetotelluric (MT) studies of the high-temperature Coso geothermal system in California identified a subvertical feature of low resistivity (2–5 Ohm m) and appreciable lateral extent (>1 km) in the producing zone of the East Flank field. However, these models could not reproduce gross 3-D effects in the recorded data. We perform 3-D full-tensor inversion and retrieve a resistivity model that out-performs previous 2-D and 3-D off-diagonal models in terms of its fit to the complete 3-D MT data set as well as the degree of modelling bias. Inclusion of secondary Zxx and Zyy data components leads to a robust east-dip (60†) to the previously identified conductive East Flank reservoir feature, which correlates strongly with recently mapped surface faults, downhole well temperatures, 3-D seismic reflection data, and local microseismicity. We perform synthetic forward modelling to test the best-fit dip of this conductor using the response at a nearby MT station. We interpret the dipping conductor as a fractured and fluidized compartment, which is structurally controlled by an unmapped blind East Flank fault zone.

Compartmentalization of the Coso East Flank geothermal field imaged by 3-D full-tensor MT inversion

NASA Astrophysics Data System (ADS)

Lindsey, Nathaniel J.; Kaven, Joern Ole; Davatzes, Nicholas; Newman, Gregory A.

2017-02-01

Previous magnetotelluric (MT) studies of the high-temperature Coso geothermal system in California identified a subvertical feature of low resistivity (2-5 Ohm m) and appreciable lateral extent (>1 km) in the producing zone of the East Flank field. However, these models could not reproduce gross 3-D effects in the recorded data. We perform 3-D full-tensor inversion and retrieve a resistivity model that out-performs previous 2-D and 3-D off-diagonal models in terms of its fit to the complete 3-D MT data set as well as the degree of modelling bias. Inclusion of secondary Zxx and Zyy data components leads to a robust east-dip (60†) to the previously identified conductive East Flank reservoir feature, which correlates strongly with recently mapped surface faults, downhole well temperatures, 3-D seismic reflection data, and local microseismicity. We perform synthetic forward modelling to test the best-fit dip of this conductor using the response at a nearby MT station. We interpret the dipping conductor as a fractured and fluidized compartment, which is structurally controlled by an unmapped blind East Flank fault zone.

On physical property tensors invariant under line groups.

PubMed

Litvin, Daniel B

2014-03-01

The form of physical property tensors of a quasi-one-dimensional material such as a nanotube or a polymer can be determined from the point group of its symmetry group, one of an infinite number of line groups. Such forms are calculated using a method based on the use of trigonometric summations. With this method, it is shown that materials invariant under infinite subsets of line groups have physical property tensors of the same form. For line group types of a family of line groups characterized by an index n and a physical property tensor of rank m, the form of the tensor for all line group types indexed with n > m is the same, leaving only a finite number of tensor forms to be determined.

Berkeley Seismological Laboratory Seismic Moment Tensor Report for the August 6, 2007 M3.9 Seismic event in central Utah

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ford, S; Dreger, D; Hellweg, P

2007-08-08

We have performed a complete moment tensor analysis of the seismic event, which occurred on Monday August 6, 2007 at 08:48:40 UTC 21 km from Mt.Pleasant, Utah. In our analysis we utilized complete three-component seismic records recorded by the USArray, University of Utah, and EarthScope seismic arrays. The seismic waveform data was integrated to displacement and filtered between 0.02 to 0.10 Hz following instrument removal. We used the Song et al. (1996) velocity model to compute Green's functions used in the moment tensor inversion. A map of the stations we used and the location of the event is shown inmore » Figure 1. In our moment tensor analysis we assumed a shallow source depth of 1 km consistent with the shallow depth reported for this event. As shown in Figure 2 the results point to a source mechanism with negligible double-couple radiation and is composed of dominant CLVD and implosive isotropic components. The total scalar seismic moment is 2.12e22 dyne cm corresponding to a moment magnitude (Mw) of 4.2. The long-period records are very well matched by the model (Figure 2) with a variance reduction of 73.4%. An all dilational (down) first motion radiation pattern is predicted by the moment tensor solution, and observations of first motions are in agreement.« less

A Tensor-Product-Kernel Framework for Multiscale Neural Activity Decoding and Control

PubMed Central

Li, Lin; Brockmeier, Austin J.; Choi, John S.; Francis, Joseph T.; Sanchez, Justin C.; Príncipe, José C.

2014-01-01

Brain machine interfaces (BMIs) have attracted intense attention as a promising technology for directly interfacing computers or prostheses with the brain's motor and sensory areas, thereby bypassing the body. The availability of multiscale neural recordings including spike trains and local field potentials (LFPs) brings potential opportunities to enhance computational modeling by enriching the characterization of the neural system state. However, heterogeneity on data type (spike timing versus continuous amplitude signals) and spatiotemporal scale complicates the model integration of multiscale neural activity. In this paper, we propose a tensor-product-kernel-based framework to integrate the multiscale activity and exploit the complementary information available in multiscale neural activity. This provides a common mathematical framework for incorporating signals from different domains. The approach is applied to the problem of neural decoding and control. For neural decoding, the framework is able to identify the nonlinear functional relationship between the multiscale neural responses and the stimuli using general purpose kernel adaptive filtering. In a sensory stimulation experiment, the tensor-product-kernel decoder outperforms decoders that use only a single neural data type. In addition, an adaptive inverse controller for delivering electrical microstimulation patterns that utilizes the tensor-product kernel achieves promising results in emulating the responses to natural stimulation. PMID:24829569

Geodesic-loxodromes for diffusion tensor interpolation and difference measurement.

PubMed

Kindlmann, Gordon; Estépar, Raúl San José; Niethammer, Marc; Haker, Steven; Westin, Carl-Fredrik

2007-01-01

In algorithms for processing diffusion tensor images, two common ingredients are interpolating tensors, and measuring the distance between them. We propose a new class of interpolation paths for tensors, termed geodesic-loxodromes, which explicitly preserve clinically important tensor attributes, such as mean diffusivity or fractional anisotropy, while using basic differential geometry to interpolate tensor orientation. This contrasts with previous Riemannian and Log-Euclidean methods that preserve the determinant. Path integrals of tangents of geodesic-loxodromes generate novel measures of over-all difference between two tensors, and of difference in shape and in orientation.

Entanglement branching operator

NASA Astrophysics Data System (ADS)

Harada, Kenji

2018-01-01

We introduce an entanglement branching operator to split a composite entanglement flow in a tensor network which is a promising theoretical tool for many-body systems. We can optimize an entanglement branching operator by solving a minimization problem based on squeezing operators. The entanglement branching is a new useful operation to manipulate a tensor network. For example, finding a particular entanglement structure by an entanglement branching operator, we can improve a higher-order tensor renormalization group method to catch a proper renormalization flow in a tensor network space. This new method yields a new type of tensor network states. The second example is a many-body decomposition of a tensor by using an entanglement branching operator. We can use it for a perfect disentangling among tensors. Applying a many-body decomposition recursively, we conceptually derive projected entangled pair states from quantum states that satisfy the area law of entanglement entropy.

Source characterization for an explosion during the 2009 eruption of Redoubt Volcano from very-long-period seismic waves

USGS Publications Warehouse

Haney, Matthew M.; Chouet, Bernard A.; Dawson, Phillip B.; Power, John A.

2013-01-01

The 2009 eruption of Redoubt produced several very-long-period (VLP) signals associated with explosions. We invert for the source location and mechanism of an explosion at Redoubt volcano using waveform methods applied to broadband recordings. Such characterization of the source carries information on the geometry of the conduit and the physics of the explosion process. Inversions are carried out assuming the volcanic source can be modeled as a point source, with mechanisms described by a) a set of 3 orthogonal forces, b) a moment tensor consisting of force couples, and c) both forces and moment tensor components. We find that the source of the VLP seismic waves during the explosion is well-described by either a combined moment/force source located northeast of the crater and at an elevation of 1.6 km ASL or a moment source at an elevation of 800 m to the southwest of the crater. The moment tensors for the solutions with moment and force and moment-only share similar characteristics. The source time functions for both moment tensors begin with inflation (pressurization) and execute two cycles of deflation-reinflation (depressurization–repressurization). Although the moment/force source provides a better fit to the data, we find that owing to the limited coverage of the broadband stations at Redoubt the moment-only source is the more robust and reliable solution. Based on the moment-only solution, we estimate a volume change of 19,000 m3 and a pressure change of 7 MPa in a dominant sill and an out-of-phase volume change of 5000 m3 and pressure change of 1.8 MPa in a subdominant dike at the source location. These results shed new light on the magmatic plumbing system beneath Redoubt and complement previous studies on Vulcanian explosions at other volcanoes.

On the magnetic polarizability tensor of US coinage

NASA Astrophysics Data System (ADS)

Davidson, John L.; Abdel-Rehim, Omar A.; Hu, Peipei; Marsh, Liam A.; O'Toole, Michael D.; Peyton, Anthony J.

2018-03-01

The magnetic dipole polarizability tensor of a metallic object gives unique information about the size, shape and electromagnetic properties of the object. In this paper, we present a novel method of coin characterization based on the spectroscopic response of the absolute tensor. The experimental measurements are validated using a combination of tests with a small set of bespoke coin surrogates and simulated data. The method is applied to an uncirculated set of US coins. Measured and simulated spectroscopic tensor responses of the coins show significant differences between different coin denominations. The presented results are encouraging as they strongly demonstrate the ability to characterize coins using an absolute tensor approach.

A unified tensor level set for image segmentation.

PubMed

Wang, Bin; Gao, Xinbo; Tao, Dacheng; Li, Xuelong

2010-06-01

This paper presents a new region-based unified tensor level set model for image segmentation. This model introduces a three-order tensor to comprehensively depict features of pixels, e.g., gray value and the local geometrical features, such as orientation and gradient, and then, by defining a weighted distance, we generalized the representative region-based level set method from scalar to tensor. The proposed model has four main advantages compared with the traditional representative method as follows. First, involving the Gaussian filter bank, the model is robust against noise, particularly the salt- and pepper-type noise. Second, considering the local geometrical features, e.g., orientation and gradient, the model pays more attention to boundaries and makes the evolving curve stop more easily at the boundary location. Third, due to the unified tensor pixel representation representing the pixels, the model segments images more accurately and naturally. Fourth, based on a weighted distance definition, the model possesses the capacity to cope with data varying from scalar to vector, then to high-order tensor. We apply the proposed method to synthetic, medical, and natural images, and the result suggests that the proposed method is superior to the available representative region-based level set method.

Automated artifact detection and removal for improved tensor estimation in motion-corrupted DTI data sets using the combination of local binary patterns and 2D partial least squares.

PubMed

Zhou, Zhenyu; Liu, Wei; Cui, Jiali; Wang, Xunheng; Arias, Diana; Wen, Ying; Bansal, Ravi; Hao, Xuejun; Wang, Zhishun; Peterson, Bradley S; Xu, Dongrong

2011-02-01

Signal variation in diffusion-weighted images (DWIs) is influenced both by thermal noise and by spatially and temporally varying artifacts, such as rigid-body motion and cardiac pulsation. Motion artifacts are particularly prevalent when scanning difficult patient populations, such as human infants. Although some motion during data acquisition can be corrected using image coregistration procedures, frequently individual DWIs are corrupted beyond repair by sudden, large amplitude motion either within or outside of the imaging plane. We propose a novel approach to identify and reject outlier images automatically using local binary patterns (LBP) and 2D partial least square (2D-PLS) to estimate diffusion tensors robustly. This method uses an enhanced LBP algorithm to extract texture features from a local texture feature of the image matrix from the DWI data. Because the images have been transformed to local texture matrices, we are able to extract discriminating information that identifies outliers in the data set by extending a traditional one-dimensional PLS algorithm to a two-dimension operator. The class-membership matrix in this 2D-PLS algorithm is adapted to process samples that are image matrix, and the membership matrix thus represents varying degrees of importance of local information within the images. We also derive the analytic form of the generalized inverse of the class-membership matrix. We show that this method can effectively extract local features from brain images obtained from a large sample of human infants to identify images that are outliers in their textural features, permitting their exclusion from further processing when estimating tensors using the DWIs. This technique is shown to be superior in performance when compared with visual inspection and other common methods to address motion-related artifacts in DWI data. This technique is applicable to correct motion artifact in other magnetic resonance imaging (MRI) techniques (e.g., the bootstrapping estimation) that use univariate or multivariate regression methods to fit MRI data to a pre-specified model. Copyright © 2011 Elsevier Inc. All rights reserved.

The gravitational wave stress–energy (pseudo)-tensor in modified gravity

NASA Astrophysics Data System (ADS)

Saffer, Alexander; Yunes, Nicolás; Yagi, Kent

2018-03-01

The recent detections of gravitational waves by the advanced LIGO and Virgo detectors open up new tests of modified gravity theories in the strong-field and dynamical, extreme gravity regime. Such tests rely sensitively on the phase evolution of the gravitational waves, which is controlled by the energy–momentum carried by such waves out of the system. We here study four different methods for finding the gravitational wave stress–energy pseudo-tensor in gravity theories with any combination of scalar, vector, or tensor degrees of freedom. These methods rely on the second variation of the action under short-wavelength averaging, the second perturbation of the field equations in the short-wavelength approximation, the construction of an energy complex leading to a Landau–Lifshitz tensor, and the use of Noether’s theorem in field theories about a flat background. We apply these methods in general relativity, Jordan–Fierz–Brans–Dicky theoy, and Einstein-Æther theory to find the gravitational wave stress–energy pseudo-tensor and calculate the rate at which energy and linear momentum is carried away from the system. The stress–energy tensor and the rate of linear momentum loss in Einstein-Æther theory are presented here for the first time. We find that all methods yield the same rate of energy loss, although the stress–energy pseudo-tensor can be functionally different. We also find that the Noether method yields a stress–energy tensor that is not symmetric or gauge-invariant, and symmetrization via the Belinfante procedure does not fix these problems because this procedure relies on Lorentz invariance, which is spontaneously broken in Einstein-Æther theory. The methods and results found here will be useful for the calculation of predictions in modified gravity theories that can then be contrasted with observations.

Determination of the Rotational Diffusion Tensor of Macromolecules in Solution from NMR Relaxation Data with a Combination of Exact and Approximate Methods—Application to the Determination of Interdomain Orientation in Multidomain Proteins

NASA Astrophysics Data System (ADS)

Ghose, Ranajeet; Fushman, David; Cowburn, David

2001-04-01

In this paper we present a method for determining the rotational diffusion tensor from NMR relaxation data using a combination of approximate and exact methods. The approximate method, which is computationally less intensive, computes values of the principal components of the diffusion tensor and estimates the Euler angles, which relate the principal axis frame of the diffusion tensor to the molecular frame. The approximate values of the principal components are then used as starting points for an exact calculation by a downhill simplex search for the principal components of the tensor over a grid of the space of Euler angles relating the diffusion tensor frame to the molecular frame. The search space of Euler angles is restricted using the tensor orientations calculated using the approximate method. The utility of this approach is demonstrated using both simulated and experimental relaxation data. A quality factor that determines the extent of the agreement between the measured and predicted relaxation data is provided. This approach is then used to estimate the relative orientation of SH3 and SH2 domains in the SH(32) dual-domain construct of Abelson kinase complexed with a consolidated ligand.

Tri-Clustered Tensor Completion for Social-Aware Image Tag Refinement.

PubMed

Tang, Jinhui; Shu, Xiangbo; Qi, Guo-Jun; Li, Zechao; Wang, Meng; Yan, Shuicheng; Jain, Ramesh

2017-08-01

Social image tag refinement, which aims to improve tag quality by automatically completing the missing tags and rectifying the noise-corrupted ones, is an essential component for social image search. Conventional approaches mainly focus on exploring the visual and tag information, without considering the user information, which often reveals important hints on the (in)correct tags of social images. Towards this end, we propose a novel tri-clustered tensor completion framework to collaboratively explore these three kinds of information to improve the performance of social image tag refinement. Specifically, the inter-relations among users, images and tags are modeled by a tensor, and the intra-relations between users, images and tags are explored by three regularizations respectively. To address the challenges of the super-sparse and large-scale tensor factorization that demands expensive computing and memory cost, we propose a novel tri-clustering method to divide the tensor into a certain number of sub-tensors by simultaneously clustering users, images and tags into a bunch of tri-clusters. And then we investigate two strategies to complete these sub-tensors by considering (in)dependence between the sub-tensors. Experimental results on a real-world social image database demonstrate the superiority of the proposed method compared with the state-of-the-art methods.

A practical introduction to tensor networks: Matrix product states and projected entangled pair states

DOE Office of Scientific and Technical Information (OSTI.GOV)

Orús, Román, E-mail: roman.orus@uni-mainz.de

This is a partly non-technical introduction to selected topics on tensor network methods, based on several lectures and introductory seminars given on the subject. It should be a good place for newcomers to get familiarized with some of the key ideas in the field, specially regarding the numerics. After a very general introduction we motivate the concept of tensor network and provide several examples. We then move on to explain some basics about Matrix Product States (MPS) and Projected Entangled Pair States (PEPS). Selected details on some of the associated numerical methods for 1d and 2d quantum lattice systems aremore » also discussed. - Highlights: • A practical introduction to selected aspects of tensor network methods is presented. • We provide analytical examples of MPS and 2d PEPS. • We provide basic aspects on several numerical methods for MPS and 2d PEPS. • We discuss a number of applications of tensor network methods from a broad perspective.« less

Quantitative assessments of traumatic axonal injury in human brain: concordance of microdialysis and advanced MRI.

PubMed

Magnoni, Sandra; Mac Donald, Christine L; Esparza, Thomas J; Conte, Valeria; Sorrell, James; Macrì, Mario; Bertani, Giulio; Biffi, Riccardo; Costa, Antonella; Sammons, Brian; Snyder, Abraham Z; Shimony, Joshua S; Triulzi, Fabio; Stocchetti, Nino; Brody, David L

2015-08-01

Axonal injury is a major contributor to adverse outcomes following brain trauma. However, the extent of axonal injury cannot currently be assessed reliably in living humans. Here, we used two experimental methods with distinct noise sources and limitations in the same cohort of 15 patients with severe traumatic brain injury to assess axonal injury. One hundred kilodalton cut-off microdialysis catheters were implanted at a median time of 17 h (13-29 h) after injury in normal appearing (on computed tomography scan) frontal white matter in all patients, and samples were collected for at least 72 h. Multiple analytes, such as the metabolic markers glucose, lactate, pyruvate, glutamate and tau and amyloid-β proteins, were measured every 1-2 h in the microdialysis samples. Diffusion tensor magnetic resonance imaging scans at 3 T were performed 2-9 weeks after injury in 11 patients. Stability of diffusion tensor imaging findings was verified by repeat scans 1-3 years later in seven patients. An additional four patients were scanned only at 1-3 years after injury. Imaging abnormalities were assessed based on comparisons with five healthy control subjects for each patient, matched by age and sex (32 controls in total). No safety concerns arose during either microdialysis or scanning. We found that acute microdialysis measurements of the axonal cytoskeletal protein tau in the brain extracellular space correlated well with diffusion tensor magnetic resonance imaging-based measurements of reduced brain white matter integrity in the 1-cm radius white matter-masked region near the microdialysis catheter insertion sites. Specifically, we found a significant inverse correlation between microdialysis measured levels of tau 13-36 h after injury and anisotropy reductions in comparison with healthy controls (Spearman's r = -0.64, P = 0.006). Anisotropy reductions near microdialysis catheter insertion sites were highly correlated with reductions in multiple additional white matter regions. We interpret this result to mean that both microdialysis and diffusion tensor magnetic resonance imaging accurately reflect the same pathophysiological process: traumatic axonal injury. This cross-validation increases confidence in both methods for the clinical assessment of axonal injury. However, neither microdialysis nor diffusion tensor magnetic resonance imaging have been validated versus post-mortem histology in humans. Furthermore, future work will be required to determine the prognostic significance of these assessments of traumatic axonal injury when combined with other clinical and radiological measures. © The Author (2015). Published by Oxford University Press on behalf of the Guarantors of Brain. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Compressed sparse tensor based quadrature for vibrational quantum mechanics integrals

DOE PAGES

Rai, Prashant; Sargsyan, Khachik; Najm, Habib N.

2018-03-20

A new method for fast evaluation of high dimensional integrals arising in quantum mechanics is proposed. Here, the method is based on sparse approximation of a high dimensional function followed by a low-rank compression. In the first step, we interpret the high dimensional integrand as a tensor in a suitable tensor product space and determine its entries by a compressed sensing based algorithm using only a few function evaluations. Secondly, we implement a rank reduction strategy to compress this tensor in a suitable low-rank tensor format using standard tensor compression tools. This allows representing a high dimensional integrand function asmore » a small sum of products of low dimensional functions. Finally, a low dimensional Gauss–Hermite quadrature rule is used to integrate this low-rank representation, thus alleviating the curse of dimensionality. Finally, numerical tests on synthetic functions, as well as on energy correction integrals for water and formaldehyde molecules demonstrate the efficiency of this method using very few function evaluations as compared to other integration strategies.« less

Compressed sparse tensor based quadrature for vibrational quantum mechanics integrals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rai, Prashant; Sargsyan, Khachik; Najm, Habib N.

A new method for fast evaluation of high dimensional integrals arising in quantum mechanics is proposed. Here, the method is based on sparse approximation of a high dimensional function followed by a low-rank compression. In the first step, we interpret the high dimensional integrand as a tensor in a suitable tensor product space and determine its entries by a compressed sensing based algorithm using only a few function evaluations. Secondly, we implement a rank reduction strategy to compress this tensor in a suitable low-rank tensor format using standard tensor compression tools. This allows representing a high dimensional integrand function asmore » a small sum of products of low dimensional functions. Finally, a low dimensional Gauss–Hermite quadrature rule is used to integrate this low-rank representation, thus alleviating the curse of dimensionality. Finally, numerical tests on synthetic functions, as well as on energy correction integrals for water and formaldehyde molecules demonstrate the efficiency of this method using very few function evaluations as compared to other integration strategies.« less

The impact of inversion and mirror reflection symmetry on Raman scattering of T'transition metal dichalcogenides

NASA Astrophysics Data System (ADS)

Yan, Jun; Chen, Shao-Yu; Naylor, Carl; Goldstein, Thomas; Johnson, Charlie; Venkataraman, Dhandapani; Ramasubramaniam, Ashwin

Distorted octahedral (T') transition metal dichalcogenides (TMDCs) are topologically interesting material systems. Inversion-symmetry-broken bulk T'-TMDCs are predicted to be type II Weyl semimetals and inversion-symmetric monolayer (1L) T'-TMDCs are shown to be 2D topological insulators. In this talk, I will show that both the inversion symmetry and the mirror symmetry are important for understanding the lattice dynamics and Raman scattering of T'-TMDCs. The mirror plane that is perpendicular to the zigzag transition metal atomic chain classifies lattice vibrations into z-modes and m-modes where ` z' stands for zigzag and ` m' stands for mirror. Raman active z- and m- modes can be experimentally determined with light-polarization and crystal angle-resolved Raman tensor analysis. We report observation of all 9 even-parity zone-center phonons in 1L-T'-MoTe2. In bulk T'-MoTe2, we monitor inversion symmetry breaking with the shear lattice vibrations, which is important for supporting Weyl fermions. This work is supported by the Armstrong Fund for Science and NSF EFRI 2DARE EFMA-1542879.

Easy handling of tectonic data: the programs TectonicVB for Mac and TectonicsFP for Windows™

NASA Astrophysics Data System (ADS)

Ortner, Hugo; Reiter, Franz; Acs, Peter

2002-12-01

TectonicVB for Macintosh and TectonicsFP for Windows TM operating systems are two menu-driven computer programs which allow the shared use of data on these environments. The programs can produce stereographic plots of orientation data (great circles, poles, lineations). Frequently used statistical procedures like calculation of eigenvalues and eigenvectors, calculation of mean vector with concentration parameters and confidence cone can be easily performed. Fault data can be plotted in stereographic projection (Angelier and Hoeppener plots). Sorting of datasets into homogeneous subsets and rotation of tectonic data can be performed in interactive two-diagram windows. The paleostress tensor can be calculated from fault data sets using graphical (calculation of kinematic axes and right dihedra method) or mathematical methods (direct inversion or numerical dynamical analysis). The calculations can be checked in dimensionless Mohr diagrams and fluctuation histograms.

Tensor Invariant Processing for Munitions/Clutter Classification

DTIC Science & Technology

2013-11-01

Report," U.S. Naval Research Laboratory Report NRL/MR/ 6110 --12-9401, April 2012. 5. ESTCP Live Site Demonstrations, Former Camp Beale, Marysville, CA ...currently valid OMB control number. 1. REPORT DATE NOV 2013 2 . REPORT TYPE 3. DATES COVERED 00-00-2013 to 00-00-2013 4. TITLE AND SUBTITLE...inversion............................................................. 4 Figure 2 . Multi-coil arrays exciting target with different primary field directions

An efficient tensor transpose algorithm for multicore CPU, Intel Xeon Phi, and NVidia Tesla GPU

NASA Astrophysics Data System (ADS)

Lyakh, Dmitry I.

2015-04-01

An efficient parallel tensor transpose algorithm is suggested for shared-memory computing units, namely, multicore CPU, Intel Xeon Phi, and NVidia GPU. The algorithm operates on dense tensors (multidimensional arrays) and is based on the optimization of cache utilization on x86 CPU and the use of shared memory on NVidia GPU. From the applied side, the ultimate goal is to minimize the overhead encountered in the transformation of tensor contractions into matrix multiplications in computer implementations of advanced methods of quantum many-body theory (e.g., in electronic structure theory and nuclear physics). A particular accent is made on higher-dimensional tensors that typically appear in the so-called multireference correlated methods of electronic structure theory. Depending on tensor dimensionality, the presented optimized algorithms can achieve an order of magnitude speedup on x86 CPUs and 2-3 times speedup on NVidia Tesla K20X GPU with respect to the naïve scattering algorithm (no memory access optimization). The tensor transpose routines developed in this work have been incorporated into a general-purpose tensor algebra library (TAL-SH).

Source characterization of underground explosions from hydrodynamic-to-elastic coupling simulations

NASA Astrophysics Data System (ADS)

Chiang, A.; Pitarka, A.; Ford, S. R.; Ezzedine, S. M.; Vorobiev, O.

2017-12-01

A major improvement in ground motion simulation capabilities for underground explosion monitoring during the first phase of the Source Physics Experiment (SPE) is the development of a wave propagation solver that can propagate explosion generated non-linear near field ground motions to the far-field. The calculation is done using a hybrid modeling approach with a one-way hydrodynamic-to-elastic coupling in three dimensions where near-field motions are computed using GEODYN-L, a Lagrangian hydrodynamics code, and then passed to WPP, an elastic finite-difference code for seismic waveform modeling. The advancement in ground motion simulation capabilities gives us the opportunity to assess moment tensor inversion of a realistic volumetric source with near-field effects in a controlled setting, where we can evaluate the recovered source properties as a function of modeling parameters (i.e. velocity model) and can provide insights into previous source studies on SPE Phase I chemical shots and other historical nuclear explosions. For example the moment tensor inversion of far-field SPE seismic data demonstrated while vertical motions are well-modeled using existing velocity models large misfits still persist in predicting tangential shear wave motions from explosions. One possible explanation we can explore is errors and uncertainties from the underlying Earth model. Here we investigate the recovered moment tensor solution, particularly on the non-volumetric component, by inverting far-field ground motions simulated from physics-based explosion source models in fractured material, where the physics-based source models are based on the modeling of SPE-4P, SPE-5 and SPE-6 near-field data. The hybrid modeling approach provides new prospects in modeling explosion source and understanding the uncertainties associated with it.

Tensor sufficient dimension reduction

PubMed Central

Zhong, Wenxuan; Xing, Xin; Suslick, Kenneth

2015-01-01

Tensor is a multiway array. With the rapid development of science and technology in the past decades, large amount of tensor observations are routinely collected, processed, and stored in many scientific researches and commercial activities nowadays. The colorimetric sensor array (CSA) data is such an example. Driven by the need to address data analysis challenges that arise in CSA data, we propose a tensor dimension reduction model, a model assuming the nonlinear dependence between a response and a projection of all the tensor predictors. The tensor dimension reduction models are estimated in a sequential iterative fashion. The proposed method is applied to a CSA data collected for 150 pathogenic bacteria coming from 10 bacterial species and 14 bacteria from one control species. Empirical performance demonstrates that our proposed method can greatly improve the sensitivity and specificity of the CSA technique. PMID:26594304

Finite frequency shear wave splitting tomography: a model space search approach

NASA Astrophysics Data System (ADS)

Mondal, P.; Long, M. D.

2017-12-01

Observations of seismic anisotropy provide key constraints on past and present mantle deformation. A common method for upper mantle anisotropy is to measure shear wave splitting parameters (delay time and fast direction). However, the interpretation is not straightforward, because splitting measurements represent an integration of structure along the ray path. A tomographic approach that allows for localization of anisotropy is desirable; however, tomographic inversion for anisotropic structure is a daunting task, since 21 parameters are needed to describe general anisotropy. Such a large parameter space does not allow a straightforward application of tomographic inversion. Building on previous work on finite frequency shear wave splitting tomography, this study aims to develop a framework for SKS splitting tomography with a new parameterization of anisotropy and a model space search approach. We reparameterize the full elastic tensor, reducing the number of parameters to three (a measure of strength based on symmetry considerations for olivine, plus the dip and azimuth of the fast symmetry axis). We compute Born-approximation finite frequency sensitivity kernels relating model perturbations to splitting intensity observations. The strong dependence of the sensitivity kernels on the starting anisotropic model, and thus the strong non-linearity of the inverse problem, makes a linearized inversion infeasible. Therefore, we implement a Markov Chain Monte Carlo technique in the inversion procedure. We have performed tests with synthetic data sets to evaluate computational costs and infer the resolving power of our algorithm for synthetic models with multiple anisotropic layers. Our technique can resolve anisotropic parameters on length scales of ˜50 km for realistic station and event configurations for dense broadband experiments. We are proceeding towards applications to real data sets, with an initial focus on the High Lava Plains of Oregon.

Tree Tensor Network State with Variable Tensor Order: An Efficient Multireference Method for Strongly Correlated Systems

PubMed Central

2015-01-01

We study the tree-tensor-network-state (TTNS) method with variable tensor orders for quantum chemistry. TTNS is a variational method to efficiently approximate complete active space (CAS) configuration interaction (CI) wave functions in a tensor product form. TTNS can be considered as a higher order generalization of the matrix product state (MPS) method. The MPS wave function is formulated as products of matrices in a multiparticle basis spanning a truncated Hilbert space of the original CAS-CI problem. These matrices belong to active orbitals organized in a one-dimensional array, while tensors in TTNS are defined upon a tree-like arrangement of the same orbitals. The tree-structure is advantageous since the distance between two arbitrary orbitals in the tree scales only logarithmically with the number of orbitals N, whereas the scaling is linear in the MPS array. It is found to be beneficial from the computational costs point of view to keep strongly correlated orbitals in close vicinity in both arrangements; therefore, the TTNS ansatz is better suited for multireference problems with numerous highly correlated orbitals. To exploit the advantages of TTNS a novel algorithm is designed to optimize the tree tensor network topology based on quantum information theory and entanglement. The superior performance of the TTNS method is illustrated on the ionic-neutral avoided crossing of LiF. It is also shown that the avoided crossing of LiF can be localized using only ground state properties, namely one-orbital entanglement. PMID:25844072

Time-Dependent Moment Tensors of the First Four Source Physics Experiments (SPE) Explosions

NASA Astrophysics Data System (ADS)

Yang, X.

2015-12-01

We use mainly vertical-component geophone data within 2 km from the epicenter to invert for time-dependent moment tensors of the first four SPE explosions: SPE-1, SPE-2, SPE-3 and SPE-4Prime. We employ a one-dimensional (1D) velocity model developed from P- and Rg-wave travel times for Green's function calculations. The attenuation structure of the model is developed from P- and Rg-wave amplitudes. We select data for the inversion based on the criterion that they show consistent travel times and amplitude behavior as those predicted by the 1D model. Due to limited azimuthal coverage of the sources and the mostly vertical-component-only nature of the dataset, only long-period, diagonal components of the moment tensors are well constrained. Nevertheless, the moment tensors, particularly their isotropic components, provide reasonable estimates of the long-period source amplitudes as well as estimates of corner frequencies, albeit with larger uncertainties. The estimated corner frequencies, however, are consistent with estimates from ratios of seismogram spectra from different explosions. These long-period source amplitudes and corner frequencies cannot be fit by classical P-wave explosion source models. The results motivate the development of new P-wave source models suitable for these chemical explosions. To that end, we fit inverted moment-tensor spectra by modifying the classical explosion model using regressions of estimated source parameters. Although the number of data points used in the regression is small, the approach suggests a way for the new-model development when more data are collected.

Moment-tensor solutions estimated using optimal filter theory: Global seismicity, 2001

USGS Publications Warehouse

Sipkin, S.A.; Bufe, C.G.; Zirbes, M.D.

2003-01-01

This paper is the 12th in a series published yearly containing moment-tensor solutions computed at the US Geological Survey using an algorithm based on the theory of optimal filter design (Sipkin, 1982 and Sipkin, 1986b). An inversion has been attempted for all earthquakes with a magnitude, mb or MS, of 5.5 or greater. Previous listings include solutions for earthquakes that occurred from 1981 to 2000 (Sipkin, 1986b; Sipkin and Needham, 1989, Sipkin and Needham, 1991, Sipkin and Needham, 1992, Sipkin and Needham, 1993, Sipkin and Needham, 1994a and Sipkin and Needham, 1994b; Sipkin and Zirbes, 1996 and Sipkin and Zirbes, 1997; Sipkin et al., 1998, Sipkin et al., 1999, Sipkin et al., 2000a, Sipkin et al., 2000b and Sipkin et al., 2002).The entire USGS moment-tensor catalog can be obtained via anonymous FTP at ftp://ghtftp.cr.usgs.gov. After logging on, change directory to “momten”. This directory contains two compressed ASCII files that contain the finalized solutions, “mt.lis.Z” and “fmech.lis.Z”. “mt.lis.Z” contains the elements of the moment tensors along with detailed event information; “fmech.lis.Z” contains the decompositions into the principal axes and best double-couples. The fast moment-tensor solutions for more recent events that have not yet been finalized and added to the catalog, are gathered by month in the files “jan01.lis.Z”, etc. “fmech.doc.Z” describes the various fields.

Crustal stress across the northern Arabian plate and the relationship with the plate boundary forces

NASA Astrophysics Data System (ADS)

Yassminh, Rayan

The region encompassing the collision of northern Arabia with Eurasia is a tectonically heterogeneous region of distributed deformation. The northern Arabia plate is bounded to the west by the subducting Sinai plate and the left-lateral Dead Sea transform. This complexity suggests that there are multiple competing processes that may influence regional tectonics in northern Arabia and adjacent areas. Earthquake mechanisms provide insight into crustal kinematics and stress; however, reliable determination of earthquake source parameters can be challenging in a complex geological region, such as the continental collision zone between the Arabian and Eurasian plates. The goal of this study is to investigate spatial patterns of the crustal stress in the northern Arabian plate and surrounding area. The focal mechanisms used in this study are based on (1) first-motion polarities for earthquakes recorded by Syrian earthquake center during 2000-2011, and (2) regional moment tensors from broadband seismic data, from Turkey and Iraq. First motion focal mechanisms were assigned quality classifications based on the variation of both nodal planes. Regional moment tensor analysis can be significantly influenced by seismic velocity structure; thus, we have divided the study area into regions based on tectonic units. For each region, the velocity model is described using a waveform-modeling technique prior to the regional moment tensor inversion. The resulting focal mechanisms, combined with other previously published focal mechanisms for the study area, provide a basis for stress inversion analysis. The resulting deviatoric stress tensors show the spatial distribution of the maximum horizontal stress varies from NW-SE along the Dead Sea Fault to the N-S toward the east. We interpret this to reflect the eastward change from the transform to collision processes in northern Arabia. Along the Dead Sea Fault, transposition of the sigma-1 and sigma-2 to vertical and horizontal, respectively, may relate to influences from the subducted part of the Sinai plate. This change in regional stress is also consistent with extensional strains observed from GPS velocities.

Motion Detection in Ultrasound Image-Sequences Using Tensor Voting

NASA Astrophysics Data System (ADS)

Inba, Masafumi; Yanagida, Hirotaka; Tamura, Yasutaka

2008-05-01

Motion detection in ultrasound image sequences using tensor voting is described. We have been developing an ultrasound imaging system adopting a combination of coded excitation and synthetic aperture focusing techniques. In our method, frame rate of the system at distance of 150 mm reaches 5000 frame/s. Sparse array and short duration coded ultrasound signals are used for high-speed data acquisition. However, many artifacts appear in the reconstructed image sequences because of the incompleteness of the transmitted code. To reduce the artifacts, we have examined the application of tensor voting to the imaging method which adopts both coded excitation and synthetic aperture techniques. In this study, the basis of applying tensor voting and the motion detection method to ultrasound images is derived. It was confirmed that velocity detection and feature enhancement are possible using tensor voting in the time and space of simulated ultrasound three-dimensional image sequences.

Designing Feature and Data Parallel Stochastic Coordinate Descent Method forMatrix and Tensor Factorization

DTIC Science & Technology

2016-05-11

AFRL-AFOSR-JP-TR-2016-0046 Designing Feature and Data Parallel Stochastic Coordinate Descent Method for Matrix and Tensor Factorization U Kang Korea...maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or   any other aspect...Designing Feature and Data Parallel Stochastic Coordinate Descent Method for Matrix and Tensor Factorization 5a.  CONTRACT NUMBER 5b.  GRANT NUMBER FA2386

Density functional theory calculations of 95Mo NMR parameters in solid-state compounds.

PubMed

Cuny, Jérôme; Furet, Eric; Gautier, Régis; Le Pollès, Laurent; Pickard, Chris J; d'Espinose de Lacaillerie, Jean-Baptiste

2009-12-21

The application of periodic density functional theory-based methods to the calculation of (95)Mo electric field gradient (EFG) and chemical shift (CS) tensors in solid-state molybdenum compounds is presented. Calculations of EFG tensors are performed using the projector augmented-wave (PAW) method. Comparison of the results with those obtained using the augmented plane wave + local orbitals (APW+lo) method and with available experimental values shows the reliability of the approach for (95)Mo EFG tensor calculation. CS tensors are calculated using the recently developed gauge-including projector augmented-wave (GIPAW) method. This work is the first application of the GIPAW method to a 4d transition-metal nucleus. The effects of ultra-soft pseudo-potential parameters, exchange-correlation functionals and structural parameters are precisely examined. Comparison with experimental results allows the validation of this computational formalism.

Rational first integrals of geodesic equations and generalised hidden symmetries

NASA Astrophysics Data System (ADS)

Aoki, Arata; Houri, Tsuyoshi; Tomoda, Kentaro

2016-10-01

We discuss novel generalisations of Killing tensors, which are introduced by considering rational first integrals of geodesic equations. We introduce the notion of inconstructible generalised Killing tensors, which cannot be constructed from ordinary Killing tensors. Moreover, we introduce inconstructible rational first integrals, which are constructed from inconstructible generalised Killing tensors, and provide a method for checking the inconstructibility of a rational first integral. Using the method, we show that the rational first integral of the Collinson-O’Donnell solution is not inconstructible. We also provide several examples of metrics admitting an inconstructible rational first integral in two and four-dimensions, by using the Maciejewski-Przybylska system. Furthermore, we attempt to generalise other hidden symmetries such as Killing-Yano tensors.

Long period seismic signals observed before the Caldera formation during the 2000 Miyake- jima volcanic activity

NASA Astrophysics Data System (ADS)

Ohminato, T.; Kobayashi, T.; Ida, Y.; Fujita, E.

