Chong, J.; Yuan, H.; French, S. W.; Romanowicz, B. A.; Ni, S.
Southeast Asia as a special region in the world which is seismically active and is surrounded by active tectonic belts, such as the Himalaya collision zone, western Pacific subduction zones and the Tianshan- Baikal tectonic belt. Seismic anisotropic tomography can shade light on the complex crust and upper mantle dynamics of this region, which is the subject of much debate. In this study, we applied full waveform time domain tomography to image 3D isotropic and anisotropic upper mantle shear velocity structure of Southeast Asia. Three component waveforms of teleseismic and far regional events (15 degree ≤ Δ≤ 165 degree) with magnitude ranges from Mw6.0 to Mw7.0 are collected from 91 permanent and 438 temporary broadband seismic stations in SE Asia. Wavepackets of both fundamental and overtone modes, filtered between 60 and 400 sec, are selected automatically according to the similarity between data and synthetic waveforms (Panning & Romanowicz, 2006). Wavepackets corresponding to event-station paths that sample the region considered are weighted according to path redundancy and signal to noise ratio. Higher modes and fundamental mode wavepackets are weighted separately in order to enhance the contribution of higher modes which are more sensitive to deeper structure compared to the fundamental mode. Synthetic waveforms and broadband sensitivity kernels are computed using normal mode asymptotic coupling theory (NACT, Li & Romanowicz, 1995). As a starting model, we consider a global anisotropic upper mantle shear velocity model based on waveform inversion using the Spectral Element Method (Lekic & Romanowicz, 2011), updated for more realistic crustal thickness (French et al., 2011) as our starting model, we correct waveforms for the effects of 3D structure outside of the region, and invert them for perturbations in the 3D structure of the target region only. We start with waveform inversion down to 60sec and after several iterations, we include shorter period
Asmerom, B. B.; Chiu, J.; Pujol, J.; Smalley, R.
Lateral crustal velocity variations across the Andean Foreland in San Juan Argentina are explored by joint hypocentral determination (JHD) analysis and 3D velocity inversion. JHD results show consistent positive station corrections beneath Precordillera and negative station corrections beneath Pie de Palo, corresponding to regions of low and high velocity, respectively. These observations are supported by the results from the 3D velocity inversion. A 20% increase in velocity is observed from the Precordilleras in the west to Pie de Palo in the east. The tomography result also reveals a narrow east dipping and NNE trending high velocity anomalous zone bisecting the southern half of Pie de Palo. This anomalous zone was previously identified by a magnetic study and was interpreted to represent the structure corresponding to the Grenvillian Precordillera-Pie de Palo tectonic boundary zone. Finally, P and S station corrections are calculated from the synthetic travel time obtained by using the resultant 3D P- and S- wave velocity model. The observed pattern and magnitude of the P- and S-wave station corrections are recovered successfully from the synthetic calculation, indicating that the resultant 3D velocity model is close to the real earth structure in the Andean Foreland region. Relocation of all intermediate events from the flat subducting slab using this newly acquired 3D velocity model shows a significant change in the slab geometry. The relocated hypocenter distribution is more clustered than previous studies obtained using a 1D model. The slab is simply flat and it resumes a normal subduction angle towards the east of the study area.
Bai, Chao-ying; Huang, Guo-jiao; Li, Xing-wang; Greenhalgh, Stewart
Traditionally, traveltime tomography entails inversion of either the velocity field and the reflector geometry sequentially, or the velocity field and the hypocenter locations simultaneously or in a cascaded fashion, but seldom are all three types (velocities, geometry of reflectors, and source locations) updated simultaneously because of the compromise between the different classes of model variable and the lack of different seismic phases to constrain these variables. By using a state-of-the-art ray-tracing algorithm for the first and later arrivals combined with a popular linearized inversion solver, it is possible to simultaneously recover the three classes of model variables. In the work discussed in this paper we combined the multistage irregular shortest-path ray-tracing algorithm with a subspace inversion solver to achieve simultaneous inversion of multi-class variables, using arrival times for different phases to concurrently obtain the velocity field, the reflector shapes, and the hypocenter locations. Simulation and comparison tests for two sets of source-receiver arrangements (one the ideal case and the other an approximated real case) indicate that the combined triple-class inversion algorithm is capable of obtaining nearly the same results as the double-class affect inversion scheme (velocity and reflector geometry, or velocity and source locations) even if a lower ray density and irregular source-receiver geometry are used to simulate the real situation. In addition, the new simultaneous inversion method is not sensitive to a modest amount of picking error in the traveltime data and reasonable uncertainty in earthquake hypocenter locations, which shows it to be a feasible and promising approach in real applications.
Stekl, I.; Warner, M.; Umpleby, A.
In the recent years 3D waveform inversion has become achievable procedure for seismic data processing. A number of datasets has been inverted and presented (Warner el al 2008, Ben Hadj at all, Sirgue et all 2010) using isotropic 3D waveform inversion. However the question arises will the results be affected by isotropic assumption. Full-wavefield inversion techniques seek to match field data, wiggle-for-wiggle, to synthetic data generated by a high-resolution model of the sub-surface. In this endeavour, correctly matching the travel times of the principal arrivals is a necessary minimal requirement. In many, perhaps most, long-offset and wide-azimuth datasets, it is necessary to introduce some form of p-wave velocity anisotropy to match the travel times successfully. If this anisotropy is not also incorporated into the wavefield inversion, then results from the inversion will necessarily be compromised. We have incorporated anisotropy into our 3D wavefield tomography codes, characterised as spatially varying transverse isotropy with a tilted axis of symmetry - TTI anisotropy. This enhancement approximately doubles both the run time and the memory requirements of the code. We show that neglect of anisotropy can lead to significant artefacts in the recovered velocity models. We will present inversion results of inverting anisotropic 3D dataset by assuming isotropic earth and compare them with anisotropic inversion result. As a test case Marmousi model extended to 3D with no velocity variation in third direction and with added spatially varying anisotropy is used. Acquisition geometry is assumed as OBC with sources and receivers everywhere at the surface. We attempted inversion using both 2D and full 3D acquisition for this dataset. Results show that if no anisotropy is taken into account although image looks plausible most features are miss positioned in depth and space, even for relatively low anisotropy, which leads to incorrect result. This may lead to
Li, Yong; Wang, Xuben; Li, Zhirong; Li, Qiong; Li, Zhengwen
The high resolution 3D nonlinear integrated inversion method is based on nonlinear theory. Under layer control, the log data from several wells (or all wells) in the study area and seismic trace data adjacent to the wells are input to a network with multiple inputs and outputs and are integratedly trained to obtain an adaptive weight function of the entire study area. Integrated nonlinear mapping relationships are built and updated by the lateral and vertical geologic variations of the reservoirs. Therefore, the inversion process and its inversion results can be constrained and controlled and a stable seismic inversion section with high resolution with velocity inversion, impedance inversion, and density inversion sections, can be gained. Good geologic effects have been obtained in model computation tests and real data processing, which verified that this method has high precision, good practicality, and can be used for quantitative reservoir analysis.
GarcíA-Yeguas, Araceli; Koulakov, Ivan; IbáñEz, Jesús M.; Rietbrock, A.
We present a high resolution 3 dimensional (3D) P wave velocity model for Tenerife Island, Canaries, covering the top of Teide volcano (3,718 m a.s.l.) down to around 8 km below sea level (b.s.l). The tomographic inversion is based on a large data set of travel times obtained from a 3D active seismic experiment using offshore shots (air guns) recorded at more than 100 onshore seismic stations. The obtained seismic velocity structure is strongly heterogeneous with significant (up to 40%) lateral variations. The main volcanic structure of the Las Cañadas-Teide-Pico Viejo Complex (CTPVC) is characterized by a high P wave velocity body, similar to many other stratovolcanoes. The presence of different high P wave velocity regions inside the CTPVC may be related to the geological and volcanological evolution of the system. The presence of high P wave velocities at the center of the island is interpreted as evidence for a single central volcanic source for the formation of Tenerife. Furthermore, reduced P wave velocities are found in a small confined region in CTPVC and are more likely related to hydrothermal alteration, as indicated by the existence of fumaroles, than to the presence of a magma chamber beneath the system. In the external regions, surrounding CTPVC a few lower P wave velocity regions can be interpreted as fractured zones, hydrothermal alterations, porous materials and thick volcaniclastic deposits.
Ballard, S.; Begnaud, M. L.; Hipp, J. R.; Chael, E. P.; Encarnacao, A.; Maceira, M.; Yang, X.; Young, C. J.; Phillips, W.
SALSA3D is a global 3D P wave velocity model of the Earth's crust and mantle developed specifically to provide seismic event locations that are more accurate and more precise than are locations from 1D and 2.5D models. In this paper, we present the most recent version of our model, for the first time jointly derived from multiple types of data: body wave travel times, surface wave group velocities, and gravity. The latter two are added to provide information in areas with poor body wave coverage, and are down-weighted in areas where body wave coverage is good. To constrain the inversions, we invoked empirical relations among the density, S velocity, and P velocity. We demonstrate the ability of the new SALSA3D model to reduce mislocations and generate statistically robust uncertainty estimates for a large set of realizations derived from a carefully chosen set of globally-distributed ground truth events. We obtain path-dependent travel time prediction uncertainties for our model by computing the full 3D model covariance matrix of our tomographic system and integrating the model slowness variance and covariance along paths of interest. This approach yields very low travel time prediction uncertainties for well-sampled paths through the Earth and higher uncertainties for paths that are poorly represented in the data set used to develop the model. While the calculation of path-dependent prediction uncertainties with this approach is computationally expensive, uncertainties can be pre-computed for a network of stations and stored in 3D lookup tables that can be quickly and efficiently interrogated using GeoTess software.
Aucejo, M.; Totaro, N.; Guyader, J.-L.
In noise control, identification of the source velocity field remains a major problem open to investigation. Consequently, methods such as nearfield acoustical holography (NAH), principal source projection, the inverse frequency response function and hybrid NAH have been developed. However, these methods require free field conditions that are often difficult to achieve in practice. This article presents an alternative method known as inverse patch transfer functions, designed to identify source velocities and developed in the framework of the European SILENCE project. This method is based on the definition of a virtual cavity, the double measurement of the pressure and particle velocity fields on the aperture surfaces of this volume, divided into elementary areas called patches and the inversion of impedances matrices, numerically computed from a modal basis obtained by FEM. Theoretically, the method is applicable to sources with complex 3D geometries and measurements can be carried out in a non-anechoic environment even in the presence of other stationary sources outside the virtual cavity. In the present paper, the theoretical background of the iPTF method is described and the results (numerical and experimental) for a source with simple geometry (two baffled pistons driven in antiphase) are presented and discussed.
3-D Crustal Velocity Structure of Central Idaho/ Eastern Oregon from Joint Inversion of Rayleigh Wave Group and Phase Velocities Derived from Ambient Seismic Noise: Newest Results from the IDOR Project
Bremner, P. M.; Panning, M. P.; Russo, R. M.; Mocanu, V. I.; Stanciu, A. C.; Torpey, M. E.; Hongsresawat, S.; VanDecar, J. C.
We present the latest 3-D isotropic crustal velocity model beneath central Idaho and eastern Oregon. We produced the velocity model from vertical component Rayleigh wave group and phase velocity measurements on data from the IDaho/ORegon (IDOR) Passive seismic network, 86 broadband seismic stations, using ambient noise tomography and the methods of Gallego et. al (2010) and Lin et. al (2008). We calculated inter-station group/phase velocities in narrow frequency bands from travel-time measurements of the stacked cross-correlations (bandpass filtered between 2 and 30 seconds), which we used to invert for velocity structure beneath the network. Goals of our work include refining models of crustal structure in the accreted Blue Mountain terranes in the western study area; determining the depth extent of the Salmon River Suture/West Idaho Shear Zone (WISZ), which crosses north-south through the middle of the network; determining the architecture of the Idaho batholith, an extensive largely crustal-derived pluton; and examining the nature of the autochthonous (?) North American crust and lithosphere beneath and east of the batholith. We derived Rayleigh wave group and phase velocity maps for each frequency band using the damped least-squares inversion method of Tarantola (2005), and then jointly inverted for velocity with depth. Moho depths are prescribed in the joint inversions based on receiver functions, also from the IDOR seismic data, and provides a starting crustal velocity model. 3-D checkerboard resolution tests indicate lateral resolution of better than 40 km. Preliminary results show higher S wave velocities in the western study area, and lower velocities in the lower crust on the east side of the network, consistent with Basin-and-Range style extension there. A tabular velocity anomaly juxtaposing higher above lower seismic velocities dips shallow west in the midcrust on the west side of the network.
Bremner, P. M.; Panning, M. P.; Russo, R.; Mocanu, V. I.; Stanciu, A. C.; Torpey, M. E.; Hongsresawat, S.; VanDecar, J. C.
We present new 3-D radially anisotropic and isotropic crustal velocity models beneath central Idaho and eastern Oregon. We produced the velocity models from Love and horizontal component Rayleigh wave group and phase velocity measurements on the IDaho/ORegon (IDOR) Passive seismic network, 86 broadband seismic stations, dataset using ambient noise tomography and the methods of Gallego et. al (2010) and Lin et. al (2008). We calculated inter-station group/phase velocities in narrow frequency bands from travel-time measurements of the rotated stacked horizontal component cross-correlations (bandpass filtered between 2 and 30 seconds), which we used to invert for velocity structure beneath the network. We derived group and phase velocity maps for each frequency band using the damped least-squares inversion method of Tarantola (2005), and then jointly inverted for velocity with depth. Moho depths are prescribed in the joint inversions based on receiver functions, also from the IDOR seismic data, and provides a starting crustal velocity model. Goals of our work include refining models of crustal structure in the accreted Blue Mountain terranes in the western study area; determining the depth extent of the Salmon River Suture/West Idaho Shear Zone (WISZ), which crosses north-south through the middle of the network; determining the architecture of the Idaho batholith, an extensive largely crustal-derived pluton; and examining the nature of the autochthonous (?) North American crust and lithosphere beneath and east of the batholith.
Pilia, S.; Rawlinson, N.; Direen, N. G.
Although the notion of Rodinia is quite well accepted in the geoscience community, the location and nature of the eastern continental margin of the Gondwana fragment in Australia is still vague and remains one of the most hotly debated topics in Australian geology. Moreover, most post-Rodinian reconstructions models choose not to tackle the ';Tasmanian challenge', and focus only on the tectonic evolution of mainland southeast Australia, thereby conveniently ignoring the wider tectonic implications of Tasmania's complex geological history. One of the chief limitations of the tectonic reconstructions in this region is a lack of information on Paleozoic (possibly Proterozoic) basement structures. Vast Mesozoic-Cainozoic sedimentary and volcanic cover sequences obscure older outcrops and limit the power of direct observational techniques. In response to these challenges, our effort is focused on ambient seismic noise for imaging 3D crustal shear velocity structure using surface waves, which is capable of illuminating basement structure beneath younger cover. The data used in this study is sourced from the WOMBAT transportable seismic array, which is compounded by around 650 stations spanning the majority of southeastern Australia, including Tasmania and several islands in Bass Strait. To produce the highest quality Green's functions, careful processing of the data has been performed, after which group velocity dispersion measurements have been carried out using a frequency-time analysis method on the symmetric component of the empirical Green's functions (EGFs). Group dispersion measurements from the EGFs have been inverted using a novel hierarchical, transdimensional, Bayesian algorithm to obtain Rayleigh-wave group velocity maps at different periods from 2 to 30 s. The new approach has several advantages in that the number and distribution of model parameters are implicitly controlled by the data, in which the noise is treated as unknown in the inversion. This
Patro, Prasanta; Uyeshima, Makoto
Three-dimensional (3-D) inversion of the magnetotelluric (MT) has become a routine practice among the MT community due to progress of algorithms for 3-D inverse problems (e.g. Mackie and Madden, 1993; Siripunvaraporn et al., 2005). While availability of such 3-D inversion codes have increased the resolving power of the MT data and improved the interpretation, on the other hand, still the galvanic effects poses difficulties in interpretation of resistivity structure obtained from the MT data. In order to tackle the galvanic distortion of MT data, Caldwell et al., (2004) introduced the concept of phase tensor. They demonstrated how the regional phase information can be retrieved from the observed impedance tensor without any assumptions for structural dimension, where both the near surface inhomogeneity and the regional conductivity structures can be 3-D. We made an attempt to modify a 3-D inversion code (Siripunvaraporn et al., 2005) to directly invert the phase tensor elements. We present here the main modification done in the sensitivity calculation and then show a few synthetic studies and its application to the real data. The synthetic model study suggests that the prior model (m_0) setting is important in retrieving the true model. This is because estimation of correct induction scale length lacks in the phase tensor inversion process. Comparison between results from conventional impedance inversion and new phase tensor inversion suggests that, in spite of presence of the galvanic distortion (due to near surface checkerboard anomalies in our case), the new inverion algorithm retrieves the regional conductivitity structure reliably. We applied the new inversion to the real data from the Indian sub continent and compared with the results from conventional impedance inversion.
Burnett, William; Fomel, Sergey
We extend time-domain velocity continuation to the zero-offset 3D azimuthally anisotropic case. Velocity continuation describes how a seismic image changes given a change in migration velocity. This description turns out to be of a wave propagation process, in which images change along a velocity axis. In the anisotropic case, the velocity model is multiparameter. Therefore, anisotropic image propagation is multidimensional. We use a three-parameter slowness model, which is related to azimuthal variations in velocity, as well as their principal directions. This information is useful for fracture and reservoir characterization from seismic data. We provide synthetic diffraction imaging examples to illustratemore » the concept and potential applications of azimuthal velocity continuation and to analyze the impulse response of the 3D velocity continuation operator.« less
Newman, G.A.; Alumbaugh, D.L.
In large scale 3D EM inverse problems it may not be possible to directly invert a full least-squares system matrix involving model sensitivity elements. Thus iterative methods must be employed. For the inverse problem, we favor either a linear or non-linear (NL) CG scheme, depending on the application. In a NL CG scheme, the gradient of the objective function is required at each relaxation step along with a univariate line search needed to determine the optimum model update. Solution examples based on both approaches will be presented.
Steklova, K.; Haber, E.
Modeling of seawater intrusions (SWI) is challenging as it involves solving the governing equations for variable density flow, multiple time scales and varying boundary conditions. Due to the nonlinearity of the equations and the large aquifer domains, 3D computations are a costly process, particularly when solving the inverse SWI problem. In addition the heads and concentration measurements are difficult to obtain due to mixing, saline wedge location is sensitive to aquifer topography, and there is general uncertainty in initial and boundary conditions and parameters. Some of these complications can be overcome by using indirect geophysical data next to standard groundwater measurements, however, the inverse problem is usually simplified, e.g. by zonation for the parameters based on geological information, steady state substitution of the unknown initial conditions, decoupling the equations or reducing the amount of unknown parameters by covariance analysis. In our work we present a discretization of the flow and solute mass balance equations for variable groundwater (GW) flow. A finite difference scheme is to solve pressure equation and a Semi - Lagrangian method for solute transport equation. In this way we are able to choose an arbitrarily large time step without losing stability up to an accuracy requirement coming from the coupled character of the variable density flow equations. We derive analytical sensitivities of the GW model for parameters related to the porous media properties and also the initial solute distribution. Analytically derived sensitivities reduce the computational cost of inverse problem, but also give insight for maximizing information in collected data. If the geophysical data are available it also enables simultaneous calibration in a coupled hydrogeophysical framework. The 3D inverse problem was tested on artificial time dependent data for pressure and solute content coming from a GW forward model and/or geophysical forward model. Two
Gavrilov, E.M.; Forslund, D.W.; Fehler, M.C.
This is the final report of a four-month, Laboratory Directed Research and Development (LDRD) project carried out at the Los Alamos National Laboratory (LANL). There is a great need for a new and effective technology with a wide scope of industrial applications to investigate media internal properties of which can be explored only from the backscattered data. The project was dedicated to the development of a three-dimensional computational inversion tool for seismic exploration. The new computational concept of the inversion algorithm was suggested. The goal of the project was to prove the concept and the practical validity of the algorithm for petroleum exploration.
Pagli, Carolina; Wang, Hua; Wright, Tim J.; Calais, Eric; Lewi, Elias
Extension, faulting, and magmatism are the main controls on the magnitude and localization of strain at mid-ocean ridges. However, the temporal and spatial patterns of such processes are not clear since the strain distribution has not been resolved in the past at sufficient spatial resolution and over extended areas. Interferometric synthetic aperture radar (InSAR) and GPS data with unprecedented resolution are now available to us from the Afar rift of Ethiopia. Here we use a velocity field method to combine InSAR and GPS to form the first high-resolution continuous three-dimensional velocity field of Afar. We study an area that is 500 km wide and 700 km long, covering three branches of the Afar continental rift and their triple junctions. Our velocity field shows that plate spreading is currently achieved in Afar in contrasting modes. A transient postdiking deformation is focused at the Dabbahu rift segment, while in central Afar, spreading is distributed over several overlapping segments and southern Afar exhibits an interdiking deformation pattern focused at the Asal-Ghoubbet segment. We find that current spreading rates at Dabbahu, following the 2005-2010 intrusions, are up to 110 mm/yr, 6 times larger than the long-term plate divergence. A segment-centered uplift of up to 80 mm/yr also occurs, indicating that magma flow is still a primary mechanism of deformation during postdiking. On the other hand, no vertical displacements are currently observed in central and southern Afar, suggesting lack of significant magmatic activity at shallow levels.
Pujol, J. M.; Chiu, J. M.
When applying seismic tomography to local arrival times from an area with a low-velocity sedimentary cover, the effect of the sediments on travel times should be taken into account. If that is not done, the resulting velocity model(s) cannot be assumed to be correct. This fairly obvious statement has been challenged recently by Powell et al. (JGR, 2010), who claimed that the sediments that cover the New Madrid seismic zone (NMSZ, central United States) can be ignored. This claim is examined here and shown to be incorrect. The NMSZ is covered by low-velocity, poorly consolidated sediments (Vp=1.8 km/s, Vs=3), which are underlain by Paleozoic rocks of much higher velocity. In the central NMSZ the sediment thickness varies between about 0.1 and 0.7 km. The JHD analysis of the data collected in that area by a portable network (PANDA) showed that the P- and S-wave station corrections spanned large ranges (0.35 and 0.63 s, respectively, Pujol et al., Eng. Geol., 1997). This study also showed that a Vp/Vs of 3 for the sediments would be too high if the lateral velocity variations were confined to the sedimentary cover. Here we generate synthetic traveltimes for a model with a sedimentary cover having variable depth (as determined from boreholes) underlain by the high-velocity layers in the 1-D model used for the JHD analysis. The synthetic data were generated for the station and event distributions corresponding to the Panda data. The tomographic inversion of the synthetic times produces spurious anomalies in Vp, Vs, and Vp/Vs, from the surface to a depth of 10 km. In addition, the events are mislocated in depth, with errors between 0 and 1 km for most of them. These results should dispel the notion that the effect of the unconsolidated sediments can be ignored. On the other hand, the inversion of the actual Panda data results in velocity anomalies similar to the synthetic anomalies, although larger, which is consistent with the conclusions of Pujol et al. (1997
Liang, Q.; Chen, C.; Li, Y.
Gravity anomaly tells how the subsurface density varies or where the mass concentrations are located at. Inversion of gravity data gives a way to directly recover the density distributions. It has been demonstrated that the inversion is capable of retrieving density structures in resources exploration on the Earth. With increasing interests in interior structures of the Moon, scientists have obtained its gravity field with improved resolution on the lunar far side. We may thus utilize the inverse method to recover the lunar density structures beneath mascon basins or the density inhomogeneities in the crust and mantle. However, if considering the spherical gravity data in global scale, there are limitations in the previous inversion because the methods were based on the Cartesian coordinates system. In order to solve the problems, we developed a new 3D inverse method with three aspects involved: 1) A new model objective function adaptive to spherical coordinate system was established in the light of the Backus-Gilbert model appraisal theory. 2) A depth weighting function in inversion was also developed to approximately compensate for the kernel’s natural decay in potential field. And, 3) Non-uniqueness was suppressed by using model constraints and Tikhonov regularization tool. With the above developments and techniques, our method can quantitatively interpret the spherical gravity data. We firstly performed the inversion of synthetic data and confirmed that the locations of anomaly bodies were well defined, and then applied this method to the Bouguer gravity anomaly of the Moon which has been previously calculated based on the Chang'E-1 topography data and the SELENE gravity field model. Results showed that, on the one hand, the positive density anomalies beneath the mascon basins concentrated at the depth of 20-50km. Their residual densities are larger than 0.3g/cm^3 close to the density difference between lunar mantle and crust. Density structures along radial
Lelièvre, Peter; Farquharson, Colin; Bijani, Rodrigo
Geologists' interpretations about the Earth typically involve distinct rock units with contacts (interfaces) between them. As such, 3D geological Earth models typically comprise wireframe contact surfaces of tessellated triangles or other polygonal planar facets. In contrast, standard minimum-structure geophysical inversions are performed on meshes of space-filling cells (typically prisms or tetrahedra) and recover smoothly varying physical property distributions that are inconsistent with typical geological interpretations. There are several approaches through which mesh-based geophysical inversion can help recover models with some of the desired characteristics. However, a more effective strategy is to consider a fundamentally different type of inversion that works directly with models that comprise surfaces representing contacts between rock units. We are researching such an approach, our goal being to perform geophysical forward and inverse modelling directly with 3D geological models of any complexity. Geological and geophysical models should be specified using the same parameterization such that they are, in essence, the same Earth model. We parameterize the wireframe contact surfaces in a 3D model as the coordinates of the nodes (facet vertices). The physical properties of each rock unit in a model remain fixed while the geophysical inversion controls the position of the contact surfaces via the control nodes, perturbing the surfaces as required to fit the geophysical data responses. This is essentially a "geometry inversion", which can be used to recover the unknown geometry of a target body or to investigate the viability of a proposed Earth model. We apply global optimization strategies to solve the inverse problem, including stochastic sampling to obtain statistical information regarding the likelihood of particular features in the model, helping to assess the viability of a proposed model. Jointly inverting multiple types of geophysical data is simple
Walter, C.; Jones, A. G.
The Taupo Volcanic Zone (TVZ) hosts the majority of the geothermal systems in New Zealand and is a valuable source for power generation and tourism. It is important for the sustainable exploitation of this area to fully understand the processes and structures in the TVZ. As part of the 'Hotter and Deeper' project of the Foundation for Research, Science and Technology (FRST), a dataset of 200 broadband magnetotelluric (MT) stations has been collected in the TVZ of New Zealand in 2009 and 2010. Combined with a smaller dataset from Reporoa, a total of 230 stations are available for 3D inversion to image the deeper structures of the TVZ. For the study presented in this paper, multiple 3D inversions of this dataset using different control parameters have been undertaken to study the influence of the choice of parameters on the inversion result. The parameters that have been varied include; the type of responses used in the inversion, the use of topography and bathymetry, and varying vertical grid spacings. All inversions commenced with a uniform half-space so that there was no preconceived structures to begin with. The results show that the main structures in the model are robust in that they are independent of the choice of parameters and become introduced in every inversion. The only differences are in the shape and exact location of the structures, which vary between the models. Furthermore, different ways to get a measure for the differences between models have been explored.
Gribenko, A. V.; Zhdanov, M. S.
Distortion of regional electric fields by local structures represent one of the major problems facing three-dimensional magnetotelluric (MT) interpretation. Effect of 3D local inhomogenities on MT data can be described by a real 2x2 distortion matrix. In this project we develop a method of simultaneous inversion of the full MT impedance data for 3D conductivity distribution and for the distortion matrix. Tikhonov regularization is employed to solve the resulting inverse problem. Integral equations method is used to compute MT responses. Minimization of the cost functional is achieved via conjugate gradient method. The inversion algorithm is tested on the synthetic data from Dublin Secret Model II (DSM 2) for which multiple inversion solutions are available for comparison. Inclusion of the distortion matrix provides faster convergence and allows coarser discretization of the near-surface while achievingsimilar or better data fits as inversion for the conductivity only with finely discretized shallow regions. As a field data example we chose a subset of the EarthScope MT dataset covering Great Basin and adjacent areas of the Western United States. Great Basin data inversion identified several prominent conductive zones which correlate well with areas of tectonic and geothermal activity.
Fadel, I.; van der Meijde, M.; Kerle, N.
Non-uniqueness of satellite gravity interpretation has been usually reduced by using a priori information from various sources, e.g. seismic tomography models. The reduction in non-uniqueness has been based on velocity-density conversion formulas or user interpretation for 3D subsurface structures (objects) in seismic tomography models. However, these processes introduce additional uncertainty through the conversion relations due to the dependency on the other physical parameters such as temperature and pressure, or through the bias in the interpretation due to user choices and experience. In this research, a new methodology is introduced to extract the 3D subsurface structures from 3D geophysical data using a state-of-art 3D Object Oriented Image Analysis (OOA) technique. 3D OOA is tested using a set of synthetic models that simulate the real situation in the study area of this research. Then, 3D OOA is used to extract 3D subsurface objects from a real 3D seismic tomography model. The extracted 3D objects are used to reconstruct a forward model and its response is compared with the measured satellite gravity. Finally, the result of the forward modelling, based on the extracted 3D objects, is used to constrain the inversion process of satellite gravity data. Through this work, a new object-based approach is introduced to interpret and extract the 3D subsurface objects from 3D geophysical data. This can be used to constrain modelling and inversion of potential field data using the extracted 3D subsurface structures from other methods. In summary, a new approach is introduced to constrain inversion of satellite gravity measurements and enhance interpretation capabilities.
Alumbaugh, D.L.; Newman, G.A.
Linearized methods are presented for appraising image resolution and parameter accuracy in images generated with two and three dimensional non-linear electromagnetic inversion schemes. When direct matrix inversion is employed, the model resolution and posterior model covariance matrices can be directly calculated. A method to examine how the horizontal and vertical resolution varies spatially within the electromagnetic property image is developed by examining the columns of the model resolution matrix. Plotting the square root of the diagonal of the model covariance matrix yields an estimate of how errors in the inversion process such as data noise and incorrect a priori assumptions about the imaged model map into parameter error. This type of image is shown to be useful in analyzing spatial variations in the image sensitivity to the data. A method is analyzed for statistically estimating the model covariance matrix when the conjugate gradient method is employed rather than a direct inversion technique (for example in 3D inversion). A method for calculating individual columns of the model resolution matrix using the conjugate gradient method is also developed. Examples of the image analysis techniques are provided on 2D and 3D synthetic cross well EM data sets, as well as a field data set collected at the Lost Hills Oil Field in Central California.
Simutė, S.; Fichtner, A.
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.
Panning, M. P.; Romanowicz, B.; Gung, Y.
Many studies have documented the existence of anisotropy in the earth's upper mantle, concentrated in the top 200 km. This evidence comes from the study of surface waves as well as shear wave splitting. There is also evidence for shear wave splitting in D", at least in well sampled regions. There are some hints of anisotropy at the base of the transition zone. Tomographic models of the upper mantle have been developed with simplifying assumptions about the nature of the anisotropy, in order to minimize the number of free parameters in the inversions. Some assume transverse isotropy (e.g Ekström and Dziewonski, 1997), others include additional degrees of freedom with some realistic constraints on mineralogy (e.g. Montagner and Tanimoto, 1991). Our goal is to investigate anisotropy in the whole mantle, using the framework of waveform inversion, and the nonlinear asymptotic mode coupling theory (NACT), previously developed and applied to the construction of whole-mantle SH velocity models (Li and Romanowicz, 1996; Mégnin and Romanowicz, 2000). For this we require a 3 component dataset, and we have extended our automatic transverse (T) component wavepicking procedures to the vertical (Z) and longitudinal (L) component - a non-trivial task given the large number of phases present in the coupled P-SV system. A useful initial assumption, for which the theory has been readily adapted, is that of transverse isotropy. As a first step towards this, we have been investigating inversions using T component and Z,L component data separately. In particular, this allows us to explore the sampling that can be achieved with Z,L component data alone in the deepest part of the mantle. Indeed, D" is in general much better sampled in SH than in SV, owing to the availability of SHdiff at large distances, while SVdiff decays more rapidly due to mantle-core coupling. We present the results of our resolution experiments and discuss the differences between the 3D SV model obtained in well
Kruglyakov, Mikhail; Geraskin, Alexey; Kuvshinov, Alexey
We present novel, robust, scalable, and fast 3-D magnetotelluric (MT) inverse solver. The solver is written in multi-language paradigm to make it as efficient, readable and maintainable as possible. Separation of concerns and single responsibility concepts go through implementation of the solver. As a forward modelling engine a modern scalable solver extrEMe, based on contracting integral equation approach, is used. Iterative gradient-type (quasi-Newton) optimization scheme is invoked to search for (regularized) inverse problem solution, and adjoint source approach is used to calculate efficiently the gradient of the misfit. The inverse solver is able to deal with highly detailed and contrasting models, allows for working (separately or jointly) with any type of MT responses, and supports massive parallelization. Moreover, different parallelization strategies implemented in the code allow optimal usage of available computational resources for a given problem statement. To parameterize an inverse domain the so-called mask parameterization is implemented, which means that one can merge any subset of forward modelling cells in order to account for (usually) irregular distribution of observation sites. We report results of 3-D numerical experiments aimed at analysing the robustness, performance and scalability of the code. In particular, our computational experiments carried out at different platforms ranging from modern laptops to HPC Piz Daint (6th supercomputer in the world) demonstrate practically linear scalability of the code up to thousands of nodes.
Nugraha, Andri Dian; Syahputra, Ahmad; Fatkhan,; Sule, Rachmat
We conducted delay time tomography to determine 3-D seismic velocity structures (Vp, Vs, and Vp/Vs ratio) using micro-seismic events in the geothermal field. The P-and S-wave arrival times of these micro-seismic events have been used as input for the tomographic inversion. Our preliminary seismic velocity results show that the subsurface condition of geothermal field can be fairly delineated the characteristic of reservoir. We then extended our understanding of the subsurface physical properties through determining of attenuation structures (Qp, Qs, and Qs/Qp ratio) using micro-seismic waveform. We combined seismic velocities and attenuation structures to get much better interpretation of the reservoir characteristic. Our preliminary attanuation structures results show reservoir characterization can be more clearly by using the 3-D attenuation model of Qp, Qs, and Qs/Qp ratio combined with 3-D seismic velocity model of Vp, Vs, and Vp/Vs ratio.
Nielsen, O. F.; Ploug, C.; Mendoza, J. A.; Martínez, K.
The need for increaseding accuracy and reduced ambiguities in the inversion results has resulted in focus on the development of more advanced inversion methods of geophysical data. Over the past few years more advanced inversion techniques have been developed to improve the results. Real 3D-inversion is time consuming and therefore often not the best solution in a cost-efficient perspective. This has motivated the development of 3D constrained inversions, where 1D-models are constrained in 3D, also known as a Spatial Constrained Inversion (SCI). Moreover, inversion of several different data types in one inversion has been developed, known as Mutually Constrained Inversion (MCI). In this paper a presentation of a Spatial Mutually Constrained Inversion method (SMCI) is given. This method allows 1D-inversion applied to different geophysical datasets and geological information constrained in 3D. Application of two or more types of geophysical methods in the inversion has proved to reduce the equivalence problem and to increase the resolution in the inversion results. The use of geological information from borehole data or digital geological models can be integrated in the inversion. In the SMCI, a 1D inversion code is used to model soundings that are constrained in three dimensions according to their relative position in space. This solution enhances the accuracy of the inversion and produces distinct layers thicknesses and resistivities. It is very efficient in the mapping of a layered geology but still also capable of mapping layer discontinuities that are, in many cases, related to fracturing and faulting or due to valley fills. Geological information may be included in the inversion directly or used only to form a starting model for the individual soundings in the inversion. In order to show the effectiveness of the method, examples are presented from both synthetic data and real data. The examples include DC-soundings as well as land-based and airborne TEM
Ožbolt, Joško; İrhan, Barış; Ruta, Daniela
An explicit three-dimensional (3D) finite element (FE) code is developed for the simulation of high velocity impact and fragmentation events. The rate sensitive microplane material model, which accounts for large deformations and rate effects, is used as a constitutive law. In the code large deformation frictional contact is treated by forward incremental Lagrange multiplier method. To handle highly distorted and damaged elements the approach based on the element deletion is employed. The code is then used in 3D FE simulations of high velocity projectile impact. The results of the numerical simulations are evaluated and compared with experimental results. It is shown that it realistically predicts failure mode and exit velocities for different geometries of plain concrete slab. Moreover, the importance of some relevant parameters, such as contact friction, rate sensitivity, bulk viscosity and deletion criteria are addressed.
Shin, Jungkyun; Shin, Changsoo; Calandra, Henri
Laplace-domain waveform inversion reconstructs long-wavelength subsurface models by using the zero-frequency component of damped seismic signals. Despite the computational advantages of Laplace-domain waveform inversion over conventional frequency-domain waveform inversion, an acoustic assumption and an iterative matrix solver have been used to invert 3D marine datasets to mitigate the intensive computing cost. In this study, we develop a Laplace-domain waveform modeling and inversion algorithm for 3D acoustic-elastic coupled media by using a parallel sparse direct solver library (MUltifrontal Massively Parallel Solver, MUMPS). We precisely simulate a real marine environment by coupling the 3D acoustic and elastic wave equations with the proper boundary condition at the fluid-solid interface. In addition, we can extract the elastic properties of the Earth below the sea bottom from the recorded acoustic pressure datasets. As a matrix solver, the parallel sparse direct solver is used to factorize the non-symmetric impedance matrix in a distributed memory architecture and rapidly solve the wave field for a number of shots by using the lower and upper matrix factors. Using both synthetic datasets and real datasets obtained by a 3D wide azimuth survey, the long-wavelength component of the P-wave and S-wave velocity models is reconstructed and the proposed modeling and inversion algorithm are verified. A cluster of 80 CPU cores is used for this study.
Alumbaugh, D.L.; Newman, G.A.
Linearized methods are presented for appraising image resolution and parameter accuracy in images generated with two and three dimensional non-linear electromagnetic inversion schemes. When direct matrix inversion is employed, the model resolution and model covariance matrices can be directly calculated. The columns of the model resolution matrix are shown to yield empirical estimates of the horizontal and vertical resolution throughout the imaging region. Plotting the square root of the diagonal of the model covariance matrix yields an estimate of how the estimated data noise maps into parameter error. When the conjugate gradient method is employed rather than a direct inversion technique (for example in 3D inversion), an iterative method can be applied to statistically estimate the model covariance matrix, as well as a regularization covariance matrix. The latter estimates the error in the inverted results caused by small variations in the regularization parameter. A method for calculating individual columns of the model resolution matrix using the conjugate gradient method is also developed. Examples of the image analysis techniques are provided on a synthetic cross well EM data set.
Cunningham, Emily C.; Deason, Alis J.; Guhathakurta, Puragra; Rockosi, Constance M.; van der Marel, Roeland P.; Sohn, S. Tony
We present the first measurement of the anisotropy parameter β using 3D kinematic information outside of the solar neighborhood. Our sample consists of 13 Milky Way halo stars with measured proper motions and radial velocities in the line of sight of M31. Proper motions were measured using deep, multi-epoch HST imaging, and radial velocities were measured from Keck II/DEIMOS spectra. We measure β = -0.3-0.9 +0.4, which is consistent with isotropy, and inconsistent with measurements in the solar neighborhood. We suggest that this may be the kinematic signature of a relatively early, massive accretion event, or perhaps several such events.
Bell, R. E.; Morgan, J. V.; Warner, M.
