Application of the concept of dynamic trim control and nonlinear system inverses to automatic control of a vertical attitude takeoff and landing aircraft

NASA Technical Reports Server (NTRS)

Smith, G. A.; Meyer, G.

1981-01-01

A full envelope automatic flight control system based on nonlinear inverse systems concepts has been applied to a vertical attitude takeoff and landing (VATOL) fighter aircraft. A new method for using an airborne digital aircraft model to perform the inversion of a nonlinear aircraft model is presented together with the results of a simulation study of the nonlinear inverse system concept for the vertical-attitude hover mode. The system response to maneuver commands in the vertical attitude was found to be excellent; and recovery from large initial offsets and large disturbances was found to be very satisfactory.

Predicting ozone profile shape from satellite UV spectra

NASA Astrophysics Data System (ADS)

Xu, Jian; Loyola, Diego; Romahn, Fabian; Doicu, Adrian

2017-04-01

Identifying ozone profile shape is a critical yet challenging job for the accurate reconstruction of vertical distributions of atmospheric ozone that is relevant to climate change and air quality. Motivated by the need to develop an approach to reliably and efficiently estimate vertical information of ozone and inspired by the success of machine learning techniques, this work proposes a new algorithm for deriving ozone profile shapes from ultraviolet (UV) absorption spectra that are recorded by satellite instruments, e.g. GOME series and the future Sentinel missions. The proposed algorithm formulates this particular inverse problem in a classification framework rather than a conventional inversion one and places an emphasis on effectively characterizing various profile shapes based on machine learning techniques. Furthermore, a comparison of the ozone profiles from real GOME-2 data estimated by our algorithm and the classical retrieval algorithm (Optimal Estimation Method) is performed.

A methodology for using borehole temperature-depth profiles under ambient, single and cross-borehole pumping conditions to estimate fracture hydraulic properties

NASA Astrophysics Data System (ADS)

Klepikova, Maria V.; Le Borgne, Tanguy; Bour, Olivier; Davy, Philippe

2011-09-01

SummaryTemperature profiles in the subsurface are known to be sensitive to groundwater flow. Here we show that they are also strongly related to vertical flow in the boreholes themselves. Based on a numerical model of flow and heat transfer at the borehole scale, we propose a method to invert temperature measurements to derive borehole flow velocities. This method is applied to an experimental site in fractured crystalline rocks. Vertical flow velocities deduced from the inversion of temperature measurements are compared with direct heat-pulse flowmeter measurements showing a good agreement over two orders of magnitudes. Applying this methodology under ambient, single and cross-borehole pumping conditions allows us to estimate fracture hydraulic head and local transmissivity, as well as inter-borehole fracture connectivity. Thus, these results provide new insights on how to include temperature profiles in inverse problems for estimating hydraulic fracture properties.

Robust Inversion and Data Compression in Control Allocation

NASA Technical Reports Server (NTRS)

Hodel, A. Scottedward

2000-01-01

We present an off-line computational method for control allocation design. The control allocation function delta = F(z)tau = delta (sub 0) (z) mapping commanded body-frame torques to actuator commands is implicitly specified by trim condition delta (sub 0) (z) and by a robust pseudo-inverse problem double vertical line I - G(z) F(z) double vertical line less than epsilon (z) where G(z) is a system Jacobian evaluated at operating point z, z circumflex is an estimate of z, and epsilon (z) less than 1 is a specified error tolerance. The allocation function F(z) = sigma (sub i) psi (z) F (sub i) is computed using a heuristic technique for selecting wavelet basis functions psi and a constrained least-squares criterion for selecting the allocation matrices F (sub i). The method is applied to entry trajectory control allocation for a reusable launch vehicle (X-33).

A study on characterization of stratospheric aerosol and gas parameters with the spacecraft solar occultation experiment

NASA Technical Reports Server (NTRS)

Chu, W. P.

1977-01-01

Spacecraft remote sensing of stratospheric aerosol and ozone vertical profiles using the solar occultation experiment has been analyzed. A computer algorithm has been developed in which a two step inversion of the simulated data can be performed. The radiometric data are first inverted into a vertical extinction profile using a linear inversion algorithm. Then the multiwavelength extinction profiles are solved with a nonlinear least square algorithm to produce aerosol and ozone vertical profiles. Examples of inversion results are shown illustrating the resolution and noise sensitivity of the inversion algorithms.

Appraisal of geodynamic inversion results: a data mining approach

NASA Astrophysics Data System (ADS)

Baumann, T. S.

2016-11-01

Bayesian sampling based inversions require many thousands or even millions of forward models, depending on how nonlinear or non-unique the inverse problem is, and how many unknowns are involved. The result of such a probabilistic inversion is not a single `best-fit' model, but rather a probability distribution that is represented by the entire model ensemble. Often, a geophysical inverse problem is non-unique, and the corresponding posterior distribution is multimodal, meaning that the distribution consists of clusters with similar models that represent the observations equally well. In these cases, we would like to visualize the characteristic model properties within each of these clusters of models. However, even for a moderate number of inversion parameters, a manual appraisal for a large number of models is not feasible. This poses the question whether it is possible to extract end-member models that represent each of the best-fit regions including their uncertainties. Here, I show how a machine learning tool can be used to characterize end-member models, including their uncertainties, from a complete model ensemble that represents a posterior probability distribution. The model ensemble used here results from a nonlinear geodynamic inverse problem, where rheological properties of the lithosphere are constrained from multiple geophysical observations. It is demonstrated that by taking vertical cross-sections through the effective viscosity structure of each of the models, the entire model ensemble can be classified into four end-member model categories that have a similar effective viscosity structure. These classification results are helpful to explore the non-uniqueness of the inverse problem and can be used to compute representative data fits for each of the end-member models. Conversely, these insights also reveal how new observational constraints could reduce the non-uniqueness. The method is not limited to geodynamic applications and a generalized MATLAB code is provided to perform the appraisal analysis.

Updated Results for the Wake Vortex Inverse Model

NASA Technical Reports Server (NTRS)

Robins, Robert E.; Lai, David Y.; Delisi, Donald P.; Mellman, George R.

2008-01-01

NorthWest Research Associates (NWRA) has developed an Inverse Model for inverting aircraft wake vortex data. The objective of the inverse modeling is to obtain estimates of the vortex circulation decay and crosswind vertical profiles, using time history measurements of the lateral and vertical position of aircraft vortices. The Inverse Model performs iterative forward model runs using estimates of vortex parameters, vertical crosswind profiles, and vortex circulation as a function of wake age. Iterations are performed until a user-defined criterion is satisfied. Outputs from an Inverse Model run are the best estimates of the time history of the vortex circulation derived from the observed data, the vertical crosswind profile, and several vortex parameters. The forward model, named SHRAPA, used in this inverse modeling is a modified version of the Shear-APA model, and it is described in Section 2 of this document. Details of the Inverse Model are presented in Section 3. The Inverse Model was applied to lidar-observed vortex data at three airports: FAA acquired data from San Francisco International Airport (SFO) and Denver International Airport (DEN), and NASA acquired data from Memphis International Airport (MEM). The results are compared with observed data. This Inverse Model validation is documented in Section 4. A summary is given in Section 5. A user's guide for the inverse wake vortex model is presented in a separate NorthWest Research Associates technical report (Lai and Delisi, 2007a).

Numerical simulations of induction and MWD logging tools and data inversion method with X-window interface on a UNIX workstation

NASA Astrophysics Data System (ADS)

Tian, Xiang-Dong

The purpose of this research is to simulate induction and measuring-while-drilling (MWD) logs. In simulation of logs, there are two tasks. The first task, the forward modeling procedure, is to compute the logs from known formation. The second task, the inversion procedure, is to determine the unknown properties of the formation from the measured field logs. In general, the inversion procedure requires the solution of a forward model. In this study, a stable numerical method to simulate induction and MWD logs is presented. The proposed algorithm is based on a horizontal eigenmode expansion method. Vertical propagation of modes is modeled by a three-layer module. The multilayer cases are treated as a cascade of these modules. The mode tracing algorithm possesses stable characteristics that are superior to other methods. This method is applied to simulate the logs in the formations with both vertical and horizontal layers, and also used to study the groove effects of the MWD tool. The results are very good. Two-dimensional inversion of induction logs is an nonlinear problem. Nonlinear functions of the apparent conductivity are expanded into a Taylor series. After truncating the high order terms in this Taylor series, the nonlinear functions are linearized. An iterative procedure is then devised to solve the inversion problem. In each iteration, the Jacobian matrix is calculated, and a small variation computed using the least-squares method is used to modify the background medium. Finally, the inverted medium is obtained. The horizontal eigenstate method is used to solve the forward problem. It is found that a good inverted formation can be obtained by using measurements. In order to help the user simulate the induction logs conveniently, a Wellog Simulator, based on the X-window system, is developed. The application software (FORTRAN codes) embedded in the Simulator is designed to simulate the responses of the induction tools in the layered formation with dipping beds. The graphic user-interface part of the Wellog Simulator is implemented with C and Motif. Through the user interface, the user can prepare the simulation data, select the tools, simulate the logs and plot the results.