2006-12-01

During the 2000 Miyake-jima volcanic activity started on 26 June 2000, an intense earthquake swarm occurred initially beneath the southwest flank near the summit and gradually migrated west of the island. A volcanic earthquake activity in the island was reactivated beneath the summit, leading to a summit eruption with a significant summit subsidence on 8 July. We detected small but numerous number of long period (LP) seismic signals during these activities. Most of them include both 0.2 and 0.4 Hz components suggesting an existence of a harmonic oscillator. Some of them have dominant frequency peak at 0.2Hz (LP1), while others have one at 0.4 Hz (LP2). At the beginning of each waveform of both LP1 and LP2, an impulsive signal with a pulse-width of about 2 s is clearly identified. The major axis of the particle motion for the initial impulsive signal is almost horizontal suggesting a shallow source beneath the summit, while the inclined particle motion for the latter phase suggests deeper source beneath the island. For both LP1 and LP2, we can identify a clear positive correlation between the amplitude of the initial pulse and that of the latter phase. We conducted waveform inversions for the LP events assuming a point source and determined the locations and mechanisms simultaneously. We assumed three types of source mechanisms; three single forces, six moment tensor components, and a combination of moment tensor and single forces. We used AIC to decide the optimal solutions. Firstly, we applied the method to the entire waveform including both the initial pulse and the latter phase. The source type with a combination of moment tensor and single force components yields the minimum values of the AIC for both LP events. However, the spatial distribution of the residual errors tends to have two local minima. Considering the error distribution and the characteristic particle motions, it is likely that the source of the LP event consists of two different parts. We thus divided the LP events into two parts; the initial and the latter phases, and applied the same waveform inversion procedure separately for each part of the waveform. The inversion results show that the initial impulsive phase and the latter oscillatory phase are well explained by a nearly horizontal single force and a moment solution, respectively. The single force solutions of the initial pulse are positioned at the depth of about 2 km beneath the summit. The single force initially oriented to the north, and then to the south. On the other hand, the sources of the moment solutions are significantly deeper than the single force solutions. The hypocenter of the later phase of LP1 is located at the depth of 5.5 km in the southern region of the island, while that for the LP2 event is at 5.1 km beneath the summit. The horizontal oscillations are relatively dominant for both the LP1 and LP2 events. Although the two sources are separated each other by several kilometers, the positive correlation between the amplitudes of the initial pulse and the latter phase strongly suggests that the shallow sources trigger the deeper sources. The source time histories of the 6 moment tensor components of the latter portion of the LP1 and LP2 are not in phase. This makes it difficult to extract information on source geometry using the amplitude ratio among moment tensor components in a traditional manner. It may suggest that the source is composed of two independent sources whose oscillations are out of phase.

Fast multipole method using Cartesian tensor in beam dynamic simulation

DOE PAGES

Zhang, He; Huang, He; Li, Rui; ...

2017-03-06

Here, the fast multipole method (FMM) using traceless totally symmetric Cartesian tensor to calculate the Coulomb interaction between charged particles will be presented. The Cartesian tensor-based FMM can be generalized to treat other non-oscillating interactions with the help of the differential algebra or the truncated power series algebra. Issues on implementation of the FMM in beam dynamic simulations are also discussed.

Very low frequency earthquakes (VLFEs) detected during episodic tremor and slip (ETS) events in Cascadia using a match filter method indicate repeating events

NASA Astrophysics Data System (ADS)

Hutchison, A. A.; Ghosh, A.

2016-12-01

Very low frequency earthquakes (VLFEs) occur in transitional zones of faults, releasing seismic energy in the 0.02-0.05 Hz frequency band over a 90 s duration and typically have magntitudes within the range of Mw 3.0-4.0. VLFEs can occur down-dip of the seismogenic zone, where they can transfer stress up-dip potentially bringing the locked zone closer to a critical failure stress. VLFEs also occur up-dip of the seismogenic zone in a region along the plate interface that can rupture coseismically during large megathrust events, such as the 2011 Tohoku-Oki earthquake [Ide et al., 2011]. VLFEs were first detected in Cascadia during the 2011 episodic tremor and slip (ETS) event, occurring coincidentally with tremor [Ghosh et al., 2015]. However, during the 2014 ETS event, VLFEs were spatially and temporally asynchronous with tremor activity [Hutchison and Ghosh, 2016]. Such contrasting behaviors remind us that the mechanics behind such events remain elusive, yet they are responsible for the largest portion of the moment release during an ETS event. Here, we apply a match filter method using known VLFEs as template events to detect additional VLFEs. Using a grid-search centroid moment tensor inversion method, we invert stacks of the resulting match filter detections to ensure moment tensor solutions are similar to that of the respective template events. Our ability to successfully employ a match filter method to VLFE detection in Cascadia intrinsically indicates that these events can be repeating, implying that the same asperities are likely responsible for generating multiple VLFEs.

Study of the Rock Mass Failure Process and Mechanisms During the Transformation from Open-Pit to Underground Mining Based on Microseismic Monitoring

NASA Astrophysics Data System (ADS)

Zhao, Yong; Yang, Tianhong; Bohnhoff, Marco; Zhang, Penghai; Yu, Qinglei; Zhou, Jingren; Liu, Feiyue

2018-05-01

To quantitatively understand the failure process and failure mechanism of a rock mass during the transformation from open-pit mining to underground mining, the Shirengou Iron Mine was selected as an engineering project case study. The study area was determined using the rock mass basic quality classification method and the kinematic analysis method. Based on the analysis of the variations in apparent stress and apparent volume over time, the rock mass failure process was analyzed. According to the recent research on the temporal and spatial change of microseismic events in location, energy, apparent stress, and displacement, the migration characteristics of rock mass damage were studied. A hybrid moment tensor inversion method was used to determine the rock mass fracture source mechanisms, the fracture orientations, and fracture scales. The fracture area can be divided into three zones: Zone A, Zone B, and Zone C. A statistical analysis of the orientation information of the fracture planes orientations was carried out, and four dominant fracture planes were obtained. Finally, the slip tendency analysis method was employed, and the unstable fracture planes were obtained. The results show: (1) The microseismic monitoring and hybrid moment tensor analysis can effectively analyze the failure process and failure mechanism of rock mass, (2) during the transformation from open-pit to underground mining, the failure type of rock mass is mainly shear failure and the tensile failure is mostly concentrated in the roof of goafs, and (3) the rock mass of the pit bottom and the upper of goaf No. 18 have the possibility of further damage.

An efficient tensor transpose algorithm for multicore CPU, Intel Xeon Phi, and NVidia Tesla GPU

DOE PAGES

Lyakh, Dmitry I.

2015-01-05

An efficient parallel tensor transpose algorithm is suggested for shared-memory computing units, namely, multicore CPU, Intel Xeon Phi, and NVidia GPU. The algorithm operates on dense tensors (multidimensional arrays) and is based on the optimization of cache utilization on x86 CPU and the use of shared memory on NVidia GPU. From the applied side, the ultimate goal is to minimize the overhead encountered in the transformation of tensor contractions into matrix multiplications in computer implementations of advanced methods of quantum many-body theory (e.g., in electronic structure theory and nuclear physics). A particular accent is made on higher-dimensional tensors that typicallymore » appear in the so-called multireference correlated methods of electronic structure theory. Depending on tensor dimensionality, the presented optimized algorithms can achieve an order of magnitude speedup on x86 CPUs and 2-3 times speedup on NVidia Tesla K20X GPU with respect to the na ve scattering algorithm (no memory access optimization). Furthermore, the tensor transpose routines developed in this work have been incorporated into a general-purpose tensor algebra library (TAL-SH).« less

Tensor Train Neighborhood Preserving Embedding

NASA Astrophysics Data System (ADS)

Wang, Wenqi; Aggarwal, Vaneet; Aeron, Shuchin

2018-05-01

In this paper, we propose a Tensor Train Neighborhood Preserving Embedding (TTNPE) to embed multi-dimensional tensor data into low dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For this embedding, we evaluate novel trade-off gain among classification, computation, and dimensionality reduction (storage) for supervised learning. It is shown that compared to the state-of-the-arts tensor embedding methods, TTNPE achieves superior trade-off in classification, computation, and dimensionality reduction in MNIST handwritten digits and Weizmann face datasets.

Elastic full waveform inversion based on the homogenization method: theoretical framework and 2-D numerical illustrations

NASA Astrophysics Data System (ADS)

Capdeville, Yann; Métivier, Ludovic

2018-05-01

Seismic imaging is an efficient tool to investigate the Earth interior. Many of the different imaging techniques currently used, including the so-called full waveform inversion (FWI), are based on limited frequency band data. Such data are not sensitive to the true earth model, but to a smooth version of it. This smooth version can be related to the true model by the homogenization technique. Homogenization for wave propagation in deterministic media with no scale separation, such as geological media, has been recently developed. With such an asymptotic theory, it is possible to compute an effective medium valid for a given frequency band such that effective waveforms and true waveforms are the same up to a controlled error. In this work we make the link between limited frequency band inversion, mainly FWI, and homogenization. We establish the relation between a true model and an FWI result model. This relation is important for a proper interpretation of FWI images. We numerically illustrate, in the 2-D case, that an FWI result is at best the homogenized version of the true model. Moreover, it appears that the homogenized FWI model is quite independent of the FWI parametrization, as long as it has enough degrees of freedom. In particular, inverting for the full elastic tensor is, in each of our tests, always a good choice. We show how the homogenization can help to understand FWI behaviour and help to improve its robustness and convergence by efficiently constraining the solution space of the inverse problem.

Gradients estimation from random points with volumetric tensor in turbulence

NASA Astrophysics Data System (ADS)

Watanabe, Tomoaki; Nagata, Koji

2017-12-01

We present an estimation method of fully-resolved/coarse-grained gradients from randomly distributed points in turbulence. The method is based on a linear approximation of spatial gradients expressed with the volumetric tensor, which is a 3 × 3 matrix determined by a geometric distribution of the points. The coarse grained gradient can be considered as a low pass filtered gradient, whose cutoff is estimated with the eigenvalues of the volumetric tensor. The present method, the volumetric tensor approximation, is tested for velocity and passive scalar gradients in incompressible planar jet and mixing layer. Comparison with a finite difference approximation on a Cartesian grid shows that the volumetric tensor approximation computes the coarse grained gradients fairly well at a moderate computational cost under various conditions of spatial distributions of points. We also show that imposing the solenoidal condition improves the accuracy of the present method for solenoidal vectors, such as a velocity vector in incompressible flows, especially when the number of the points is not large. The volumetric tensor approximation with 4 points poorly estimates the gradient because of anisotropic distribution of the points. Increasing the number of points from 4 significantly improves the accuracy. Although the coarse grained gradient changes with the cutoff length, the volumetric tensor approximation yields the coarse grained gradient whose magnitude is close to the one obtained by the finite difference. We also show that the velocity gradient estimated with the present method well captures the turbulence characteristics such as local flow topology, amplification of enstrophy and strain, and energy transfer across scales.

Research on maximum level noise contaminated of remote reference magnetotelluric measurements using synthesized data

NASA Astrophysics Data System (ADS)

Gang, Zhang; Fansong, Meng; Jianzhong, Wang; Mingtao, Ding

2018-02-01

Determining magnetotelluric impedance precisely and accurately is fundamental to valid inversion and geological interpretation. This study aims to determine the minimum value of signal-to-noise ratio (SNR) which maintains the effectiveness of remote reference technique. Results of standard time series simulation, addition of different Gaussian noises to obtain the different SNR time series, and analysis of the intermediate data, such as polarization direction, correlation coefficient, and impedance tensor, show that when the SNR value is larger than 23.5743, the polarization direction disorder at morphology and a smooth and accurate sounding carve value can be obtained. At this condition, the correlation coefficient value of nearly complete segments between the base and remote station is larger than 0.9, and impedance tensor Zxy presents only one aggregation, which meet the natural magnetotelluric signal characteristic.

Chameleons with field-dependent couplings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brax, Philippe; Bruck, Carsten van de; Mota, David F.

2010-10-15

Certain scalar-tensor theories exhibit the so-called chameleon mechanism, whereby observational signatures of scalar fields are hidden by a combination of self-interactions and interactions with ambient matter. Not all scalar-tensor theories exhibit such a chameleon mechanism, which has been originally found in models with inverse power runaway potentials and field-independent couplings to matter. In this paper we investigate field theories with field-dependent couplings and a power-law potential for the scalar field. We show that the theory indeed is a chameleon field theory. We find the thin-shell solution for a spherical body and investigate the consequences for Eoet-Wash experiments, fifth-force searches andmore » Casimir-force experiments. Requiring that the scalar field evades gravitational tests, we find that the coupling is sensitive to a mass scale which is of order of the Hubble scale today.« less

Interpolation of orientation distribution functions in diffusion weighted imaging using multi-tensor model.

PubMed

Afzali, Maryam; Fatemizadeh, Emad; Soltanian-Zadeh, Hamid

2015-09-30

Diffusion weighted imaging (DWI) is a non-invasive method for investigating the brain white matter structure and can be used to evaluate fiber bundles. However, due to practical constraints, DWI data acquired in clinics are low resolution. This paper proposes a method for interpolation of orientation distribution functions (ODFs). To this end, fuzzy clustering is applied to segment ODFs based on the principal diffusion directions (PDDs). Next, a cluster is modeled by a tensor so that an ODF is represented by a mixture of tensors. For interpolation, each tensor is rotated separately. The method is applied on the synthetic and real DWI data of control and epileptic subjects. Both experiments illustrate capability of the method in increasing spatial resolution of the data in the ODF field properly. The real dataset show that the method is capable of reliable identification of differences between temporal lobe epilepsy (TLE) patients and normal subjects. The method is compared to existing methods. Comparison studies show that the proposed method generates smaller angular errors relative to the existing methods. Another advantage of the method is that it does not require an iterative algorithm to find the tensors. The proposed method is appropriate for increasing resolution in the ODF field and can be applied to clinical data to improve evaluation of white matter fibers in the brain. Copyright © 2015 Elsevier B.V. All rights reserved.

Toward regional corrections of long period CMT inversions using InSAR

NASA Astrophysics Data System (ADS)

Shakibay Senobari, N.; Funning, G.; Ferreira, A. M.

2017-12-01

One of InSAR's main strengths, with respect to other methods of studying earthquakes, is finding the accurate location of the best point source (or `centroid') for an earthquake. While InSAR data have great advantages for study of shallow earthquakes, the number of earthquakes for which we have InSAR data is low, compared with the number of earthquakes recorded seismically. And though improvements to SAR satellite constellations have enhanced the use of InSAR data during earthquake response, post-event data still have a latency on the order of days. On the other hand, earthquake centroid inversion methods using long period seismic data (e.g. the Global CMT method) are fast but include errors caused by inaccuracies in both the Earth velocity model and in wave propagation assumptions (e.g. Hjörleifsdóttir and Ekström, 2010; Ferreira and Woodhouse, 2006). Here we demonstrate a method that combines the strengths of both methods, calculating regional travel-time corrections for long-period waveforms using accurate centroid locations from InSAR, then applying these to other events that occur in the same region. Our method is based on the observation that synthetic seismograms produced from InSAR source models and locations match the data very well except for some phase shifts (travel time biases) between the two waveforms, likely corresponding to inaccuracies in Earth velocity models (Weston et al., 2014). Our previous work shows that adding such phase shifts to the Green's functions can improve the accuracy of long period seismic CMT inversions by reducing tradeoffs between the moment tensor components and centroid location (e.g. Shakibay Senobari et al., AGU Fall Meeting 2015). Preliminary work on several pairs of neighboring events (e.g. Landers-Hector Mine, the 2000 South Iceland earthquake sequences) shows consistent azimuthal patterns of these phase shifts for nearby events at common stations. These phase shift patterns strongly suggest that it is possible to determine regional corrections for the source regions of these events. The aim of this project is to perform a full CMT inversion using the phase shift corrections, calculated for nearby events, to observe improvement in CMT locations and solutions. We will demonstrate our method on the five M 6 events that occurred in central Italy between 1997 and 2016.

Accelerated High-Dimensional MR Imaging with Sparse Sampling Using Low-Rank Tensors

PubMed Central

He, Jingfei; Liu, Qiegen; Christodoulou, Anthony G.; Ma, Chao; Lam, Fan

2017-01-01

High-dimensional MR imaging often requires long data acquisition time, thereby limiting its practical applications. This paper presents a low-rank tensor based method for accelerated high-dimensional MR imaging using sparse sampling. This method represents high-dimensional images as low-rank tensors (or partially separable functions) and uses this mathematical structure for sparse sampling of the data space and for image reconstruction from highly undersampled data. More specifically, the proposed method acquires two datasets with complementary sampling patterns, one for subspace estimation and the other for image reconstruction; image reconstruction from highly undersampled data is accomplished by fitting the measured data with a sparsity constraint on the core tensor and a group sparsity constraint on the spatial coefficients jointly using the alternating direction method of multipliers. The usefulness of the proposed method is demonstrated in MRI applications; it may also have applications beyond MRI. PMID:27093543

Improve the efficiency of the Cartesian tensor based fast multipole method for Coulomb interaction using the traces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huang, He; Luo, Li -Shi; Li, Rui

To compute the non-oscillating mutual interaction for a systems with N points, the fast multipole method (FMM) has an efficiency that scales linearly with the number of points. Specifically, for Coulomb interaction, FMM can be constructed using either the spherical harmonic functions or the totally symmetric Cartesian tensors. In this paper, we will present that the effciency of the Cartesian tensor-based FMM for the Coulomb interaction can be significantly improved by implementing the traces of the Cartesian tensors in calculation to reduce the independent elements of the n-th rank totally symmetric Cartesian tensor from (n + 1)(n + 2)=2 tomore » 2n + 1. The computation complexity for the operations in FMM are analyzed and expressed as polynomials of the highest rank of the Cartesian tensors. For most operations, the complexity is reduced by one order. Numerical examples regarding the convergence and the effciency of the new algorithm are demonstrated. As a result, a reduction of computation time up to 50% has been observed for a moderate number of points and rank of tensors.« less

Improve the efficiency of the Cartesian tensor based fast multipole method for Coulomb interaction using the traces

DOE PAGES

Huang, He; Luo, Li -Shi; Li, Rui; ...

2018-05-17

To compute the non-oscillating mutual interaction for a systems with N points, the fast multipole method (FMM) has an efficiency that scales linearly with the number of points. Specifically, for Coulomb interaction, FMM can be constructed using either the spherical harmonic functions or the totally symmetric Cartesian tensors. In this paper, we will present that the effciency of the Cartesian tensor-based FMM for the Coulomb interaction can be significantly improved by implementing the traces of the Cartesian tensors in calculation to reduce the independent elements of the n-th rank totally symmetric Cartesian tensor from (n + 1)(n + 2)=2 tomore » 2n + 1. The computation complexity for the operations in FMM are analyzed and expressed as polynomials of the highest rank of the Cartesian tensors. For most operations, the complexity is reduced by one order. Numerical examples regarding the convergence and the effciency of the new algorithm are demonstrated. As a result, a reduction of computation time up to 50% has been observed for a moderate number of points and rank of tensors.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lyakh, Dmitry I.

An efficient parallel tensor transpose algorithm is suggested for shared-memory computing units, namely, multicore CPU, Intel Xeon Phi, and NVidia GPU. The algorithm operates on dense tensors (multidimensional arrays) and is based on the optimization of cache utilization on x86 CPU and the use of shared memory on NVidia GPU. From the applied side, the ultimate goal is to minimize the overhead encountered in the transformation of tensor contractions into matrix multiplications in computer implementations of advanced methods of quantum many-body theory (e.g., in electronic structure theory and nuclear physics). A particular accent is made on higher-dimensional tensors that typicallymore » appear in the so-called multireference correlated methods of electronic structure theory. Depending on tensor dimensionality, the presented optimized algorithms can achieve an order of magnitude speedup on x86 CPUs and 2-3 times speedup on NVidia Tesla K20X GPU with respect to the na ve scattering algorithm (no memory access optimization). Furthermore, the tensor transpose routines developed in this work have been incorporated into a general-purpose tensor algebra library (TAL-SH).« less

Simplified derivation of the gravitational wave stress tensor from the linearized Einstein field equations.

PubMed

Balbus, Steven A

2016-10-18

A conserved stress energy tensor for weak field gravitational waves propagating in vacuum is derived directly from the linearized general relativistic wave equation alone, for an arbitrary gauge. In any harmonic gauge, the form of the tensor leads directly to the classical expression for the outgoing wave energy. The method described here, however, is a much simpler, shorter, and more physically motivated approach than is the customary procedure, which involves a lengthy and cumbersome second-order (in wave-amplitude) calculation starting with the Einstein tensor. Our method has the added advantage of exhibiting the direct coupling between the outgoing wave energy flux and the work done by the gravitational field on the sources. For nonharmonic gauges, the directly derived wave stress tensor has an apparent index asymmetry. This coordinate artifact may be straightforwardly removed, and the symmetrized (still gauge-invariant) tensor then takes on its widely used form. Angular momentum conservation follows immediately. For any harmonic gauge, however, the stress tensor found is manifestly symmetric from the start, and its derivation depends, in its entirety, on the structure of the linearized wave equation.

Tensor scale: An analytic approach with efficient computation and applications☆

PubMed Central

Xu, Ziyue; Saha, Punam K.; Dasgupta, Soura

2015-01-01

Scale is a widely used notion in computer vision and image understanding that evolved in the form of scale-space theory where the key idea is to represent and analyze an image at various resolutions. Recently, we introduced a notion of local morphometric scale referred to as “tensor scale” using an ellipsoidal model that yields a unified representation of structure size, orientation and anisotropy. In the previous work, tensor scale was described using a 2-D algorithmic approach and a precise analytic definition was missing. Also, the application of tensor scale in 3-D using the previous framework is not practical due to high computational complexity. In this paper, an analytic definition of tensor scale is formulated for n-dimensional (n-D) images that captures local structure size, orientation and anisotropy. Also, an efficient computational solution in 2- and 3-D using several novel differential geometric approaches is presented and the accuracy of results is experimentally examined. Also, a matrix representation of tensor scale is derived facilitating several operations including tensor field smoothing to capture larger contextual knowledge. Finally, the applications of tensor scale in image filtering and n-linear interpolation are presented and the performance of their results is examined in comparison with respective state-of-art methods. Specifically, the performance of tensor scale based image filtering is compared with gradient and Weickert’s structure tensor based diffusive filtering algorithms. Also, the performance of tensor scale based n-linear interpolation is evaluated in comparison with standard n-linear and windowed-sinc interpolation methods. PMID:26236148

Simultaneous Tensor Decomposition and Completion Using Factor Priors.

PubMed

Chen, Yi-Lei; Hsu, Chiou-Ting Candy; Liao, Hong-Yuan Mark

2013-08-27

Tensor completion, which is a high-order extension of matrix completion, has generated a great deal of research interest in recent years. Given a tensor with incomplete entries, existing methods use either factorization or completion schemes to recover the missing parts. However, as the number of missing entries increases, factorization schemes may overfit the model because of incorrectly predefined ranks, while completion schemes may fail to interpret the model factors. In this paper, we introduce a novel concept: complete the missing entries and simultaneously capture the underlying model structure. To this end, we propose a method called Simultaneous Tensor Decomposition and Completion (STDC) that combines a rank minimization technique with Tucker model decomposition. Moreover, as the model structure is implicitly included in the Tucker model, we use factor priors, which are usually known a priori in real-world tensor objects, to characterize the underlying joint-manifold drawn from the model factors. We conducted experiments to empirically verify the convergence of our algorithm on synthetic data, and evaluate its effectiveness on various kinds of real-world data. The results demonstrate the efficacy of the proposed method and its potential usage in tensor-based applications. It also outperforms state-of-the-art methods on multilinear model analysis and visual data completion tasks.

Development of the Tensoral Computer Language

NASA Technical Reports Server (NTRS)

Ferziger, Joel; Dresselhaus, Eliot

1996-01-01

The research scientist or engineer wishing to perform large scale simulations or to extract useful information from existing databases is required to have expertise in the details of the particular database, the numerical methods and the computer architecture to be used. This poses a significant practical barrier to the use of simulation data. The goal of this research was to develop a high-level computer language called Tensoral, designed to remove this barrier. The Tensoral language provides a framework in which efficient generic data manipulations can be easily coded and implemented. First of all, Tensoral is general. The fundamental objects in Tensoral represent tensor fields and the operators that act on them. The numerical implementation of these tensors and operators is completely and flexibly programmable. New mathematical constructs and operators can be easily added to the Tensoral system. Tensoral is compatible with existing languages. Tensoral tensor operations co-exist in a natural way with a host language, which may be any sufficiently powerful computer language such as Fortran, C, or Vectoral. Tensoral is very-high-level. Tensor operations in Tensoral typically act on entire databases (i.e., arrays) at one time and may, therefore, correspond to many lines of code in a conventional language. Tensoral is efficient. Tensoral is a compiled language. Database manipulations are simplified optimized and scheduled by the compiler eventually resulting in efficient machine code to implement them.

Bayesian inference and interpretation of centroid moment tensors of the 2016 Kumamoto earthquake sequence, Kyushu, Japan

NASA Astrophysics Data System (ADS)

Hallo, Miroslav; Asano, Kimiyuki; Gallovič, František

2017-09-01

On April 16, 2016, Kumamoto prefecture in Kyushu region, Japan, was devastated by a shallow M JMA7.3 earthquake. The series of foreshocks started by M JMA6.5 foreshock 28 h before the mainshock. They have originated in Hinagu fault zone intersecting the mainshock Futagawa fault zone; hence, the tectonic background for this earthquake sequence is rather complex. Here we infer centroid moment tensors (CMTs) for 11 events with M JMA between 4.8 and 6.5, using strong motion records of the K-NET, KiK-net and F-net networks. We use upgraded Bayesian full-waveform inversion code ISOLA-ObsPy, which takes into account uncertainty of the velocity model. Such an approach allows us to reliably assess uncertainty of the CMT parameters including the centroid position. The solutions show significant systematic spatial and temporal variations throughout the sequence. Foreshocks are right-lateral steeply dipping strike-slip events connected to the NE-SW shear zone. Those located close to the intersection of the Hinagu and Futagawa fault zones are dipping slightly to ESE, while those in the southern area are dipping to WNW. Contrarily, aftershocks are mostly normal dip-slip events, being related to the N-S extensional tectonic regime. Most of the deviatoric moment tensors contain only minor CLVD component, which can be attributed to the velocity model uncertainty. Nevertheless, two of the CMTs involve a significant CLVD component, which may reflect complex rupture process. Decomposition of those moment tensors into two pure shear moment tensors suggests combined right-lateral strike-slip and normal dip-slip mechanisms, consistent with the tectonic settings of the intersection of the Hinagu and Futagawa fault zones.[Figure not available: see fulltext.

Multimodal MRI in cerebral small vessel disease: its relationship with cognition and sensitivity to change over time.

PubMed

Nitkunan, Arani; Barrick, Tom R; Charlton, Rebecca A; Clark, Chris A; Markus, Hugh S

2008-07-01

Cerebral small vessel disease is the most common cause of vascular dementia. Interest in using MRI parameters as surrogate markers of disease to assess therapies is increasing. In patients with symptomatic sporadic small vessel disease, we determined which MRI parameters best correlated with cognitive function on cross-sectional analysis and which changed over a period of 1 year. Thirty-five patients with lacunar stroke and leukoaraiosis were recruited. They underwent multimodal MRI (brain volume, fluid-attenuated inversion recovery lesion load, lacunar infarct number, fractional anisotropy, and mean diffusivity from diffusion tensor imaging) and neuropsychological testing. Twenty-seven agreed to reattend for repeat MRI and neuropsychology at 1 year. An executive function score correlated most strongly with diffusion tensor imaging (fractional anisotropy histogram, r=-0.640, P=0.004) and brain volume (r=0.501, P=0.034). Associations with diffusion tensor imaging were stronger than with all other MRI parameters. On multiple regression of all imaging parameters, a model that contained brain volume and fractional anisotropy, together with age, gender, and premorbid IQ, explained 74% of the variance of the executive function score (P=0.0001). Changes in mean diffusivity and fractional anisotropy were detectable over the 1-year follow-up; in contrast, no change in other MRI parameters was detectable over this time period. A multimodal MRI model explains a large proportion of the variation in executive function in cerebral small vessel disease. In particular, diffusion tensor imaging correlates best with executive function and is the most sensitive to change. This supports the use of MRI, in particular diffusion tensor imaging, as a surrogate marker in treatment trials.

Solving large-scale PDE-constrained Bayesian inverse problems with Riemann manifold Hamiltonian Monte Carlo

NASA Astrophysics Data System (ADS)

Bui-Thanh, T.; Girolami, M.

2014-11-01

We consider the Riemann manifold Hamiltonian Monte Carlo (RMHMC) method for solving statistical inverse problems governed by partial differential equations (PDEs). The Bayesian framework is employed to cast the inverse problem into the task of statistical inference whose solution is the posterior distribution in infinite dimensional parameter space conditional upon observation data and Gaussian prior measure. We discretize both the likelihood and the prior using the H1-conforming finite element method together with a matrix transfer technique. The power of the RMHMC method is that it exploits the geometric structure induced by the PDE constraints of the underlying inverse problem. Consequently, each RMHMC posterior sample is almost uncorrelated/independent from the others providing statistically efficient Markov chain simulation. However this statistical efficiency comes at a computational cost. This motivates us to consider computationally more efficient strategies for RMHMC. At the heart of our construction is the fact that for Gaussian error structures the Fisher information matrix coincides with the Gauss-Newton Hessian. We exploit this fact in considering a computationally simplified RMHMC method combining state-of-the-art adjoint techniques and the superiority of the RMHMC method. Specifically, we first form the Gauss-Newton Hessian at the maximum a posteriori point and then use it as a fixed constant metric tensor throughout RMHMC simulation. This eliminates the need for the computationally costly differential geometric Christoffel symbols, which in turn greatly reduces computational effort at a corresponding loss of sampling efficiency. We further reduce the cost of forming the Fisher information matrix by using a low rank approximation via a randomized singular value decomposition technique. This is efficient since a small number of Hessian-vector products are required. The Hessian-vector product in turn requires only two extra PDE solves using the adjoint technique. Various numerical results up to 1025 parameters are presented to demonstrate the ability of the RMHMC method in exploring the geometric structure of the problem to propose (almost) uncorrelated/independent samples that are far away from each other, and yet the acceptance rate is almost unity. The results also suggest that for the PDE models considered the proposed fixed metric RMHMC can attain almost as high a quality performance as the original RMHMC, i.e. generating (almost) uncorrelated/independent samples, while being two orders of magnitude less computationally expensive.

Developing a Near Real-time System for Earthquake Slip Distribution Inversion

NASA Astrophysics Data System (ADS)

Zhao, Li; Hsieh, Ming-Che; Luo, Yan; Ji, Chen

2016-04-01

Advances in observational and computational seismology in the past two decades have enabled completely automatic and real-time determinations of the focal mechanisms of earthquake point sources. However, seismic radiations from moderate and large earthquakes often exhibit strong finite-source directivity effect, which is critically important for accurate ground motion estimations and earthquake damage assessments. Therefore, an effective procedure to determine earthquake rupture processes in near real-time is in high demand for hazard mitigation and risk assessment purposes. In this study, we develop an efficient waveform inversion approach for the purpose of solving for finite-fault models in 3D structure. Full slip distribution inversions are carried out based on the identified fault planes in the point-source solutions. To ensure efficiency in calculating 3D synthetics during slip distribution inversions, a database of strain Green tensors (SGT) is established for 3D structural model with realistic surface topography. The SGT database enables rapid calculations of accurate synthetic seismograms for waveform inversion on a regular desktop or even a laptop PC. We demonstrate our source inversion approach using two moderate earthquakes (Mw~6.0) in Taiwan and in mainland China. Our results show that 3D velocity model provides better waveform fitting with more spatially concentrated slip distributions. Our source inversion technique based on the SGT database is effective for semi-automatic, near real-time determinations of finite-source solutions for seismic hazard mitigation purposes.

Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination.

PubMed

Zhao, Qibin; Zhang, Liqing; Cichocki, Andrzej

2015-09-01

CANDECOMP/PARAFAC (CP) tensor factorization of incomplete data is a powerful technique for tensor completion through explicitly capturing the multilinear latent factors. The existing CP algorithms require the tensor rank to be manually specified, however, the determination of tensor rank remains a challenging problem especially for CP rank . In addition, existing approaches do not take into account uncertainty information of latent factors, as well as missing entries. To address these issues, we formulate CP factorization using a hierarchical probabilistic model and employ a fully Bayesian treatment by incorporating a sparsity-inducing prior over multiple latent factors and the appropriate hyperpriors over all hyperparameters, resulting in automatic rank determination. To learn the model, we develop an efficient deterministic Bayesian inference algorithm, which scales linearly with data size. Our method is characterized as a tuning parameter-free approach, which can effectively infer underlying multilinear factors with a low-rank constraint, while also providing predictive distributions over missing entries. Extensive simulations on synthetic data illustrate the intrinsic capability of our method to recover the ground-truth of CP rank and prevent the overfitting problem, even when a large amount of entries are missing. Moreover, the results from real-world applications, including image inpainting and facial image synthesis, demonstrate that our method outperforms state-of-the-art approaches for both tensor factorization and tensor completion in terms of predictive performance.

Synthetic velocity gradient tensors and the identification of statistically significant aspects of the structure of turbulence

NASA Astrophysics Data System (ADS)

Keylock, Christopher J.

2017-08-01

A method is presented for deriving random velocity gradient tensors given a source tensor. These synthetic tensors are constrained to lie within mathematical bounds of the non-normality of the source tensor, but we do not impose direct constraints upon scalar quantities typically derived from the velocity gradient tensor and studied in fluid mechanics. Hence, it becomes possible to ask hypotheses of data at a point regarding the statistical significance of these scalar quantities. Having presented our method and the associated mathematical concepts, we apply it to homogeneous, isotropic turbulence to test the utility of the approach for a case where the behavior of the tensor is understood well. We show that, as well as the concentration of data along the Vieillefosse tail, actual turbulence is also preferentially located in the quadrant where there is both excess enstrophy (Q>0 ) and excess enstrophy production (R<0 ). We also examine the topology implied by the strain eigenvalues and find that for the statistically significant results there is a particularly strong relative preference for the formation of disklike structures in the (Q<0 ,R<0 ) quadrant. With the method shown to be useful for a turbulence that is already understood well, it should be of even greater utility for studying complex flows seen in industry and the environment.

An enhanced structure tensor method for sea ice ridge detection from GF-3 SAR imagery

NASA Astrophysics Data System (ADS)

Zhu, T.; Li, F.; Zhang, Y.; Zhang, S.; Spreen, G.; Dierking, W.; Heygster, G.

2017-12-01

In SAR imagery, ridges or leads are shown as the curvilinear features. The proposed ridge detection method is facilitated by their curvilinear shapes. The bright curvilinear features are recognized as the ridges while the dark curvilinear features are classified as the leads. In dual-polarization HH or HV channel of C-band SAR imagery, the bright curvilinear feature may be false alarm because the frost flowers of young leads may show as bright pixels associated with changes in the surface salinity under calm surface conditions. Wind roughened leads also trigger the backscatter increasing that can be misclassified as ridges [1]. Thus the width limitation is considered in this proposed structure tensor method [2], since only shape feature based method is not enough for detecting ridges. The ridge detection algorithm is based on the hypothesis that the bright pixels are ridges with curvilinear shapes and the ridge width is less 30 meters. Benefited from GF-3 with high spatial resolution of 3 meters, we provide an enhanced structure tensor method for detecting the significant ridge. The preprocessing procedures including the calibration and incidence angle normalization are also investigated. The bright pixels will have strong response to the bandpass filtering. The ridge training samples are delineated from the SAR imagery in the Log-Gabor filters to construct structure tensor. From the tensor, the dominant orientation of the pixel representing the ridge is determined by the dominant eigenvector. For the post-processing of structure tensor, the elongated kernel is desired to enhance the ridge curvilinear shape. Since ridge presents along a certain direction, the ratio of the dominant eigenvector will be used to measure the intensity of local anisotropy. The convolution filter has been utilized in the constructed structure tensor is used to model spatial contextual information. Ridge detection results from GF-3 show the proposed method performs better compared to the direct threshold method.

Diffusion Tensor Image Registration Using Hybrid Connectivity and Tensor Features

PubMed Central

Wang, Qian; Yap, Pew-Thian; Wu, Guorong; Shen, Dinggang

2014-01-01

Most existing diffusion tensor imaging (DTI) registration methods estimate structural correspondences based on voxelwise matching of tensors. The rich connectivity information that is given by DTI, however, is often neglected. In this article, we propose to integrate complementary information given by connectivity features and tensor features for improved registration accuracy. To utilize connectivity information, we place multiple anchors representing different brain anatomies in the image space, and define the connectivity features for each voxel as the geodesic distances from all anchors to the voxel under consideration. The geodesic distance, which is computed in relation to the tensor field, encapsulates information of brain connectivity. We also extract tensor features for every voxel to reflect the local statistics of tensors in its neighborhood. We then combine both connectivity features and tensor features for registration of tensor images. From the images, landmarks are selected automatically and their correspondences are determined based on their connectivity and tensor feature vectors. The deformation field that deforms one tensor image to the other is iteratively estimated and optimized according to the landmarks and their associated correspondences. Experimental results show that, by using connectivity features and tensor features simultaneously, registration accuracy is increased substantially compared with the cases using either type of features alone. PMID:24293159

Late Pan-African and early Mesozoic brittle compressions in East and Central Africa: lithospheric deformation within the Congo-Tanzania Cratonic area

NASA Astrophysics Data System (ADS)

Delvaux, D.; Kipata, M. L.; Macheyeki, A. S.

2012-04-01

Tectonic reconstructions leading to the formation of the Central-African part of Gondwana have so far not much taken into account constraints provided by the evolution of brittle structures and related stress field. This is largely because little is known on continental brittle deformation in Equatorial Africa before the onset of the Mesozoic Central-African and Late Cenozoic East-African rifts. We present a synthesis of fault-kinematic data and paleostress inversion results from field surveys covering parts of Tanzania, Zambia and the Democratic Republic of Congo. It is based on investigations along the eastern margin of the Tanzanian craton, in the Ubendian belt between the Tanzanian craton and Bangweulu block, in the Lufilian Arc between the Kalahari and Congo cratons and along the Congo intracratonic basin. Paleostress tensors were computed for a substantial database by interactive stress tensor inversion and data subset separation, and the relative succession of major brittle events established. Two of them appear to be of regional importance and could be traced from one region to the other. The oldest one is the first brittle event recorded after the paroxysm of the Terminal Pan-African event that led to the amalgamation Gondwana at the Precambrian-Cambrian transition. It is related to compressional deformation with horizontal stress trajectories fluctuating from an E-W compression in Central Tanzania to NE-SW in the Ubende belt and Lufilian Arc. The second event is a transpressional inversion with a consistent NW-SE compression that we relate to the far-field effects of the active margin south of Gondwana during the late Triassic - early Jurassic.

Schizophrenia symptomatic associations with diffusion tensor imaging measured fractional anisotropy of brain: a meta-analysis.

PubMed

Yang, Xu; Cao, Ding; Liang, Xiumei; Zhao, Jiannong

2017-07-01

Several studies have examined the relationships between diffusion tensor imaging (DTI)-measured fractional anisotropy (FA) and the symptoms of schizophrenia, but results vary across the studies. The aim of this study was to carry out a meta-analysis of correlation coefficients reported by relevant studies to evaluate the correlative relationships between FA of various parts of the brain and schizophrenia symptomatic assessments. Literature was searched in several electronic databases, and study selection was based on précised eligibility criteria. Correlation coefficients between FA of a part of the brain and schizophrenia symptom were first converted into Fisher's z-scores for meta-analyses, and then overall effect sizes were back transformed to correlation coefficients. Thirty-three studies (1121 schizophrenia patients; age 32.66 years [95% confidence interval (CI) 30.19, 35.13]; 65.95 % [57.63, 74.28] males) were included in this meta-analysis. Age was inversely associated with brain FA (z-scores [95% CI] -0.23 [-0.14, -0.32]; p ˂ 0.00001). Brain FA of various areas was inversely associated with negative symptoms of schizophrenia (z-score -0.30 [-0.23, -0.36]; p ˂ 0.00001) but was positively associated with positive symptoms of schizophrenia (z-score 0.16 [0.04, 0.27]; p = 0.007) and general psychopathology of schizophrenia (z-score 0.26 [0.15, 0.37]; p = 0.00001). Although, DTI-measured brain FA is found to be inversely associated with negative symptoms and positively associated with positive symptoms and general psychopathology of schizophrenia, the effect sizes of these correlations are low and may not be clinically significant. Moreover, brain FA was also negatively associated with age of patients.