Our understanding of subduction margin seismogenesis has been revolutionised in the last couple of decades with the discovery that the size of the seismogenic zone may not be controlled simply by temperature and a broad spectrum of seismic behaviour exists from stick-slip to stable sliding. Laboratory and numerical experiments suggest that physical properties, particularly fluid pressure may play an important role in controlling the seismic behaviour of subduction margins. Although drilling can provide information on physical properties along subduction thrust faults at point locations at relatively shallow depths, correlations between physical properties and seismic velocity using rock physics relationships are required to resolve physical properties along the margin and down-dip. Therefore, high resolution seismic velocity models are key to recovering physical property information at subduction plate boundaries away from drill sites. 3D Full waveform inversion (FWI) is a technique pioneered by the oil industry to obtain high-resolution high-fidelity models of physical properties in the sub-surface. 3D FWI involves the inversion of low-frequency (>2 to <7 Hz), early arriving (principally transmitted) seismic data, to recover the macro (intermediate to long-wavelength) velocity structure. Although 2D FWI has been used to improve velocity models of subduction plate boundaries before, 3D FWI has not yet been attempted. 3D inversions have superior convergence and accuracy, as they sample the subsurface with multi-azimuth multiply-crossing wavefields. In this contribution we perform a suite of synthetic tests to investigate if 3D FWI could be used to better resolve physical property information along subduction margin plate boundaries using conventionally collected 3D seismic data. We base our analysis on the Muroto Basin area of the Nankai margin and investigate if the acquisition parameters and geometry of the subduction margin render 3D seismic data collected across
Etienne, V.; Virieux, J.; Hu, G.; Jia, Y.; Operto, S.
Full waveform inversion (FWI) is one of the most promising techniques for seismic imaging. It relies on a formalism taking into account every piece of information contained in the seismic data as opposed to more classical techniques such as travel time tomography. As a result, FWI is a high resolution imaging process able to reach a spatial accuracy equal to half a wavelength. FWI is based on a local optimization scheme and therefore the main limitation concerns the starting model which has to be closed enough to the real one in order to converge to the global minimum. Another counterpart of FWI is the required computational resources when considering models and frequencies of interest. The task becomes even more tremendous when one tends to perform the inversion using the elastic equation instead of using the acoustic approximation. This is the reason why until recently most studies were limited to 2D cases. In the last few years, due to the increase of the available computational power, FWI has focused a lot of interests and continuous efforts towards inversion of 3D models, leading to remarkable applications up to the continental scale. We investigate the computational burden induced by FWI in 3D elastic media and propose some strategic features leading to the reduction of the numerical cost while providing a great flexibility in the inversion parametrization. First, in order to release the memory requirements, we developed our FWI algorithm in the frequency domain and take benefit of the wave-number redundancy in the seismic data to process a quite reduced number of frequencies. To do so, we extract frequency solutions from time marching techniques which are efficient for 3D structures. Moreover, this frequency approach permits a multi-resolution strategy by proceeding from low to high frequencies: the final model at one frequency is used as the starting model for the next frequency. This procedure overcomes partially the non-linear behavior of the inversion
White, Victor; Wiberg, Dean
According to a proposal, basic x-ray lithography would be extended to incorporate a technique, called inverse tomography, that would enable the fabrication of microscopic three-dimensional (3D) objects. The proposed inverse tomo-lithographic process would make it possible to produce complex shaped, submillimeter-sized parts that would be difficult or impossible to make in any other way. Examples of such shapes or parts include tapered helices, paraboloids with axes of different lengths, and even Archimedean screws that could serve as rotors in microturbines. The proposed inverse tomo-lithographic process would be based partly on a prior microfabrication process known by the German acronym LIGA (lithographie, galvanoformung, abformung, which means lithography, electroforming, molding). In LIGA, one generates a precise, high-aspect ratio pattern by exposing a thick, x-ray-sensitive resist material to an x-ray beam through a mask that contains the pattern. One can electrodeposit metal into the developed resist pattern to form a precise metal part, then dissolve the resist to free the metal. Aspect ratios of 100:1 and patterns into resist thicknesses of several millimeters are possible.
Işık, S. E.; Gurbuz, C.
The 3D P wave velocity model of upper and lower crust of the Marmara Region between 40.200- 41.200N and 26.500- 30.500E is obtained by tomographic inversion (Simulps) of 47034 P wave arrivals of local earthquakes recorded at 90 land stations between October 2009 and December 2012 and 30 OBO stations and 14162 shot arrivals recorded at 35 OBO stations (Seismarmara Survey, 2001). We first obtained a 1D minimum model with Velest code in order to obtain an initial model for 3D inversion with 648 well located earthquakes located within the study area. After several 3D inversion trials we decided to create a more adequate initial model for 3D inversion. Choosing the initial model we estimated the 3D P wave velocity model representing the whole region both for land and sea. The results are tested by making Checkerboard , Restoring Resolution and Characteristic Tests, and the reliable areas of the resulting model is defined in terms of RDE, DWS, SF and Hit count distributions. By taking cross sections from the resulting model we observed the vertical velocity change along profiles crossing both land and sea. All the profiles crossing the basins showed that the high velocities of lower crust make extensions towards the basin area which looks like the force that gives a shape to the basins. These extensions of lower crust towards the basins appeared with an average velocity of 6.3 km/s which might be the result of the deformation due the shearing in the region. It is also interpreted that the development of these high velocities coincide with the development of the basins. Thus, both the basins and the high velocity zones around them might be resulted from the entrance of the NAF into the Marmara Sea and at the same time a shear regime was dominated due to the resistance of the northern Marmara Region (Yılmaz, 2010). The seismicity is observed between 5 km and 15 km after the 3D location of the earthquakes. The locations of the earthquakes improved and the seismogenic zone
I describe a new Bayesian-based algorithm to infer the full three dimensional velocity field from observed distances and spectroscopic galaxy catalogues. In addition to the velocity field itself, the algorithm reconstructs true distances, some cosmological parameters and specific non-linearities in the velocity field. The algorithm takes care of selection effects, miscalibration issues and can be easily extended to handle direct fitting of e.g. the inverse Tully-Fisher relation. I first describe the algorithm in details alongside its performances. This algorithm is implemented in the VIRBIUS (VelocIty Reconstruction using Bayesian Inference Software) software package. I then test it on different mock distance catalogues with a varying complexity of observational issues. The model proved to give robust measurement of velocities for mock catalogues of 3000 galaxies. I expect the core of the algorithm to scale to tens of thousands galaxies. It holds the promises of giving a better handle on future large and deep distance surveys for which individual errors on distance would impede velocity field inference.
Muench, Thomas; Koch, Manfred; Schlittenhardt, Jörg
There is now ample evidence from both refraction seismic studies, done already a quarter century ago and from more recent local earthquake traveltime analysis of some of the authors above that large sections of the upper mantle underneath Europe and Germany, in particular, are anisotropic. Employing a modified version of the method of simultaneous inversion for structure and hypocenters (SSH) of the first author, including a priori known upper mantle anisotropy, the investigations of Song et al.  and Song et al.  by means of a 1D time-term analysis and a full 2D Pn anisotropic inversion of regional traveltime data are extended here to a full 3D SSH-inversion underneath Germany. Regional traveltimes from local events occurring between 1975 - 2003 are used which, after application of several selection criteria, results in ~1300 events with a total of ~30000 P- and S-phases for the SSH inversion. Because many of the recorded events appear to suffer from relatively poor hypocentral depth locations a full SSH analysis becomes an intricate undertaking. To alleviate the problem the SSH procedure is carried out in several incremental steps of increasing complexity. First of all improved vertically inhomogeneous velocity (1D) models are derived assuming an isotropic as well as an anisotropic upper mantle. In addition of a slightly better model fit for the anisotropic than for the isotropic model, the latter gives also a somewhat lower Pn-velocity of ~7.90 km/s, compared with ~8.0 km/s for the former. This indicates that inclusion of upper mantle anisotropy into the model is required to obtain physically reasonable Pn-velocities. The results for the P-velocity in the lower crustal layer of the model are less clear, as there appears to be some trade-off in the velocity of that layer and that of the upper mantle. During the course of this part of the study the 3D models have been increasingly refined, starting with a lateral discretization into 15 x 15 blocs
Newman, Gregory A.; Boggs, Paul T.
We provide a framework for preconditioning nonlinear 3D electromagnetic inverse scattering problems using nonlinear conjugate gradient (NLCG) and limited memory (LM) quasi-Newton methods. Key to our approach is the use of an approximate adjoint method that allows for an economical approximation of the Hessian that is updated at each inversion iteration. Using this approximate Hessian as a preconditoner, we show that the preconditioned NLCG iteration converges significantly faster than the non-preconditioned iteration, as well as converging to a data misfit level below that observed for the non-preconditioned method. Similar conclusions are also observed for the LM iteration; preconditioned with the approximate Hessian, the LM iteration converges faster than the non-preconditioned version. At this time, however, we see little difference between the convergence performance of the preconditioned LM scheme and the preconditioned NLCG scheme. A possible reason for this outcome is the behavior of the line search within the LM iteration. It was anticipated that, near convergence, a step size of one would be approached, but what was observed, instead, were step lengths that were nowhere near one. We provide some insights into the reasons for this behavior and suggest further research that may improve the performance of the LM methods.
Cubuk-Sabuncu, Yesim; Taymaz, Tuncay; Fichtner, Andreas
We present a 3D radially anisotropic velocity model of the crust and uppermost mantle structure beneath the Sea of Marmara and surroundings based on the full waveform inversion method. The intense seismic activity and crustal deformation are observed in the Northwest Turkey due to transition tectonics between the strike-slip North Anatolian Fault (NAF) and the extensional Aegean region. We have selected and simulated complete waveforms of 62 earthquakes (Mw > 4.0) occurred during 2007-2015, and recorded at (Δ < 10°) distances. Three component earthquake data is obtained from broadband seismic stations of Kandilli Observatory and Earthquake Research Center (KOERI, Turkey), Hellenic Unified Seismic Network (HUSN, Greece) and Earthquake Research Center of Turkey (AFAD-DAD). The spectral-element solver of the wave equation, SES3D algorithm, is used to simulate seismic wave propagation in 3D spherical coordinates (Fichtner, 2009). The Large Scale Seismic Inversion Framework (LASIF) workflow tool is also used to perform full seismic waveform inversion (Krischer et al., 2015). The initial 3D Earth model is implemented from the multi-scale seismic tomography study of Fichtner et al. (2013). Discrepancies between the observed and simulated synthetic waveforms are determined using the time-frequency misfits which allows a separation between phase and amplitude information (Fichtner et al., 2008). The conjugate gradient optimization method is used to iteratively update the initial Earth model when minimizing the misfit. The inversion is terminated after 19 iterations since no further advances are observed in updated models. Our analysis revealed shear wave velocity variations of the shallow and deeper crustal structure beneath western Turkey down to depths of ~35-40 km. Low shear wave velocity anomalies are observed in the upper and mid crustal depths beneath major fault zones located in the study region. Low velocity zones also tend to mark the outline of young volcanic
Shin, Jungkyun; Ha, Wansoo; Jun, Hyunggu; Min, Dong-Joo; Shin, Changsoo
The Laplace-domain full waveform inversion is an efficient long-wavelength velocity estimation method for seismic datasets lacking low-frequency components. However, to invert a 3D velocity model, a large cluster of CPU cores have commonly been required to overcome the extremely long computing time caused by a large impedance matrix and a number of source positions. In this study, a workstation with a single GPU card (NVIDIA GTX 580) is successfully used for the 3D Laplace-domain full waveform inversion rather than a large cluster of CPU cores. To exploit a GPU for our inversion algorithm, the routine for the iterative matrix solver is ported to the CUDA programming language for forward and backward modeling parts with minimized modification of the remaining parts, which were originally written in Fortran 90. Using a uniformly structured grid set, nonzero values in the sparse impedance matrix can be arranged according to certain rules, which efficiently parallelize the preconditioned conjugate gradient method for a number of threads contained in the GPU card. We perform a numerical experiment to verify the accuracy of a floating point operation performed by a GPU to calculate the Laplace-domain wavefield. We also measure the efficiencies of the original CPU and modified GPU programs using a cluster of CPU cores and a workstation with a GPU card, respectively. Through the analysis, the parallelized inversion code for a GPU achieves the speedup of 14.7-24.6x compared to a CPU-based serial code depending on the degrees of freedom of the impedance matrix. Finally, the practicality of the proposed algorithm is examined by inverting a 3D long-wavelength velocity model using wide azimuth real datasets in 3.7 days.
Max, N.; Crawfis, R.; Grant, C.
Vector field rendering is difficult in 3D because the vector icons overlap and hide each other. We propose four different techniques for visualizing vector fields only near surfaces. The first uses motion blurred particles in a thickened region around the surface. The second uses a voxel grid to contain integral curves of the vector field. The third uses many antialiased lines through the surface, and the fourth uses hairs sprouting from the surface and then bending in the direction of the vector field. All the methods use the graphite pipeline, allowing real time rotation and interaction, and the first two methods can animate the texture to move in the flow determined by the velocity field.
Brocher, T. M.; Aagaard, B.; Simpson, R. W.; Jachens, R. C.
We present a new regional 3D seismic velocity model for Northern California for use in strong motion simulations of the 1906 San Francisco and other earthquakes. The model includes compressional-wave velocity (Vp), shear-wave velocity (Vs), density, and intrinsic attenuation (Qp, Qs). These properties were assigned for each rock type in a 3D geologic model derived from surface outcrops, boreholes, gravity and magnetic data, and seismic reflection, refraction, and tomography studies. A detailed description of the model, USGS Bay Area Velocity Model 05.1.0, is available online [http://www.sf06simulation.org/geology/velocitymodel]. For ground motion simulations Vs and Qs are more important parameters than Vp and Qp because the strongest ground motions are generated chiefly by shear and surface wave arrivals. Because Vp data are more common than Vs data, however, we first developed Vp versus depth relations for each rock type and then converted these to Vs versus depth relations. For the most important rock types in Northern California we compiled measurements of Vp versus depth using borehole logs, laboratory measurements on hand samples, seismic refraction profiles, and tomography models. These rock types include Salinian and Sierran granitic rocks, metagraywackes and greenstones of the Franciscan Complex, Tertiary and Mesozoic sedimentary and volcanic rocks, and Quaternary and Holocene deposits (Brocher, USGS OFR 05-1317, 2005). Vp versus depth curves were converted to Vs versus depth curves using new empirical nonlinear relations between Vs and Vp (Brocher, BSSA, 2005). These relations, showing that Poisson's ratio is a nonlinear function of Vp, were similarly based on compilations of diverse Vs and Vp measurements on a large suite of rock types, mainly from California and the Pacific Northwest. The model is distributed in a discretized form with routines to query the model using C++, C, and Fortran 77 programming languages. The geologic model was discretized at
Ullmann, A.; Scheunert, M.; Afanasjew, M.; Börner, R.-U.; Siemon, B.; Spitzer, K.
As a standard procedure, multi-frequency helicopter-borne electromagnetic (HEM) data are inverted to conductivity-depth models using 1-D inversion methods, which may, however, fail in areas of strong lateral conductivity contrasts (so-called induction anomalies). Such areas require more realistic multi-dimensional modelling. Since the full 3-D inversion of an entire HEM data set is still extremely time consuming, our idea is to combine fast 1-D and accurate but numerically expensive 3-D inversion of HEM data in such a way that the full 3-D inversion is only carried out for those parts of a HEM survey which are affected by induction anomalies. For all other parts, a 1-D inversion method is sufficient. We present a newly developed algorithm for identification, selection, and extraction of induction anomalies in HEM data sets and show how the 3-D inversion model of the anomalous area is re-integrated into the quasi-1-D background. Our proposed method is demonstrated to work properly on a synthetic and a field HEM data set from the Cuxhaven tunnel valley in Germany. We show that our 1-D/3-D approach yields better results compared to 1-D inversions in areas where 3-D effects occur.
Bai, Chao-ying; Wang, Tao; Yang, Shang-bei; Li, Xing-wang; Huang, Guo-jiao
Traditional traveltime inversion for anisotropic medium is, in general, based on a "weak" assumption in the anisotropic property, which simplifies both the forward part (ray tracing is performed once only) and the inversion part (a linear inversion solver is possible). But for some real applications, a general (both "weak" and "strong") anisotropic medium should be considered. In such cases, one has to develop a ray tracing algorithm to handle with the general (including "strong") anisotropic medium and also to design a non-linear inversion solver for later tomography. Meanwhile, it is constructive to investigate how much the tomographic resolution can be improved by introducing the later arrivals. For this motivation, we incorporated our newly developed ray tracing algorithm (multistage irregular shortest-path method) for general anisotropic media with a non-linear inversion solver (a damped minimum norm, constrained least squares problem with a conjugate gradient approach) to formulate a non-linear inversion solver for anisotropic medium. This anisotropic traveltime inversion procedure is able to combine the later (reflected) arrival times. Both 2-D/3-D synthetic inversion experiments and comparison tests show that (1) the proposed anisotropic traveltime inversion scheme is able to recover the high contrast anomalies and (2) it is possible to improve the tomographic resolution by introducing the later (reflected) arrivals, but not as expected in the isotropic medium, because the different velocity (qP, qSV and qSH) sensitivities (or derivatives) respective to the different elastic parameters are not the same but are also dependent on the inclination angle.
Meng, Zhaohai; Xu, Xuechun; Zheng, Changqing
The inversion of three-dimensional geophysical properties (density, magnetic susceptibility, electrical resistivity) has occupies very important position in geophysical interpretation for geophysical interpreters, combining with the corresponding geological data, it will produce a very good solution to solve the corresponding geological problems, especially, in the separate abnormal body of ore bodies .the method would have produce much more good results. There are mainly three kinds of mainstream geophysical inversion methods in the now geophysical inversion method : 1. The minimum model method, 2. the most gentle model method, 3. The smoothest model. The main solution is the optimal solution by solving mixed set equations to solve the corresponding inverse problem, the main difference of the three methods is the differences of the weighting function mode, and in essence, it is to find the best solution based on regularization principle, finally, the reaction of the convergence are obtained. The methods are based on the minimum volume, such as compression inversion and focusing inversion. The two methods also can get much more clearer and sharper boundaries. This abstract choose of the inversion method is based on the theory of minimum volume method. The selection of weighted function can effectively reduce the inversion of the number of iterations and accelerate the rate of inversion. it can conform to the requirements of the current large-scale airborne gravity. Without reducing the quality of the inversion, at the same time, it can accelerate the rate of inversion. The inversion can get the sharp boundary, spatial location, and density attributes of the abnormal body. it needs the quality of the computer performance and geophysical data. Therefore it requests to reduce the random and random noise as far as possible. According to a lot of model tests, It proves that the choice of the weighting function can get very good inversion result. In the inversion
Zheng, J.; Ben-Zion, Y.; Zhu, L.; Ross, Z.
We develop and apply a method to invert earthquake seismograms for source properties using a general tensor representation and 3D Green's functions. The method employs (i) a general representation of earthquake potency/moment tensors with double couple (DC), compensated linear vector dipole (CLVD), and isotropic (ISO) components, and (ii) a corresponding generalized CAP (gCap) scheme where the continuous wave trains are broken into Pnl and surface waves (Zhu & Ben-Zion, 2013). For comparison, we also use the waveform inversion method of Zheng & Chen (2012) and Ammon et al. (1998). Sets of 3D Green's functions are calculated on a grid of 1 km3 using the 3-D community velocity model CVM-4 (Kohler et al. 2003). A bootstrap technique is adopted to establish robustness of the inversion results using the gCap method (Ross & Ben-Zion, 2013). Synthetic tests with 1-D and 3-D waveform calculations show that the source tensor inversion procedure is reasonably reliable and robust. As initial application, the method is used to investigate source properties of the March 11, 2013, Mw=4.7 earthquake on the San Jacinto fault using recordings of ~45 stations up to ~0.2Hz. Both the best fitting and most probable solutions include ISO component of ~1% and CLVD component of ~0%. The obtained ISO component, while small, is found to be a non-negligible positive value that can have significant implications for the physics of the failure process. Work on using higher frequency data for this and other earthquakes is in progress.
Guo, Yujia; Koketsu, Kazuki; Ohno, Taichi
A notable feature of the 1995 Kobe (Hyogo-ken Nanbu) earthquake is that violent ground motions occurred in a narrow zone. Previous studies have shown that the origin of such motions can be explained by the 3D velocity structure in this zone. This indicates not only that the 3D velocity structure significantly affects strong ground motions, but also that we should consider its effects in order to determine accurately the rupture process of the earthquake. Therefore, we have performed a joint source inversion of strong-motion, geodetic, and teleseismic data, where 3D Green's functions were calculated for strong-motion and geodetic data in the Osaka basin. Our source model estimates the total seismic moment to be about 2.1 × 1019 N m and the maximum slip reaches 2.9 m near the hypocenter. Although the locations of large slips are similar to those reported by Yoshida et al. (1996), there are quantitative differences between our results and their results due to the differences between the 3D and 1D Green's functions. We have also confirmed that our source model realized a better fit to the strong motion observations, and a similar fit as Yoshida et al. (1996) to the observed static displacements.
Kim, B.; Byun, J.; Seol, S. J.; Jeong, S.; Chung, Y.; Kwon, T.
For many decades, gas hydrates have been received great attention as a potential source of natural gas. Therefore, the detailed information of structures of buried gas hydrates and their concentrations are prerequisite for the production for the gas hydrate as a reliable source of alternate energy. Recently, for this reason, a lot of gas hydrate assessment methods have been proposed by many researchers. However, it is still necessary to establish as new method for the further improvement of the accuracy of the 3D gas hydrate distribution. In this study, we present a 3D joint inversion method that provides superior quantitative information of gas hydrate distributions using 3D seismic data obtained by ocean-bottom cable (OBC) and marine controlled-source electromagnetic (CSEM) data. To verify our inversion method, we first built the general 3D gas hydrate model containing vertical methane-flow pathways. With the described model, we generated synthetic 3D OBC data and marine CSEM data using finite element modeling algorithms, respectively. In the joint inversion process, to obtain the high-resolution volumetric P-wave velocity structure, we applied the 3D full waveform inversion algorithm to the acquired OBC data. After that, the obtained P-wave velocity model is used as the structure constraint to compute cross-gradients with the updated resistivity model in the EM inversion process. Finally, petrophysical relations were applied to estimate volumetric gas hydrate concentrations. The proposed joint inversion process makes possible to obtain more precise quantitative gas hydrate assessment than inversion processes using only seismic or EM data. This technique can be helpful for accurate decision-making in gas hydrate development as well as in their production monitoring.
Gill, D.; Small, P.; Maechling, P. J.; Jordan, T. H.; Shaw, J. H.; Plesch, A.; Chen, P.; Lee, E. J.; Taborda, R.; Olsen, K. B.; Callaghan, S.
Three-dimensional (3D) seismic velocity models provide foundational data for ground motion simulations that calculate the propagation of earthquake waves through the Earth. The Southern California Earthquake Center (SCEC) has developed the Unified Community Velocity Model (UCVM) package for both Linux and OS X. This unique framework provides a cohesive way for querying and visualizing 3D models. UCVM v14.3.0, supports many Southern California velocity models including CVM-S4, CVM-H 11.9.1, and CVM-S4.26. The last model was derived from 26 full-3D tomographic iterations on CVM-S4. Recently, UCVM has been used to deliver a prototype of a new 3D model of central California (CCA) also based on full-3D tomographic inversions. UCVM was used to provide initial plots of this model and will be used to deliver CCA to users when the model is publicly released. Visualizing models is also possible with UCVM. Integrated within the platform are plotting utilities that can generate 2D cross-sections, horizontal slices, and basin depth maps. UCVM can also export models in NetCDF format for easy import into IDV and ParaView. UCVM has also been prototyped to export models that are compatible with IRIS' new Earth Model Collaboration (EMC) visualization utility. This capability allows for user-specified horizontal slices and cross-sections to be plotted in the same 3D Earth space. UCVM was designed to help a wide variety of researchers. It is currently being use to generate velocity meshes for many SCEC wave propagation codes, including AWP-ODC-SGT and Hercules. It is also used to provide the initial input to SCEC's CyberShake platform. For those interested in specific data points, the software framework makes it easy to extract P and S wave propagation speeds and other material properties from 3D velocity models by providing a common interface through which researchers can query earth models for a given location and depth. Also included in the last release was the ability to add small
Lomax, A.; Husen, S.
Earthquake monitoring agencies, such as local networks or CTBTO, are faced with the dilemma of providing routine earthquake locations in near real-time with high precision and meaningful uncertainty information. Traditionally, routine earthquake locations are obtained from linearized inversion using layered seismic velocity models. This approach is fast and simple. However, uncertainties derived from a linear approximation to a set of non-linear equations can be imprecise, unreliable, or even misleading. In addition, 1-D velocity models are a poor approximation to real Earth structure in tectonically complex regions. In this paper, we discuss the routine location of earthquakes in near real-time with high precision using non-linear, probabilistic location methods and 3-D velocity models. The combination of non-linear, global search algorithms with probabilistic earthquake location provides a fast and reliable tool for earthquake location that can be used with any kind of velocity model. The probabilistic solution to the earthquake location includes a complete description of location uncertainties, which may be irregular and multimodal. We present applications of this approach to determine seismicity in Switzerland and in Yellowstone National Park, WY. Comparing our earthquake locations to earthquake locations obtained using linearized inversion and 1-D velocity models clearly demonstrates the advantages of probabilistic earthquake location and 3-D velocity models. For example, the more complete and reliable uncertainty information of non-linear, probabilistic earthquake location greatly facilitates the identification of poorly constrained hypocenters. Such events are often not identified in linearized earthquake location, since the location uncertainties are determined with a simplified, localized and approximate Gaussian statistic.
Dziewonski, A. M.; Lekic, V.; Romanowicz, B. A.
The range of shear velocity anomalies in published whole mantle models is considerable. This impedes drawing conclusions of importance for geodynamic modeling and for interpretation of mineral physics results. However, if one considers only the models that were built using data that are sensitive to mantle structure at all depths, these models show robust features in their power spectra as a function of depth. On this basis we propose that there are five depth intervals with distinct spectral characteristics. 1. Heterosphere (Moho - 300 km) is characterized by strong power spectrum relatively flat up to degree 6. With lateral shear wavespeed variations as large as 15%, this zone accounts for more than 50% of the entire heterogeneity in the mantle. Differences among models for different tectonic regions decrease rapidly below 300 km depth. 2. Upper mantle buffer zone (300- 500 km) has a flat spectrum and the overall power of heterogeneity drops by an order of magnitude compared to the region above. There may be still weak difference between continents and oceans, but the oceanic regions lose their age dependence. The spectral characteristics do not change across the 410 km discontinuity. 3. Transition zone (500 - 650 km) The degree 2 anomaly becomes dominant. There are long wavelength anomalies in regions of the fastest plate subduction during the last 15-20 Ma, suggesting slab ponding above the 650 km discontinuity. Several slower-than-average anomalies of unknown origin are present in this depth range. 4. Lower mantle buffer zone (650 - 2300 km) has a weak, flat spectrum without long wavelength velocity anomalies that could be interpreted as unfragmented subducted slabs. However, there are three relatively narrow and short high velocity anomalies under Peru, Tonga and Indonesia that may indicate limited slab penetration. 5 Abyssal layer (2300 - CMB) Strong spectrum dominated by degrees 2 and 3. The amplitude is the largest at the CMB and decreases rapidly up to
Emanuele Maesano, Francesco; D'Ambrogi, Chiara
3D modelling is a powerful tool that is experiencing increasing applications in data analysis and dissemination. At the same time the need of quantitative uncertainty evaluation is strongly requested in many aspects of the geological sciences and by the stakeholders. In many cases the starting point for 3D model building is the interpretation of seismic profiles that provide indirect information about the geology of the subsurface in the domain of time. The most problematic step in the 3D modelling construction is the conversion of the horizons and faults interpreted in time domain to the depth domain. In this step the dominant variable that could lead to significantly different results is the velocity. The knowledge of the subsurface velocities is related mainly to punctual data (sonic logs) that are often sparsely distributed in the areas covered by the seismic interpretation. The extrapolation of velocity information to wide extended horizons is thus a critical step to obtain a 3D model in depth that can be used for predictive purpose. In the EU-funded GeoMol Project, the availability of a dense network of seismic lines (confidentially provided by ENI S.p.A.) in the Central Po Plain, is paired with the presence of 136 well logs, but few of them have sonic logs and in some portion of the area the wells are very widely spaced. The depth conversion of the 3D model in time domain has been performed testing different strategies for the use and the interpolation of velocity data. The final model has been obtained using a 4 layer cake 3D instantaneous velocity model that considers both the initial velocity (v0) in every reference horizon and the gradient of velocity variation with depth (k). Using this method it is possible to consider the geological constraint given by the geometries of the horizons and the geo-statistical approach to the interpolation of velocities and gradient. Here we present an experiment based on the use of set of pseudo-wells obtained from the
In this thesis we present the development of new techniques for the interpretation of potential field (gravity and magnetic data), which are the most widespread economic geophysical methods used for oil and mineral exploration. These new techniques help to address the long-standing issue with the interpretation of potential fields, namely the intrinsic non-uniqueness inversion of these types of data. The thesis takes the form of three papers (four including Appendix), which have been published, or soon to be published, in respected international journals. The purpose of the thesis is to introduce new methods based on 3D stochastical approaches for: 1) Inversion of potential field data (magnetic), 2) Multiscale Inversion using surface and borehole data and 3) Joint inversion of geophysical potential field data. We first present a stochastic inversion method based on a geostatistical approach to recover 3D susceptibility models from magnetic data. The aim of applying geostatistics is to provide quantitative descriptions of natural variables distributed in space or in time and space. We evaluate the uncertainty on the parameter model by using geostatistical unconditional simulations. The realizations are post-conditioned by cokriging to observation data. In order to avoid the natural tendency of the estimated structure to lay near the surface, depth weighting is included in the cokriging system. Then, we introduce algorithm for multiscale inversion, the presented algorithm has the capability of inverting data on multiple supports. The method involves four main steps: i. upscaling of borehole parameters (It could be density or susceptibility) to block parameters, ii. selection of block to use as constraints based on a threshold on kriging variance, iii. inversion of observation data with selected block densities as constraints, and iv. downscaling of inverted parameters to small prisms. Two modes of application are presented: estimation and simulation. Finally, a novel
Budraitis, M.; Kozlovskaya, E.; Janutyte, I.; Motuza, G.
the density model is approximated by relationship between seismic velocity and density and the latter is found using inversion of the Bouguer anomaly. Comparison of the inversion result to the observed Bouguer anomaly showed that the upper part of the model needs to be corrected, in particular, in the areas not covered by the profiles. The corrected velocity model was then used to improve location of local events. The epicenters of events relocated with the use of a 3-D model are much less scattered and some of the clusters are confined to known areas of human activity.
Yao, H.; Fang, H.; Li, C.; Liu, Y.; Zhang, H.; van der Hilst, R. D.; Huang, Y. C.
Ambient noise tomography has provided essential constraints on crustal and uppermost mantle shear velocity structure in global seismology. Recent studies demonstrate that high frequency (e.g., ~ 1 Hz) surface waves between receivers at short distances can be successfully retrieved from ambient noise cross-correlation and then be used for imaging near surface or shallow crustal shear velocity structures. This approach provides important information for strong ground motion prediction in seismically active area and overburden structure characterization in oil and gas fields. Here we propose a new tomographic method to invert all surface wave dispersion data for 3-D variations of shear wavespeed without the intermediate step of phase or group velocity maps.The method uses frequency-dependent propagation paths and a wavelet-based sparsity-constrained tomographic inversion. A fast marching method is used to compute, at each period, surface wave traveltimes and ray paths between sources and receivers. This avoids the assumption of great-circle propagation that is used in most surface wave tomographic studies, but which is not appropriate in complex media. The wavelet coefficients of the velocity model are estimated with an iteratively reweighted least squares (IRLS) algorithm, and upon iterations the surface wave ray paths and the data sensitivity matrix are updated from the newly obtained velocity model. We apply this new method to determine the 3-D near surface wavespeed variations in the Taipei basin of Taiwan, Hefei urban area and a shale and gas production field in China using the high-frequency interstation Rayleigh wave dispersion data extracted from ambient noisecross-correlation. The results reveal strong effects of off-great-circle propagation of high-frequency surface waves in these regions with above 30% shear wavespeed variations. The proposed approach is more efficient and robust than the traditional two-step surface wave tomography for imaging complex
Cox, Leif H.; Wilson, Glenn A.; Zhdanov, Michael S.
It is often argued that 3D inversion of entire airborne electromagnetic (AEM) surveys is impractical, and that 1D methods provide the only viable option for quantitative interpretation. However, real geological formations are 3D by nature and 3D inversion is required to produce accurate images of the subsurface. To that end, we show that it is practical to invert entire AEM surveys to 3D conductivity models with hundreds of thousands if not millions of elements. The key to solving a 3D AEM inversion problem is the application of a moving footprint approach. We have exploited the fact that the area of the footprint of an AEM system is significantly smaller than the area of an AEM survey, and developed a robust 3D inversion method that uses a moving footprint. Our implementation is based on the 3D integral equation method for computing data and sensitivities, and uses the re-weighted regularised conjugate gradient method for minimising the objective functional. We demonstrate our methodology with the 3D inversion of AEM data acquired for salinity mapping over the Bookpurnong Irrigation District in South Australia. We have inverted 146 line km of RESOLVE data for a 3D conductivity model with ~310000 elements in 45min using just five processors of a multi-processor workstation.
Xie, G.; Li, J.; Majer, E.
In this paper, a new parallel modeling and inversion algorithm using a Stochastic Global Integral and Local Differential equation (SGILD) is presented. The authors derived new acoustic integral equations and differential equation for statistical moments of the parameters and field. The new statistical moments integral equation on the boundary and local differential equations in domain will be used together to obtain mean wave field and its moments in the modeling. The new moments global Jacobian volume integral equation and the local Jacobian differential equations in domain will be used together to update the mean parameters and their moments in the inversion. A new parallel multiple hierarchy substructure direct algorithm or direct-iteration hybrid algorithm will be used to solve the sparse matrices and one smaller full matrix from domain to the boundary, in parallel. The SGILD modeling and imaging algorithm has many advantages over the conventional imaging approaches. The SGILD algorithm can be used for the stochastic acoustic, electromagnetic, and flow modeling and inversion, and are important for the prediction of oil, gas, coal, and geothermal energy reservoirs in geophysical exploration.
Javad Fallahi, Mohammad; Mousavi, Sima; Korn, Michael; Sens-Schönfelder, Christoph; Bauer, Klaus; Rößler, Dirk
The 3D structure of the upper crust beneath west Bohemia/Vogtland region, analyzed with travel time tomography and ambient noise surface wave tomography using existing data. This region is characterized by a series of phenomena like occurrence of repeated earthquake swarms, surface exhalation, CO2 enriched fluids, mofettes, mineral springs and enhanced heat flow, and has been proposed as an excellent location for an ICDP drilling project targeted to a better understanding of the crust in an active magmatic environment. We performed a 3D tomography using P-and S-wave travel times of local earthquakes and explosions. The data set were taken from permanent and temporary seismic networks in Germany and Czech Republic from 2000 to 2010, as well as active seismic experiments like Celebration 2000 and quarry blasts. After picking P and S wave arrival times, 399 events which were recorded by 9 or more stations and azimuthal gap<160° were selected for inversion. A simultaneous inversion of P and S wave 1D velocity models together with relocations of hypocenters and station corrections was performed. The obtained minimum 1D velocity model was used as starting model for the 3D Vp and Vp/Vs velocity models. P and S wave travel time tomography employs damped least-square method and ray tracing by pseudo-bending algorithm. For model parametrization different cell node spacings have been tested to evaluate the resolution in each node. Synthetic checkerboard tests have been done to check the structural resolution. Then Vp and Vp/Vs in the preferred 3D grid model have been determined. Earthquakes locations in iteration process change till the hypocenter adjustments and travel time residuals become smaller than the defined threshold criteria. Finally the analysis of the resolution depicts the well resolved features for interpretation. We observed lower Vp/Vs ratio in depth of 5-10 km close to the foci of earthquake swarms and higher Vp/Vs ratio is observed in Saxoturingian zone and
Podorov, Sergei G; Förster, Eckhart
Differential Fourier holography (DFH) gives an exact mathematical solution of the inverse problem of diffraction in the Fraunhofer regime. After the first publication [Opt. Express15, 9954 (2007)], DFH was successfully applied in many experiments to obtain amplitude and phase information about two-dimensional images. In this paper, we demonstrate numerically the possibility to apply DFH also for investigation of unknown three-dimensional objects. The first simulation is made for a double-spiral structure plus a line as a reference object. PMID:26835947
Portal, Angélie; Fargier, Yannick; Lénat, Jean-François; Labazuy, Philippe
The electrical resistivity tomography (ERT) method, initially developed for environmental and engineering exploration, is now commonly used for geological structures imaging. Such structures can present complex characteristics that conventional 2D inversion processes cannot perfectly integrate. Here we present a new 3D inversion algorithm named EResI, firstly developed for levee investigation, and presently applied to the study of a complex lava dome (the Puy de Dôme volcano, France). EResI algorithm is based on a conventional regularized Gauss-Newton inversion scheme and a 3D non-structured discretization of the model (double grid method based on tetrahedrons). This discretization allows to accurately model the topography of investigated structure (without a mesh deformation procedure) and also permits a precise location of the electrodes. Moreover, we demonstrate that a complete 3D unstructured discretization limits the number of inversion cells and is better adapted to the resolution capacity of tomography than a structured discretization. This study shows that a 3D inversion with a non-structured parametrization has some advantages compared to classical 2D inversions. The first advantage comes from the fact that a 2D inversion leads to artefacts due to 3D effects (3D topography, 3D internal resistivity). The second advantage comes from the fact that the capacity to experimentally align electrodes along an axis (for 2D surveys) depends on the constrains on the field (topography...). In this case, a 2D assumption induced by 2.5D inversion software prevents its capacity to model electrodes outside this axis leading to artefacts in the inversion result. The last limitation comes from the use of mesh deformation techniques used to accurately model the topography in 2D softwares. This technique used for structured discretization (Res2dinv) is prohibed for strong topography (>60 %) and leads to a small computational errors. A wide geophysical survey was carried out
Yang, Pengliang; Brossier, Romain; Métivier, Ludovic; Virieux, Jean
In this paper we study 3D multiparameter full waveform inversion (FWI) in viscoelastic media based on the generalized Maxwell/Zener body (GMB/GZB) including arbitrary number of attenuation mechanisms. We present a frequency-domain energy analysis to establish the stability condition of a full anisotropic viscoelastic system, according to zero-valued boundary condition and the elastic-viscoelastic correspondence principle: the real-valued stiffness matrix becomes a complex-valued one in Fourier domain when seismic attenuation is taken into account. We develop a least-squares optimization approach to linearly relate the quality factor with the anelastic coefficients by estimating a set of constants which are independent of the spatial coordinates, which supplies an explicit incorporation of the parameter Q in the general viscoelastic wave equation. By introducing the Lagrangian multipliers into the matrix expression of the wave equation with implicit time integration, we build a systematic formulation of multiparameter full waveform inversion for full anisotropic viscoelastic wave equation, while the equivalent form of the state and adjoint equation with explicit time integration is available to be resolved efficiently. In particular, this formulation lays the foundation for the inversion of the parameter Q in the time domain with full anisotropic viscoelastic properties. In the 3D isotropic viscoelastic settings, the anelastic coefficients and the quality factors using bulk and shear moduli parameterization can be related to the counterparts using P- and S- velocity. Gradients with respect to any other parameter of interest can be found by chain rule. Pioneering numerical validations as well as the real applications of this most generic framework will be carried out to disclose the potential of viscoelastic FWI when adequate high performance computing resources and the field data are available.
Nikolova, S.; Ilinski, D.; Makris, J.; Chonia, T.; Stavrakakis, J.