On the optimization of electromagnetic geophysical data: Application of the PSO algorithm

NASA Astrophysics Data System (ADS)

Godio, A.; Santilano, A.

2018-01-01

Particle Swarm optimization (PSO) algorithm resolves constrained multi-parameter problems and is suitable for simultaneous optimization of linear and nonlinear problems, with the assumption that forward modeling is based on good understanding of ill-posed problem for geophysical inversion. We apply PSO for solving the geophysical inverse problem to infer an Earth model, i.e. the electrical resistivity at depth, consistent with the observed geophysical data. The method doesn't require an initial model and can be easily constrained, according to external information for each single sounding. The optimization process to estimate the model parameters from the electromagnetic soundings focuses on the discussion of the objective function to be minimized. We discuss the possibility to introduce in the objective function vertical and lateral constraints, with an Occam-like regularization. A sensitivity analysis allowed us to check the performance of the algorithm. The reliability of the approach is tested on synthetic, real Audio-Magnetotelluric (AMT) and Long Period MT data. The method appears able to solve complex problems and allows us to estimate the a posteriori distribution of the model parameters.

2-D inversion of VES data in Saqqara archaeological area, Egypt

NASA Astrophysics Data System (ADS)

El-Qady, Gad; Sakamoto, Chika; Ushijima, Keisuke

1999-10-01

The interpretation of actual geophysical field data still has a problem for obtaining a unique solution. In order to investigate the groundwater potentials in Saqqara archaeological area, vertical electrical soundings with Schlumberger array have been carried out. In the interpretation of VES data, 1D resistivity inversion has been performed based on a horizontally layered earth model by El-Qady (1995). However, some results of 1D inversion are not fully satisfied for actual 3D structures such as archaeological tombs. Therefore, we have carried out 2D inversion based on ABIC least squares method for Schlumberger VES data obtained in Saqqara area. Although the results of 2D cross sections were correlated with the previous interpretation, the 2D inversion still shows a rough spatial resistivity distribution, which is the abrupt change in resistivity between two neighboring blocks of the computed region. It is concluded that 3D interpretation is recommended for visualizing ground water distribution with depth in the Saqqara area.

Gravimorphism in rice and barley: promotion of leaf elongation by vertical inversion in agravitropically growing plants.

PubMed

Abe, K; Takahashi, H; Suge, H

1998-12-01

We have compared shoot responses of agravitropic rice and barley plants to vertical inversion with those of normal ones. When rice plants were vertically inverted, the main stems of a japonica type of rice, cv. Kamenoo, showed negative gravitropism at nodes 2-15 of both elongated and non-elongated internodes. However, shoots of lazy line of rice, lazy-Kamenoo, bent gravitropically at nodes 11-15 only elongated internodes but not at nodes 2-10 of non-elongated ones. Thus, shoots of Kamenoo responded gravitropically at all stages of growth, whereas shoots of lazy-Kamenoo did not show gravitropic response before heading. In Kamenoo plants, lengths of both leaf-sheath and leaf-blade were shortened by vertical inversion, but those of the vertically inverted plants of lazy-Kamenoo were significantly longer than the plants in an upright position. When agravitropic and normal plants of barley were vertically inverted, the same results as in rice were obtained; elongation of both leaf-sheath and leaf-blade was inhibited in normal barley plants, Chikurin-Ibaragi No. 1, but significantly stimulated in agravitropic plants of serpentina barley. These results suggest that vertical inversion of rice and barley plants enhances the elongation growth of leaves in the absence of tropistic response.

Temporal Variability of the Trade Wind Inversion: Measured with a Boundary Layer Vertical Profiler

DTIC Science & Technology

1992-05-01

direction change . Consequently, the frequency of vertical observations is every 70 s and each measu t is a 30 s average. T. Riddle combined the raw data set... changes to superadiabatic. There is no change to the temperature at the inversion top. 25 Temperature ( and Dewpoint (-): 8 Aug. 1200 UTC 5000 4500 ! 4000...inversion base is the last level before the lapse rate changes to superadiaatc, (2) There is no change to temperature at the inversion top, and (3) A

Full-Physics Inverse Learning Machine for Satellite Remote Sensing of Ozone Profile Shapes and Tropospheric Columns

NASA Astrophysics Data System (ADS)

Xu, J.; Heue, K.-P.; Coldewey-Egbers, M.; Romahn, F.; Doicu, A.; Loyola, D.

2018-04-01

Characterizing vertical distributions of ozone from nadir-viewing satellite measurements is known to be challenging, particularly the ozone information in the troposphere. A novel retrieval algorithm called Full-Physics Inverse Learning Machine (FP-ILM), has been developed at DLR in order to estimate ozone profile shapes based on machine learning techniques. In contrast to traditional inversion methods, the FP-ILM algorithm formulates the profile shape retrieval as a classification problem. Its implementation comprises a training phase to derive an inverse function from synthetic measurements, and an operational phase in which the inverse function is applied to real measurements. This paper extends the ability of the FP-ILM retrieval to derive tropospheric ozone columns from GOME- 2 measurements. Results of total and tropical tropospheric ozone columns are compared with the ones using the official GOME Data Processing (GDP) product and the convective-cloud-differential (CCD) method, respectively. Furthermore, the FP-ILM framework will be used for the near-real-time processing of the new European Sentinel sensors with their unprecedented spectral and spatial resolution and corresponding large increases in the amount of data.

Cross-borehole flowmeter tests for transient heads in heterogeneous aquifers.

PubMed

Le Borgne, Tanguy; Paillet, Frederick; Bour, Olivier; Caudal, Jean-Pierre

2006-01-01

Cross-borehole flowmeter tests have been proposed as an efficient method to investigate preferential flowpaths in heterogeneous aquifers, which is a major task in the characterization of fractured aquifers. Cross-borehole flowmeter tests are based on the idea that changing the pumping conditions in a given aquifer will modify the hydraulic head distribution in large-scale flowpaths, producing measurable changes in the vertical flow profiles in observation boreholes. However, inversion of flow measurements to derive flowpath geometry and connectivity and to characterize their hydraulic properties is still a subject of research. In this study, we propose a framework for cross-borehole flowmeter test interpretation that is based on a two-scale conceptual model: discrete fractures at the borehole scale and zones of interconnected fractures at the aquifer scale. We propose that the two problems may be solved independently. The first inverse problem consists of estimating the hydraulic head variations that drive the transient borehole flow observed in the cross-borehole flowmeter experiments. The second inverse problem is related to estimating the geometry and hydraulic properties of large-scale flowpaths in the region between pumping and observation wells that are compatible with the head variations deduced from the first problem. To solve the borehole-scale problem, we treat the transient flow data as a series of quasi-steady flow conditions and solve for the hydraulic head changes in individual fractures required to produce these data. The consistency of the method is verified using field experiments performed in a fractured-rock aquifer.

Temperature and Relative Humidity Vertical Profiles within Planetary Boundary Layer in Winter Urban Airshed

NASA Astrophysics Data System (ADS)

Bendl, Jan; Hovorka, Jan

2017-12-01

The planetary boundary layer is a dynamic system with turbulent flow where horizontal and vertical air mixing depends mainly on the weather conditions and geomorphology. Normally, air temperature from the Earth surface decreases with height but inversion situation may occur, mainly during winter. Pollutant dispersion is poor during inversions so air pollutant concentration can quickly rise, especially in urban closed valleys. Air pollution was evaluated by WHO as a human carcinogen (mostly by polycyclic aromatic hydrocarbons) and health effects are obvious. Knowledge about inversion layer height is important for estimation of the pollution impact and it can give us also information about the air pollution sources. Temperature and relative humidity vertical profiles complement ground measurements. Ground measurements were conducted to characterize comprehensively urban airshed in Svermov, residential district of the city of Kladno, about 30 km NW of Prague, from the 2nd Feb. to the 3rd of March 2016. The Svermov is an air pollution hot-spot for long time benzo[a]pyrene (B[a]P) limit exceedances, reaching the highest B[a]P annual concentration in Bohemia - west part of the Czech Republic. Since the Svermov sits in a shallow valley, frequent vertical temperature inversion in winter and low emission heights of pollution sources prevent pollutant dispersal off the valley. Such orography is common to numerous small settlements in the Czech Republic. Ground measurements at the sports field in the Svermov were complemented by temperature and humidity vertical profiles acquired by a Vaisala radiosonde positioned at tethered He-filled balloon. Total number of 53 series of vertical profiles up to the height of 300 m was conducted. Meteorology parameters were acquired with 4 Hz frequency. The measurements confirmed frequent early-morning and night formation of temperature inversion within boundary layer up to the height of 50 m. This rather shallow inversion had significant influence on air quality due to inversion cap over the valley. Nevertheless, formation of an inversion showed strong diurnal variability. For example, on the 18th Feb. early morning shallow inversion quickly disappeared within less than 2 hours. According to this study tethered balloon measurements has proved to be a good tool for completion comprehensive ground air quality measurements.