Invited review article: physics and Monte Carlo techniques as relevant to cryogenic, phonon, and ionization readout of Cryogenic Dark Matter Search radiation detectors.

PubMed

Leman, Steven W

2012-09-01

This review discusses detector physics and Monte Carlo techniques for cryogenic, radiation detectors that utilize combined phonon and ionization readout. A general review of cryogenic phonon and charge transport is provided along with specific details of the Cryogenic Dark Matter Search detector instrumentation. In particular, this review covers quasidiffusive phonon transport, which includes phonon focusing, anharmonic decay, and isotope scattering. The interaction of phonons in the detector surface is discussed along with the downconversion of phonons in superconducting films. The charge transport physics include a mass tensor which results from the crystal band structure and is modeled with a Herring-Vogt transformation. Charge scattering processes involve the creation of Neganov-Luke phonons. Transition-edge-sensor (TES) simulations include a full electric circuit description and all thermal processes including Joule heating, cooling to the substrate, and thermal diffusion within the TES, the latter of which is necessary to model normal-superconducting phase separation. Relevant numerical constants are provided for these physical processes in germanium, silicon, aluminum, and tungsten. Random number sampling methods including inverse cumulative distribution function (CDF) and rejection techniques are reviewed. To improve the efficiency of charge transport modeling, an additional second order inverse CDF method is developed here along with an efficient barycentric coordinate sampling method of electric fields. Results are provided in a manner that is convenient for use in Monte Carlo and references are provided for validation of these models.

Numerical Approximation of Elasticity Tensor Associated With Green-Naghdi Rate.

PubMed

Liu, Haofei; Sun, Wei

2017-08-01

Objective stress rates are often used in commercial finite element (FE) programs. However, deriving a consistent tangent modulus tensor (also known as elasticity tensor or material Jacobian) associated with the objective stress rates is challenging when complex material models are utilized. In this paper, an approximation method for the tangent modulus tensor associated with the Green-Naghdi rate of the Kirchhoff stress is employed to simplify the evaluation process. The effectiveness of the approach is demonstrated through the implementation of two user-defined fiber-reinforced hyperelastic material models. Comparisons between the approximation method and the closed-form analytical method demonstrate that the former can simplify the material Jacobian evaluation with satisfactory accuracy while retaining its computational efficiency. Moreover, since the approximation method is independent of material models, it can facilitate the implementation of complex material models in FE analysis using shell/membrane elements in abaqus.

LiDAR point classification based on sparse representation

NASA Astrophysics Data System (ADS)

Li, Nan; Pfeifer, Norbert; Liu, Chun

2017-04-01

In order to combine the initial spatial structure and features of LiDAR data for accurate classification. The LiDAR data is represented as a 4-order tensor. Sparse representation for classification(SRC) method is used for LiDAR tensor classification. It turns out SRC need only a few of training samples from each class, meanwhile can achieve good classification result. Multiple features are extracted from raw LiDAR points to generate a high-dimensional vector at each point. Then the LiDAR tensor is built by the spatial distribution and feature vectors of the point neighborhood. The entries of LiDAR tensor are accessed via four indexes. Each index is called mode: three spatial modes in direction X ,Y ,Z and one feature mode. Sparse representation for classification(SRC) method is proposed in this paper. The sparsity algorithm is to find the best represent the test sample by sparse linear combination of training samples from a dictionary. To explore the sparsity of LiDAR tensor, the tucker decomposition is used. It decomposes a tensor into a core tensor multiplied by a matrix along each mode. Those matrices could be considered as the principal components in each mode. The entries of core tensor show the level of interaction between the different components. Therefore, the LiDAR tensor can be approximately represented by a sparse tensor multiplied by a matrix selected from a dictionary along each mode. The matrices decomposed from training samples are arranged as initial elements in the dictionary. By dictionary learning, a reconstructive and discriminative structure dictionary along each mode is built. The overall structure dictionary composes of class-specified sub-dictionaries. Then the sparse core tensor is calculated by tensor OMP(Orthogonal Matching Pursuit) method based on dictionaries along each mode. It is expected that original tensor should be well recovered by sub-dictionary associated with relevant class, while entries in the sparse tensor associated with other classed should be nearly zero. Therefore, SRC use the reconstruction error associated with each class to do data classification. A section of airborne LiDAR points of Vienna city is used and classified into 6classes: ground, roofs, vegetation, covered ground, walls and other points. Only 6 training samples from each class are taken. For the final classification result, ground and covered ground are merged into one same class(ground). The classification accuracy for ground is 94.60%, roof is 95.47%, vegetation is 85.55%, wall is 76.17%, other object is 20.39%.

Simultaneous tensor decomposition and completion using factor priors.

PubMed

Chen, Yi-Lei; Hsu, Chiou-Ting; Liao, Hong-Yuan Mark

2014-03-01

The success of research on matrix completion is evident in a variety of real-world applications. Tensor completion, which is a high-order extension of matrix completion, has also generated a great deal of research interest in recent years. Given a tensor with incomplete entries, existing methods use either factorization or completion schemes to recover the missing parts. However, as the number of missing entries increases, factorization schemes may overfit the model because of incorrectly predefined ranks, while completion schemes may fail to interpret the model factors. In this paper, we introduce a novel concept: complete the missing entries and simultaneously capture the underlying model structure. To this end, we propose a method called simultaneous tensor decomposition and completion (STDC) that combines a rank minimization technique with Tucker model decomposition. Moreover, as the model structure is implicitly included in the Tucker model, we use factor priors, which are usually known a priori in real-world tensor objects, to characterize the underlying joint-manifold drawn from the model factors. By exploiting this auxiliary information, our method leverages two classic schemes and accurately estimates the model factors and missing entries. We conducted experiments to empirically verify the convergence of our algorithm on synthetic data and evaluate its effectiveness on various kinds of real-world data. The results demonstrate the efficacy of the proposed method and its potential usage in tensor-based applications. It also outperforms state-of-the-art methods on multilinear model analysis and visual data completion tasks.

Isometric Non-Rigid Shape-from-Motion with Riemannian Geometry Solved in Linear Time.

PubMed

Parashar, Shaifali; Pizarro, Daniel; Bartoli, Adrien

2017-10-06

We study Isometric Non-Rigid Shape-from-Motion (Iso-NRSfM): given multiple intrinsically calibrated monocular images, we want to reconstruct the time-varying 3D shape of a thin-shell object undergoing isometric deformations. We show that Iso-NRSfM is solvable from local warps, the inter-image geometric transformations. We propose a new theoretical framework based on the Riemmanian manifold to represent the unknown 3D surfaces as embeddings of the camera's retinal plane. This allows us to use the manifold's metric tensor and Christoffel Symbol (CS) fields. These are expressed in terms of the first and second order derivatives of the inverse-depth of the 3D surfaces, which are the unknowns for Iso-NRSfM. We prove that the metric tensor and the CS are related across images by simple rules depending only on the warps. This forms a set of important theoretical results. We show that current solvers cannot solve for the first and second order derivatives of the inverse-depth simultaneously. We thus propose an iterative solution in two steps. 1) We solve for the first order derivatives assuming that the second order derivatives are known. We initialise the second order derivatives to zero, which is an infinitesimal planarity assumption. We derive a system of two cubics in two variables for each image pair. The sum-of-squares of these polynomials is independent of the number of images and can be solved globally, forming a well-posed problem for N ≥ 3 images. 2) We solve for the second order derivatives by initialising the first order derivatives from the previous step. We solve a linear system of 4N-4 equations in three variables. We iterate until the first order derivatives converge. The solution for the first order derivatives gives the surfaces' normal fields which we integrate to recover the 3D surfaces. The proposed method outperforms existing work in terms of accuracy and computation cost on synthetic and real datasets.

Seismicity and Crustal Anisotropy Beneath the Western Segment of the North Anatolian Fault: Results from a Dense Seismic Array

NASA Astrophysics Data System (ADS)

Turkelli, N.; Teoman, U.; Altuncu Poyraz, S.; Cambaz, D.; Mutlu, A. K.; Kahraman, M.; Houseman, G. A.; Rost, S.; Thompson, D. A.; Cornwell, D. G.; Utkucu, M.; Gülen, L.

2013-12-01

The North Anatolian Fault (NAF) is one of the major strike slip fault systems on Earth comparable to San Andreas Fault in some ways. Devastating earthquakes have occurred along this system causing major damage and casualties. In order to comprehensively investigate the shallow and deep crustal structure beneath the western segment of NAF, a temporary dense seismic network for North Anatolia (DANA) consisting of 73 broadband sensors was deployed in early May 2012 surrounding a rectangular grid of by 70 km and a nominal station spacing of 7 km with the aim of further enhancing the detection capability of this dense seismic array. This joint project involves researchers from University of Leeds, UK, Bogazici University Kandilli Observatory and Earthquake Research Institute (KOERI), and University of Sakarya and primarily focuses on upper crustal studies such as earthquake locations (especially micro-seismic activity), receiver functions, moment tensor inversions, shear wave splitting, and ambient noise correlations. To begin with, we obtained the hypocenter locations of local earthquakes that occured within the DANA network. The dense 2-D grid geometry considerably enhanced the earthquake detection capability which allowed us to precisely locate events with local magnitudes (Ml) less than 1.0. Accurate earthquake locations will eventually lead to high resolution images of the upper crustal structure beneath the northern and southern branches of NAF in Sakarya region. In order to put additional constraints on the active tectonics of the western part of NAF, we also determined fault plane solutions using Regional Moment Tensor Inversion (RMT) and P wave first motion methods. For the analysis of high quality fault plane solutions, data from KOERI and the DANA project were merged. Furthermore, with the aim of providing insights on crustal anisotropy, shear wave splitting parameters such as lag time and fast polarization direction were obtained for local events recorded within the seismic network with magnitudes larger than 2.5.

Geometry of Lax pairs: Particle motion and Killing-Yano tensors

NASA Astrophysics Data System (ADS)

Cariglia, Marco; Frolov, Valeri P.; Krtouš, Pavel; Kubizňák, David

2013-01-01

A geometric formulation of the Lax pair equation on a curved manifold is studied using the phase-space formalism. The corresponding (covariantly conserved) Lax tensor is defined and the method of generation of constants of motion from it is discussed. It is shown that when the Hamilton equations of motion are used, the conservation of the Lax tensor translates directly to the well-known Lax pair equation, with one matrix identified with components of the Lax tensor and the other matrix constructed from the (metric) connection. A generalization to Clifford objects is also discussed. Nontrivial examples of Lax tensors for geodesic and charged particle motion are found in spacetimes admitting a hidden symmetry of Killing-Yano tensors.

8 January 2013 Mw=5.7 North Aegean Sea Earthquake Sequence

NASA Astrophysics Data System (ADS)

Kürçer, Akın; Yalçın, Hilal; Gülen, Levent; Kalafat, Doǧan

2014-05-01

The deformation of the North Aegean Sea is mainly controlled by the westernmost segments of North Anatolian Fault Zone (NAFZ). On January 8, 2013, a moderate earthquake (Mw= 5.7) occurred in the North Aegean Sea, which may be considered to be a part of westernmost splay of the NAFZ. A series of aftershocks were occurred within four months following the mainschock, which have magnitudes varying from 1.9 to 5.0. In this study, a total of 23 earthquake moment tensor solutions that belong to the 2013 earthquake sequence have been obtained by using KOERI and AFAD seismic data. The most widely used Gephart & Forsyth (1984) and Michael (1987) methods have been used to carry out stress tensor inversions. Based on the earthquake moment tensor solutions, distribution of epicenters and seismotectonic setting, the source of this earthquake sequence is a N75°E trending pure dextral strike-slip fault. The temporal and spatial distribution of earthquakes indicate that the rupture unilaterally propagated from SW to NE. The length of the fault has been calculated as approximately 12 km. using the afterschock distribution and empirical equations, suggested by Wells and Coppersmith (1994). The stress tensor analysis indicate that the dominant faulting type in the region is strike-slip and the direction of the regional compressive stress is WNW-ESE. The 1968 Aghios earthquake (Ms=7.3; Ambraseys and Jackson, 1998) and 2013 North Aegean Sea earthquake sequences clearly show that the regional stress has been transferred from SW to NE in this region. The last historical earthquake, the Bozcaada earthquake (M=7.05) had been occurred in the northeast of the 2013 earthquake sequence in 1672. The elapsed time (342 year) and regional stress transfer point out that the 1672 earthquake segment is probably a seismic gap. According to the empirical equations, the surface rupture length of the 1672 Earthquake segment was about 47 km, with a maximum displacement of 170 cm and average displacement of 107 cm. These values indicate that the 1672 earthquake segment is a potential earthquake hazard for this region.

On the phantom barrier crossing and the bounds on the speed of sound in non-minimal derivative coupling theories

NASA Astrophysics Data System (ADS)

Quiros, Israel; Gonzalez, Tame; Nucamendi, Ulises; García-Salcedo, Ricardo; Horta-Rangel, Francisco Antonio; Saavedra, Joel

2018-04-01

In this paper we investigate the so-called ‘phantom barrier crossing’ issue in a cosmological model based on the scalar–tensor theory with non-minimal derivative coupling to the Einstein tensor. Special attention will be paid to the physical bounds on the squared sound speed. The numeric results are geometrically illustrated by means of a qualitative procedure of analysis that is based on the mapping of the orbits in the phase plane onto the surfaces that represent physical quantities in the extended phase space, that is: the phase plane complemented with an additional dimension relative to the given physical parameter. We find that the cosmological model based on the non-minimal derivative coupling theory—this includes both the quintessence and the pure derivative coupling cases—has serious causality problems related to superluminal propagation of the scalar and tensor perturbations. Even more disturbing is the finding that, despite the fact that the underlying theory is free of the Ostrogradsky instability, the corresponding cosmological model is plagued by the Laplacian (classical) instability related with negative squared sound speed. This instability leads to an uncontrollable growth of the energy density of the perturbations that is inversely proportional to their wavelength. We show that, independent of the self-interaction potential, for positive coupling the tensor perturbations propagate superluminally, while for negative coupling a Laplacian instability arises. This latter instability invalidates the possibility for the model to describe the primordial inflation.

Source Parameters for Moderate Earthquakes in the Zagros Mountains with Implications for the Depth Extent of Seismicity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adams, A; Brazier, R; Nyblade, A

2009-02-23

Six earthquakes within the Zagros Mountains with magnitudes between 4.9 and 5.7 have been studied to determine their source parameters. These events were selected for study because they were reported in open catalogs to have lower crustal or upper mantle source depths and because they occurred within an area of the Zagros Mountains where crustal velocity structure has been constrained by previous studies. Moment tensor inversion of regional broadband waveforms have been combined with forward modeling of depth phases on short period teleseismic waveforms to constrain source depths and moment tensors. Our results show that all six events nucleated withinmore » the upper crust (<11 km depth) and have thrust mechanisms. This finding supports other studies that call into question the existence of lower crustal or mantle events beneath the Zagros Mountains.« less

Skyrme density functional description of the double magic 78Ni nucleus

NASA Astrophysics Data System (ADS)

Brink, D. M.; Stancu, Fl.

2018-06-01

We calculate the single-particle spectrum of the double magic nucleus 78Ni in a Hartree-Fock approach using the Skyrme density-dependent effective interaction containing central, spin-orbit, and tensor parts. We show that the tensor part has an important effect on the spin-orbit splitting of the proton 1 f orbit that may explain the survival of magicity so far from the stability valley. We confirm the inversion of the 1 f 5 /2 and 2 p 3 /2 levels at the neutron number 48 in the Ni isotopic chain expected from previous Monte Carlo shell-model calculations and supported by experimental observation.

A Simple Method for Calculating Clebsch-Gordan Coefficients

ERIC Educational Resources Information Center

Klink, W. H.; Wickramasekara, S.

2010-01-01

This paper presents a simple method for calculating Clebsch-Gordan coefficients for the tensor product of two unitary irreducible representations (UIRs) of the rotation group. The method also works for multiplicity-free irreducible representations appearing in the tensor product of any number of UIRs of the rotation group. The generalization to…

Controlling sign problems in spin models using tensor renormalization

NASA Astrophysics Data System (ADS)

Denbleyker, Alan; Liu, Yuzhi; Meurice, Y.; Qin, M. P.; Xiang, T.; Xie, Z. Y.; Yu, J. F.; Zou, Haiyuan

2014-01-01

We consider the sign problem for classical spin models at complex β =1/g02 on L ×L lattices. We show that the tensor renormalization group method allows reliable calculations for larger Imβ than the reweighting Monte Carlo method. For the Ising model with complex β we compare our results with the exact Onsager-Kaufman solution at finite volume. The Fisher zeros can be determined precisely with the tensor renormalization group method. We check the convergence of the tensor renormalization group method for the O(2) model on L×L lattices when the number of states Ds increases. We show that the finite size scaling of the calculated Fisher zeros agrees very well with the Kosterlitz-Thouless transition assumption and predict the locations for larger volume. The location of these zeros agree with Monte Carlo reweighting calculation for small volume. The application of the method for the O(2) model with a chemical potential is briefly discussed.

Information geometry and its application to theoretical statistics and diffusion tensor magnetic resonance imaging

NASA Astrophysics Data System (ADS)

Wisniewski, Nicholas Andrew

This dissertation is divided into two parts. First we present an exact solution to a generalization of the Behrens-Fisher problem by embedding the problem in the Riemannian manifold of Normal distributions. From this we construct a geometric hypothesis testing scheme. Secondly we investigate the most commonly used geometric methods employed in tensor field interpolation for DT-MRI analysis and cardiac computer modeling. We computationally investigate a class of physiologically motivated orthogonal tensor invariants, both at the full tensor field scale and at the scale of a single interpolation by doing a decimation/interpolation experiment. We show that Riemannian-based methods give the best results in preserving desirable physiological features.

Approximate arbitrary κ-state solutions of Dirac equation with Schiöberg and Manning-Rosen potentials within the coulomb-like Yukawa-like and generalized tensor interactions

NASA Astrophysics Data System (ADS)

Ikot, Akpan N.; Hassanabadi, Hassan; Obong, Hillary Patrick; Mehraban, H.; Yazarloo, Bentol Hoda

2015-07-01

The effects of Coulomb-like tensor (CLT), Yukawa-like tensor (YLT) and generalized tensor (GLT) interactions are investigated in the Dirac theory with Schiöberg and Manning-Rosen potentials within the framework of spin and pseudospin symmetries using the Nikiforov-Uvarov method. The bound state energy spectra and the radial wave functions have been approximately obtained in the case of spin and pseudospin symmetries. We have also reported some numerical results and figures to show the effects these tensor interactions.

The advantages of complementing MT profiles in 3-D environments with geomagnetic transfer function and interstation horizontal magnetic transfer function data: results from a synthetic case study

NASA Astrophysics Data System (ADS)

Campanyà, Joan; Ogaya, Xènia; Jones, Alan G.; Rath, Volker; Vozar, Jan; Meqbel, Naser

2016-12-01

As a consequence of measuring time variations of the electric and the magnetic field, which are related to current flow and charge distribution, magnetotelluric (MT) data in 2-D and 3-D environments are not only sensitive to the geoelectrical structures below the measuring points but also to any lateral anomalies surrounding the acquisition site. This behaviour complicates the characterization of the electrical resistivity distribution of the subsurface, particularly in complex areas. In this manuscript we assess the main advantages of complementing the standard MT impedance tensor (Z) data with interstation horizontal magnetic tensor (H) and geomagnetic transfer function (T) data in constraining the subsurface in a 3-D environment beneath a MT profile. Our analysis was performed using synthetic responses with added normally distributed and scattered random noise. The sensitivity of each type of data to different resistivity anomalies was evaluated, showing that the degree to which each site and each period is affected by the same anomaly depends on the type of data. A dimensionality analysis, using Z, H and T data, identified the presence of the 3-D anomalies close to the profile, suggesting a 3-D approach for recovering the electrical resistivity values of the subsurface. Finally, the capacity for recovering the geoelectrical structures of the subsurface was evaluated by performing joint inversion using different data combinations, quantifying the differences between the true synthetic model and the models from inversion process. Four main improvements were observed when performing joint inversion of Z, H and T data: (1) superior precision and accuracy at characterizing the electrical resistivity values of the anomalies below and outside the profile; (2) the potential to recover high electrical resistivity anomalies that are poorly recovered using Z data alone; (3) improvement in the characterization of the bottom and lateral boundaries of the anomalies with low electrical resistivity; and (4) superior imaging of the horizontal continuity of structures with low electrical resistivity. These advantages offer new opportunities for the MT method by making the results from a MT profile in a 3-D environment more convincing, supporting the possibility of high-resolution studies in 3-D areas without expending a large amount of economical and computational resources, and also offering better resolution of targets with high electrical resistivity.

FAST TRACK COMMUNICATION Single-charge rotating black holes in four-dimensional gauged supergravity

NASA Astrophysics Data System (ADS)

Chow, David D. K.

2011-02-01

We consider four-dimensional U(1)4 gauged supergravity, and obtain asymptotically AdS4, non-extremal, charged, rotating black holes with one non-zero U(1) charge. The thermodynamic quantities are computed. We obtain a generalization that includes a NUT parameter. The general solution has a discrete symmetry involving inversion of the rotation parameter, and has a string frame metric that admits a rank-2 Killing-Stäckel tensor.

Gas-induced friction and diffusion of rigid rotors

NASA Astrophysics Data System (ADS)

Martinetz, Lukas; Hornberger, Klaus; Stickler, Benjamin A.

2018-05-01

We derive the Boltzmann equation for the rotranslational dynamics of an arbitrary convex rigid body in a rarefied gas. It yields as a limiting case the Fokker-Planck equation accounting for friction, diffusion, and nonconservative drift forces and torques. We provide the rotranslational friction and diffusion tensors for specular and diffuse reflection off particles with spherical, cylindrical, and cuboidal shape, and show that the theory describes thermalization, photophoresis, and the inverse Magnus effect in the free molecular regime.

Tensorial Calibration. 2. Second Order Tensorial Calibration.

DTIC Science & Technology

1987-10-12

index is repeated more than once only in one side of an equation, it implies a summation over the index valid range. 12 To avoid confusion of terms...and higher order tensor, the rank can be higher than the maximum dimensionality. 13 ,ON 6 LINEAR SECOND ORDER TENSORIAL CALIBRATION MODEL From...these equations are valid only if all the elements of the diagonal matrix B3 are non-zero because its inverse (-1) must be computed. This implies that M

Comparison of magmatic and amagmatic rift zone kinematics using full moment tensor inversions of regional earthquakes

NASA Astrophysics Data System (ADS)

Jaye Oliva, Sarah; Ebinger, Cynthia; Shillington, Donna; Albaric, Julie; Deschamps, Anne; Keir, Derek; Drooff, Connor

2017-04-01

Temporary seismic networks deployed in the magmatic Eastern rift and the mostly amagmatic Western rift in East Africa present the opportunity to compare the depth distribution of strain, and fault kinematics in light of rift age and the presence or absence of surface magmatism. The largest events in local earthquake catalogs (ML > 3.5) are modeled using the Dreger and Ford full moment tensor algorithm (Dreger, 2003; Minson & Dreger, 2008) to better constrain source depth and to investigate non-double-couple components. A bandpass filter of 0.02 to 0.10 Hz is applied to the waveforms prior to inversion. Synthetics are based on 1D velocity models derived during seismic analysis and constrained by reflection and tomographic data where available. Results show significant compensated linear vector dipole (CLVD) and isotropic components for earthquakes in magmatic rift zones, whereas double-couple mechanisms predominate in weakly magmatic rift sectors. We interpret the isotropic components as evidence for fluid-involved faulting in the Eastern rift where volatile emissions are large, and dike intrusions well documented. Lower crustal earthquakes are found in both amagmatic and magmatic sectors. These results are discussed in the context of the growing database of complementary geophysical, geochemical, and geological studies in these regions as we seek to understand the role of magmatism and faulting in accommodating strain during early continental rifting.

Deciphering the role of fluids in early stage rifting from full moment tensor inversion of East African earthquakes

NASA Astrophysics Data System (ADS)

Oliva, S. J. C.; Ebinger, C. J.; Keir, D.; Shillington, D. J.; Chindandali, P. R. N.

2016-12-01

The East African Rift splits around the Archaean Tanzania craton into the magmatic Eastern branch and the mostly amagmatic Western branch, which continues south of the craton. Temporary seismic networks recently deployed in three rift sectors allow for comparison and insights into the early stages of rifting, including areas with lower crustal earthquakes. We analyze earthquakes with ML > 3.5 in the area recorded by CRAFTI (northern Tanzania/Kenya), TANGA (Tanganyika rift), and/or SEGMeNT (Malawi rift) networks. For events not well enclosed by these arrays, nearby permanent stations are used to improve azimuthal coverage when possible. We present source mechanisms as well as better-constrained source depth estimates from moment tensor inversion using Dreger and Ford TDMT algorithm (Dreger, 2003; Minson & Dreger, 2008). Data and synthetic waveforms are bandpass filtered between 0.02 to 0.10 Hz, or a narrower frequency band within this range, depending on lake noise, which can interfere strongly on the lower end of this frequency range. Results suggest local stress reorientations as well as significant dilatation components on some events within magmatic rift sectors. The implications of these results for crustal rheology and magmatic modification will be discussed in light of the growing complementary data sets from the three projects to inform our understanding of early rifting as a whole.

Benefits of rotational ground motions for planetary seismology

NASA Astrophysics Data System (ADS)

Donner, S.; Joshi, R.; Hadziioannou, C.; Nunn, C.; van Driel, M.; Schmelzbach, C.; Wassermann, J. M.; Igel, H.

2017-12-01

Exploring the internal structure of planetary objects is fundamental to understand the evolution of our solar system. In contrast to Earth, planetary seismology is hampered by the limited number of stations available, often just a single one. Classic seismology is based on the measurement of three components of translational ground motion. Its methods are mainly developed for a larger number of available stations. Therefore, the application of classical seismological methods to other planets is very limited. Here, we show that the additional measurement of three components of rotational ground motion could substantially improve the situation. From sparse or single station networks measuring translational and rotational ground motions it is possible to obtain additional information on structure and source. This includes direct information on local subsurface seismic velocities, separation of seismic phases, propagation direction of seismic energy, crustal scattering properties, as well as moment tensor source parameters for regional sources. The potential of this methodology will be highlighted through synthetic forward and inverse modeling experiments.

Stochastic DT-MRI connectivity mapping on the GPU.

PubMed

McGraw, Tim; Nadar, Mariappan

2007-01-01

We present a method for stochastic fiber tract mapping from diffusion tensor MRI (DT-MRI) implemented on graphics hardware. From the simulated fibers we compute a connectivity map that gives an indication of the probability that two points in the dataset are connected by a neuronal fiber path. A Bayesian formulation of the fiber model is given and it is shown that the inversion method can be used to construct plausible connectivity. An implementation of this fiber model on the graphics processing unit (GPU) is presented. Since the fiber paths can be stochastically generated independently of one another, the algorithm is highly parallelizable. This allows us to exploit the data-parallel nature of the GPU fragment processors. We also present a framework for the connectivity computation on the GPU. Our implementation allows the user to interactively select regions of interest and observe the evolving connectivity results during computation. Results are presented from the stochastic generation of over 250,000 fiber steps per iteration at interactive frame rates on consumer-grade graphics hardware.

Hidden symmetries in Sasaki-Einstein geometries

NASA Astrophysics Data System (ADS)

Slesar, V.; Visinescu, M.; Vîlcu, G. E.

2017-07-01

We describe a method for constructing Killing-Yano tensors on Sasaki spaces using their geometrical properties, without the need of solving intricate generalized Killing equations. We obtain the Killing-Yano tensors on toric Sasaki-Einstein spaces using the fact that the metric cones of these spaces are Calabi-Yau manifolds which in turn are described in terms of toric data. We extend the search of Killing-Yano tensors on mixed 3-Sasakian manifolds. We illustrate the method by explicit construction of Killing forms on some spaces of current interest.

Low-Rank Tensor Subspace Learning for RGB-D Action Recognition.

PubMed

Jia, Chengcheng; Fu, Yun

2016-07-09

Since RGB-D action data inherently equip with extra depth information compared with RGB data, recently many works employ RGB-D data in a third-order tensor representation containing spatio-temporal structure to find a subspace for action recognition. However, there are two main challenges of these methods. First, the dimension of subspace is usually fixed manually. Second, preserving local information by finding intraclass and inter-class neighbors from a manifold is highly timeconsuming. In this paper, we learn a tensor subspace, whose dimension is learned automatically by low-rank learning, for RGB-D action recognition. Particularly, the tensor samples are factorized to obtain three Projection Matrices (PMs) by Tucker Decomposition, where all the PMs are performed by nuclear norm in a close-form to obtain the tensor ranks which are used as tensor subspace dimension. Additionally, we extract the discriminant and local information from a manifold using a graph constraint. This graph preserves the local knowledge inherently, which is faster than the previous way by calculating both the intra-class and inter-class neighbors of each sample. We evaluate the proposed method on four widely used RGB-D action datasets including MSRDailyActivity3D, MSRActionPairs, MSRActionPairs skeleton and UTKinect-Action3D datasets, and the experimental results show higher accuracy and efficiency of the proposed method.

Complete set of invariants of a 4th order tensor: the 12 tasks of HARDI from ternary quartics.

PubMed

Papadopoulo, Théo; Ghosh, Aurobrata; Deriche, Rachid

2014-01-01

Invariants play a crucial role in Diffusion MRI. In DTI (2nd order tensors), invariant scalars (FA, MD) have been successfully used in clinical applications. But DTI has limitations and HARDI models (e.g. 4th order tensors) have been proposed instead. These, however, lack invariant features and computing them systematically is challenging. We present a simple and systematic method to compute a functionally complete set of invariants of a non-negative 3D 4th order tensor with respect to SO3. Intuitively, this transforms the tensor's non-unique ternary quartic (TQ) decomposition (from Hilbert's theorem) to a unique canonical representation independent of orientation - the invariants. The method consists of two steps. In the first, we reduce the 18 degrees-of-freedom (DOF) of a TQ representation by 3-DOFs via an orthogonal transformation. This transformation is designed to enhance a rotation-invariant property of choice of the 3D 4th order tensor. In the second, we further reduce 3-DOFs via a 3D rotation transformation of coordinates to arrive at a canonical set of invariants to SO3 of the tensor. The resulting invariants are, by construction, (i) functionally complete, (ii) functionally irreducible (if desired), (iii) computationally efficient and (iv) reversible (mappable to the TQ coefficients or shape); which is the novelty of our contribution in comparison to prior work. Results from synthetic and real data experiments validate the method and indicate its importance.

New constraints on micro-seismicity and stress state in the western part of the North Anatolian Fault Zone: Observations from a dense seismic array

NASA Astrophysics Data System (ADS)

Altuncu Poyraz, Selda; Teoman, M. Uğur; Türkelli, Niyazi; Kahraman, Metin; Cambaz, Didem; Mutlu, Ahu; Rost, Sebastian; Houseman, Gregory A.; Thompson, David A.; Cornwell, David; Utkucu, Murat; Gülen, Levent

2015-08-01

With the aim of extensively investigating the crustal structure beneath the western segment of the North Anatolian Fault Zone where it splays into northern and southern branches, a temporary seismic network (dense array for North Anatolia-DANA) consisting of 70 stations was deployed in early May 2012 and operated for 18 months in the Sakarya region during the FaultLab experiment. Out of 2437 events contaminated by explosions, we extracted 1371 well located earthquakes. The enhanced station coverage having a nominal station spacing of 7 km, lead to a minimum magnitude calculation of 0.1. Horizontal and vertical location uncertainties within the array do not exceed 0.8 km and 0.9 km, respectively. We observe considerable seismic activity along both branches of the fault where the depth of the seismogenic zone was mostly confined to 15 km. Using our current earthquake catalog we obtained a b-value of 1. We also mapped the b-value variation with depth and observed a gradual decrease. Furthermore, we determined the source parameters of 41 earthquakes with magnitudes greater than 1.8 using P-wave first motion polarity method. Regional Moment Tensor Inversion method was also applied to earthquakes with magnitudes greater than 3.0. Focal mechanism solutions confirm that Sakarya and its vicinity is stressed by a compressional regime showing a primarily oblique-slip motion character. Stress tensor analysis indicates that the maximum principal stress is aligned in WNW-ESE direction and the tensional axis is aligned in NNE-SSW direction.

Present Kinematic Regime and Recent Seismicity of Gulf Suez, Egypt

NASA Astrophysics Data System (ADS)

Mohamed, G.-E. A.; Abd El-Aal, A. K.

2018-01-01

In this study we computed recent seismicity and present kinematic regime in the northern and middle zones of Gulf of Suez as inferred from moment tensor settlings and focal mechanism of local earthquakes that happened in this region. On 18 and 22 of July, 2014 two moderate size earthquakes of local magnitudes 4.2 and 4.1 struck the northern zone of Gulf of Suez near Suez City. These events are instrumentally recorded by Egyptian National Seismic Network (ENSN). The earthquakes have been felt at Suez City and greater Cairo metropolitan zone while no losses were reported. The source mechanism and source parameters of the calculated events were considered by the near-source waveform data listed at very broadband stations of ENSN and supported by the P-wave polarity data of short period stations. The new settling method and software used deem the action of the source time function, which has been ignored in most of the program series of the moment tensor settling analysis with near source seismograms. The obtained results from settling technique indicate that the estimated seismic moments of both earthquakes are 0.6621E + 15 and 0.4447E + 15 Nm conforming to a moment magnitude Mw 3.8 and 3.7 respectively. The fault plan settlings obtained from both settling technique and polarity of first-arrival indicate the dominance of normal faulting. We also evaluated the stress field in north and middle zones of Gulf of Suez using a multiple inverse method. The prime strain axis shows that the deformation is taken up mainly as stretching in the E-W and NE-SW direction.

Earthquake mechanisms from linear-programming inversion of seismic-wave amplitude ratios

USGS Publications Warehouse

Julian, B.R.; Foulger, G.R.

1996-01-01

The amplitudes of radiated seismic waves contain far more information about earthquake source mechanisms than do first-motion polarities, but amplitudes are severely distorted by the effects of heterogeneity in the Earth. This distortion can be reduced greatly by using the ratios of amplitudes of appropriately chosen seismic phases, rather than simple amplitudes, but existing methods for inverting amplitude ratios are severely nonlinear and require computationally intensive searching methods to ensure that solutions are globally optimal. Searching methods are particularly costly if general (moment tensor) mechanisms are allowed. Efficient linear-programming methods, which do not suffer from these problems, have previously been applied to inverting polarities and wave amplitudes. We extend these methods to amplitude ratios, in which formulation on inequality constraint for an amplitude ratio takes the same mathematical form as a polarity observation. Three-component digital data for an earthquake at the Hengill-Grensdalur geothermal area in southwestern Iceland illustrate the power of the method. Polarities of P, SH, and SV waves, unusually well distributed on the focal sphere, cannot distinguish between diverse mechanisms, including a double couple. Amplitude ratios, on the other hand, clearly rule out the double-couple solution and require a large explosive isotropic component.

An optimization approach for fitting canonical tensor decompositions.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dunlavy, Daniel M.; Acar, Evrim; Kolda, Tamara Gibson

Tensor decompositions are higher-order analogues of matrix decompositions and have proven to be powerful tools for data analysis. In particular, we are interested in the canonical tensor decomposition, otherwise known as the CANDECOMP/PARAFAC decomposition (CPD), which expresses a tensor as the sum of component rank-one tensors and is used in a multitude of applications such as chemometrics, signal processing, neuroscience, and web analysis. The task of computing the CPD, however, can be difficult. The typical approach is based on alternating least squares (ALS) optimization, which can be remarkably fast but is not very accurate. Previously, nonlinear least squares (NLS) methodsmore » have also been recommended; existing NLS methods are accurate but slow. In this paper, we propose the use of gradient-based optimization methods. We discuss the mathematical calculation of the derivatives and further show that they can be computed efficiently, at the same cost as one iteration of ALS. Computational experiments demonstrate that the gradient-based optimization methods are much more accurate than ALS and orders of magnitude faster than NLS.« less

Estimation of integral curves from high angular resolution diffusion imaging (HARDI) data.

PubMed

Carmichael, Owen; Sakhanenko, Lyudmila

2015-05-15

We develop statistical methodology for a popular brain imaging technique HARDI based on the high order tensor model by Özarslan and Mareci [10]. We investigate how uncertainty in the imaging procedure propagates through all levels of the model: signals, tensor fields, vector fields, and fibers. We construct asymptotically normal estimators of the integral curves or fibers which allow us to trace the fibers together with confidence ellipsoids. The procedure is computationally intense as it blends linear algebra concepts from high order tensors with asymptotical statistical analysis. The theoretical results are illustrated on simulated and real datasets. This work generalizes the statistical methodology proposed for low angular resolution diffusion tensor imaging by Carmichael and Sakhanenko [3], to several fibers per voxel. It is also a pioneering statistical work on tractography from HARDI data. It avoids all the typical limitations of the deterministic tractography methods and it delivers the same information as probabilistic tractography methods. Our method is computationally cheap and it provides well-founded mathematical and statistical framework where diverse functionals on fibers, directions and tensors can be studied in a systematic and rigorous way.

Estimation of integral curves from high angular resolution diffusion imaging (HARDI) data

PubMed Central

Carmichael, Owen; Sakhanenko, Lyudmila

2015-01-01

We develop statistical methodology for a popular brain imaging technique HARDI based on the high order tensor model by Özarslan and Mareci [10]. We investigate how uncertainty in the imaging procedure propagates through all levels of the model: signals, tensor fields, vector fields, and fibers. We construct asymptotically normal estimators of the integral curves or fibers which allow us to trace the fibers together with confidence ellipsoids. The procedure is computationally intense as it blends linear algebra concepts from high order tensors with asymptotical statistical analysis. The theoretical results are illustrated on simulated and real datasets. This work generalizes the statistical methodology proposed for low angular resolution diffusion tensor imaging by Carmichael and Sakhanenko [3], to several fibers per voxel. It is also a pioneering statistical work on tractography from HARDI data. It avoids all the typical limitations of the deterministic tractography methods and it delivers the same information as probabilistic tractography methods. Our method is computationally cheap and it provides well-founded mathematical and statistical framework where diverse functionals on fibers, directions and tensors can be studied in a systematic and rigorous way. PMID:25937674

Holographic stress-energy tensor near the Cauchy horizon inside a rotating black hole

NASA Astrophysics Data System (ADS)

Ishibashi, Akihiro; Maeda, Kengo; Mefford, Eric

2017-07-01

We investigate a stress-energy tensor for a conformal field theory (CFT) at strong coupling inside a small five-dimensional rotating Myers-Perry black hole with equal angular momenta by using the holographic method. As a gravitational dual, we perturbatively construct a black droplet solution by applying the "derivative expansion" method, generalizing the work of Haddad [Classical Quantum Gravity 29, 245001 (2012), 10.1088/0264-9381/29/24/245001] and analytically compute the holographic stress-energy tensor for our solution. We find that the stress-energy tensor is finite at both the future and past outer (event) horizons and that the energy density is negative just outside the event horizons due to the Hawking effect. Furthermore, we apply the holographic method to the question of quantum instability of the Cauchy horizon since, by construction, our black droplet solution also admits a Cauchy horizon inside. We analytically show that the null-null component of the holographic stress-energy tensor negatively diverges at the Cauchy horizon, suggesting that a singularity appears there, in favor of strong cosmic censorship.