Since June 2000, active and passive seismic observations have been carried out by IfG, GeoPro GmbH, Hamburg and Institute of Geodynamics, Athens within the frame of the project GEOWARN (Geo-Spacial Warning Systems Nisyros Volcano, Greece: An Emergency Case Study of the Volcanic Area of Nisyros) supported by the European Community. In the active experiment 48 recording seismic units were deployed and recorded more than 7000 shots in 3D array. The Nisyros volcano has been identified as an apophytic intrusion of much larger volcanic structure with a caldera of 35 km diameter, extending between the southern coasts of the islands of Kos and Nisyros. To obtain 3-D velocity structure of the area a tomographic inversion was made using 6800 rays which probed the area with a very high ray density. The method applied and the high accuracy of active tomographic data allowed to resolve the high velocity bodies in the caldera. The complex volcanic structure is identified by high velocity rocks in- truding through the upper crust and penetrating the volcanic cone to depth of approx. 1.0 km to 1.8 km below the surface. Particularly high velocity bodies were identified below the islands of Yali and the central caldera of Nisyros. The high velocity bodies at shallow depth were interpreted as high-density cumulates of solidified magma intru- sion in the caldera. These intrusions explain very high temperature of 300C observed in the lower aquifer in the caldera at 1.5 km depth as confirmed by drilling. The vol- canic edifices of Kos, Yali, Nisyros and Strongily are part of a major volcanic caldera nearly 35 km in diameter. This size of the volcanic caldera explains the large volume of ignimbrites erupted 160 000 years ago. By combining geodetic, geophysical, geo- chemical and geological observations it is intended to correlate magma movements and associated changes of physical and chemical parameters of the recent volcanism.
Lestari, Titik; Nugraha, Andri Dian
Southern Sumatra region has a high level of seismicity due to the influence of the subduction system, Sumatra fault, Mentawai fault and stretching zone activities. The seismic activities of Southern Sumatra region are recorded by Meteorological Climatological and Geophysical Agency (MCGA’s) Seismograph network. In this study, we used earthquake data catalog compiled by MCGA for 3013 events from 10 seismic stations around Southern Sumatra region for time periods of April 2009 – April 2014 in order to invert for the 3-D seismic velocities structure (Vp, Vs, and Vp/Vs ratio). We applied double-difference seismic tomography method (tomoDD) to determine Vp, Vs and Vp/Vs ratio with hypocenter adjustment. For the inversion procedure, we started from the initial 1-D seismic velocity model of AK135 and constant Vp/Vs of 1.73. The synthetic travel time from source to receiver was calculated using ray pseudo-bending technique, while the main tomographic inversion was applied using LSQR method. The resolution model was evaluated using checkerboard test and Derivative Weigh Sum (DWS). Our preliminary results show low Vp and Vs anomalies region along Bukit Barisan which is may be associated with weak zone of Sumatran fault and migration of partial melted material. Low velocity anomalies at 30-50 km depth in the fore arc region may indicated the hydrous material circulation because the slab dehydration. We detected low seismic seismicity in the fore arc region that may be indicated as seismic gap. It is coincides contact zone of high and low velocity anomalies. And two large earthquakes (Jambi and Mentawai) also occurred at the contact of contrast velocity.
Lestari, Titik; Nugraha, Andri Dian
Southern Sumatra region has a high level of seismicity due to the influence of the subduction system, Sumatra fault, Mentawai fault and stretching zone activities. The seismic activities of Southern Sumatra region are recorded by Meteorological Climatological and Geophysical Agency (MCGA's) Seismograph network. In this study, we used earthquake data catalog compiled by MCGA for 3013 events from 10 seismic stations around Southern Sumatra region for time periods of April 2009 - April 2014 in order to invert for the 3-D seismic velocities structure (Vp, Vs, and Vp/Vs ratio). We applied double-difference seismic tomography method (tomoDD) to determine Vp, Vs and Vp/Vs ratio with hypocenter adjustment. For the inversion procedure, we started from the initial 1-D seismic velocity model of AK135 and constant Vp/Vs of 1.73. The synthetic travel time from source to receiver was calculated using ray pseudo-bending technique, while the main tomographic inversion was applied using LSQR method. The resolution model was evaluated using checkerboard test and Derivative Weigh Sum (DWS). Our preliminary results show low Vp and Vs anomalies region along Bukit Barisan which is may be associated with weak zone of Sumatran fault and migration of partial melted material. Low velocity anomalies at 30-50 km depth in the fore arc region may indicated the hydrous material circulation because the slab dehydration. We detected low seismic seismicity in the fore arc region that may be indicated as seismic gap. It is coincides contact zone of high and low velocity anomalies. And two large earthquakes (Jambi and Mentawai) also occurred at the contact of contrast velocity.
Levander, Alan R.
Under ER63662, 3-D Seismic Experimentation and Advanced Processing/Inversion Development for Investigations of the Shallow Subsurface, we have completed a number of subprojects associated with the Hill Air Force Base (HAFB) high resolution 3-D reflection/tomography dataset.
The most complete representation of an elastic medium consists of an elastic tensor with 21 independent moduli. All 21 can be estimated from compressional and shear wave polarization and slowness vectors corresponding to wide apertures of polar and azimuth angles. In isotropic media, when seismic source and receiver components have the same orientation (such as XX and YY), the reflection amplitude contours align approximately perpendicular to the particle motions. The mixed components (such as XY and YX) have amplitude patterns that are in symmetrical pairs of either the same, or of opposite, polarity on either side of the diagonal of the 9-C response matrix. In anisotropic media, amplitude variations with azimuth show the same basic patterns and symmetries as for isotropic, but with a superimposed tendency for alignment parallel to the strike of the vertical cracks. Solutions for elastic tensor elements from synthetic slowness and polarization data calculated directly from the Christoffel equation are more sensitive to the polar angle aperture than to the azimuth aperture. Nine-component synthetic elastic vertical seismic profile data for a model with triclinic symmetry calculated by finite-differencing allows estimation of the elastic 21 tensor elements in the vicinity of a three-component borehole receiver. Wide polar angle and azimuth apertures are needed for accurately estimating the elastic tensor elements. The tensor elements become less independent as the data apertures decrease. Results obtained by extracting slowness and polarization data from the corresponding synthetic seismograms show similar results. The inversion algorithm has produced good results from field vertical seismic profile data set from the Weyburn Field in Southern Saskatchewan in Canada. Synthetic nine-component seismograms calculated from the extracted tensor are able to explain most of the significant features in the field data. The inverted stiffness elastic tensor shows orthorhombic
Gai, Neville D.; Butman, John A.
Purpose To design and evaluate a new reduced scan time 3D FLuid Attenuated Inversion Recovery (FLAIR) sequence. Materials and Methods The 3D FLAIR sequence was modified so that the repetition time was modulated in a predetermined smooth fashion (3D mFLAIR). Inversion times were adjusted accordingly to maintain CSF suppression. Simulations were performed to determine SNR for gray matter (GM), white matter (WM) and CSF. Fourteen volunteers were imaged using the modified and product sequence. SNR measurements were performed in GM, WM and CSF. Mean value and the 95% confidence interval ([CI]) were assessed. Scan time for the 3D FLAIR and 3D mFLAIR sequences was measured. Results There was no statistically significant difference in the SNR measured in GM (P value = 0.5; mean SNR = 42.8 [CI]: 38.2-45.5 vs 42.2 [CI]: 38.3-46.1 for 3D FLAIR and 3D mFLAIR, respectively) and WM (P value = 0.25; mean SNR = 32.1 [CI]: 30.3-33.8 vs 32.9 [CI]: 31.1-34.7). Scan time reduction greater than 30% was achieved for the given parameter set with the 3D mFLAIR sequence. Conclusion Scan time for 3D FLAIR can be effectively reduced by modulating repetition and inversion time in a predetermined fashion while maintaining the SNR and CNR of a constant TR sequence. PMID:24979311
Landes, M.; Readman, P. W.; O'Reilly, B. M.; Shannon, P. M.
In the VARNET-96 experiment three seismic refraction profiles were acquired to examine the crustal structure in the south-west of Ireland. The shotpoint geometry allowed for both in-line and off-line fan shot recordings on the three profiles. Results of 3-D inversion modelling illustrate that there is pervasive lateral heterogeneity of the sedimentary and crustal velocity structure south of the Shannon Estuary. Palaeozoic strata at the south coast are about 5-6 km thick associated with the sedimentary infill of the Munster and South Munster Basins. To the north, shallow upper crust in the vicinity of the Killarney-Mallow Fault Zone is followed by a 3-4 km thick sedimentary succession in the Dingle-Shannon Basin. A zone of high-velocity upper crust (6.4-6.6 km/s) beneath the South Munster Basin correlates with a gravity high between the Kenmare-Killarney and the Leinster Granite gravity lows. Other high-velocity zones beneath Dingle Bay and the Kenmare River region may be associated with the deep traces of the Killarney-Mallow Fault Zone and the Cork-Kenmare Line. The 3-D velocity model was taken as a basis for the computation of PmP reflected arrivals from the crust-mantle boundary. The Moho depth varies from 28-29 km at the south coast to 32-33 km beneath the Dingle-Shannon Basin. Pervasive Variscan deformation appears to be confined to the sedimentary and upper crustal structure thus supporting a thin-skinned tectonic model for Variscan deformation. Deep-crustal variations only occur where they can be correlated with major tectonic features such as the Caledonian Iapetus Suture near the Shannon Estuary. The shallowing of the Moho towards the coast may result from Mesozoic crustal extension in the adjacent offshore sedimentary basins.
Because of the properties of gravity data, it is made difficult to solve the problem of multiple solutions. There are two main types of 3D gravity inversion methods：One of two methods is based on the improvement of the instability of the sensitive matrix, solving the problem of multiple solutions and instability in 3D gravity inversion. Another is to join weight function into the 3D gravity inversion iteration. Through constant iteration, it can renewal density values and weight function to achieve the purpose to solve the multiple solutions and instability of the 3D gravity data inversion. Thanks to the sparse nature of the solutions of 3D gravity data inversions, we can transform it into a sparse equation. Then, through solving the sparse equations, we can get perfect 3D gravity inversion results. The main principle is based on zero norm of sparse matrix solution of the equation. Zero norm is mainly to solve the nonzero solution of the sparse matrix. However, the method of this article adopted is same as the principle of zero norm. But the method is the opposite of zero norm to obtain zero value solution. Through the form of a Gaussian fitting solution of the zero norm, we can find the solution by using regularization principle. Moreover, this method has been proved that it had a certain resistance to random noise in the mathematics, and it was more suitable than zero norm for the solution of the geophysical data. 3D gravity which is adopted in this article can well identify abnormal body density distribution characteristics, and it can also recognize the space position of abnormal distribution very well. We can take advantage of the density of the upper and lower limit penalty function to make each rectangular residual density within a reasonable range. Finally, this 3D gravity inversion is applied to a variety of combination model test, such as a single straight three-dimensional model, the adjacent straight three-dimensional model and Y three
Three dimensional velocity models constructed through seismic tomography are seldom digitally processed further for imaging structural features. A study conducted to evaluate the potential for imaging subsurface discontinuities in horizontal and vertical direction from three dimensional velocity models using image processing/computer vision techniques has provided significant results. Three-dimensional velocity models constructed through tomographic inversion of active source and/or earthquake traveltime data are generally built from an initial 1-D velocity model that varies only with depth. Regularized tomographic inversion algorithms impose constraints on the roughness of the model that help to stabilize the inversion process. Final velocity models obtained from regularized tomographic inversions have smooth three-dimensional structures that are required by the data. Final velocity models are usually analyzed and interpreted either as a perturbation velocity model or as an absolute velocity model. Compared to perturbation velocity model, absolute velocity model has an advantage of providing constraints on lithology. Both velocity models lack the ability to provide sharp constraints on subsurface faults. However, results from the analysis of the 3-D velocity model from northern Cascadia using Roberts, Prewitt, Sobel, and Canny operators show that subsurface faults that are not clearly interpretable from velocity model plots can be identified through this approach. This analysis resulted in inferring the locations of Tacoma Fault, Seattle Fault, Southern Whidbey Island Fault, and Darrington Devils Mountain fault much clearly. The Coast Range Boundary Fault, previously hypothesized on the basis of sedimentological and tectonic observations is inferred clearly from processed images. Many of the fault locations so imaged correlate with earthquake hypocenters indicating their seismogenic nature.
Li, Z.; Ni, S.; Chong, J.; Wang, X.
Surface wave tomography based on the noise correlation function of seismic ambient noise has been widely used in studies of crustal and mantle structure . However, the periods of surface wave dispersions in the ambient noise tomography are typically less than 40 s, which limits its resolution on the lower crust. Travel times of earthquake body waves, such as Sg and SmS, could provide additional constraints to the crustal structure, especially to the lower crust due to the ray paths of SmS traveling through the lower crust twice. Here, we proposed a joint inversion method for 3D crustal structure with ambient noise and earthquake body wave travel time data, with the goal of providing better constraints and resolutions on the whole crust. We constructed the linear equations for joint inversion of crustal S velocity structure with the surface wave dispersion and body wave travel time data, and solved the equations with LSQR algorithm. Different weighting and damping factors, together with smoothing constraints, are adopted for surface wave dispersion and body wave travel time data to fit both dataset simultaneously. Synthetics experiments showed that the joint inversion could resolve the crust structure better than sole tomography of ambient noise or body wave travel time. We conducted the joint inversion around the Yangtze block in the eastern China. Rayleigh wave dispersions are extracted from the seismic ambient noise tomography by Zheng et al (2011) in this area. The body waves (e.g., Sg, SmS, Sn) are coherent to be identified and their travel times are measured with accuracy from high quality waveforms of some recent local earthquakes in this area. In order to minimize the travel time uncertainties, the focal depth and epicenter of these local earthquakes were resolved by depth phases and temporary aftershock observations. The result from joint inversion suggests that the crustal velocity structure, especially the lower crust, was well improved, which not only
Rocha, João.; Bezzeghoud, Mourad; Caldeira, Bento; Dias, Nuno; Borges, José; Matias, Luís.; Dorbath, Catherine; Carrilho, Fernando
The present seismic tomographic study is focused around Algarve region, in South of Portugal. To locate the seismic events and find the local velocity structure of epicentral area, the P and S arrival times at 38 stations are used. The data used in this study were obtained during the Algarve campaign which worked from January/2006 to July/2007. The preliminary estimate of origin times and hypocentral coordinates are determined by the Hypoinverse program. Linearized inversion procedure was applied to comprise the following two steps: 1) finding the minimum 1D velocity model using Velest and 2) simultaneous relocation of hypocenters and determination of local velocity structure. The velocity model we have reached is a 10 layer model which gave the lowest RMS, after several runnings of eight different velocity models that we used "a priori". The model parameterization assumes a continuous velocity field between 4.5 km/s and 7.0 km/s until 30 km depth. The earth structure is represented in 3D by velocity at discrete points, and velocity at any intervening point is determined by linear interpolation among the surrounding eight grid points. A preliminary analysis of the resolution capabilities of the dataset, based on the Derivative Weight Sum (DWS) distribution, shows that the velocity structure is better resolved in the West part of the region between the surface to15 km. The resulting tomographic image has a prominent low-velocity anomaly that shows a maximum decrease in P-wave velocity in the first 12 kms in the studied region. We also identified the occurrence of local seismic events of reduced magnitude not catalogued, in the neighbourhood of Almodôvar (low Alentejo). The spatial distribution of epicentres defines a NE-SW direction that coincides with the strike of the mapped geological faults of the region and issued from photo-interpretation. Is still expectable to refine the seismicity of the region of Almodôvar and establish more rigorously its role in the
Panning, M. P.; Romanowicz, B. A.; Kim, A.
We are developing a new approach which relies on a cascade of increasingly accurate theoretical approximations for computation of the seismic wavefield to develop a model of regional seismic velocity structure for eastern Eurasia using full seismic waveforms. The selected area is particularly suitable for the purpose of this experiment, as it is highly heterogeneous, presenting a challenge for standard modeling techniques, but it is well surrounded by earthquake sources and a significant number of high quality broadband digital stations exist, for which data are readily accessible through IRIS (Incorporated Research Institutions for Seismology) and the FDSN (Federation of Digital Seismic Networks). The initial model is derived from a large database of teleseismic long period waveforms (surface waves and overtone wavepackets) using well-developed theoretical approximations, the Path Average Approximation (PAVA) and Nonlinear Asymptotic Coupling Theory (NACT). These approaches assume waveforms are only sensitive to the 1D (PAVA) and 2D (NACT) structure in the vertical plane between source and receiver, which is adequate for the development of a smooth initial 3D velocity model. We refine this model using a more accurate theoretical approach. We utilize an implementation of a 3D Born approximation, which takes into account the contribution to the waveform from single scattering throughout the model, giving full 3D waveform sensitivity kernels. We perform verification tests of this approach for synthetic models, and show that it can accurately represent the wavefield as predicted by numerical approaches in several situations where approximations such as PAVA and NACT are insufficient. The Born 3D waveform sensitivity kernels are used to perform a higher resolution inversion of regional waveforms for a smaller subregion between longitudes 90 and 150 degrees E, and latitudes 15 and 40 degrees N. To further increase the accuracy of this model, we intend to utilize a very
Zhu, Jiajian; Gao, Jinlong; Ehn, Andreas; Aldén, Marcus; Li, Zhongshan E-mail: email@example.com; Moseev, Dmitry; Kusano, Yukihiro; Salewski, Mirko; Alpers, Andreas E-mail: firstname.lastname@example.org; Gritzmann, Peter; Schwenk, Martin
A non-thermal gliding arc discharge was generated at atmospheric pressure in an air flow. The dynamics of the plasma column and tracer particles were recorded using two synchronized high-speed cameras. Whereas the data analysis for such systems has previously been performed in 2D (analyzing the single camera image), we provide here a 3D data analysis that includes 3D reconstructions of the plasma column and 3D particle tracking velocimetry based on discrete tomography methods. The 3D analysis, in particular, the determination of the 3D slip velocity between the plasma column and the gas flow, gives more realistic insight into the convection cooling process. Additionally, with the determination of the 3D slip velocity and the 3D length of the plasma column, we give more accurate estimates for the drag force, the electric field strength, the power per unit length, and the radius of the conducting zone of the plasma column.
Cox, L. H.; Wilson, G. A.; Zhdanov, M. S.; Sunwall, D. A.
Geophysicists know and accept that geology is inherently 3D, and is resultant from complex, overlapping processes related to genesis, metamorphism, deformation, alteration, weathering, and/or hydrogeology. Yet, the geophysics community has long relied on qualitative analysis, conductivity depth imaging (CDIs), 1D inversion, and/or plate modeling. There are many reasons for this deficiency, not the least of which has been the lack of capacity for historic 3D AEM inversion algorithms to invert entire surveys so as to practically affect exploration decisions. Our recent introduction of a moving sensitivity domain (footprint) methodology has been a paradigm shift in AEM interpretation. The basis of this method is that one needs only to calculate the responses and sensitivities for that part of the 3D earth model that is within the AEM system's sensitivity domain (footprint), and then superimpose all sensitivity domains into a single, sparse sensitivity matrix for the entire 3D earth model which is then updated in a regularized inversion scheme. This has made it practical to rigorously invert entire surveys with thousands of line kilometers of AEM data to mega-cell 3D models in hours using multi-processor workstations. Since 2010, over eighty individual projects have been completed for Aerodat, AEROTEM, DIGHEM, GEOTEM, HELITEM, HoisTEM, MEGATEM, RepTEM, RESOLVE, SkyTEM, SPECTREM, TEMPEST, and VTEM data from Australia, Brazil, Canada, Finland, Ghana, Peru, Tanzania, the US, and Zambia. Examples of 3D AEM inversion have been published for a variety of applications, including mineral exploration, oil sands exploration, salinity, permafrost, and bathymetry mapping. In this paper, we present a comparison of 3D inversions for SkyTEM, SPECTREM, TEMPET and VTEM data acquired over the same area in the Musgrave region of South Australia for exploration under cover.
Tietze, Kristina; Ritter, Oliver; Egbert, Gary D.
With advancing computational resources, 3-D inversion techniques have become feasible in recent years and are now a more widely used tool for magnetotelluric (MT) data interpretation. Galvanic distortion caused by small-scale near-surface inhomogeneities remains an obstacle for 3-D MT inversion which so far has experienced little attention. If not considered properly, the effect on 3-D inversion can be immense and result in erroneous subsurface models and interpretations. To tackle the problem we implemented inversion of the distortion-free phase tensor into the ModEM inversion package. The dimensionless phase tensor components describe only variations of the conductivity structure. When inverting these data, particular care has to be taken of the conductivity structure in the a priori model, which provides the reference frame when transferring the information from phase tensors into absolute conductivity values. Our results obtained with synthetic data show that phase tensor inversion can recover the regional conductivity structure in presence of galvanic distortion if the a priori model provides a reasonable assumption for the regional resistivity average. Joint inversion of phase tensor data and vertical magnetic transfer functions improves recovery of the absolute resistivity structure and is less dependent on the prior model. We also used phase tensor inversion for a data set of more than 250 MT sites from the central San Andreas fault, California, where a number of sites showed significant galvanic distortion. We find the regional structure of the phase tensor inversion results compatible with previously obtained models from impedance inversion. In the vicinity of distorted sites, phase tensor inversion models exhibit more homogeneous/smoother conductivity structures.
Hejrani, B.; Tkalcic, H.; Fichtner, A.
Australia is surrounded by active complex tectonic belts causing significant seismicity. The recent expansion of permanent seismic networks in the Australasian region provides great opportunity to study Earth structure and a great variety of physical mechanisms responsible for earthquakes.On one hand, a better understanding of the Australasian lithosphere, which is now available through tomographic images from full waveform modelling (Fichtner et al. 2010), provides a powerful tool to scrutinize the determination of earthquake source parameters. Even at relatively long periods (40-200s), the 3D effects of regional structure were shown to significantly alter the global centroid moment tensor solutions (Hingee et al. 2012). Thus, we can now explore other types of uncertainties and test the accuracy of global centroid moment tensor (GCMT) solution for the earthquakes in the Australasian region while checking for the systematic inconsistencies in the solutions. This has a significant bearing on tectonic interpretations. For example, azimuth and plunge of fault planes can be investigated in search for systematic biases.On the other hand, the time has come to take a full advantage of the 3D Earth structural model and embrace ongoing advances in computational power and storage. We develop a semi-automated procedure to calculate the Centroid Moment Tensors in a 3D heterogeneous Earth. We utilize the reciprocity theorem to create Green's functions for point sources covering seismogenic zones of Australasia. We focus on improving the capacity of the method to fully complement the existing monitoring tools at Geosciences Australia. Furthermore, we investigate the effects of detailed velocity structure on Centroid location and double-couple percentages. Moreover Azimuth and Plunge of focal mechanisms in GCMT (Global CMT), were investigated in search for any systematic bias.References: Fichtner, A., Kennett, B.L.N., Igel, H., Bunge, H.-P., 2010. Full waveform tomography for
Hicks, S. P.; Rietbrock, A.; Ryder, I. M.; Nippress, S.; Haberland, C. A.
The 2010 Mw=8.8 Maule, Chile earthquake is one of the largest subduction zone earthquakes ever recorded. Up to now numerous co-seismic and some post-seismic slip models have been published based entirely on seismological, geodetic, or tsunami run-up heights, or combinations of these data. Most of these models use a simplified megathrust geometry derived mainly from global earthquake catalogues, and also simplified models of seismic parameters (e.g. shear modulus). By using arrival times for a vast number of aftershocks that have been recorded on a temporary seismic array, we present a new model for the slab geometry based on earthquake locations together with a new 3D seismic velocity model of the region, for both vp and vp/vs. We analyzed 3552 aftershocks that occurred between 18 March and 24 May 2011, recorded by the International Maule Aftershock Dataset (IMAD) seismic network. Event selection from a catalogue of automatically-determined events was based on 20 or more arrival times, from which at least 10 are S-wave observations. In total over 170,000 arrival times (~125,000 and 45,000 P and S wave arrival times respectively) are used for the tomographic reconstructions. Initially, events were relocated in a 2D velocity model based on a previously published model for the southern end of the rupture area (Haberland et al., 2009). Afterwards a staggered inversion scheme is implemented, starting with a 2D inversion followed by a coarse 3D and a subsequent fine 3D inversion. Based on our preliminary inversions we conclude that aftershock seismicity is mainly concentrated between 20 and 35 km depth along the subduction interface. A second band of seismicity between 40 and 50 km depth is also observed. Low seismic velocities and an increased vp/vs ratio characterize the marine forearc. The obtained velocity model will be discussed.
López-Caballero, Miguel; Burguete, Javier
The existence of energy cascades as signatures of conserved magnitudes is one of the universal characteristics of turbulent flows. In homogeneous 3D turbulence, the energy conservation produces a direct cascade from large to small scales, although in 2D, it produces an inverse cascade pointing towards small wave numbers. In this Letter, we present the first evidence of an inverse cascade in a fully developed 3D experimental turbulent flow where the conserved magnitude is the angular momentum. Two counterrotating flows collide in a central region where very large fluctuations are produced, generating a turbulent drag that transfers the external torque between different fluid layers. PMID:25166809
Kozlovskaya, Elena; Budraitis, Mantas; Janutyte, Ilma; Motuza, Gediminas; Lazauskiene, Jurga; Passeq-Working Group
into a density model using a special procedure, in which the density model is approximated by relationship between seismic velocity and density and the latter is found by inverting of the Bouguer anomaly. Comparison of the inversion results to the observed Bouguer anomaly showed that the upper part of the model needs to be corrected, in particular, in the regions not covered by the profiles. The epicentres of events relocated with the use of both VELEST algorithm and a 3-D velocity model are much less scattered and can be grouped into several clusters, some of which are confined to known areas of human activity. However, one group of events is spatially coincident with the region of two large earthquakes in Kaliningrad region in September, 2004, while another cluster shows good coincidence with known region of historical seismicity in Latvia.
Sun, Y.; Martin, R. V.; Toksoz, M. N.; Pei, S.
The lithospheric structure in central Asia features large blocks such as the Indian plate, the Afghan block, the Turan plate, and the Tarim block. This geologically and tectonically complicated area is also one of the most seismically active regions in the world. We developed P- and S- wave velocity structures of the central Asia in the crust using the traveltime data from Kyrgyzstan, Tajikistan, Kazakhstan, and Uzbek. We chose the events and stations between 32N65E and 45N85E and focused on the areas of Pamir and western Tianshan. In this data set, there are more than 6000 P and S arrivals received at 80 stations from about 300 events. The double difference tomography is applied to relocate events and to invert for seismic structures simultaneously. Our results provide accurate locations of earthquakes and high resolution crustal structure in this region. To extend the model deeper into the mantle through the upper mantle transition zone, ISC/EHB data for P and PP phases are combined with the ABCE data. To counteract the “smearing effect,” the crust and upper mantle velocity structure, derived from regional travel-times, is used. An adaptive grid method based on ray density is used in the inversion. A P-wave velocity model extending down to a depth of 2000 km is obtained. regional-teleseismic tomography provides a high-resolution, 3-D P-wave velocity model for the crust, upper mantle, and the transition zone. The crustal models correlate well with geologic and tectonic features. The upper mantle tomograms show the images of Tian Shan. The slab geometry is quite complex, reflecting the history of the changes in the plate motions and collision processes. Vp/Vs tomography was also determined in the study region, and an attenuation tomography was obtained as well.
Carlson, Leland A.
Several inverse methods have been compared and initial results indicate that differences in results are primarily due to coordinate systems and fuselage representations and not to design procedures. Further, results from a direct-inverse method that includes 3-D wing boundary layer effects, wake curvature, and wake displacement are presented. These results show that boundary layer displacements must be included in the design process for accurate results.
Shamsipour, Pejman; Schetselaar, Ernst; Bellefleur, Gilles; Marcotte, Denis
We introduce a new method to include structural orientation constraints into potential field inversion using a stochastic framework. The method considers known geological interfaces and planar orientation data such as stratification estimated from seismic surveys or drill hole information. Integrating prior geological information into inversion methods can effectively reduce ambiguity and improve inversion results. The presented approach uses cokriging prediction with derivatives. The method is applied to two synthetic models to demonstrate its suitability for 3D inversion of potential field data. The method is also applied to the inversion of gravity data collected over the Lalor volcanogenic massive sulfide deposit at Snow Lake, Central Manitoba, Canada. The results show that using a structurally-constrained inversion leads to a better-resolved solution.
Chen, Hao-peng; Zhu, Liang-bao; Wang, Qing-dong; Zhang, Pan; Yang, Ying-hang
We constructed the S-wave velocity structure of the crust and uppermost mantle (10-100 km) beneath the North China based on the teleseismic data recorded by 187 portable broadband stations deployed in this region. The traditional two-step inversion scheme was adopted. Firstly, we measured the interstation fundamental Rayleigh wave phase velocity of 10-60 s and imaged the phase velocity distributions using the Tarantola inversion method. Secondly, we inverted the 1-D S-wave velocity structure with a grid spacing of 0.25° × 0.25° and constructed the 3-D S-wave velocity structure of the North China. The 3-D S-wave velocity model provides valuable information about the destruction mechanism and geodynamics of the North China Craton (NCC). The S-wave velocity structures in the northwestern and southwestern sides of the North-South Gravity Lineament (NSGL) are obviously different. The southeastern side is high velocity (high-V) while the northeastern side is low velocity (low-V) at the depth of 60-80 km. The upwelling asthenosphere above the stagnated Pacific plate may cause the destruction of the Eastern Block and form the NSGL. A prominent low-V anomaly exists around Datong from 50 to 100 km, which may due to the upwelling asthenosphere originating from the mantle transition zone beneath the Western Block. The upwelling asthenosphere beneath the Datong may also contribute to the destruction of the Eastern Block. The Zhangjiakou-Penglai fault zone (ZPFZ) may cut through the lithosphere and act as a channel of the upwelling asthenosphere. A noticeable low-V zone also exists in the lower crust and upper mantle lid (30-50 km) beneath the Beijing-Tianjin-Tangshan (BTT) region, which may be caused by the upwelling asthenosphere through the ZPFZ.
Ground penetrating radar is increasingly being used to provide quantitative information of layered structures. For application in civil engineering these can be roads, highway pavements, airport runways, bridges, tunnels, or buildings. Monitoring is important for the management and safety of these structures. Standard imaging uses a modeled wavefield extrapolator to image the data and the quality of the image depends heavily on the quality of the modeled extrapolator. Usually, data inversion is implemented by minimizing a cost function involving the measured data and the modeled data. The model is modified such that data computed from the model fits to the measured data. The data itself is not used, except as a measure of the model data fit. A recently developed alternative method is to use results from inverse scattering theory to first construct an image while all multiple reflections are simultaneously eliminated from the data. This image can be constructed from surface reflection data if the data allows separating the subsurface reflection response from the down going emitted field. For 3D waves in a layered medium this requires knowledge of all horizontal electric and magnetic field components. If the data is properly sampled the solution is unique. In layered media the plane wave decomposition allows computing the image for each angle of incidence separately as a function of image time that is equal to the one-way intercept time. Once the image is constructed for all available angles of incidence a simple matrix inversion leads to the desired electric permittivity and magnetic permeability values in each layer. Finally these values provide interval velocities that can be used to convert image time to depth and the inverse problem is solved. The theory requires infinite bandwidth frequency domain data, which is equivalent to measuring the true impulse response. This is not possible in practice and numerical results show that data with finite bandwidths can be
Floriane, Provost; Jean-Philippe, Malet; Cécile, Doubre; Julien, Gance; Alessia, Maggi; Agnès, Helmstetter
Characterizing the micro-seismic activity of landslides is an important parameter for a better understanding of the physical processes controlling landslide behaviour. However, the location of the seismic sources on landslides is a challenging task mostly because of (a) the recording system geometry, (b) the lack of clear P-wave arrivals and clear wave differentiation, (c) the heterogeneous velocities of the ground. The objective of this work is therefore to test whether the integration of a 3D velocity model in probabilistic seismic source location codes improves the quality of the determination especially in depth. We studied the clay-rich landslide of Super-Sauze (French Alps). Most of the seismic events (rockfalls, slidequakes, tremors...) are generated in the upper part of the landslide near the main scarp. The seismic recording system is composed of two antennas with four vertical seismometers each located on the east and west sides of the seismically active part of the landslide. A refraction seismic campaign was conducted in August 2014 and a 3D P-wave model has been estimated using the Quasi-Newton tomography inversion algorithm. The shots of the seismic campaign are used as calibration shots to test the performance of the different location methods and to further update the 3D velocity model. Natural seismic events are detected with a semi-automatic technique using a frequency threshold. The first arrivals are picked using a kurtosis-based method and compared to the manual picking. Several location methods were finally tested. We compared a non-linear probabilistic method coupled with the 3D P-wave model and a beam-forming method inverted for an apparent velocity. We found that the Quasi-Newton tomography inversion algorithm provides results coherent with the original underlaying topography. The velocity ranges from 500 m.s-1 at the surface to 3000 m.s-1 in the bedrock. For the majority of the calibration shots, the use of a 3D velocity model
Zeng, X.; Thurber, C. H.; Shelly, D. R.; Bennington, N. L.; Cochran, E. S.; Harrington, R. M.
We have assembled a new dataset to refine the 3D seismic velocity model in the Parkfield region. The S arrivals from 184 earthquakes recorded by the Parkfield Experiment to Record MIcroseismicity and Tremor array (PERMIT) during 2010-2011 were picked by a new S wave picker, which is based on machine learning. 74 blasts have been assigned to four quarries, whose locations were identified with Google Earth. About 1000 P and S wave arrivals from these blasts at permanent seismic network were also incorporated. Low frequency earthquakes (LFEs) occurring within non-volcanic tremor (NVT) are valuable for improving the precision of NVT location and the seismic velocity model at greater depths. Based on previous work (Shelley and Hardebeck, 2010), waveforms of hundreds of LFEs in same family were stacked to improve signal qualify. In a previous study (McClement et al., 2013), stacked traces of more than 30 LFE families at the Parkfileld Array Seismic Observatory (PASO) have been picked. We expanded our work to include LFEs recorded by the PERMIT array. The time-frequency Phase Weight Stacking (tf-PWS) method was introduced to improve the stack quality, as direct stacking does not produce clear S-wave arrivals on the PERMIT stations. This technique uses the coherence of the instantaneous phase among the stacked signals to enhance the signal-to-noise ratio (SNR) of the stack. We found that it is extremely effective for picking LFE arrivals (Thurber et al., 2014). More than 500 P and about 1000 S arrivals from 58 LFE families were picked at the PERMIT and PASO arrays. Since the depths of LFEs are much deeper than earthquakes, we are able to extend model resolution to lower crustal depths. Both P and S wave velocity structure have been obtained with the tomoDD method. The result suggests that there is a low velocity zone (LVZ) in the lower crust and the location of the LVZ is consistent with the high conductivity zone beneath the southern segment of the Rinconada fault that
Petrov, P.; Newman, G. A.
An application of the 3D elastic full-waveform inversion (FWI) to wide-aperture seismic data obtained for a complex geological setting is presented. Imaging is implemented in the Fourier domain, exploiting damped wave fields. The modeling part is solved with a finite-difference method. The non-linear conjugate gradient method is used for the inverse problem solution. The nonlinearity of FWI leads to the presence of local and multiple minima in the least-squares error functional especially for large offset problems. That leads to the shutdown of the inverse problem convergence and uncertainty in the solution. An accurate starting velocity model can avoid this problem, but in many cases may not be available. Hence other strategies are necessary to address the problem. We propose a robust inversion process for an arbitrary starting velocity model, which allows avoiding local minima and obtaining acceptable images of the deep seated structures defined by large offset data. We proceed from the assumption that decreasing data offset reduces local minima problems but decreases the depth of the recovered image. So, the inversion process is realized sequentially from small to large offsets, allowing recovery of geological structures over the entire depth range of interest from the near surface to deeper depths sensed only by large aperture offsets. Increasing of data offset is first performed at the lowest frequency and then proceeding with treatment of all data offsets from low to high frequencies. A reverse loop is also implemented in the laddering of frequencies, where after the inversion at high frequencies and all offsets we return to the lower frequencies data to continue the IP. Returning to lower frequency data provides helping to ameliorate multiple minima encountered in the inversion. The inversion then concludes by sweeping over higher frequency data, at all offsets. We demonstrate our strategies for treating wide aperture offset data on the Marmousi model, using
Hartzell, S.; Harmsen, S.; Frankel, A.
Three-dimensional, finite-difference simulations of a realistic finite-fault rupture on the southern Hayward fault are used to evaluate the effects of random, correlated velocity perturbations on predicted ground motions. Velocity perturbations are added to a three-dimensional (3D) regional seismic velocity model of the San Francisco Bay Area using a 3D von Karman random medium. Velocity correlation lengths of 5 and 10 km and standard deviations in the velocity of 5% and 10% are considered. The results show that significant deviations in predicted ground velocities are seen in the calculated frequency range (≤1 Hz) for standard deviations in velocity of 5% to 10%. These results have implications for the practical limits on the accuracy of scenario ground-motion calculations and on retrieval of source parameters using higher-frequency, strong-motion data.
Jaysaval, Piyoosh; Shantsev, Daniil; de la Kethulle de Ryhove, Sébastien
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.
Shentu, Nanying; Qiu, Guohua; Li, Qing; Tong, Renyuan; Shentu, Nankai; Wang, Yanjie
Underground displacement monitoring is a key means to monitor and evaluate geological disasters and geotechnical projects. There exist few practical instruments able to monitor subsurface horizontal and vertical displacements simultaneously due to monitoring invisibility and complexity. A novel underground displacement 3D measuring sensor had been proposed in our previous studies, and great efforts have been taken in the basic theoretical research of underground displacement sensing and measuring characteristics by virtue of modeling, simulation and experiments. This paper presents an innovative underground displacement joint inversion method by mixing a specific forward modeling approach with an approximate optimization inversion procedure. It can realize a joint inversion of underground horizontal displacement and vertical displacement for the proposed 3D sensor. Comparative studies have been conducted between the measured and inversed parameters of underground horizontal and vertical displacements under a variety of experimental and inverse conditions. The results showed that when experimentally measured horizontal displacements and vertical displacements are both varied within 0 ~ 30 mm, horizontal displacement and vertical displacement inversion discrepancies are generally less than 3 mm and 1 mm, respectively, under three kinds of simulated underground displacement monitoring circumstances. This implies that our proposed underground displacement joint inversion method is robust and efficient to predict the measuring values of underground horizontal and vertical displacements for the proposed sensor. PMID:25871714
Liu, Q.; Tape, C.; Maggi, A.; Tromp, J.
We use adjoint methods popular in climate and ocean dynamics to calculate Fréchet derivatives for tomographic inversions in southern California. The Fréchet derivative of an objective function χ(m), where m denotes the Earth model, may be written in the generic form δχ=int Km(x) δln m(x) d3x, where δln m=δ m/m denotes the relative model perturbation. For illustrative purposes, we construct the 3-D finite-frequency banana-doughnut kernel Km, corresponding to the misfit of a single traveltime measurement, by simultaneously computing the 'adjoint' wave field s† forward in time and reconstructing the regular wave field s backward in time. The adjoint wave field is produced by using the time-reversed velocity at the receiver as a fictitious source, while the regular wave field is reconstructed on the fly by propagating the last frame of the wave field saved by a previous forward simulation backward in time. The approach is based upon the spectral-element method, and only two simulations are needed to produce density, shear-wave, and compressional-wave sensitivity kernels. This method is applied to the SCEC southern California velocity model. Various density, shear-wave, and compressional-wave sensitivity kernels are presented for different phases in the seismograms. We also generate 'event' kernels for Pnl, S and surface waves, which are the Fréchet kernels of misfit functions that measure the P, S or surface wave traveltime residuals at all the receivers simultaneously for one particular event. Effectively, an event kernel is a sum of weighted Fréchet kernels, with weights determined by the associated traveltime anomalies. By the nature of the 3-D simulation, every event kernel is also computed based upon just two simulations, i.e., its construction costs the same amount of computation time as an individual banana-doughnut kernel. One can think of the sum of the event kernels for all available earthquakes, called the 'misfit' kernel, as a graphical
Kang, Peter K.; Anna, Pietro; Nunes, Joao P.; Bijeljic, Branko; Blunt, Martin J.; Juanes, Ruben
We study the nature of non-Fickian particle transport in 3-D porous media by simulating fluid flow in the intricate pore space of real rock. We solve the full Navier-Stokes equations at the same resolution as the 3-D micro-CT (computed tomography) image of the rock sample and simulate particle transport along the streamlines of the velocity field. We find that transport at the pore scale is markedly anomalous: longitudinal spreading is superdiffusive, while transverse spreading is subdiffusive. We demonstrate that this anomalous behavior originates from the intermittent structure of the velocity field at the pore scale, which in turn emanates from the interplay between velocity heterogeneity and velocity correlation. Finally, we propose a continuous time random walk model that honors this intermittent structure at the pore scale and captures the anomalous 3-D transport behavior at the macroscale.