Ant colony optimisation inversion of surface and borehole magnetic data under lithological constraints

NASA Astrophysics Data System (ADS)

Liu, Shuang; Hu, Xiangyun; Liu, Tianyou; Xi, Yufei; Cai, Jianchao; Zhang, Henglei

2015-01-01

The ant colony optimisation algorithm has successfully been used to invert for surface magnetic data. However, the resolution of the distributions of the recovered physical property for deeply buried magnetic sources is not generally very high because of geophysical ambiguities. We use three approaches to deal with this problem. First, the observed surface magnetic data are taken together with the three-component borehole magnetic anomalies to recover the distributions of the physical properties. This cooperative inversion strategy improves the resolution of the inversion results in the vertical direction. Additionally, as the ant colony tours the discrete nodes, we force it to visit the nodes with physical properties that agree with the drilled lithologies. These lithological constraints reduce the non-uniqueness of the inversion problem. Finally, we also implement a K-means cluster analysis for the distributions of the magnetic cells after each iteration, in order to separate the distributions of magnetisation intensity instead of concentrating the distribution in a single area. We tested our method using synthetic data and found that all tests returned favourable results. In the case study of the Mengku iron-ore deposit in northwest China, the recovered distributions of magnetisation are in good agreement with the locations and shapes of the magnetite orebodies as inferred by drillholes. Uncertainty analysis shows that the ant colony algorithm is robust in the presence of noise and that the proposed approaches significantly improve the quality of the inversion results.

Particle Swarm Optimization algorithms for geophysical inversion, practical hints

NASA Astrophysics Data System (ADS)

Garcia Gonzalo, E.; Fernandez Martinez, J.; Fernandez Alvarez, J.; Kuzma, H.; Menendez Perez, C.

2008-12-01

PSO is a stochastic optimization technique that has been successfully used in many different engineering fields. PSO algorithm can be physically interpreted as a stochastic damped mass-spring system (Fernandez Martinez and Garcia Gonzalo 2008). Based on this analogy we present a whole family of PSO algorithms and their respective first order and second order stability regions. Their performance is also checked using synthetic functions (Rosenbrock and Griewank) showing a degree of ill-posedness similar to that found in many geophysical inverse problems. Finally, we present the application of these algorithms to the analysis of a Vertical Electrical Sounding inverse problem associated to a seawater intrusion in a coastal aquifer in South Spain. We analyze the role of PSO parameters (inertia, local and global accelerations and discretization step), both in convergence curves and in the a posteriori sampling of the depth of an intrusion. Comparison is made with binary genetic algorithms and simulated annealing. As result of this analysis, practical hints are given to select the correct algorithm and to tune the corresponding PSO parameters. Fernandez Martinez, J.L., Garcia Gonzalo, E., 2008a. The generalized PSO: a new door to PSO evolution. Journal of Artificial Evolution and Applications. DOI:10.1155/2008/861275.

Near Surface Seismic Hazard Characterization in the Presence of High Velocity Contrasts

NASA Astrophysics Data System (ADS)

Gribler, G.; Mikesell, D.; Liberty, L. M.

2017-12-01

We present new multicomponent surface wave processing techniques that provide accurate characterization of near-surface conditions in the presence of large lateral or vertical shear wave velocity boundaries. A common problem with vertical component Rayleigh wave analysis in the presence of high contrast subsurface conditions is Rayleigh wave propagation mode misidentification due to an overlap of frequency-phase velocity domain dispersion, leading to an overestimate of shear wave velocities. By using the vertical and horizontal inline component signals, we isolate retrograde and prograde particle motions to separate fundamental and higher mode signals, leading to more accurate and confident dispersion curve picks and shear wave velocity estimates. Shallow, high impedance scenarios, such as the case with shallow bedrock, are poorly constrained when using surface wave dispersion information alone. By using a joint inversion of dispersion and horizontal-to-vertical (H/V) curves within active source frequency ranges (down to 3 Hz), we can accurately estimate the depth to high impedance boundaries, a significant improvement compared to the estimates based on dispersion information alone. We compare our approach to body wave results that show comparable estimates of bedrock topography. For lateral velocity contrasts, we observe horizontal polarization of Rayleigh waves identified by an increase in amplitude and broadening of the horizontal spectra with little variation in the vertical component spectra. The horizontal spectra offer a means to identify and map near surface faults where there is no topographic or clear body wave expression. With these new multicomponent active source seismic data processing and inversion techniques, we better constrain a variety of near surface conditions critical to the estimation of local site response and seismic hazards.

Aircraft automatic-flight-control system with inversion of the model in the feed-forward path using a Newton-Raphson technique for the inversion

NASA Technical Reports Server (NTRS)

Smith, G. A.; Meyer, G.; Nordstrom, M.

1986-01-01

A new automatic flight control system concept suitable for aircraft with highly nonlinear aerodynamic and propulsion characteristics and which must operate over a wide flight envelope was investigated. This exact model follower inverts a complete nonlinear model of the aircraft as part of the feed-forward path. The inversion is accomplished by a Newton-Raphson trim of the model at each digital computer cycle time of 0.05 seconds. The combination of the inverse model and the actual aircraft in the feed-forward path alloys the translational and rotational regulators in the feedback path to be easily designed by linear methods. An explanation of the model inversion procedure is presented. An extensive set of simulation data for essentially the full flight envelope for a vertical attitude takeoff and landing aircraft (VATOL) is presented. These data demonstrate the successful, smooth, and precise control that can be achieved with this concept. The trajectory includes conventional flight from 200 to 900 ft/sec with path accelerations and decelerations, altitude changes of over 6000 ft and 2g and 3g turns. Vertical attitude maneuvering as a tail sitter along all axes is demonstrated. A transition trajectory from 200 ft/sec in conventional flight to stationary hover in the vertical attitude includes satisfactory operation through lift-cure slope reversal as attitude goes from horizontal to vertical at constant altitude. A vertical attitude takeoff from stationary hover to conventional flight is also demonstrated.

An Algorithm for the Vertical Structure of Aerosol Extinction in the Lowest Kilometer of the Atmosphere: Rev. 1

DTIC Science & Technology

2017-11-01

inversion layer, or the well-mixed boundary layer. In such cases a low cloud ceiling is not present. In all instances the atmospheric extinction profiles...height, radiation fog depth, or the inversion layer height. The visibility regions and several representative vertical profiles of extinction are...the coefficient B can be found by B = ln(D/A) . (2) The coefficient B is sometimes a function of the cloud ceiling height, the inversion layer height

Interpretation of magnetic anomalies using a genetic algorithm

NASA Astrophysics Data System (ADS)

Kaftan, İlknur

2017-08-01

A genetic algorithm (GA) is an artificial intelligence method used for optimization. We applied a GA to the inversion of magnetic anomalies over a thick dike. Inversion of nonlinear geophysical problems using a GA has advantages because it does not require model gradients or well-defined initial model parameters. The evolution process consists of selection, crossover, and mutation genetic operators that look for the best fit to the observed data and a solution consisting of plausible compact sources. The efficiency of a GA on both synthetic and real magnetic anomalies of dikes by estimating model parameters, such as depth to the top of the dike ( H), the half-width of the dike ( B), the distance from the origin to the reference point ( D), the dip of the thick dike ( δ), and the susceptibility contrast ( k), has been shown. For the synthetic anomaly case, it has been considered for both noise-free and noisy magnetic data. In the real case, the vertical magnetic anomaly from the Pima copper mine in Arizona, USA, and the vertical magnetic anomaly in the Bayburt-Sarıhan skarn zone in northeastern Turkey have been inverted and interpreted. We compared the estimated parameters with the results of conventional inversion methods used in previous studies. We can conclude that the GA method used in this study is a useful tool for evaluating magnetic anomalies for dike models.

Face Inversion Disproportionately Disrupts Sensitivity to Vertical over Horizontal Changes in Eye Position

ERIC Educational Resources Information Center

Crookes, Kate; Hayward, William G.

2012-01-01

Presenting a face inverted (upside down) disrupts perceptual sensitivity to the spacing between the features. Recently, it has been shown that this disruption is greater for vertical than horizontal changes in eye position. One explanation for this effect proposed that inversion disrupts the processing of long-range (e.g., eye-to-mouth distance)…

The genetic algorithm: A robust method for stress inversion

NASA Astrophysics Data System (ADS)

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

2017-01-01

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

Geoacoustic inversion with two source-receiver arrays in shallow water.