Maxwell–Dirac stress–energy tensor in terms of Fierz bilinear currents

DOE Office of Scientific and Technical Information (OSTI.GOV)

Inglis, Shaun, E-mail: sminglis@utas.edu.au; Jarvis, Peter, E-mail: Peter.Jarvis@utas.edu.au

We analyse the stress–energy tensor for the self-coupled Maxwell–Dirac system in the bilinear current formalism, using two independent approaches. The first method used is that attributed to Belinfante: starting from the spinor form of the action, the well-known canonical stress–energy tensor is augmented, by extending the Noether symmetry current to include contributions from the Lorentz group, to a manifestly symmetric form. This form admits a transcription to bilinear current form. The second method used is the variational derivation based on the covariant coupling to general relativity. The starting point here at the outset is the transcription of the action using,more » as independent field variables, both the bilinear currents, together with a gauge invariant vector field (a proxy for the electromagnetic vector potential). A central feature of the two constructions is that they both involve the mapping of the Dirac contribution to the stress–energy from the spinor fields to the equivalent set of bilinear tensor currents, through the use of appropriate Fierz identities. Although this mapping is done at quite different stages, nonetheless we find that the two forms of the bilinear stress–energy tensor agree. Finally, as an application, we consider the reduction of the obtained stress–energy tensor in bilinear form, under the assumption of spherical symmetry. -- Highlights: •Maxwell–Dirac stress–energy tensor derived in manifestly gauge invariant bilinear form. •Dirac spinor Belinfante tensor transcribed to bilinear fields via Fierz mapping. •Variational stress–energy obtained via bilinearized action, in contrast to Belinfante case. •Independent derivations via the Belinfante and variational methods agree, as required. •Spherical symmetry reduction given as a working example for wider applications.« less

Seismic monitoring at Cascade Volcanic Centers, 2004?status and recommendations

USGS Publications Warehouse

Moran, Seth C.

2004-01-01

The purpose of this report is to assess the current (May, 2004) status of seismic monitoring networks at the 13 major Cascade volcanic centers. Included in this assessment are descriptions of each network, analyses of the ability of each network to detect and to locate seismic activity, identification of specific weaknesses in each network, and a prioritized list of those networks that are most in need of additional seismic stations. At the outset it should be recognized that no Cascade volcanic center currently has an adequate seismic network relative to modern-day networks at Usu Volcano (Japan) or Etna and Stromboli volcanoes (Italy). For a system the size of Three Sisters, for example, a modern-day, cutting-edge seismic network would ideally consist of a minimum of 10 to 12 short-period three-component seismometers (for determining particle motions, reliable S-wave picks, moment tensor inversions, fault-plane solutions, and other important seismic parameters) and 7 to 10 broadband sensors (which, amongst other considerations, enable detection and location of very long period (VLP) and other low-frequency events, moment tensor inversions, and, because of their wide dynamic range, on-scale recording of large-amplitude events). Such a dense, multi component seismic network would give the ability to, for example, detect in near-real-time earthquake migrations over a distance of ~0.5km or less, locate tremor sources, determine the nature of a seismic source (that is, pure shear, implosive, explosive), provide on-scale recordings of very small and very large-amplitude seismic signals, and detect localized changes in seismic stress tensor orientations caused by movement of magma bodies. However, given that programmatic resources are currently limited, installation of such networks at this time is unrealistic. Instead, this report focuses on identifying what additional stations are needed to guarantee that anomalous seismicity associated with volcanic unrest will be detected in a timely manner and, in the case of magnitude = 1 earthquakes, reliably located.

Improved source inversion from joint measurements of translational and rotational ground motions

NASA Astrophysics Data System (ADS)

Donner, S.; Bernauer, M.; Reinwald, M.; Hadziioannou, C.; Igel, H.

2017-12-01

Waveform inversion for seismic point (moment tensor) and kinematic sources is a standard procedure. However, especially in the local and regional distances a lack of appropriate velocity models, the sparsity of station networks, or a low signal-to-noise ratio combined with more complex waveforms hamper the successful retrieval of reliable source solutions. We assess the potential of rotational ground motion recordings to increase the resolution power and reduce non-uniquenesses for point and kinematic source solutions. Based on synthetic waveform data, we perform a Bayesian (i.e. probabilistic) inversion. Thus, we avoid the subjective selection of the most reliable solution according the lowest misfit or other constructed criterion. In addition, we obtain unbiased measures of resolution and possible trade-offs. Testing different earthquake mechanisms and scenarios, we can show that the resolution of the source solutions can be improved significantly. Especially depth dependent components show significant improvement. Next to synthetic data of station networks, we also tested sparse-network and single station cases.

Structural Assembly of Multidomain Proteins and Protein Complexes Guided by the Overall Rotational Diffusion Tensor

PubMed Central

Ryabov, Yaroslav; Fushman, David

2008-01-01

We present a simple and robust approach that uses the overall rotational diffusion tensor as a structural constraint for domain positioning in multidomain proteins and protein-protein complexes. This method offers the possibility to use NMR relaxation data for detailed structure characterization of such systems provided the structures of individual domains are available. The proposed approach extends the concept of using long-range information contained in the overall rotational diffusion tensor. In contrast to the existing approaches, we use both the principal axes and principal values of protein’s rotational diffusion tensor to determine not only the orientation but also the relative positioning of the individual domains in a protein. This is achieved by finding the domain arrangement in a molecule that provides the best possible agreement with all components of the overall rotational diffusion tensor derived from experimental data. The accuracy of the proposed approach is demonstrated for two protein systems with known domain arrangement and parameters of the overall tumbling: the HIV-1 protease homodimer and Maltose Binding Protein. The accuracy of the method and its sensitivity to domain positioning is also tested using computer-generated data for three protein complexes, for which the experimental diffusion tensors are not available. In addition, the proposed method is applied here to determine, for the first time, the structure of both open and closed conformations of Lys48-linked di-ubiquitin chain, where domain motions render impossible accurate structure determination by other methods. The proposed method opens new avenues for improving structure characterization of proteins in solution. PMID:17550252

Tensor network method for reversible classical computation

NASA Astrophysics Data System (ADS)

Yang, Zhi-Cheng; Kourtis, Stefanos; Chamon, Claudio; Mucciolo, Eduardo R.; Ruckenstein, Andrei E.

2018-03-01

We develop a tensor network technique that can solve universal reversible classical computational problems, formulated as vertex models on a square lattice [Nat. Commun. 8, 15303 (2017), 10.1038/ncomms15303]. By encoding the truth table of each vertex constraint in a tensor, the total number of solutions compatible with partial inputs and outputs at the boundary can be represented as the full contraction of a tensor network. We introduce an iterative compression-decimation (ICD) scheme that performs this contraction efficiently. The ICD algorithm first propagates local constraints to longer ranges via repeated contraction-decomposition sweeps over all lattice bonds, thus achieving compression on a given length scale. It then decimates the lattice via coarse-graining tensor contractions. Repeated iterations of these two steps gradually collapse the tensor network and ultimately yield the exact tensor trace for large systems, without the need for manual control of tensor dimensions. Our protocol allows us to obtain the exact number of solutions for computations where a naive enumeration would take astronomically long times.

Conductivity of an inverse lyotropic lamellar phase under shear flow

NASA Astrophysics Data System (ADS)

Panizza, P.; Soubiran, L.; Coulon, C.; Roux, D.

2001-08-01

We report conductivity measurements on solutions of closed compact monodisperse multilamellar vesicles (the so-called ``onion texture'') formed by shearing an inverse lyotropic lamellar Lα phase. The conductivity measured in different directions as a function of the applied shear rate reveals a small anisotropy of the onion structure due to the existence of free oriented membranes. The results are analyzed in terms of a simple model that allows one to deduce the conductivity tensor of the Lα phase itself and the proportion of free oriented membranes. The variation of these two parameters is measured along a dilution line and discussed. The high value of the conductivity perpendicular to the layers with respect to that of solvent suggests the existence of a mechanism of ionic transport through the insulating solvent.

The Topology of Three-Dimensional Symmetric Tensor Fields

NASA Technical Reports Server (NTRS)

Lavin, Yingmei; Levy, Yuval; Hesselink, Lambertus

1994-01-01

We study the topology of 3-D symmetric tensor fields. The goal is to represent their complex structure by a simple set of carefully chosen points and lines analogous to vector field topology. The basic constituents of tensor topology are the degenerate points, or points where eigenvalues are equal to each other. First, we introduce a new method for locating 3-D degenerate points. We then extract the topological skeletons of the eigenvector fields and use them for a compact, comprehensive description of the tensor field. Finally, we demonstrate the use of tensor field topology for the interpretation of the two-force Boussinesq problem.

MRI diffusion tensor reconstruction with PROPELLER data acquisition.

PubMed

Cheryauka, Arvidas B; Lee, James N; Samsonov, Alexei A; Defrise, Michel; Gullberg, Grant T

2004-02-01

MRI diffusion imaging is effective in measuring the diffusion tensor in brain, cardiac, liver, and spinal tissue. Diffusion tensor tomography MRI (DTT MRI) method is based on reconstructing the diffusion tensor field from measurements of projections of the tensor field. Projections are obtained by appropriate application of rotated diffusion gradients. In the present paper, the potential of a novel data acquisition scheme, PROPELLER (Periodically Rotated Overlapping ParallEL Lines with Enhanced Reconstruction), is examined in combination with DTT MRI for its capability and sufficiency for diffusion imaging. An iterative reconstruction algorithm is used to reconstruct the diffusion tensor field from rotated diffusion weighted blades by appropriate rotated diffusion gradients. DTT MRI with PROPELLER data acquisition shows significant potential to reduce the number of weighted measurements, avoid ambiguity in reconstructing diffusion tensor parameters, increase signal-to-noise ratio, and decrease the influence of signal distortion.

Tensor completion for estimating missing values in visual data.

PubMed

Liu, Ji; Musialski, Przemyslaw; Wonka, Peter; Ye, Jieping

2013-01-01

In this paper, we propose an algorithm to estimate missing values in tensors of visual data. The values can be missing due to problems in the acquisition process or because the user manually identified unwanted outliers. Our algorithm works even with a small amount of samples and it can propagate structure to fill larger missing regions. Our methodology is built on recent studies about matrix completion using the matrix trace norm. The contribution of our paper is to extend the matrix case to the tensor case by proposing the first definition of the trace norm for tensors and then by building a working algorithm. First, we propose a definition for the tensor trace norm that generalizes the established definition of the matrix trace norm. Second, similarly to matrix completion, the tensor completion is formulated as a convex optimization problem. Unfortunately, the straightforward problem extension is significantly harder to solve than the matrix case because of the dependency among multiple constraints. To tackle this problem, we developed three algorithms: simple low rank tensor completion (SiLRTC), fast low rank tensor completion (FaLRTC), and high accuracy low rank tensor completion (HaLRTC). The SiLRTC algorithm is simple to implement and employs a relaxation technique to separate the dependent relationships and uses the block coordinate descent (BCD) method to achieve a globally optimal solution; the FaLRTC algorithm utilizes a smoothing scheme to transform the original nonsmooth problem into a smooth one and can be used to solve a general tensor trace norm minimization problem; the HaLRTC algorithm applies the alternating direction method of multipliers (ADMMs) to our problem. Our experiments show potential applications of our algorithms and the quantitative evaluation indicates that our methods are more accurate and robust than heuristic approaches. The efficiency comparison indicates that FaLTRC and HaLRTC are more efficient than SiLRTC and between FaLRTC an- HaLRTC the former is more efficient to obtain a low accuracy solution and the latter is preferred if a high-accuracy solution is desired.

Federated Tensor Factorization for Computational Phenotyping

PubMed Central

Kim, Yejin; Sun, Jimeng; Yu, Hwanjo; Jiang, Xiaoqian

2017-01-01

Tensor factorization models offer an effective approach to convert massive electronic health records into meaningful clinical concepts (phenotypes) for data analysis. These models need a large amount of diverse samples to avoid population bias. An open challenge is how to derive phenotypes jointly across multiple hospitals, in which direct patient-level data sharing is not possible (e.g., due to institutional policies). In this paper, we developed a novel solution to enable federated tensor factorization for computational phenotyping without sharing patient-level data. We developed secure data harmonization and federated computation procedures based on alternating direction method of multipliers (ADMM). Using this method, the multiple hospitals iteratively update tensors and transfer secure summarized information to a central server, and the server aggregates the information to generate phenotypes. We demonstrated with real medical datasets that our method resembles the centralized training model (based on combined datasets) in terms of accuracy and phenotypes discovery while respecting privacy. PMID:29071165

Graphical tensor product reduction scheme for the Lie algebras so(5) = sp(2) , su(3) , and g(2)

NASA Astrophysics Data System (ADS)

Vlasii, N. D.; von Rütte, F.; Wiese, U.-J.

2016-08-01

We develop in detail a graphical tensor product reduction scheme, first described by Antoine and Speiser, for the simple rank 2 Lie algebras so(5) = sp(2) , su(3) , and g(2) . This leads to an efficient practical method to reduce tensor products of irreducible representations into sums of such representations. For this purpose, the 2-dimensional weight diagram of a given representation is placed in a ;landscape; of irreducible representations. We provide both the landscapes and the weight diagrams for a large number of representations for the three simple rank 2 Lie algebras. We also apply the algebraic ;girdle; method, which is much less efficient for calculations by hand for moderately large representations. Computer code for reducing tensor products, based on the graphical method, has been developed as well and is available from the authors upon request.

Symmetric Positive 4th Order Tensors & Their Estimation from Diffusion Weighted MRI⋆

PubMed Central

Barmpoutis, Angelos; Jian, Bing; Vemuri, Baba C.; Shepherd, Timothy M.

2009-01-01

In Diffusion Weighted Magnetic Resonance Image (DW-MRI) processing a 2nd order tensor has been commonly used to approximate the diffusivity function at each lattice point of the DW-MRI data. It is now well known that this 2nd-order approximation fails to approximate complex local tissue structures, such as fibers crossings. In this paper we employ a 4th order symmetric positive semi-definite (PSD) tensor approximation to represent the diffusivity function and present a novel technique to estimate these tensors from the DW-MRI data guaranteeing the PSD property. There have been several published articles in literature on higher order tensor approximations of the diffusivity function but none of them guarantee the positive semi-definite constraint, which is a fundamental constraint since negative values of the diffusivity coefficients are not meaningful. In our methods, we parameterize the 4th order tensors as a sum of squares of quadratic forms by using the so called Gram matrix method from linear algebra and its relation to the Hilbert’s theorem on ternary quartics. This parametric representation is then used in a nonlinear-least squares formulation to estimate the PSD tensors of order 4 from the data. We define a metric for the higher-order tensors and employ it for regularization across the lattice. Finally, performance of this model is depicted on synthetic data as well as real DW-MRI from an isolated rat hippocampus. PMID:17633709

The spectral element method (SEM) on variable-resolution grids: evaluating grid sensitivity and resolution-aware numerical viscosity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guba, O.; Taylor, M. A.; Ullrich, P. A.

2014-11-27

We evaluate the performance of the Community Atmosphere Model's (CAM) spectral element method on variable-resolution grids using the shallow-water equations in spherical geometry. We configure the method as it is used in CAM, with dissipation of grid scale variance, implemented using hyperviscosity. Hyperviscosity is highly scale selective and grid independent, but does require a resolution-dependent coefficient. For the spectral element method with variable-resolution grids and highly distorted elements, we obtain the best results if we introduce a tensor-based hyperviscosity with tensor coefficients tied to the eigenvalues of the local element metric tensor. The tensor hyperviscosity is constructed so that, formore » regions of uniform resolution, it matches the traditional constant-coefficient hyperviscosity. With the tensor hyperviscosity, the large-scale solution is almost completely unaffected by the presence of grid refinement. This later point is important for climate applications in which long term climatological averages can be imprinted by stationary inhomogeneities in the truncation error. We also evaluate the robustness of the approach with respect to grid quality by considering unstructured conforming quadrilateral grids generated with a well-known grid-generating toolkit and grids generated by SQuadGen, a new open source alternative which produces lower valence nodes.« less

The spectral element method on variable resolution grids: evaluating grid sensitivity and resolution-aware numerical viscosity

DOE PAGES

Guba, O.; Taylor, M. A.; Ullrich, P. A.; ...

2014-06-25

We evaluate the performance of the Community Atmosphere Model's (CAM) spectral element method on variable resolution grids using the shallow water equations in spherical geometry. We configure the method as it is used in CAM, with dissipation of grid scale variance implemented using hyperviscosity. Hyperviscosity is highly scale selective and grid independent, but does require a resolution dependent coefficient. For the spectral element method with variable resolution grids and highly distorted elements, we obtain the best results if we introduce a tensor-based hyperviscosity with tensor coefficients tied to the eigenvalues of the local element metric tensor. The tensor hyperviscosity ismore » constructed so that for regions of uniform resolution it matches the traditional constant coefficient hyperviscsosity. With the tensor hyperviscosity the large scale solution is almost completely unaffected by the presence of grid refinement. This later point is important for climate applications where long term climatological averages can be imprinted by stationary inhomogeneities in the truncation error. We also evaluate the robustness of the approach with respect to grid quality by considering unstructured conforming quadrilateral grids generated with a well-known grid-generating toolkit and grids generated by SQuadGen, a new open source alternative which produces lower valence nodes.« less

Fast Approximations of the Rotational Diffusion Tensor and their Application to Structural Assembly of Molecular Complexes

PubMed Central

Berlin, Konstantin; O’Leary, Dianne P.; Fushman, David

2011-01-01

We present and evaluate a rigid-body, deterministic, molecular docking method, called ELMDOCK, that relies solely on the three-dimensional structure of the individual components and the overall rotational diffusion tensor of the complex, obtained from nuclear spin-relaxation measurements. We also introduce a docking method, called ELMPATIDOCK, derived from ELMDOCK and based on the new concept of combining the shape-related restraints from rotational diffusion with those from residual dipolar couplings, along with ambiguous contact/interface-related restraints obtained from chemical shift perturbations. ELMDOCK and ELMPATIDOCK use two novel approximations of the molecular rotational diffusion tensor that allow computationally efficient docking. We show that these approximations are accurate enough to properly dock the two components of a complex without the need to recompute the diffusion tensor at each iteration step. We analyze the accuracy, robustness, and efficiency of these methods using synthetic relaxation data for a large variety of protein-protein complexes. We also test our method on three protein systems for which the structure of the complex and experimental relaxation data are available, and analyze the effect of flexible unstructured tails on the outcome of docking. Additionally, we describe a method for integrating the new approximation methods into the existing docking approaches that use the rotational diffusion tensor as a restraint. The results show that the proposed docking method is robust against experimental errors in the relaxation data or structural rearrangements upon complex formation and is computationally more efficient than current methods. The developed approximations are accurate enough to be used in structure refinement protocols. PMID:21604302

Fast approximations of the rotational diffusion tensor and their application to structural assembly of molecular complexes.

PubMed

Berlin, Konstantin; O'Leary, Dianne P; Fushman, David

2011-07-01

We present and evaluate a rigid-body, deterministic, molecular docking method, called ELMDOCK, that relies solely on the three-dimensional structure of the individual components and the overall rotational diffusion tensor of the complex, obtained from nuclear spin-relaxation measurements. We also introduce a docking method, called ELMPATIDOCK, derived from ELMDOCK and based on the new concept of combining the shape-related restraints from rotational diffusion with those from residual dipolar couplings, along with ambiguous contact/interface-related restraints obtained from chemical shift perturbations. ELMDOCK and ELMPATIDOCK use two novel approximations of the molecular rotational diffusion tensor that allow computationally efficient docking. We show that these approximations are accurate enough to properly dock the two components of a complex without the need to recompute the diffusion tensor at each iteration step. We analyze the accuracy, robustness, and efficiency of these methods using synthetic relaxation data for a large variety of protein-protein complexes. We also test our method on three protein systems for which the structure of the complex and experimental relaxation data are available, and analyze the effect of flexible unstructured tails on the outcome of docking. Additionally, we describe a method for integrating the new approximation methods into the existing docking approaches that use the rotational diffusion tensor as a restraint. The results show that the proposed docking method is robust against experimental errors in the relaxation data or structural rearrangements upon complex formation and is computationally more efficient than current methods. The developed approximations are accurate enough to be used in structure refinement protocols. Copyright © 2011 Wiley-Liss, Inc.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Klima, Matej; Kucharik, MIlan; Shashkov, Mikhail Jurievich

We analyze several new and existing approaches for limiting tensor quantities in the context of deviatoric stress remapping in an ALE numerical simulation of elastic flow. Remapping and limiting of the tensor component-by-component is shown to violate radial symmetry of derived variables such as elastic energy or force. Therefore, we have extended the symmetry-preserving Vector Image Polygon algorithm, originally designed for limiting vector variables. This limiter constrains the vector (in our case a vector of independent tensor components) within the convex hull formed by the vectors from surrounding cells – an equivalent of the discrete maximum principle in scalar variables.more » We compare this method with a limiter designed specifically for deviatoric stress limiting which aims to constrain the J 2 invariant that is proportional to the specific elastic energy and scale the tensor accordingly. We also propose a method which involves remapping and limiting the J 2 invariant independently using known scalar techniques. The deviatoric stress tensor is then scaled to match this remapped invariant, which guarantees conservation in terms of elastic energy.« less

Inverse bootstrapping conformal field theories

NASA Astrophysics Data System (ADS)

Li, Wenliang

2018-01-01

We propose a novel approach to study conformal field theories (CFTs) in general dimensions. In the conformal bootstrap program, one usually searches for consistent CFT data that satisfy crossing symmetry. In the new method, we reverse the logic and interpret manifestly crossing-symmetric functions as generating functions of conformal data. Physical CFTs can be obtained by scanning the space of crossing-symmetric functions. By truncating the fusion rules, we are able to concentrate on the low-lying operators and derive some approximate relations for their conformal data. It turns out that the free scalar theory, the 2d minimal model CFTs, the ϕ 4 Wilson-Fisher CFT, the Lee-Yang CFTs and the Ising CFTs are consistent with the universal relations from the minimal fusion rule ϕ 1 × ϕ 1 = I + ϕ 2 + T , where ϕ 1 , ϕ 2 are scalar operators, I is the identity operator and T is the stress tensor.

Controlling effect of geometrically defined local structural changes on chaotic Hamiltonian systems.

PubMed

Ben Zion, Yossi; Horwitz, Lawrence

2010-04-01

An effective characterization of chaotic conservative Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor derived from the structure of the Hamiltonian has been extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce the Hamilton equations of the original potential model through an inverse map in the tangent space. The second covariant derivative of the geodesic deviation in this space generates a dynamical curvature, resulting in (energy-dependent) criteria for unstable behavior different from the usual Lyapunov criteria. We show here that this criterion can be constructively used to modify locally the potential of a chaotic Hamiltonian model in such a way that stable motion is achieved. Since our criterion for instability is local in coordinate space, these results provide a minimal method for achieving control of a chaotic system.

High Resolution Magnetotelluric Imaging of the Nisyros Caldera and Geothermal Resource (Greece)

NASA Astrophysics Data System (ADS)

Tzanis, Andreas; Sakkas, Vassilis; Lagios, Evangelos

2017-04-01

This work reports the qualitative and quantitative re-examination of legacy magnetotelluric soundings data obtained in the caldera of Nisyros, a small island volcano at the eastern end of the Hellenic Volcanic Arc (HVA), Greece, in an attempt to explore the high temperature geothermal resource of the area. The data set comprises 39 single-site soundings and is re-examined with improved data processing methods, new hypothetical event analysis techniques to study the spatial configuration of the telluric field and two-dimensional inversion tools. Iteratively reweighted least squares have been implemented to compute stable and smooth Earth response functions, which were found to exhibit 2-D to weakly 3-D attributes as a result of induction in low-contrast local geoelectric inhomogeneities, superimposed on a dominantly 2-D background structure. The transfer functions appear to be free of coastal and island induction effects due to the low offshore/onshore resistivity contrast at, and below sea level. The spatial properties of the telluric field are studied with hypothetical event analysis based on 3-D decompositions of the impedance tensor [1]. The results indicate that convection and hydrothermal circulation is controlled by a system of antithetic NE-SW oriented active normal faults which form a graben-like structure and define the 2-D background, as well as a conjugate system of NNW-SSE normal faults which is particularly active at the SW quadrant of the island and define the main convection path. It was determined that under these conditions the data can be interpreted with 2-D inversion, which was carried out with [2]. The inversion has successfully reconstructed detailed images of the structural and functional elements of the hydrothermal system. The structural elements include a number of shallow hot water reservoirs in the argillic and phyllic alteration zones and a laterally extended deep (approx. 1km) circulation zone, all embedded in a low-resistivity matrix with very low lateral contrasts. The functional elements include images of the most important convection conduits created by the intersection of major fault planes. The results are corroborated by the logs of two deep exploration wells. Overall, on the basis of a carefully reworked data set, our analysis has provided detailed images of the volcano's interior and valuable insight into its structure, function and geothermal potential. References [1] Tzanis, A., 2014. The Characteristic States of the Magnetotelluric Impedance Tensor: Construction, analytic properties and utility in the analysis of general Earth conductivity distributions, arXiv:1404.1478 [physics.geo-ph]; last accessed, January 2017. [2] Rodi, W. and Mackie, R.L., 2001. Nonlinear conjugate gradients algorithm for 2-D magnetotelluric inversion, Geophysics, 66 (1), 174-187.

In flight estimations of Cassini spacecraft inertia tensor and thruster magnitude

NASA Technical Reports Server (NTRS)

Feldman, Antonette; Lee, Allan Y.

2006-01-01

This paper describes two methods used by the Cassini Attitude Control team to determine these key parameters and how flight telemetry was used to estimate them. The method for estimating the spacecraft inertia tensor exploits the conservation of angular momentum during spacecraft slews under reaction wheel control.

g-Tensor determination from single-crystal ESR data

NASA Astrophysics Data System (ADS)

Byrn, Marianne P.; Strouse, Charles E.

A general method is presented for extraction of the g tensor from single-crystal electron spin resonance data. This method does not depend on knowledge of crystal morphology or on the presence of crystallographic symmetry. The g values are obtained from rotations around three arbitrarily chosen but accurately known axes.

Detection, localization and classification of multiple dipole-like magnetic sources using magnetic gradient tensor data

NASA Astrophysics Data System (ADS)

Gang, Yin; Yingtang, Zhang; Hongbo, Fan; Zhining, Li; Guoquan, Ren

2016-05-01

We have developed a method for automatic detection, localization and classification (DLC) of multiple dipole sources using magnetic gradient tensor data. First, we define modified tilt angles to estimate the approximate horizontal locations of the multiple dipole-like magnetic sources simultaneously and detect the number of magnetic sources using a fixed threshold. Secondly, based on the isotropy of the normalized source strength (NSS) response of a dipole, we obtain accurate horizontal locations of the dipoles. Then the vertical locations are calculated using magnitude magnetic transforms of magnetic gradient tensor data. Finally, we invert for the magnetic moments of the sources using the measured magnetic gradient tensor data and forward model. Synthetic and field data sets demonstrate effectiveness and practicality of the proposed method.

Newton-based optimization for Kullback-Leibler nonnegative tensor factorizations

DOE PAGES

Plantenga, Todd; Kolda, Tamara G.; Hansen, Samantha

2015-04-30

Tensor factorizations with nonnegativity constraints have found application in analysing data from cyber traffic, social networks, and other areas. We consider application data best described as being generated by a Poisson process (e.g. count data), which leads to sparse tensors that can be modelled by sparse factor matrices. In this paper, we investigate efficient techniques for computing an appropriate canonical polyadic tensor factorization based on the Kullback–Leibler divergence function. We propose novel subproblem solvers within the standard alternating block variable approach. Our new methods exploit structure and reformulate the optimization problem as small independent subproblems. We employ bound-constrained Newton andmore » quasi-Newton methods. Finally, we compare our algorithms against other codes, demonstrating superior speed for high accuracy results and the ability to quickly find sparse solutions.« less

Decentralized Dimensionality Reduction for Distributed Tensor Data Across Sensor Networks.

PubMed

Liang, Junli; Yu, Guoyang; Chen, Badong; Zhao, Minghua

2016-11-01

This paper develops a novel decentralized dimensionality reduction algorithm for the distributed tensor data across sensor networks. The main contributions of this paper are as follows. First, conventional centralized methods, which utilize entire data to simultaneously determine all the vectors of the projection matrix along each tensor mode, are not suitable for the network environment. Here, we relax the simultaneous processing manner into the one-vector-by-one-vector (OVBOV) manner, i.e., determining the projection vectors (PVs) related to each tensor mode one by one. Second, we prove that in the OVBOV manner each PV can be determined without modifying any tensor data, which simplifies corresponding computations. Third, we cast the decentralized PV determination problem as a set of subproblems with consensus constraints, so that it can be solved in the network environment only by local computations and information communications among neighboring nodes. Fourth, we introduce the null space and transform the PV determination problem with complex orthogonality constraints into an equivalent hidden convex one without any orthogonality constraint, which can be solved by the Lagrange multiplier method. Finally, experimental results are given to show that the proposed algorithm is an effective dimensionality reduction scheme for the distributed tensor data across the sensor networks.

White matter degeneration in schizophrenia: a comparative diffusion tensor analysis

NASA Astrophysics Data System (ADS)

Ingalhalikar, Madhura A.; Andreasen, Nancy C.; Kim, Jinsuh; Alexander, Andrew L.; Magnotta, Vincent A.

2010-03-01

Schizophrenia is a serious and disabling mental disorder. Diffusion tensor imaging (DTI) studies performed on schizophrenia have demonstrated white matter degeneration either due to loss of myelination or deterioration of fiber tracts although the areas where the changes occur are variable across studies. Most of the population based studies analyze the changes in schizophrenia using scalar indices computed from the diffusion tensor such as fractional anisotropy (FA) and relative anisotropy (RA). The scalar measures may not capture the complete information from the diffusion tensor. In this paper we have applied the RADTI method on a group of 9 controls and 9 patients with schizophrenia. The RADTI method converts the tensors to log-Euclidean space where a linear regression model is applied and hypothesis testing is performed between the control and patient groups. Results show that there is a significant difference in the anisotropy between patients and controls especially in the parts of forceps minor, superior corona radiata, anterior limb of internal capsule and genu of corpus callosum. To check if the tensor analysis gives a better idea of the changes in anisotropy, we compared the results with voxelwise FA analysis as well as voxelwise geodesic anisotropy (GA) analysis.

Tractography from HARDI using an Intrinsic Unscented Kalman Filter

PubMed Central

Cheng, Guang; Salehian, Hesamoddin; Forder, John R.; Vemuri, Baba C.

2014-01-01

A novel adaptation of the unscented Kalman filter (UKF) was recently introduced in literature for simultaneous multi-tensor estimation and fiber tractography from diffusion MRI. This technique has the advantage over other tractography methods in terms of computational efficiency, due to the fact that the UKF simultaneously estimates the diffusion tensors and propagates the most consistent direction to track along. This UKF and its variants reported later in literature however are not intrinsic to the space of diffusion tensors. Lack of this key property can possibly lead to inaccuracies in the multi-tensor estimation as well as in the tractography. In this paper, we propose a novel intrinsic unscented Kalman filter (IUKF) in the space of diffusion tensors which are symmetric positive definite matrices, that can be used for simultaneous recursive estimation of multi-tensors and propagation of directional information for use in fiber tractography from diffusion weighted MR data. In addition to being more accurate, IUKF retains all the advantages of UKF mentioned above. We demonstrate the accuracy and effectiveness of the proposed method via experiments publicly available phantom data from the fiber cup-challenge (MICCAI 2009) and diffusion weighted MR scans acquired from human brains and rat spinal cords. PMID:25203986

Spatial distribution of F-net moment tensors for the 2005 West Off Fukuoka Prefecture Earthquake determined by the extended method of the NIED F-net routine

NASA Astrophysics Data System (ADS)

Matsumoto, Takumi; Ito, Yoshihiro; Matsubayashi, Hirotoshi; Sekiguchi, Shoji

2006-01-01

The 2005 West Off Fukuoka Prefecture Earthquake with a Japan Meteorological Agency (JMA) magnitude (MJMA) of 7.0 occurred on March 20, 2005. We determined moment tensor solutions, using a surface wave with an extended method of the NIED F-net routine processing. The horizontal distance to the station is rounded to the nearest interval of 1 km, and the variance reduction approach is applied to a focal depth from 2 km with an interval of 1 km. We obtain the moment tensors of 101 events with (MJMA) exceeding 3.0 and spatial distribution of these moment tensors. The focal mechanism of aftershocks is mainly of the strike-slip type. The alignment of the epicenters in the rupture zone of the main-shock is oriented between N110°E and N130°E, which is close to the strike of the main-shock's moment tensor solutions (N122°E). These moment tensor solutions of intermediatesized aftershocks around the focal region represent basic and important information concerning earthquakes in investigating regional tectonic stress fields, source mechanisms and so on.

A general theory of linear cosmological perturbations: scalar-tensor and vector-tensor theories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lagos, Macarena; Baker, Tessa; Ferreira, Pedro G.

We present a method for parametrizing linear cosmological perturbations of theories of gravity, around homogeneous and isotropic backgrounds. The method is sufficiently general and systematic that it can be applied to theories with any degrees of freedom (DoFs) and arbitrary gauge symmetries. In this paper, we focus on scalar-tensor and vector-tensor theories, invariant under linear coordinate transformations. In the case of scalar-tensor theories, we use our framework to recover the simple parametrizations of linearized Horndeski and ''Beyond Horndeski'' theories, and also find higher-derivative corrections. In the case of vector-tensor theories, we first construct the most general quadratic action for perturbationsmore » that leads to second-order equations of motion, which propagates two scalar DoFs. Then we specialize to the case in which the vector field is time-like (à la Einstein-Aether gravity), where the theory only propagates one scalar DoF. As a result, we identify the complete forms of the quadratic actions for perturbations, and the number of free parameters that need to be defined, to cosmologically characterize these two broad classes of theories.« less

Seamless Warping of Diffusion Tensor Fields

PubMed Central

Hao, Xuejun; Bansal, Ravi; Plessen, Kerstin J.; Peterson, Bradley S.

2008-01-01

To warp diffusion tensor fields accurately, tensors must be reoriented in the space to which the tensors are warped based on both the local deformation field and the orientation of the underlying fibers in the original image. Existing algorithms for warping tensors typically use forward mapping deformations in an attempt to ensure that the local deformations in the warped image remains true to the orientation of the underlying fibers; forward mapping, however, can also create “seams” or gaps and consequently artifacts in the warped image by failing to define accurately the voxels in the template space where the magnitude of the deformation is large (e.g., |Jacobian| > 1). Backward mapping, in contrast, defines voxels in the template space by mapping them back to locations in the original imaging space. Backward mapping allows every voxel in the template space to be defined without the creation of seams, including voxels in which the deformation is extensive. Backward mapping, however, cannot reorient tensors in the template space because information about the directional orientation of fiber tracts is contained in the original, unwarped imaging space only, and backward mapping alone cannot transfer that information to the template space. To combine the advantages of forward and backward mapping, we propose a novel method for the spatial normalization of diffusion tensor (DT) fields that uses a bijection (a bidirectional mapping with one-to-one correspondences between image spaces) to warp DT datasets seamlessly from one imaging space to another. Once the bijection has been achieved and tensors have been correctly relocated to the template space, we can appropriately reorient tensors in the template space using a warping method based on Procrustean estimation. PMID:18334425

Yield Scaling of Frequency Domain Moment Tensors from Contained Chemical Explosions Detonated in Granite

NASA Astrophysics Data System (ADS)

MacPhail, M. D.; Stump, B. W.; Zhou, R.

2017-12-01

The Source Phenomenology Experiment (SPE - Arizona) was a series of nine, contained and partially contained chemical explosions within the porphyry granite at the Morenci Copper mine in Arizona. Its purpose was to detonate, record and analyze seismic waveforms from these single-fired explosions. Ground motion data from the SPE is analyzed in this study to assess the uniqueness of the time domain moment tensor source representation and its ability to quantify containment and yield scaling. Green's functions were computed for each of the explosions based on a 1D velocity model developed for the SPE. The Green's functions for the sixteen, near-source stations focused on observations from 37 to 680 m. This study analyzes the three deepest, fully contained explosions with a depth of burial of 30 m and yields of 0.77e-3, 3.08e-3 and 6.17e-3 kt. Inversions are conducted within the frequency domain and moment tensors are decomposed into deviatoric and isotropic components to evaluate the effects of containment and yield on the resulting source representation. Isotropic moments are compared to those for other contained explosions as reported by Denny and Johnson, 1991, and are in good agreement with their scaling results. The explosions in this study have isotropic moments of 1.2e12, 3.1e12 and 6.1e13 n*m. Isotropic and Mzz moment tensor spectra are compared to Mueller-Murphy, Denny-Johnson and revised Heard-Ackerman (HA) models and suggest that the larger explosions fit the HA model better. Secondary source effects resulting from free surface interactions including the effects of spallation contribute to the resulting moment tensors which include a CLVD component. Hudson diagrams, using frequency domain moment tensor data, are computed as a tool to assess how these containment scenarios affect the source representation. Our analysis suggests that, within our band of interest (2-20 Hz), as the frequency increases, the source representation becomes more explosion like, peaking at around 20 Hz. These results guide additional analysis of the observational data and the practical resolution of physical phenomenology accompanying underground explosions.

Conformal Yano-Killing Tensors for Space-times with Cosmological Constant

NASA Astrophysics Data System (ADS)

Czajka, P.; Jezierski, J.

We present a new method for constructing conformal Yano-Killing tensors in five-di\\-men\\-sio\\-nal Anti-de Sitter space-time. The found tensors are represented in two different coordinate systems. We also discuss, in terms of CYK tensors, global charges which are well defined for asymptotically (five-dimensional) Anti-de Sitter space-time. Additionally in Appendix we present our own derivation of conformal Killing one-forms in four-dimensional Anti-de Sitter space-time as an application of the Theorem presented in the paper.

Renormalization group contraction of tensor networks in three dimensions

NASA Astrophysics Data System (ADS)

García-Sáez, Artur; Latorre, José I.

2013-02-01

We present a new strategy for contracting tensor networks in arbitrary geometries. This method is designed to follow as strictly as possible the renormalization group philosophy, by first contracting tensors in an exact way and, then, performing a controlled truncation of the resulting tensor. We benchmark this approximation procedure in two dimensions against an exact contraction. We then apply the same idea to a three-dimensional quantum system. The underlying rational for emphasizing the exact coarse graining renormalization group step prior to truncation is related to monogamy of entanglement.

OPERATOR NORM INEQUALITIES BETWEEN TENSOR UNFOLDINGS ON THE PARTITION LATTICE

PubMed Central

Wang, Miaoyan; Duc, Khanh Dao; Fischer, Jonathan; Song, Yun S.

2017-01-01

Interest in higher-order tensors has recently surged in data-intensive fields, with a wide range of applications including image processing, blind source separation, community detection, and feature extraction. A common paradigm in tensor-related algorithms advocates unfolding (or flattening) the tensor into a matrix and applying classical methods developed for matrices. Despite the popularity of such techniques, how the functional properties of a tensor changes upon unfolding is currently not well understood. In contrast to the body of existing work which has focused almost exclusively on matricizations, we here consider all possible unfoldings of an order-k tensor, which are in one-to-one correspondence with the set of partitions of {1, …, k}. We derive general inequalities between the lp-norms of arbitrary unfoldings defined on the partition lattice. In particular, we demonstrate how the spectral norm (p = 2) of a tensor is bounded by that of its unfoldings, and obtain an improved upper bound on the ratio of the Frobenius norm to the spectral norm of an arbitrary tensor. For specially-structured tensors satisfying a generalized definition of orthogonal decomposability, we prove that the spectral norm remains invariant under specific subsets of unfolding operations. PMID:28286347

OPERATOR NORM INEQUALITIES BETWEEN TENSOR UNFOLDINGS ON THE PARTITION LATTICE.