Abd allah, S.; Mogi, T.; Kim, H.; Fomenko, E.
Previous studies conducted by the Grounded Electrical-Source Airborne Transient Electromagnetic (GREATEM) have shown that, this system is a promising method for modelling 3D resistivity structures in coastal areas. To expand the application of the GREATEM system in the future for studying hazardous wastes, sea water incursion and hydrocarbon exploration, a 3D-resistivity modelling that considers large lateral resistivity variations is required in case of large resistivity contrasts between land and sea in surveys of coastal areas where 1D resistivity model that assumes a horizontally layered structure might be inaccurate. In this abstract we present the preparation for developing a consistent three dimensional electromagnetic inversion algorithm to calculate the EM response over arbitrary 3D conductivity structure using GREATEM system. In forward modelling the second order partial differential equations for scalar and vector potential are discretized on a staggered-grid using the finite difference method (Fomenko and Mogi, 2002, Mogi et al., 2011). In the inversion method the 3D model discretized into a large number of rectangular cells of constant conductivity and the final solution is obtained by minimizing a global objective function composed of the model objective function and data misfit. To deal with a huge number of grids and wide range of frequencies in air borne data sets, a method for approximating sensitivities is introduced for the efficient 3-D inversion. Approximate sensitivities are derived by replacing adjoint secondary electric fields with those computed in the previous iteration. These sensitivities can reduce the computation time, without significant loss of accuracy when constructing a full sensitivity matrix for 3-D inversion, based on the Gauss-Newton method (N. Han et al., 2008). Now, we tested the algorithm in the frequency domain electromagnetic response of synthetic model considering a 3D conductor. Frequency-domain computation is executed
Rosas-Carbajal, M.; Linde, N.; Peacock, J.; Zyserman, F. I.; Kalscheuer, T.; Thiel, S.
Surface-based monitoring of mass transfer caused by injections and extractions in deep boreholes is crucial to maximize oil, gas and geothermal production. Inductive electromagnetic methods, such as magnetotellurics, are appealing for these applications due to their large penetration depths and sensitivity to changes in fluid conductivity and fracture connectivity. In this work, we propose a 3-D Markov chain Monte Carlo inversion of time-lapse magnetotelluric data to image mass transfer following a saline fluid injection. The inversion estimates the posterior probability density function of the resulting plume, and thereby quantifies model uncertainty. To decrease computation times, we base the parametrization on a reduced Legendre moment decomposition of the plume. A synthetic test shows that our methodology is effective when the electrical resistivity structure prior to the injection is well known. The centre of mass and spread of the plume are well retrieved. We then apply our inversion strategy to an injection experiment in an enhanced geothermal system at Paralana, South Australia, and compare it to a 3-D deterministic time-lapse inversion. The latter retrieves resistivity changes that are more shallow than the actual injection interval, whereas the probabilistic inversion retrieves plumes that are located at the correct depths and oriented in a preferential north-south direction. To explain the time-lapse data, the inversion requires unrealistically large resistivity changes with respect to the base model. We suggest that this is partly explained by unaccounted subsurface heterogeneities in the base model from which time-lapse changes are inferred.
Meng, Zhaohai; Li, Fengting; Zhang, Dailei; Xu, Xuechun; Huang, Danian
We developed a new fast inversion method for to process and interpret airborne gravity gradiometry data, which was based on Lanczos bidiagonalization algorithm. Here, we describe the application of this new 3D gravity gradiometry inversion method to recover a subsurface density distribution model from the airborne measured gravity gradiometry anomalies. For this purpose, the survey area is divided into a large number of rectangular cells with each cell possessing a constant unknown density. It is well known that the solution of large linear gravity gradiometry is an ill-posed problem since using the smoothest inversion method is considerably time consuming. We demonstrate that the Lanczos bidiagonalization method can be an appropriate algorithm to solve a Tikhonov solver time cost function for resolving the large equations within a short time. Lanczos bidiagonalization is designed to make the very large gravity gradiometry forward modeling matrices to become low-rank, which will considerably reduce the running time of the inversion method. We also use a weighted generalized cross validation method to choose the appropriate Tikhonov parameter to improve inversion results. The inversion incorporates a model norm that allows us to attain the smoothing and depth of the solution; in addition, the model norm counteracts the natural decay of the kernels, which concentrate at shallow depths. The method is applied on noise-contaminated synthetic gravity gradiometry data to demonstrate its suitability for large 3D gravity gradiometry data inversion. The airborne gravity gradiometry data from the Vinton Salt Dome, USE, were considered as a case study. The validity of the new method on real data is discussed with reference to the Vinton Dome inversion result. The intermediate density values in the constructed model coincide well with previous results and geological information. This demonstrates the validity of the gravity gradiometry inversion method.
Bayrakci, Gaye; Minshull, Timothy A.; Davy, Richard G.; Karplus, Marianne S.; Kaeschen, Dirk; Papenberg, Cord; Krabbenhoeft, Anne; Sawyer, Dale; Reston, Timothy J.; Shillington, Donna J.; Ranero, César R.
Galicia 3D, a reflection-refraction and long offset seismic experiment was carried out from May through September 2013, at the Galicia rifted margin (in the northeast Atlantic Ocean, west of Spain) as a collaboration between US, UK, German and Spanish groups. The 3D multichannel seismic acquisition conducted by R/V Marcus Langseth covered a 64 km by 20 km (1280 km2) zone where the main geological features are the Peridotite Ridge (PR), composed of serpentinized peridotite and thought be upper mantle exhumed to the seafloor during rifting, and the S reflector which has been interpreted to be a low angle detachment fault overlain by fault bounded, rotated, continental crustal blocks. In the 3D box, two airgun arrays of 3300 cu.in. were fired alternately (in flip-flop configuration) every 37.5 m. All shots are recorded by 44 short period four component ocean bottom seismometers (OBS) and 26 ocean bottom hydrophones (OBH) deployed and recovered by R/V Poseidon, as well as four 6 km hydrophone streamers with 12.5 m channel spacing towed by R/V Marcus Langseth. We present the preliminary results of the first arrival time tomography study which is carried out with a subset of the wide-angle dataset, in order to generate a 3D P-wave velocity volume for the entire depth sampled by the reflection data. After the relocation of OBSs and OBHs, an automatic first-arrival time picking approach is applied to a subset of the dataset, which comprises more than 5.5 million source-receiver pairs. Then, the first-arrival times are checked visually, in 3-dimensions. The a priori model used for the first-arrival time tomography is built up using information from previous seismic surveys carried out at the Galicia margin (e.g. ISE, 1997). The FAST algorithm of Zelt and Barton (1998) is used for the first-arrival time inversion. The 3D P-wave velocity volume can be used in interpreting the reflection dataset, as a starting point for migration, to quantify the thinning of the crustal layers
Chaves, C. M.; Ussami, N.
Modeling density perturbations is very important to understand geodynamic processes which occur within the Earth's mantle. Commonly, the Earth's density is predicted by converting a velocity model into a density model using either a constant scaling factor or a relationship provided by mineral physics. Nonetheless, several factors such as temperature, composition and melting can affect the wave propagation speed so that a seismically converted density model may not retrieve the actual density distribution. This limitation may hamper the modeling the geodynamic processes. Due to advances in satellite-derived gravity data acquisition (e.g. GRACE, GOCE), the gravity field is now obtained with an unprecedented accuracy and resolution allowing us to estimate more uniformly the 3-D density distribution for the whole Earth. Here we present a computational algorithm to invert geoid anomalies in order to estimate density variations in the mantle. Using an ellipsoidal-Earth approximation, the model space is represented by a set of tesseroids. From a synthetic geoid anomaly caused by a plume tail ascending through the mantle with Gaussian noise added, the inversion code is capable to recover with good accuracy the density contrast and the body geometry when compared to the synthetic model. This algorithm was also tested in a natural case study, where geoid anomalies from the Yellowstone Province (YP) were inverted. The estimated density model (EDM) has a predominantly negative density contrast (~ -50 kg/m3) relative to the surrounding upper mantle and extends to the depth of 1000 km. The EDM exhibits an anti-correlation of up to -0.7 with one of the most recent S-velocity model for the western United States. The predicted dynamic topography from the EDM explains almost 80 % of the observed dynamic topography in the YP. From our results, we conclude that a joint-interpretation of density anomalies derived from geoid and velocity perturbations from seismic tomography models
Barnoud, Anne; Coutant, Olivier; Bouligand, Claire; Gunawan, Hendra; Deroussi, Sébastien
We use a Bayesian formalism combined with a grid node discretization for the linear inversion of gravimetric data in terms of 3-D density distribution. The forward modelling and the inversion method are derived from seismological inversion techniques in order to facilitate joint inversion or interpretation of density and seismic velocity models. The Bayesian formulation introduces covariance matrices on model parameters to regularize the ill-posed problem and reduce the non-uniqueness of the solution. This formalism favours smooth solutions and allows us to specify a spatial correlation length and to perform inversions at multiple scales. We also extract resolution parameters from the resolution matrix to discuss how well our density models are resolved. This method is applied to the inversion of data from the volcanic island of Basse-Terre in Guadeloupe, Lesser Antilles. A series of synthetic tests are performed to investigate advantages and limitations of the methodology in this context. This study results in the first 3-D density models of the island of Basse-Terre for which we identify: (i) a southward decrease of densities parallel to the migration of volcanic activity within the island, (ii) three dense anomalies beneath Petite Plaine Valley, Beaugendre Valley and the Grande-Découverte-Carmichaël-Soufrière Complex that may reflect the trace of former major volcanic feeding systems, (iii) shallow low-density anomalies in the southern part of Basse-Terre, especially around La Soufrière active volcano, Piton de Bouillante edifice and along the western coast, reflecting the presence of hydrothermal systems and fractured and altered rocks.
Duindam, Vincent; Xu, Jijie; Alterovitz, Ron; Sastry, Shankar; Goldberg, Ken
Steerable needles can be used in medical applications to reach targets behind sensitive or impenetrable areas. The kinematics of a steerable needle are nonholonomic and, in 2D, equivalent to a Dubins car with constant radius of curvature. In 3D, the needle can be interpreted as an airplane with constant speed and pitch rate, zero yaw, and controllable roll angle. We present a constant-time motion planning algorithm for steerable needles based on explicit geometric inverse kinematics similar to the classic Paden-Kahan subproblems. Reachability and path competitivity are analyzed using analytic comparisons with shortest path solutions for the Dubins car (for 2D) and numerical simulations (for 3D). We also present an algorithm for local path adaptation using null-space results from redundant manipulator theory. Finally, we discuss several ways to use and extend the inverse kinematics solution to generate needle paths that avoid obstacles. PMID:21359051
Miller, C. R.; Routh, P. S.; Donaldson, P.; Oldenburg, D. W.
Controlled Source Audio-Frequency Magnetotellurics (CSAMT) is a frequency domain EM sounding technique. The CSAMT source is a grounded horizontal electric dipole approximately one to two kilometers in length. This dipole source generates both inductive and galvanic currents so that the observed electric field arises due to both the static the vector potentials. At low frequencies, the behavior of the fields is similar to that observed in a geometric sounding such as a direct current experiment. At higher frequencies, the inductive character of the source modifies the behavior of the fields so that the experiment becomes more like a frequency sounding. Higher frequency data are useful for imaging near-surface features and lower frequency data are sensitive to deeper structure. Inversion of controlled source EM data provides a means to image the subsurface electrical conductivity structure. We consider a 3D CSAMT data set acquired over a known geothermal resource area in Western Idaho. The data are amplitudes and phases of the electric and magnetic fields acquired at 25 frequencies. The conductivity contrast between the geothermal fluid conduits and the resistive host material allows us to relate the inverted conductivity image to the distribution of fluid flow pathways in the geothermal system. Our 1D CSAMT inversion of the 3D data set indicates regions of conductive fluid pathways in the subsurface. Our next step is to invert these data using the full Maxwell's equations in 3D. Inversion of a single frequency data set at 2 Hz using the 3D frequency domain inversion algorithm (Haber et. al, 2004) shows regions of fluid circulation indicated by zones of higher conductivity. Comparing the images from different single frequency inversions allows us to identify persistent features in the conductivity image that adequately satisfy the data. With the aid of synthetic modeling we are investigating what frequencies? and what geometries? are appropriate to better resolve
Trovato, Claudio; Aochi, Hideo; De Martin, Florent
Understanding the source mechanism of long-period (LP) seismic signals on volcanoes is an important key point in volcanology and for the hazard forecasting. In the last decades, moment tensor inversions have led to various descriptions of the kinematic source mechanism. These inversions suppose a relatively simple structure of the medium. However, the seismic wave propagation in a realistic 3-D volcano model should be taken into account for understanding the complicated physical processes of magma and gas behaviors at depth. We are studying Etna volcano, Italy, to understand the volcanic processes during different stages of activity. We adopt a spectral element method (SEM), a code EFISPEC3D (De Martin, BSSA, 2011), which shows a good accuracy and numerical stability in the simulations of seismic wave propagation. First we construct the geometrical model. We use a digital elevation model (DEM) to generate finite element meshes with a spacing of 50 m on the ground surface. We aim to calculate the ground motions until 3 Hz for the shallowest layer with Vs = ~500 m/s. The minimal size of the hexahedral elements is required to be around 100 m, with a total number of elements n = ~2 10 ^ 6 for the whole model. We compare different velocity structure configurations. We start with a homogeneous medium and add complexities taking in account the shallow low velocity structure. We also introduce a velocity gradient towards depth. Simulations performed in the homogeneous medium turn in approximately 20 hours for calculations parallelized on 16 CPUs. Complex velocity models should take approximately the same time of computation. We then try to simulate the ground motion from the LP sources (0.1-1.5 Hz) obtained by the inversion for the Etna volcano in 2008 (De Barros, GRL, 2009 and De Barros, JGR, 2011). Some vertical and horizontal structures can be added to reproduce injected dikes or sills respectively.
Hegge, R.F.; Herman, G.C.; Sevink, A.G.J.
The application of high-frequency asymptotic Born inverse scattering methods to cross-well imaging is discussed and illustrated with a number of model studies for synthetic data. In particular, attention is given to imaging problems that are associated with typical cross-well geometries. A severe problem is the existence of multiple travel paths between sources and receivers that are particularly apparent if low-velocity layers are present. When this occurs, the high-frequency asymptotic imaging method is no longer valid and large artifacts in the images can result. However, it is concluded that, even in the case of multiple travel paths, good images can be obtained by omitting the singularities in the imaging formula and by combining the results for different source locations.
Kılıç, Emre Eibert, Thomas F.
An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems. Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained.
Tavakoli, M.; Nejati Kalateh, A.; Ghomi, S.
The thick sedimentary units in Central Iran contain structures that form oil traps and are underlain by a basaltic layer which is amenable for study using its magnetic susceptibility. The study and modeling of such sedimentary structures provide valuable exploratory information. In this study, we locate and interpret an underground magnetic susceptibility interface using 3D non-linear inverse modeling of magnetic data to make a better judgment in the context of hydrocarbon existence. The 3D structure is reconstructed by making it equal to a number of side by side rectangular hexahedrons or prisms and calculating their thicknesses such that the bottoms of the prisms are corresponding to the magnetic susceptibility interface. By one of the most important mathematical tool in computational science, Taylor series, the non-linear problem changes to a linear problem near to initial model. In many inverse problems, we often need to invert large size matrices. To find the inverse of these matrices we use Singular Value Decomposition (SVD) method. The algorithm by an iterative method comparing model response with actual data will modify the initial guess of model parameters. The efficiency of the method and subprograms, programmed in MATLAB, has been shown by inverse modeling of free noise and noise-contaminated synthetic data. Finally, we inverted magnetic field data from Garmsar area in Central Iran which the results were acceptable.
Grayver, Alexander; Streich, Rita; Ritter, Oliver
We present 3D inversion of land controlled-source electromagnetic (CSEM) data collected across the CO2 storage test site at Ketzin, Germany. The CSEM data were generated by injecting currents into the earth at eight locations using a newly developed transmitter equipped with three grounded electrodes. Electric and magnetic field responses were recorded by 39 receivers along a line approximately perpendicular to the main geological trend. The survey aimed at imaging large-scale resistivity structure beyond the near-well region monitored by higher-resolution electrical techniques. Infrastructure present in the survey area, such as pipelines with impressed-current cathodic protection systems, power lines, and wind power plants cause strong noise in the data. The noise is effectively suppressed by adopting statistically robust processing techniques known from passive magnetotellurics. A newly developed Gauss-Newton type parallel distributed inversion scheme, which is based on a direct forward solver and explicitly calculates the full sensitivity matrix, is applied to recover subsurface conductivity images. As 3D inversion is demanding on computer time and memory, we run inversions on parallel distributed machines. We achieve good scalability by distributing computations and memory uniformly among the processes involved. We carry out cumulative sensitivity and resolution analyses for the sparse CSEM acquisition geometry. These studies indicate reasonable spatial coverage along the main survey line. Synthetic studies calculated for the real survey layout and representative conductivity models indicate that the magnetic field components are practically insensitive to resistive structures, whereas the electric field components resolve resistors and conductors similarly well. Because the magnetic field contributes little subsurface information, we concentrate on inverting the electric field, which is also more computer-efficient than inverting all components. We test
Bayrakci, Gaye; Minshull, Timothy; Davy, Richard; Sawyer, Dale; Klaeschen, Dirk; Papenberg, Cord; Reston, Timothy; Shillington, Donna; Ranero, Cesar
The combined wide-angle reflection-refraction and multi-channel seismic (MCS) experiment, Galicia 3D, was carried out in 2013 at the Galicia rifted margin in the northeast Atlantic Ocean, west of Spain. The main geological features within the 64 by 20 km (1280 km²) 3D box investigated by the survey are the peridotite ridge (PR), the fault bounded, rotated basement blocks and the S reflector, which has been interpreted to be a low angle detachment fault. 44 short period four-component ocean bottom seismometers and 28 ocean bottom hydrophones were deployed in the 3D box. 3D MCS profiles sampling the whole box were acquired with two airgun arrays of 3300 cu.in. fired alternately every 37.5 m. We present the results from 3D first-arrival time tomography that constrains the P-wave velocity in the 3D box, for the entire depth sampled by reflection data. Results are validated by synthetic tests and by the comparison with Galicia 3D MCS lines. The main outcomes are as follows: 1- The 3.5 km/s iso-velocity contour mimics the top of the acoustic basement observed on MCS profiles. Block bounding faults are imaged as velocity contrasts and basement blocks exhibit 3D topographic variations. 2- On the southern profiles, the top of the PR rises up to 5.5 km depth whereas, 20 km northward, its basement expression (at 6.5 km depth) nearly disappears. 3- The 6.5 km/s iso-velocity contour matches the topography of the S reflector where the latter is visible on MCS profiles. Within a depth interval of 0.6 km (in average), velocities beneath the S reflector increase from 6.5 km/s to 7 km/s, which would correspond to a decrease in the degree of serpentinization from ~45 % to ~30 % if these velocity variations are caused solely by variations in hydration. At the intersections between the block bounding normal faults and the S reflector, this decrease happens over a larger depth interval (> 1 km), suggesting that faults act as conduit for the water flow in the upper mantle.
Son, Jeong-Sul; Kim, Jung-ho; Park, Sam-gyu; Park, My-Kyung
Complex resistivity (CR) method is a frequency domain induced polarization (IP) method. It is also known as Spectral IP (SIP) method, if wider frequencies are used in data acquisition and interpretation. Although it takes more times than conventional time domain IP method, its data quality is more stable because its data acquisition which measures amplitude and phase is done when the source current is being injected. Our research group has been studying the modeling and inversion algorithms of complex resistivity (CR) method since several years ago and recently applied developed algorithms to various real field application. Due to tough terrain in our country, Profile survey and 2D interpretation were generally used. But to get more precise interpretation, three dimensional modeling and inversion algorithm is required. We developed three dimensional inversion algorithm for this purpose. In the inversion, we adopt the method of adaptive lagraingian multiplier which is automatically set based on the size of error misfit and model regularization norm. It was applied on the real data acquired for mineral exploration sites. CR data was acquired with the Zeta system, manufactured by Zonge Co. In the inversion, only the lower frequency data is used considering its quality and developed 3D inversion algorithm was applied to the acquired data set. Its results were compared to those of time domain IP data conducted at the same site. Resistivity image sections of CR and conventional resistivity method were almost identical. Phase anomalies were well matched with chargeability anomalies and the mining history of the test site. Each anomalies were well discriminated in 3D interpretation than those of 2D. From those experiments, we know that CR method was very effective for the mineral exploration.
Qin, Pengbo; Huang, Danian; Yuan, Yuan; Geng, Meixia; Liu, Jie
Gravity data, which are critical in mineral, oil, and gas exploration, are obtained from the vertical component of the gravity field, while gravity gradient data are measured from changes in the gravity field in three directions. However, few studies have sought to improve exploration techniques by integrating gravity and gravity gradient data using inversion methods. In this study, we developed a new method to integrate gravity and gravity gradient data in a 3D density inversion using the non-linear conjugate gradient (NLCG) method and the minimum gradient support (MGS) functional to regularize the 3D inverse problem and to obtain a clear and accurate image of the anomalous body. The NLCG algorithm, which is suitable for solving large-scale nonlinear optimization problems and requires no memory storage, was compared to the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton algorithm and the results indicated that the convergence rate of NLCG is slower, but that the storage requirement and computation time is lower. To counteract the decay in kernel function, we introduced a depth weighting function for anomalous bodies at the same depth, with information about anomalous body depth obtained from well log and seismic exploration data. For anomalous bodies at different depths, we introduced a spatial gradient weighting function to incorporate additional information obtained in the inversion. We concluded that the spatial gradient weighting function enhanced the spatial resolution of the recovered model. Furthermore, our results showed that including multiple components for inversion increased the resolution of the recovered model. We validated our model by applying our inversion method to survey data from Vinton salt dome, Louisiana, USA. The results showed good agreement with known geologic information; thus confirming the accuracy of this approach.
Rosas-Carbajal, Marina; Linde, Nicolas; Peacock, Jared R.; Zyserman, F. I.; Kalscheuer, Thomas; Thiel, Stephan
Surface-based monitoring of mass transfer caused by injections and extractions in deep boreholes is crucial to maximize oil, gas and geothermal production. Inductive electromagnetic methods, such as magnetotellurics, are appealing for these applications due to their large penetration depths and sensitivity to changes in fluid conductivity and fracture connectivity. In this work, we propose a 3-D Markov chain Monte Carlo inversion of time-lapse magnetotelluric data to image mass transfer following a saline fluid injection. The inversion estimates the posterior probability density function of the resulting plume, and thereby quantifies model uncertainty. To decrease computation times, we base the parametrization on a reduced Legendre moment decomposition of the plume. A synthetic test shows that our methodology is effective when the electrical resistivity structure prior to the injection is well known. The centre of mass and spread of the plume are well retrieved.We then apply our inversion strategy to an injection experiment in an enhanced geothermal system at Paralana, South Australia, and compare it to a 3-D deterministic time-lapse inversion. The latter retrieves resistivity changes that are more shallow than the actual injection interval, whereas the probabilistic inversion retrieves plumes that are located at the correct depths and oriented in a preferential north-south direction. To explain the time-lapse data, the inversion requires unrealistically large resistivity changes with respect to the base model. We suggest that this is partly explained by unaccounted subsurface heterogeneities in the base model from which time-lapse changes are inferred.
Dongari, Nishanth; Barber, Robert W.; Emerson, David R.; Zhang, Yonghao; Reese, Jason M.
We investigate a power-law probability distribution function to describe the mean free path of rarefied gas molecules in non-planar geometries. A new curvature-dependent model is derived by taking into account the boundary-limiting effects on the molecular mean free path for surfaces with both convex and concave curvatures. In comparison to a planar wall, we find that the mean free path for a convex surface is higher at the wall and exhibits a sharper gradient within the Knudsen layer. In contrast, a concave wall exhibits a lower mean free path near the surface and the gradients in the Knudsen layer are shallower. The Navier-Stokes constitutive relations and velocity-slip boundary conditions are modified based on a power-law scaling to describe the mean free path, in accordance with the kinetic theory of gases, i.e. transport properties can be described in terms of the mean free path. Velocity profiles for isothermal cylindrical Couette flow are obtained using the power-law model. We demonstrate that our model is more accurate than the classical slip solution, especially in the transition regime, and we are able to capture important non-linear trends associated with the non-equilibrium physics of the Knudsen layer. In addition, we establish a new criterion for the critical accommodation coefficient that leads to the non-intuitive phenomena of velocity-inversion. Our results are compared with conventional hydrodynamic models and direct simulation Monte Carlo data. The power-law model predicts that the critical accommodation coefficient is significantly lower than that calculated using the classical slip solution and is in good agreement with available DSMC data. Our proposed constitutive scaling for non-planar surfaces is based on simple physical arguments and can be readily implemented in conventional fluid dynamics codes for arbitrary geometric configurations.
Slawinski, Jean; Dumas, Raphaël; Cheze, Laurence; Ontanon, Guy; Miller, Christian; Mazure-Bonnefoy, Alice
Few studies have focused on the effect of posture during sprint start. The aim of this study was to measure the effect of the modification of horizontal distance between the blocks during sprint start on three dimensional (3D) joint angular velocity. Nine trained sprinters started using three different starting positions (bunched, medium and elongated). They were equipped with 63 passive reflective markers, and an opto-electronic Motion Analysis system was used to collect the 3D marker trajectories. During the pushing phase on the blocks, norm of the joint angular velocity (NJAV), 3D Euler angular velocity (EAV) and pushing time on the blocks were calculated. The results demonstrated that the decrease of the block spacing induces an opposite effect on the angular velocity of joints of the lower and the upper limbs. The NJAV of the upper limbs is greater in the bunched start, whereas the NJAV of the lower limbs is smaller. The modifications of NJAV were due to a combination of the movement of the joints in the different degrees of freedom. The medium start seems to be the best compromise because it leads, in a short pushing time, to a combination of optimal joint velocities for upper and lower segments. PMID:23062070
Weston, J.; Ferreira, A. M. G.; Funning, G. J.
A joint earthquake source inversion technique is presented that uses InSAR and long-period teleseismic data, and, for the first time, takes 3-D Earth structure into account when modelling seismic surface and body waves. Ten average source parameters (Moment, latitude, longitude, depth, strike, dip, rake, length, width and slip) are estimated; hence, the technique is potentially useful for rapid source inversions of moderate magnitude earthquakes using multiple data sets. Unwrapped interferograms and long-period seismic data are jointly inverted for the location, fault geometry and seismic moment, using a hybrid downhill Powell-Monte Carlo algorithm. While the InSAR data are modelled assuming a rectangular dislocation in a homogeneous half-space, seismic data are modelled using the spectral element method for a 3-D earth model. The effect of noise and lateral heterogeneity on the inversions is investigated by carrying out realistic synthetic tests for various earthquakes with different faulting mechanisms and magnitude (Mw 6.0-6.6). Synthetic tests highlight the improvement in the constraint of fault geometry (strike, dip and rake) and moment when InSAR and seismic data are combined. Tests comparing the effect of using a 1-D or 3-D earth model show that long-period surface waves are more sensitive than long-period body waves to the change in earth model. Incorrect source parameters, particularly incorrect fault dip angles, can compensate for systematic errors in the assumed Earth structure, leading to an acceptable data fit despite large discrepancies in source parameters. Three real earthquakes are also investigated: Eureka Valley, California (1993 May 17, Mw 6.0), Aiquile, Bolivia (1998 February 22, Mw 6.6) and Zarand, Iran (2005 May 22, Mw 6.5). These events are located in different tectonic environments and show large discrepancies between InSAR and seismically determined source models. Despite the 40-50 km discrepancies in location between previous geodetic and
Weckmann, U.; Toelg, D.; Ritter, O.
The electrical conductivity structure of the crust beneath the Southern Uplands of Scotland has been investigated with electromagnetic and magneto-variational studies since the early 1970ies. The Southern Uplands formed in Ordovician and Silurian times as an accretionary prism on the Laurentian margin of the Iapetus Ocean as overthrusted wedges of sediments bounded by thrust faults. A pronounced zone of high electrical conductivity extending in northeast to southwest direction for at least 150 km was a common feature of many of these studies. The anomaly follows major structural trends of the Caledonian orogeny, such as the Southern Uplands Fault, the Orlock Bridge Fault and the Moniave Shear Zone. Graphite enrichment at mid-crustal levels trapped during the closure of the Iapetus Ocean or in detachment zones was discussed as possible causes for the high conductivity. In 1997, a high resolution MT experiment was conducted in southwestern Scotland across the most prominent faults. The station distribution, with an average spacing of 1-2km, concentrated on three parallel NW-SE profiles perpendicular to the tectonic structures and a strike parallel profile. Strike and dimensionality analyses indicated three-dimensional subsurface structures which also became evident in phases exceeding 90°. Nevertheless, 2D inversion of a sub-set of data revealed good spatial correlation of conductive zones and surface expressions of known faults. The 2D inversion results supported a mid-crustal detachment zone. However, some of the smaller profiles as well as the strike parallel profile could not be interpreted adequately with a 2D approach. Since 3D inversion algorithms are now available, we present a re-interpretation of the MT data set. We reprocessed the time series to improve estimates of the full impedance tensor for subsequent 3D inversion. 3D inversion reproduces the main features found along the published profiles. However, significant deviation from a 2D subsurface can be
Wilson, G. A.; Cuma, M.; Zhdanov, M. S.; Gribenko, A.; Black, N.
Three-dimensional (3D) inversion is required for defining 3D geoelectric structures associated with hydrocarbon (HC) deposits from marine controlled-source electromagnetic (CSEM) data. In 3D inversion, regularization is introduced to ensure uniqueness and stability in the inverse model. However, a common misconception is that regularization implies smoothing of the inverse model when in fact regularization and the stabilizing functionals are used to select the class of model from which an inverse solution is sought. Smooth stabilizers represent just one inverse model class from which the minimum norm or first or second derivatives of the 3D resistivity distribution are minimized. Smooth stabilizers have limited physical basis in geological interpretation aimed at exploration for HC reservoirs. Focusing stabilizers on the other hand make it possible to recover subsurface models with sharp resistivity contrasts which are typical for HC reservoirs. Using a synthetic example of the stacked anticlinal structures and reservoir units of the Shtokman gas field in the Barents Sea, we demonstrate that focusing stabilizers not only recover more geologically meaningful models than smooth stabilizers, but they provide better convergence for iterative inversion. This makes it practical to run multiple inversion scenarios based on the suite of a priori models, different data combinations, and various other parameters so as to build confidence in the recovered 3D resistivity model and to discriminate any artifacts that may arise from the interpretation of a single 3D inversion result.
Gil, M.; Götz, J.; Ivanova, A.; Juhlin, C.; Krawczyk, C. M.; Lüth, S.; Yang, C.
The Ketzin test site, located near Berlin, is Europe's longest-operating on-shore CO2 storage site. As of December 2011, more than 56,000 tons of food grade CO2 has been injected since June 2008 in an anticlinal structure of the Northeast German Basin. The target reservoir consists of porous, brine bearing sandstone units of the Upper Triassic Stuttgart Formation at approximately 630 to 650 m depth. In order to enhance the understanding of the structural geometry of the site and to investigate the extension of the CO2-plume, several geophysical monitoring methods are being applied at Ketzin, among these are active seismic measurements, geoelectrics and borehole measurements. Among the various seismic techniques (e.g. 2D reflection surveys, crosshole tomography, Vertical Seismic Profiling, 2D- and 3D-Moving Source Profiling) employed at this pilot site, 3D time-lapse reflection surveys are an important component. The baseline 3D survey was acquired in 2005 and the first repeat measurements were performed in 2009 after injection of about 22,000 tons of CO2. The second repeat survey is planned to be carried out in fall 2012. These measurements allow the time-lapse signature of the injected CO2 to be imaged. The time-lapse amplitude variation attributed to the injected CO2 in the reservoir matches, considering detection limits of seismic surface measurements, the expected distribution of the CO2 plume derived from reservoir simulations. Previous attempts towards a quantitative interpretation were based on integrative considerations of different types of geophysical measurements using strict assumptions and characterized by large error bars. In order to increase the resolution and reliability of the data and to improve estimation of rock properties and especially to enhance the imaging resolution of the CO2-plume, the time-lapse 3D seismic data have now been inverted for seismic impedances with different methods, which is the focus of this presentation. One difficulty
Kanaujia, Jyotima; Kumar, Ashwani; Gupta, S. C.
We investigate the upper crustal velocity structure beneath the Tehri region of the Garhwal Himalaya. The investigated region is situated within the 700-km-long central seismic gap of the Himalaya that has experienced three gap-filling earthquakes since 1991 including the recent 2015 Nepal earthquake (Mw 7.8). The local tomographic inversion is based on a dataset of 1365 events collected from January 2008 to December 2012 by a 12-station local network that covers an area of about 100 × 80 km around Tehri Dam. We perform a simultaneous inversion for P- and S-wave velocity anomalies. Tomograms are interpreted in the backdrop of the regional geological and tectonic framework of the region. The spatial distribution of relocated events from the 3- D velocity model has shed new light on the pattern of seismicity in the vicinity of the Main Central thrust (MCT), and has elucidated the structure of the underthrusting Indian plate. Our model exhibits a significant negative velocity anomaly up to ˜5 per cent beneath the central part of the Garhwal Inner Lesser Himalaya, and a P-wave low velocity anomaly near the Chamoli region. The seismicity zone around the Chamoli region may be attributed to the presence of fluid filled rocks. Furthermore, an area with˜3-4 per cent positive velocity anomaly is delineated to the northwest of the Uttarkashi thrust in the vicinity of the MCT. Significant findings of the study include: a flat-ramp-flat type sub-surface geometry of the underthrusting Indian plate below the Garhwal Himalaya, high velocity images representing the trend and configuration of Delhi-Haridwar-ridge below the Sub Himalaya and Lesser Himalaya, and a seismically active zone representing geometrical asperity on the basement thrust in the vicinity of the MCT.
Tchikaya, Euloge Budet; Chouteau, Michel; Keating, Pierre; Shamsipour, Pejman
We present an inversion tool for airborne gravity gradient data that yields a 3D density model using stochastic methods i.e. cokriging and conditional simulation. This method uses geostatistical properties of the measured gravity gradient to estimate a 3D density model whose gravity response fits the measured gravity gradient anomaly. Linearity between gravity gradient data and density allows estimation of the model (density) covariance using observed data, i.e. we adjust iteratively the density covariance matrix by fitting experimental and theoretical gravity gradient covariance matrices. Inversion can be constrained by including densities known at some locations. In addition we can explore various reasonable solutions that honour both the estimated density covariance model and the gravity gradient data using geostatistical simulation. The proposed method is first tested with two synthetic datasets generated from a sharp-boundary model and a smooth stochastic model respectively. The results show the method to be capable of retrieving models compatible with the true models; it also allows the integration of complex a priori information. The technique is then applied to gravity gradient survey data collected for the Geological Survey of Canada in the area of McFaulds Lake (Ontario, Canada) using the Falcon airborne gravity system. Unconstrained inversion returns a density model that is geologically plausible and the computed response exactly fits the observed gravity gradient anomaly.
Gill, D.; Small, P.; Maechling, P. J.; Jordan, T. H.; Shaw, J. H.; Plesch, A.; Chen, P.; Lee, E. J.; Taborda, R.; Olsen, K. B.; Callaghan, S.
Physics-based ground motion simulations can calculate the propagation of earthquake waves through 3D velocity models of the Earth. The Southern California Earthquake Center (SCEC) has developed the Unified Community Velocity Model (UCVM) framework to help researchers build structured or unstructured velocity meshes from 3D velocity models for use in wave propagation simulations. The UCVM software framework makes it easy to extract P and S wave propagation speeds and other material properties from 3D velocity models by providing a common interface through which researchers can query earth models for a given location and depth. Currently, the platform supports multiple California models, including SCEC CVM-S4 and CVM-H 11.9.1, and has been designed to support models from any region on earth. UCVM is currently being use to generate velocity meshes for many SCEC wave propagation codes, including AWP-ODC-SGT and Hercules. In this presentation, we describe improvements to the UCVM software. The current version, UCVM 14.3.0, released in March of 2014, supports the newest Southern California velocity model, CVM-S4.26, which was derived from 26 full-3D tomographic iterations using CVM-S4 as the starting model (Lee et al., this meeting), and the Broadband 1D velocity model used in the CyberShake 14.2 study. We have ported UCVM to multiple Linux distributions and OS X. Also included in this release is the ability to add small-scale stochastic heterogeneities to extract Cartesian meshes for use in high-frequency ground motion simulations. This tool was built using the C language open-source FFT library, FFTW. The stochastic parameters (Hurst exponent, correlation length, and the horizontal/vertical aspect ratio) can be customized by the user. UCVM v14.3.0 also provides visualization scripts for constructing cross-sections, horizontal slices, basin depths, and Vs30 maps. The interface allows researchers to visually review velocity models . Also, UCVM v14.3.0 can extract
Schiemenz, A.; Igel, H.
We present results of 3-D full-waveform inversion (FWI) utilizing a Python-driven workflow which incorporates the SPECFEM3D solver, a time-domain spectral element method, and the Obpsy software, a toolbox for computational seismology. We examine source encoding strategies, where multiple seismic sources are simultaneously excited, reducing in the number of required simulations per FWI iteration. Applications to synthetic case studies are presented which demonstrate a sensitivity of source encoding to source-receiver offset and number of encoded supershots. We detail workflow methodologies suitable for large-scale (i.e. many sources and receivers) FWI applications, as encountered in exploration geophysics problems in the marine environment.
Macquet, M.; Paul, A.; Pedersen, H.
Barmin et al. (2001). The last step of our tomography is the inversion of local group velocity dispersion curves for the 3-D Vs structure. For this step, we carried out a combination of full non-linear inversion and linearized inversion. This combination is motivated by the strong lateral variation in seismic structure beneath the array, ranging from deep sedimentary basins to the Pyrenees mountain range. During the first step, we fully explore a ~2 700 000 models library averaging the 200 best fitting models to build an input model. We then use this average as input for a linearized inversion using the program package of Herrnann and Ammon (2002). This method makes it possibly to automatically and consistently build a 3-D Vs model in spite of the lateral variations of seismic structure.
Sayanagi, Kunio M.; Showman, A. P.