PubMed

Sukhovich, Alexey; Roux, Philippe; Wathelet, Marc

2010-08-01

A geoacoustic inversion scheme based on a double beamforming algorithm in shallow water is proposed and tested. Double beamforming allows identification of multi-reverberated eigenrays propagating between two vertical transducer arrays according to their emission and reception angles and arrival times. Analysis of eigenray intensities yields the bottom reflection coefficient as a function of angle of incidence. By fitting the experimental reflection coefficient with a theoretical prediction, values of the acoustic parameters of the waveguide bottom can be extracted. The procedure was initially tested in a small-scale tank experiment for a waveguide with a Plexiglas bottom. Inversion results for the speed of shear waves in Plexiglas are in good agreement with the table values. A similar analysis was applied to data collected during an at-sea experiment in shallow coastal waters of the Mediterranean. Bottom reflection coefficient was fitted with the theory in which bottom sediments are modeled as a multi-layered system. Retrieved bottom parameters are in quantitative agreement with those determined from a prior inversion scheme performed in the same area. The present study confirms the interest in processing source-receiver array data through the double beamforming algorithm, and indicates the potential for application of eigenray intensity analysis to geoacoustic inversion problems.

Elastic-Waveform Inversion with Compressive Sensing for Sparse Seismic Data

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

Lin, Youzuo; Huang, Lianjie

2015-01-28

Accurate velocity models of compressional- and shear-waves are essential for geothermal reservoir characterization and microseismic imaging. Elastic-waveform inversion of multi-component seismic data can provide high-resolution inversion results of subsurface geophysical properties. However, the method requires seismic data acquired using dense source and receiver arrays. In practice, seismic sources and/or geophones are often sparsely distributed on the surface and/or in a borehole, such as 3D vertical seismic profiling (VSP) surveys. We develop a novel elastic-waveform inversion method with compressive sensing for inversion of sparse seismic data. We employ an alternating-minimization algorithm to solve the optimization problem of our new waveform inversionmore » method. We validate our new method using synthetic VSP data for a geophysical model built using geologic features found at the Raft River enhanced-geothermal-system (EGS) field. We apply our method to synthetic VSP data with a sparse source array and compare the results with those obtained with a dense source array. Our numerical results demonstrate that the velocity models produced with our new method using a sparse source array are almost as accurate as those obtained using a dense source array.« less

Thermomagnetic instabilities in a vertical layer of ferrofluid: nonlinear analysis away from a critical point

NASA Astrophysics Data System (ADS)

Dey, Pinkee; Suslov, Sergey A.

2016-12-01

A finite amplitude instability has been analysed to discover the exact mechanism leading to the appearance of stationary magnetoconvection patterns in a vertical layer of a non-conducting ferrofluid heated from the side and placed in an external magnetic field perpendicular to the walls. The physical results have been obtained using a version of a weakly nonlinear analysis that is based on the disturbance amplitude expansion. It enables a low-dimensional reduction of a full nonlinear problem in supercritical regimes away from a bifurcation point. The details of the reduction are given in comparison with traditional small-parameter expansions. It is also demonstrated that Squire’s transformation can be introduced for higher-order nonlinear terms thus reducing the full three-dimensional problem to its equivalent two-dimensional counterpart and enabling significant computational savings. The full three-dimensional instability patterns are subsequently recovered using the inverse transforms The analysed stationary thermomagnetic instability is shown to occur as a result of a supercritical pitchfork bifurcation.

Transect-scale imaging of root zone electrical conductivity by inversion of multiple-height EMI measurements under different salinity conditions

NASA Astrophysics Data System (ADS)

Piero Deidda, Gian; Coppola, Antonio; Dragonetti, Giovanna; Comegna, Alessandro; Rodriguez, Giuseppe; Vignoli, Giulio

2017-04-01

The ability to determine the effects of salts on soils and plants, are of great importance to agriculture. To control its harmful effects, soil salinity needs to be monitored in space and time. This requires knowledge of its magnitude, temporal dynamics, and spatial variability. Soil salinity can be evaluated by measuring the bulk electrical conductivity (σb) in the field. Measurements of σb can be made with either in situ or remote devices (Rhoades and Oster, 1986; Rhoades and Corwin, 1990; Rhoades and Miyamoto, 1990). Time Domain Reflectometry (TDR) sensors allow simultaneous measurements of water content, θ, and σb. They may be calibrated in the laboratory for estimating the electrical conductivity of the soil solution (σw). However, they have a relatively small observation volume and thus they only provide local-scale measurements. The spatial range of the sensors is limited to tens of centimeters and extension of the information to a large area can be problematic. Also, information on the vertical distribution of the σb soil profile may only be obtained by installing sensors at different depths. In this sense, the TDR may be considered as an invasive technique. Compared to the TDR, non-invasive electromagnetic induction (EMI) techniques can be used for extensively mapping the bulk electrical conductivity in the field. The problem is that all these techniques give depth-weighted apparent electrical conductivity (ECa) measurements, depending on the specific depth distribution of the σb, as well as on the depth response function of the sensor used. In order to deduce the actual distribution of local σb in the soil profile, one may invert the signal coming from EMI sensors. Most studies use the linear model proposed by McNeill (1980), describing the relative depth-response of the ground conductivity meter. By using the forward linear model of McNeill, Borchers et al. (1997) implemented a Least Squares inverse procedure with second order Tikhonov regularization, to estimate σb vertical distribution from EMI field data. More recent studies (Hendrickx et al., 2002; Deidda et al., 2003; Deidda et al., 2014, among others), extended the approach to a more complicated non linear model of the response of a ground conductivity meter to changes with depth of σb. Noteworthy, these inverse procedures are only based on electromagnetic physics. Thus, they are only based on ECa readings, possibly taken with both the horizontal and vertical configurations and with the sensor at different heights above the ground, and do not require any further field calibration. Nevertheless, as discussed by Hendrickx et al. (2002), important issues on inverse approaches are about: i) the applicability to heterogeneous field soils of physical equations originally developed for the electromagnetic response of homogeneous media and ii) nonuniqueness and instability problems inherent to inverse procedures, even after Tikhonov regularization. Besides, as discussed by Cook and Walker (1992), these mathematical inversions procedures using layered-earth models were originally designed for interpreting porous systems with distinct layering. Where subsurface layers are not sharply defined, this type of inversion may be subject to considerable error. With these premises, the main aim of this study is estimating the vertical σb distribution by ECa measured using ground surface EMI methods under different salinity conditions and using TDR data as ground-truth data for validation of the inversion procedure. The latter is based on a regularized 1D inversion procedure designed to swiftly manage nonlinear multiple EMI-depth responses (Deidda et al., 2014). It is based on the coupling of the damped Gauss-Newton method with either the truncated singular value decomposition (TSVD) or the truncated generalized singular value decomposition (TGSVD), and it implements an explicit (exact) representation of the Jacobian to solve the nonlinear inverse problem. The experimental field (30 m x 15.6 m; for a total area of 468 m2) was divided into three transects 30 m long and 4.2 width, cultivated with green bean and irrigated with three different salinity levels (1 dS/m, 3 dS/m, and 6 dS/m). Each transect consisted of seven rows equipped with a sprinkler irrigation system, which supplied a water flux of 2 l/h. As for the salt application, CaCl2 were dissolved in tap water, and subsequently siphoned into the irrigation system. For each transect, 24 regularly spaced monitoring sites (1 m apart) were selected for soil measurements, using different equipments: i) a TDR100, ii), a Geonics EM-38; iii). Overall, fifteen measurement campaigns were carried out.

Multi-parameter Full-waveform Inversion for Acoustic VTI Medium with Surface Seismic Data

NASA Astrophysics Data System (ADS)

Cheng, X.; Jiao, K.; Sun, D.; Huang, W.; Vigh, D.

2013-12-01

Full-waveform Inversion (FWI) attracts wide attention recently in oil and gas industry as a new promising tool for high resolution subsurface velocity model building. While the traditional common image point gather based tomography method aims to focus post-migrated data in depth domain, FWI aims to directly fit the observed seismic waveform in either time or frequency domain. The inversion is performed iteratively by updating the velocity fields to reduce the difference between the observed and the simulated data. It has been shown the inversion is very sensitive to the starting velocity fields, and data with long offsets and low frequencies is crucial for the success of FWI to overcome this sensitivity. Considering the importance of data with long offsets and low frequencies, in most geologic environment, anisotropy is an unavoidable topic for FWI especially at long offsets, since anisotropy tends to have more pronounced effects on waves traveled for a great distance. In VTI medium, this means more horizontal velocity will be registered in middle-to-long offset data, while more vertical velocity will be registered in near-to-middle offset data. Up to date, most of real world applications of FWI still remain in isotropic medium, and only a few studies have been shown to account for anisotropy. And most of those studies only account for anisotropy in waveform simulation, but not invert for those anisotropy fields. Multi-parameter inversion for anisotropy fields, even in VTI medium, remains as a hot topic in the field. In this study, we develop a strategy for multi-parameter FWI for acoustic VTI medium with surface seismic data. Because surface seismic data is insensitivity to the delta fields, we decide to hold the delta fields unchanged during our inversion, and invert only for vertical velocity and epsilon fields. Through parameterization analysis and synthetic tests, we find that it is more feasible to invert for the parameterization as vertical and horizontal velocities instead of inverting for the parameterization as vertical velocity and epsilon fields. We develop a hierarchical approach to invert for vertical velocity first but hold epsilon unchanged and only switch to simultaneous inversion when vertical velocity inversion are approaching convergence. During simultaneous inversion, we observe significant acceleration in the convergence when incorporates second order information and preconditioning into inversion. We demonstrate the success of our strategy for VTI FWI using synthetic and real data examples from the Gulf of Mexico. Our results show that incorporation of VTI FWI improves migration of large offset acquisition data, and produces better focused migration images to be used in exploration, production and development of oil fields.