PubMed

Wang, Miaoyan; Duc, Khanh Dao; Fischer, Jonathan; Song, Yun S

2017-05-01

Interest in higher-order tensors has recently surged in data-intensive fields, with a wide range of applications including image processing, blind source separation, community detection, and feature extraction. A common paradigm in tensor-related algorithms advocates unfolding (or flattening) the tensor into a matrix and applying classical methods developed for matrices. Despite the popularity of such techniques, how the functional properties of a tensor changes upon unfolding is currently not well understood. In contrast to the body of existing work which has focused almost exclusively on matricizations, we here consider all possible unfoldings of an order- k tensor, which are in one-to-one correspondence with the set of partitions of {1, …, k }. We derive general inequalities between the l p -norms of arbitrary unfoldings defined on the partition lattice. In particular, we demonstrate how the spectral norm ( p = 2) of a tensor is bounded by that of its unfoldings, and obtain an improved upper bound on the ratio of the Frobenius norm to the spectral norm of an arbitrary tensor. For specially-structured tensors satisfying a generalized definition of orthogonal decomposability, we prove that the spectral norm remains invariant under specific subsets of unfolding operations.

Focal Mechanisms at the convergent plate boundary in Southern Aegean, Greece.

NASA Astrophysics Data System (ADS)

Moshou, Alexandra; Papadimitriou, Eleftheria; Drakatos, George; Evangelidis, Christos; Karakostas, Vasilios; Vallianatos, Filippos; Makropoulos, Konstantinos

2014-05-01

Greece is characterized by high seismicity, mainly due to the collision between the European and the African lithospheric plates and the dextral strike slip motion along the North Anatolia Fault zone and North Aegean Trough. The subduction of the Eastern Mediterranean oceanic plate along the Hellenic Arc under the Aegean microplate along with the accompanied roll back of the descending slab is considered the main tectonic feature of the region (Papazachos and Comninakis 1971; Makropoulos and Burton 1984; Papazachos et al. 2000a, b). The divergent motion between the Aegean block and mainland Europe is indicated by an extension zone in the northern Aegean, with Crete and Aegean diverging from mainland Europe at a rate of about 3.5 cm yr-1 with Africa moving northward relative to Europe at a rate of about 1 cm yr-1 (Dewey et al., 1989; Papazachos et al., 1998; Mc-Clusky et al., 2000; Reilinger et al., 2006). In this tectonically complicated area diverge types of deformation are manifested, in addition to the dominant subduction processes. Aiming to shed more light in the seismotectonic properties and faulting seismological data from the Hellenic Unified Seismological Network (HUSN) were selected and analyzed for determining focal mechanisms using the method of moment tensor inversion, additional to the ones being available from the routine moment tensor solutions and several publications. Thus, 31 new fault plane solutions for events with magnitude M>4.0, are presented in this study, by using the software of Ammon (Randall et al., 1995). For this scope the data from at least 4 stations were used with an adequate azimuthal coverage and with an epicentral distance not more than 350 km. The preparation of the data includes the deconvolution of instruments response, then the velocity was integrated to displacement and finally the horizontal components were rotated to radial and transverse. Following, the signal was inverted using the reflectivity method of Kennett (1983) as implemented by Randall (1994) in order to determine Green's functions. Initially, iterative inversions were performed considering a crude depth interval of 5 km and the relative misfit functions were computed. In a second stage, inversions were performed considering a finer depth interval of 1-2 km around the depth where the lowest misfit was exhibited. During the analysis different velocity models were used (Karagianni et al., 2005; Novotny et al., 2001; Papazachos et al., 1997). This research has been funded by the European Union (European Social Fund) and Greek national resources under the framework of the "THALES Program: SEISMO FEAR HELLARC" project of the "Education & Lifelong Learning" Operational Programme.

Quantification of the electrical anisotropy in the pro­cess of numerical modelling for hydrogeological characterization

NASA Astrophysics Data System (ADS)

Gernez, S.; Bouchedda, A.; Gloaguen, E.; Paradis, D.

2017-12-01

In order to understand groundwater flow and contaminant transport in the subsurface, it is important to characterize accurately its permeability. Hydrogeophysics, which involves the use of geophysical data to infer the hydraulic properties of the subsurface, is a relatively new geoscience field that is promising to improve hydrogeological characterization. Amongst existing geophysical methods, Electrical Resistivity Tomography (ERT), that can cover a large continuous underground surface or volume, has been widely applied. The inversed electrical resistivities obtained are related to the permeabilities by different means and the resistivity anisotropy should theoretically be a proxy to the permeability anisotropy. However, the existing hydrogeophysical inversion tools usually do not take into account anisotropy. In this paper, we present an anisotropic forward- and inverse-problem 2.5D finite-differences electrical study, which allows to produce improved anisotropic permeability characterization models. We first detail the theoretical basis of the anisotropic ERT, which introduces a resistivity tensor in place of a scalar, and its numerical implementation. After that, we build a synthetic case presenting a simple but representative geological structure in two horizontal homogeneous and anisotropic beds: the numerical forward modelling shows a difference of less than 1% with the analytical solution; the inverse modelling is able to reproduce the initial structure well, with resistivity values close to the initial synthetic model (see attached figure). We show that by using both surface and single-borehole arrays, we overcome the equivalence principle making sure that a unique solution arises. The latter cannot be obtained when considering the media isotropic as typically assumed with existing inversion tools. Finally, we discuss the consequences of the integration of anisotropy in the data-integrated characterization of the permeability. We show that it has a significant influence on the electrical inversion results and then on the hydrogeological characterization. It suggests that anisotropy should be taken into account in any characterization study when its presence is presumed or known in order to produce a model closer to the true hydraulic state of the ground.

Supervised Variational Relevance Learning, An Analytic Geometric Feature Selection with Applications to Omic Datasets.

PubMed

Boareto, Marcelo; Cesar, Jonatas; Leite, Vitor B P; Caticha, Nestor

2015-01-01

We introduce Supervised Variational Relevance Learning (Suvrel), a variational method to determine metric tensors to define distance based similarity in pattern classification, inspired in relevance learning. The variational method is applied to a cost function that penalizes large intraclass distances and favors small interclass distances. We find analytically the metric tensor that minimizes the cost function. Preprocessing the patterns by doing linear transformations using the metric tensor yields a dataset which can be more efficiently classified. We test our methods using publicly available datasets, for some standard classifiers. Among these datasets, two were tested by the MAQC-II project and, even without the use of further preprocessing, our results improve on their performance.

Isotropic source terms of San Jacinto fault zone earthquakes based on waveform inversions with a generalized CAP method

NASA Astrophysics Data System (ADS)

Ross, Z. E.; Ben-Zion, Y.; Zhu, L.

2015-02-01

We analyse source tensor properties of seven Mw > 4.2 earthquakes in the complex trifurcation area of the San Jacinto Fault Zone, CA, with a focus on isotropic radiation that may be produced by rock damage in the source volumes. The earthquake mechanisms are derived with generalized `Cut and Paste' (gCAP) inversions of three-component waveforms typically recorded by >70 stations at regional distances. The gCAP method includes parameters ζ and χ representing, respectively, the relative strength of the isotropic and CLVD source terms. The possible errors in the isotropic and CLVD components due to station variability is quantified with bootstrap resampling for each event. The results indicate statistically significant explosive isotropic components for at least six of the events, corresponding to ˜0.4-8 per cent of the total potency/moment of the sources. In contrast, the CLVD components for most events are not found to be statistically significant. Trade-off and correlation between the isotropic and CLVD components are studied using synthetic tests with realistic station configurations. The associated uncertainties are found to be generally smaller than the observed isotropic components. Two different tests with velocity model perturbation are conducted to quantify the uncertainty due to inaccuracies in the Green's functions. Applications of the Mann-Whitney U test indicate statistically significant explosive isotropic terms for most events consistent with brittle damage production at the source.

A Block Coordinate Descent Method for Multi-Convex Optimization with Applications to Nonnegative Tensor Factorization and Completion

DTIC Science & Technology

2012-08-01

model appears in cosmic microwave background analysis [10] which solves min A,Y λ 2 trace ( (ABY − X)>C−1(ABY − X) ) + r(Y), subject to A ∈ D (1.5...and “×n” represent outer product and tensor-matrix multiplication, respectively. (The necessary background of tensor is reviewed in Sec. 3) Most

Multi-physics and multi-scale characterization of shale anisotropy

NASA Astrophysics Data System (ADS)

Sarout, J.; Nadri, D.; Delle Piane, C.; Esteban, L.; Dewhurst, D.; Clennell, M. B.

2012-12-01

Shales are the most abundant sedimentary rock type in the Earth's shallow crust. In the past decade or so, they have attracted increased attention from the petroleum industry as reservoirs, as well as more traditionally for their sealing capacity for hydrocarbon/CO2 traps or underground waste repositories. The effectiveness of both fundamental and applied shale research is currently limited by (i) the extreme variability of physical, mechanical and chemical properties observed for these rocks, and by (ii) the scarce data currently available. The variability in observed properties is poorly understood due to many factors that are often irrelevant for other sedimentary rocks. The relationships between these properties and the petrophysical measurements performed at the field and laboratory scales are not straightforward, translating to a scale dependency typical of shale behaviour. In addition, the complex and often anisotropic micro-/meso-structures of shales give rise to a directional dependency of some of the measured physical properties that are tensorial by nature such as permeability or elastic stiffness. Currently, fundamental understanding of the parameters controlling the directional and scale dependency of shale properties is far from complete. Selected results of a multi-physics laboratory investigation of the directional and scale dependency of some critical shale properties are reported. In particular, anisotropic features of shale micro-/meso-structures are related to the directional-dependency of elastic and fluid transport properties: - Micro-/meso-structure (μm to cm scale) characterization by electron microscopy and X-ray tomography; - Estimation of elastic anisotropy parameters on a single specimen using elastic wave propagation (cm scale); - Estimation of the permeability tensor using the steady-state method on orthogonal specimens (cm scale); - Estimation of the low-frequency diffusivity tensor using NMR method on orthogonal specimens (<μm scale). For each of the above properties, leading-edge experimental techniques have been associated with novel interpretation tools. In this contribution, these experimental and interpretation methods are described. Relationships between the measured properties and the corresponding micro-/meso-structural features are discussed. For example, P-wave velocity was measured along 100 different propagation paths on a single cylindrical shale specimen using miniature ultrasonic transducers. Assuming that (i) the elastic tensor of this shale is transversely isotropic; and (i) the sample has been cored perfectly perpendicular to the bedding plane (symmetry plane is horizontal), Thomsen's anisotropy parameters inverted from the measured velocities are: - P-wave velocity along the symmetry axis (perpendicular to the bedding plane) αo=3.45km/s; - P-wave anisotropy ɛ=0.12; - Parameter controlling the wave front geometry δ=0.058. A novel inversion algorithm allows for recovering these parameters without assuming a priori a horizontal bedding (symmetry) plane. The inversion of the same data set using this algorithm yields (i) αo=3.23km/s, ɛ=0.25 and δ=0.18, and (ii) the elastic symmetry axis is inclined of ω=30° with respect to the specimen's axis. Such difference can have strong impact on field applications (AVO, ray tracing, tomography).

North Korea nuclear test analysis results using KMA seismic and infrasound networks

NASA Astrophysics Data System (ADS)

Jeon, Y. S.; Park, E.; Lee, D.; Min, K.; CHO, S.

2017-12-01

Democratic People's Republic of Korea(DPRK) carried out 6th nuclear test on 3 Sep. 2017 at 03:30 UTC. Seismic and infrasound network operated by Korea Meteorological Administration(KMA) successfully detected signals took place in the DPRK's test site, Punggye-ri. First, we checked that Pg/Lg spectral amplitude ratio greater than 1 in the frequency range from 1.0 to 10.0 Hz is useful to discriminate between DPRK test signals and natural earthquakes. KMA's infrasound stations of Cheorwon(CW) and Yanggu(YG) successfully monitored the azimuth direction of the arrival of the infrasound signals generated from DPRK underground nuclear explosions, including the recent test on September 03, 2017. The azimuthal direction of 210(CW) and 130 (YG) point out Punggye-ri test site. Complete waveforms at stations MDJ, CHC2, YNCB in long period(0.05 to 0.1 HZ) are jointly inverted with local P-wave polarities to generate moment tensor inversion result of the explosive moment 1.20e+24 dyne cm(Mw 5.31) and 65% of ISO. The moment magnitude of 5th, 4th and 3rd are 4.61, 4.69 and 4.46 respectively. Source type moment tensor inversion result of DPRK nuclear tests show that the event is significantly away from the deviatoric line of the Hudson et at. (1989) source-type diagram and identifies as having a significant explosive component. Analysis results using seismic and infrasound network verify that the DPRK's explosion tests classified as nuclear test.

Robotic Online Path Planning on Point Cloud.

PubMed

Liu, Ming

2016-05-01

This paper deals with the path-planning problem for mobile wheeled- or tracked-robot which drive in 2.5-D environments, where the traversable surface is usually considered as a 2-D-manifold embedded in a 3-D ambient space. Specially, we aim at solving the 2.5-D navigation problem using raw point cloud as input. The proposed method is independent of traditional surface parametrization or reconstruction methods, such as a meshing process, which generally has high-computational complexity. Instead, we utilize the output of 3-D tensor voting framework on the raw point clouds. The computation of tensor voting is accelerated by optimized implementation on graphics computation unit. Based on the tensor voting results, a novel local Riemannian metric is defined using the saliency components, which helps the modeling of the latent traversable surface. Using the proposed metric, we prove that the geodesic in the 3-D tensor space leads to rational path-planning results by experiments. Compared to traditional methods, the results reveal the advantages of the proposed method in terms of smoothing the robot maneuver while considering the minimum travel distance.

Improvement of Accuracy for Background Noise Estimation Method Based on TPE-AE

NASA Astrophysics Data System (ADS)

Itai, Akitoshi; Yasukawa, Hiroshi

This paper proposes a method of a background noise estimation based on the tensor product expansion with a median and a Monte carlo simulation. We have shown that a tensor product expansion with absolute error method is effective to estimate a background noise, however, a background noise might not be estimated by using conventional method properly. In this paper, it is shown that the estimate accuracy can be improved by using proposed methods.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rajbhandari, Samyam; NIkam, Akshay; Lai, Pai-Wei

Tensor contractions represent the most compute-intensive core kernels in ab initio computational quantum chemistry and nuclear physics. Symmetries in these tensor contractions makes them difficult to load balance and scale to large distributed systems. In this paper, we develop an efficient and scalable algorithm to contract symmetric tensors. We introduce a novel approach that avoids data redistribution in contracting symmetric tensors while also avoiding redundant storage and maintaining load balance. We present experimental results on two parallel supercomputers for several symmetric contractions that appear in the CCSD quantum chemistry method. We also present a novel approach to tensor redistribution thatmore » can take advantage of parallel hyperplanes when the initial distribution has replicated dimensions, and use collective broadcast when the final distribution has replicated dimensions, making the algorithm very efficient.« less

Spin and pseudospin symmetric Dirac particles in the field of Tietz—Hua potential including Coulomb tensor interaction

NASA Astrophysics Data System (ADS)

Sameer, M. Ikhdair; Majid, Hamzavi

2013-09-01

Approximate analytical solutions of the Dirac equation for Tietz—Hua (TH) potential including Coulomb-like tensor (CLT) potential with arbitrary spin—orbit quantum number κ are obtained within the Pekeris approximation scheme to deal with the spin—orbit coupling terms κ(κ ± 1)r-2. Under the exact spin and pseudospin symmetric limitation, bound state energy eigenvalues and associated unnormalized two-component wave functions of the Dirac particle in the field of both attractive and repulsive TH potential with tensor potential are found using the parametric Nikiforov—Uvarov (NU) method. The cases of the Morse oscillator with tensor potential, the generalized Morse oscillator with tensor potential, and the non-relativistic limits have been investigated.

Video denoising using low rank tensor decomposition

NASA Astrophysics Data System (ADS)

Gui, Lihua; Cui, Gaochao; Zhao, Qibin; Wang, Dongsheng; Cichocki, Andrzej; Cao, Jianting

2017-03-01

Reducing noise in a video sequence is of vital important in many real-world applications. One popular method is block matching collaborative filtering. However, the main drawback of this method is that noise standard deviation for the whole video sequence is known in advance. In this paper, we present a tensor based denoising framework that considers 3D patches instead of 2D patches. By collecting the similar 3D patches non-locally, we employ the low-rank tensor decomposition for collaborative filtering. Since we specify the non-informative prior over the noise precision parameter, the noise variance can be inferred automatically from observed video data. Therefore, our method is more practical, which does not require knowing the noise variance. The experimental on video denoising demonstrates the effectiveness of our proposed method.

Tensor-product preconditioners for higher-order space-time discontinuous Galerkin methods

NASA Astrophysics Data System (ADS)

Diosady, Laslo T.; Murman, Scott M.

2017-02-01

A space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equations. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high-order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.

Tensor-Product Preconditioners for Higher-Order Space-Time Discontinuous Galerkin Methods

NASA Technical Reports Server (NTRS)

Diosady, Laslo T.; Murman, Scott M.

2016-01-01

space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equat ions. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.

The tensor hypercontracted parametric reduced density matrix algorithm: coupled-cluster accuracy with O(r(4)) scaling.

PubMed

Shenvi, Neil; van Aggelen, Helen; Yang, Yang; Yang, Weitao; Schwerdtfeger, Christine; Mazziotti, David

2013-08-07

Tensor hypercontraction is a method that allows the representation of a high-rank tensor as a product of lower-rank tensors. In this paper, we show how tensor hypercontraction can be applied to both the electron repulsion integral tensor and the two-particle excitation amplitudes used in the parametric 2-electron reduced density matrix (p2RDM) algorithm. Because only O(r) auxiliary functions are needed in both of these approximations, our overall algorithm can be shown to scale as O(r(4)), where r is the number of single-particle basis functions. We apply our algorithm to several small molecules, hydrogen chains, and alkanes to demonstrate its low formal scaling and practical utility. Provided we use enough auxiliary functions, we obtain accuracy similar to that of the standard p2RDM algorithm, somewhere between that of CCSD and CCSD(T).

Neurocognitive and neuroimaging correlates of pediatric traumatic brain injury: A diffusion tensor imaging (DTI) study

PubMed Central

Wozniak, Jeffrey R.; Krach, Linda; Ward, Erin; Mueller, Bryon A.; Muetzel, Ryan; Schnoebelen, Sarah; Kiragu, Andrew; Lim, Kelvin O.

2010-01-01

This study examined the sensitivity of diffusion tensor imaging (DTI) to microstructural white matter (WM) damage in mild and moderate pediatric traumatic brain injury (TBI). Fourteen children with TBI and 14 controls ages 10–18 had DTI scans and neurocognitive evaluations at 6–12 months post-injury. Groups did not differ in intelligence, but children with TBI showed slower processing speed, working memory and executive deficits, and greater behavioral dysregulation. The TBI group had lower fractional anisotropy (FA) in three WM regions: inferior frontal, superior frontal, and supracallosal. There were no group differences in corpus callosum. FA in the frontal and supracallosal regions was correlated with executive functioning. Supracallosal FA was also correlated with motor speed. Behavior ratings showed correlations with supracallosal FA. Parent-reported executive deficits were inversely correlated with FA. Results suggest that DTI measures are sensitive to long-term WM changes and associated with cognitive functioning following pediatric TBI. PMID:17446039

Brans-Dicke inflation in light of the Planck 2015 data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tahmasebzadeh, B.; Rezazadeh, K.; Karami, K., E-mail: b.tahmasebzadeh@iasbs.ac.ir, E-mail: rezazadeh86@gmail.com, E-mail: kkarami@uok.ac.ir

We study inflation in the Brans-Dicke gravity as a special model of the scalar-tensor gravity. We obtain the inflationary observables containing the scalar spectral index, the tensor-to-scalar ratio, the running of the scalar spectral index and the equilateral non-Gaussianity parameter in terms of the general form of the potential in the Jordan frame. Then, we compare the results for various inflationary potentials in light of the Planck 2015 data. Our study shows that in the Brans-Dicke gravity, the power-law, inverse power-law and exponential potentials are ruled out by the Planck 2015 data. But, the hilltop, Higgs, Coleman-Weinberg and natural potentialsmore » can be compatible with Planck 2015 TT,TE,EE+lowP data at 95% CL. Moreover, the D-brane, SB SUSY and displaced quadratic potentials can be in well agreement with the observational data since their results can lie inside the 68% CL region of Planck 2015 TT,TE,EE+lowP data.« less

Moment-tensor solutions for the 24 November 1987 Superstition Hills, California, earthquakes

USGS Publications Warehouse

Sipkin, S.A.

1989-01-01

The teleseismic long-period waveforms recorded by the Global Digital Seismograph Network from the two largest Superstition Hills earthquakes are inverted using an algorithm based on optimal filter theory. These solutions differ slightly from those published in the Preliminary Determination of Epicenters Monthly Listing because a somewhat different, improved data set was used in the inversions and a time-dependent moment-tensor algorithm was used to investigate the complexity of the main shock. The foreshock (origin time 01:54:14.5, mb 5.7, Ms6.2) had a scalar moment of 2.3 ?? 1025 dyne-cm, a depth of 8km, and a mechanism of strike 217??, dip 79??, rake 4??. The main shock (origin time 13:15:56.4, mb 6.0, Ms6.6) was a complex event, consisting of at least two subevents, with a combined scalar moment of 1.0 ?? 1026 dyne-cm, a depth of 10km, and a mechanism of strike 303??, dip 89??, rake -180??. -Authors

The 2017 North Korea M6 seismic sequence: moment tensor, source time function, and aftershocks

NASA Astrophysics Data System (ADS)

Ni, S.; Zhan, Z.; Chu, R.; He, X.

2017-12-01

On September 3rd, 2017, an M6 seismic event occurred in North Korea, with location near previous nuclear test sites. The event features strong P waves and short period Rayleigh waves are observed in contrast to weak S waves, suggesting mostly explosion mechanism. We performed joint inversion for moment tensor and depth with both local and teleseismic waveforms, and find that the event is shallow with mostly isotropic yet substantial non-isotropic components. Deconvolution of seismic waveforms of this event with respect to previous nuclear test events shows clues of complexity in source time function. The event is followed by smaller earthquakes, as early as 8.5 minutes and lasted at least to October. The later events occurred in a compact region, and show clear S waves, suggesting double couple focal mechanism. Via analyzing Rayleigh wave spectrum, these smaller events are found to be shallow. Relative locations, difference in waveforms of the events are used to infer their possible links and generation mechanism.

New seismogenic stress fields for southern Italy from a Bayesian approach

NASA Astrophysics Data System (ADS)

Totaro, Cristina; Orecchio, Barbara; Presti, Debora; Scolaro, Silvia; Neri, Giancarlo

2017-04-01

A new database of high-quality waveform inversion focal mechanism has been compiled for southern Italy by integrating the highest quality solutions, available from literature and catalogues, and 146 newly-computed ones. All the selected focal mechanisms are (i) coming from the Italian CMT, Regional CMT and TDMT catalogues (Pondrelli et al., PEPI 2006, PEPI 2011; http://www.ingv.it), or (ii) computed by using the Cut And Paste (CAP) method (Zhao & Helmberger, BSSA 1994; Zhu & Helmberger, BSSA 1996). Specific tests have been carried out in order to evaluate the robustness of the obtained solutions (e.g., by varying both seismic network configuration and Earth structure parameters) and to estimate uncertainties on the focal mechanism parameters. Only the resulting highest-quality solutions have been enclosed in the database, that has then been used for computation of posterior density distributions of stress tensor components by a Bayesian method (Arnold & Townend, GJI 2007). This algorithm furnishes the posterior density function of the principal components of stress tensor (maximum σ1, intermediate σ2, and minimum σ3 compressive stress, respectively) and the stress-magnitude ratio (R). Before stress computation, we applied the k-means clustering algorithm to subdivide the focal mechanism catalog on the basis of earthquake locations. This approach allows identifying the sectors to be investigated without any "a priori" constraint from faulting type distribution. The large amount of data and the application of the Bayesian algorithm allowed us to provide a more accurate local-to-regional scale stress distribution that has shed new light on the kinematics and dynamics of this very complex area, where lithospheric unit configuration and geodynamic engines are still strongly debated. The new high-quality information here furnished will then represent very useful tools and constraints for future geophysical analyses and geodynamic modeling.

Electron paramagnetic resonance g-tensors from state interaction spin-orbit coupling density matrix renormalization group

NASA Astrophysics Data System (ADS)

Sayfutyarova, Elvira R.; Chan, Garnet Kin-Lic

2018-05-01

We present a state interaction spin-orbit coupling method to calculate electron paramagnetic resonance g-tensors from density matrix renormalization group wavefunctions. We apply the technique to compute g-tensors for the TiF3 and CuCl42 - complexes, a [2Fe-2S] model of the active center of ferredoxins, and a Mn4CaO5 model of the S2 state of the oxygen evolving complex. These calculations raise the prospects of determining g-tensors in multireference calculations with a large number of open shells.

Kronecker-Basis-Representation Based Tensor Sparsity and Its Applications to Tensor Recovery.

PubMed

Xie, Qi; Zhao, Qian; Meng, Deyu; Xu, Zongben

2017-08-02

It is well known that the sparsity/low-rank of a vector/matrix can be rationally measured by nonzero-entries-number ($l_0$ norm)/nonzero- singular-values-number (rank), respectively. However, data from real applications are often generated by the interaction of multiple factors, which obviously cannot be sufficiently represented by a vector/matrix, while a high order tensor is expected to provide more faithful representation to deliver the intrinsic structure underlying such data ensembles. Unlike the vector/matrix case, constructing a rational high order sparsity measure for tensor is a relatively harder task. To this aim, in this paper we propose a measure for tensor sparsity, called Kronecker-basis-representation based tensor sparsity measure (KBR briefly), which encodes both sparsity insights delivered by Tucker and CANDECOMP/PARAFAC (CP) low-rank decompositions for a general tensor. Then we study the KBR regularization minimization (KBRM) problem, and design an effective ADMM algorithm for solving it, where each involved parameter can be updated with closed-form equations. Such an efficient solver makes it possible to extend KBR to various tasks like tensor completion and tensor robust principal component analysis. A series of experiments, including multispectral image (MSI) denoising, MSI completion and background subtraction, substantiate the superiority of the proposed methods beyond state-of-the-arts.

Scalar field coupling to Einstein tensor in regular black hole spacetime

NASA Astrophysics Data System (ADS)

Zhang, Chi; Wu, Chen

2018-02-01

In this paper, we study the perturbation property of a scalar field coupling to Einstein's tensor in the background of the regular black hole spacetimes. Our calculations show that the the coupling constant η imprints in the wave equation of a scalar perturbation. We calculated the quasinormal modes of scalar field coupling to Einstein's tensor in the regular black hole spacetimes by the 3rd order WKB method.

Stimulated echo diffusion tensor imaging and SPAIR T2 -weighted imaging in chronic exertional compartment syndrome of the lower leg muscles.

PubMed

Sigmund, Eric E; Sui, Dabang; Ukpebor, Obehi; Baete, Steven; Fieremans, Els; Babb, James S; Mechlin, Michael; Liu, Kecheng; Kwon, Jane; McGorty, KellyAnne; Hodnett, Philip A; Bencardino, Jenny

2013-11-01

To evaluate the performance of diffusion tensor imaging (DTI) in the evaluation of chronic exertional compartment syndrome (CECS) as compared to T2 -weighted (T2w) imaging. Using an Institutional Review Board (IRB)-approved, Health Insurance Portability and Accountability Act (HIPAA)-compliant protocol, spectral adiabatic inversion recovery (SPAIR) T2w imaging and stimulated echo DTI were applied to eight healthy volunteers and 14 suspected CECS patients before and after exertion. Longitudinal and transverse diffusion eigenvalues, mean diffusivity (MD), and fractional anisotropy (FA) were measured in seven calf muscle compartments, which in patients were classified by their response on T2w: normal (<20% change), and CECS (>20% change). Mixed model analysis of variance compared subject groups and compartments in terms of response factors (post/pre-exercise ratios) of DTI parameters. All diffusivities significantly increased (P < 0.0001) and FA decreased (P = 0.0014) with exercise. Longitudinal diffusion responses were significantly smaller than transversal diffusion responses (P < 0.0001). Nineteen of 98 patient compartments were classified as CECS on T2w. MD increased by 3.8 ± 3.4% (volunteer), 7.4 ± 4.2% (normal), and 9.1 ± 7.0% (CECS) with exercise. DTI shows promise as an ancillary imaging method in the diagnosis and understanding of the pathophysiology in CECS. Future studies may explore its utility in predicting response to treatment. Copyright © 2013 Wiley Periodicals, Inc.

Influence of APOE Genotype on Hippocampal Atrophy over Time - An N=1925 Surface-Based ADNI Study

PubMed Central

Li, Bolun; Shi, Jie; Gutman, Boris A.; Baxter, Leslie C.; Thompson, Paul M.; Caselli, Richard J.; Wang, Yalin

2016-01-01

The apolipoprotein E (APOE) e4 genotype is a powerful risk factor for late-onset Alzheimer’s disease (AD). In the Alzheimer’s Disease Neuroimaging Initiative (ADNI) cohort, we previously reported significant baseline structural differences in APOE e4 carriers relative to non-carriers, involving the left hippocampus more than the right—a difference more pronounced in e4 homozygotes than heterozygotes. We now examine the longitudinal effects of APOE genotype on hippocampal morphometry at 6-, 12- and 24-months, in the ADNI cohort. We employed a new automated surface registration system based on conformal geometry and tensor-based morphometry. Among different hippocampal surfaces, we computed high-order correspondences, using a novel inverse-consistent surface-based fluid registration method and multivariate statistics consisting of multivariate tensor-based morphometry (mTBM) and radial distance. At each time point, using Hotelling’s T2 test, we found significant morphological deformation in APOE e4 carriers relative to non-carriers in the full cohort as well as in the non-demented (pooled MCI and control) subjects at each follow-up interval. In the complete ADNI cohort, we found greater atrophy of the left hippocampus than the right, and this asymmetry was more pronounced in e4 homozygotes than heterozygotes. These findings, combined with our earlier investigations, demonstrate an e4 dose effect on accelerated hippocampal atrophy, and support the enrichment of prevention trial cohorts with e4 carriers. PMID:27065111

Gaussian mixtures on tensor fields for segmentation: applications to medical imaging.

PubMed

de Luis-García, Rodrigo; Westin, Carl-Fredrik; Alberola-López, Carlos

2011-01-01

In this paper, we introduce a new approach for tensor field segmentation based on the definition of mixtures of Gaussians on tensors as a statistical model. Working over the well-known Geodesic Active Regions segmentation framework, this scheme presents several interesting advantages. First, it yields a more flexible model than the use of a single Gaussian distribution, which enables the method to better adapt to the complexity of the data. Second, it can work directly on tensor-valued images or, through a parallel scheme that processes independently the intensity and the local structure tensor, on scalar textured images. Two different applications have been considered to show the suitability of the proposed method for medical imaging segmentation. First, we address DT-MRI segmentation on a dataset of 32 volumes, showing a successful segmentation of the corpus callosum and favourable comparisons with related approaches in the literature. Second, the segmentation of bones from hand radiographs is studied, and a complete automatic-semiautomatic approach has been developed that makes use of anatomical prior knowledge to produce accurate segmentation results. Copyright © 2010 Elsevier Ltd. All rights reserved.

The exponentiated Hencky-logarithmic strain energy. Part II: Coercivity, planar polyconvexity and existence of minimizers

NASA Astrophysics Data System (ADS)

Neff, Patrizio; Lankeit, Johannes; Ghiba, Ionel-Dumitrel; Martin, Robert; Steigmann, David

2015-08-01

We consider a family of isotropic volumetric-isochoric decoupled strain energies based on the Hencky-logarithmic (true, natural) strain tensor log U, where μ > 0 is the infinitesimal shear modulus, is the infinitesimal bulk modulus with the first Lamé constant, are dimensionless parameters, is the gradient of deformation, is the right stretch tensor and is the deviatoric part (the projection onto the traceless tensors) of the strain tensor log U. For small elastic strains, the energies reduce to first order to the classical quadratic Hencky energy which is known to be not rank-one convex. The main result in this paper is that in plane elastostatics the energies of the family are polyconvex for , extending a previous finding on its rank-one convexity. Our method uses a judicious application of Steigmann's polyconvexity criteria based on the representation of the energy in terms of the principal invariants of the stretch tensor U. These energies also satisfy suitable growth and coercivity conditions. We formulate the equilibrium equations, and we prove the existence of minimizers by the direct methods of the calculus of variations.

Fully Anisotropic Rotational Diffusion Tensor from Molecular Dynamics Simulations.

PubMed

Linke, Max; Köfinger, Jürgen; Hummer, Gerhard

2018-05-31

We present a method to calculate the fully anisotropic rotational diffusion tensor from molecular dynamics simulations. Our approach is based on fitting the time-dependent covariance matrix of the quaternions that describe the rigid-body rotational dynamics. Explicit analytical expressions have been derived for the covariances by Favro, which are valid irrespective of the degree of anisotropy. We use these expressions to determine an optimal rotational diffusion tensor from trajectory data. The molecular structures are aligned against a reference by optimal rigid-body superposition. The quaternion covariances can then be obtained directly from the rotation matrices used in the alignment. The rotational diffusion tensor is determined by a fit to the time-dependent quaternion covariances, or directly by Laplace transformation and matrix diagonalization. To quantify uncertainties in the fit, we derive analytical expressions and compare them with the results of Brownian dynamics simulations of anisotropic rotational diffusion. We apply the method to microsecond long trajectories of the Dickerson-Drew B-DNA dodecamer and of horse heart myoglobin. The anisotropic rotational diffusion tensors calculated from simulations agree well with predictions from hydrodynamics.

Tensor Rank Preserving Discriminant Analysis for Facial Recognition.

PubMed

Tao, Dapeng; Guo, Yanan; Li, Yaotang; Gao, Xinbo

2017-10-12

Facial recognition, one of the basic topics in computer vision and pattern recognition, has received substantial attention in recent years. However, for those traditional facial recognition algorithms, the facial images are reshaped to a long vector, thereby losing part of the original spatial constraints of each pixel. In this paper, a new tensor-based feature extraction algorithm termed tensor rank preserving discriminant analysis (TRPDA) for facial image recognition is proposed; the proposed method involves two stages: in the first stage, the low-dimensional tensor subspace of the original input tensor samples was obtained; in the second stage, discriminative locality alignment was utilized to obtain the ultimate vector feature representation for subsequent facial recognition. On the one hand, the proposed TRPDA algorithm fully utilizes the natural structure of the input samples, and it applies an optimization criterion that can directly handle the tensor spectral analysis problem, thereby decreasing the computation cost compared those traditional tensor-based feature selection algorithms. On the other hand, the proposed TRPDA algorithm extracts feature by finding a tensor subspace that preserves most of the rank order information of the intra-class input samples. Experiments on the three facial databases are performed here to determine the effectiveness of the proposed TRPDA algorithm.

Accurate calculation of the geometric measure of entanglement for multipartite quantum states

NASA Astrophysics Data System (ADS)

Teng, Peiyuan

2017-07-01

This article proposes an efficient way of calculating the geometric measure of entanglement using tensor decomposition methods. The connection between these two concepts is explored using the tensor representation of the wavefunction. Numerical examples are benchmarked and compared. Furthermore, we search for highly entangled qubit states to show the applicability of this method.

FORGE Newberry 3D Gravity Density Model for Newberry Volcano

DOE Data Explorer

Alain Bonneville

2016-03-11

These data are Pacific Northwest National Lab inversions of an amalgamation of two surface gravity datasets: Davenport-Newberry gravity collected prior to 2012 stimulations and Zonge International gravity collected for the project "Novel use of 4D Monitoring Techniques to Improve Reservoir Longevity and Productivity in Enhanced Geothermal Systems" in 2012. Inversions of surface gravity recover a 3D distribution of density contrast from which intrusive igneous bodies are identified. The data indicate a body name, body type, point type, UTM X and Y coordinates, Z data is specified as meters below sea level (negative values then indicate elevations above sea level), thickness of the body in meters, suscept, density anomaly in g/cc, background density in g/cc, and density in g/cc. The model was created using a commercial gravity inversion software called ModelVision 12.0 (http://www.tensor-research.com.au/Geophysical-Products/ModelVision). The initial model is based on the seismic tomography interpretation (Beachly et al., 2012). All the gravity data used to constrain this model are on the GDR: https://gdr.openei.org/submissions/760.

Periodic domain inversion in x-cut single-crystal lithium niobate thin film

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mackwitz, P., E-mail: peterm@mail.upb.de; Rüsing, M.; Berth, G.

2016-04-11

We report the fabrication of periodically poled domain patterns in x-cut lithium niobate thin-film. Here, thin films on insulator have drawn particular attention due to their intrinsic waveguiding properties offering high mode confinement and smaller devices compared to in-diffused waveguides in bulk material. In contrast to z-cut thin film lithium niobate, the x-cut geometry does not require back electrodes for poling. Further, the x-cut geometry grants direct access to the largest nonlinear and electro-optical tensor element, which overall promises smaller devices. The domain inversion was realized via electric field poling utilizing deposited aluminum top electrodes on a stack of LNmore » thin film/SiO{sub 2} layer/Bulk LN, which were patterned by optical lithography. The periodic domain inversion was verified by non-invasive confocal second harmonic microscopy. Our results show domain patterns in accordance to the electrode mask layout. The second harmonic signatures can be interpreted in terms of spatially, overlapping domain filaments which start their growth on the +z side.« less

Tensor-based tracking of the aorta in phase-contrast MR images

NASA Astrophysics Data System (ADS)

Azad, Yoo-Jin; Malsam, Anton; Ley, Sebastian; Rengier, Fabian; Dillmann, Rüdiger; Unterhinninghofen, Roland

2014-03-01

The velocity-encoded magnetic resonance imaging (PC-MRI) is a valuable technique to measure the blood flow velocity in terms of time-resolved 3D vector fields. For diagnosis, presurgical planning and therapy control monitoring the patient's hemodynamic situation is crucial. Hence, an accurate and robust segmentation of the diseased vessel is the basis for further methods like the computation of the blood pressure. In the literature, there exist some approaches to transfer the methods of processing DT-MR images to PC-MR data, but the potential of this approach is not fully exploited yet. In this paper, we present a method to extract the centerline of the aorta in PC-MR images by applying methods from the DT-MRI. On account of this, in the first step the velocity vector fields are converted into tensor fields. In the next step tensor-based features are derived and by applying a modified tensorline algorithm the tracking of the vessel course is accomplished. The method only uses features derived from the tensor imaging without the use of additional morphology information. For evaluation purposes we applied our method to 4 volunteer as well as 26 clinical patient datasets with good results. In 29 of 30 cases our algorithm accomplished to extract the vessel centerline.

A Magic-Angle Spinning NMR Method for the Site-Specific Measurement of Proton Chemical-Shift Anisotropy in Biological and Organic Solids.

PubMed

Hou, Guangjin; Gupta, Rupal; Polenova, Tatyana; Vega, Alexander J

2014-02-01

Proton chemical shifts are a rich probe of structure and hydrogen bonding environments in organic and biological molecules. Until recently, measurements of 1 H chemical shift tensors have been restricted to either solid systems with sparse proton sites or were based on the indirect determination of anisotropic tensor components from cross-relaxation and liquid-crystal experiments. We have introduced an MAS approach that permits site-resolved determination of CSA tensors of protons forming chemical bonds with labeled spin-1/2 nuclei in fully protonated solids with multiple sites, including organic molecules and proteins. This approach, originally introduced for the measurements of chemical shift tensors of amide protons, is based on three RN -symmetry based experiments, from which the principal components of the 1 H CS tensor can be reliably extracted by simultaneous triple fit of the data. In this article, we expand our approach to a much more challenging system involving aliphatic and aromatic protons. We start with a review of the prior work on experimental-NMR and computational-quantum-chemical approaches for the measurements of 1 H chemical shift tensors and for relating these to the electronic structures. We then present our experimental results on U- 13 C, 15 N-labeled histdine demonstrating that 1 H chemical shift tensors can be reliably determined for the 1 H 15 N and 1 H 13 C spin pairs in cationic and neutral forms of histidine. Finally, we demonstrate that the experimental 1 H(C) and 1 H(N) chemical shift tensors are in agreement with Density Functional Theory calculations, therefore establishing the usefulness of our method for characterization of structure and hydrogen bonding environment in organic and biological solids.