The atmospheric zonal jets on Jupiter and Saturn are characterized by the broad, prograde, equatorial jet and the narrower, higher-latitude jets that alternate between prograde and retrograde. The question of what controls the widths and directions of those jets remains a major unsolved problem in geophysical fluid dynamics. Past studies have shown that, in shallow flows on a rotating sphere, small random vortices can undergo inverse cascade to form zonal jets with a characteristic width called the Rhines scale. Most of the studies to date use 2D non-divergent or shallow-water models in studying this zonal jet formation mechanism. However, in the parameter ranges representative of the Jovian conditions, the flows produced by 2D non-divergent models are typically dominated by strong circumpolar jets, and the shallow-water models produce a robust retrograde equatorial jet. These models' apparent inabilities in reproducing some key Jovian jet features may suggest the importance of 3D effects in controlling the jets' large-scale horizontal structures. To date, Kitamura and Matsuda (Fluid Dynamics Research, 34, 33-57, 2004) is the only published study that analyzes the 3D effects in the zonalization of fine-scale random turbulence through the inverse cascade. Their two-layer primitive equation simulations of free-evolving flows resulted in circumpolar jet dominated flows, although slower mid-latitude jets are also present. Our study is a significant extension over that by Kitamura and Matsuda and includes substantially more layers to study the zonalization process to more fully resolve relevant 3D effects in the inverse cascade. We test the flow behavior's dependence on the deformation radius and the resulting vertical structures in both spherical and beta-plane geometries. Our study uses the Explicit Planetary Isentropic Coordinate (EPIC) model (Dowling et al, Icarus, 32, 221-238., 1998). The research is supported by a NASA Planetary Atmospheres grant to APS.
Sayanagi, K. M.; Showman, A. P.
The atmospheric zonal jets on Jupiter and Saturn are characterized by the broad, prograde, equatorial jet and the narrower, higher-latitude jets that alternate between prograde and retrograde. The question of what controls the widths and directions of those jets remains a major unsolved problem in geophysical fluid dynamics. Past studies have shown that, in shallow flows on a rotating sphere, small random vortices can undergo inverse cascade to form zonal jets with a characteristic width called the Rhines scale. Most of the studies to date use 2D non-divergent or shallow-water models in studying this zonal jet formation mechanism. However, in the parameter ranges representative of the Jovian conditions, the flows produced by 2D non- divergent models are typically dominated by strong circumpolar jets, and the shallow-water models produce a robust retrograde equatorial jet. These models' apparent inabilities in reproducing some key Jovian jet features may suggest the importance of 3D effects in controlling the jets' large-scale horizontal structures. To date, Kitamura and Matsuda (Fluid Dynamics Research, 34, 33-57, 2004) is the only published study that analyzes the 3D effects in the zonalization of fine-scale random turbulence through the inverse cascade. Their two-layer primitive equation simulations of free-evolving flows resulted in circumpolar jet dominated flows, although slower mid-latitude jets are also present. Our study is a significant extension over that by Kitamura and Matsuda and includes substantially more layers to study the zonalization process to more fully resolve relevant 3D effects in the inverse cascade. We test the flow behavior's dependence on the deformation radius and the resulting vertical structures in both spherical and beta-plane geometries. Our study uses the Explicit Planetary Isentropic Coordinate (EPIC) model (Dowling et al, Icarus, 32, 221-238., 1998). The research is supported by a NASA Planetary Atmospheres grant to APS.
Savage, B.; Wiens, D. A.; Tromp, J.
The current understanding of a subduction zone's temperature and composition is limited. Much of our recent knowledge of subduction zones comes from earthquake locations, geochemical measurements, and lab based experiments. Recently, two studies of the Tonga-Fiji subduction zone have presented tomographic images of velocity and attenuation (Roth et al., 1999; Zhao et al., 1997). Roth et al. (2000) then combined these two tomographic models of the Tonga-Fiji subduction zone to derive an empirical relationship between changes in velocity and attenuation. This relationship agrees well with two independent, experimental data sets (Jackson et al., 1992; Sato et al., 1989). Using the tomographic velocity model and the empirical relationship between velocity and attenuation we create synthetic seismograms for the Tonga-Fiji subduction zone to test whether a simple increase in velocity accurately depicts this subduction zone. To construct the model we use the tomographic model of Zhao et al. (1997) to create a shear velocity model using a simple Vs/Vp ratio. Following Roth et al. (2000) these tomographic models are combined with the empirical relation between velocity and attenuation to create an attenuation model. The resulting synthetics are compared to recorded data to validate the tomographic velocity model and the empirical relation between velocity and attenuation. Any mismatch in this comparison will provide a basis for further refinement of the tomographic models and the velocity-attenuation relation. The synthetics are created using the SPECFEM3D global code (Komatitsch et al., 2002) with the new addition of a three-dimensional attenuation operator. Attenuation is simulated by a set of standard linear solids over the desired frequency range as described in Liu et al. (1976). Our initial results at a minimum period of 3.3 seconds suggest that the attenuation structure plays a minor role for the present source-receiver geometry. The addition of the 3D attenuation
Yang, Dikun; Oldenburg, Douglas W.; Haber, Eldad
Airborne electromagnetic (AEM) methods are highly efficient tools for assessing the Earth's conductivity structures in a large area at low cost. However, the configuration of AEM measurements, which typically have widely distributed transmitter-receiver pairs, makes the rigorous modelling and interpretation extremely time-consuming in 3-D. Excessive overcomputing can occur when working on a large mesh covering the entire survey area and inverting all soundings in the data set. We propose two improvements. The first is to use a locally optimized mesh for each AEM sounding for the forward modelling and calculation of sensitivity. This dedicated local mesh is small with fine cells near the sounding location and coarse cells far away in accordance with EM diffusion and the geometric decay of the signals. Once the forward problem is solved on the local meshes, the sensitivity for the inversion on the global mesh is available through quick interpolation. Using local meshes for AEM forward modelling avoids unnecessary computing on fine cells on a global mesh that are far away from the sounding location. Since local meshes are highly independent, the forward modelling can be efficiently parallelized over an array of processors. The second improvement is random and dynamic down-sampling of the soundings. Each inversion iteration only uses a random subset of the soundings, and the subset is reselected for every iteration. The number of soundings in the random subset, determined by an adaptive algorithm, is tied to the degree of model regularization. This minimizes the overcomputing caused by working with redundant soundings. Our methods are compared against conventional methods and tested with a synthetic example. We also invert a field data set that was previously considered to be too large to be practically inverted in 3-D. These examples show that our methodology can dramatically reduce the processing time of 3-D inversion to a practical level without losing resolution
Persaud, P.; Stock, J. M.; Fuis, G. S.; Hole, J. A.; Goldman, M.; Scheirer, D. S.
We have analyzed explosive shot data from the 2011 Salton Seismic Imaging Project (SSIP) across a 2-D seismic array and 5 profiles in the Coachella Valley to produce a 3-D P-wave velocity model that will be used in calculations of strong ground shaking. Accurate maps of seismicity and active faults rely both on detailed geological field mapping and a suitable velocity model to accurately locate earthquakes. Adjoint tomography of an older version of the SCEC 3-D velocity model shows that crustal heterogeneities strongly influence seismic wave propagation from moderate earthquakes (Tape et al., 2010). These authors improve the crustal model and subsequently simulate the details of ground motion at periods of 2 s and longer for hundreds of ray paths. Even with improvements such as the above, the current SCEC velocity model for the Salton Trough does not provide a match of the timing or waveforms of the horizontal S-wave motions, which Wei et al. (2013) interpret as caused by inaccuracies in the shallow velocity structure. They effectively demonstrate that the inclusion of shallow basin structure improves the fit in both travel times and waveforms. Our velocity model benefits from the inclusion of known location and times of a subset of 126 shots detonated over a 3-week period during the SSIP. This results in an improved velocity model particularly in the shallow crust. In addition, one of the main challenges in developing 3-D velocity models is an uneven stations-source distribution. To better overcome this challenge, we also include the first arrival times of the SSIP shots at the more widely spaced Southern California Seismic Network (SCSN) in our inversion, since the layout of the SSIP is complementary to the SCSN. References: Tape, C., et al., 2010, Seismic tomography of the Southern California crust based on spectral-element and adjoint methods: Geophysical Journal International, v. 180, no. 1, p. 433-462. Wei, S., et al., 2013, Complementary slip distributions
Scheunert, M.; Ullmann, A.; Afanasjew, M.; Börner, R.-U.; Siemon, B.; Spitzer, K.
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%.
Zhdanov, M. S.; Gribenko, A.; Wilson, G. A.
Geophysical monitoring of reservoir fluids and rock properties is relevant to oil and gas production, carbon sequestration, and enhanced geothermal systems. Different geophysical fields provide information about different physical properties of the earth. Multiple geophysical surveys spanning gravity, magnetic, electromagnetic, seismic, and thermal methods are often interpreted to infer geology from models of different physical properties. In many cases, the various geophysical data are complimentary, making it natural to consider a formal mathematical framework for their joint inversion to a shared earth model. We introduce a new approach to the 3D joint inversion of multiple geophysical datasets using Gramian spaces of model parameters and Gramian constraints, computed as determinants of the corresponding Gram matrices of the multimodal model parameters and/or their attributes. The basic underlying idea of this approach is that the Gramian provides a measure of correlation between the model parameters. By imposing an additional requirement of the minimum of the Gramian, we arrive at the solution of the joint multimodal inverse problem with the enhanced correlation between the different model parameters and/or their attributes. We demonstrate that this new approach is a generalized technique that can be applied to the simultaneous joint inversion of any number and combination of geophysical datasets. Our approach includes as special cases those extant methods based on correlations and/or structural constraints of different physical properties. We illustrate this approach by a model study of reservoir monitoring using different geophysical data.
A 3-D magnetotelluric (MT) inversion code using unstructured tetrahedral elements has been developed in order to correct the topographic effect by directly incorporating it into computational grids. The electromagnetic field and response functions get distorted at the observation sites of MT surveys because of the undulating surface topography, and without correcting this distortion, the subsurface structure can be misinterpreted. Of the two methods proposed to correct the topographic effect, the method incorporating topography explicitly in the inversion is applicable to a wider range of surveys. For forward problems, it has been shown that the finite element method using unstructured tetrahedral elements is useful for the incorporation of topography. Therefore, this paper shows the applicability of unstructured tetrahedral elements in MT inversion using the newly developed code. The inversion code is capable of using the impedance tensor, the vertical magnetic transfer function (VMTF), and the phase tensor as observational data, and it estimates the subsurface resistivity values and the distortion tensor of each observation site. The forward part of the code was verified using two test models, one incorporating topographic effect and one without, and the verifications showed that the results were almost the same as those of previous works. The developed inversion code was then applied to synthetic data from a MT survey, and was verified as being able to recover the resistivity structure as well as other inversion codes. Finally, to confirm its applicability to the data affected by topography, inversion was performed using the synthetic data of the model that included two overlapping mountains. In each of the cases using the impedance tensor, the VMTF and the phase tensor, by including the topography in the mesh, the subsurface resistivity was determined more proficiently than in the case using the flat-surface mesh. Although the locations of the anomalies were
Background Cardiovascular-MR (CMR) is the gold standard for quantifying myocardial infarction using late gadolinium enhancement (LGE) technique. Both 2D- and 3D-LGE-sequences are used in clinical practise and in clinical and experimental studies for infarct quantification. Therefore the aim of this study was to investigate if image acquisitions with 2D- and 3D-LGE show the same infarct size in patients and ex vivo. Methods Twenty-six patients with previous myocardial infarction who underwent a CMR scan were included. Images were acquired 10-20 minutes after an injection of 0.2 mmol/kg gadolinium-based contrast agent. Two LGE-sequences, 3D-inversion recovery (IR) and 2D-phase-sensitive (PS) IR, were used in all patients to quantify infarction size. Furthermore, six pigs with reperfused infarction in the left anterior descending artery (40 minutes occlusion and 4 hours of reperfusion) were scanned with 2D- and 3D-LGE ex vivo. A high resolution T1-sequence was used as reference for the infarct quantification ex vivo. Spearman’s rank-order correlation, Wilcoxon matched pairs test and bias according to Bland-Altman was used for comparison of infarct size with different LGE-sequences. Results There was no significant difference between the 2D- and 3D-LGE sequence in left ventricular mass (LVM) (2D: 115 ± 25 g; 3D: 117 ± 24 g: p = 0.35). Infarct size in vivo using 2D- and 3D-LGE showed high correlation and low bias for both LGE-sequences both in absolute volume of infarct (r = 0.97, bias 0.47 ± 2.1 ml) and infarct size as part of LVM (r = 0.94, bias 0.16 ± 2.0%). The 2D- and 3D-LGE-sequences ex vivo correlated well (r = 0.93, bias 0.67 ± 2.4%) for infarct size as part of the LVM. The IR LGE-sequences overestimated infarct size as part of the LVM ex vivo compared to the high resolution T1-sequence (bias 6.7 ± 3.0%, 7.3 ± 2.7% for 2D-PSIR and 3D-IR respectively, p < 0.05 for both). Conclusions Infarct quantification with
Morgan, Joanna; Warner, Michael; Arnoux, Gillean; Hooft, Emilie; Toomey, Douglas; VanderBeek, Brandon; Wilcock, William
3-D full-waveform inversion (FWI) is an advanced seismic imaging technique that has been widely adopted by the oil and gas industry to obtain high-fidelity models of P-wave velocity that lead to improvements in migrated images of the reservoir. Most industrial applications of 3-D FWI model the acoustic wavefield, often account for the kinematic effect of anisotropy, and focus on matching the low-frequency component of the early arriving refractions that are most sensitive to P-wave velocity structure. Here, we have adopted the same approach in an application of 3-D acoustic, anisotropic FWI to an ocean-bottom-seismometer (OBS) field data set acquired across the Endeavour oceanic spreading centre in the northeastern Pacific. Starting models for P-wave velocity and anisotropy were obtained from traveltime tomography; during FWI, velocity is updated whereas anisotropy is kept fixed. We demonstrate that, for the Endeavour field data set, 3-D FWI is able to recover fine-scale velocity structure with a resolution that is 2-4 times better than conventional traveltime tomography. Quality assurance procedures have been employed to monitor each step of the workflow; these are time consuming but critical to the development of a successful inversion strategy. Finally, a suite of checkerboard tests has been performed which shows that the full potential resolution of FWI can be obtained if we acquire a 3-D survey with a slightly denser shot and receiver spacing than is usual for an academic experiment. We anticipate that this exciting development will encourage future seismic investigations of earth science targets that would benefit from the superior resolution offered by 3-D FWI.
Kamel, Benoumessad; Ilhem, Kriba; Ali, Fourar; Abdelbaki, Djebaili
Simulation of open channel flow or river flow presents unique challenge to numerical simulators, which is widely used in the applications of computational fluid dynamics. The prediction is extremely difficult because the flow in open channel is usually transient and turbulent, the geometry is irregular and curved, and the free-surface elevation is varying with time. The results from a 3D non-linear k- ɛ turbulence model are presented to investigate the flow structure, the velocity distribution and mass transport process in a meandering compound open channel and a straight open channel. The 3D numerical model for calculating flow is set up in cylinder coordinates in order to calculate the complex boundary channel. The finite volume method is used to disperse the governing equations and the SIMPLE algorithm is applied to acquire the coupling of velocity and pressure. The non-linear k- ɛ turbulent model has good useful value because of taking into account the anisotropy and not increasing the computational time. The main contributions of this study are developing a numerical method that can be applied to predict the flow in river bends with various bend curvatures and different width-depth ratios. This study demonstrates that the 3D non-linear k- ɛ turbulence model can be used for analyzing flow structures, the velocity distribution and pollutant transport in the complex boundary open channel, this model is applicable for real river and wetland problem.
Cherevatova, M.; Smirnov, M.; Korja, T. J.; Egbert, G. D.
In this work we investigate the geoelectrical structure of the cratonic margin of Fennoscandian Shield by means of magnetotelluric (MT) measurements carried out in Northern Norway and Sweden during summer 2011-2012. The project Magnetotellurics in the Scandes (MaSca) focuses on the investigation of the crust, upper mantle and lithospheric structure in a transition zone from a stable Precambrian cratonic interior to a passive continental margin beneath the Caledonian Orogen and the Scandes Mountains in western Fennoscandia. Recent MT profiles in the central and southern Scandes indicated a large contrast in resistivity between Caledonides and Precambrian basement. The alum shales as a highly conductive layers between the resistive Precambrian basement and the overlying Caledonian nappes are revealed from this profiles. Additional measurements in the Northern Scandes were required. All together data from 60 synchronous long period (LMT) and about 200 broad band (BMT) sites were acquired. The array stretches from Lofoten and Bodo (Norway) in the west to Kiruna and Skeleftea (Sweden) in the east covering an area of 500x500 square kilometers. LMT sites were occupied for about two months, while most of the BMT sites were measured during one day. We have used new multi-grid approach for 3D electromagnetic (EM) inversion and modelling. Our approach is based on the OcTree discretization where the spatial domain is represented by rectangular cells, each of which might be subdivided (recursively) into eight sub-cells. In this simplified implementation the grid is refined only in the horizontal direction, uniformly in each vertical layer. Using multi-grid we manage to have a high grid resolution near the surface (for instance, to tackle with galvanic distortions) and lower resolution at greater depth as the EM fields decay in the Earth according to the diffusion equation. We also have a benefit in computational costs as number of unknowns decrease. The multi-grid forward
Čuma, Martin; Zhdanov, Michael S.
We have recently introduced a massively parallel regularized 3D inversion of potential fields data. This program takes as an input gravity or magnetic vector, tensor and Total Magnetic Intensity (TMI) measurements and produces 3D volume of density, susceptibility, or three dimensional magnetization vector, the latest also including magnetic remanence information. The code uses combined MPI and OpenMP approach that maps well onto current multiprocessor multicore clusters and exhibits nearly linear strong and weak parallel scaling. It has been used to invert regional to continental size data sets with up to billion cells of the 3D Earth's volume on large clusters for interpretation of large airborne gravity and magnetics surveys. In this paper we explain the features that made this massive parallelization feasible and extend the code to add GPU support in the form of the OpenACC directives. This implementation resulted in up to a 22x speedup as compared to the scalar multithreaded implementation on a 12 core Intel CPU based computer node. Furthermore, we also introduce a mixed single-double precision approach, which allows us to perform most of the calculation at a single floating point number precision while keeping the result as precise as if the double precision had been used. This approach provides an additional 40% speedup on the GPUs, as compared to the pure double precision implementation. It also has about half of the memory footprint of the fully double precision version.
Frankel, A. D.; Stephenson, W. J.; Carver, D.; Odum, J.; Williams, R. A.; Rhea, S.
We have produced probabilistic seismic hazard maps of Seattle for 1 Hz spectral acceleration, using over five hundred 3D finite-difference simulations of earthquakes on the Seattle fault, Southern Whidbey Island fault, and Cascadia subduction zone, as well as for random deep and shallow earthquakes at various locations. The 3D velocity model was validated by modeling the observed waveforms for the 2001 M6.8 Nisqually earthquake and several smaller events in the region. At these longer periods (≥ 1 sec) that are especially important to the response of buildings of ten stories or higher, seismic waves are strongly influenced by sedimentary basins and rupture directivity. We are investigating how random spatial variations in the 3D velocity model affect the simulated ground motions for M6.7 earthquakes on the Seattle fault. A fractal random variation of shear-wave velocity with a Von Karman correlation function produces spatial variations of peak ground velocity with multiple scale lengths. We find that a 3D velocity model with a 10% standard deviation in shear-wave velocity in the top 1.5 km and 5% standard deviation from 1.5-10 km depth produces variations in peak ground velocities of as much as a factor of two, relative to the case with no random variations. The model with random variations generally reduces the peak ground velocity of the forward rupture directivity pulse for sites near the fault where basin-edge focusing of S-waves occurs. It also tends to reduce the peak velocity of localized areas where basin surface waves are focused. However, the medium with random variations also causes small-scale amplification of ground motions over distances of a few kilometers. We are also evaluating alternative methods of characterizing the aleatory uncertainty in the probabilistic hazard calculations.
Coviello, Velio; Manconi, Andrea; Occhiena, Cristina; Arattano, Massimo; Scavia, Claudio
Rock-falls are one of the most common and hazardous phenomena occurring in mountainous areas. The formation of cracks in rocks is often accompanied by a sudden release of energy, which propagates in form of elastic waves and can be detected by a suitable transducer array. Therefore, geophones are among the most effective monitoring devices to investigate eventual precursors of rock-fall phenomena. However, the identification of an efficient procedure to forecast rock-fall occurrence in space and time is still an open challenge. In this study, we aim at developing an efficient procedure to locate microseismic sources relevant to cracking mechanisms, and thus gather indications on eventual precursors of rock-fall phenomena. Common seismic location tools usually implement homogeneous or multilayered velocity models but, in case of high slope gradients and heavily fractured rock masses, these simplifications may lead to errors on the correct estimation of the source location. Thus, we analyzed how the consideration of 3D material properties on the propagation medium may influence the location. In the framework of the Alcotra 2007-2013 Project MASSA (Medium And Small Size rock-fall hazard Assessment), a monitoring system composed by 8 triaxial geophones was installed in 2010 at the J.A. Carrel hut (3829 m a.s.l., Matterhorn, NW Italian Alps) and during the first year of operation the network recorded more than 600 natural events that exceeded a fixed threshold . Despite the harsh environmental conditions of the study area, eighteen points distributed as uniformly as possible in space were selected for hammering. The artificial source dataset of known coordinates was used to constrain a 3D heterogeneous velocity model through a Simultaneous Iterative Reconstructive Technique. In order to mitigate the intrinsic uncertainties of the inversion procedure, bootstrapping was performed to extend the dataset and a statistical analysis was issued to improve the model
Slob, E. C.
The number of GPR applications is large and still increasing. In several applications fixed-offset measurements can be sufficient and many dedicated imaging and inversion methods have been developed. Because there is insufficient amounts of data, these are necessarily model-driven schemes. For problems where quantitative information is needed, usually it is better to record multi-offset and possibly multicomponent data. Even for this data inversion is usually model-driven. This means the inverse problem is formulated as an iterative forward modeling problem and is solved by minimizing the amplitude difference between modeled and measured data. The model is modified such that data computed from the model fits the measured data. The information in the measured data itself is not used, except as a measure of the model data fit. For multi-offset multicomponent data a data-driven scheme is here developed to perform full waveform inversion of 3D ground-penetrating radar reflection data acquired on the surface of a layered medium. For data-driven models to work well, the data has to be properly sampled. The advantage is that no model information is necessary to carry out the inversion. The inversion is carried out in three steps. First the data is decomposed into up- and downgoing wave modes. In a layered earth the two modes are separable and are treated separately. This step provides the reflection response of the layered medium. For 3D waves in a layered medium this requires knowledge of the horizontal electric and magnetic field components. If the data is properly sampled the solution is unique. The second step consists of wave field synthesis, where the reflection response is used to construct a focusing wave field that can focus in a virtual receiver position at any depth level. At this stage of the process the depth level is only known in terms of one-way travel time. This is the intercept time in the slowness domain obtained directly from the data. A virtual
Tokarev, M. P.; Sharaborin, D. K.; Lobasov, A. S.; Chikishev, L. M.; Dulin, V. M.; Markovich, D. M.
Tomographic particle image velocimetry (PIV) has become a standard tool for 3D velocity measurements in non-reacting flows. However, the majority of the measurements in flows with combustion are limited to small resolved depth compared to the size of the field of view (typically 1 : 10). The limitations are associated with inhomogeneity of the volume illumination and the non-uniform flow seeding, the optical distortions and errors in the 3D calibration, and the unwanted flame luminosity. In the present work, the above constraints were overcome for the tomographic PIV experiment in a laminar axisymmetric premixed flame. The measurements were conducted for a 1 : 1 depth-to-size ratio using a system of eight CCD cameras and a 200 mJ pulsed laser. The results show that camera calibration based on the triangulation of the tracer particles in the non-reacting conditions provided reliable accuracy for the 3D image reconstruction in the flame. The modification of the tomographic reconstruction allowed a posteriori removal of unwanted bright objects, which were located outside of the region of interest but affected the reconstruction quality. This study reports on a novel experience for the instantaneous 3D velocimetry in laboratory-scale flames by using tomographic PIV.
Amaya, M.; Hansen, K. R.; Morten, J. P.
For the first time in 3D controlled source electromagnetic data inversion, we explore the use of the Newton and the Halley optimization methods, which may show their potential when the cost function has a complex topology. The inversion is formulated as a constrained nonlinear least-squares problem which is solved by iterative optimization. These methods require the derivatives up to second order of the residuals with respect to model parameters. We show how Green's functions determine the high-order derivatives, and develop a diagrammatical representation of the residual derivatives. The Green's functions are efficiently calculated on-the-fly, making use of a finite-difference frequency-domain forward modelling code based on a multi-frontal sparse direct solver. This allow us to build the second-order derivatives of the residuals keeping the memory cost in the same order as in a Gauss-Newton (GN) scheme. Model updates are computed with a trust-region based conjugate-gradient solver which does not require the computation of a stabilizer. We present inversion results for a synthetic survey and compare the GN, Newton, and super-Halley optimization schemes, and consider two different approaches to set the initial trust-region radius. Our analysis shows that the Newton and super-Halley schemes, using the same regularization configuration, add significant information to the inversion so that the convergence is reached by different paths. In our simple resistivity model examples, the convergence speed of the Newton and the super-Halley schemes are either similar or slightly superior with respect to the convergence speed of the GN scheme, close to the minimum of the cost function. Due to the current noise levels and other measurement inaccuracies in geophysical investigations, this advantageous behaviour is at present of low consequence, but may, with the further improvement of geophysical data acquisition, be an argument for more accurate higher-order methods like those
Minty, Brian; Brodie, Ross
We present a new method for the inversion of airborne gamma-ray spectrometric line data to a regular grid of radioelement concentration estimates on the ground. The method incorporates the height of the aircraft, the 3D terrain within the field of view of the spectrometer, the directional sensitivity of rectangular detectors, and a source model comprising vertical rectangular prisms with the same horizontal dimensions as the required grid cell size. The top of each prism is a plane surface derived from a best-fit plane to the digital elevation model of the earth's surface within each grid cell area. The method is a significant improvement on current methods, and gives superior interpolation between flight lines. It also eliminates terrain effects that would normally remain in the data after the conventional processing of these data assuming a flat-earth model.
Levander, Alan Richard; Zelt, Colin A.
The work plan for this project was to develop and apply advanced seismic reflection and wide-angle processing and inversion techniques to high resolution seismic data for the shallow subsurface to seismically characterize the shallow subsurface at hazardous waste sites as an aid to containment and cleanup activities. We proposed to continue work on seismic data that we had already acquired under a previous DoE grant, as well as to acquire additional new datasets for analysis. The project successfully developed and/or implemented the use of 3D reflection seismology algorithms, waveform tomography and finite-frequency tomography using compressional and shear waves for high resolution characterization of the shallow subsurface at two waste sites. These two sites have markedly different near-surface structures, groundwater flow patterns, and hazardous waste problems. This is documented in the list of refereed documents, conference proceedings, and Rice graduate theses, listed below.
Yin, Junlian; Wang, Dezhong
The 3D inverse design method, which methodology is far superior to the conventional design method that based on geometrical description, is gradually applied in pump blade design. However, no complete description about the method is outlined. Also, there are no general rules available to set the two important input parameters, blade loading distribution and stacking condition. In this sense, the basic theory and the mechanism why the design method can suppress the formation of secondary flow are summarized. And also, several typical pump design cases with different specific speeds ranging from centrifugal pump to axial pump are surveyed. The results indicates that, for centrifugal pump and mixed pump or turbine, the ratio of blade loading on the hub to that on the shroud is more than unit in the fore part of the blade, whereas in the aft part, the ratio is decreased to satisfy the same wrap angle for hub and shroud. And the choice of blade loading type depends on the balancing of efficiency and cavitation. If the cavitation is more weighted, the better choice is aft-loaded, otherwise, the fore-loaded or mid-loaded is preferable to improve the efficiency. The stacking condition, which is an auxiliary to suppress the secondary flow, can have great effect on the jet-wake outflow and the operation range for pump. Ultimately, how to link the design method to modern optimization techniques is illustrated. With the know-how design methodology and the know-how systematic optimization approach, the application of optimization design is promising for engineering. This paper summarizes the 3D inverse design method systematically.
Ślęzak, Katarzyna; Jóźwiak, Waldemar; Nowożyński, Krzysztof; Brasse, Heinrich
The Pomerania region (northwest part of Poland) occupies a significant position, where the largest European tectonic boundary is situated. This is the area of the contact between the East European Craton (EEC) and the Paleozoic Platform (PP) and it is known as the Trans-European Suture Zone (TESZ). The TESZ was formed during Paleozoic time as a consequence of the collision of several crustal units and it extends from the Black Sea in the southeast to the British Isles in the northwest. It is a region of key importance for our understanding of the tectonic history of Europe. Previous magnetotelluric (MT) results, based on 2-D inverse modeling, show that the contact zone is of lithospheric discontinuity character and there are distinct differences in geoelectric structures between the Precambrian EEC, transitional zone (TESZ), and the younger PP. The presence of a significant conductor at mid and lower crustal depths was also shown. Thus, the main aim of the research presented here was to obtain detailed, 3-D images of electrical conductivity in the crust and upper mantle and its regional distribution below the TESZ in the northwest part of Poland. To accomplish this task we applied the latest 3-D inversion codes, which allowed us to get more realistic model geometries. Additionally, to confirm and complement the study, the Horizontal Magnetic Tensor (HMT) analysis was realized. This method gives us an opportunity to efficiently locate the position of well-conducting structures. As a result we obtain a clearer, three-dimensional model of conductivity distribution, where highly conductive rock complexes appear which we tentatively connected to deformation fronts.
Ślęzak, Katarzyna; Jóźwiak, Waldemar; Nowożyński, Krzysztof; Brasse, Heinrich
The Pomerania region (northwest part of Poland) occupies a significant position, where the largest European tectonic boundary is situated. This is the area of the contact between the East European Craton (EEC) and the Paleozoic Platform (PP) and it is known as the Trans-European Suture Zone (TESZ). The TESZ was formed during Paleozoic time as a consequence of the collision of several crustal units and it extends from the Black Sea in the southeast to the British Isles in the northwest. It is a region of key importance for our understanding of the tectonic history of Europe. Previous magnetotelluric (MT) results, based on 2-D inverse modeling, show that the contact zone is of lithospheric discontinuity character and there are distinct differences in geoelectric structures between the Precambrian EEC, transitional zone (TESZ), and the younger PP. The presence of a significant conductor at mid and lower crustal depths was also shown. Thus, the main aim of the research presented here was to obtain detailed, 3-D images of electrical conductivity in the crust and upper mantle and its regional distribution below the TESZ in the northwest part of Poland. To accomplish this task we applied the latest 3-D inversion codes, which allowed us to get more realistic model geometries. Additionally, to confirm and complement the study, the Horizontal Magnetic Tensor (HMT) analysis was realized. This method gives us an opportunity to efficiently locate the position of well-conducting structures. As a result we obtain a clearer, three-dimensional model of conductivity distribution, where highly conductive rock complexes appear which we tentatively connected to deformation fronts.
Kormann, Jean; Marti, David; Rodriguez, Juan-Esteban; Marzan, Ignacio; Ferrer, Miguel; Gutierrez, Natalia; Farres, Albert; Hanzich, Mauricio; de la Puente, Josep; Carbonell, Ramon
Full Waveform Inversion (FWI) is one of the most advanced processing methods that is recently reaching a mature state after years of solving theoretical and technical issues such as the non-uniqueness of the solution and harnessing the huge computational power required by realistic scenarios. BSIT (Barcelona Subsurface Imaging Tools, www.bsc.es/bsit) includes a FWI algorithm that can tackle with very complex problems involving large datasets. We present here the application of this system to a 3D dataset acquired to constrain the shallow subsurface. This is where the wavefield is the most complicated, because most of the wavefield conversions takes place in the shallow region and also because the media is much more laterally heterogeneous. With this in mind, at least isotropic elastic approximation would be suitable as kernel engine for FWI. The current study explores the possibilities to apply elastic isotropic FWI using only the vertical component of the recorded seismograms. The survey covers an area of 500×500 m2, and consists in a receivers grid of 10 m×20 m combined with a 250 kg accelerated weight-drop as source on a displaced grid of 20 m×20 m. One of the main challenges in this case study is the costly 3D modeling that includes topography and substantial free surface effects. FWI is applied to a data subset (shooting lines 4 to 12), and is performed for 3 frequencies ranging from 15 to 25 Hz. The starting models are obtained from travel-time tomography and the all computation is run on 75 nodes of Mare Nostrum supercomputer during 3 days. The resulting models provide a higher resolution of the subsurface structures, and show a good correlation with the available borehole measurements. FWI allows to extend in a reliable way this 1D knowledge (borehole) to 3D.
Landes, M.; Hauser, F.; Ritter, J. R. R.; Fielitz, W.; Popa, M.
The Vrancea zone in the southeastern Carpathians is one of the most active seismic regions in Europe. In order to study the crustal and upper-mantle structure in this region, two seismic refraction experiments were carried out in 1999 and 2001. The 1999 campaign comprised a 320 km long N-S profile and a 80 km long transverse profile. All shots were recorded simultaneously on both profiles. The profile conducted in 2001 extended in E-W direction from the Hungarian border across the Vrancea zone to the Black Sea. A first ever 3-D crustal velocity model of the south-eastern Carpathians within a 115 x 235 km wide region around the Vrancea zone is presented. This model was generated by application of a 3-D refraction and reflection tomography algorithm (Hole 1992, 1995). In order to enhance the model resolution, first arrival data from local earthquakes were also included. The results indicate a high-velocity structure above the Vrancea zone extending from shallow levels to depths of about 11 km. A possible relation to the Trotus and Capidava-Ovidiu faults, which converge to the north of it, is deemed unlikely. However,the existence of the outstanding high velocities may be explained by crystalline basement thrust onto the sub-Carpathian nappes. The high-velocity region is surrounded by the lower velocity Focsani and Brasov basins. The sedimentary succession beneath the southern part of the model area extends to 18 km depth, while in the north sediment thickness varies between 10 and 15 km. Further results of the interface modelling of prominent reflections show that the mid-crustal and Moho interfaces shallow northwards from 30 km to 22 km and from 42 km to 38 km, respectively.
Park, J.; Morgan, J.K.; Zelt, C.A.; Okubo, P.G.; Peters, L.; Benesh, N.
We present a 3-D P-wave velocity model of the combined subaerial and submarine portions of the southeastern part of the Island of Hawaii, based on first-arrival seismic tomography of marine airgun shots recorded by the onland seismic network. Our model shows that high-velocity materials (6.5-7.0??km/s) lie beneath Kilauea's summit, Koae fault zone, and the upper Southwest Rift Zone (SWRZ) and upper and middle East Rift Zone (ERZ), indicative of magma cumulates within the volcanic edifice. A separate high-velocity body of 6.5-6.9??km/s within Kilauea's lower ERZ and upper Puna Ridge suggests a distinct body of magma cumulates, possibly connected to the summit magma cumulates at depth. The two cumulate bodies within Kilauea's ERZ may have undergone separate ductile flow seaward, influencing the submarine morphology of Kilauea's south flank. Low velocities (5.0-6.3??km/s) seaward of Kilauea's Hilina fault zone, and along Mauna Loa's seaward facing Kao'iki fault zone, are attributed to thick piles of volcaniclastic sediments deposited on the submarine flanks. Loihi seamount shows high-velocity anomalies beneath the summit and along the rift zones, similar to the interpreted magma cumulates below Mauna Loa and Kilauea volcanoes, and a low-velocity anomaly beneath the oceanic crust, probably indicative of melt within the upper mantle. Around Kilauea's submarine flank, a high-velocity anomaly beneath the outer bench suggests the presence of an ancient seamount that may obstruct outward spreading of the flank. Mauna Loa's southeast flank is also marked by a large, anomalously high-velocity feature (7.0-7.4??km/s), interpreted to define an inactive, buried volcanic rift zone, which might provide a new explanation for the westward migration of Mauna Loa's current SWRZ and the growth of Kilauea's SWRZ. ?? 2007 Elsevier B.V. All rights reserved.
Zhdanov, M. S.; Cuma, M.; Black, N.; Wilson, G. A.
The marine controlled source electromagnetic (MCSEM) method has become widely used in offshore oil and gas exploration. Interpretation of MCSEM data is still a very challenging problem, especially if one would like to take into account the realistic 3D structure of the subsurface. The inversion of MCSEM data is complicated by the fact that the EM response of a hydrocarbon-bearing reservoir is very weak in comparison with the background EM fields generated by an electric dipole transmitter in complex geoelectrical structures formed by a conductive sea-water layer and the terranes beneath it. In this paper, we present a review of the recent developments in the area of large-scale 3D EM forward modeling and inversion. Our approach is based on using a new integral form of Maxwell’s equations allowing for an inhomogeneous background conductivity, which results in a numerically effective integral representation for 3D EM field. This representation provides an efficient tool for the solution of 3D EM inverse problems. To obtain a robust inverse model of the conductivity distribution, we apply regularization based on a focusing stabilizing functional which allows for the recovery of models with both smooth and sharp geoelectrical boundaries. The method is implemented in a fully parallel computer code, which makes it possible to run large-scale 3D inversions on grids with millions of inversion cells. This new technique can be effectively used for active EM detection and monitoring of the subsurface targets.
Lallement, R.; Vergely, J.-L.; Valette, B.; Puspitarini, L.; Eyer, L.; Casagrande, L.
Aims: Three-dimensional (3D) maps of the Galactic interstellar matter (ISM) are a potential tool of wide use, but accurate and detailed maps are still lacking. One of the ways to construct the maps is to invert individual distance-limited ISM measurements, a method we have applied here to measurements of stellar color excess in the optical. Methods: We assembled color excess data together with the associated parallax or photometric distances to constitute a catalog of ≃23 000 sightlines for stars within 2.5 kpc. The photometric data are taken from Strömgren catalogs, the Geneva photometric database, and the Geneva-Copenhagen survey. We also included extinctions derived towards open clusters. We applied an inversion method based on a regularized Bayesian approach to this color excess dataset, a method previously used for mapping at closer distances. Results: We show the dust spatial distribution resulting from the inversion by means of planar cuts through the differential opacity 3D distribution, and by means of 2D maps of the integrated opacity from the Sun up to various distances. The mapping assigns locations to the nearby dense clouds and represents their distribution at the spatial resolution that is allowed by the dataset properties, i.e. ≃10 pc close to the Sun and increasing to ≃100 pc beyond 1 kpc. Biases toward nearby and/or weakly extincted stars make this dataset particularly appropriate to mapping the local and neighboring cavities and to locating faint, extended nearby clouds, which are both goals that are difficult or impossible with other mapping methods. The new maps reveal a ≃1 kpc wide empty region in the third quadrant in the continuation of the so-called CMa tunnel of the Local Cavity, a cavity that we identify as the Superbubble GSH238+00+09 detected in radio emission maps and that is found to be bounded by the Orion and Vela clouds. The maps also show an extended narrower tunnel in the opposite direction (l ≃ 70°) that also extends
Sommer, M.; Jegen, M. D.
Computationally, the most expensive part of a 3D time domain CSEM inversion is the computation of the Jacobian matrix in every Gauss-Newton step. An other problem is its size for large data sets. We use a model reduction method (Zaslavsky et al, 2013), that compresses the Jacobian by projecting it with a Rational Krylov Subspace (RKS). It also reduces the runtime drastically, compared to the most common adjoint approach and was implemented on GPU.It depends on an analytic derivation of the implicit Anzatz function, which solves Maxwell's diffusion equation in the Eigenspace giving a Jacobian dependent on the Eigenpairs and its derivatives of the forward problem. The Eigenpairs are approximated by Ritz-pairs in the Rational Krylov subspace. Determination of the derivived Ritz-pairs is the most time consuming and was fully GPU-optimized. Furthermore, the amount of inversion cells is reduced by using Octree meshes. The gridding allows for the incorporation of complicated survey geometries, as they are encountered in marine CSEM datasets.As a first result, the Jacobian computation is, even on a Desktop, faster than the most common adjoint approach on a super computer for realistic data sets. We will present careful benchmarking and accuracy tests of the new method and show how it can be applied to a real marine scenario.
Carry, B.; Kaasalainen, M.; Merline, W. J.; Drummond, J. D.; Durech, J.; Berthier, J.; Conrad, A.