The Effects of Face Inversion on the Perception of Long-Range and Local Spatial Relations in Eye and Mouth Configuration

ERIC Educational Resources Information Center

Sekunova, Alla; Barton, Jason J. S.

2008-01-01

A recent study hypothesized a configurational anisotropy in the face inversion effect, with vertical relations more difficult to process. However, another difference in the stimuli of that report was that the vertical but not horizontal shifts lacked local spatial references. Difficulty processing long-range spatial relations might also be…

A Vertical Differential Configuration in GPR prospecting

NASA Astrophysics Data System (ADS)

Persico, Raffaele; Pochanin, Gennadiy; Varianytsia-Roshchupkina, Liudmyla; Catapano, Ilaria; Gennarelli, Gianluca; Soldovieri, Francesco

2015-04-01

The rejection of the direct coupling between the antennas is an issue of interest in several GPR applications, especially when it is important to distinguish the targets of interest from the clutter and the signal reflected from the air soil interface. Therefore, in this framework several hardware and software strategies have been proposed. Among the software strategies, probably the most common one is the background removal [1], whereas as an hardware strategy the differential configuration has been introduced in [2-3] and then further on studied in [4] with respect to the spatial filtering properties of the relevant mathematical operator. In particular, the studies proposed in [1] and [4] have shown that, in general, all the strategies for the rejection of the direct coupling have necessarily some drawback, essentially because it is not possible to erase all and only the undesired contributions leaving "untouched" the contributions of the targets of interest to the gathered signal. With specific regard to the differential configuration, in [2-3], the differential configuration consisted in a couple of receiving antennas symmetrically placed around the transmitting one, being the three antennas placed along the same horizontal segment. Therefore, we might define that configuration as a "horizontal differential configuration". Here, we propose a novel differential GPR configuration, where the two receiving antennas are still symmetrically located with respect to the transmitting one, but are placed piled on each other at different heights from the air-soil interface, whereas the transmitting antenna is at the medium height between the two receiving one (however, it is not at the same abscissa but at a fixed horizontal offset from the receiving antennas). Such a differential configuration has been previously presented in [5-6] and allows a good isolation between the antennas, while preserving the possibility to collect backscattered signals from both electrically small objects and interfaces. This configuration can be labeled as a vertical differential configuration. At the conference, the reconstruction capabilities of this differential GPR configuration system will be discussed by means of an analysis of the problem based on a properly designed microwave tomographic inversion approach. The proposed approach exploits the Born approximation and faces the imaging as the solution of a linear inverse scattering problem. In this way, the problem of the local minima is avoided [7] and it is possible to impose some regularization to the problem in an easy way problem [8-9]. At the conference, a theoretical analysis of the mathematical propserties of the scattering operator under the vertical differential configuration will be presented showing that, with respect to the horizontal differential configuration, the vertical one allows to reject the direct coupling between the antennas but not the coupling of the antennas occurring through the air-soil interface. On the other hand, the filtering properties of the operator at hand con be considered, let say, less severe in some cases. At the conference, both some numerical and experimental results will be shown. References [1] R. Persico, F. Soldovieri, "Effects of the background removal in linear inverse scattering", IEEE Trans. Geosci. Remote Sens, vol. 46, pp. 1104-1114, April 2008. [2] L. Gurel, U. Oguz, "Three-Dimensional FDTD modeling of a ground penetrating radar", IEEE Trans. Geosci. Remote Sens, vol. 38, pp. 1513-1521, July 2000. [3] L. Gurel, U. Oguz, "Optimization of the transmitter-receiver separation in the ground penetrating radar", IEEE Trans. Antennas and Propag., vol. 51, no 3, pp. 362-370, March 2003. [4] R. Persico, F. Soldovieri, "A microwave tomography approach for a differential configuration in GPR prospecting", IEEE Trans. Antennas and Propag., vol. 54, pp. 3541 - 3548, 2006. [5] Y.A. Kopylov, S.A. Masalov, G.P. Pochanin, "The way of isolation between transmitting and receiving modules of antenna", Patent 81652 Ukraine: IPC (2006) H01Q 9/00 H01Q 19/10 / publ. 25.01.08, Bull. N. 2 [6] G.P. Pochanin, "Some Advances in UWB GPR," in "Unexploded Ordnance Detection and Mitigation, - NATO Science for Peace and Security Series -B: Physics and Biophysics - Ed. by Jim Byrnes, Springer: Dordrecht, (The Nederland), 2009. pp.223-233. [7] R. Persico, F. Soldovieri, R. Pierri, "Convergence Properties of a Quadratic Approach to the Inverse Scattering Problem", Journal of Optical Society of America Part A, vol. 19, n. 12, pp. 2424-2428, December 2002. [8] R. Pierri, G. Leone, F. Soldovieri, R. Persico, "Electromagnetic inversion for subsurface applications under the distorted Born approximation" Nuovo Cimento, vol. 24C, N. 2, pp 245-261, March-April 2001. [9] R. Persico, Introduction to ground penetrating Radar: Inverse Scattering and data Processing, in print on Wiley and Sons, 2014, ISBN 9781118305003.

Hydrologic characterization of desert soils with varying degrees of pedogenesis: 2. Inverse modeling for eff ective properties

USGS Publications Warehouse

Mirus, B.B.; Perkins, K.S.; Nimmo, J.R.; Singha, K.

2009-01-01

To understand their relation to pedogenic development, soil hydraulic properties in the Mojave Desert were investi- gated for three deposit types: (i) recently deposited sediments in an active wash, (ii) a soil of early Holocene age, and (iii) a highly developed soil of late Pleistocene age. Eff ective parameter values were estimated for a simplifi ed model based on Richards' equation using a fl ow simulator (VS2D), an inverse algorithm (UCODE-2005), and matric pressure and water content data from three ponded infi ltration experiments. The inverse problem framework was designed to account for the eff ects of subsurface lateral spreading of infi ltrated water. Although none of the inverse problems converged on a unique, best-fi t parameter set, a minimum standard error of regression was reached for each deposit type. Parameter sets from the numerous inversions that reached the minimum error were used to develop probability distribu tions for each parameter and deposit type. Electrical resistance imaging obtained for two of the three infi ltration experiments was used to independently test fl ow model performance. Simulations for the active wash and Holocene soil successfully depicted the lateral and vertical fl uxes. Simulations of the more pedogenically developed Pleistocene soil did not adequately replicate the observed fl ow processes, which would require a more complex conceptual model to include smaller scale heterogeneities. The inverse-modeling results, however, indicate that with increasing age, the steep slope of the soil water retention curve shitis toward more negative matric pressures. Assigning eff ective soil hydraulic properties based on soil age provides a promising framework for future development of regional-scale models of soil moisture dynamics in arid environments for land-management applications. ?? Soil Science Society of America.

Reducing uncertainties in the velocities determined by inversion of phase velocity dispersion curves using synthetic seismograms

NASA Astrophysics Data System (ADS)

Hosseini, Seyed Mehrdad

Characterizing the near-surface shear-wave velocity structure using Rayleigh-wave phase velocity dispersion curves is widespread in the context of reservoir characterization, exploration seismology, earthquake engineering, and geotechnical engineering. This surface seismic approach provides a feasible and low-cost alternative to the borehole measurements. Phase velocity dispersion curves from Rayleigh surface waves are inverted to yield the vertical shear-wave velocity profile. A significant problem with the surface wave inversion is its intrinsic non-uniqueness, and although this problem is widely recognized, there have not been systematic efforts to develop approaches to reduce the pervasive uncertainty that affects the velocity profiles determined by the inversion. Non-uniqueness cannot be easily studied in a nonlinear inverse problem such as Rayleigh-wave inversion and the only way to understand its nature is by numerical investigation which can get computationally expensive and inevitably time consuming. Regarding the variety of the parameters affecting the surface wave inversion and possible non-uniqueness induced by them, a technique should be established which is not controlled by the non-uniqueness that is already affecting the surface wave inversion. An efficient and repeatable technique is proposed and tested to overcome the non-uniqueness problem; multiple inverted shear-wave velocity profiles are used in a wavenumber integration technique to generate synthetic time series resembling the geophone recordings. The similarity between synthetic and observed time series is used as an additional tool along with the similarity between the theoretical and experimental dispersion curves. The proposed method is proven to be effective through synthetic and real world examples. In these examples, the nature of the non-uniqueness is discussed and its existence is shown. Using the proposed technique, inverted velocity profiles are estimated and effectiveness of this technique is evaluated; in the synthetic example, final inverted velocity profile is compared with the initial target velocity model, and in the real world example, final inverted shear-wave velocity profile is compared with the velocity model from independent measurements in a nearby borehole. Real world example shows that it is possible to overcome the non-uniqueness and distinguish the representative velocity profile for the site that also matches well with the borehole measurements.