A new validation technique for estimations of body segment inertia tensors: Principal axes of inertia do matter.

PubMed

Rossi, Marcel M; Alderson, Jacqueline; El-Sallam, Amar; Dowling, James; Reinbolt, Jeffrey; Donnelly, Cyril J

2016-12-08

The aims of this study were to: (i) establish a new criterion method to validate inertia tensor estimates by setting the experimental angular velocity data of an airborne objects as ground truth against simulations run with the estimated tensors, and (ii) test the sensitivity of the simulations to changes in the inertia tensor components. A rigid steel cylinder was covered with reflective kinematic markers and projected through a calibrated motion capture volume. Simulations of the airborne motion were run with two models, using inertia tensor estimated with geometric formula or the compound pendulum technique. The deviation angles between experimental (ground truth) and simulated angular velocity vectors and the root mean squared deviation angle were computed for every simulation. Monte Carlo analyses were performed to assess the sensitivity of simulations to changes in magnitude of principal moments of inertia within ±10% and to changes in orientation of principal axes of inertia within ±10° (of the geometric-based inertia tensor). Root mean squared deviation angles ranged between 2.9° and 4.3° for the inertia tensor estimated geometrically, and between 11.7° and 15.2° for the compound pendulum values. Errors up to 10% in magnitude of principal moments of inertia yielded root mean squared deviation angles ranging between 3.2° and 6.6°, and between 5.5° and 7.9° when lumped with errors of 10° in principal axes of inertia orientation. The proposed technique can effectively validate inertia tensors from novel estimation methods of body segment inertial parameter. Principal axes of inertia orientation should not be neglected when modelling human/animal mechanics. Copyright © 2016 Elsevier Ltd. All rights reserved.

Visualization of 3-D tensor fields

NASA Technical Reports Server (NTRS)

Hesselink, L.

1996-01-01

Second-order tensor fields have applications in many different areas of physics, such as general relativity and fluid mechanics. The wealth of multivariate information in tensor fields makes them more complex and abstract than scalar and vector fields. Visualization is a good technique for scientists to gain new insights from them. Visualizing a 3-D continuous tensor field is equivalent to simultaneously visualizing its three eigenvector fields. In the past, research has been conducted in the area of two-dimensional tensor fields. It was shown that degenerate points, defined as points where eigenvalues are equal to each other, are the basic singularities underlying the topology of tensor fields. Moreover, it was shown that eigenvectors never cross each other except at degenerate points. Since we live in a three-dimensional world, it is important for us to understand the underlying physics of this world. In this report, we describe a new method for locating degenerate points along with the conditions for classifying them in three-dimensional space. Finally, we discuss some topological features of three-dimensional tensor fields, and interpret topological patterns in terms of physical properties.

Grid-based lattice summation of electrostatic potentials by assembled rank-structured tensor approximation

NASA Astrophysics Data System (ADS)

Khoromskaia, Venera; Khoromskij, Boris N.

2014-12-01

Our recent method for low-rank tensor representation of sums of the arbitrarily positioned electrostatic potentials discretized on a 3D Cartesian grid reduces the 3D tensor summation to operations involving only 1D vectors however retaining the linear complexity scaling in the number of potentials. Here, we introduce and study a novel tensor approach for fast and accurate assembled summation of a large number of lattice-allocated potentials represented on 3D N × N × N grid with the computational requirements only weakly dependent on the number of summed potentials. It is based on the assembled low-rank canonical tensor representations of the collected potentials using pointwise sums of shifted canonical vectors representing the single generating function, say the Newton kernel. For a sum of electrostatic potentials over L × L × L lattice embedded in a box the required storage scales linearly in the 1D grid-size, O(N) , while the numerical cost is estimated by O(NL) . For periodic boundary conditions, the storage demand remains proportional to the 1D grid-size of a unit cell, n = N / L, while the numerical cost reduces to O(N) , that outperforms the FFT-based Ewald-type summation algorithms of complexity O(N3 log N) . The complexity in the grid parameter N can be reduced even to the logarithmic scale O(log N) by using data-sparse representation of canonical N-vectors via the quantics tensor approximation. For justification, we prove an upper bound on the quantics ranks for the canonical vectors in the overall lattice sum. The presented approach is beneficial in applications which require further functional calculus with the lattice potential, say, scalar product with a function, integration or differentiation, which can be performed easily in tensor arithmetics on large 3D grids with 1D cost. Numerical tests illustrate the performance of the tensor summation method and confirm the estimated bounds on the tensor ranks.

Atomic orbital-based SOS-MP2 with tensor hypercontraction. II. Local tensor hypercontraction

NASA Astrophysics Data System (ADS)

Song, Chenchen; Martínez, Todd J.

2017-01-01

In the first paper of the series [Paper I, C. Song and T. J. Martinez, J. Chem. Phys. 144, 174111 (2016)], we showed how tensor-hypercontracted (THC) SOS-MP2 could be accelerated by exploiting sparsity in the atomic orbitals and using graphical processing units (GPUs). This reduced the formal scaling of the SOS-MP2 energy calculation to cubic with respect to system size. The computational bottleneck then becomes the THC metric matrix inversion, which scales cubically with a large prefactor. In this work, the local THC approximation is proposed to reduce the computational cost of inverting the THC metric matrix to linear scaling with respect to molecular size. By doing so, we have removed the primary bottleneck to THC-SOS-MP2 calculations on large molecules with O(1000) atoms. The errors introduced by the local THC approximation are less than 0.6 kcal/mol for molecules with up to 200 atoms and 3300 basis functions. Together with the graphical processing unit techniques and locality-exploiting approaches introduced in previous work, the scaled opposite spin MP2 (SOS-MP2) calculations exhibit O(N2.5) scaling in practice up to 10 000 basis functions. The new algorithms make it feasible to carry out SOS-MP2 calculations on small proteins like ubiquitin (1231 atoms/10 294 atomic basis functions) on a single node in less than a day.

Atomic orbital-based SOS-MP2 with tensor hypercontraction. II. Local tensor hypercontraction.

PubMed

Song, Chenchen; Martínez, Todd J

2017-01-21

In the first paper of the series [Paper I, C. Song and T. J. Martinez, J. Chem. Phys. 144, 174111 (2016)], we showed how tensor-hypercontracted (THC) SOS-MP2 could be accelerated by exploiting sparsity in the atomic orbitals and using graphical processing units (GPUs). This reduced the formal scaling of the SOS-MP2 energy calculation to cubic with respect to system size. The computational bottleneck then becomes the THC metric matrix inversion, which scales cubically with a large prefactor. In this work, the local THC approximation is proposed to reduce the computational cost of inverting the THC metric matrix to linear scaling with respect to molecular size. By doing so, we have removed the primary bottleneck to THC-SOS-MP2 calculations on large molecules with O(1000) atoms. The errors introduced by the local THC approximation are less than 0.6 kcal/mol for molecules with up to 200 atoms and 3300 basis functions. Together with the graphical processing unit techniques and locality-exploiting approaches introduced in previous work, the scaled opposite spin MP2 (SOS-MP2) calculations exhibit O(N 2.5 ) scaling in practice up to 10 000 basis functions. The new algorithms make it feasible to carry out SOS-MP2 calculations on small proteins like ubiquitin (1231 atoms/10 294 atomic basis functions) on a single node in less than a day.

gamAID: Greedy CP tensor decomposition for supervised EHR-based disease trajectory differentiation.

PubMed

Henderson, Jette; Ho, Joyce; Ghosh, Joydeep

2017-07-01

We propose gamAID, an exploratory, supervised nonnegative tensor factorization method that iteratively extracts phenotypes from tensors constructed from medical count data. Using data from diabetic patients who later on get diagnosed with chronic kidney disorder (CKD) as well as diabetic patients who do not receive a CKD diagnosis, we demonstrate the potential of gamAID to discover phenotypes that characterize patients who are at risk for developing a disease.

An Adaptive Shifted Power Method for Computing Generalized Tensor Eigenpairs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kolda, Tamara G.; Mayo, Jackson R.

2014-12-11

Several tensor eigenpair definitions have been put forth in the past decade, but these can all be unified under generalized tensor eigenpair framework, introduced by Chang, Pearson, and Zhang [J. Math. Anal. Appl., 350 (2009), pp. 416--422]. Given mth-order, n-dimensional real-valued symmetric tensorsmore » $${\\mathscr{A}}$$ and $$\\boldsymbol{\\mathscr{B}}$$, the goal is to find $$\\lambda \\in \\mathbb{R}$$ and $$\\mathbf{x} \\in \\mathbb{R}^{n}, \\mathbf{x} \

Tectonic stress orientations and magnitudes, and friction of faults, deduced from earthquake focal mechanism inversions over the Korean Peninsula

NASA Astrophysics Data System (ADS)

Soh, Inho; Chang, Chandong; Lee, Junhyung; Hong, Tae-Kyung; Park, Eui-Seob

2018-05-01

We characterize the present-day stress state in and around the Korean Peninsula using formal inversions of earthquake focal mechanisms. Two different methods are used to select preferred fault planes in the double-couple focal mechanism solutions: one that minimizes average misfit angle and the other choosing faults with higher instability. We invert selected sets of fault planes for estimating the principal stresses at regularly spaced grid points, using a circular-area data-binning method, where the bin radius is optimized to yield the best possible stress inversion results based on the World Stress Map quality ranking scheme. The inversions using the two methods yield well constrained and fairly comparable results, which indicate that the prevailing stress regime is strike-slip, and the maximum horizontal principal stress (SHmax) is oriented ENE-WSW throughout the study region. Although the orientation of the stresses is consistent across the peninsula, the relative stress magnitude parameter (R-value) varies significantly, from 0.22 in the northwest to 0.89 in the southeast. Based on our knowledge of the R-values and stress regime, and using a value for vertical stress (Sv) estimated from the overburden weight of rock, together with a value for the maximum differential stress (based on the Coulomb friction of faults optimally oriented for slip), we estimate the magnitudes of the two horizontal principal stresses. The horizontal stress magnitudes increase from west to east such that SHmax/Sv ratio rises from 1.5 to 2.4, and the Shmin/Sv ratio from 0.6 to 0.8. The variation in the magnitudes of the tectonic stresses appears to be related to differences in the rigidity of crustal rocks. Using the complete stress tensors, including both orientations and magnitudes, we assess the possible ranges of frictional coefficients for different types of faults. We show that normal and reverse faults have lower frictional coefficients than strike-slip faults, suggesting that the former types of faults can be activated under a strike-slip stress regime. Our observations of the seismicity, with normal faulting concentrated offshore to the northwest and reverse faulting focused offshore to the east, are compatible with the results of our estimates of stress magnitudes.

Testing the seismology-based landquake monitoring system

NASA Astrophysics Data System (ADS)

Chao, Wei-An

2016-04-01

I have developed a real-time landquake monitoring system (RLMs), which monitor large-scale landquake activities in the Taiwan using real-time seismic network of Broadband Array in Taiwan for Seismology (BATS). The RLM system applies a grid-based general source inversion (GSI) technique to obtain the preliminary source location and force mechanism. A 2-D virtual source-grid on the Taiwan Island is created with an interval of 0.2° in both latitude and longitude. The depth of each grid point is fixed on the free surface topography. A database is stored on the hard disk for the synthetics, which are obtained using Green's functions computed by the propagator matrix approach for 1-D average velocity model, at all stations from each virtual source-grid due to nine elementary source components: six elementary moment tensors and three orthogonal (north, east and vertical) single-forces. Offline RLM system was carried out for events detected in previous studies. An important aspect of the RLM system is the implementation of GSI approach for different source types (e.g., full moment tensor, double couple faulting, and explosion source) by the grid search through the 2-D virtual source to automatically identify landquake event based on the improvement in waveform fitness and evaluate the best-fit solution in the monitoring area. With this approach, not only the force mechanisms but also the event occurrence time and location can be obtained simultaneously about 6-8 min after an occurrence of an event. To improve the insufficient accuracy of GSI-determined lotion, I further conduct a landquake epicenter determination (LED) method that maximizes the coherency of the high-frequency (1-3 Hz) horizontal envelope functions to determine the final source location. With good knowledge about the source location, I perform landquake force history (LFH) inversion to investigate the source dynamics (e.g., trajectory) for the relatively large-sized landquake event. With providing aforementioned source information in real-time, the government and emergency response agencies have sufficient reaction time for rapid assessment and response to landquake hazards. Since 2016, the RLM system has operated online.

A continuous tensor field approximation of discrete DT-MRI data for extracting microstructural and architectural features of tissue.

PubMed

Pajevic, Sinisa; Aldroubi, Akram; Basser, Peter J

2002-01-01

The effective diffusion tensor of water, D, measured by diffusion tensor MRI (DT-MRI), is inherently a discrete, noisy, voxel-averaged sample of an underlying macroscopic effective diffusion tensor field, D(x). Within fibrous tissues this field is presumed to be continuous and smooth at a gross anatomical length scale. Here a new, general mathematical framework is proposed that uses measured DT-MRI data to produce a continuous approximation to D(x). One essential finding is that the continuous tensor field representation can be constructed by repeatedly performing one-dimensional B-spline transforms of the DT-MRI data. The fidelity and noise-immunity of this approximation are tested using a set of synthetically generated tensor fields to which background noise is added via Monte Carlo methods. Generally, these tensor field templates are reproduced faithfully except at boundaries where diffusion properties change discontinuously or where the tensor field is not microscopically homogeneous. Away from such regions, the tensor field approximation does not introduce bias in useful DT-MRI parameters, such as Trace(D(x)). It also facilitates the calculation of several new parameters, particularly differential quantities obtained from the tensor of spatial gradients of D(x). As an example, we show that they can identify tissue boundaries across which diffusion properties change rapidly using in vivo human brain data. One important application of this methodology is to improve the reliability and robustness of DT-MRI fiber tractography.

A Framework for Load Balancing of Tensor Contraction Expressions via Dynamic Task Partitioning

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lai, Pai-Wei; Stock, Kevin; Rajbhandari, Samyam

In this paper, we introduce the Dynamic Load-balanced Tensor Contractions (DLTC), a domain-specific library for efficient task parallel execution of tensor contraction expressions, a class of computation encountered in quantum chemistry and physics. Our framework decomposes each contraction into smaller unit of tasks, represented by an abstraction referred to as iterators. We exploit an extra level of parallelism by having tasks across independent contractions executed concurrently through a dynamic load balancing run- time. We demonstrate the improved performance, scalability, and flexibility for the computation of tensor contraction expressions on parallel computers using examples from coupled cluster methods.

Cyberinfrastructure for the Unified Study of Earth Structure and Earthquake Sources in Complex Geologic Environments

NASA Astrophysics Data System (ADS)

Zhao, L.; Chen, P.; Jordan, T. H.; Olsen, K. B.; Maechling, P.; Faerman, M.

2004-12-01

The Southern California Earthquake Center (SCEC) is developing a Community Modeling Environment (CME) to facilitate the computational pathways of physics-based seismic hazard analysis (Maechling et al., this meeting). Major goals are to facilitate the forward modeling of seismic wavefields in complex geologic environments, including the strong ground motions that cause earthquake damage, and the inversion of observed waveform data for improved models of Earth structure and fault rupture. Here we report on a unified approach to these coupled inverse problems that is based on the ability to generate and manipulate wavefields in densely gridded 3D Earth models. A main element of this approach is a database of receiver Green tensors (RGT) for the seismic stations, which comprises all of the spatial-temporal displacement fields produced by the three orthogonal unit impulsive point forces acting at each of the station locations. Once the RGT database is established, synthetic seismograms for any earthquake can be simply calculated by extracting a small, source-centered volume of the RGT from the database and applying the reciprocity principle. The partial derivatives needed for point- and finite-source inversions can be generated in the same way. Moreover, the RGT database can be employed in full-wave tomographic inversions launched from a 3D starting model, because the sensitivity (Fréchet) kernels for travel-time and amplitude anomalies observed at seismic stations in the database can be computed by convolving the earthquake-induced displacement field with the station RGTs. We illustrate all elements of this unified analysis with an RGT database for 33 stations of the California Integrated Seismic Network in and around the Los Angeles Basin, which we computed for the 3D SCEC Community Velocity Model (SCEC CVM3.0) using a fourth-order staggered-grid finite-difference code. For a spatial grid spacing of 200 m and a time resolution of 10 ms, the calculations took ~19,000 node-hours on the Linux cluster at USC's High-Performance Computing Center. The 33-station database with a volume of ~23.5 TB was archived in the SCEC digital library at the San Diego Supercomputer Center using the Storage Resource Broker (SRB). From a laptop, anyone with access to this SRB collection can compute synthetic seismograms for an arbitrary source in the CVM in a matter of minutes. Efficient approaches have been implemented to use this RGT database in the inversions of waveforms for centroid and finite moment tensors and tomographic inversions to improve the CVM. Our experience with these large problems suggests areas where the cyberinfrastructure currently available for geoscience computation needs to be improved.

Estimation of full moment tensors, including uncertainties, for earthquakes, volcanic events, and nuclear explosions

NASA Astrophysics Data System (ADS)

Alvizuri, Celso; Silwal, Vipul; Krischer, Lion; Tape, Carl

2017-04-01

A seismic moment tensor is a 3 × 3 symmetric matrix that provides a compact representation of seismic events within Earth's crust. We develop an algorithm to estimate moment tensors and their uncertainties from observed seismic data. For a given event, the algorithm performs a grid search over the six-dimensional space of moment tensors by generating synthetic waveforms at each grid point and then evaluating a misfit function between the observed and synthetic waveforms. 'The' moment tensor M for the event is then the moment tensor with minimum misfit. To describe the uncertainty associated with M, we first convert the misfit function to a probability function. The uncertainty, or rather the confidence, is then given by the 'confidence curve' P(V ), where P(V ) is the probability that the true moment tensor for the event lies within the neighborhood of M that has fractional volume V . The area under the confidence curve provides a single, abbreviated 'confidence parameter' for M. We apply the method to data from events in different regions and tectonic settings: small (Mw < 2.5) events at Uturuncu volcano in Bolivia, moderate (Mw > 4) earthquakes in the southern Alaska subduction zone, and natural and man-made events at the Nevada Test Site. Moment tensor uncertainties allow us to better discriminate among moment tensor source types and to assign physical processes to the events.

Plate convergence at the westernmost Philippine Sea Plate

NASA Astrophysics Data System (ADS)

Wu, Wen-Nan; Hsu, Shu-Kun; Lo, Chung-Liang; Chen, How-Wei; Ma, Kuo-Fong

2009-03-01

To understand the convergent characteristics of the westernmost plate boundary between the Philippine Sea Plate (PSP) and Eurasian Plate (EP), we have calculated the stress states of plate motion by focal mechanisms. Cataloged by the Harvard centroid moment tensor solutions (Harvard CMT) and the Broadband Array in Taiwan (BATS) moment tensor, 251 focal mechanisms are used to determine the azimuths of the principal stress axes. We first used all the data to derive the mean stress tensor of the study area. The inversion result shows that the stress regime has a maximum compression along the direction of azimuth N299°. This result is consistent with the general direction of the rigid plate motion between the PSP and EP in the study area. In order to understand the spatial variation of the regional stress pattern, we divided the study area into six sub-areas (blocks A to F) based on the feature of the free-air gravity anomaly. We compare the compressive directions obtained from the stress inversion with the plate motions calculated by the Euler pole and the Global Positioning System (GPS) analysis. As a result, the azimuth of the maximum stress axis, σ1, generally agrees with the directions of the theoretical plate motion and GPS velocity vectors except block C (Lanhsu region) and block F (Ilan plain region). The discrepancy of convergent direction near the Ilan plain region is probably caused by the rifting of the Okinawa Trough. The deviation of the σ1 azimuth in the Lanhsu region could be attributed to a southwestward extrusion of the Luzon Arc (LA) block between 21°N and 22°N whose northern boundary may be associated with the right-lateral NE-SW trending fault (i.e. Huatung Fault, HF) along the Taitung Canyon. Comparing the σ1 stress patterns between block C and block D, great strain energy along HF may not be completely released yet. Alternatively, the upper crust of block C may significantly have decoupled from its lower crust or uppermost mantle.

Measuring the quantum geometric tensor in two-dimensional photonic and exciton-polariton systems

NASA Astrophysics Data System (ADS)

Bleu, O.; Solnyshkov, D. D.; Malpuech, G.

2018-05-01

We propose theoretically a method that allows to measure all the components of the quantum geometric tensor (the metric tensor and the Berry curvature) in a photonic system. The method is based on standard optical measurements. It applies to two-band systems, which can be mapped to a pseudospin, and to four-band systems, which can be described by two entangled pseudospins. We apply this method to several specific cases. We consider a 2D planar cavity with two polarization eigenmodes, where the pseudospin measurement can be performed via polarization-resolved photoluminescence. We also consider the s band of a staggered honeycomb lattice with polarization-degenerate modes (scalar photons), where the sublattice pseudospin can be measured by performing spatially resolved interferometric measurements. We finally consider the s band of a honeycomb lattice with polarized (spinor) photons as an example of a four-band model. We simulate realistic experimental situations in all cases. We find the photon eigenstates by solving the Schrödinger equation including pumping and finite lifetime, and then simulate the measurements to finally extract realistic mappings of the k-dependent tensor components.

Performance of tensor decomposition-based modal identification under nonstationary vibration

NASA Astrophysics Data System (ADS)

Friesen, P.; Sadhu, A.

2017-03-01

Health monitoring of civil engineering structures is of paramount importance when they are subjected to natural hazards or extreme climatic events like earthquake, strong wind gusts or man-made excitations. Most of the traditional modal identification methods are reliant on stationarity assumption of the vibration response and posed difficulty while analyzing nonstationary vibration (e.g. earthquake or human-induced vibration). Recently tensor decomposition based methods are emerged as powerful and yet generic blind (i.e. without requiring a knowledge of input characteristics) signal decomposition tool for structural modal identification. In this paper, a tensor decomposition based system identification method is further explored to estimate modal parameters using nonstationary vibration generated due to either earthquake or pedestrian induced excitation in a structure. The effects of lag parameters and sensor densities on tensor decomposition are studied with respect to the extent of nonstationarity of the responses characterized by the stationary duration and peak ground acceleration of the earthquake. A suite of more than 1400 earthquakes is used to investigate the performance of the proposed method under a wide variety of ground motions utilizing both complete and partial measurements of a high-rise building model. Apart from the earthquake, human-induced nonstationary vibration of a real-life pedestrian bridge is also used to verify the accuracy of the proposed method.

Separation of specular and diffuse components using tensor voting in color images.

PubMed

Nguyen, Tam; Vo, Quang Nhat; Yang, Hyung-Jeong; Kim, Soo-Hyung; Lee, Guee-Sang

2014-11-20

Most methods for the detection and removal of specular reflections suffer from nonuniform highlight regions and/or nonconverged artifacts induced by discontinuities in the surface colors, especially when dealing with highly textured, multicolored images. In this paper, a novel noniterative and predefined constraint-free method based on tensor voting is proposed to detect and remove the highlight components of a single color image. The distribution of diffuse and specular pixels in the original image is determined using tensors' saliency analysis, instead of comparing color information among neighbor pixels. The achieved diffuse reflectance distribution is used to remove specularity components. The proposed method is evaluated quantitatively and qualitatively over a dataset of highly textured, multicolor images. The experimental results show that our result outperforms other state-of-the-art techniques.

Joint 3D Inversion of ZTEM Airborne and Ground MT Data with Application to Geothermal Exploration

NASA Astrophysics Data System (ADS)

Wannamaker, P. E.; Maris, V.; Kordy, M. A.

2017-12-01

ZTEM is an airborne electromagnetic (EM) geophysical technique developed by Geotech Inc® where naturally propagated EM fields originating with regional and global lightning discharges (sferics) are measured as a means of inferring subsurface electrical resistivity structure. A helicopter-borne coil platform (bird) measuring the vertical component of magnetic (H) field variations along a flown profile is referenced to a pair of horizontal coils at a fixed location on the ground in order to estimate a tensor H-field transfer function. The ZTEM method is distinct from the traditional magnetotelluric (MT) method in that the electric (E) fields are not considered because of the technological challenge of measuring E-fields in the dielectric air medium. This can lend some non-uniqueness to ZTEM interpretation because a range of conductivity structures in the earth depending upon an assumed background earth resistivity model can fit ZTEM data to within tolerance. MT data do not suffer this particular problem, but they are cumbersome to acquire in their common need for land-based transport often in near-roadless areas and for laying out and digging the electrodes and H coils. The complementary nature of ZTEM and MT logistics and resolution has motivated development of schemes to acquire appropriate amounts of each data type in a single survey and to produce an earth image through joint inversion. In particular, consideration is given to surveys where only sparse MT soundings are needed to drastically reduce the non-uniqueness associated with background uncertainty while straining logistics minimally. Synthetic and field data are analysed using 2D and 3D finite element platforms developed for this purpose. Results to date suggest that indeed dense ZTEM surveys can provide detailed heterogeneous model images with large-scale averages constrained by a modest number of MT soundings. Further research is needed in determining the allowable degree of MT sparseness and the relative weighting of the two data sets in joint inversion.

Waveform inversion of volcano-seismic signals for an extended source

USGS Publications Warehouse

Nakano, M.; Kumagai, H.; Chouet, B.; Dawson, P.

2007-01-01

We propose a method to investigate the dimensions and oscillation characteristics of the source of volcano-seismic signals based on waveform inversion for an extended source. An extended source is realized by a set of point sources distributed on a grid surrounding the centroid of the source in accordance with the source geometry and orientation. The source-time functions for all point sources are estimated simultaneously by waveform inversion carried out in the frequency domain. We apply a smoothing constraint to suppress short-scale noisy fluctuations of source-time functions between adjacent sources. The strength of the smoothing constraint we select is that which minimizes the Akaike Bayesian Information Criterion (ABIC). We perform a series of numerical tests to investigate the capability of our method to recover the dimensions of the source and reconstruct its oscillation characteristics. First, we use synthesized waveforms radiated by a kinematic source model that mimics the radiation from an oscillating crack. Our results demonstrate almost complete recovery of the input source dimensions and source-time function of each point source, but also point to a weaker resolution of the higher modes of crack oscillation. Second, we use synthetic waveforms generated by the acoustic resonance of a fluid-filled crack, and consider two sets of waveforms dominated by the modes with wavelengths 2L/3 and 2W/3, or L and 2L/5, where W and L are the crack width and length, respectively. Results from these tests indicate that the oscillating signature of the 2L/3 and 2W/3 modes are successfully reconstructed. The oscillating signature of the L mode is also well recovered, in contrast to results obtained for a point source for which the moment tensor description is inadequate. However, the oscillating signature of the 2L/5 mode is poorly recovered owing to weaker resolution of short-scale crack wall motions. The triggering excitations of the oscillating cracks are successfully reconstructed. Copyright 2007 by the American Geophysical Union.

Paleogeodesy of the Southern Santa Cruz Mountains Frontal Thrusts, Silicon Valley, CA

NASA Astrophysics Data System (ADS)

Aron, F.; Johnstone, S. A.; Mavrommatis, A. P.; Sare, R.; Hilley, G. E.

2015-12-01

We present a method to infer long-term fault slip rate distributions using topography by coupling a three-dimensional elastic boundary element model with a geomorphic incision rule. In particular, we used a 10-m-resolution digital elevation model (DEM) to calculate channel steepness (ksn) throughout the actively deforming southern Santa Cruz Mountains in Central California. We then used these values with a power-law incision rule and the Poly3D code to estimate slip rates over seismogenic, kilometer-scale thrust faults accommodating differential uplift of the relief throughout geologic time. Implicit in such an analysis is the assumption that the topographic surface remains unchanged over time as rock is uplifted by slip on the underlying structures. The fault geometries within the area are defined based on surface mapping, as well as active and passive geophysical imaging. Fault elements are assumed to be traction-free in shear (i.e., frictionless), while opening along them is prohibited. The free parameters in the inversion include the components of the remote strain-rate tensor (ɛij) and the bedrock resistance to channel incision (K), which is allowed to vary according to the mapped distribution of geologic units exposed at the surface. The nonlinear components of the geomorphic model required the use of a Markov chain Monte Carlo method, which simulated the posterior density of the components of the remote strain-rate tensor and values of K for the different mapped geologic units. Interestingly, posterior probability distributions of ɛij and K fall well within the broad range of reported values, suggesting that the joint use of elastic boundary element and geomorphic models may have utility in estimating long-term fault slip-rate distributions. Given an adequate DEM, geologic mapping, and fault models, the proposed paleogeodetic method could be applied to other crustal faults with geological and morphological expressions of long-term uplift.

Mean template for tensor-based morphometry using deformation tensors.

PubMed

Leporé, Natasha; Brun, Caroline; Pennec, Xavier; Chou, Yi-Yu; Lopez, Oscar L; Aizenstein, Howard J; Becker, James T; Toga, Arthur W; Thompson, Paul M

2007-01-01

Tensor-based morphometry (TBM) studies anatomical differences between brain images statistically, to identify regions that differ between groups, over time, or correlate with cognitive or clinical measures. Using a nonlinear registration algorithm, all images are mapped to a common space, and statistics are most commonly performed on the Jacobian determinant (local expansion factor) of the deformation fields. In, it was shown that the detection sensitivity of the standard TBM approach could be increased by using the full deformation tensors in a multivariate statistical analysis. Here we set out to improve the common space itself, by choosing the shape that minimizes a natural metric on the deformation tensors from that space to the population of control subjects. This method avoids statistical bias and should ease nonlinear registration of new subjects data to a template that is 'closest' to all subjects' anatomies. As deformation tensors are symmetric positive-definite matrices and do not form a vector space, all computations are performed in the log-Euclidean framework. The control brain B that is already the closest to 'average' is found. A gradient descent algorithm is then used to perform the minimization that iteratively deforms this template and obtains the mean shape. We apply our method to map the profile of anatomical differences in a dataset of 26 HIV/AIDS patients and 14 controls, via a log-Euclidean Hotelling's T2 test on the deformation tensors. These results are compared to the ones found using the 'best' control, B. Statistics on both shapes are evaluated using cumulative distribution functions of the p-values in maps of inter-group differences.

A contribution toward rational modeling of the pressure-strain-rate correlation

NASA Technical Reports Server (NTRS)

Lee, Moon Joo

1990-01-01

A novel method of obtaining an analytical expression of the 'linear part' of the pressure-strain-rate tensor in terms of the anisotropy tensor of the Reynolds stresses has been developed, where the coefficients of the seven independent tensor terms are functions of the invariants of the Reynolds-stress anisotropy. The coefficients are evaluated up to fourth order in the anisotropy of the Reynolds stresses to provide guidance for development of a turbulence model.

Correlators in tensor models from character calculus

NASA Astrophysics Data System (ADS)

Mironov, A.; Morozov, A.

2017-11-01

We explain how the calculations of [20], which provided the first evidence for non-trivial structures of Gaussian correlators in tensor models, are efficiently performed with the help of the (Hurwitz) character calculus. This emphasizes a close similarity between technical methods in matrix and tensor models and supports a hope to understand the emerging structures in very similar terms. We claim that the 2m-fold Gaussian correlators of rank r tensors are given by r-linear combinations of dimensions with the Young diagrams of size m. The coefficients are made from the characters of the symmetric group Sm and their exact form depends on the choice of the correlator and on the symmetries of the model. As the simplest application of this new knowledge, we provide simple expressions for correlators in the Aristotelian tensor model as tri-linear combinations of dimensions.

Ward identities and combinatorics of rainbow tensor models

NASA Astrophysics Data System (ADS)

Itoyama, H.; Mironov, A.; Morozov, A.

2017-06-01

We discuss the notion of renormalization group (RG) completion of non-Gaussian Lagrangians and its treatment within the framework of Bogoliubov-Zimmermann theory in application to the matrix and tensor models. With the example of the simplest non-trivial RGB tensor theory (Aristotelian rainbow), we introduce a few methods, which allow one to connect calculations in the tensor models to those in the matrix models. As a byproduct, we obtain some new factorization formulas and sum rules for the Gaussian correlators in the Hermitian and complex matrix theories, square and rectangular. These sum rules describe correlators as solutions to finite linear systems, which are much simpler than the bilinear Hirota equations and the infinite Virasoro recursion. Search for such relations can be a way to solving the tensor models, where an explicit integrability is still obscure.

A General Sparse Tensor Framework for Electronic Structure Theory

DOE PAGES

Manzer, Samuel; Epifanovsky, Evgeny; Krylov, Anna I.; ...

2017-01-24

Linear-scaling algorithms must be developed in order to extend the domain of applicability of electronic structure theory to molecules of any desired size. But, the increasing complexity of modern linear-scaling methods makes code development and maintenance a significant challenge. A major contributor to this difficulty is the lack of robust software abstractions for handling block-sparse tensor operations. We therefore report the development of a highly efficient symbolic block-sparse tensor library in order to provide access to high-level software constructs to treat such problems. Our implementation supports arbitrary multi-dimensional sparsity in all input and output tensors. We then avoid cumbersome machine-generatedmore » code by implementing all functionality as a high-level symbolic C++ language library and demonstrate that our implementation attains very high performance for linear-scaling sparse tensor contractions.« less

Using Tensor Completion Method to Achieving Better Coverage of Traffic State Estimation from Sparse Floating Car Data

PubMed Central

Ran, Bin; Song, Li; Cheng, Yang; Tan, Huachun

2016-01-01

Traffic state estimation from the floating car system is a challenging problem. The low penetration rate and random distribution make available floating car samples usually cover part space and time points of the road networks. To obtain a wide range of traffic state from the floating car system, many methods have been proposed to estimate the traffic state for the uncovered links. However, these methods cannot provide traffic state of the entire road networks. In this paper, the traffic state estimation is transformed to solve a missing data imputation problem, and the tensor completion framework is proposed to estimate missing traffic state. A tensor is constructed to model traffic state in which observed entries are directly derived from floating car system and unobserved traffic states are modeled as missing entries of constructed tensor. The constructed traffic state tensor can represent spatial and temporal correlations of traffic data and encode the multi-way properties of traffic state. The advantage of the proposed approach is that it can fully mine and utilize the multi-dimensional inherent correlations of traffic state. We tested the proposed approach on a well calibrated simulation network. Experimental results demonstrated that the proposed approach yield reliable traffic state estimation from very sparse floating car data, particularly when dealing with the floating car penetration rate is below 1%. PMID:27448326

Using Tensor Completion Method to Achieving Better Coverage of Traffic State Estimation from Sparse Floating Car Data.

PubMed

Ran, Bin; Song, Li; Zhang, Jian; Cheng, Yang; Tan, Huachun

2016-01-01

Traffic state estimation from the floating car system is a challenging problem. The low penetration rate and random distribution make available floating car samples usually cover part space and time points of the road networks. To obtain a wide range of traffic state from the floating car system, many methods have been proposed to estimate the traffic state for the uncovered links. However, these methods cannot provide traffic state of the entire road networks. In this paper, the traffic state estimation is transformed to solve a missing data imputation problem, and the tensor completion framework is proposed to estimate missing traffic state. A tensor is constructed to model traffic state in which observed entries are directly derived from floating car system and unobserved traffic states are modeled as missing entries of constructed tensor. The constructed traffic state tensor can represent spatial and temporal correlations of traffic data and encode the multi-way properties of traffic state. The advantage of the proposed approach is that it can fully mine and utilize the multi-dimensional inherent correlations of traffic state. We tested the proposed approach on a well calibrated simulation network. Experimental results demonstrated that the proposed approach yield reliable traffic state estimation from very sparse floating car data, particularly when dealing with the floating car penetration rate is below 1%.

Calculation of the Maxwell stress tensor and the Poisson-Boltzmann force on a solvated molecular surface using hypersingular boundary integrals

NASA Astrophysics Data System (ADS)

Lu, Benzhuo; Cheng, Xiaolin; Hou, Tingjun; McCammon, J. Andrew

2005-08-01

The electrostatic interaction among molecules solvated in ionic solution is governed by the Poisson-Boltzmann equation (PBE). Here the hypersingular integral technique is used in a boundary element method (BEM) for the three-dimensional (3D) linear PBE to calculate the Maxwell stress tensor on the solvated molecular surface, and then the PB forces and torques can be obtained from the stress tensor. Compared with the variational method (also in a BEM frame) that we proposed recently, this method provides an even more efficient way to calculate the full intermolecular electrostatic interaction force, especially for macromolecular systems. Thus, it may be more suitable for the application of Brownian dynamics methods to study the dynamics of protein/protein docking as well as the assembly of large 3D architectures involving many diffusing subunits. The method has been tested on two simple cases to demonstrate its reliability and efficiency, and also compared with our previous variational method used in BEM.

Fully probabilistic seismic source inversion - Part 2: Modelling errors and station covariances

NASA Astrophysics Data System (ADS)

Stähler, Simon C.; Sigloch, Karin

2016-11-01

Seismic source inversion, a central task in seismology, is concerned with the estimation of earthquake source parameters and their uncertainties. Estimating uncertainties is particularly challenging because source inversion is a non-linear problem. In a companion paper, Stähler and Sigloch (2014) developed a method of fully Bayesian inference for source parameters, based on measurements of waveform cross-correlation between broadband, teleseismic body-wave observations and their modelled counterparts. This approach yields not only depth and moment tensor estimates but also source time functions. A prerequisite for Bayesian inference is the proper characterisation of the noise afflicting the measurements, a problem we address here. We show that, for realistic broadband body-wave seismograms, the systematic error due to an incomplete physical model affects waveform misfits more strongly than random, ambient background noise. In this situation, the waveform cross-correlation coefficient CC, or rather its decorrelation D = 1 - CC, performs more robustly as a misfit criterion than ℓp norms, more commonly used as sample-by-sample measures of misfit based on distances between individual time samples. From a set of over 900 user-supervised, deterministic earthquake source solutions treated as a quality-controlled reference, we derive the noise distribution on signal decorrelation D = 1 - CC of the broadband seismogram fits between observed and modelled waveforms. The noise on D is found to approximately follow a log-normal distribution, a fortunate fact that readily accommodates the formulation of an empirical likelihood function for D for our multivariate problem. The first and second moments of this multivariate distribution are shown to depend mostly on the signal-to-noise ratio (SNR) of the CC measurements and on the back-azimuthal distances of seismic stations. By identifying and quantifying this likelihood function, we make D and thus waveform cross-correlation measurements usable for fully probabilistic sampling strategies, in source inversion and related applications such as seismic tomography.

Fast and Analytical EAP Approximation from a 4th-Order Tensor.

PubMed

Ghosh, Aurobrata; Deriche, Rachid

2012-01-01

Generalized diffusion tensor imaging (GDTI) was developed to model complex apparent diffusivity coefficient (ADC) using higher-order tensors (HOTs) and to overcome the inherent single-peak shortcoming of DTI. However, the geometry of a complex ADC profile does not correspond to the underlying structure of fibers. This tissue geometry can be inferred from the shape of the ensemble average propagator (EAP). Though interesting methods for estimating a positive ADC using 4th-order diffusion tensors were developed, GDTI in general was overtaken by other approaches, for example, the orientation distribution function (ODF), since it is considerably difficult to recuperate the EAP from a HOT model of the ADC in GDTI. In this paper, we present a novel closed-form approximation of the EAP using Hermite polynomials from a modified HOT model of the original GDTI-ADC. Since the solution is analytical, it is fast, differentiable, and the approximation converges well to the true EAP. This method also makes the effort of computing a positive ADC worthwhile, since now both the ADC and the EAP can be used and have closed forms. We demonstrate our approach with 4th-order tensors on synthetic data and in vivo human data.