We describe our on-going observing program to determine the physical properties of asteroids from groundbased facilities. We combine disk-resolved images from adaptive optics, optical lightcurves, and stellar occultations to put tighter constraints on the spin, 3-D shape, and size of asteroids. We will discuss the relevance of the determination of physical properties to help understand the asteroid population (e.g., density, composition, and non-gravitational forces). We will then briefly describe our multi-data inversion algorithm KOALA (Carry et al. 2010a, Kaasalainen 2011, see also Kaasalainen et al., same meeting), which allows the determination of certain physical properties of an asteroid from the combination of different techniques of observation. A comparison of results obtained with KOALA on asteroid (21) Lutetia, prior to the ESA Rosetta flyby, with the high spatial resolution images returned from that flyby, will then be presented, showing the high accuracy of KOALA inversion. Finally, we will describe our current development of the algorithm, and focus on examples of other asteroids currently being studied with KOALA.
Mousavi, Sima; Bauer, Klaus; Korn, Michael
3-D Vp and Vp/Vs structure of the geodynamically active NW Bohemia/Vogtland area, located at the border region between Germany and Czech republic, has been determined from local earthquake tomography using 543 earthquakes which have been recorded during 2000 to 2010. This region is known for the occurrence of earthquake swarms that are supposed to be triggered by fluid upwelling in the crust, although fluid behaviour and migration paths in the subsurface of NW Bohemia is still poorly known. The events used in this study were selected based on a minimum 12 P and S phase observations and an azimuthal gap less than 160º. This data set is employed to derive a minimum 1-D velocity model and to relocate the hypocenters. The minimum 1-D velocity model is then used as an initial model in non-linear inversion to derive 3-D P-velocity and Vp/Vs ratio. Using synthetic tests, it can be shown that a high resolution is obtained in the central part of the studied region with the given source and receiver configuration. Two branches of high Vp/Vs ratio anomalies have been detected above the swarm quakes' focal zone. These anomalies support the existence of two main fluid passages toward Bad Brambach and Bublak moffette. Another interesting result is a high Vp/Vs line-like anomaly along Mariánské Lázně fault where most of the swarm quakes occur, which could be due to a fluid saturated area around the cracked zone of the fault plain. Hypocenters in the swarm region are located in a low Vp and Vp/Vs anomaly. The correlation between the detected Vp and Vp/Vs anomalies and the location of earthquake swarm suggests a model in which CO2 as part of magmatic fluids exist in a vast area beneath NW Bohemia and frequently migrate up to the surface.
Spicer, B.; Morris, B.; Ugalde, H.
Hosted within the Pacquet Harbour Group (PHG) on the Baie Verte Peninsula of north-central Newfoundland, the Rambler rhyolite is a 487 Ma unit of felsic tuffs, flows and subvolcanic intrusive rocks. The PHG has been affected by multiple phases of deformation with the youngest D4 deformation event producing broad northeast plunging upright cross folds in the Rambler rhyolite. Fold culminations on the upper bounding surface of the rhyolite host Cu +/- Au volcanogenic massive sulfide deposits (e.g. Rambler and Ming mines). Geophysical inversions of recently acquired high resolution gravity and magnetic data have been implemented to determine the extent of the fold axis (dome) at depth. To direct the outcome of the inversion process towards a more geologically reasonable solution this study outlines a procedure which permits the inclusion of known geological and geophysical constraints into the input (reference) model for inversion using the MAG3D and GRAV3D algorithms provided by the University of British Columbia Geophysical Inversion Facility. Reference model constraints included surficial geological contacts as defined by aeromagnetic data, and subsurface distribution of physical property variations from a series of drill-hole logs. The output (computed) model images the surface of the rhyolite dome as dipping roughly 40° to the northeast as a series of voxels with density values ranging from 2.71 to 2.75 g/cm3. While previously published ore deposit models parallel this structure in the near surface, results from these inversions suggest deeper exploration may be favorable. Magnetic inversion modeling has not provided any insight into dome morphology however it outlines the distribution of gabbroic dykes surrounding the dome.
Barnoud, A.; Coutant, O.; Bouligand, C.
We propose to use a Bayesian methodology combined with a grid node discretization to invert linearly for 3D density distributions. The inversion and the forward modeling are derived from seismological travel-time inversion techniques in order to facilitate joint inversion or interpretation of density and seismic velocity models. The Bayesian method (Tarantola, 2005) introduces covariance matrices to regularize this ill-posed problem and reduce the non-uniqueness of the solution. Spatial covariances and grid discretization favor smooth and compact solutions that compare to usual seismic tomographic results. Compared to similar approaches our development includes i) the computation of the gravity field for linear vertical gradients and layers, including surface topography, a standard model description in seismology, ii) an explicit formulation of the a-priori covariance matrix. This last point allows to easily modify the spatial a-priori covariance (or scale, or wavelength) and hence, to perform successive linear inversions at different wavelengths. A series of synthetic tests is performed for validation, and used to show the advantage and limitation of this methodology. The method is appropriate for crustal and volcanological area studies, and allows a natural coupling with seismological inversions (Coutant et al., 2012). We present here two case studies for 3D gravity inversions. First, the inversion is performed in a crustal alpine context, the area of the well studied Ivrea Body in Italy. Secondly, we apply the inversion to gravity data from the volcanic island of Basse-Terre whose internal structure is badly constrained. We use data from previous studies supplemented with new high quality data acquired in 2012 within the frame of the Domoscan project. A 3D density model of the island of Basse-Terre is derived for the first time.
Ramachandran, K.; Ramachandran, K.; Spence, G. D.; Dosso, S.; Hyndman, R. D.; Hyndman, R. D.; Brocher, T. M.; Fisher, M. M.
A seismic tomography analysis in S.W. British Columbia and N. Washington has been used to define the velocity structure of the forearc crust and underlying subducting Juan de Fuca plate, and to obtain precise earthquake locations. First arrival travel-times from earthquakes and from the large airgun array used in the `Seismic Hazards Investigation of Puget Sound' (SHIPS) 1998 experiment, were simultaneously inverted for hypocentral parameters and velocity structure. Approximately 16,000 picks from 1,400 earthquakes recorded at 46 permanent stations, and 35,000 picks from the SHIPS experiment were used in the inversion. The velocity model was parameterized in the forward/inverse step by a node/cell spacing of 3 X 3 X 3 km over a volume of 360 X 450 X 93 km depth. The starting and final RMS travel time misfits were 479 ms and 120 ms respectively. Checkerboard tests conducted on the final velocity model imply good lateral resolution ranging from 30 to 50 km. The SHIPS airgun data mainly constrained the upper ~12 km and the earthquake data the deeper structure. The high velocity mafic Crescent Terrane that dips beneath the margin is well mapped in the velocity model on a regional scale. Its thickness beneath southern Vancouver Island is interpreted to reach ~20 km. Three high velocity structures above the subducting Juan de Fuca plate, having mafic to ultramafic velocities of 7.25-7.5 km/s, occur beneath southern Vancouver Island and Puget Sound at a depth of ~25 km. They may be associated with deeper parts of the Crescent Terrane, or with structures such as seamounts on the subducting Juan de Fuca plate. At the southern tip of Vancouver Islands, the Leech River Fault, Southern Whidbey Island Fault, and the Devils Mountain Fault appear to correlate with mapped seismicity. The subducting Juan de Fuca plate is well mapped beneath southern Vancouver Island, Olympic Peninsula, Strait of Georgia, and Puget Sound. The velocity model identifies the steepening dip in the
Wang, Gongwen; Zhu, Yanyan; Zhang, Shouting; Yan, Changhai; Song, Yaowu; Ma, Zhenbo; Hong, Dongming; Chen, Tianzhen
Three-dimensional (3D) geological modeling is an important method for understanding geological structures and exploring for mineral deposits. The Luanchuan super-large molybdenum polymetallic ore region has a complex geological setting and multiple metallogenic types. 3D geological modeling is implemented by combining geological knowledge with gravitational and magnetic data inversion in the study area. The 3D geological modeling methodology and the results are summarized as follows. (1) Based on the geological setting and the deposits/occurrences, the aim was to constrain and determine the main geological objects in 3D space to construct geological and metallogenic models. (2) Based on geological observations and rock physical measurements to derive qualitative information about geological objects at depths using gravitational and magnetic data inversion, 2.5D forward modeling was used to identify shallow/subsurface geological objects, and the 3D probability method of potential field inversion was used for coarse constraining of geological objects at depths. (3) A combination of geological information with gravitational and magnetic data inversion information was used to determine the space-time genesis of metallogenic objects in potential mineral targets (i.e., Late Jurassic granite intrusions, ore-forming strata, and ore mineralization favorable faults). (4)A 3D model of the study area (17.7 km × 12.0 km × 2.5 km) is associated with the surface and subsurface geological data, which has geophysical information that is beneficial for identifying and evaluating potential prospecting zones.
Ghofrani Tabari, M.; Goodfellow, S. D.; Nasseri, M. B.; Young, R.
A cubic specimen of water saturated Fontainebleau Sandstone is tested in the laboratory under true-triaxial loading where three different principal stresses are applied under drained conditions. Due to the loading arrangement, closure and opening of the pre-existing cracks in the rock, as well as creation and growth of the aligned cracks cause elliptical anisotropy and distributed heterogeneities. A Geophysical Imaging Cell equipped with an Acoustic Emission monitoring system is employed to image velocity structure of the sample during the experiment through repeated transducer to transducer non-destructive ultrasonic surveys. Apparent P-wave velocities along the rock body are calculated in different directions and shown in stereonet plots which demonstrate an overall anisotropy of the sample. The apparent velocities in the main three orthogonal cubic directions are used as raw data for building a mean spatial distribution model of anisotropy ratios. This approach is based on the concept of semi-principal axes in an elliptical anisotropic model and appointing two ratios between the three orthogonal velocities in each of the cubic grid cells. The spatial distribution model of anisotropy ratios are used to calculate the anisotropic ray-path segment matrix elements (Gij). These contain segment lengths of the ith ray in the jth cell in three dimensions where, length of each ray in each cell is computed for one principal direction based on the dip and strike of the ray and these lengths differ from the ones in an isotropic G Matrix. 3D strain of the squeezed rock and the consequent geometrical deformation is also included in the ray-path segment matrix. A Singular Value Decomposition (SVD) method is used for inversion from the data space of apparent velocities to the model space of P-wave propagation velocities in the three principal directions. Finally, spatial variation and temporal evolution of induced damages in the rock, representing uniformly distributed or
Finite difference methods for solving the wave equation more accurately capture the physics of waves propagating through the earth than asymptotic solution methods. Unfortunately, finite difference simulations for 3D elastic wave propagation are expensive. The authors model waves in a 3D isotropic elastic earth. The wave equation solution consists of three velocity components and six stresses. The partial derivatives are discretized using 2nd-order in time and 4th-order in space staggered finite difference operators. Staggered schemes allow one to obtain additional accuracy (via centered finite differences) without requiring additional storage. The serial code is most unique in its ability to model a number of different types of seismic sources. The parallel implementation uses the MPI library, thus allowing for portability between platforms. Spatial parallelism provides a highly efficient strategy for parallelizing finite difference simulations. In this implementation, one can decompose the global problem domain into one-, two-, and three-dimensional processor decompositions with 3D decompositions generally producing the best parallel speedup. Because I/O is handled largely outside of the time-step loop (the most expensive part of the simulation) the authors have opted for straight-forward broadcast and reduce operations to handle I/O. The majority of the communication in the code consists of passing subdomain face information to neighboring processors for use as ghost cells. When this communication is balanced against computation by allocating subdomains of reasonable size, they observe excellent scaled speedup. Allocating subdomains of size 25 x 25 x 25 on each node, they achieve efficiencies of 94% on 128 processors. Numerical examples for both a layered earth model and a homogeneous medium with a high-velocity blocky inclusion illustrate the accuracy of the parallel code.
Finite difference methods for solving the wave equation more accurately capture the physics of waves propagating through the earth than asymptotic solution methods. Unfortunately. finite difference simulations for 3D elastic wave propagation are expensive. We model waves in a 3D isotropic elastic earth. The wave equation solution consists of three velocity components and six stresses. The partial derivatives are discretized using 2nd-order in time and 4th-order in space staggered finite difference operators. Staggered schemes allow one to obtain additional accuracy (via centered finite differences) without requiring additional storage. The serial code is most unique in its ability to model a number of different types of seismic sources. The parallel implementation uses the MP1 library, thus allowing for portability between platforms. Spatial parallelism provides a highly efficient strategy for parallelizing finite difference simulations. In this implementation, one can decompose the global problem domain into one-, two-, and three-dimensional processor decompositions with 3D decompositions generally producing the best parallel speed up. Because i/o is handled largely outside of the time-step loop (the most expensive part of the simulation) we have opted for straight-forward broadcast and reduce operations to handle i/o. The majority of the communication in the code consists of passing subdomain face information to neighboring processors for use as ''ghost cells''. When this communication is balanced against computation by allocating subdomains of reasonable size, we observe excellent scaled speed up. Allocating subdomains of size 25 x 25 x 25 on each node, we achieve efficiencies of 94% on 128 processors. Numerical examples for both a layered earth model and a homogeneous medium with a high-velocity blocky inclusion illustrate the accuracy of the parallel code.
Liew, R.; Zeegers, J. C. H.; Kuerten, J. G. M.; Michalek, W. R.
The Ranque-Hilsch vortex tube is a known device that is used to generate spot cooling. In this study, we experimentally investigate the behavior of small water droplets in the vortex tube by means of Phase Doppler Particle Analysis. In an experimental vortex tube, droplets were injected together with a carrier gas to form a fast rotating (up to 80.000 rpm) droplet-gas mixture. Droplet sizes, 3D velocity components, and turbulent properties were measured, showing high intensity isotropic turbulence in the core region. To investigate the cause of the high intensity turbulence, a frequency analysis was applied on the measured velocity. The frequency spectrum of the velocity is presented and indicates that wobbling of the vortex axis is the cause of the high turbulence intensity. It was expected that larger droplets have a higher radial velocity because of the larger centrifugal force. Results show, however, that small and lager droplets behave similar. This research is supported by the Dutch Technology Foundation STW, which is the applied science division of NWO, and the Technology Programme of the Ministry of Economic Affairs.
Kiyan, D.; Jones, A. G.; Fullea, J.; Ledo, J.; Siniscalchi, A.; Romano, G.
The overarching objectives of the second phase of the PICASSO (Program to Investigate Convective Alboran Sea System Overturn) project and the concomitant TopoMed (Plate re-organization in the western Mediterranean: Lithospheric causes and topographic consequences - an ESF EUROSCORES TOPO-EUROPE project) project are (i) to provide new electrical conductivity constraints on the crustal and lithospheric structures of the Atlas Mountains, and (ii) to test the hypotheses for explaining the observation of a 'missing' mantle root inferred from surface heat flow, gravity and geoid anomalies, elevation and seismic data modeling (i.e. Zeyen et al., 2005; Teixell et al., 2005; Fullea et al., 2010). We present the results from three-dimensional (3-D) MT inversion of data from two MT profiles employing the parallel version of Modular system for Electromagnetic inversion (ModEM; Egbert & Kelbert, 2012) code. For the profile in eastern Morocco, passing through Midelt, a distinct conductivity difference between the Middle-High Atlas (conductive) and Anti Atlas (resistive) correlates with the South Atlas Front fault, the depth extent of which appears to be limited to the uppermost mantle (approximately 55 km). In all inverse solutions, the crust and the upper mantle show a resistive signature (750 Ωm - 1,000 Ωm) beneath the Anti Atlas to a depth of 100 km, which is the part of stable West African Craton. Our results are at variance with the proposed thin lithosphere beneath the Middle-High Atlas as we see no evidence for a shallow asthenosphere. Our second profile lies in western Morocco traversing through Marrakech. For the first time, the electrical resistivity distribution in the crust and in the upper mantle of Western High Atlas has been studied. Our 3-D resistivity model shows that conductive (1-20 Ωm) western High Atlas is confined by two resistive basins (>1,000 Ωm), Souss basin to the south and Houz basin to the north. At the southern boundary of the western High Atlas
Xie, G.; Li, J.; Majer, E.; Zuo, D.
This paper describes a new 3D parallel GILD electromagnetic (EM) modeling and nonlinear inversion algorithm. The algorithm consists of: (a) a new magnetic integral equation instead of the electric integral equation to solve the electromagnetic forward modeling and inverse problem; (b) a collocation finite element method for solving the magnetic integral and a Galerkin finite element method for the magnetic differential equations; (c) a nonlinear regularizing optimization method to make the inversion stable and of high resolution; and (d) a new parallel 3D modeling and inversion using a global integral and local differential domain decomposition technique (GILD). The new 3D nonlinear electromagnetic inversion has been tested with synthetic data and field data. The authors obtained very good imaging for the synthetic data and reasonable subsurface EM imaging for the field data. The parallel algorithm has high parallel efficiency over 90% and can be a parallel solver for elliptic, parabolic, and hyperbolic modeling and inversion. The parallel GILD algorithm can be extended to develop a high resolution and large scale seismic and hydrology modeling and inversion in the massively parallel computer.
Koch, M.; Muench, T.
There is now ample evidence from both refraction seismic studies and from more recent local earthquake travel-time analysis of some of the authors that large sections of the upper mantle underneath Europe and Germany, in particular, are anisotropic. Employing a modified version of the method of simultaneous inversion for structure and hypocenters (SSH) of the first author, including a priori known upper mantle anisotropy, a full 3D SSH-inversion underneath Germany is carried out. Regional travel times from local events occurring between 1975 - 2003 are used which, after application of several selection criteria, results in ~1300 events with a total of ~30000 P- and S-phases for the SSH inversion. The SSH procedure is carried out in several incremental steps. First of all improved 1D seismic velocity models are derived assuming an isotropic as well as an anisotropic upper mantle. In addition of a slightly better model fit for the anisotropic than for the isotropic model, the latter gives also a somewhat lower Pn-velocity of ~7.90 km/s, compared with ~8.0 km/s for the former. This indicates that inclusion of upper mantle anisotropy into the SSH model is required to obtain physically reasonable Pn-velocities. The results for the P-velocity in the lower crust are less clear, because of some trade-off with the upper mantle layer. Increasingly refined 3D seismic models are then computed, starting with a lateral discretization into 15 x 15 blocs (=40 x 40 km per bloc) and finally going up to 35 × 35 blocs, (=16 x 16 km). For each of the models, inversion solutions for the isotropic, as well as the anisotropic case are examined. The quality of the solution is estimated by means of various tests for resolution, covariance and other trade-off characteristics of the data- and the model-space. Significant improvements for both the isotropic and anisotropic upper mantle cases are obtained for full 3D SSH inversion models. Similar to the 1D Pn-velocity models there are
A design modification of Rotor 67 is carried out with a full 3D inverse method. The blade camber surface is modified to produce a prescribed pressure loading distribution, with the blade tangential thickness distribution and the blade stacking line at midchord kept the same as the original Rotor 67 design. Because of the inviscid-flow assumption used in the current version of the method, Rotor 67 geometry is modified for use at a design point different from the original design value. A parametric study with the prescribed pressure loading distribution yields the following results. In the subsonic section, smooth pressure loading shapes generally produce blades with well-behaved blade surface pressure distributions. In the supersonic section, the study shows that the strength and position of the passage shock correlate with the characteristics of the blade pressure loading shape. In general, "smooth" prescribed blade pressure loading distributions generate blade designs with reverse cambers which have the effect of weakening the passage shock.
Wang, G.L.; Chew, W.C.; Cui, T.J.; Aydiner, A.A.; Wright, D.L.; Smith, D.V.
Three-dimensional (3D) subsurface imaging by using inversion of data obtained from the very early time electromagnetic system (VETEM) was discussed. The study was carried out by using the distorted Born iterative method to match the internal nonlinear property of the 3D inversion problem. The forward solver was based on the total-current formulation bi-conjugate gradient-fast Fourier transform (BCCG-FFT). It was found that the selection of regularization parameter follow a heuristic rule as used in the Levenberg-Marquardt algorithm so that the iteration is stable.
Romani, Roger W.
PSR J2030+4415 is a LAT-discovered 0.5My-old gamma-ray pulsar with an X-ray synchrotron trail and a rare Halpha bowshock. We have obtained GMOS IFU spectroscopic imaging of this shell, and show a sweep through the remarkable Halpha structure, comparing with the high energy emission. These data provide a unique 3D map of the momentum distribution of the relativistic pulsar wind. This shows that the pulsar is moving nearly in the plane of the sky and that the pulsar wind has a polar component misaligned with the space velocity. The spin axis is shown to be inclined some 95degrees to the Earth line of sight, explaining why this is a radio-quiet, gamma-only pulsar. Intriguingly, the shell also shows multiple bubbles that suggest that the pulsar wind power has varied substantially over the past 500 years.
Detection of Morrow A sandstones is a major problem in the exploration of new fields and the characterization of existing fields because they are very thin and laterally discontinuous. The present research shows the advantages of S-wave data in detecting and characterizing the Morrow A sandstone. Full-waveform modeling is done to understand the sandstone signature in P-, PS- and S-wave gathers. The sandstone shows a distinct high-amplitude event in pure S-wave reflections as compared to the weaker P- and PS-wave events. Modeling also helps in understanding the effect of changing sandstone thickness, interbed multiples (generated by shallow high-velocity anhydrite layers) and sidelobe interference effect (due to Morrow shale) at the Morrow A level. Multicomponent data need proper care while processing, especially the S-wave data which are aected by the near-surface complexity. Cross-spread geometry and 3D FK filtering are effective in removing the low-velocity noise trends. The S-wave data obtained after stripping the S-wave splitting in the overburden show improvement for imaging and reservoir property determination. Individual P- and S-wave attributes as well as their combinations have been analyzed to predict the A sandstone thickness. A multi-attribute map and collocated cokriging procedure is used to derive the seismic-guided isopach of the A sandstone. Postle Field is undergoing CO2 flooding and it is important to understand the characteristics of the reservoir for successful flood management. Density can play an important role in finding and monitoring high-quality reservoirs, and to predict reservoir porosity. prestack P- and S-wave AVO inversion and joint P- and S-wave inversion provide density estimates along with the P- and S-impedance for better characterization of the Morrow A sandstone. The research provides a detailed multicomponent processing, inversion and interpretation work flow for reservoir characterization, which can be used for exploration in
Stephenson, William J.
INTRODUCTION In support of earthquake hazards and ground motion studies in the Pacific Northwest, three-dimensional P- and S-wave velocity (3D Vp and Vs) and density (3D rho) models incorporating the Cascadia subduction zone have been developed for the region encompassed from about 40.2?N to 50?N latitude, and from about -122?W to -129?W longitude. The model volume includes elevations from 0 km to 60 km (elevation is opposite of depth in model coordinates). Stephenson and Frankel (2003) presented preliminary ground motion simulations valid up to 0.1 Hz using an earlier version of these models. The version of the model volume described here includes more structural and geophysical detail, particularly in the Puget Lowland as required for scenario earthquake simulations in the development of the Seattle Urban Hazards Maps (Frankel and others, 2007). Olsen and others (in press) used the model volume discussed here to perform a Cascadia simulation up to 0.5 Hz using a Sumatra-Andaman Islands rupture history. As research from the EarthScope Program (http://www.earthscope.org) is published, a wealth of important detail can be added to these model volumes, particularly to depths of the upper-mantle. However, at the time of development for this model version, no EarthScope-specific results were incorporated. This report is intended to be a reference for colleagues and associates who have used or are planning to use this preliminary model in their research. To this end, it is intended that these models will be considered a beginning template for a community velocity model of the Cascadia region as more data and results become available.
Landes, M.; Hauser, F.; Popa, M.
The Vrancea zone in the south-eastern Carpathians is one of the most active seismic zones in Europe. In order to study the crustal and upper-mantle structure in this region, two seismic refraction/wide-angle reflection experiments were carried out in 1999 and 2001. The 1999 campaign comprised a 320 km long N-S profile and a 80 km long transverse profile (E-W). All shots were recorded simultaneously on both profiles. The profile conducted in 2001 extended in E-W direction from the Hungarian border across the Vrancea zone to the Black Sea. We present an application of a 3-D refraction and reflection tomography algorithm (Hole 1992, 1995), elaborating the crustal velocity and interface structure within a 115 x 235 km wide region around the Vrancea zone. In order to enhance the model resolution, first arrival data from local earthquakes of the CALIXTO-99 teleseismic project were also included. The results indicate a high-velocity structure beneath the northern part of the Vrancea zone extending from shallow levels to depths of about 11 km. This structure may be related to the Trotus and Capidava-Ovidiu faults, which converge to the north of it. The high-velocity region is surrounded by the lower velocity Focsani and Brasov basins. The sedimentary succession beneath the southern part of the model extends to 18 km depth, while in the north sediment thickness varies between 10 and 15 km. Further results of the interface modelling of prominent reflections show that the mid-crustal and Moho interfaces shallow northwards from 30 km to 22 km and from 42 km to 38 km, respectively. This correlates well with previous results of Hauser et al. (2001).
Yuan, H.; Marone, F.; Romanowicz, B.; Abt, D.; Fischer, K.
The tectonic diversity of the North American continent has led to a number of geological, tectonic and geodynamical models, many of which can be better tested with high resolution 3-d tomographic models of the isotropic and anisotropic mantle structure of the continent. In the framework of non-linear asymptotic coupling theory (NACT), we recently developed tools to invert long period seismic waveforms combined with SKS splitting data, for both isotropic and radial and azimuthal anisotropic S-wave velocity structure in the upper mantle at the continental scale (Marone et al., 2007; Marone and Romanowicz, 2007). Striking differences in both isotropic and anisotropic velocity structure were observed: beneath the high velocity stable cratonic region a distinct two-layer anisotropic domain is present, with the bottom layer fast axis direction aligned with the absolute plate motion, and a shallower lithospheric layer with north pointing fast axis most likely showing records of past tectonic history; under the active western US the direction of tomographically inferred anisotropy is stable with depth and compatible with the absolute plate motion direction. Here we present an updated model which includes nearly five more years of data, including data from newly operative USArray stations, and a somewhat more extended frequency band. Our new model confirms our previous results, and reveals greater yet complex details of the anisotropic velocity structure beneath the western U.S.. We also show initial results of incorporating constraints on the depth to the lithosphere-asthenosphere boundary (LAB) using teleseismic receiver functions. We discuss the different anisotropic domains resolved both laterally and in depth, in the context of tectonic history of the north American continent.
Woollam, Jack; Fuenzallida, Amaya; Garth, Tom; Rietbrock, Andreas; Ruiz, Sergio; Tavera, Hernando
Seismic velocity tomography is one of the key tools in Earth sciences to image the physical properties of the subsurface. In recent years significant advances have been made to image the Chilean subductions zone, especially in the area of the 2010 M8.8 Maule earthquake (e.g. Hicks et al., 2014), providing much needed physical constraints for earthquakes source inversions and rupture models. In 2014 the M8.2 Iquique earthquake struck the northern part of the Chilean subduction zone in close proximity to the Peruvian boarder. The pre- and aftershock sequence of this major earthquake was recorded by a densified seismological network in Northern Chile and Southern Peru, which provides an excellent data set to study in depth the 3D velocity structure along the subduction megathrust. Based on an automatic event catalogue of nearly 10,000 events spanning the time period March to May 2014 we selected approximately 450 events for a staggered 3D inversion approach. Events are selected to guarantee an even ray coverage through the inversion volume. We only select events with a minimum GAP of 200 to improve depth estimates and therefore increase resolution in the marine forearc. Additionally, we investigate secondary arrivals between the P- and S-wave arrival to improve depth location. Up to now we have processed about 450 events, from which about 150 with at least 30 P- and S-wave observations have been selected for the subsequent 3D tomography. Overall the data quality is very high, which allows arrival time estimates better than 0.05s on average. We will show results from the 1D, 2D, and preliminary 3D inversions and discuss the results together with the obtained seismicity distribution.
Dong, H.; Kun, Z.; Zhang, L.
This magnetotelluric (MT) system contains static shift correction and 3D inversion. The correction method is based on the data study on 3D forward modeling and field test. The static shift can be detected by the quantitative analysis of apparent parameters (apparent resistivity and impedance phase) of MT in high frequency range, and completed correction with inversion. The method is an automatic processing technology of computer with zero-cost, and avoids the additional field work and indoor processing with good results shown in Figure 1a-e. Figure 1a shows a normal model (I) without any local heterogeneity. Figure 1b shows a static-shifted model (II) with two local heterogeneous bodies (10 and 1000 ohm.m). Figure 1c is the inversion result (A) for the synthetic data generated from model I. Figure 1d is the inversion result (B) for the static-shifted data generated from model II. Figure 1e is the inversion result (C) for the static-shifted data from model II, but with static shift correction. The results show that the correction method is useful. The 3D inversion algorithm is improved base on the NLCG method of Newman & Alumbaugh (2000) and Rodi & Mackie (2001). For the algorithm, we added the frequency based parallel structure, improved the computational efficiency, reduced the memory of computer, added the topographic and marine factors, and added the constraints of geology and geophysics. So the 3D inversion could even work in PAD with high efficiency and accuracy. The application example of theoretical assessment in oil and gas exploration is shown in Figure 1f-i. The synthetic geophysical model consists of five layers (from top to downwards): shale, limestone, gas, oil, groundwater and limestone overlying a basement rock. Figure 1f-g show the 3D model and central profile. Figure 1h shows the centrel section of 3D inversion, the resultsd show a high degree of reduction in difference on the synthetic model. Figure 1i shows the seismic waveform reflects the
Miensopust, Marion P.; Queralt, Pilar; Jones, Alan G.; 3D MT modellers
Over the last half decade the need for, and importance of, three-dimensional (3-D) modelling of magnetotelluric (MT) data have increased dramatically and various 3-D forward and inversion codes are in use and some have become commonly available. Comparison of forward responses and inversion results is an important step for code testing and validation prior to `production' use. The various codes use different mathematical approximations to the problem (finite differences, finite elements or integral equations), various orientations of the coordinate system, different sign conventions for the time dependence and various inversion strategies. Additionally, the obtained results are dependent on data analysis, selection and correction as well as on the chosen mesh, inversion parameters and regularization adopted, and therefore, a careful and knowledge-based use of the codes is essential. In 2008 and 2011, during two workshops at the Dublin Institute for Advanced Studies over 40 people from academia (scientists and students) and industry from around the world met to discuss 3-D MT inversion. These workshops brought together a mix of code writers as well as code users to assess the current status of 3-D modelling, to compare the results of different codes, and to discuss and think about future improvements and new aims in 3-D modelling. To test the numerical forward solutions, two 3-D models were designed to compare the responses obtained by different codes and/or users. Furthermore, inversion results of these two data sets and two additional data sets obtained from unknown models (secret models) were also compared. In this manuscript the test models and data sets are described (supplementary files are available) and comparisons of the results are shown. Details regarding the used data, forward and inversion parameters as well as computational power are summarized for each case, and the main discussion points of the workshops are reviewed. In general, the responses
Adhikari, Deepak; Gemmell, Brad J; Hallberg, Michael P; Longmire, Ellen K; Buskey, Edward J
We describe an automated, volumetric particle image velocimetry (PIV) and tracking method that measures time-resolved, 3D zooplankton trajectories and surrounding volumetric fluid velocity fields simultaneously and non-intrusively. The method is demonstrated for groups of copepods flowing past a wall-mounted cylinder. We show that copepods execute escape responses when subjected to a strain rate threshold upstream of a cylinder, but the same threshold range elicits no escape responses in the turbulent wake downstream. The method was also used to document the instantaneous slip velocity of zooplankton and the resulting differences in trajectory between zooplankton and non-inertial fluid particles in the unsteady wake flow, showing the method's capability to quantify drift for both passive and motile organisms in turbulent environments. Applications of the method extend to any group of organisms interacting with the surrounding fluid environment, where organism location, larger-scale eddies and smaller-scale fluid deformation rates can all be tracked and analyzed. PMID:26486364
Strachan, L.; Panasyuk, A. V.; Dobrzycka, D.; Gibson, S.; Biesecker, D. A.; Ko, Y.-K.; Galvin, A. B.; Romoli, M.; Kohn, J. L.
We constrain coronal outflow velocity solutions, resolved along the line-of-sight, by using Doppler dimming models of H I Lyman alpha and O VI 1032/1037 Angstrom emissivities obtained with data from the Ultraviolet Coronagraph Spectrometer (UVCS) on SOHO. The local emissivities, from heliocentric heights of 1.5 to 3.0 radii, were determined from 3-D reconstructions of line-of-sight intensities obtained during the Whole Sun Month Campaign (10 Aug. -- 8 Sep. 1996). The models use electron densities derived from polarized brightness measurements made with the visible light coronagraphs on UVCS and LASCO, supplemented with data from Mark III at NCAR/MLSO. Electron temperature profiles are derived from `freezing-in' temperatures obtained from an analysis of charge state data from SWICS/Ulysses. The work concentrates on O5+ outflow velocities which are determined from an analysis of the the O VI line ratios. This analysis is less sensitive to the uncertainties in the electron density and independent of the ionization balance and elemental abundance than the analyses which use individual spectral lines. This work is supported in part by NASA under grant NAG-3192 to the Smithsonian Astrophysical Observatory, by the Italian Space Agency and by Swiss funding agencies.
Pare, Pascal; Gribenko, Alexander V.; Cox, Leif H.; Čuma, Martin; Wilson, Glenn A.; Zhdanov, Michael S.; Legault, Jean; Smit, Jaco; Polome, Louis
Geological, geochemical, and geophysical surveys have been conducted in the area of the Pebble Cu-Au-Mo porphyry deposit in south-west Alaska since 1985. This case study compares three-dimensional (3D) inversion results from Anglo American's proprietary SPECTREM 2000 fixed-wing time-domain airborne electromagnetic (AEM) and Geotech's ZTEM airborne audio-frequency magnetics (AFMAG) systems flown over the Pebble deposit. Within the commonality of their physics, 3D inversions of both SPECTREM and ZTEM recover conductivity models consistent with each other and the known geology. Both 3D inversions recover conductors coincident with alteration associated with both Pebble East and Pebble West. The high grade CuEqn 0.6% ore shell is not consistently following the high conductive trend, suggesting that the SPECTREM and ZTEM responses correspond in part to the sulphide distribution, but not directly with the ore mineralization. As in any exploration project, interpretation of both surveys has yielded an improved understanding of the geology, alteration and mineralization of the Pebble system and this will serve well for on-going exploration activities. There are distinct practical advantages to the use of both SPECTREM and ZTEM, so we draw no recommendation for either system. We can conclude however, that 3D inversion of both AEM and ZTEM surveys is now a practical consideration and that it has added value to exploration at Pebble.
Sherburn, S.; White, R.
Mt Taranaki is a 2518 m andesite cone-volcano (last eruption AD1755) within an oil-bearing sedimentary basin approximately 50 km west of the deepest part of the Benioff zone beneath the North Island of New Zealand. It is the most recent of a series of volcanoes that have erupted in the Taranaki region in the last 1.7 million years. Although a permanent six-station seismic network monitors Mt Taranaki for signs of unrest, little is known of the structure at the depths earthquakes occur and magma maybe stored. This information is vital for interpreting precursors to any future eruption. For nine months in 2001-2002, a temporary network of 75 three-component, broadband (0.03 - 50 Hz) seismographs (area c. 100 km by 100 km) was used to collect data to image crustal structure and accurately locate earthquakes in the Taranaki region. Three hundred and eighty-nine earthquakes were located using more than 15,000 phase picks (55% P and 45% S). A joint inversion for 1D Vp, Vs and hypocentres was undertaken using Velest followed by a 3D inversion for Vp, Vp/Vs ratio and hypocentres using Simul2000. The base of the seismogenic zone increases gradually from a depth of 20 km immediately west of Mt Taranaki to 35 km deep 100 km to the east, corresponding to a previously observed increase in crustal thickness. The area close to Mt Taranaki is anomalous in that there are few earthquakes and all are shallower than 10 km. Within the upper 5-10 km of the crust Vp is closely related to surface geology, being high beneath Mt Taranaki, low beneath the surrounding sedimentary basin, and very high to the east of the basin. We present the Vp and Vp/Vs structure and hypocentre distribution of the Taranaki region and discuss features that can be attributed to volcanism at Mt Taranaki and older volcanic centres.
Prutkin, Ilya; Vajda, Peter; Jentzsch, Gerhard
wavelengths for the Thuringian Basin have shown, that if we explain negative anomalies with topography of near-surface layers, the obtained solution is not supported by boreholes data. Upper part of a geological section is usually well studied, therefore, it is not always possible, to shift sources upward, because it can contradict to available geological information. For each local anomaly, its interpretation includes several steps. We subtract the model of the regional field (2D harmonic function). Then, we approximate the residuals with 3D line segments, it provides reliable estimates for mass and center of mass coordinates. For the Kolarovo anomaly of 25 mGal, residuals by approximation have RMS = 0.57 mGal. Here we find very few parameters (14 for two segments) according to several thousand observations, which is quite stable. Finally, we transform a chosen set of line segments into a restricted object or a contact surface with the same field (in the situation where a solution of the inverse problem is unique). We have obtained a model for intermediate wavelengths in the Thuringian Basin, which includes three restricted bodies (granitic intrusions) and a density interface with topography below them.
Maceira, M.; Rowe, C. A.; Allen, R. M.; Obrebski, M. J.
As seismic instrumentation, data storage and dissemination and computational power improve, seismic velocity models attempt to resolve smaller structures and cover larger areas. However, it is unclear how accurate these velocity models are and, while the best models available are used for event determination, it is difficult to put uncertainties on seismic event parameters. Model validation is typically done using resolution tests that assume the imaging theory used is accurate and thus only considers the impact of the data coverage on resolution. We present the results of a more rigorous approach to model validation via full three-dimensional waveform propagation using Spectral Element Methods (SEM). This approach makes no assumptions about the theory used to generate the models but require substantial computational resources. We first validate 3D tomographic models for the Western USA generated using both ray-theoretical and finite-frequency methods. The Dynamic North America (DNA) Models of P- and S- velocity structure (DNA09-P and DNA09-S) use teleseismic body-wave traveltime residuals recorded at over 800 seismic stations provided by the Earthscope USArray and regional seismic networks. We performed systematic computations of synthetics for the dataset used to generate the DNA models. Direct comparison of these synthetic seismograms to the actual observations allows us to accurately assess and validate the models. Implementation of the method for a densely instrumented region such as that covered by the DNA model provides a useful testbed for the validation methods that we will subsequently apply to other, more challenging study areas.
Thurber, C. H.; Lin, G.; Zhang, H.; Hauksson, E.; Shearer, P.; Waldhauser, F.; Hardebeck, J.; Brocher, T.
Network and the Southern California Seismic Network. These events are critical to the determination of the seismic velocity model in central California, in the former `no-mans-land' between the Northern and Southern California networks. Ultimately, a combination of active-source datasets, composite events, original catalog picks, and differential times from both waveform cross-correlation and catalog picks will be used in a double-difference tomography inversion.
Green, A.; Gribenko, A.; Cuma, M.; Zhdanov, M. S.
In this paper we apply 3D inversion to MT data collected in Oregon as a part of the EarthScope project. We use the integral equation method as a forward modeling engine. Quasi-analytical approximation with a variable background (QAVB) method of Frechet derivative calculation is applied. This technique allows us to simplify the inversion algorithm and to use just one forward modeling on every iteration step. The receiver footprint approach considerably reduces the computational resources needed to invert the large volumes of data covering vast areas. The data set, which was used in the inversion, was obtained through the Incorporated Research Institutions for Seismology (IRIS). The long-period MT data was collected in Eastern Oregon in 2006. The inverted electrical conductivity distribution agrees reasonably well with geological features of the region as well as with 3D MT inversion results obtained by other researchers. The geoelectrical model of the Oregon deep interior produced by 3D inversion indicates several lithospheres' electrical conductivity anomalies, including a linear zone marked by low-high conductivity transition along the Klamath Blue Mountain Lineament associated with a linear trend of gravity minima. High electrical conductivity values occur in the upper crust under the accreted terrains in the Blue Mountains region.