Approach to simultaneously denoise and invert backscatter and extinction from photon-limited atmospheric lidar observations.

PubMed

Marais, Willem J; Holz, Robert E; Hu, Yu Hen; Kuehn, Ralph E; Eloranta, Edwin E; Willett, Rebecca M

2016-10-10

Atmospheric lidar observations provide a unique capability to directly observe the vertical column of cloud and aerosol scattering properties. Detector and solar-background noise, however, hinder the ability of lidar systems to provide reliable backscatter and extinction cross-section estimates. Standard methods for solving this inverse problem are most effective with high signal-to-noise ratio observations that are only available at low resolution in uniform scenes. This paper describes a novel method for solving the inverse problem with high-resolution, lower signal-to-noise ratio observations that are effective in non-uniform scenes. The novelty is twofold. First, the inferences of the backscatter and extinction are applied to images, whereas current lidar algorithms only use the information content of single profiles. Hence, the latent spatial and temporal information in noisy images are utilized to infer the cross-sections. Second, the noise associated with photon-counting lidar observations can be modeled using a Poisson distribution, and state-of-the-art tools for solving Poisson inverse problems are adapted to the atmospheric lidar problem. It is demonstrated through photon-counting high spectral resolution lidar (HSRL) simulations that the proposed algorithm yields inverted backscatter and extinction cross-sections (per unit volume) with smaller mean squared error values at higher spatial and temporal resolutions, compared to the standard approach. Two case studies of real experimental data are also provided where the proposed algorithm is applied on HSRL observations and the inverted backscatter and extinction cross-sections are compared against the standard approach.

Ultra-low velocity zones beneath the Philippine and Tasman Seas revealed by a trans-dimensional Bayesian waveform inversion

NASA Astrophysics Data System (ADS)

Pachhai, Surya; Dettmer, Jan; Tkalčić, Hrvoje

2015-11-01

Ultra-low velocity zones (ULVZs) are small-scale structures in the Earth's lowermost mantle inferred from the analysis of seismological observations. These structures exhibit a strong decrease in compressional (P)-wave velocity, shear (S)-wave velocity, and an increase in density. Quantifying the elastic properties of ULVZs is crucial for understanding their physical origin, which has been hypothesized either as partial melting, iron enrichment, or a combination of the two. Possible disambiguation of these hypotheses can lead to a better understanding of the dynamic processes of the lowermost mantle, such as, percolation, stirring and thermochemical convection. To date, ULVZs have been predominantly studied by forward waveform modelling of seismic waves that sample the core-mantle boundary region. However, ULVZ parameters (i.e. velocity, density, and vertical and lateral extent) obtained through forward modelling are poorly constrained because inferring Earth structure from seismic observations is a non-linear inverse problem with inherent non-uniqueness. To address these issues, we developed a trans-dimensional hierarchical Bayesian inversion that enables rigorous estimation of ULVZ parameter values and their uncertainties, including the effects of model selection. The model selection includes treating the number of layers and the vertical extent of the ULVZ as unknowns. The posterior probability density (solution to the inverse problem) of the ULVZ parameters is estimated by reversible jump Markov chain Monte Carlo sampling that employs parallel tempering to improve efficiency/convergence. First, we apply our method to study the resolution of complex ULVZ structure (including gradually varying structure) by probabilistically inverting simulated noisy waveforms. Then, two data sets sampling the CMB beneath the Philippine and Tasman Seas are considered in the inversion. Our results indicate that both ULVZs are more complex than previously suggested. For the Philippine Sea data, we find a strong decrease in S-wave velocity, which indicates the presence of iron-rich material, albeit this result is accompanied with larger parameter uncertainties than in a previous study. For the Tasman Sea data, our analysis yields a well-constrained S-wave velocity that gradually decreases with depth. We conclude that this ULVZ represents a partial melt of iron-enriched material with higher melt content near its bottom.

Correlation between the norm and the geometry of minimal networks

NASA Astrophysics Data System (ADS)

Laut, I. L.

2017-05-01

The paper is concerned with the inverse problem of the minimal Steiner network problem in a normed linear space. Namely, given a normed space in which all minimal networks are known for any finite point set, the problem is to describe all the norms on this space for which the minimal networks are the same as for the original norm. We survey the available results and prove that in the plane a rotund differentiable norm determines a distinctive set of minimal Steiner networks. In a two-dimensional space with rotund differentiable norm the coordinates of interior vertices of a nondegenerate minimal parametric network are shown to vary continuously under small deformations of the boundary set, and the turn direction of the network is determined. Bibliography: 15 titles.

Subjective Vertical Conflict Theory and Space Motion Sickness.

PubMed

Chen, Wei; Chao, Jian-Gang; Wang, Jin-Kun; Chen, Xue-Wen; Tan, Cheng

2016-02-01

Space motion sickness (SMS) remains a troublesome problem during spaceflight. The subjective vertical (SV) conflict theory postulates that all motion sickness provoking situations are characterized by a condition in which the SV sensed from gravity and visual and idiotropic cues differs from the expected vertical. This theory has been successfully used to predict motion sickness in different vehicles on Earth. We have summarized the most outstanding and recent studies on the illusions and characteristics associated with spatial disorientation and SMS during weightlessness, such as cognitive map and mental rotation, the visual reorientation and inversion illusions, and orientation preferences between visual scenes and the internal z-axis of the body. The relationships between the SV and the incidence of and susceptibility to SMS as well as spatial disorientation were addressed. A consistent framework was presented to understand and explain SMS characteristics in more detail on the basis of the SV conflict theory, which is expected to be more advantageous in SMS prediction, prevention, and training.

Face Inversion Disproportionately Impairs the Perception of Vertical but Not Horizontal Relations between Features

ERIC Educational Resources Information Center

Goffaux, Valerie; Rossion, Bruno

2007-01-01

Upside-down inversion disrupts the processing of spatial relations between the features of a face, while largely preserving local feature analysis. However, recent studies on face inversion failed to observe a clear dissociation between relational and featural processing. To resolve these discrepancies and clarify how inversion affects face…

Can earthquake source inversion benefit from rotational ground motion observations?

NASA Astrophysics Data System (ADS)

Igel, H.; Donner, S.; Reinwald, M.; Bernauer, M.; Wassermann, J. M.; Fichtner, A.

2015-12-01

With the prospects of instruments to observe rotational ground motions in a wide frequency and amplitude range in the near future we engage in the question how this type of ground motion observation can be used to solve seismic inverse problems. Here, we focus on the question, whether point or finite source inversions can benefit from additional observations of rotational motions. In an attempt to be fair we compare observations from a surface seismic network with N 3-component translational sensors (classic seismometers) with those obtained with N/2 6-component sensors (with additional colocated 3-component rotational motions). Thus we keep the overall number of traces constant. Synthetic seismograms are calculated for known point- or finite-source properties. The corresponding inverse problem is posed in a probabilistic way using the Shannon information content as a measure how the observations constrain the seismic source properties. The results show that with the 6-C subnetworks the source properties are not only equally well recovered (even that would be benefitial because of the substantially reduced logistics installing N/2 sensors) but statistically significant some source properties are almost always better resolved. We assume that this can be attributed to the fact the (in particular vertical) gradient information is contained in the additional rotational motion components. We compare these effects for strike-slip and normal-faulting type sources. Thus the answer to the question raised is a definite "yes". The challenge now is to demonstrate these effects on real data.

Dynamically consistent hydrography and absolute velocity in the eastern North Atlantic Ocean

NASA Technical Reports Server (NTRS)

Wunsch, Carl

1994-01-01

The problem of mapping a dynamically consistent hydrographic field and associated absolute geostrophic flow in the eastern North Atlantic between 24 deg and 36 deg N is related directly to the solution of the so-called thermocline equations. A nonlinear optimization problem involving Needler's P equation is solved to find the hydrography and resulting flow that minimizes the vertical mixing above about 1500 m in the ocean and is simultaneously consistent with the observations. A sharp minimum (at least in some dimensions) is found, apparently corresponding to a solution nearly conserving potential vorticity and with vertical eddy coefficient less than about 10(exp -5) sq m/s. Estimates of `residual' quantities such as eddy coefficients are extremely sensitive to slight modifications to the observed fields. Boundary conditions, vertical velocities, etc., are a product of the optimization and produce estimates differing quantitatively from prior ones relying directly upon observed hydrography. The results are generally insensitive to particular elements of the solution methodology, but many questions remain concerning the extent to which different synoptic sections can be asserted to represent the same ocean. The method can be regarded as a practical generalization of the beta spiral and geostrophic balance inverses for the estimate of absolute geostrophic flows. Numerous improvements to the methodology used in this preliminary attempt are possible.