Fast and Analytical EAP Approximation from a 4th-Order Tensor

PubMed Central

Ghosh, Aurobrata; Deriche, Rachid

2012-01-01

Generalized diffusion tensor imaging (GDTI) was developed to model complex apparent diffusivity coefficient (ADC) using higher-order tensors (HOTs) and to overcome the inherent single-peak shortcoming of DTI. However, the geometry of a complex ADC profile does not correspond to the underlying structure of fibers. This tissue geometry can be inferred from the shape of the ensemble average propagator (EAP). Though interesting methods for estimating a positive ADC using 4th-order diffusion tensors were developed, GDTI in general was overtaken by other approaches, for example, the orientation distribution function (ODF), since it is considerably difficult to recuperate the EAP from a HOT model of the ADC in GDTI. In this paper, we present a novel closed-form approximation of the EAP using Hermite polynomials from a modified HOT model of the original GDTI-ADC. Since the solution is analytical, it is fast, differentiable, and the approximation converges well to the true EAP. This method also makes the effort of computing a positive ADC worthwhile, since now both the ADC and the EAP can be used and have closed forms. We demonstrate our approach with 4th-order tensors on synthetic data and in vivo human data. PMID:23365552

Tensor-Dictionary Learning with Deep Kruskal-Factor Analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stevens, Andrew J.; Pu, Yunchen; Sun, Yannan

We introduce new dictionary learning methods for tensor-variate data of any order. We represent each data item as a sum of Kruskal decomposed dictionary atoms within the framework of beta-process factor analysis (BPFA). Our model is nonparametric and can infer the tensor-rank of each dictionary atom. This Kruskal-Factor Analysis (KFA) is a natural generalization of BPFA. We also extend KFA to a deep convolutional setting and develop online learning methods. We test our approach on image processing and classification tasks achieving state of the art results for 2D & 3D inpainting and Caltech 101. The experiments also show that atom-rankmore » impacts both overcompleteness and sparsity.« less

Resonant ultrasound spectroscopy for materials with high damping and samples of arbitrary geometry

DOE PAGES

Remillieux, Marcel C.; Ulrich, T. J.; Payan, Cédric; ...

2015-07-23

This paper describes resonant ultrasound spectroscopy (RUS) as a powerful and established technique for measuring elastic constants of a material with general anisotropy. The first step of this technique consists of extracting resonance frequencies and damping from the vibrational frequency spectrum measured on a sample with free boundary conditions. An inversion technique is then used to retrieve the elastic tensor from the measured resonance frequencies. As originally developed, RUS has been mostly applicable to (i) materials with small damping such that the resonances of the sample are well separated and (ii) samples with simple geometries for which analytical solutions exist.more » In this paper, these limitations are addressed with a new RUS approach adapted to materials with high damping and samples of arbitrary geometry. Resonances are extracted by fitting a sum of exponentially damped sinusoids to the measured frequency spectrum. The inversion of the elastic tensor is achieved with a genetic algorithm, which allows searching for a global minimum within a discrete and relatively wide solution space. First, the accuracy of the proposed approach is evaluated against numerical data simulated for samples with isotropic symmetry and transversely isotropic symmetry. Subsequently, the applicability of the approach is demonstrated using experimental data collected on a composite structure consisting of a cylindrical sample of Berea sandstone glued to a large piezoelectric disk. In the proposed experiments, RUS is further enhanced by the use of a 3-D laser vibrometer allowing the visualization of most of the modes in the frequency band studied.« less

On the local field method with the account of spatial dispersion. Application to the optical activity theory

NASA Astrophysics Data System (ADS)

Tyu, N. S.; Ekhilevsky, S. G.

1992-07-01

For the perfect molecular crystals the equations of the local field method (LFM) with the account of spatial dispersion are formulated. They are used to derive the expression for the crystal polarizability tensor. For the first time within the framework of this method the formula for the gyrotropy tensor of an arbitrary optically active molecular crystal is obtained. This formula is analog of well known relationships of Lorentz-Lorenz.

Joint Data Management for MOVINT Data-to-Decision Making

DTIC Science & Technology

2011-07-01

flux tensor , aligned motion history images, and related approaches have been shown to be versatile approaches [12, 16, 17, 18]. Scaling these...methods include voting , neural networks, fuzzy logic, neuro-dynamic programming, support vector machines, Bayesian and Dempster-Shafer methods. One way...Information Fusion, 2010. [16] F. Bunyak, K. Palaniappan, S. K. Nath, G. Seetharaman, “Flux tensor constrained geodesic active contours with sensor fusion

13C and (15)N chemical shift tensors in adenosine, guanosine dihydrate, 2'-deoxythymidine, and cytidine.

PubMed

Stueber, Dirk; Grant, David M

2002-09-04

The (13)C and (15)N chemical shift tensor principal values for adenosine, guanosine dihydrate, 2'-deoxythymidine, and cytidine are measured on natural abundance samples. Additionally, the (13)C and (15)N chemical shielding tensor principal values in these four nucleosides are calculated utilizing various theoretical approaches. Embedded ion method (EIM) calculations improve significantly the precision with which the experimental principal values are reproduced over calculations on the corresponding isolated molecules with proton-optimized geometries. The (13)C and (15)N chemical shift tensor orientations are reliably assigned in the molecular frames of the nucleosides based upon chemical shielding tensor calculations employing the EIM. The differences between principal values obtained in EIM calculations and in calculations on isolated molecules with proton positions optimized inside a point charge array are used to estimate the contributions to chemical shielding arising from intermolecular interactions. Moreover, the (13)C and (15)N chemical shift tensor orientations and principal values correlate with the molecular structure and the crystallographic environment for the nucleosides and agree with data obtained previously for related compounds. The effects of variations in certain EIM parameters on the accuracy of the shielding tensor calculations are investigated.

Chemical shift and electric field gradient tensors for the amide and carboxyl hydrogens in the model peptide N-acetyl-D,L-valine. Single-crystal deuterium NMR study.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gerald, R. E., II; Bernhard, T.; Haeberlen, U.

1993-01-01

Solid-state NMR spectroscopy is well established as a method for describing molecular structure with resolution on the atomic scale. Many of the NMR observables result from anisotropic interactions between the nuclear spin and its environment. These observables can be described by second-rank tensors. For example, the eigenvalues of the traceless symmetric part of the hydrogen chemical shift (CS) tensor provide information about the strength of inter- or intramolecular hydrogen bonding. On the other hand, the eigenvectors of the deuterium electric field gradient (EFG) tensor give deuteron/proton bond directions with an accuracy rivalled only by neutron diffraction. In this paper themore » authors report structural information of this type for the amide and carboxyl hydrogen sites in a single crystal of the model peptide N-acetyl-D,L-valine (NAV). They use deuterium NMR to infer both the EFG and CS tensors at the amide and carboxyl hydrogen sites in NAV. Advantages of this technique over multiple-pulse proton NMR are that it works in the presence of {sup 14}N spins which are very hard to decouple from protons and that additional information in form of the EFG tensors can be derived. The change in the CS and EFG tensors upon exchange of a deuteron for a proton (the isotope effect) is anticipated to be very small; the effect on the CS tensors is certainly smaller than the experimental errors. NAV has served as a model peptide before in a variety of NMR studies, including those concerned with developing solid-state NMR spectroscopy as a method for determining the structure of proteins. NMR experiments on peptide or protein samples which are oriented in at least one dimension can provide important information about the three-dimensional structure of the peptide or the protein. In order to interpret the NMR data in terms of the structure of the polypeptide, the relationship of the CS and EFG tensors to the local symmetry elements of an amino acide, e.g., the peptide plane, is essential. The main purpose of this work is to investigate this relationship for the amide hydrogen CS tensor. The amide hydrogen CS tensor will also provide orientational information for peptide bonds in proteins complementary to that from the nitrogen CS and EFG tensors and the nitrogen-hydrogen heteronuclear dipole-dipole coupling which have been used previously to determine protein structures by solid-state NMR spectroscopy. This information will be particularly valuable because the amide hydrogen CS tensor is not axially symmetric. In addition, the use of the amide hydrogen CS interaction in high-field solid-state NMR experiments will increase the available resolution among peptide sites.« less

Low-rank factorization of electron integral tensors and its application in electronic structure theory

DOE PAGES

Peng, Bo; Kowalski, Karol

2017-01-25

In this paper, we apply reverse Cuthill-McKee (RCM) algorithm to transform two-electron integral tensors to their block diagonal forms. By further applying Cholesky decomposition (CD) on each of the diagonal blocks, we are able to represent the high-dimensional two-electron integral tensors in terms of permutation matrices and low-rank Cholesky vectors. This representation facilitates low-rank factorizations of high-dimensional tensor contractions in post-Hartree-Fock calculations. Finally, we discuss the second-order Møller-Plesset (MP2) method and the linear coupled-cluster model with doubles (L-CCD) as examples to demonstrate the efficiency of this technique in representing the two-electron integrals in a compact form.

Low-rank factorization of electron integral tensors and its application in electronic structure theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Peng, Bo; Kowalski, Karol

In this paper, we apply reverse Cuthill-McKee (RCM) algorithm to transform two-electron integral tensors to their block diagonal forms. By further applying Cholesky decomposition (CD) on each of the diagonal blocks, we are able to represent the high-dimensional two-electron integral tensors in terms of permutation matrices and low-rank Cholesky vectors. This representation facilitates low-rank factorizations of high-dimensional tensor contractions in post-Hartree-Fock calculations. Finally, we discuss the second-order Møller-Plesset (MP2) method and the linear coupled-cluster model with doubles (L-CCD) as examples to demonstrate the efficiency of this technique in representing the two-electron integrals in a compact form.

Direct coordinate-free derivation of the compatibility equation for finite strains

NASA Astrophysics Data System (ADS)

Ryzhak, E. I.

2014-07-01

The compatibility equation for the Cauchy-Green tensor field (squared tensor of pure extensionwith respect to the reference configuration) is directly derived from the well-known relation expressing this tensor via the vector field determining the mapping (transformation) of the reference configuration into the actual one. The derivation is based on the use of the apparatus of coordinatefree tensor calculus and does not apply any notions and relations of Riemannian geometry at all. The method is illustrated by deriving the well-known compatibility equation for small strains. It is shown that when the obtained compatibility equation for finite strains is linearized, it becomes the compatibility equation for small strains which indirectly confirms its correctness.

Approximate bound-state solutions of the Dirac equation for the generalized yukawa potential plus the generalized tensor interaction

NASA Astrophysics Data System (ADS)

Ikot, Akpan N.; Maghsoodi, Elham; Hassanabadi, Hassan; Obu, Joseph A.

2014-05-01

In this paper, we obtain the approximate analytical bound-state solutions of the Dirac particle with the generalized Yukawa potential within the framework of spin and pseudospin symmetries for the arbitrary к state with a generalized tensor interaction. The generalized parametric Nikiforov-Uvarov method is used to obtain the energy eigenvalues and the corresponding wave functions in closed form. We also report some numerical results and present figures to show the effect of the tensor interaction.

Estimating locations and total magnetization vectors of compact magnetic sources from scalar, vector, or tensor magnetic measurements through combined Helbig and Euler analysis

USGS Publications Warehouse

Phillips, J.D.; Nabighian, M.N.; Smith, D.V.; Li, Y.

2007-01-01

The Helbig method for estimating total magnetization directions of compact sources from magnetic vector components is extended so that tensor magnetic gradient components can be used instead. Depths of the compact sources can be estimated using the Euler equation, and their dipole moment magnitudes can be estimated using a least squares fit to the vector component or tensor gradient component data. ?? 2007 Society of Exploration Geophysicists.

Solutions of the Dirac Equation with the Shifted DENG-FAN Potential Including Yukawa-Like Tensor Interaction

NASA Astrophysics Data System (ADS)

Yahya, W. A.; Falaye, B. J.; Oluwadare, O. J.; Oyewumi, K. J.

2013-08-01

By using the Nikiforov-Uvarov method, we give the approximate analytical solutions of the Dirac equation with the shifted Deng-Fan potential including the Yukawa-like tensor interaction under the spin and pseudospin symmetry conditions. After using an improved approximation scheme, we solved the resulting schr\\"{o}dinger-like equation analytically. Numerical results of the energy eigenvalues are also obtained, as expected, the tensor interaction removes degeneracies between spin and pseudospin doublets.

Magnetic resonance neurography and diffusion tensor imaging: origins, history, and clinical impact of the first 50,000 cases with an assessment of efficacy and utility in a prospective 5000-patient study group.

PubMed

Filler, Aaron

2009-10-01

Methods were invented that made it possible to image peripheral nerves in the body and to image neural tracts in the brain. The history, physical basis, and dyadic tensor concept underlying the methods are reviewed. Over a 15-year period, these techniques-magnetic resonance neurography (MRN) and diffusion tensor imaging-were deployed in the clinical and research community in more than 2500 published research reports and applied to approximately 50,000 patients. Within this group, approximately 5000 patients having MRN were carefully tracked on a prospective basis. A uniform Neurography imaging methodology was applied in the study group, and all images were reviewed and registered by referral source, clinical indication, efficacy of imaging, and quality. Various classes of image findings were identified and subjected to a variety of small targeted prospective outcome studies. Those findings demonstrated to be clinically significant were then tracked in the larger clinical volume data set. MRN demonstrates mechanical distortion of nerves, hyperintensity consistent with nerve irritation, nerve swelling, discontinuity, relations of nerves to masses, and image features revealing distortion of nerves at entrapment points. These findings are often clinically relevant and warrant full consideration in the diagnostic process. They result in specific pathological diagnoses that are comparable to electrodiagnostic testing in clinical efficacy. A review of clinical outcome studies with diffusion tensor imaging also shows convincing utility. MRN and diffusion tensor imaging neural tract imaging have been validated as indispensable clinical diagnostic methods that provide reliable anatomic pathological information. There is no alternative diagnostic method in many situations. With the elapsing of 15 years, tens of thousands of imaging studies, and thousands of publications, these methods should no longer be considered experimental.

Introduction to Vector Field Visualization

NASA Technical Reports Server (NTRS)

Kao, David; Shen, Han-Wei

2010-01-01

Vector field visualization techniques are essential to help us understand the complex dynamics of flow fields. These can be found in a wide range of applications such as study of flows around an aircraft, the blood flow in our heart chambers, ocean circulation models, and severe weather predictions. The vector fields from these various applications can be visually depicted using a number of techniques such as particle traces and advecting textures. In this tutorial, we present several fundamental algorithms in flow visualization including particle integration, particle tracking in time-dependent flows, and seeding strategies. For flows near surfaces, a wide variety of synthetic texture-based algorithms have been developed to depict near-body flow features. The most common approach is based on the Line Integral Convolution (LIC) algorithm. There also exist extensions of LIC to support more flexible texture generations for 3D flow data. This tutorial reviews these algorithms. Tensor fields are found in several real-world applications and also require the aid of visualization to help users understand their data sets. Examples where one can find tensor fields include mechanics to see how material respond to external forces, civil engineering and geomechanics of roads and bridges, and the study of neural pathway via diffusion tensor imaging. This tutorial will provide an overview of the different tensor field visualization techniques, discuss basic tensor decompositions, and go into detail on glyph based methods, deformation based methods, and streamline based methods. Practical examples will be used when presenting the methods; and applications from some case studies will be used as part of the motivation.

A novel anisotropic inversion approach for magnetotelluric data from subsurfaces with orthogonal geoelectric strike directions

NASA Astrophysics Data System (ADS)

Schmoldt, Jan-Philipp; Jones, Alan G.

2013-12-01

The key result of this study is the development of a novel inversion approach for cases of orthogonal, or close to orthogonal, geoelectric strike directions at different depth ranges, for example, crustal and mantle depths. Oblique geoelectric strike directions are a well-known issue in commonly employed isotropic 2-D inversion of MT data. Whereas recovery of upper (crustal) structures can, in most cases, be achieved in a straightforward manner, deriving lower (mantle) structures is more challenging with isotropic 2-D inversion in the case of an overlying region (crust) with different geoelectric strike direction. Thus, investigators may resort to computationally expensive and more limited 3-D inversion in order to derive the electric resistivity distribution at mantle depths. In the novel approaches presented in this paper, electric anisotropy is used to image 2-D structures in one depth range, whereas the other region is modelled with an isotropic 1-D or 2-D approach, as a result significantly reducing computational costs of the inversion in comparison with 3-D inversion. The 1- and 2-D versions of the novel approach were tested using a synthetic 3-D subsurface model with orthogonal strike directions at crust and mantle depths and their performance was compared to results of isotropic 2-D inversion. Structures at crustal depths were reasonably well recovered by all inversion approaches, whereas recovery of mantle structures varied significantly between the different approaches. Isotropic 2-D inversion models, despite decomposition of the electric impedance tensor and using a wide range of inversion parameters, exhibited severe artefacts thereby confirming the requirement of either an enhanced or a higher dimensionality inversion approach. With the anisotropic 1-D inversion approach, mantle structures of the synthetic model were recovered reasonably well with anisotropy values parallel to the mantle strike direction (in this study anisotropy was assigned to the mantle region), indicating applicability of the novel approach for basic subsurface cases. For the more complex subsurface cases, however, the anisotropic 1-D inversion approach is likely to yield implausible models of the electric resistivity distribution due to inapplicability of the 1-D approximation. Owing to the higher number of degrees of freedom, the anisotropic 2-D inversion approach can cope with more complex subsurface cases and is the recommended tool for real data sets recorded in regions with orthogonal geoelectric strike directions.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liakh, Dmitry I

While the formalism of multiresolution analysis (MRA), based on wavelets and adaptive integral representations of operators, is actively progressing in electronic structure theory (mostly on the independent-particle level and, recently, second-order perturbation theory), the concepts of multiresolution and adaptivity can also be utilized within the traditional formulation of correlated (many-particle) theory which is based on second quantization and the corresponding (generally nonorthogonal) tensor algebra. In this paper, we present a formalism called scale-adaptive tensor algebra (SATA) which exploits an adaptive representation of tensors of many-body operators via the local adjustment of the basis set quality. Given a series of locallymore » supported fragment bases of a progressively lower quality, we formulate the explicit rules for tensor algebra operations dealing with adaptively resolved tensor operands. The formalism suggested is expected to enhance the applicability and reliability of local correlated many-body methods of electronic structure theory, especially those directly based on atomic orbitals (or any other localized basis functions).« less

Low-rank factorization of electron integral tensors and its application in electronic structure theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Peng, Bo; Kowalski, Karol

In this letter, we introduce the reverse Cuthill-McKee (RCM) algorithm, which is often used for the bandwidth reduction of sparse tensors, to transform the two-electron integral tensors to their block diagonal forms. By further applying the pivoted Cholesky decomposition (CD) on each of the diagonal blocks, we are able to represent the high-dimensional two-electron integral tensors in terms of permutation matrices and low-rank Cholesky vectors. This representation facilitates the low-rank factorization of the high-dimensional tensor contractions that are usually encountered in post-Hartree-Fock calculations. In this letter, we discuss the second-order Møller-Plesset (MP2) method and linear coupled- cluster model with doublesmore » (L-CCD) as two simple examples to demonstrate the efficiency of the RCM-CD technique in representing two-electron integrals in a compact form.« less

Tensor hypercontracted ppRPA: Reducing the cost of the particle-particle random phase approximation from O(r {sup 6}) to O(r {sup 4})

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shenvi, Neil; Yang, Yang; Yang, Weitao

In recent years, interest in the random-phase approximation (RPA) has grown rapidly. At the same time, tensor hypercontraction has emerged as an intriguing method to reduce the computational cost of electronic structure algorithms. In this paper, we combine the particle-particle random phase approximation with tensor hypercontraction to produce the tensor-hypercontracted particle-particle RPA (THC-ppRPA) algorithm. Unlike previous implementations of ppRPA which scale as O(r{sup 6}), the THC-ppRPA algorithm scales asymptotically as only O(r{sup 4}), albeit with a much larger prefactor than the traditional algorithm. We apply THC-ppRPA to several model systems and show that it yields the same results as traditionalmore » ppRPA to within mH accuracy. Our method opens the door to the development of post-Kohn Sham functionals based on ppRPA without the excessive asymptotic cost of traditional ppRPA implementations.« less

Tensor hypercontracted ppRPA: Reducing the cost of the particle-particle random phase approximation from O(r 6) to O(r 4)

NASA Astrophysics Data System (ADS)

Shenvi, Neil; van Aggelen, Helen; Yang, Yang; Yang, Weitao

2014-07-01

In recent years, interest in the random-phase approximation (RPA) has grown rapidly. At the same time, tensor hypercontraction has emerged as an intriguing method to reduce the computational cost of electronic structure algorithms. In this paper, we combine the particle-particle random phase approximation with tensor hypercontraction to produce the tensor-hypercontracted particle-particle RPA (THC-ppRPA) algorithm. Unlike previous implementations of ppRPA which scale as O(r6), the THC-ppRPA algorithm scales asymptotically as only O(r4), albeit with a much larger prefactor than the traditional algorithm. We apply THC-ppRPA to several model systems and show that it yields the same results as traditional ppRPA to within mH accuracy. Our method opens the door to the development of post-Kohn Sham functionals based on ppRPA without the excessive asymptotic cost of traditional ppRPA implementations.

Six dimensional X-ray Tensor Tomography with a compact laboratory setup

NASA Astrophysics Data System (ADS)

Sharma, Y.; Wieczorek, M.; Schaff, F.; Seyyedi, S.; Prade, F.; Pfeiffer, F.; Lasser, T.

2016-09-01

Attenuation based X-ray micro computed tomography (XCT) provides three-dimensional images with micrometer resolution. However, there is a trade-off between the smallest size of the structures that can be resolved and the measurable sample size. In this letter, we present an imaging method using a compact laboratory setup that reveals information about micrometer-sized structures within samples that are several orders of magnitudes larger. We combine the anisotropic dark-field signal obtained in a grating interferometer and advanced tomographic reconstruction methods to reconstruct a six dimensional scattering tensor at every spatial location in three dimensions. The scattering tensor, thus obtained, encodes information about the orientation of micron-sized structures such as fibres in composite materials or dentinal tubules in human teeth. The sparse acquisition schemes presented in this letter enable the measurement of the full scattering tensor at every spatial location and can be easily incorporated in a practical, commercially feasible laboratory setup using conventional X-ray tubes, thus allowing for widespread industrial applications.

The complex-scaled multiconfigurational spin-tensor electron propagator method for low-lying shape resonances in Be-, Mg- and Ca-

NASA Astrophysics Data System (ADS)

Tsogbayar, Tsednee; Yeager, Danny L.

2017-01-01

We further apply the complex scaled multiconfigurational spin-tensor electron propagator method (CMCSTEP) for the theoretical determination of resonance parameters with electron-atom systems including open-shell and highly correlated (non-dynamical correlation) atoms and molecules. The multiconfigurational spin-tensor electron propagator method (MCSTEP) developed and implemented by Yeager and his coworkers for real space gives very accurate and reliable ionization potentials and electron affinities. CMCSTEP uses a complex scaled multiconfigurational self-consistent field (CMCSCF) state as an initial state along with a dilated Hamiltonian where all of the electronic coordinates are scaled by a complex factor. CMCSTEP is designed for determining resonances. We apply CMCSTEP to get the lowest 2P (Be-, Mg-) and 2D (Mg-, Ca-) shape resonances using several different basis sets each with several complete active spaces. Many of these basis sets we employ have been used by others with different methods. Hence, we can directly compare results with different methods but using the same basis sets.

Ground-state and magnetocaloric properties of a coupled spin-electron double-tetrahedral chain (exact study at the half filling)

NASA Astrophysics Data System (ADS)

Gálisová, Lucia; Jakubczyk, Dorota

2017-01-01

Ground-state and magnetocaloric properties of a double-tetrahedral chain, in which nodal lattice sites occupied by the localized Ising spins regularly alternate with triangular clusters half filled with mobile electrons, are exactly investigated by using the transfer-matrix method in combination with the construction of the Nth tensor power of the discrete Fourier transformation. It is shown that the ground state of the model is formed by two non-chiral phases with the zero residual entropy and two chiral phases with the finite residual entropy S = NkB ln 2. Depending on the character of the exchange interaction between the localized Ising spins and mobile electrons, one or three magnetization plateaus can be observed in the magnetization process. Their heights basically depend on the values of Landé g-factors of the Ising spins and mobile electrons. It is also evidenced that the system exhibits both the conventional and inverse magnetocaloric effect depending on values of the applied magnetic field and temperature.

Magnetotelluric imaging of anisotropic crust near Fort McMurray, Alberta: implications for engineered geothermal system development

NASA Astrophysics Data System (ADS)

Liddell, Mitch; Unsworth, Martyn; Pek, Josef

2016-06-01

Viability for the development of an engineered geothermal system (EGS) in the oilsands region near Fort McMurray, Alberta, is investigated by studying the structure of the Precambrian basement rocks with magnetotellurics (MT). MT data were collected at 94 broad-band stations on two east-west profiles. Apparent resistivity and phase data showed little variation along each profile. The short period MT data detected a 1-D resistivity structure that could be identified as the shallow sedimentary basin underlain by crystalline basement rocks to a depth of 4-5 km. At lower frequencies a strong directional dependence, large phase splits, and regions of out-of-quadrant (OOQ) phase were detected. 2-D isotropic inversions of these data failed to produce a realistic resistivity model. A detailed dimensionality analysis found links between large phase tensor skews (˜15°), azimuths, OOQ phases and tensor decomposition strike angles at periods greater than 1 s. Low magnitude induction vectors, as well as uniformity of phase splits and phase tensor character between the northern and southern profiles imply that a 3-D analysis is not necessary or appropriate. Therefore, 2-D anisotropic forward modelling was used to generate a resistivity model to interpret the MT data. The preferred model was based on geological observations of outcropping anisotropic mylonitic basement rocks of the Charles Lake shear zone, 150 km to the north, linked to the study area by aeromagnetic and core sample data. This model fits all four impedance tensor elements with an rms misfit of 2.82 on the southern profile, and 3.3 on the northern. The conductive phase causing the anisotropy is interpreted to be interconnected graphite films within the metamorphic basement rocks. Characterizing the anisotropy is important for understanding how artificial fractures, necessary for EGS development, would form. Features of MT data commonly interpreted to be 3-D (e.g. out of OOQ phase and large phase tensor skew) are shown to be interpretable with this 2-D anisotropic model.

Navigating the Functional Landscape of Transcription Factors via Non-Negative Tensor Factorization Analysis of MEDLINE Abstracts

PubMed Central

Roy, Sujoy; Yun, Daqing; Madahian, Behrouz; Berry, Michael W.; Deng, Lih-Yuan; Goldowitz, Daniel; Homayouni, Ramin

2017-01-01

In this study, we developed and evaluated a novel text-mining approach, using non-negative tensor factorization (NTF), to simultaneously extract and functionally annotate transcriptional modules consisting of sets of genes, transcription factors (TFs), and terms from MEDLINE abstracts. A sparse 3-mode term × gene × TF tensor was constructed that contained weighted frequencies of 106,895 terms in 26,781 abstracts shared among 7,695 genes and 994 TFs. The tensor was decomposed into sub-tensors using non-negative tensor factorization (NTF) across 16 different approximation ranks. Dominant entries of each of 2,861 sub-tensors were extracted to form term–gene–TF annotated transcriptional modules (ATMs). More than 94% of the ATMs were found to be enriched in at least one KEGG pathway or GO category, suggesting that the ATMs are functionally relevant. One advantage of this method is that it can discover potentially new gene–TF associations from the literature. Using a set of microarray and ChIP-Seq datasets as gold standard, we show that the precision of our method for predicting gene–TF associations is significantly higher than chance. In addition, we demonstrate that the terms in each ATM can be used to suggest new GO classifications to genes and TFs. Taken together, our results indicate that NTF is useful for simultaneous extraction and functional annotation of transcriptional regulatory networks from unstructured text, as well as for literature based discovery. A web tool called Transcriptional Regulatory Modules Extracted from Literature (TREMEL), available at http://binf1.memphis.edu/tremel, was built to enable browsing and searching of ATMs. PMID:28894735

Tensor hypercontraction. II. Least-squares renormalization

NASA Astrophysics Data System (ADS)

Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J.; Sherrill, C. David

2012-12-01

The least-squares tensor hypercontraction (LS-THC) representation for the electron repulsion integral (ERI) tensor is presented. Recently, we developed the generic tensor hypercontraction (THC) ansatz, which represents the fourth-order ERI tensor as a product of five second-order tensors [E. G. Hohenstein, R. M. Parrish, and T. J. Martínez, J. Chem. Phys. 137, 044103 (2012)], 10.1063/1.4732310. Our initial algorithm for the generation of the THC factors involved a two-sided invocation of overlap-metric density fitting, followed by a PARAFAC decomposition, and is denoted PARAFAC tensor hypercontraction (PF-THC). LS-THC supersedes PF-THC by producing the THC factors through a least-squares renormalization of a spatial quadrature over the otherwise singular 1/r12 operator. Remarkably, an analytical and simple formula for the LS-THC factors exists. Using this formula, the factors may be generated with O(N^5) effort if exact integrals are decomposed, or O(N^4) effort if the decomposition is applied to density-fitted integrals, using any choice of density fitting metric. The accuracy of LS-THC is explored for a range of systems using both conventional and density-fitted integrals in the context of MP2. The grid fitting error is found to be negligible even for extremely sparse spatial quadrature grids. For the case of density-fitted integrals, the additional error incurred by the grid fitting step is generally markedly smaller than the underlying Coulomb-metric density fitting error. The present results, coupled with our previously published factorizations of MP2 and MP3, provide an efficient, robust O(N^4) approach to both methods. Moreover, LS-THC is generally applicable to many other methods in quantum chemistry.

Tensor hypercontraction. II. Least-squares renormalization.

PubMed

Parrish, Robert M; Hohenstein, Edward G; Martínez, Todd J; Sherrill, C David

2012-12-14

The least-squares tensor hypercontraction (LS-THC) representation for the electron repulsion integral (ERI) tensor is presented. Recently, we developed the generic tensor hypercontraction (THC) ansatz, which represents the fourth-order ERI tensor as a product of five second-order tensors [E. G. Hohenstein, R. M. Parrish, and T. J. Martínez, J. Chem. Phys. 137, 044103 (2012)]. Our initial algorithm for the generation of the THC factors involved a two-sided invocation of overlap-metric density fitting, followed by a PARAFAC decomposition, and is denoted PARAFAC tensor hypercontraction (PF-THC). LS-THC supersedes PF-THC by producing the THC factors through a least-squares renormalization of a spatial quadrature over the otherwise singular 1∕r(12) operator. Remarkably, an analytical and simple formula for the LS-THC factors exists. Using this formula, the factors may be generated with O(N(5)) effort if exact integrals are decomposed, or O(N(4)) effort if the decomposition is applied to density-fitted integrals, using any choice of density fitting metric. The accuracy of LS-THC is explored for a range of systems using both conventional and density-fitted integrals in the context of MP2. The grid fitting error is found to be negligible even for extremely sparse spatial quadrature grids. For the case of density-fitted integrals, the additional error incurred by the grid fitting step is generally markedly smaller than the underlying Coulomb-metric density fitting error. The present results, coupled with our previously published factorizations of MP2 and MP3, provide an efficient, robust O(N(4)) approach to both methods. Moreover, LS-THC is generally applicable to many other methods in quantum chemistry.

Highly Efficient and Scalable Compound Decomposition of Two-Electron Integral Tensor and Its Application in Coupled Cluster Calculations.

PubMed

Peng, Bo; Kowalski, Karol

2017-09-12

The representation and storage of two-electron integral tensors are vital in large-scale applications of accurate electronic structure methods. Low-rank representation and efficient storage strategy of integral tensors can significantly reduce the numerical overhead and consequently time-to-solution of these methods. In this work, by combining pivoted incomplete Cholesky decomposition (CD) with a follow-up truncated singular vector decomposition (SVD), we develop a decomposition strategy to approximately represent the two-electron integral tensor in terms of low-rank vectors. A systematic benchmark test on a series of 1-D, 2-D, and 3-D carbon-hydrogen systems demonstrates high efficiency and scalability of the compound two-step decomposition of the two-electron integral tensor in our implementation. For the size of the atomic basis set, N b , ranging from ∼100 up to ∼2,000, the observed numerical scaling of our implementation shows [Formula: see text] versus [Formula: see text] cost of performing single CD on the two-electron integral tensor in most of the other implementations. More importantly, this decomposition strategy can significantly reduce the storage requirement of the atomic orbital (AO) two-electron integral tensor from [Formula: see text] to [Formula: see text] with moderate decomposition thresholds. The accuracy tests have been performed using ground- and excited-state formulations of coupled cluster formalism employing single and double excitations (CCSD) on several benchmark systems including the C 60 molecule described by nearly 1,400 basis functions. The results show that the decomposition thresholds can be generally set to 10 -4 to 10 -3 to give acceptable compromise between efficiency and accuracy.

Symplectic Quantization of a Vector-Tensor Gauge Theory with Topological Coupling

NASA Astrophysics Data System (ADS)

Barcelos-Neto, J.; Silva, M. B. D.

We use the symplectic formalism to quantize a gauge theory where vectors and tensors fields are coupled in a topological way. This is an example of reducible theory and a procedure like of ghosts-of-ghosts of the BFV method is applied but in terms of Lagrange multipliers. Our final results are in agreement with the ones found in the literature by using the Dirac method.

Shape-from-focus by tensor voting.

PubMed

Hariharan, R; Rajagopalan, A N

2012-07-01

In this correspondence, we address the task of recovering shape-from-focus (SFF) as a perceptual organization problem in 3-D. Using tensor voting, depth hypotheses from different focus operators are validated based on their likelihood to be part of a coherent 3-D surface, thereby exploiting scene geometry and focus information to generate reliable depth estimates. The proposed method is fast and yields significantly better results compared with existing SFF methods.

A Type-2 Block-Component-Decomposition Based 2D AOA Estimation Algorithm for an Electromagnetic Vector Sensor Array

PubMed Central

Gao, Yu-Fei; Gui, Guan; Xie, Wei; Zou, Yan-Bin; Yang, Yue; Wan, Qun

2017-01-01

This paper investigates a two-dimensional angle of arrival (2D AOA) estimation algorithm for the electromagnetic vector sensor (EMVS) array based on Type-2 block component decomposition (BCD) tensor modeling. Such a tensor decomposition method can take full advantage of the multidimensional structural information of electromagnetic signals to accomplish blind estimation for array parameters with higher resolution. However, existing tensor decomposition methods encounter many restrictions in applications of the EMVS array, such as the strict requirement for uniqueness conditions of decomposition, the inability to handle partially-polarized signals, etc. To solve these problems, this paper investigates tensor modeling for partially-polarized signals of an L-shaped EMVS array. The 2D AOA estimation algorithm based on rank-(L1,L2,·) BCD is developed, and the uniqueness condition of decomposition is analyzed. By means of the estimated steering matrix, the proposed algorithm can automatically achieve angle pair-matching. Numerical experiments demonstrate that the present algorithm has the advantages of both accuracy and robustness of parameter estimation. Even under the conditions of lower SNR, small angular separation and limited snapshots, the proposed algorithm still possesses better performance than subspace methods and the canonical polyadic decomposition (CPD) method. PMID:28448431

A Type-2 Block-Component-Decomposition Based 2D AOA Estimation Algorithm for an Electromagnetic Vector Sensor Array.

PubMed

Gao, Yu-Fei; Gui, Guan; Xie, Wei; Zou, Yan-Bin; Yang, Yue; Wan, Qun

2017-04-27

This paper investigates a two-dimensional angle of arrival (2D AOA) estimation algorithm for the electromagnetic vector sensor (EMVS) array based on Type-2 block component decomposition (BCD) tensor modeling. Such a tensor decomposition method can take full advantage of the multidimensional structural information of electromagnetic signals to accomplish blind estimation for array parameters with higher resolution. However, existing tensor decomposition methods encounter many restrictions in applications of the EMVS array, such as the strict requirement for uniqueness conditions of decomposition, the inability to handle partially-polarized signals, etc. To solve these problems, this paper investigates tensor modeling for partially-polarized signals of an L-shaped EMVS array. The 2D AOA estimation algorithm based on rank- ( L 1 , L 2 , · ) BCD is developed, and the uniqueness condition of decomposition is analyzed. By means of the estimated steering matrix, the proposed algorithm can automatically achieve angle pair-matching. Numerical experiments demonstrate that the present algorithm has the advantages of both accuracy and robustness of parameter estimation. Even under the conditions of lower SNR, small angular separation and limited snapshots, the proposed algorithm still possesses better performance than subspace methods and the canonical polyadic decomposition (CPD) method.

Dissipation consistent fabric tensor definition from DEM to continuum for granular media

NASA Astrophysics Data System (ADS)

Li, X. S.; Dafalias, Y. F.

2015-05-01

In elastoplastic soil models aimed at capturing the impact of fabric anisotropy, a necessary ingredient is a measure of anisotropic fabric in the form of an evolving tensor. While it is possible to formulate such a fabric tensor based on indirect phenomenological observations at the continuum level, it is more effective and insightful to have the tensor defined first based on direct particle level microstructural observations and subsequently deduce a corresponding continuum definition. A practical means able to provide such observations, at least in the context of fabric evolution mechanisms, is the discrete element method (DEM). Some DEM defined fabric tensors such as the one based on the statistics of interparticle contact normals have already gained widespread acceptance as a quantitative measure of fabric anisotropy among researchers of granular material behavior. On the other hand, a fabric tensor in continuum elastoplastic modeling has been treated as a tensor-valued internal variable whose evolution must be properly linked to physical dissipation. Accordingly, the adaptation of a DEM fabric tensor definition to a continuum constitutive modeling theory must be thermodynamically consistent in regards to dissipation mechanisms. The present paper addresses this issue in detail, brings up possible pitfalls if such consistency is violated and proposes remedies and guidelines for such adaptation within a recently developed Anisotropic Critical State Theory (ACST) for granular materials.

Experimental evaluation of electrical conductivity imaging of anisotropic brain tissues using a combination of diffusion tensor imaging and magnetic resonance electrical impedance tomography

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sajib, Saurav Z. K.; Jeong, Woo Chul; Oh, Tong In

Anisotropy of biological tissues is a low-frequency phenomenon that is associated with the function and structure of cell membranes. Imaging of anisotropic conductivity has potential for the analysis of interactions between electromagnetic fields and biological systems, such as the prediction of current pathways in electrical stimulation therapy. To improve application to the clinical environment, precise approaches are required to understand the exact responses inside the human body subjected to the stimulated currents. In this study, we experimentally evaluate the anisotropic conductivity tensor distribution of canine brain tissues, using a recently developed diffusion tensor-magnetic resonance electrical impedance tomography method. At lowmore » frequency, electrical conductivity of the biological tissues can be expressed as a product of the mobility and concentration of ions in the extracellular space. From diffusion tensor images of the brain, we can obtain directional information on diffusive movements of water molecules, which correspond to the mobility of ions. The position dependent scale factor, which provides information on ion concentration, was successfully calculated from the magnetic flux density, to obtain the equivalent conductivity tensor. By combining the information from both techniques, we can finally reconstruct the anisotropic conductivity tensor images of brain tissues. The reconstructed conductivity images better demonstrate the enhanced signal intensity in strongly anisotropic brain regions, compared with those resulting from previous methods using a global scale factor.« less

The Riemann-Lanczos equations in general relativity and their integrability

NASA Astrophysics Data System (ADS)

Dolan, P.; Gerber, A.

2008-06-01

The aim of this paper is to examine the Riemann-Lanczos equations and how they can be made integrable. They consist of a system of linear first-order partial differential equations that arise in general relativity, whereby the Riemann curvature tensor is generated by an unknown third-order tensor potential field called the Lanczos tensor. Our approach is based on the theory of jet bundles, where all field variables and all their partial derivatives of all relevant orders are treated as independent variables alongside the local manifold coordinates (xa) on the given space-time manifold M. This approach is adopted in (a) Cartan's method of exterior differential systems, (b) Vessiot's dual method using vector field systems, and (c) the Janet-Riquier theory of systems of partial differential equations. All three methods allow for the most general situations under which integrability conditions can be found. They give equivalent results, namely, that involutivity is always achieved at all generic points of the jet manifold M after a finite number of prolongations. Two alternative methods that appear in the general relativity literature to find integrability conditions for the Riemann-Lanczos equations generate new partial differential equations for the Lanczos potential that introduce a source term, which is nonlinear in the components of the Riemann tensor. We show that such sources do not occur when either of method (a), (b), or (c) are used.