Petrov, P.; Newman, G. A.
-Fourier domain we had developed 3D code for full-wave field simulation in the elastic media which take into account nonlinearity introduced by free-surface effects. Our approach is based on the velocity-stress formulation. In the contrast to conventional formulation we defined the material properties such as density and Lame constants not at nodal points but within cells. This second order finite differences method formulated in the cell-based grid, generate numerical solutions compatible with analytical ones within the range errors determinate by dispersion analysis. Our simulator will be embedded in an inversion scheme for joint seismic- electromagnetic imaging. It also offers possibilities for preconditioning the seismic wave propagation problems in the frequency domain. References. Shin, C. & Cha, Y. (2009), Waveform inversion in the Laplace-Fourier domain, Geophys. J. Int. 177(3), 1067- 1079. Shin, C. & Cha, Y. H. (2008), Waveform inversion in the Laplace domain, Geophys. J. Int. 173(3), 922-931. Commer, M. & Newman, G. (2008), New advances in three-dimensional controlled-source electromagnetic inversion, Geophys. J. Int. 172(2), 513-535. Newman, G. A., Commer, M. & Carazzone, J. J. (2010), Imaging CSEM data in the presence of electrical anisotropy, Geophysics, in press.
Begnaud, M. L.; Ballard, S.; Young, C. J.; Hipp, J. R.; Encarnacao, A.; Phillips, W. S.; Chael, E. P.; Rowe, C. A.
We are developing a global 3D P wave velocity model of the Earth's crust and mantle using seismic tomography to assess improvement to seismic event locations obtained using high quality 3D Earth models in lieu of 1D and 2/2.5D models. We present the most recent version of SALSA3D (SAndia LoS Alamos 3D) version 1.9, and demonstrate its ability to reduce mislocations for a large set of realizations derived from a carefully chosen set of globally-distributed ground truth (GT) events. Our model is derived from the latest version of the GT catalog of P/Pn travel-time picks assembled by Los Alamos National Laboratory. For this current version, we employ more robust data quality control measures than previously used, as well as additional global GT data sources. To prevent over-weighting due to ray path redundancy and to reduce the computational burden, we cluster rays into representative rays. The model is represented using the triangular tessellation system described by Ballard et al. (2009), which incorporates variable resolution in both the geographic and radial dimensions. For our starting model, we use a simplified layer crustal model derived from the NNSA Unified model in Eurasia and Crust 2.0 model everywhere else, overlying a uniform ak135 mantle. Sufficient damping is used to reduce velocity adjustments so that ray path changes between iterations are small. We obtain proper model smoothness by using progressive grid refinement, refining the grid only in areas where the data warrant such a refinement. In previous versions, we based this refinement on velocity changes from previous model iterations. For the current version, we utilize the diagonal of the model resolution matrix to control where grid refinement occurs, resulting in more consistent and continuous areas of refinement than before. In addition to the changes in grid refinement, we also employ a more robust convergence criterion between successive grid refinements, allowing a better fit to first broader
Burgess, Ian B; Aizenberg, Joanna; Lončar, Marko
Structural hierarchy and complex 3D architecture are characteristics of biological photonic designs that are challenging to reproduce in synthetic materials. Top-down lithography allows for designer patterning of arbitrary shapes, but is largely restricted to planar 2D structures. Self-assembly techniques facilitate easy fabrication of 3D photonic crystals, but controllable defect-integration is difficult. In this paper we combine the advantages of top-down and bottom-up fabrication, developing two techniques to deposit 2D-lithographically-patterned planar layers on top of or in between inverse-opal 3D photonic crystals and creating hierarchical structures that resemble the architecture of the bright green wing scales of the butterfly, Parides sesostris. These fabrication procedures, combining advantages of both top-down and bottom-up fabrication, may prove useful in the development of omnidirectional coloration elements and 3D-2D photonic crystal devices. PMID:24263010
Gao, Fengxia; Wang, Yanghua
Seismic waveform tomography can invert for the velocity and attenuation (Q- 1) variations simultaneously. For this simultaneous inversion, we propose two strategies for waveform tomography. First, we analyze the contributions of the real part and the imaginary part of the gradients, associated with the velocity and attenuation parameters respectively, and determine that the combination of the real part of the gradient subvector for the velocity parameter and the imaginary part of the gradient subvector for the attenuation parameter would produce an optimal inversion result. Second, we attempt to balance the sensitivities of the objective function to the velocity and the attenuation parameters. Considering the magnitude differences between these two-type parameters in the simultaneous inversion, we apply preliminarily a normalization to both the velocity model and the attenuation model. However, for balancing their sensitivities, we further adjust the corresponding model updates using a tuning factor. We determine this tuning parameter adaptively, based on the sensitivities of these two parameters, at each iteration. Numerical tests demonstrate the feasibility and reliability of these two strategies in full waveform inversion.
Ballard, S.; Young, C. J.; Hipp, J. R.; Chang, M.; Lewis, J.; Begnaud, M. L.; Rowe, C. A.
further refinement takes place around adjusted nodes to form a new model, and the process is repeated until no more improvement can be obtained. We thus produce a smooth, multi-resolution model with node density appropriate to both ray coverage and the velocity gradients required by the data. This scheme is computationally expensive, so we use a Java-based distributed computing framework developed by Sandia National Laboratories (SNL), providing us with 300+ processors having an efficiency of better than 90% for the calculations. We evaluate our model both in terms of travel time residual variance reduction and in location improvement for GT events. For the latter, we use a new multi-threaded version of the SNL-developed LocOO code modified to use 3D velocity models.
Lelievre, Peter; Farquharson, Colin; Hurich, Charles
methods for use when such a relationship is not available or can not be prescribed. In our joint inversion approach, we discretise the subsurface on an unstructured tetrahedral 3D grid, which, compared to rectilinear discretisation, allows 1) efficient generation of complicated subsurface geometries when such information is known a priori, and 2) can significantly reduce the problem size. The Fast Marching Method is used for the first arrival travel time forward solution and the gravity solution can be calculated using an analytic response for tetrahedra or via a finite element solution to Poisson's equation. When an empirical relationship between physical properties can be developed, our inversion approach can enforce that relationship to some degree commensurate with our confidence in the relationship. In the absence of an empirical relationship, we employ a correlation measure to encourage the properties to maintain a general linear or log-linear relationship. Again, the strength of this correlation constraint can be adjusted based on our confidence in the underlying assumption. In a further extension, we apply an additional fuzzy c-mean measure to encourage the recovered physical property distributions to cluster following the characteristics of the joint physical property distributions determined a priori. If such a priori information is not available, suitable cluster locations can be estimated through an iterative strategy. Rather than moving to a computationally intensive statistical sampling methodology, we work in a deterministic framework, where well-behaved functions are minimized via a descent search. After some instructional mathematical preliminaries, we present our methods on synthetic and real data scenarios from the Voisey's Bay massive sulphide deposit in Labrador, Canada.
Shibutani, T.; Imai, M.; Hirahara, K.; Nakao, S.
Kii Peninsula is a part of the source area of Nankai Trough megaquakes and the region through which the strong seismic waves propagate to big cities in Kansai such as Osaka, Kyoto, Nara, Kobe, and so on. Moreover, the rupture starting point is thought to be possibly at off the peninsula. Therefore, it is important for simulations of the megaquakes and the strong motions to estimate accurately the configuration of the Philippine Sea slab and the seismic velocity structure around the slab and to investigate properties and conditions of the plate boundary surface. Deep low frequency events (DLFEs) are widely distributed from western Shikoku to central Tokai at 30 - 40 km depths on the plate boundary (Obara, 2002). Results from seismic tomography and receiver function analyses revealed that the oceanic crust of the Philippine Sea plate had a low velocity and a high Vp/Vs ratio (Hirose et al., 2007; Ueno et al., 2008). Hot springs with high 3He/4He ratios are found in an area between central Kinki and Kii Peninsula despite in the forearc region (Sano and Wakita, 1985). These phenomena suggest the process that H2O subducting with the oceanic crust dehydrates at the depths, causes the DLFEs, and moves to shallower depths. We carried out linear array seismic observations in the Kii Peninsula since 2004 in order to estimate the structure of the Philippine Sea slab and the surrounding area. We have performed receiver function analyses for four profile lines in the dipping direction of the slab and two lines in the perpendicular direction so far. We estimated three dimensional shapes of seismic velocity discontinuities such as the continental Moho, the upper surface of the oceanic crust and the oceanic Moho (Imai et al., 2013, this session). In addition, we performed seismic tomography with a velocity model embedded the discontinuities and observed travel times at stations in the linear arrays, and successfully estimated 3D seismic velocity structure around the Philippine Sea
Barnoud, Anne; Bouligand, Claire; Coutant, Olivier
We linearly invert magnetic data for 3D magnetization distribution using a Bayesian methodology with a grid discretization of the space. The Bayesian approach introduces covariance matrices to regularize the ill-posed problem and overcome the non-uniqueness of the solution (Tarantola & Valette, 1982). The use of spatial covariance matrices and grid discretization leads to smooth and compact models. The algorithm provides 3D magnetization models along with resolution parameters extracted from the resolution matrix. The direct computation of the magnetic field includes the surface topography and assumes a linear relationship between rock magnetization and the magnetic field they produce. The methodology is applied to aeromagnetic data from the volcanic island of Basse-Terre in Guadeloupe, Lesser Antilles (Le Borgne & Le Mouël 1976, Le Mouël et al., 1979). Low magnetizations (a few A/m) allow linear inversion that takes into account polarity inversions of the geomagnetic field that occurred across the volcanic history of the island. Inverted magnetizations are consistent with paleomagnetic measurements on surface samples (Carlut et al., 2000 ; Samper et al., 2007). The resulting 3D model is validated against a 2D inversion performed in the Fourier domain (Parker & Huestis, 1974; Bouligand et al., 2014). The 3D distribution of magnetization helps identifying the different volcanic edifices that build the island both at the surface and up to 3 km depth.
Begnaud, M. L.; Ballard, S.; Young, C. J.; Hipp, J. R.; Chang, M.; Encarnacao, A.; Rowe, C. A.; Phillips, W. S.; Steck, L.
To test the hypothesis that high quality 3D Earth models will produce seismic event locations that are more accurate and more precise than currently used 1D and 2/2.5D models, we are developing a global 3D P wave velocity model of the Earth's crust and mantle using seismic tomography. In this paper, we present the most recent version of our model, SALSA3D (SAndia LoS Alamos 3D) version 1.7, and demonstrate its ability to reduce mislocations for a large set of realizations derived from a carefully chosen set of globally-distributed ground truth (GT) events, compared to existing models and/or systems. Our model is derived from the latest version of the GT catalog of P and Pn travel time picks assembled by Los Alamos National Laboratory. To prevent over-weighting due to ray path redundancy and to reduce the computational burden, we cluster rays to produce representative rays. Reduction in the total number of ray paths is ~50%. The model is represented using the triangular tessellation system described by Ballard et al. (2009), which incorporates variable resolution in both the geographic and radial dimensions. For our starting model, we use a simplified layer crustal model derived from the NNSA Unified model in Eurasia and Crust 2.0 model elsewhere, over a uniform ak135 mantle. Sufficient damping is used to reduce velocity adjustments so that ray path changes between iterations are small. We obtain proper model smoothness by using progressive grid refinement, refining the grid only in areas where the data warrant it. In previous versions of SALSA3D, we based this refinement on velocity changes from previous model iterations. For version 1.7, we utilize the diagonal of the model resolution matrix to control where grid refinement occurs, resulting in more consistent and continuous areas of refinement than before. Our approach produces a smooth, multi-resolution model with node density appropriate to both ray coverage and the velocity gradients required by the data. We
We present a new method dedicated to the interpretation of full gravity gradient tensor data, based on SL0 sparse recovery inversion. The SL0 sparse recovery method aims to find out the minimum value of the objective function to fit the data function and to solve the non-zero solution to the objective function. Based on continuous iteration, we can easily obtain the final global minimum (namely the property and space attribute of the inversion target). We consider which type of tensor data combination produces the best inversion results based on the inversion results of different full gravity gradient tensor data combinations (separate tensor data and combined tensor data). We compare the recovered models obtained by inverting the different combinations of different gravity gradient tensor components to understand how different component combinations contribute to the resolution of the recovered model. Based on the comparison between the SL0 sparse recovery inversion results and the smoothest and focusing inversion results of the full gravity gradient tensor data, we show that SL0 sparse recovery inversion can obtain more stable and efficient inversion results with relatively sharp edge information, and that this method can also produce a stable solution of the inverse problem for complex geological structures. This new method to resolve very large full gravity gradient tensor datasets has the considerable advantage of being highly efficient; the full gravity gradient tensor inversion requires very little time. This new method is very effective in explaining the full gravity tensor which is very sensitive to small changes in local anomaly. The numerical simulation and inversion results of the compositional model indicates that including multiple components for inversion increases the resolution of the recovered density model and improves the structure delineation. We apply our inversion method to invert the gravity gradient tensor survey data from the Vinton salt
Figueiredo, Pedro; Barbosa, Tiago M; Vilas-Boas, João Paulo; Fernandes, Ricardo J
The purpose of this study was to examine the relationship between the energy cost (C) and the 3D intracycle velocity variation (IVV; swimming direction--x, vertical--y and lateral--z axes) throughout the 200 m front crawl event. Ten international level swimmers performed a maximal 200 m front crawl swim followed by 50, 100 and 150 m bouts at the same pace as in the 200 m splits. Oxygen consumption was measured during the bouts and blood samples were collected before and after each one. The C was calculated for each 50 m lap as the ratio of the total energy expenditure (three energy pathways) to the distance. A respiratory snorkel and valve system with low hydrodynamic resistance was used to measure pulmonary ventilation and to collect breathing air samples. Two above water and four underwater cameras videotaped the swim bouts and thereafter APAS was used to assess the centre of mass IVV (x, y and z components). The increase in the C was significantly associated with the increase in the IVV in x for the first 50 m lap (R = -0.83, P < 0.01). It is concluded that the IVV relationship with C in a competitive event does not present the direct relationship found in the literature, revealing a great specificity, which suggests that the relation between these two parameters could not be used as a performance predictor in competitive events. PMID:22262010
Eusemann, Christian D.; Ritman, Erik L.; Robb, Richard A.
Quantitative assessment of regional heart motion has the potential to provide diagnostic data for assessment of cardiac malfunction. Local heart motion may be obtained with various medical imaging scanners, so the goal is to provide an imaging modality-independent display/analysis technique. In this study, 3D reconstructions of a canine heart before and after infarction were obtained from the Dynamic Spatial Reconstructor (DSR) at 15 time points throughout one cardiac cycle. Deformable models of each time point were created. Through this process regional excursions and velocities in the mesh can be assigned to represent a piece of endocardium, which can be calculated for each time-point interval. These calculations are based on the distance change between a single vertex of the mesh and the model centerline from LV apex to aortic/mitral valve separation. This allows computation of color maps corresponding to regional values of contraction or dilation motion of the endocardium relative to the LV long axis (centerline) during systole and/or diastole. These color maps can be illustrated through model animations and multi view static images. Using functional parametric mappings of disturbances in regional contractility and relaxation facilitates appreciation of the effect of altered structure-to-function relationships in the myocardium.
Gray, S.; Hagin, F.
A family of one-dimensional inverse problems are considered with the goal of reconstructing velocity profiles to reasonably high accuracy. The travel-time variable change is used together with an iteration scheme to produce an effective algorithm for computation. Under modest assumptions the scheme is shown to be convergent.
Koch, Stephan; Kuvshinov, Alexey
We present the first inversion of geomagnetic Sq data in a framework of 3-D conductivity models. This problem has been considered as immensely difficult due to the complex spatial structure of the Sq source which, in addition, varies with season and solar activity. Recently, we developed a 3-D electromagnetic (EM) inversion solution that allows one to work in a consistent manner with data that originates from sources, irrespective of their spatial complexity. In this paper, we apply our 3-D EM inversion scheme to Sq data collected during the Australian Wide Array of Geomagnetic Stations project. Within this project, three components of the geomagnetic field were recorded between 1989 November and 1990 December with the use of 53 portable vector magnetometers. The instruments were distributed over the Australian mainland with an average spacing of 275 km between sites. Inverting this unique-in a sense of its spatial regularity, density and long operational time-data set, we recovered the 3-D conductivity distribution beneath Australia at upper mantle depths (100-520 km). This depth range was justified in the paper from resolution studies using checkerboard tests. In addition, we performed extensive modelling to estimate quantitatively the influence of various factors on Sq signals, namely from hypothetical anomalies, inaccuracy in the source, ocean, and model discretization. As expected, the ocean (coastal) effect appeared to be the largest so that it has to be accounted for during 3-D inversion as accurately as possible. Our 3-D inversions-of data from either single or multiple days-revealed a strong offshore conductor near the south-east coast of Australia, which persists at all considered depths. Varying in details, this anomaly is remarkably robust irrespective of the considered day(s). We compared our results to those obtained from a different inversion scheme and an independent induction data set, and observed encouraging similarity. Combination of the two
Grünsteidl, Clemens; Murray, Todd W; Berer, Thomas; Veres, István A
In the presented work, the characterization of plates using zero group velocity Lamb modes is discussed. First, analytical expressions are shown for the determination of the k-ω location of the zero group velocity Lamb modes as a function of the Poisson's ratio. The analytical expressions are solved numerically and an inverse problem is formulated to determine the unknown wave velocities in plates of known thickness. The analysis is applied to determine the elastic properties of tungsten and aluminum plates based on the experimentally measured frequency spectra. PMID:26527393
Wang, Y.; Forsyth, D. W.; Savage, B.
In our previous surface wave study in Gulf of California area, we developed a moderate-resolution 3D shear velocity model by employing two-plane wave field representation array technique and 2D finite frequency kernels based on Born’s approximation. Using both amplitude and phase information of 22-111s teleseismic Rayleigh wave, we were able to constrain a lateral resolution on the order of 100 km in the upper 160 km depth. In order to enhance resolution beneath the highly heterogeneous Gulf region, we carry on further study using Spectral element method (SEM) for forward wave propagation simulation and adjoint method for tomographic inversion. The code we are using is SPECFEM3D_GLOBE by Komatitsch and Tromp et al. To enhance the resolution in the Gulf, we will minimize the waveform difference between the regional earthquake seismograms, recorded by NARS-Baja seismic array and stations in southern California, and synthetic seismograms simulated by SEM, to iteratively update the current model based on an adjoint inversion. Taking our current 3D moderate-resolution model as starting point and a recently developed crustal structure of Gulf region should help to reduce the number of iterations. There are two reasons that resolution should be enhanced compared to surface wave tomography: first, regional events contain more high frequency signals than teleseismic events; second, SEM is a full waveform synthesis method avoiding many of the usual approximations in tomographic studies. Improved tomographic images of 3D velocity heterogeneities in the upper mantle of Gulf of California will help to identify compositional and temperature variations, leading to a better understanding of mantle dynamics in the region.
Klotzsche, A.; Van Der Kruk, J.; Oberroehrmann, M.; Vanderborght, J.; Vereecken, H.
Soil moisture is a key state variable that controls water and mass fluxes in soil-plant systems and is variable in space and time. Over the last year's, hydrogeophysical methods such as ground penetrating radar (GPR) have been used to determine electromagnetic properties as proxies for soil water content (SWC). Here, we combined zero-offset-profiles (ZOP) GPR measurements within multiple horizontal minirhizotubes at different depths to determine the spatial and temporal variability of SWC under a winter wheat stand at the Selhausen test site (Germany). We studied spatio-temporal variations of SWC under three different treatments: rainfed, irrigated and sheltered. We acquired 15 time-lapse ZOP GPR dataset during the growing season of the wheat in the rhizotron facility using horizontal boreholes with a separation of 0.75m and a length of 6m at six depths between 0.1-1.2m. The obtained radar velocities were converted to SWC using the 4-phase volumetric complex refractive index model. SWC values obtained using standard ray-based processing methods were not reliable close to the surface (0.1-0.2m depth) because of the inference of the critically refracted air wave and the direct wave through the subsurface. Therefore, we implemented a full-waveform inversion that uses accurate 3D forward modeling of GPRMax that incorporates the air and soil interactions. The shuffled complex evolution (SCE) method allowed us to retrieve quantitative medium properties that explained the measured data with a R² of at least 0.95, and improved SWC estimates at all depths. The final SWC distributions for wet and dry conditions showed that the vertical variability is significantly larger than the lateral variability caused by strong influence of precipitation and irrigation events.
Burkhard, N.; Jackson, D. D.
The tau method, developed by Bessonova et al. (1974), of inversion of travel times is applied to lunar P-wave travel time data to find limits on the velocity structure of the moon. Tau is the singular solution to the Clairaut equation. Models with low-velocity zones, with low-velocity zones at differing depths, and without low-velocity zones, were found to be consistent with data and within the determined limits. Models with and without a discontinuity at about 25-km depth have been found which agree with all travel time data to within two standard deviations. In other words, the existence of the discontinuity and its size and location have not been uniquely resolved. Models with low-velocity channels are also possible.
Moorkamp, M.; Fishwick, S.; Jones, A. G.
Typical surface wave tomography can recover well the velocity structure of the upper mantle in the depth range between 70-200km. For a successful inversion, we have to constrain the crustal structure and assess the impact on the resulting models. In addition,we often observe potentially interesting features in the uppermost lithosphere which are poorly resolved and thus their interpretationhas to be approached with great care.We are currently developing a seismically constrained magnetotelluric (MT) inversion approach with the aim of better recovering the lithospheric properties (and thus seismic velocities) in these problematic areas. We perform a 3D MT inversion constrained by a fixed seismic velocity model from surface wave tomography. In order to avoid strong bias, we only utilize information on structural boundaries to combine these two methods. Within the region that is well resolved by both methods, we can then extract a velocity-conductivity relationship. By translating the conductivitiesretrieved from MT into velocities in areas where the velocity model is poorly resolved, we can generate an updated velocity model and test what impactthe updated velocities have on the predicted data.We test this new approach using a MT dataset acquired in central Botswana over the Okwa terrane and the adjacent Kaapvaal and Zimbabwe Cratons togetherwith a tomographic models for the region. Here, both datasets have previously been used to constrain lithospheric structure and show some similarities.We carefully asses the validity of our results by comparing with observations and petrophysical predictions for the conductivity-velocity relationship.
Środa, Piotr; Dec, Monika
The area of Trans-European Suture Zone in SE Poland represents a contact of major tectonic units of different consolidation age - from the Precambrian East European Craton, through Palaeozoic West European Platform to Cenozoic Carpathian orogen. The region was built by several phases of crustal accretion, which resulted in a complex collage of tectonic blocks. In 2000, this region was studied by several seismic wide-angle profiles of CELEBRATION 2000 experiment, providing a dense coverage of seismic data in SE Poland and allowing for detailed investigations of the crustal structure and properties in this area. Beneath the marginal part of the EEC, the 2-D modelling of in-line data form several CELEBRATION profiles revealed a prominent high P-wave velocity anomaly in the upper crust, with Vp of 6.7-7.1 km/s, starting at 10-16 km depth (e.g., Środa et al., 2006). Anomalously high velocities are observed in the area located approximately beneath Lublin trough, to the NE of Teisseyre-Tornquist Zone. Based on 3-D tomography of first arrivals of in- and off-line CELEBRATION 2000 recordings (Malinowski et al., 2008), elevated velocities are also reported in the same area and seem to continue to the SW, off the craton margin. Gravimetric modelling also revealed anomalously high density in the same region at similar depths. High seismic velocities and densities are interpreted as indicative for a pronounced mafic intrusion, possibly related to extensional processes at the EEC margin. Previous 3-D models of the high-velocity intrusion were based on first arrivals (crustal refractions) only. In this study, also off-line reflections (not modelled up to now) are used, in order to enlarge the data set and to better constrain the geometry and properties of the velocity anomaly. A code for 3-D joint tomographic inversion of refracted and reflected arrivals, with model parametrization allowing for velocity discontinuities was used (Rawlinson, 2007). With this approach, besides the
Jia, Jia; Liu, Juan; Jin, Guofan; Wang, Yongtian
Occlusion culling is an important process that produces correct depth cues for observers in holographic displays, whereas current methods suffer from occlusion errors or high computational loads. We propose a fast and effective method for occlusion culling based on multiple light-point sampling planes and an inverse orthographic projection technique. Multiple light-point sampling planes are employed to remove the hidden surfaces for each direction of the view of the three-dimensional (3D) scene by forward orthographic projection, and the inverse orthographic projection technique is used to determine the effective sampling points of the 3D scene. A numerical simulation and an optical experiment are performed. The results show that this approach can realize accurate occlusion effects, smooth motion parallax, and continuous depth using low angular sampling without any extra computation costs. PMID:25322109
Eden, A.; Sigurdson, M.; Mezić, I.; Meinhart, C. D.
Knowledge of 3D, three component velocity fields is central to the understanding and development of effective microfluidic devices for lab-on-chip mixing applications. In this paper we present a hybrid experimental-numerical method for the generation of 3D flow information from 2D particle image velocimetry (PIV) experimental data and finite element simulations of an alternating current electrothermal (ACET) micromixer. A numerical least-squares optimization algorithm is applied to a theory-based 3D multiphysics simulation in conjunction with 2D PIV data to generate an improved estimation of the steady state velocity field. This 3D velocity field can be used to assess mixing phenomena more accurately than would be possible through simulation alone. Our technique can also be used to estimate uncertain quantities in experimental situations by fitting the gathered field data to a simulated physical model. The optimization algorithm reduced the root-mean-squared difference between the experimental and simulated velocity fields in the target region by more than a factor of 4, resulting in an average error less than 12% of the average velocity magnitude.
Chen, P.; Lee, E.; Jordan, T. H.; Maechling, P. J.
Accurate and rapid CMT inversion is important for seismic hazard analysis. We have developed an algorithm for very rapid CMT inversions in a 3D Earth structure model and applied it on small to medium-sized earthquakes recorded by the Southern California Seismic Network (SCSN). Our CMT inversion algorithm is an integral component of the scattering-integral (SI) method for full-3D waveform tomography (F3DT). In the SI method for F3DT, the sensitivity (Fréchet) kernels are constructed through the temporal convolution between the earthquake wavefield (EWF) and the receiver Green tensor (RGT), which is the wavefield generated by 3 orthogonal unit impulsive body forces acting at the receiver location. The RGTs are also the partial derivatives of the waveform with respect to the moment tensors. In this study, our RGTs are computed in a 3D seismic structure model for Southern California (CVM4SI1) using the finite-difference method, which allows us to account for 3D path effects in our source inversion. We used three component broadband waveforms below 0.2 Hz. An automated waveform-picking algorithm based on continuous wavelet transform is applied on observed waveforms to pick P, S and surface waves. A multi-scale grid-searching algorithm is then applied on the picked waveforms to find the optimal strike, dip and rake values that minimize the amplitude misfit and maximize the correlation coefficient. In general, our CMT solutions agree with solutions inverted using other methods and provide better fit to the observed waveforms.
Mu, D.; Lee, E.; Chen, P.; Jordan, T. H.; Maechling, P. J.
Accurate and rapid CMT inversion is important for seismic hazard analysis. We have developed an algorithm for very rapid CMT inversions in a 3D Earth structure model and applied it on small to medium-sized earthquakes recorded by the Southern California Seismic Network (SCSN). Our CMT inversion algorithm is an integral component of the scattering-integral (SI) method for full-3D waveform tomography (F3DT). In the SI method for F3DT, the sensitivity (Fréchet) kernels are constructed through the temporal convolution between the earthquake wavefield (EWF) from the source and the receiver Green tensor (RGT) from the receiver. In this study, our RGTs were computed in a 3D seismic structure model for Southern California (CVM4SI1) using the finite-difference method, which allows us to account for 3D path effects in our source inversion. By storing the RGTs, synthetic seismograms for any source in our modeling volume could be generated rapidly by applying the reciprocity principle. An automated waveform-picking algorithm based on continuous wavelet transform is applied on observed waveforms to pick P, S and surface waves. A grid-searching algorithm is then applied on the picked waveforms to find an optimal focal mechanism that minimizes the amplitude misfit and maximize the weighted correlation coefficient. The grid-search result is then used as the initial solution in a gradient-based optimization algorithm that minimizes the L2 norm of the generalized seismological data functionals (GSDF), which quantifies waveform differences between observed and synthetic seismograms using frequencies-dependent phase-delay and amplitude anomalies. In general, our CMT solutions agree with solutions inverted using other methods and provide better fit to the observed waveforms.
Ballard, S.; Begnaud, M. L.; Young, C. J.; Hipp, J. R.; Chang, M.; Encarnacao, A. V.; Rowe, C. A.; Phillips, W. S.; Steck, L.
To test the hypothesis that high quality 3D Earth models will produce seismic event locations which are more accurate and more precise, we are developing a global 3D P wave velocity model of the Earth’s crust and mantle using seismic tomography. In this paper, we present the most recent version of our model, SALSA3D version 1.5, and demonstrate its ability to reduce mislocations for a large set of realizations derived from a carefully chosen set of globally-distributed ground truth events. Our model is derived from the latest version of the Ground Truth (GT) catalog of P and Pn travel time picks assembled by Los Alamos National Laboratory. To prevent over-weighting due to ray path redundancy and to reduce the computational burden, we cluster rays to produce representative rays. Reduction in the total number of ray paths is ~50%. The model is represented using the triangular tessellation system described by Ballard et al. (2009), which incorporates variable resolution in both the geographic and radial dimensions.. For our starting model, we use a simplified two layer crustal model derived from the Crust 2.0 model over a uniform AK135 mantle. Sufficient damping is used to reduce velocity adjustments so that ray path changes between iterations are small. We obtain proper model smoothness by using progressive grid refinement, refining the grid only around areas with significant velocity changes from the starting model. At each grid refinement level except the last one we limit the number of iterations to prevent convergence thereby preserving aspects of broad features resolved at coarser resolutions. Our approach produces a smooth, multi-resolution model with node density appropriate to both ray coverage and the velocity gradients required by the data. This scheme is computationally expensive, so we use a distributed computing framework based on the Java Parallel Processing Framework, providing us with ~400 processors. Resolution of our model is assessed using a
Thurow, Brian; Johnson, Kyle; Kim, Taehoon; Blois, Gianluca; Best, Jim; Christensen, Ken
The application of Plenoptic PIV in a Refractive Index Matched (RIM) facility housed at Illinois is presented. Plenoptic PIV is an emerging 3D diagnostic that exploits the light-field imaging capabilities of a plenoptic camera. Plenoptic cameras utilize a microlens array to measure the position and angle of light rays captured by the camera. 3D/3C velocity fields are determined through application of the MART algorithm for volume reconstruction and a conventional 3D cross-correlation PIV algorithm. The RIM facility is a recirculating tunnel with a 62.5% aqueous solution of sodium iodide used as the working fluid. Its resulting index of 1.49 is equal to that of acrylic. Plenoptic PIV was used to measure the 3D velocity field of a turbulent boundary layer flow over a smooth wall, a single wall-mounted hemisphere and a full array of hemispheres (i.e. a rough wall) with a k/ δ ~ 4.6. Preliminary time averaged and instantaneous 3D velocity fields will be presented. This material is based upon work supported by the National Science Foundation under Grant No. 1235726.
Gao, J.; Zhang, H.
Near surface geophysical exploration for the purpose of engineering design or construction For this reason, geophysical imaging demands a higher resolution and a better quantitative interpretation. Seismic travel time tomography and direct current resistivity tomography are two main methods for the near surface survey. Because of the limited coverage of observation system and the complex physical relationship between physical parameters and observations, individual geophysical method suffers issues of non-uniqueness and resolution limitation to some degree. We have developed a joint inversion method to combine seismic travel time tomography and full channel resistivity tomography. For the full channel resistivity survey, it uses two electrodes for power supply and all the other electrodes for recording. Compared with the traditional resistivity method, it collects more data and has a better model converge. Our joint inversion strategy relies on the structure constraint enforced through minimizing cross gradients between seismic velocity and resistivity models (Gallardo, 2003). For resistivity tomography, sensitivity kernels are obtained through the adjoint method by solving the electrostatic field equation with the finite-difference method. For seismic travel time tomography, ray paths and travel times are calculated using the fast marching method. We have tested our joint inversion method for a 2D cross-hole problem where two small zones with high and low velocity/resistivity anomalies. Seismic/electrical sources/receivers are installed in two boreholes. For separate seismic inversion, the smearing effect is evident and two anomaly zones are distorted and misplaced. For separate electric resistivity inversion, although two anomaly zones are positioned correctly their values are not accurate. By joint inversion, two velocity anomaly zones are clearly imaged and the smearing effect is greatly reduced. In comparison, for the resistivity model, the two anomaly zones
Zhang, Yi; Yan, Jianguo; Li, Fei; Chen, Chao; Mei, Bao; Jin, Shuanggen; Dohm, James H.
In this paper, we present a method for incorporating prior geological information into potential field data inversion problem. As opposed to the traditional inverse algorithm, our proposed method takes full advantage of prior geological information as a constraint and thus obtains a new objective function for inversion by adding Lagrangian multipliers and slack variables to the traditional inversion method. These additional parameters can be easily solved during iterations. We used both synthetic and observed data sets to test the stability and validity of the proposed method. Our results using synthetic gravity data show that our new method predicts depth and density anomalies more efficiently and accurately than the traditional inversion method that does not include prior geological constraints. Then using observed gravity data in the Three Gorges area and geological constraint information, we obtained the density distribution of the upper and middle crust in this area thus revealing its geological structure. These results confirm the proposed method's validity and indicate its potential application for magnetism data inversion and exploration of geological structures.
Polkowski, Marcin; Grad, Marek
The 3D P-wave seismic velocity model was obtained by combining data from multiple studies during past 50 years. Data sources included refraction seismology, reflection seismology, geological boreholes, vertical seismic profiling, magnetotellurics and gravimetry. Use of many data sources allowed creation of detailed 3D P-wave velocity model that reaches to depth of 60 km and includes 6-layers of sediments and 3-layers of the crust. Purpose of this study is to analyze how 3D model influences local (accuracy of location and source time estimation for local events), regional (identification of wide-angle seismic phases) and global (teleseismic tomography) seismic travel times. Additionally we compare results of forward seismic wave propagation with signals observed on short period and broadband stations. National Science Centre Poland provided financial support for this work by NCN grant DEC-2011/02/A/ST10/00284.
Reiter, D.; Vincent, C.; Johnson, M.
A 3-D velocity model for the crust and upper mantle (WINPAK3D) has been developed to improve regional event location in the India-Pakistan region. Results of extensive testing demonstrate that the model improves location accuracy for this region, specifically for the case of small regionally recorded events, for which teleseismic data may not be available. The model was developed by integrating the results of more than sixty previous studies related to crustal velocity structure in the region. We evaluated the validity of the 3-D model using the following methods: (1) cross validation analysis for a variety of events, (2) comparison of model determined hypocenters with known event location, and (3) comparison of model-derived and empirically-derived source-specific station corrections (SSSC) generated for the International Monitoring System (IMS) auxiliary seismic station located at Nilore. The 3-D model provides significant improvement in regional location compared to both global and regional 1-D models in this area of complex structural variability. For example, the epicenter mislocation for an event with a well known location was only 6.4 km using the 3-D model, compared with a mislocation of 13.0 km using an average regional 1-D model and 15.1 km for the IASPEI91 model. We will present these and other results to demonstrate that 3-D velocity models are essential to improving event location accuracy in regions with complicated crustal geology and structures. Such 3-D models will be a prerequisite for achieving improved location accuracies for regions of high monitoring interest.
Magnússon, E.; Nagler, T.; Hetzenecker, M.; Palsson, F.; Scharrer, K.; Floricioiu, D.; Berthier, E.; Gudmundsson, S.; Rott, H.
We present 3D velocity fields obtained from time series of TerraSAR-X and TanDEM-X images acquired over the ablation area of the Breidamerkurjökull outlet glacier of Vatnjökull Ice Cap (Iceland) in 2008-2012. Coherent and incoherent offset tracking is applied to repeat pass X-Band data to obtain ice displacement in cross and along track direction. Three methods are tested and compared to extract fields of the 3D ice velocity. First, the conventional surface parallel approach, which we consider as an approximation for deriving the horizontal motion rate, but does not reveal a realistic vertical motion. Second, the combination of offset tracking results from almost simultaneous observations from ascending and descending orbits measuring the glacier motion in four different directions, allowing calculation of the 3D velocity fields without any additional approximations. Third, deriving full 3D velocity fields by using the horizontal flow direction, derived from the ascending-descending combination, as constrain on offset tracking results from a single pair of SAR images. The latter two methods reveal a measurement of the vertical ice motion plus ablation, hence equivalent to the vertical motion component measured by GPS station fixed on a platform laying on the ice surface. The results from all methods are compared with such GPS measurements recorded by permanent stations on the glacier in 2008-2012 and the errors of the different methods are calculated. Additionally, we approximate the contribution of these 3D flow fields to elevation changes (emergence/submergence velocity plus net balance) and compare it with elevation changes from surface DEMs obtained in 2008 (SPIRIT), 2010 (airborne LIDAR) and 2012 (TanDEM-X).
NLCGCS inverts electromagnetic responses for a 3D distribution of electrical conductivity and dielectric permittivity within the earth for geophysical applications using single processor computers. The software comes bundled with a graphical user interface to aid in model construction and analysis and viewing of earth images. The solution employs both dipole and finite size source configurations for harmonic oscillatory sources. A new nonlinear preconditioner is included in the solution to speed up solution convergence.
Santhanam, Anand P.; Min, Yugang; Mudur, Sudhir P.; Rastogi, Abhinav; Ruddy, Bari H.; Shah, Amish; Divo, Eduardo; Kassab, Alain; Rolland, Jannick P.; Kupelian, Patrick
A method to estimate the deformation operator for the 3D volumetric lung dynamics of human subjects is described in this paper. For known values of air flow and volumetric displacement, the deformation operator and subsequently the elastic properties of the lung are estimated in terms of a Green's function. A Hyper-Spherical Harmonic (HSH) transformation is employed to compute the deformation operator. The hyper-spherical coordinate transformation method discussed in this paper facilitates accounting for the heterogeneity of the deformation operator using a finite number of frequency coefficients. Spirometry measurements are used to provide values for the airflow inside the lung. Using a 3D optical flow-based method, the 3D volumetric displacement of the left and right lungs, which represents the local anatomy and deformation of a human subject, was estimated from 4D-CT dataset. Results from an implementation of the method show the estimation of the deformation operator for the left and right lungs of a human subject with non-small cell lung cancer. Validation of the proposed method shows that we can estimate the Young's modulus of each voxel within a 2% error level.
Carlson, Leland A.
The primary tasks performed were the continued development of inverse design procedures for the TAWFIVE code, the development of corresponding relofting and trailing edge closure procedures, and the testing of the methods for a variety of cases. The period from July 1, 1986 through December 31, 1986 is covered.