The heat transfer coefficient determination with the use of the Beck-Trefftz method in flow boiling in a minichannel

NASA Astrophysics Data System (ADS)

Strąk, Kinga; Maciejewska, Beata; Piasecka, Magdalena

2018-06-01

In this paper, the solution of the two-dimensional inverse heat transfer problem with the use of the Beck method coupled with the Trefftz method is proposed. This method was applied for solving an inverse heat conduction problem. The aim of the calculation was to determine the boiling heat transfer coefficient on the basis of temperature measurements taken by infrared thermography. The experimental data of flow boiling heat transfer in a single vertical minichannel of 1.7 mm depth, heated asymmetrically, were used in calculations. The heating element for two refrigerants (FC-72 and HFE-7100, 3M) flowing in the minichannel was the plate enhanced on the side contacting with the fluid. The analysis of the results was performed on the basis of experimental series obtained for the same heat flux and two different mass flow velocities. The results were presented as infrared thermographs, heated wall temperature and heat transfer coefficient as a function of the distance from the minichannel inlet. The results was discussed for the subcooled and saturated boiling regions separately.

Inversion of the conical Radon transform with vertices on a surface of revolution arising in an application of a Compton camera

NASA Astrophysics Data System (ADS)

Moon, Sunghwan

2017-06-01

A Compton camera has been introduced for use in single photon emission computed tomography to improve the low efficiency of a conventional gamma camera. In general, a Compton camera brings about the conical Radon transform. Here we consider a conical Radon transform with the vertices on a rotation symmetric set with respect to a coordinate axis. We show that this conical Radon transform can be decomposed into two transforms: the spherical sectional transform and the weighted fan beam transform. After finding inversion formulas for these two transforms, we provide an inversion formula for the conical Radon transform.

Unanticipated ankle inversions are significantly different from anticipated ankle inversions during drop landings: overcoming anticipation bias.

PubMed

Dicus, Jeremy R; Seegmiller, Jeff G

2012-05-01

Few ankle inversion studies have taken anticipation bias into account or collected data with an experimental design that mimics actual injury mechanisms. Twenty-three participants performed randomized single-leg vertical drop landings from 20 cm. Subjects were blinded to the landing surface (a flat force plate or 30° inversion wedge on the force plate). After each trial, participants reported whether they anticipated the landing surface. Participant responses were validated with EMG data. The protocol was repeated until four anticipated and four unanticipated landings onto the inversion wedge were recorded. Results revealed a significant main effect for landing condition. Normalized vertical ground reaction force (% body weights), maximum ankle inversion (degrees), inversion velocity (degrees/second), and time from contact to peak muscle activation (seconds) were significantly greater in unanticipated landings, and the time from peak muscle activation to maximum VGRF (second) was shorter. Unanticipated landings presented different muscle activation patterns than landings onto anticipated surfaces, which calls into question the usefulness of clinical studies that have not controlled for anticipation bias.

Boundary layer flow of MHD generalized Maxwell fluid over an exponentially accelerated infinite vertical surface with slip and Newtonian heating at the boundary

NASA Astrophysics Data System (ADS)

Imran, M. A.; Riaz, M. B.; Shah, N. A.; Zafar, A. A.

2018-03-01

The aim of this article is to investigate the unsteady natural convection flow of Maxwell fluid with fractional derivative over an exponentially accelerated infinite vertical plate. Moreover, slip condition, radiation, MHD and Newtonian heating effects are also considered. A modern definition of fractional derivative operator recently introduced by Caputo and Fabrizio has been used to formulate the fractional model. Semi analytical solutions of the dimensionless problem are obtained by employing Stehfest's and Tzou's algorithms in order to find the inverse Laplace transforms for temperature and velocity fields. Temperature and rate of heat transfer for non-integer and integer order derivatives are computed and reduced to some known solutions from the literature. Finally, in order to get insight of the physical significance of the considered problem regarding velocity and Nusselt number, some graphical illustrations are made using Mathcad software. As a result, in comparison between Maxwell and viscous fluid (fractional and ordinary) we found that viscous (fractional and ordinary) fluids are swiftest than Maxwell (fractional and ordinary) fluids.

Inverse design of near unity efficiency perfectly vertical grating couplers

NASA Astrophysics Data System (ADS)

Michaels, Andrew; Yablonovitch, Eli

2018-02-01

Efficient coupling between integrated optical waveguides and optical fibers is essential to the success of integrated photonics. While many solutions exist, perfectly vertical grating couplers which scatter light out of a waveguide in the direction normal to the waveguide's top surface are an ideal candidate due to their potential to reduce packaging complexity. Designing such couplers with high efficiency, however, has proven difficult. In this paper, we use electromagnetic inverse design techniques to optimize a high efficiency two-layer perfectly vertical silicon grating coupler. Our base design achieves a chip-to-fiber coupling efficiency of over 99% (-0.04 dB) at 1550 nm. Using this base design, we apply subsequent constrained optimizations to achieve vertical couplers with over 96% efficiency which are fabricable using a 65 nm process.

Imaging with cross-hole seismoelectric tomography

USGS Publications Warehouse

Araji, A.H.; Revil, A.; Jardani, A.; Minsley, Burke J.; Karaoulis, M.

2012-01-01

We propose a cross-hole imaging approach based on seismoelectric conversions (SC) associated with the transmission of seismic waves from seismic sources located in a borehole to receivers (electrodes) located in a second borehole. The seismoelectric (seismic-to-electric) problem is solved using Biot theory coupled with a generalized Ohm's law with an electrokinetic streaming current contribution. The components of the displacement of the solid phase, the fluid pressure, and the electrical potential are solved using a finite element approach with Perfect Match Layer (PML) boundary conditions for the seismic waves and boundary conditions mimicking an infinite material for the electrostatic problem. We develop an inversion algorithm using the electrical disturbances recorded in the second borehole to localize the position of the heterogeneities responsible for the SC. Because of the ill-posed nature of the inverse problem (inherent to all potential-field problems), regularization is used to constrain the solution at each time in the SC-time window comprised between the time of the seismic shot and the time of the first arrival of the seismic waves in the second borehole. All the inverted volumetric current source densities are aggregated together to produce an image of the position of the heterogeneities between the two boreholes. Two simple synthetic case studies are presented to test this concept. The first case study corresponds to a vertical discontinuity between two homogeneous sub-domains. The second case study corresponds to a poroelastic inclusion (partially saturated by oil) embedded into an homogenous poroelastic formation. In both cases, the position of the heterogeneity is recovered using only the electrical disturbances associated with the SC. That said, a joint inversion of the seismic and seismoelectric data could improve these results.

3D linear inversion of magnetic susceptibility data acquired by frequency domain EMI

NASA Astrophysics Data System (ADS)

Thiesson, J.; Tabbagh, A.; Simon, F.-X.; Dabas, M.

2017-01-01

Low induction number EMI instruments are able to simultaneously measure a soil's apparent magnetic susceptibility and electrical conductivity. This family of dual measurement instruments is highly useful for the analysis of soils and archeological sites. However, the electromagnetic properties of soils are found to vary over considerably different ranges: whereas their electrical conductivity varies from ≤ 0.1 to ≥ 100 mS/m, their relative magnetic permeability remains within a very small range, between 1.0001 and 1.01 SI. Consequently, although apparent conductivity measurements need to be inverted using non-linear processes, the variations of the apparent magnetic susceptibility can be approximated through the use of linear processes, as in the case of the magnetic prospection technique. Our proposed 3D inversion algorithm starts from apparent susceptibility data sets, acquired using different instruments over a given area. A reference vertical profile is defined by considering the mode of the vertical distributions of both the electrical resistivity and of the magnetic susceptibility. At each point of the mapped area, the reference vertical profile response is subtracted to obtain the apparent susceptibility variation dataset. A 2D horizontal Fourier transform is applied to these variation datasets and to the dipole (impulse) response of each instrument, a (vertical) 1D inversion is performed at each point in the spectral domain, and finally the resulting dataset is inverse transformed to restore the apparent 3D susceptibility variations. It has been shown that when applied to synthetic results, this method is able to correct the apparent deformations of a buried object resulting from the geometry of the instrument, and to restore reliable quantitative susceptibility contrasts. It also allows the thin layer solution, similar to that used in magnetic prospection, to be implemented. When applied to field data it initially delivers a level of contrast comparable to that obtained with a non-linear 3D inversion. Over four different sites, this method is able to produce, following an acceptably short computation time, realistic values for the lateral and vertical variations in susceptibility, which are significantly different to those given by a point-by-point 1D inversion.