Geometry of matrix product states: Metric, parallel transport, and curvature

DOE Office of Scientific and Technical Information (OSTI.GOV)

Haegeman, Jutho, E-mail: jutho.haegeman@gmail.com; Verstraete, Frank; Faculty of Physics and Astronomy, University of Ghent, Krijgslaan 281 S9, 9000 Gent

2014-02-15

We study the geometric properties of the manifold of states described as (uniform) matrix product states. Due to the parameter redundancy in the matrix product state representation, matrix product states have the mathematical structure of a (principal) fiber bundle. The total space or bundle space corresponds to the parameter space, i.e., the space of tensors associated to every physical site. The base manifold is embedded in Hilbert space and can be given the structure of a Kähler manifold by inducing the Hilbert space metric. Our main interest is in the states living in the tangent space to the base manifold,more » which have recently been shown to be interesting in relation to time dependence and elementary excitations. By lifting these tangent vectors to the (tangent space) of the bundle space using a well-chosen prescription (a principal bundle connection), we can define and efficiently compute an inverse metric, and introduce differential geometric concepts such as parallel transport (related to the Levi-Civita connection) and the Riemann curvature tensor.« less

A priori testing of subgrid-scale models for large-eddy simulation of the atmospheric boundary layer

NASA Astrophysics Data System (ADS)

Juneja, Anurag; Brasseur, James G.

1996-11-01

Subgrid-scale models are generally developed assuming homogeneous isotropic turbulence with the filter cutoff lying in the inertial range. In the surface layer and capping inversion regions of the atmospheric boundary layer, the turbulence is strongly anisotropic and, in general, influenced by both buoyancy and shear. Furthermore, the integral scale motions are under-resolved in these regions. Herein we perform direct numerical simulations of shear and buoyancy-generated homogeneous anisotropic turbulence to compute and analyze the actual subgrid-resolved-scale (SGS-RS) dynamics as the filter cutoff moves into the energy-containing scales. These are compared with the SGS-RS dynamics predicted by Smagorinsky-based models with a focus on motivating improved closures. We find that, in general, the underlying assumption of such models, that the anisotropic part of the subgrid stress tensor be aligned with the resolved strain rate tensor, is a poor approximation. Similarly, we find poor alignment between the actual and predicted stress divergence, and find low correlations between the actual and modeled subgrid-scale contribution to the pressure and pressure gradient. Details will be given in the talk.

Method and apparatus for second-rank tensor generation

NASA Technical Reports Server (NTRS)

Liu, Hua-Kuang (Inventor)

1991-01-01

A method and apparatus are disclosed for generation of second-rank tensors using a photorefractive crystal to perform the outer-product between two vectors via four-wave mixing, thereby taking 2n input data to a control n squared output data points. Two orthogonal amplitude modulated coherent vector beams x and y are expanded and then parallel sides of the photorefractive crystal in exact opposition. A beamsplitter is used to direct a coherent pumping beam onto the crystal at an appropriate angle so as to produce a conjugate beam that is the matrix product of the vector beam that propagates in the exact opposite direction from the pumping beam. The conjugate beam thus separated is the tensor output xy (sup T).

Natural chemical shielding analysis of nuclear magnetic resonance shielding tensors from gauge-including atomic orbital calculations

NASA Astrophysics Data System (ADS)

Bohmann, Jonathan A.; Weinhold, Frank; Farrar, Thomas C.

1997-07-01

Nuclear magnetic shielding tensors computed by the gauge including atomic orbital (GIAO) method in the Hartree-Fock self-consistent-field (HF-SCF) framework are partitioned into magnetic contributions from chemical bonds and lone pairs by means of natural chemical shielding (NCS) analysis, an extension of natural bond orbital (NBO) analysis. NCS analysis complements the description provided by alternative localized orbital methods by directly calculating chemical shieldings due to delocalized features in the electronic structure, such as bond conjugation and hyperconjugation. Examples of NCS tensor decomposition are reported for CH4, CO, and H2CO, for which a graphical mnemonic due to Cornwell is used to illustrate the effect of hyperconjugative delocalization on the carbon shielding.

Simulation of hydrodynamically interacting particles near a no-slip boundary

NASA Astrophysics Data System (ADS)

Swan, James W.; Brady, John F.

2007-11-01

The dynamics of spherical particles near a single plane wall are computed using an extension of the Stokesian dynamics method that includes long-range many-body and pairwise lubrication interactions between the spheres and the wall in Stokes flow. Extra care is taken to ensure that the mobility and resistance tensors are symmetric, positive, and definite—something which is ineluctable for particles in low-Reynolds-number flows. We discuss why two previous simulation methods for particles near a plane wall, one using multipole expansions and the other using the Rotne-Prager tensor, fail to produce symmetric resistance and mobility tensors. Additionally, we offer some insight on how the Stokesian dynamics paradigm might be extended to study the dynamics of particles in any confining geometry.

Obtaining molecular and structural information from 13C-14N systems with 13C FIREMAT experiments.

PubMed

Strohmeier, Mark; Alderman, D W; Grant, David M

2002-04-01

The effect of dipolar coupling to 14N on 13C FIREMAT (five pi replicated magic angle turning) experiments is investigated. A method is developed for fitting the 13C FIREMAT FID employing the full theory to extract the 13C-14N dipolar and 13C chemical shift tensor information. The analysis requires prior knowledge of the electric field gradient (EFG) tensor at the 14N nucleus. In order to validate the method the analysis is done for the amino acids alpha-glycine, gamma-glycine, l-alanine, l-asparagine, and l-histidine on FIREMAT FIDs recorded at 13C frequencies of 50 and 100 MHz. The dipolar and chemical shift data obtained with this analysis are in very good agreement with the previous single-crystal 13C NMR results and neutron diffraction data on alpha-glycine, l-alanine, and l-asparagine. The values for gamma-glycine and l-histidine obtained with this new method are reported for the first time. The uncertainties in the EFG tensor on the resultant 13C chemical shift and dipolar tensor values are assessed. (c) 2002 Elsevier Science (USA).

Intermolecular shielding contributions studied by modeling the 13C chemical-shift tensors of organic single crystals with plane waves

PubMed Central

Johnston, Jessica C.; Iuliucci, Robbie J.; Facelli, Julio C.; Fitzgerald, George; Mueller, Karl T.

2009-01-01

In order to predict accurately the chemical shift of NMR-active nuclei in solid phase systems, magnetic shielding calculations must be capable of considering the complete lattice structure. Here we assess the accuracy of the density functional theory gauge-including projector augmented wave method, which uses pseudopotentials to approximate the nodal structure of the core electrons, to determine the magnetic properties of crystals by predicting the full chemical-shift tensors of all 13C nuclides in 14 organic single crystals from which experimental tensors have previously been reported. Plane-wave methods use periodic boundary conditions to incorporate the lattice structure, providing a substantial improvement for modeling the chemical shifts in hydrogen-bonded systems. Principal tensor components can now be predicted to an accuracy that approaches the typical experimental uncertainty. Moreover, methods that include the full solid-phase structure enable geometry optimizations to be performed on the input structures prior to calculation of the shielding. Improvement after optimization is noted here even when neutron diffraction data are used for determining the initial structures. After geometry optimization, the isotropic shift can be predicted to within 1 ppm. PMID:19831448

Imaging of isotropic and anisotropic conductivities from power densities in three dimensions

NASA Astrophysics Data System (ADS)

Monard, François; Rim, Donsub

2018-07-01

We present numerical reconstructions of anisotropic conductivity tensors in three dimensions, from knowledge of a finite family of power density functionals. Such a problem arises in the coupled-physics imaging modality ultrasound modulated electrical impedance tomography for instance. We improve on the algorithms previously derived in Bal et al (2013 Inverse Problems Imaging 7 353–75) Monard and Bal (2013 Commun. PDE 38 1183–207) for both isotropic and anisotropic cases, and we address the well-known issue of vanishing determinants in particular. The algorithm is implemented and we provide numerical results that illustrate the improvements.

The method of planes pressure tensor for a spherical subvolume

DOE Office of Scientific and Technical Information (OSTI.GOV)

Heyes, D. M., E-mail: d.heyes@imperial.ac.uk; Smith, E. R., E-mail: edward.smith05@imperial.ac.uk; Dini, D., E-mail: d.dini@imperial.ac.uk

2014-02-07

Various formulas for the local pressure tensor based on a spherical subvolume of radius, R, are considered. An extension of the Method of Planes (MOP) formula of Todd et al. [Phys. Rev. E 52, 1627 (1995)] for a spherical geometry is derived using the recently proposed Control Volume formulation [E. R. Smith, D. M. Heyes, D. Dini, and T. A. Zaki, Phys. Rev. E 85, 056705 (2012)]. The MOP formula for the purely radial component of the pressure tensor is shown to be mathematically identical to the Radial Irving-Kirkwood formula. Novel offdiagonal elements which are important for momentum conservation emergemore » naturally from this treatment. The local pressure tensor formulas for a plane are shown to be the large radius limits of those for spherical surfaces. The radial-dependence of the pressure tensor computed by Molecular Dynamics simulation is reported for virtual spheres in a model bulk liquid where the sphere is positioned randomly or whose center is also that of a molecule in the liquid. The probability distributions of angles relating to pairs of atoms which cross the surface of the sphere, and the center of the sphere, are presented as a function of R. The variance in the shear stress calculated from the spherical Volume Averaging method is shown to converge slowly to the limiting values with increasing radius, and to be a strong function of the number of molecules in the simulation cell.« less

Complex conductivity of organic-rich shales

NASA Astrophysics Data System (ADS)

Woodruff, W. F.; Revil, A.; Torres-Verdin, C.

2013-12-01

We can accurately determine the intrinsic anisotropy and material properties in the laboratory, providing empirical evidence of transverse isotropy and the polarization of the organic and metallic fractions in saturated and unsaturated shales. We develop two distinct approaches to obtain the complex conductivity tensor from spectral induced polarization (SIP) measurements. Experimental results indicate clear anisotropy, and characterize the effects of thermal maturation, TOC, and pyrite, aiding in the calibration and interpretation of geophysical data. SIP is a non-intrusive measurement, sensitive to the surface conductance of mineral grains, frequency-dependent polarization of the electrical double layer, and bulk conductivity of the pore water. The in-phase and quadrature components depend upon parameters of principal importance in unconventional shale formation evaluation (e.g., the distribution of pore throat sizes, formation factor, permeability, salinity and cation exchange capacity (CEC), fluid saturation and wettability). In addition to the contribution of the electrical double layer of non-conducting minerals to surface conductivity, we have observed a clear relaxation associated with kerogen pyrolysis, pyrite distribution, and evidence that the CEC of the kerogen fraction may also contribute, depending on thermal maturation history. We utilize a recent model for anisotropic complex conductivity, and rigorous experimental protocols to quantify the role of kerogen and pyrolysis on surface and quadrature conductivity in mudrocks. The complex conductivity tensor σ* describes the directional dependence of electrical conduction in a porous medium, and accounts for both conduction and polarization. The complex-valued tensor components are given as σ*ij , where σ'ij represents in-phase and σ"ij denotes quadrature conductivities. The directional dependence of the complex conductivity tensor is relegated to the textural properties of the material. The components of the formation factor and connectivity (tortuosity) tensors Fij and Tij (affecting the bulk and surface conductivity, respectively) are correlated as Fij=TijΦ. Both conductivity and connectivity tensors share the same eigenvectors; the anisotropy ratio is equivalent in TI media. At high pore water salinity, surface and quadrature conductivity share the same bulk tortuosity; when surface conductivity dominates (low salinity), conductivity is controlled by the surface conductance, and the tortuosity of electrical current along mineral surfaces usually higher than that of the pore water. We developed two distinct SIP measurement protocols to obtain the tensor: (1) azimuthal sampling and inversion of phasor potentials through the full-field solution of the Laplace equation; (2) direct measurement of complex conductivity eigenvalues by polarized, single-component stimulus current. Experiments also include unsaturated and saturated measurements with three brines of known salinity and pH, at log-distributed frequencies ranging 1 mHz to 45 kHz. Both azimuthal spectra and eigenvalue spectra validate the theoretical model and illustrate the effectiveness of the protocols themselves. We obtain the textural tensors and invert key parameters including Archie exponents and CEC, and characterize the relaxation phenomena associated with kerogen content and maturity for multiphase fluid systems.

Atomic-batched tensor decomposed two-electron repulsion integrals

NASA Astrophysics Data System (ADS)

Schmitz, Gunnar; Madsen, Niels Kristian; Christiansen, Ove

2017-04-01

We present a new integral format for 4-index electron repulsion integrals, in which several strategies like the Resolution-of-the-Identity (RI) approximation and other more general tensor-decomposition techniques are combined with an atomic batching scheme. The 3-index RI integral tensor is divided into sub-tensors defined by atom pairs on which we perform an accelerated decomposition to the canonical product (CP) format. In a first step, the RI integrals are decomposed to a high-rank CP-like format by repeated singular value decompositions followed by a rank reduction, which uses a Tucker decomposition as an intermediate step to lower the prefactor of the algorithm. After decomposing the RI sub-tensors (within the Coulomb metric), they can be reassembled to the full decomposed tensor (RC approach) or the atomic batched format can be maintained (ABC approach). In the first case, the integrals are very similar to the well-known tensor hypercontraction integral format, which gained some attraction in recent years since it allows for quartic scaling implementations of MP2 and some coupled cluster methods. On the MP2 level, the RC and ABC approaches are compared concerning efficiency and storage requirements. Furthermore, the overall accuracy of this approach is assessed. Initial test calculations show a good accuracy and that it is not limited to small systems.

Atomic-batched tensor decomposed two-electron repulsion integrals.

PubMed

Schmitz, Gunnar; Madsen, Niels Kristian; Christiansen, Ove

2017-04-07

We present a new integral format for 4-index electron repulsion integrals, in which several strategies like the Resolution-of-the-Identity (RI) approximation and other more general tensor-decomposition techniques are combined with an atomic batching scheme. The 3-index RI integral tensor is divided into sub-tensors defined by atom pairs on which we perform an accelerated decomposition to the canonical product (CP) format. In a first step, the RI integrals are decomposed to a high-rank CP-like format by repeated singular value decompositions followed by a rank reduction, which uses a Tucker decomposition as an intermediate step to lower the prefactor of the algorithm. After decomposing the RI sub-tensors (within the Coulomb metric), they can be reassembled to the full decomposed tensor (RC approach) or the atomic batched format can be maintained (ABC approach). In the first case, the integrals are very similar to the well-known tensor hypercontraction integral format, which gained some attraction in recent years since it allows for quartic scaling implementations of MP2 and some coupled cluster methods. On the MP2 level, the RC and ABC approaches are compared concerning efficiency and storage requirements. Furthermore, the overall accuracy of this approach is assessed. Initial test calculations show a good accuracy and that it is not limited to small systems.

A diffusion tensor imaging tractography algorithm based on Navier-Stokes fluid mechanics.

PubMed

Hageman, Nathan S; Toga, Arthur W; Narr, Katherine L; Shattuck, David W

2009-03-01

We introduce a fluid mechanics based tractography method for estimating the most likely connection paths between points in diffusion tensor imaging (DTI) volumes. We customize the Navier-Stokes equations to include information from the diffusion tensor and simulate an artificial fluid flow through the DTI image volume. We then estimate the most likely connection paths between points in the DTI volume using a metric derived from the fluid velocity vector field. We validate our algorithm using digital DTI phantoms based on a helical shape. Our method segmented the structure of the phantom with less distortion than was produced using implementations of heat-based partial differential equation (PDE) and streamline based methods. In addition, our method was able to successfully segment divergent and crossing fiber geometries, closely following the ideal path through a digital helical phantom in the presence of multiple crossing tracts. To assess the performance of our algorithm on anatomical data, we applied our method to DTI volumes from normal human subjects. Our method produced paths that were consistent with both known anatomy and directionally encoded color images of the DTI dataset.

A Diffusion Tensor Imaging Tractography Algorithm Based on Navier-Stokes Fluid Mechanics

PubMed Central

Hageman, Nathan S.; Toga, Arthur W.; Narr, Katherine; Shattuck, David W.

2009-01-01

We introduce a fluid mechanics based tractography method for estimating the most likely connection paths between points in diffusion tensor imaging (DTI) volumes. We customize the Navier-Stokes equations to include information from the diffusion tensor and simulate an artificial fluid flow through the DTI image volume. We then estimate the most likely connection paths between points in the DTI volume using a metric derived from the fluid velocity vector field. We validate our algorithm using digital DTI phantoms based on a helical shape. Our method segmented the structure of the phantom with less distortion than was produced using implementations of heat-based partial differential equation (PDE) and streamline based methods. In addition, our method was able to successfully segment divergent and crossing fiber geometries, closely following the ideal path through a digital helical phantom in the presence of multiple crossing tracts. To assess the performance of our algorithm on anatomical data, we applied our method to DTI volumes from normal human subjects. Our method produced paths that were consistent with both known anatomy and directionally encoded color (DEC) images of the DTI dataset. PMID:19244007

Vessel Enhancement and Segmentation of 4D CT Lung Image Using Stick Tensor Voting

NASA Astrophysics Data System (ADS)

Cong, Tan; Hao, Yang; Jingli, Shi; Xuan, Yang

2016-12-01

Vessel enhancement and segmentation plays a significant role in medical image analysis. This paper proposes a novel vessel enhancement and segmentation method for 4D CT lung image using stick tensor voting algorithm, which focuses on addressing the vessel distortion issue of vessel enhancement diffusion (VED) method. Furthermore, the enhanced results are easily segmented using level-set segmentation. In our method, firstly, vessels are filtered using Frangi's filter to reduce intrapulmonary noises and extract rough blood vessels. Secondly, stick tensor voting algorithm is employed to estimate the correct direction along the vessel. Then the estimated direction along the vessel is used as the anisotropic diffusion direction of vessel in VED algorithm, which makes the intensity diffusion of points locating at the vessel wall be consistent with the directions of vessels and enhance the tubular features of vessels. Finally, vessels can be extracted from the enhanced image by applying level-set segmentation method. A number of experiments results show that our method outperforms traditional VED method in vessel enhancement and results in satisfied segmented vessels.

Stress inversion using borehole images and geometry evolution of the fractures in the Rittershoffen EGS project (Alsace, France).

NASA Astrophysics Data System (ADS)

Azzola, Jérôme; Valley, Benoît; Schmittbuhl, Jean; Genter, Albert; Hehn, Régis

2017-04-01

In the Upper Rhine Graben, several deep geothermal projects based on the Enhanced Geothermal System (EGS) exploit local geothermal reservoirs. The principle underlying this technology consists of increasing the hydraulic performances of the reservoir by stimulating natural fractures using different methods, in order to extract hot water with commercially flow rates. In this domain, the knowledge of the in-situ stress state is of central importance to predict the response of the rock mass to stimulations. Here we characterized the stress tensor from Ultrasonic Borehole Imager (UBI) in the open hole section of the EGS doublet located in Rittershoffen, France (in the Upper Rhine Graben). Interestingly extensive logging programs were leaded at different key moments of the development of the injection well using hydraulic, thermal and chemical stimulation (Baujard et al., 2017)1. The time lapse UBI dataset consists of images of the injection well before, shortly and lastly after the stimulation. The geometry of the induced fractures in compression (breakouts) picked on the UBI images are used to determine the orientation of the in-situ stress tensor. The magnitude of the principal stresses is deduced from the drilling data. The magnitude of the maximum horizontal principal stress is evaluated using an inversion method with three failure criteria (Mohr-Coulomb, Mogi-Coulomb and modified Hoek-Brown criterion) and under the assumption of a vertical or a deviated well. Moreover, the characteristic of the dataset enables the analysis of the evolution of the borehole fracturing, as the deepening or widening of the induced fractures. The correlation of the UBI image allows firstly to determine the tool trajectory and to adapt the post and pre-stimulation images. It secondly leads to the estimation of a complete displacement field which characterizes the deformation induced by the stimulations. Even if the variable image quality deeply conditions the comparison, the considered dataset enabled a consistent evaluation of the in-situ stress field taking place in the underground of the EGS plant, as showed by the comparison to results obtained in the vicinity. Moreover, the study of the evolution of fracturing shows the influence of the stimulation process on the fractures geometry. 1(Baujard, C., Genter, A., Dalmais, E., Maurer, V., Hehn, R., Rosillette, R., Vidal, J., Schmittbuhl, J., 2017). Hydrothermal Characterization of wells GRT-1 and GRT-2 in Rittershoffen, France: Implications on the understanding of natural flow systems in the Rhine Graben, Geothermics, 65, 255-268.

Evolution of the stress field in the southern Scotia Arc from the late Mesozoic to the present-day

NASA Astrophysics Data System (ADS)

Maestro, Adolfo; López-Martínez, Jerónimo; Galindo-Zaldívar, Jesús; Bohoyo, Fernando; Mink, Sandra

2014-12-01

The geological evolution of the Scotia Arc, which developed between Antarctica and South America, has facilitated the connection between the Pacific and Atlantic oceans and, has important global implications. To improve the knowledge of the late Mesozoic evolution of the southern Scotia Arc, over 6000 brittle mesostructures were measured over the last 20 years at different outcrops from the northern Antarctic Peninsula and the South Shetland Islands as well as the James Ross and South Orkney archipelagos. This dataset covers a length of more than 1000 km of the arc. Fault data were analysed using the Etchecopar, y-R, Right Dihedra, Stress Inversion and Search Grid Inversion Palaeostress Determination methods. A total of 275 stress tensors were obtained. The results showed that the maximum horizontal stress was in the ENE-WSW and the NW-SE orientations and that the horizontal extension tensors were oriented NE-SW and NW-SE. In addition, seismic activity and focal mechanism solutions were analysed using the Gephart method to establish the present-day stress field and characterise the active tectonics. The results obtained suggest that there is a regional NE-SW compression and a NW-SE extension regime at the present day. The Southern Scotia Arc has a complex geological history due to the different tectonic settings (transform, convergent and divergent) that have affected this sector during its geological evolution from the late Mesozoic until the present day. Six stress fields were obtained from the brittle mesostructure population analysis in the region. The NW-SE and N-S maximum horizontal stresses were related to a combination of Mesozoic oceanic subduction of the former Phoenix Plate under the Pacific margin of the Antarctic Plate, Mesozoic-Cenozoic subduction of the northern Weddell Sea and the Oligocene to the Middle Miocene dextral strike-slip movement between the Scotia and Antarctic plates along the South Scotia Ridge. The NE-SW compression was related to late Miocene to present-day sinistral transcurrent movement along the South Scotia Ridge. Finally, the NW-SE extensional stress field may be related to the development of the following back-arc basins: the Late Cretaceous-Eocene Larsen Basin, the Lower to Middle Miocene Jane Basin and the Pliocene to present-day Bransfield Basin. In addition, the NE-SW and the E-W tensional stress fields were related to the Oligocene opening of the Powell Basin.

A Riemannian geometric mapping technique for identifying incompressible equivalents to subsonic potential flows

NASA Astrophysics Data System (ADS)

German, Brian Joseph

This research develops a technique for the solution of incompressible equivalents to planar steady subsonic potential flows. Riemannian geometric formalism is used to develop a gauge transformation of the length measure followed by a curvilinear coordinate transformation to map the given subsonic flow into a canonical Laplacian flow with the same boundary conditions. The effect of the transformation is to distort both the immersed profile shape and the domain interior nonuniformly as a function of local flow properties. The method represents the full nonlinear generalization of the classical methods of Prandtl-Glauert and Karman-Tsien. Unlike the classical methods which are "corrections," this method gives exact results in the sense that the inverse mapping produces the subsonic full potential solution over the original airfoil, up to numerical accuracy. The motivation for this research was provided by an observed analogy between linear potential flow and the special theory of relativity that emerges from the invariance of the d'Alembert wave equation under Lorentz transformations. This analogy is well known in an operational sense, being leveraged widely in linear unsteady aerodynamics and acoustics, stemming largely from the work of Kussner. Whereas elements of the special theory can be invoked for compressibility effects that are linear and global in nature, the question posed in this work was whether other mathematical techniques from the realm of relativity theory could be used to similar advantage for effects that are nonlinear and local. This line of thought led to a transformation leveraging Riemannian geometric methods common to the general theory of relativity. A gauge transformation is used to geometrize compressibility through the metric tensor of the underlying space to produce an equivalent incompressible flow that lives not on a plane but on a curved surface. In this sense, forces owing to compressibility can be ascribed to the geometry of space in much the same way that general relativity ascribes gravitational forces to the curvature of space-time. Although the analogy with general relativity is fruitful, it is important not to overstate the similarities between compressibility and the physics of gravity, as the interest for this thesis is primarily in the mathematical framework and not physical phenomenology or epistemology. The thesis presents the philosophy and theory for the transformation method followed by a numerical method for practical solutions of equivalent incompressible flows over arbitrary closed profiles. The numerical method employs an iterative approach involving the solution of the equivalent incompressible flow with a panel method, the calculation of the metric tensor for the gauge transformation, and the solution of the curvilinear coordinate mapping to the canonical flow with a finite difference approach for the elliptic boundary value problem. This method is demonstrated for non-circulatory flow over a circular cylinder and both symmetric and lifting flows over a NACA 0012 profile. Results are validated with accepted subcritical full potential test cases available in the literature. For chord-preserving mapping boundary conditions, the results indicate that the equivalent incompressible profiles thicken with Mach number and develop a leading edge droop with increased angle of attack. Two promising areas of potential applicability of the method have been identified. The first is in airfoil inverse design methods leveraging incompressible flow knowledge including heuristics and empirical data for the potential field effects on viscous phenomena such as boundary layer transition and separation. The second is in aerodynamic testing using distorted similarity-scaled models.

Monitoring the refinement of crystal structures with {sup 15}N solid-state NMR shift tensor data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kalakewich, Keyton; Eloranta, Harriet; Harper, James K.

The {sup 15}N chemical shift tensor is shown to be extremely sensitive to lattice structure and a powerful metric for monitoring density functional theory refinements of crystal structures. These refinements include lattice effects and are applied here to five crystal structures. All structures improve based on a better agreement between experimental and calculated {sup 15}N tensors, with an average improvement of 47.0 ppm. Structural improvement is further indicated by a decrease in forces on the atoms by 2–3 orders of magnitude and a greater similarity in atom positions to neutron diffraction structures. These refinements change bond lengths by more thanmore » the diffraction errors including adjustments to X–Y and X–H bonds (X, Y = C, N, and O) of 0.028 ± 0.002 Å and 0.144 ± 0.036 Å, respectively. The acquisition of {sup 15}N tensors at natural abundance is challenging and this limitation is overcome by improved {sup 1}H decoupling in the FIREMAT method. This decoupling dramatically narrows linewidths, improves signal-to-noise by up to 317%, and significantly improves the accuracy of measured tensors. A total of 39 tensors are measured with shifts distributed over a range of more than 400 ppm. Overall, experimental {sup 15}N tensors are at least 5 times more sensitive to crystal structure than {sup 13}C tensors due to nitrogen’s greater polarizability and larger range of chemical shifts.« less

The influence of intraoperative soft tissue balance on patellar pressure in posterior-stabilized total knee arthroplasty.

PubMed

Matsumoto, Tomoyuki; Shibanuma, Nao; Takayama, Koji; Sasaki, Hiroshi; Ishida, Kazunari; Matsushita, Takehiko; Kuroda, Ryosuke; Kurosaka, Masahiro

2016-06-01

Appropriate soft tissue balance is essential for the success of total knee arthroplasty (TKA), and assessment with an offset-type tensor provides useful information about the femorotibial (FT) joint. The purpose of the study was to investigate the relationship between intraoperative soft tissue balance and patellar pressure at both medial and lateral sides. Thirty varus-type osteoarthritis patients who received mobile-bearing posterior-stabilized TKAs were enrolled in the study. Using the tensor, soft tissue balance, including joint component gap and varus ligament balance, was recorded at 0°, 10°, 30°, 60°, 90°, 120°, and 135° with patellofemoral (PF) joint reduction and femoral component placement. Following final prostheses implanted with appropriate insert, the medial and lateral patellar pressures were measured at each flexion angle. A simple regression analysis was performed between each patellar pressure, parameter of soft tissue balance, and postoperative flexion angle. Both lateral and medial patellar pressures increased with flexion. The lateral patellar pressure was significantly higher than the medial patellar pressure at 60°, 90°, and 135° of flexion (p<0.05). The lateral patellar pressure inversely correlated with the varus ligament balance at 60° and 90° of flexion (p<0.05). The lateral patellar pressure at 120° and 135° of flexion inversely correlated with the postoperative flexion angle (p<0.05). Soft tissue balance influenced patellar pressure. In particular, a reduced lateral patellar pressure was found at the lateral laxity at flexion, leading to high postoperative flexion angle. III. Copyright © 2016 Elsevier B.V. All rights reserved.

Stress tensor and focal mechanisms in the Dead Sea basin

NASA Astrophysics Data System (ADS)

Hofstetter, A.; Dorbath, C.; Dorbath, L.; Braeuer, B.; Weber, M. H.

2015-12-01

We use the recorded seismicity, confined to the Dead Sea basin and its boundaries, by the Dead Sea Integrated Research (DESIRE) portable seismic network and the Israel and Jordan permanent seismic networks for studying the mechanisms of earthquakes that occurred in the Dead Sea basin. The observed seismicity in the Dead Sea basin was divided into 9 regions according to the spatial distribution of the earthquakes and the known tectonic features. The large number of recording stations and the good station distribution allowed the reliable determinations of 494 earthquake focal mechanisms. For each region, based on the inversion of the observed polarities of the earthquakes, we determine the focal mechanisms and the associated stress tensor. For 159 earthquakes out of the 494 mechanisms we could determine compatible fault planes. On the eastern side, the focal mechanisms are mainly strike-slip mechanism with nodal planes in the N-S and E-W directions. The azimuths of the stress axes are well constrained presenting minimal variability in the inversion of the data, which is in good agreement with the Arava fault on the eastern side of the Dead Sea basin and what we had expected from the regional geodynamics. However, larger variabilities of the azimuthal and dip angles are observed on the western side of the basin. Due to the wider range of azimuths of the fault planes, we observe the switching of sigma1 and sigma2 or the switching of sigma2 and sigma3as major horizontal stress directions. This observed switching of stress axes allows having dip-slip and normal mechanisms in a region that is dominated by strike-slip motion.

DR-TAMAS: Diffeomorphic Registration for Tensor Accurate alignMent of Anatomical Structures

PubMed Central

Irfanoglu, M. Okan; Nayak, Amritha; Jenkins, Jeffrey; Hutchinson, Elizabeth B.; Sadeghi, Neda; Thomas, Cibu P.; Pierpaoli, Carlo

2016-01-01

In this work, we propose DR-TAMAS (Diffeomorphic Registration for Tensor Accurate alignMent of Anatomical Structures), a novel framework for intersubject registration of Diffusion Tensor Imaging (DTI) data sets. This framework is optimized for brain data and its main goal is to achieve an accurate alignment of all brain structures, including white matter (WM), gray matter (GM), and spaces containing cerebrospinal fluid (CSF). Currently most DTI-based spatial normalization algorithms emphasize alignment of anisotropic structures. While some diffusion-derived metrics, such as diffusion anisotropy and tensor eigenvector orientation, are highly informative for proper alignment of WM, other tensor metrics such as the trace or mean diffusivity (MD) are fundamental for a proper alignment of GM and CSF boundaries. Moreover, it is desirable to include information from structural MRI data, e.g., T1-weighted or T2-weighted images, which are usually available together with the diffusion data. The fundamental property of DR-TAMAS is to achieve global anatomical accuracy by incorporating in its cost function the most informative metrics locally. Another important feature of DR-TAMAS is a symmetric time-varying velocity-based transformation model, which enables it to account for potentially large anatomical variability in healthy subjects and patients. The performance of DR-TAMAS is evaluated with several data sets and compared with other widely-used diffeomorphic image registration techniques employing both full tensor information and/or DTI-derived scalar maps. Our results show that the proposed method has excellent overall performance in the entire brain, while being equivalent to the best existing methods in WM. PMID:26931817

Hidden discriminative features extraction for supervised high-order time series modeling.

PubMed

Nguyen, Ngoc Anh Thi; Yang, Hyung-Jeong; Kim, Sunhee

2016-11-01

In this paper, an orthogonal Tucker-decomposition-based extraction of high-order discriminative subspaces from a tensor-based time series data structure is presented, named as Tensor Discriminative Feature Extraction (TDFE). TDFE relies on the employment of category information for the maximization of the between-class scatter and the minimization of the within-class scatter to extract optimal hidden discriminative feature subspaces that are simultaneously spanned by every modality for supervised tensor modeling. In this context, the proposed tensor-decomposition method provides the following benefits: i) reduces dimensionality while robustly mining the underlying discriminative features, ii) results in effective interpretable features that lead to an improved classification and visualization, and iii) reduces the processing time during the training stage and the filtering of the projection by solving the generalized eigenvalue issue at each alternation step. Two real third-order tensor-structures of time series datasets (an epilepsy electroencephalogram (EEG) that is modeled as channel×frequency bin×time frame and a microarray data that is modeled as gene×sample×time) were used for the evaluation of the TDFE. The experiment results corroborate the advantages of the proposed method with averages of 98.26% and 89.63% for the classification accuracies of the epilepsy dataset and the microarray dataset, respectively. These performance averages represent an improvement on those of the matrix-based algorithms and recent tensor-based, discriminant-decomposition approaches; this is especially the case considering the small number of samples that are used in practice. Copyright © 2016 Elsevier Ltd. All rights reserved.

Novel region of interest interrogation technique for diffusion tensor imaging analysis in the canine brain.

PubMed

Li, Jonathan Y; Middleton, Dana M; Chen, Steven; White, Leonard; Ellinwood, N Matthew; Dickson, Patricia; Vite, Charles; Bradbury, Allison; Provenzale, James M

2017-08-01

Purpose We describe a novel technique for measuring diffusion tensor imaging metrics in the canine brain. We hypothesized that a standard method for region of interest placement could be developed that is highly reproducible, with less than 10% difference in measurements between raters. Methods Two sets of canine brains (three seven-week-old full-brains and two 17-week-old single hemispheres) were scanned ex-vivo on a 7T small-animal magnetic resonance imaging system. Strict region of interest placement criteria were developed and then used by two raters to independently measure diffusion tensor imaging metrics within four different white-matter regions within each specimen. Average values of fractional anisotropy, radial diffusivity, and the three eigenvalues (λ1, λ2, and λ3) within each region in each specimen overall and within each individual image slice were compared between raters by calculating the percentage difference between raters for each metric. Results The mean percentage difference between raters for all diffusion tensor imaging metrics when pooled by each region and specimen was 1.44% (range: 0.01-5.17%). The mean percentage difference between raters for all diffusion tensor imaging metrics when compared by individual image slice was 2.23% (range: 0.75-4.58%) per hemisphere. Conclusion Our results indicate that the technique described is highly reproducible, even when applied to canine specimens of differing age, morphology, and image resolution. We propose this technique for future studies of diffusion tensor imaging analysis in canine brains and for cross-sectional and longitudinal studies of canine brain models of human central nervous system disease.

DR-TAMAS: Diffeomorphic Registration for Tensor Accurate Alignment of Anatomical Structures.

PubMed

Irfanoglu, M Okan; Nayak, Amritha; Jenkins, Jeffrey; Hutchinson, Elizabeth B; Sadeghi, Neda; Thomas, Cibu P; Pierpaoli, Carlo

2016-05-15

In this work, we propose DR-TAMAS (Diffeomorphic Registration for Tensor Accurate alignMent of Anatomical Structures), a novel framework for intersubject registration of Diffusion Tensor Imaging (DTI) data sets. This framework is optimized for brain data and its main goal is to achieve an accurate alignment of all brain structures, including white matter (WM), gray matter (GM), and spaces containing cerebrospinal fluid (CSF). Currently most DTI-based spatial normalization algorithms emphasize alignment of anisotropic structures. While some diffusion-derived metrics, such as diffusion anisotropy and tensor eigenvector orientation, are highly informative for proper alignment of WM, other tensor metrics such as the trace or mean diffusivity (MD) are fundamental for a proper alignment of GM and CSF boundaries. Moreover, it is desirable to include information from structural MRI data, e.g., T1-weighted or T2-weighted images, which are usually available together with the diffusion data. The fundamental property of DR-TAMAS is to achieve global anatomical accuracy by incorporating in its cost function the most informative metrics locally. Another important feature of DR-TAMAS is a symmetric time-varying velocity-based transformation model, which enables it to account for potentially large anatomical variability in healthy subjects and patients. The performance of DR-TAMAS is evaluated with several data sets and compared with other widely-used diffeomorphic image registration techniques employing both full tensor information and/or DTI-derived scalar maps. Our results show that the proposed method has excellent overall performance in the entire brain, while being equivalent to the best existing methods in WM. Copyright © 2016 Elsevier Inc. All rights reserved.

Fermionic topological quantum states as tensor networks

NASA Astrophysics Data System (ADS)

Wille, C.; Buerschaper, O.; Eisert, J.

2017-06-01

Tensor network states, and in particular projected entangled pair states, play an important role in the description of strongly correlated quantum lattice systems. They do not only serve as variational states in numerical simulation methods, but also provide a framework for classifying phases of quantum matter and capture notions of topological order in a stringent and rigorous language. The rapid development in this field for spin models and bosonic systems has not yet been mirrored by an analogous development for fermionic models. In this work, we introduce a tensor network formalism capable of capturing notions of topological order for quantum systems with fermionic components. At the heart of the formalism are axioms of fermionic matrix-product operator injectivity, stable under concatenation. Building upon that, we formulate a Grassmann number tensor network ansatz for the ground state of fermionic twisted quantum double models. A specific focus is put on the paradigmatic example of the fermionic toric code. This work shows that the program of describing topologically ordered systems using tensor networks carries over to fermionic models.

Light-cone distribution amplitudes of light JPC = 2- tensor mesons in QCD

NASA Astrophysics Data System (ADS)

Aliev, T. M.; Bilmis, S.; Yang, Kwei-Chou

2018-06-01

We present a study for two-quark light-cone distribution amplitudes for the 13D2 light tensor meson states with quantum number JPC =2-. Because of the G-parity, the chiral-even two-quark light-cone distribution amplitudes of this tensor meson are antisymmetric under the interchange of momentum fractions of the quark and antiquark in the SU(3) limit, while the chiral-odd ones are symmetric. The asymptotic leading-twist LCDAs with the strange quark mass correction are shown. We estimate the relevant parameters, the decay constants fT and fT⊥, and first Gegenbauer moment a1⊥ , by using the QCD sum rule method. These parameters play a central role in the investigation of B meson decaying into the 2- tensor mesons.

Diffractometric measurement of the temperature dependence of piezoelectric tensor in GMO monocrystal

NASA Astrophysics Data System (ADS)

Breczko, Teodor; Lempaszek, Andrzej

2007-04-01

Functional materials, of which an example is ferroelectric, ferroelastic monocrystal of molybdate (III) gadolinium (VI), are often used in the micro-motor operators (micro-servo motors) working in changeable environment conditions. Most frequently this change refers to temperature. That is why the important practical problem is the precise measurement of the value of piezoelectric tensor elements in dependence on the temperature of a particular monocrystal. In the presented article for this kind of measurements, the use of X-ray diffractometer has been shown. The advantage of the method presented is that, apart from precise dependence measurement between the temperature of a monocrystal and the value of piezoelectric tensor elements, it enables synchronous measurement of the value of thermal expansion tensor elements for a monocrystal.