Béthoux, Nicole; Theunissen, Thomas; Beslier, Marie-Odile; Font, Yvonne; Thouvenot, François; Dessa, Jean-Xavier; Simon, Soazig; Courrioux, Gabriel; Guillen, Antonio
The region between the inner zones of the Alps and Corsica juxtaposes an overthickened crust to an oceanic domain, which makes difficult to ascertain the focal depth of seismic events using routine location codes and average 1D velocity models. The aim of this article is to show that, even with a rather lose monitoring network, accurate routine locations can be achieved by using realistic 3D modelling and advanced location techniques. Previous earthquake tomography studies cover the whole region with spatial resolutions of several tens of kilometres on land, but they fail to resolve the marine domain due to the absence of station coverage and sparse seismicity. To overcome these limitations, we first construct a 3D a-priori P and S velocity model integrating known geophysical and geological information. Significant progress has been achieved in the 3D numerical modelling of complex geological structures by the development of dedicated softwares (e.g. 3D GeoModeller), capable at once of elaborating a 3D structural model from geological and geophysical constraints and, possibly, of refining it by inversion processes (Calcagno et al., 2008). Then, we build an arrival-time catalogue of 1500 events recorded from 2000 to 2011. Hypocentres are then located in this model using a numerical code based on the maximum intersection method (Font et al., 2004), updated by Theunissen et al. (2012), as well as another 3D location technique, the NonLinLoc software (Lomax and Curtis, 2001). The reduction of arrival-time residuals and uncertainties (dh, dz) with respect to classical 1D locations demonstrates the improved accuracy allowed by our approach and confirms the coherence of the 3D geological model built and used in this study. Our results are also compared with previous works that benefitted from the installation of dense temporary networks surrounding the studied epicentre area. The resulting 3D location catalogue allows us to improve the regional seismic hazard assessment
Sasaki, Yutaka; Yi, Myeong-Jong; Choi, Jihyang
The ZTEM (Z-axis Tipper Electromagnetic) method measures naturally occurring audio-frequency magnetic fields and obtains the tipper function that defines the relationship among the three components of the magnetic field. Since the anomalous tipper responses are caused by the presence of lateral resistivity variations, the ZTEM survey is most suited for detecting and delineating conductive bodies extending to considerable depths, such as graphitic dykes encountered in the exploration of unconformity type uranium deposit. Our simulations shows that inversion of ZTEM data can detect reasonably well multiple conductive dykes placed 1 km apart. One important issue regarding ZTEM inversion is the effect of the initial model, because homogeneous half-space and (1D) layered structures produce no responses. For the 2D model with multiple conductive dykes, the inversion results were useful for locating the dykes even when the initial model was not close to the true background resistivity. For general 3D structures, however, the resolution of the conductive bodies can be reduced considerably depending on the initial model. This is because the tipper magnitudes from 3D conductors are smaller due to boundary charges than the 2D responses. To alleviate this disadvantage of ZTEM surveys, we combined ZTEM and audio-frequency magnetotelluric (AMT) data. Inversion of sparse AMT data was shown to be effective in providing a good initial model for ZTEM inversion. Moreover, simultaneously inverting both data sets led to better results than the sequential approach by enabling to identify structural features that were difficult to resolve from the individual data sets.
There are numerous geophysical methods used to investigate geothermal areas. The major purpose of this magnetic survey is to locate the boudaries of active hydrothermal system in the South of Gediz Graben in Salihli (Manisa/Turkey). The presence of the hydrothermal system had already been inferred from surface evidence of hydrothermal activity and drillings. Firstly, 3-D prismatic models were theoretically investigated and edge detection methods were utilized with an iterative inversion method to define the boundaries and the parameters of the structure. In the first step of the application, it was necessary to convert the total field anomaly into a pseudo-gravity anomaly map. Then the geometric boudaries of the structures were determined by applying a MATLAB based software with 3 different edge detection algorithms. The exact location of the structures were obtained by using these boundary coordinates as initial geometric parameters in the inversion process. In addition to these methods, reduction to pole and horizontal gradient methods were applied to the data to achieve more information about the location and shape of the possible reservoir. As a result, the edge detection methods were found to be successful, both in the field and as theoretical data sets for delineating the boundaries of the possible geothermal reservoir structure. The depth of the geothermal reservoir was determined as 2,4 km from 3-D inversion and 2,1 km from power spectrum methods.
Li, Yong; Guo, Yunhua; Zhu, Weishen; Li, Shucai; Zhou, Hao
To improve the accuracy of an initial in-situ stress field determined by inversion, we describe a modi fied initial in-situ stress inversion method that uses partial least-squares regression based on FLAC3D. First, each stress component is regressed to improve the fitting accuracy of locally abnormal stress regions, and then the relationship between element stress and unbalanced node force is analyzed according to the computational principles of FLAC3D. The initial in-situ stresses obtained from these regression calculations are added to a numerical model, and the unbalanced node forces are recalculated. An external force equal to the recalculated unbalanced node force is then exerted on the node in the direction opposing the original unbalanced node force to satisfy the equilibrium condition. For the in-situ stresses of elements that do not satisfy the strength conditions, they are modi fied by assuming the average stress is constant and reducing the partial stress to satisfy the equilibrium and strength conditions, which also resolves the unreasonable distribution of the boundary nodal forces and results in good regression estimates. A three-dimensional hypersurface spline interpolation method is developed to calculate the in-situ stress tensor at arbitrary coordinates. Finally, we apply this method to an underground engineering project, and the results are shown to agree well with those obtained from field monitoring. Therefore, it is concluded that this modified in-situ stress inversion method could effectively improve the fitting accuracy of locally abnormal stress regions.
Carlson, Leland A.
An inverse wing design method was developed around an existing transonic wing analysis code. The original analysis code, TAWFIVE, has as its core the numerical potential flow solver, FLO30, developed by Jameson and Caughey. Features of the analysis code include a finite-volume formulation; wing and fuselage fitted, curvilinear grid mesh; and a viscous boundary layer correction that also accounts for viscous wake thickness and curvature. The development of the inverse methods as an extension of previous methods existing for design in Cartesian coordinates is presented. Results are shown for inviscid wing design cases in super-critical flow regimes. The test cases selected also demonstrate the versatility of the design method in designing an entire wing or discontinuous sections of a wing.
Roshandel Kahoo, Amin; Nejati Kalateh, Ali; Salajegheh, Farshad
Recently the continuous wavelet transform has been proposed for interpretation of potential field anomalies. In this paper, we introduced a 2D wavelet based method that uses a new mother wavelet for determination of the location and the depth to the top and base of gravity anomaly. The new wavelet is the first horizontal derivatives of gravity anomaly of a buried cube with unit dimensions. The effectiveness of the proposed method is compared with Li and Oldenburg inversion algorithm and is demonstrated with synthetics and real gravity data. The real gravity data is taken over the Mobrun massive sulfide ore body in Noranda, Quebec, Canada. The obtained results of the 2D wavelet based algorithm and Li and Oldenburg inversion on the Mobrun ore body had desired similarities to the drill-hole depth information. In all of the inversion algorithms the model non-uniqueness is the challenging problem. Proposed method is based on a simple theory and there is no model non-uniqueness on it.
Simmons, N. A.; Myers, S. C.; Johannesson, G.; Matzel, E.
LLNL-G3D is a global-scale model of P-wave velocity designed to accurately predict seismic travel times at regional and teleseismic distances simultaneously. The underlying goal of the model is to provide enhanced seismic event location capabilities. Previous versions of LLNL-G3D (versions 1 and 2) provide substantial improvements in event location accuracy via 3-D ray tracing. The latest models are based on ~2.7 million P and Pn arrivals that are re-processed using our global multi-event locator known as BayesLoc. Bayesloc is a formulation of the joint probability distribution across multiple-event location parameters, including hypocenters, travel time corrections, pick precision, and phase labels. Modeling the whole multiple-event system results in accurate locations and an internally consistent data set that is ideal for tomography. Our recently developed inversion approach (called Progressive Multi-level Tessellation Inversion or PMTI) captures regional trends and fine details where data warrant. Using PMTI, we model multiple heterogeneity scale lengths without defining parameter grids with variable densities based on some ad hoc criteria. LLNL-G3Dv3 (version 3) is produced with data generated with the BayesLoc procedure, recently modified to account for localized travel time trends via a multiple event clustering technique. We demonstrate the significance of BayesLoc processing, the impact on the resulting tomographic images, and the application of LLNL-G3D to seismic event location. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LLNL-ABS-491805.
Ekinci, Yunus Levent; Ertekin, Can
Concern about sedimentary basins is generally related to their genetic and economic significance. Analysis of sedimentary basins requires the acquisition of data through outcrop studies and subsurface investigations that encompass drilling and geophysics. These data are commonly analysed by computer-assisted techniques. One of these methods is based on analysing gravity anomalies to compute the depth of sedimentary basin-basement rock interface. Sedimentary basins produce negative gravity anomalies, because they have mostly lower densities than that of the surrounding basement rocks. Density variations in a sedimentary fill increase rapidly at shallower depths then gradually reach the density of surrounding basement rocks due to the geostatic pressure i.e. compaction. The decrease of the density contrast can be easily estimated by a quadratic function. Hence, if the densities are chosen properly and the regional background is removed correctly, the topographical relief of the sedimentary basin-basement rock interface might be estimated by the inversion of the gravity data using an exponential density-depth relation. Three dimensional forward modelling procedure can be carried out by introducing a Cartesian coordinate system, and placing vertical prisms just below observation points on the grid plane. Depth to the basement, namely depths to the bottom of the vertical prisms are adjusted in an iterative manner by minimizing the differences between measured and calculated residual gravity anomalies. In this study, we present a MATLAB-based inversion code for the interpretation of sedimentary basins by approximating the topographical relief of sedimentary basin-basement rock interfaces. For a given gridded residual gravity anomaly map, the procedure estimates the bottom depths of vertical prisms by considering some published formulas and assumptions. The utility of the developed inversion code was successfully tested on theoretically produced gridded gravity data set
Martin, Roland; Monteiller, Vadim; Chevrot, Sébastien; Wang, Yi; Komatitsch, Dimitri; Dufréchou, Grégory
We describe here a method of inversion applied to seismic data sets constrained by gravity data at the regional scale. This will allow us to obtain robust models of P and S wave velocities but also of density, providing key constraints on the composition and thermal state of the lithosphere. Our approach relies on teleseimic waves, which illuminate the medium from below. We have developped a hybrid method in which a wave propagation method at the global scale (DSM/Direct solution method) is coupled with a spectral element method at the regional scale (Monteiller et al. 2013). With the spectral element method, we are able to model the 3D wave propagation effects in a computational domain of 400km long x 400km wide and 200 km deep, for an incident teleseismic wavefront introduced at the boundaries of this domain with periods as short as 2 s. The DSM global method allows to compute this incident field for a spherical Earth model. We use a multi-scale joint inversion of both gravity and seismic waveform data, accounting for the long wavelengths of the gravity field taken from a global model. In terms of inversion technique, we have validated an adjoint method for the inversion of seismic waveforms. An optimized BFGS inversion technique is used to minimize the difference between observed and computed full waveforms. The gradient of the misfit function gives the direction over which the model must be perturbed to minimize this difference. At each step of the inversion procedure we choose an optimal step length that accelerates the minimization. This is the crucial ingredient that allows us to build an efficient iterative full waveform inversion. We have extended this method by incorporating gravity data provided by the BGI/Bureau Gravimétrique International into the inversion. If the waveforms allow us to constrain the seismic velocities, they are less sensitive to the structure in density, which gives independent and crucial information to constrain the nature of rocks
Aydmer, A.A.; Chew, W.C.; Cui, T.J.; Wright, D.L.; Smith, D.V.; Abraham, J.D.
A simple and efficient method for large scale three-dimensional (3-D) subsurface imaging of inhomogeneous background is presented. One-dimensional (1-D) multifrequency distorted Born iterative method (DBIM) is employed in the inversion. Simulation results utilizing synthetic scattering data are given. Calibration of the very early time electromagnetic (VETEM) experimental waveforms is detailed along with major problems encountered in practice and their solutions. This discussion is followed by the results of a large scale application of the method to the experimental data provided by the VETEM system of the U.S. Geological Survey. The method is shown to have a computational complexity that is promising for on-site inversion.
Bhattacharya, Jishnu; Wolverton, C
Spinel oxides represent an important class of cathode materials for Li-ion batteries. Two major variants of the spinel crystal structure are normal and inverse. The relative stability of normal and inverse ordering at different stages of lithiation has important consequences in lithium diffusivity, voltage, capacity retention and battery life. In this paper, we investigate the relative structural stability of normal and inverse structures of the 3d transition metal oxide spinels with first-principles DFT calculations. We have considered ternary spinel oxides LixM2O4 with M = Ti, V, Cr, Mn, Fe, Co and Ni in both lithiated (x = 1) and delithiated (x = 0) conditions. We find that for all lithiated spinels, the normal structure is preferred regardless of the metal. We observe that the normal structure for all these oxides has a lower size mismatch between octahedral cations compared to the inverse structure. With delithiation, many of the oxides undergo a change in stability with vanadium in particular, showing a tendency to occupy tetrahedral sites. We find that in the delithiated oxide, only vanadium ions can access a +5 oxidation state which prefers tetrahedral coordination. We have also calculated the average voltage of lithiation for these spinels. The calculated voltages agree well with the previously measured and calculated values, wherever available. For the yet to be characterized spinels, our calculation provides voltage values which can motivate further experimental attention. Lastly, we observe that all the normal spinel oxides of the 3d transition metal series have a driving force for a transformation to the non-spinel structure upon delithiation. PMID:23529669
Slawinski, J; Bonnefoy, A; Ontanon, G; Leveque, J M; Miller, C; Riquet, A; Chèze, L; Dumas, R
The aim of the present study was to measure during a sprint start the joint angular velocity and the kinetic energy of the different segments in elite sprinters. This was performed using a 3D kinematic analysis of the whole body. Eight elite sprinters (10.30+/-0.14s 100 m time), equipped with 63 passive reflective markers, realised four maximal 10 m sprints start on an indoor track. An opto-electronic Motion Analysis system consisting of 12 digital cameras (250 Hz) was used to collect the 3D marker trajectories. During the pushing phase on the blocks, the 3D angular velocity vector and its norm were calculated for each joint. The kinetic energy of 16 segments of the lower and upper limbs and of the total body was calculated. The 3D kinematic analysis of the whole body demonstrated that joints such as shoulders, thoracic or hips did not reach their maximal angular velocity with a movement of flexion-extension, but with a combination of flexion-extension, abduction-adduction and internal-external rotation. The maximal kinetic energy of the total body was reached before clearing block (respectively, 537+/-59.3 J vs. 514.9+/-66.0 J; p< or =0.01). These results suggested that a better synchronization between the upper and lower limbs could increase the efficiency of pushing phase on the blocks. Besides, to understand low interindividual variances in the sprint start performance in elite athletes, a 3D complete body kinematic analysis shall be used. PMID:20226465
Minsley, B. J.; Sogade, J.; Briggs, V.; Lambert, M.; Reppert, P.; Coles, D.; Morgan, F.; Rossabi, J.; Riha, B.; Shi, W.
Due to the complicated nature of subsurface contaminant migration, it is difficult to determine the spatial extent and severity of contamination, which can provide essential information for efficient remediation efforts. Self-potential (SP) geophysics is employed to provide a minimally invasive, fast, and inexpensive method for remote in-situ detection and three-dimensional mapping of subsurface DNAPL (Dense Non-Aqueous Phase Liquid) in conjunction with inverse methods. The self-potential method is commonly used to detect a variety of phenomena that are typically related to thermoelectric, electrochemical, or electrokinetic coupling processes. Surface self-potential surveys have been documented to show anomalies over areas known to be contaminated, but interpretation of these datasets is often mostly qualitative, and can be plagued with problems of non-uniqueness. In this study, oxidation-reduction (redox) reactions, one of the mechanisms associated with the attenuation of chemicals released into the environment, provide an electrochemical source for the SP signal. Electrochemical potentials associated with subsurface zones of redox activity are analogous to localized 'batteries' buried within native earth materials, and produce an electric field that is remotely detected using electrodes placed at the surface and in nearby boreholes. Three-dimensional inversion of the self-potential data incorporating resistivity information is the necessary step in characterizing the source parameters, which are directly related to the redox activity, and therefore to the contaminant itself. Surface and borehole SP data are collected in order to help constrain the solution in depth, and resistivity information is taken from an induced polarization survey performed over the same area during this field excursion. Inversion results are correlated with contaminant concentration data sampled from a series of ground-truth boreholes within the region of interest.
Levander, Alan R.
Gian Fradelizio, a Rice Ph.D. student has completed reprocessing the 3D seismic reflection data acquired at Hill AFB through post-stack depth migration for comparison to the traveltime and waveform tomography results. Zelt, Levander, Fradelizio, and 5 others spent a week at Hill AFB in September 2005, acquiring an elastic wave data set along 2 profiles. We used 60 3-component Galperin mounted 40 Hz geophones recorded by 3 GEOMETRICS Stratavision systems. The seismic source employed was a sledgehammer used to generate transverse, and radial, and vertical point source data. Data processing has begun at Rice to generate S-wave reflection and refraction images. We also acquired surface wave and ground penetrating rada data to complement the elastic wave dataset.
Heincke, B.; Moorkamp, M.; Jegen, M.; Hobbs, R. W.
collected along parallel lines by a shipborne gradiometer and the marine MT data set is composed of 41 stations that are distributed over the whole investigation area. Logging results from a borehole located in the central part of the investigation area enable us to derive parameter relationships between seismic velocities, resistivities and densities that are adequately describe the rock property behaviors of both the basaltic lava flows and sedimentary layers in this region. In addition, a 3-D reflection seismic survey covering the central part allows us to incorporate the top of basalt and other features as constraints in the joint inversions and to evaluate the quality of the final results. Literature: D. Colombo, M. Mantovani, S. Hallinan, M. Virgilio, 2008. Sub-basalt depth imaging using simultaneous joint inversion of seismic and electromagnetic (MT) data: a CRB field study. SEG Expanded Abstract, Las Vegas, USA, 2674-2678. M. Jordan, J. Ebbing, M. Brönner, J. Kamm , Z. Du, P. Eliasson, 2012. Joint Inversion for Improved Sub-salt and Sub-basalt Imaging with Application to the More Margin. EAGE Expanded Abstracts, Copenhagen, DK. M. Moorkamp, B. Heincke, M. Jegen, A.W.Roberts, R.W. Hobbs, 2011. A framework for 3-D joint inversion of MT, gravity and seismic refraction data. Geophysical Journal International, 184, 477-493.
Hines, T.; Hetland, E. A.
Geodetic measurements of postseismic deformation are rich signals with which the mechanical behavior of the lithosphere can be inferred, predominantly localized fault creep and distributed viscoelastic deformation. Numerous studies have used postseismic deformation to estimate the lithosphere's rheology but they are hindered by potentially computationally intensive forward problems with nonlinear relationships between surface deformation and the rheologic properties. As a result, most studies oversimplify the rheologic structure of the lithosphere and rely on forward estimation methods, such as grid or monte carlo searches. We present a novel method to simultaneously estimate patterns of fault slip and heterogeneous distribution of effective Maxwell viscoelasticity from postseismic deformation. Our method utilizes an approximation which linearizes the viscoelastic contribution to postseismic deformation with respect to the inverse relaxation time of discrete regions in the lithosphere, allowing the use of least squares techniques, akin to seismic tomographic methods. The validity of this approximation is inversely proportional to the time since the main rupture and holds for roughly as long as the lowest relaxation time in the lithosphere proximal to the coseismic rupture. Our estimation of both the slip history on a fault and the effective Maxwell relaxation times of the lithosphere takes a matter of minutes. We apply our method to postseismic deformation following the 2010 El Mayor earthquake, as well as the 1999 İzmit-Düzce earthquake sequence. We discuss the significance of both fault creep and three dimensional viscosity structure in describing postseismic deformation.
Let (u , b) be a smooth enough solution of 3-D incompressible MHD system. We prove that if (u , b) blows up at a finite time T*, then for any p ∈ ] 4 , ∞ [, there holds ∫0T* (‖u3(t‧) ‖ H ˙ 1/2 +2/p p + ‖b(t‧) ‖ H ˙ 1/2 +2/p p) dt‧ = ∞. We remark that all these quantities are in the critical regularity of the MHD system.
Krams, R; Wentzel, J J; Cespedes, I; Vinke, R; Carlier, S; van der Steen, A F; Lancee, C T; Slager, C J
Novel measurement techniques based on intravenous ultrasound (IVUS) technology ('IVUS-Flowmetry') require the location of a catheter inside the coronary bed. The present study quantifies disturbances in the 3-D velocity profile induced by catheter placement inside a tube, applying computational fluid dynamics. Two curved, circular meshes (radius K = 0.025 m and K = 0.035 m) with and without a catheter inside the lumen were applied. The catheter was located at the inner curve, the outer curve and at the top position. Boundary conditions were: no slip on the wall, zero stress at the outlet, uniform inflow with entrance velocities of 0.1, 0.2 and 0.4 m/s. Curvature-associated centrifugal forces shifted the maximal velocity to the outer curve and introduced two symmetrical vortices. Additional catheter placement redistributed the 3-D axial velocity field away from the catheter, which was accompanied by the appearance of multiple low-strength vortices. In addition, peak axial velocity increased, peak secondary velocities decreased, axial pressure drop increased and shear stress increased. Flow calculations simulated to resemble IVUS-based flowmetry changed by only 1% after considering secondary velocity. In conclusion, placement of a catheter inside a curved tube resembling the human coronary system changes the velocity field and reduces secondary patterns. The present study supports the usefulness of catheter-based flowmetry during resting flow conditions. During hyperemic flow conditions, flow measurements might be accompanied by large axial pressure drops because the catheter, itself, might act as a significant stenosis. PMID:10414897
Eilon, Zachary; Abers, Geoffrey A.; Gaherty, James B.
Tradeoffs between velocity and anisotropy heterogeneity complicate the interpretation of differential travel time data and have the potential to bias isotropic tomographic models. By constructing a simple parameterisation to describe an elastic tensor with hexagonal symmetry, we find analytic solutions to the Christoffel equations in terms of fast and slow horizontal velocities that allow us to simultaneously invert differential travel time data and splitting data from teleseismic S arrivals to recover 3-D velocity and anisotropy structure. This technique provides a constraint on the depth-extent of shallow anisotropy, otherwise absent from interpretations based on SKS splitting alone. This approach is well suited to the young Woodlark Rift, where previous studies have found strong velocity variation and substantial SKS splitting in a continental rift with relatively simple geometry. This study images a low velocity rift axis with ≤4% spreading-parallel anisotropy at 50-100 km depth that separates regions of pre-existing lithospheric fabric, indicating the synchronous development of extensional crystallographic preferred orientation and lithospheric thinning. A high-velocity slab fragment north of the rift axis is associated with strike-parallel anisotropic fast axes, similar to that seen in the shallow mantle of some subduction zones. In addition to the insights provided by the anisotropy structure, the improvement in fit to the differential travel time data demonstrates the merit to a joint inversion that accounts for anisotropy.
Eilon, Zachary; Abers, Geoffrey A.; Gaherty, James B.
Trade-offs between velocity and anisotropy heterogeneity complicate the interpretation of differential traveltime data and have the potential to bias isotropic tomographic models. By constructing a simple parametrisation to describe an elastic tensor with hexagonal symmetry, we find analytic solutions to the Christoffel equations in terms of fast and slow horizontal velocities that allow us to simultaneously invert differential traveltime data and splitting data from teleseismic S arrivals to recover 3-D velocity and anisotropy structure. This technique provides a constraint on the depth-extent of shallow anisotropy, otherwise absent from interpretations based on SKS splitting alone. This approach is well suited to the young Woodlark Rift, where previous studies have found strong velocity variation and substantial SKS splitting in a continental rift with relatively simple geometry. This study images a low-velocity rift axis with ≤4 per cent spreading-parallel anisotropy at 50-100 km depth that separates regions of pre-existing lithospheric fabric, indicating the synchronous development of extensional crystallographic preferred orientation and lithospheric thinning. A high-velocity slab fragment north of the rift axis is associated with strike-parallel anisotropic fast axes, similar to that seen in the shallow mantle of some subduction zones. In addition to the insights provided by the anisotropy structure, the improvement in fit to the differential traveltime data demonstrates the merit to a joint inversion that accounts for anisotropy.
Yu, X.; Wang, X.; Zhang, W.
The double difference seismic tomography method is applied to the absolute first arrival P wave arrival times and high quality relative P arrival times of the Lushan seismic sequence to determine the detailed crustal 3D P wave velocity structure and the hypocenter parameters in the Lushan seismic area. The results show that the Lushan mainshock locates at 30.28 N, 103.98 E, with the depth of 16.38 km. The leading edge of aftershock in the northeast of mainshock present a spade with a steep dip angle, the aftershocks' extended length is about 12 km. In the southwest of the Lushan mainshock, the leading edge of aftershock in low velocity zone slope gently, the aftershocks' extended length is about 23 km. The P wave velocity structure of the Lushan seismic area shows obviously lateral heterogeneity. The P wave velocity anomalies represent close relationship with topographic relief and geological structure. In Baoxing area the complex rocks correspond obvious high-velocity anomalies extending down to 15 km depth，while the Cenozoic rocks are correlated with low-velocity anomalies. Our high-resolution tomographic model not only displays the general features contained in the previous models, but also reveals some new features. An obvious high-velocity anomaly is visible in Daxing area. The high-velocity anomalies beneath Baoxing and Daxing connect each other in 10 km depth, which makes the contrast between high and low velocity anomalies more sharp. Above 20 km depth the velocity structure in southwest and northeast segment of the mainshock shows a big difference: low-velocity anomalies are dominated the southwest segment, while high-velocity anomalies rule the northeast segment. The Lushan mainshock locates at the leading edge of a low-velocity anomaly surrounded by the Baoxing and Daxing high-velocity anomalies. The Lushan aftershocks in southwest are distributed in low-velocity anomalies or the transition belt: the footwall represents low-velocity anomalies, while
Kadic, Muamer; Schittny, Robert; Bückmann, Tiemo; Kern, Christian; Wegener, Martin
In 2009, Briane and Milton proved mathematically the existence of three-dimensional isotropic metamaterials with a classical Hall coefficient that is negative with respect to that of all of the metamaterial constituents. Here, we significantly simplify their blueprint towards an architecture composed of only a single-constituent material in vacuum or air, which can be seen as a special type of porosity. We show numerically that the sign of the Hall voltage is determined by a separation parameter between adjacent tori. This qualitative behavior is robust even for only a small number of metamaterial unit cells. The combination of simplification and robustness brings experimental verification of this striking sign inversion into reach. Furthermore, we provide a simple intuitive explanation of the underlying physical mechanism.
Carlson, Leland A.
Progress in the direct-inverse wing design method in curvilinear coordinates has been made. This includes the remedying of a spanwise oscillation problem and the assessment of grid skewness, viscous interaction, and the initial airfoil section on the final design. It was found that, in response to the spanwise oscillation problem that designing at every other spanwise station produced the best results for the cases presented, a smoothly varying grid is especially needed for the accurate design at the wing tip, the boundary layer displacement thicknesses must be included in a successful wing design, the design of high and medium aspect ratio wings is possible with this code, and the final airfoil section designed is fairly independent of the initial section.
Barlebo, H.C.; Rosbjerg, D.; Hill, M.C.
An extensive amount of data including hydraulic heads, hydraulic conductivities and concentrations of several solutes from controlled injections have been collected during the MADE 1 and MADE 2 experiments at a heterogeneous site near Columbus, Mississippi. In this paper the use of three-dimensional inverse groundwater models including simultaneous estimation of flow and transport parameters is proposed to help identify the dominant characteristics at the site. Simulations show that using a hydraulic conductivity distribution obtained from 2187 borehole flowmeter tests directly in the model produces poor matches to the measured hydraulic heads and tritium concentrations. Alternatively, time averaged hydraulic head maps are used to define zones of constant hydraulic conductivity to be estimated. Preliminary simulations suggest that in the case of conservative transport many, but not all, of the major plume characteristics can be explained by large-scale heterogeneity in recharge and hydraulic conductivity.
Brosten, T.R.; Day-Lewis, F. D.; Schultz, G.M.; Curtis, G.P.; Lane, J.W.
Electromagnetic induction (EMI) instruments provide rapid, noninvasive, and spatially dense data for characterization of soil and groundwater properties. Data from multi-frequency EMI tools can be inverted to provide quantitative electrical conductivity estimates as a function of depth. In this study, multi-frequency EMI data collected across an abandoned uranium mill site near Naturita, Colorado, USA, are inverted to produce vertical distribution of electrical conductivity (EC) across the site. The relation between measured apparent electrical conductivity (ECa) and hydraulic conductivity (K) is weak (correlation coefficient of 0.20), whereas the correlation between the depth dependent EC obtained from the inversions, and K is sufficiently strong to be used for hydrologic estimation (correlation coefficient of -0.62). Depth-specific EC values were correlated with co-located K measurements to develop a site-specific ln(EC)-ln(K) relation. This petrophysical relation was applied to produce a spatially detailed map of K across the study area. A synthetic example based on ECa values at the site was used to assess model resolution and correlation loss given variations in depth and/or measurement error. Results from synthetic modeling indicate that optimum correlation with K occurs at ~0.5m followed by a gradual correlation loss of 90% at 2.3m. These results are consistent with an analysis of depth of investigation (DOI) given the range of frequencies, transmitter-receiver separation, and measurement errors for the field data. DOIs were estimated at 2.0??0.5m depending on the soil conductivities. A 4-layer model, with varying thicknesses, was used to invert the ECa to maximize available information within the aquifer region for improved correlations with K. Results show improved correlation between K and the corresponding inverted EC at similar depths, underscoring the importance of inversion in using multi-frequency EMI data for hydrologic estimation. ?? 2011.
Brosten, Troy R.; Day-Lewis, Frederick D.; Schultz, Gregory M.; Curtis, Gary P.; Lane, John W., Jr.
Electromagnetic induction (EMI) instruments provide rapid, noninvasive, and spatially dense data for characterization of soil and groundwater properties. Data from multi-frequency EMI tools can be inverted to provide quantitative electrical conductivity estimates as a function of depth. In this study, multi-frequency EMI data collected across an abandoned uranium mill site near Naturita, Colorado, USA, are inverted to produce vertical distribution of electrical conductivity ( EC) across the site. The relation between measured apparent electrical conductivity ( ECa) and hydraulic conductivity ( K) is weak (correlation coefficient of 0.20), whereas the correlation between the depth dependent EC obtained from the inversions, and K is sufficiently strong to be used for hydrologic estimation (correlation coefficient of - 0.62). Depth-specific EC values were correlated with co-located K measurements to develop a site-specific ln( EC)-ln( K) relation. This petrophysical relation was applied to produce a spatially detailed map of K across the study area. A synthetic example based on ECa values at the site was used to assess model resolution and correlation loss given variations in depth and/or measurement error. Results from synthetic modeling indicate that optimum correlation with K occurs at ~ 0.5 m followed by a gradual correlation loss of 90% at 2.3 m. These results are consistent with an analysis of depth of investigation (DOI) given the range of frequencies, transmitter-receiver separation, and measurement errors for the field data. DOIs were estimated at 2.0 ± 0.5 m depending on the soil conductivities. A 4-layer model, with varying thicknesses, was used to invert the ECa to maximize available information within the aquifer region for improved correlations with K. Results show improved correlation between K and the corresponding inverted EC at similar depths, underscoring the importance of inversion in using multi-frequency EMI data for hydrologic estimation.
Gaite, B.; Villaseñor, A.; Iglesias, A.; Herraiz, M.; Jiménez-Munt, I.
We use group velocities from earthquake tomography together with group and phase velocities from ambient noise tomography (ANT) of Rayleigh waves to invert for the 3-D shear-wave velocity structure (5-70 km) of the Caribbean (CAR) and southern North American (NAM) plates. The lithospheric model proposed offers a complete image of the crust and uppermost-mantle with imprints of the tectonic evolution. One of the most striking features inferred is the main role of the Ouachita-Marathon-Sonora orogeny front on the crustal seismic structure of the NAM plate. A new imaged feature is the low crustal velocities along the USA-Mexico border. The model also shows a break of the east-west mantle velocity dichotomy of the NAM and CAR plates beneath the Isthmus of the Tehuantepec and the Yucatan Block. High upper-mantle velocities along the Mesoamerican Subduction Zone coincide with inactive volcanic areas while the lowest velocities correspond to active volcanic arcs and thin lithospheric mantle regions.
Hartzell, S.; Harmsen, S.; Williams, R.A.; Carver, D.; Frankel, A.; Choy, G.; Liu, P.-C.; Jachens, R.C.; Brocher, T.M.; Wentworth, C.M.
A 3D seismic velocity and attenuation model is developed for Santa Clara Valley, California, and its surrounding uplands to predict ground motions from scenario earthquakes. The model is developed using a variety of geologic and geophysical data. Our starting point is a 3D geologic model developed primarily from geologic mapping and gravity and magnetic surveys. An initial velocity model is constructed by using seismic velocities from boreholes, reflection/refraction lines, and spatial autocorrelation microtremor surveys. This model is further refined and the seismic attenuation is estimated through waveform modeling of weak motions from small local events and strong-ground motion from the 1989 Loma Prieta earthquake. Waveforms are calculated to an upper frequency of 1 Hz using a parallelized finite-difference code that utilizes two regions with a factor of 3 difference in grid spacing to reduce memory requirements. Cenozoic basins trap and strongly amplify ground motions. This effect is particularly strong in the Evergreen Basin on the northeastern side of the Santa Clara Valley, where the steeply dipping Silver Creek fault forms the southwestern boundary of the basin. In comparison, the Cupertino Basin on the southwestern side of the valley has a more moderate response, which is attributed to a greater age and velocity of the Cenozoic fill. Surface waves play a major role in the ground motion of sedimentary basins, and they are seen to strongly develop along the western margins of the Santa Clara Valley for our simulation of the Loma Prieta earthquake.
Wimmer, Markus A; Alini, Mauro; Grad, Sibylle
Sliding motion and shear are important mediators for the synthesis of cartilage matrix and surface molecules. This study investigated the effects of velocity magnitude and motion path on the response of bovine chondrocytes cultured in polyurethane scaffolds and subjected to oscillation against a ceramic ball. In order to vary velocity magnitude, the ball oscillated +/-25 degrees at 0.01, 0.1, and 1Hz to generate 0.28, 2.8, and 28mm/s, respectively. The median velocity of these 'open' motion trajectories was tested against 'closed' motion trajectories in that the scaffold oscillated +/-20 degrees against the ball at 1Hz, reaching 2.8mm/s. Constructs were loaded twice a day for 1h over 5 days. Gene expression of cartilage oligomeric matrix protein (COMP), proteoglycan 4 (PRG4, lubricin), and hyaluronan synthase 1 (HAS1) and release of COMP, PRG4, and hyaluronan (HA) were analyzed. Velocity magnitude determined both gene expression and release of target molecules. Using regression analysis, there was a positive and significant relationship with all outcome variables. However, only COMP reacted significantly at 0.28mm/s, while all other measured variables were considerably up-regulated at 28mm/s. Motion path characteristics affected COMP, but not PRG4 and HAS1/HA. To conclude, velocity magnitude is a critical determinant for cellular responses in tissue engineered cartilage constructs. The motion type also plays a role. However, different molecules are affected in different ways. A molecule specific velocity threshold appears necessary to induce a significant response. This should be considered in further studies investigating the effects of continuous or intermittent motion. PMID:19152917
Mordret, A.; Landès, M.; Shapiro, N. M.; Singh, S. C.; Roux, P.
This study presents a depth inversion of Scholte wave group and phase velocity maps obtained from cross-correlation of 6.5 hr of noise data from the Valhall Life of Field Seismic network. More than 2 600 000 vertical-vertical component cross-correlations are computed from the 2320 available sensors, turning each sensor into a virtual source emitting Scholte waves. We used a traditional straight-ray surface wave tomography to compute the group velocity map. The phase velocity maps have been computed using the Eikonal tomography method. The inversion of these maps in depth are done with the Neighbourhood Algorithm. To reduce the number of free parameters to invert, geological a priori information are used to propose a power-law 1-D velocity profile parametrization extended with a gaussian high-velocity layer where needed. These parametrizations allowed us to create a high-resolution 3-D S-wave model of the first 600 m of the Valhall subsurface and to precise the locations of geological structures at depth. These results would have important implication for shear wave statics and monitoring of seafloor subsidence due to oil extraction. The 3-D model could also be a good candidate for a starting model used in full-waveform inversions.
Jesús Moral García, Francisco; Rebollo Castillo, Francisco Javier; Monteiro Santos, Fernando
Maps of apparent electrical conductivity of the soil are commonly used in precision agriculture to indirectly characterize some important properties like salinity, water, and clay content. Traditionally, these studies are made through an empirical relationship between apparent electrical conductivity and properties measured in soil samples collected at a few locations in the experimental area and at a few selected depths. Recently, some authors have used not the apparent conductivity values but the soil bulk conductivity (in 2D or 3D) calculated from measured apparent electrical conductivity through the application of an inversion method. All the published works used data collected with electromagnetic (EM) instruments. We present a new software to invert the apparent electrical conductivity data collected with VERIS 3100 and 3150 (or the more recent version with three pairs of electrodes) using the 1D spatially constrained inversion method (1D SCI). The software allows the calculation of the distribution of the bulk electrical conductivity in the survey area till a depth of 1 m. The algorithm is applied to experimental data and correlations with clay and water content have been established using soil samples collected at some boreholes. Keywords: Digital soil mapping; inversion modelling; VERIS; soil apparent electrical conductivity.
Kaus, B.; Pusok, A. E.; Popov, A.
The marker-in-cell method is generally considered to be a flexible and robust method to model advection of heterogenous non-diffusive properties (i.e. rock type or composition) in geodynamic problems or incompressible Stokes problems. In this method, Lagrangian points carrying compositional information are advected with the ambient velocity field on an immobile, Eulerian grid. However, velocity interpolation from grid points to marker locations is often performed without preserving the zero divergence of the velocity field at the interpolated locations (i.e. non-conservative). Such interpolation schemes can induce non-physical clustering of markers when strong velocity gradients are present (Jenny et al., 2001) and this may, eventually, result in empty grid cells, a serious numerical violation of the marker-in-cell method. Solutions to this problem include: using larger mesh resolutions and/or marker densities, or repeatedly controlling the marker distribution (i.e. inject/delete), but which does not have an established physical background. To remedy this at low computational costs, Jenny et al. (2001) and Meyer and Jenny (2004) proposed a simple, conservative velocity interpolation (CVI) scheme for 2-D staggered grid, while Wang et al. (2015) extended the formulation to 3-D finite element methods. Here, we follow up with these studies and report on the quality of velocity interpolation methods for 2-D and 3-D staggered grids. We adapt the formulations from both Jenny et al. (2001) and Wang et al. (2015) for use on 3-D staggered grids, where the velocity components have different node locations as compared to finite element, where they share the same node location. We test the different interpolation schemes (CVI and non-CVI) in combination with different advection schemes (Euler, RK2 and RK4) and with/out marker control on Stokes problems with strong velocity gradients, which are discretized using a finite difference method. We show that a conservative formulation
Oh, Ju-Won; Alkhalifah, Tariq
Multi-parameter full waveform inversion (FWI) applied to an elastic orthorhombic model description of the subsurface requires in theory a nine-parameter representation of each pixel of the model. Even with optimal acquisition on the Earth surface that includes large offsets, full azimuth, and multi component sensors, the potential for tradeoff between the elastic orthorhombic parameters are large. The first step to understanding such trade-off is analysing the scattering potential of each parameter, and specifically, its scattering radiation patterns. We investigate such radiation patterns for diffraction and for scattering from a horizontal reflector considering a background isotropic model. The radiation patterns show considerable potential for trade-off between the parameters and the potentially limited resolution in their recovery. The radiation patterns of C11, C22 and C33 are well separated so that we expect to recover these parameters with limited trade-offs. However, the resolution of their recovery represented by recovered range of model wavenumbers varies between these parameters. We can only invert for the short wavelength components (reflection) of C33 while we can mainly invert for the long wavelength components (transmission) of the elastic coefficients C11 and C22 if we have large enough offsets. The elastic coefficients C13, C23 and C12 suffer from strong trade-offs with C55, C44 and C66, respectively. The trade-offs between C13 and C55, as well as C23 and C44, can be partially mitigated if we acquire P-SV and SV-SV waves. However, to reduce the trade-offs between C12 and C66, we require credible SH-SH waves. The analytical radiation patterns of the elastic constants are supported by numerical gradients of these parameters.