CO2 Flux Estimation Errors Associated with Moist Atmospheric Processes

NASA Technical Reports Server (NTRS)

Parazoo, N. C.; Denning, A. S.; Kawa, S. R.; Pawson, S.; Lokupitiya, R.

2012-01-01

Vertical transport by moist sub-grid scale processes such as deep convection is a well-known source of uncertainty in CO2 source/sink inversion. However, a dynamical link between vertical transport, satellite based retrievals of column mole fractions of CO2, and source/sink inversion has not yet been established. By using the same offline transport model with meteorological fields from slightly different data assimilation systems, we examine sensitivity of frontal CO2 transport and retrieved fluxes to different parameterizations of sub-grid vertical transport. We find that frontal transport feeds off background vertical CO2 gradients, which are modulated by sub-grid vertical transport. The implication for source/sink estimation is two-fold. First, CO2 variations contained in moist poleward moving air masses are systematically different from variations in dry equatorward moving air. Moist poleward transport is hidden from orbital sensors on satellites, causing a sampling bias, which leads directly to small but systematic flux retrieval errors in northern mid-latitudes. Second, differences in the representation of moist sub-grid vertical transport in GEOS-4 and GEOS-5 meteorological fields cause differences in vertical gradients of CO2, which leads to systematic differences in moist poleward and dry equatorward CO2 transport and therefore the fraction of CO2 variations hidden in moist air from satellites. As a result, sampling biases are amplified and regional scale flux errors enhanced, most notably in Europe (0.43+/-0.35 PgC /yr). These results, cast from the perspective of moist frontal transport processes, support previous arguments that the vertical gradient of CO2 is a major source of uncertainty in source/sink inversion.

Bayesian prestack seismic inversion with a self-adaptive Huber-Markov random-field edge protection scheme

NASA Astrophysics Data System (ADS)

Tian, Yu-Kun; Zhou, Hui; Chen, Han-Ming; Zou, Ya-Ming; Guan, Shou-Jun

2013-12-01

Seismic inversion is a highly ill-posed problem, due to many factors such as the limited seismic frequency bandwidth and inappropriate forward modeling. To obtain a unique solution, some smoothing constraints, e.g., the Tikhonov regularization are usually applied. The Tikhonov method can maintain a global smooth solution, but cause a fuzzy structure edge. In this paper we use Huber-Markov random-field edge protection method in the procedure of inverting three parameters, P-velocity, S-velocity and density. The method can avoid blurring the structure edge and resist noise. For the parameter to be inverted, the Huber-Markov random-field constructs a neighborhood system, which further acts as the vertical and lateral constraints. We use a quadratic Huber edge penalty function within the layer to suppress noise and a linear one on the edges to avoid a fuzzy result. The effectiveness of our method is proved by inverting the synthetic data without and with noises. The relationship between the adopted constraints and the inversion results is analyzed as well.

Research on Inversion Models for Forest Height Estimation Using Polarimetric SAR Interferometry

NASA Astrophysics Data System (ADS)

Zhang, L.; Duan, B.; Zou, B.

2017-09-01

The forest height is an important forest resource information parameter and usually used in biomass estimation. Forest height extraction with PolInSAR is a hot research field of imaging SAR remote sensing. SAR interferometry is a well-established SAR technique to estimate the vertical location of the effective scattering center in each resolution cell through the phase difference in images acquired from spatially separated antennas. The manipulation of PolInSAR has applications ranging from climate monitoring to disaster detection especially when used in forest area, is of particular interest because it is quite sensitive to the location and vertical distribution of vegetation structure components. However, some of the existing methods can't estimate forest height accurately. Here we introduce several available inversion models and compare the precision of some classical inversion approaches using simulated data. By comparing the advantages and disadvantages of these inversion methods, researchers can find better solutions conveniently based on these inversion methods.

High-resolution resistivity imaging of marine gas hydrate structures by combined inversion of CSEM towed and ocean-bottom receiver data

NASA Astrophysics Data System (ADS)

Attias, Eric; Weitemeyer, Karen; Hölz, Sebastian; Naif, Samer; Minshull, Tim A.; Best, Angus I.; Haroon, Amir; Jegen-Kulcsar, Marion; Berndt, Christian

2018-06-01

We present high-resolution resistivity imaging of gas hydrate pipe-like structures, as derived from marine controlled-source electromagnetic (CSEM) inversions that combine towed and ocean-bottom electric field receiver data, acquired from the Nyegga region, offshore Norway. Two-dimensional CSEM inversions applied to the towed receiver data detected four new prominent vertical resistive features that are likely gas hydrate structures, located in proximity to a major gas hydrate pipe-like structure, known as the CNE03 pockmark. The resistivity model resulting from the CSEM data inversion resolved the CNE03 hydrate structure in high resolution, as inferred by comparison to seismically constrained inversions. Our results indicate that shallow gas hydrate vertical features can be delineated effectively by inverting both ocean-bottom and towed receiver CSEM data simultaneously. The approach applied here can be utilised to map and monitor seafloor mineralisation, freshwater reservoirs, CO2 sequestration sites and near-surface geothermal systems.

High resolution tsunami inversion for 2010 Chile earthquake

NASA Astrophysics Data System (ADS)

Wu, T.-R.; Ho, T.-C.

2011-12-01

We investigate the feasibility of inverting high-resolution vertical seafloor displacement from tsunami waveforms. An inversion method named "SUTIM" (small unit tsunami inversion method) is developed to meet this goal. In addition to utilizing the conventional least-square inversion, this paper also enhances the inversion resolution by Grid-Shifting method. A smooth constraint is adopted to gain stability. After a series of validation and performance tests, SUTIM is used to study the 2010 Chile earthquake. Based upon data quality and azimuthal distribution, we select tsunami waveforms from 6 GLOSS stations and 1 DART buoy record. In total, 157 sub-faults are utilized for the high-resolution inversion. The resolution reaches 10 sub-faults per wavelength. The result is compared with the distribution of the aftershocks and waveforms at each gauge location with very good agreement. The inversion result shows that the source profile features a non-uniform distribution of the seafloor displacement. The highly elevated vertical seafloor is mainly concentrated in two areas: one is located in the northern part of the epicentre, between 34° S and 36° S; the other is in the southern part, between 37° S and 38° S.

The inverse problem of refraction travel times, part II: Quantifying refraction nonuniqueness using a three-layer model

USGS Publications Warehouse

Ivanov, J.; Miller, R.D.; Xia, J.; Steeples, D.

2005-01-01

This paper is the second of a set of two papers in which we study the inverse refraction problem. The first paper, "Types of Geophysical Nonuniqueness through Minimization," studies and classifies the types of nonuniqueness that exist when solving inverse problems depending on the participation of a priori information required to obtain reliable solutions of inverse geophysical problems. In view of the classification developed, in this paper we study the type of nonuniqueness associated with the inverse refraction problem. An approach for obtaining a realistic solution to the inverse refraction problem is offered in a third paper that is in preparation. The nonuniqueness of the inverse refraction problem is examined by using a simple three-layer model. Like many other inverse geophysical problems, the inverse refraction problem does not have a unique solution. Conventionally, nonuniqueness is considered to be a result of insufficient data and/or error in the data, for any fixed number of model parameters. This study illustrates that even for overdetermined and error free data, nonlinear inverse refraction problems exhibit exact-data nonuniqueness, which further complicates the problem of nonuniqueness. By evaluating the nonuniqueness of the inverse refraction problem, this paper targets the improvement of refraction inversion algorithms, and as a result, the achievement of more realistic solutions. The nonuniqueness of the inverse refraction problem is examined initially by using a simple three-layer model. The observations and conclusions of the three-layer model nonuniqueness study are used to evaluate the nonuniqueness of more complicated n-layer models and multi-parameter cell models such as in refraction tomography. For any fixed number of model parameters, the inverse refraction problem exhibits continuous ranges of exact-data nonuniqueness. Such an unfavorable type of nonuniqueness can be uniquely solved only by providing abundant a priori information. Insufficient a priori information during the inversion is the reason why refraction methods often may not produce desired results or even fail. This work also demonstrates that the application of the smoothing constraints, typical when solving ill-posed inverse problems, has a dual and contradictory role when applied to the ill-posed inverse problem of refraction travel times. This observation indicates that smoothing constraints may play such a two-fold role when applied to other inverse problems. Other factors that contribute to inverse-refraction-problem nonuniqueness are also considered, including indeterminacy, statistical data-error distribution, numerical error and instability, finite data, and model parameters. ?? Birkha??user Verlag, Basel, 2005.

Identifying seawater intrusion in coastal areas by means of 1D and quasi-2D joint inversion of TDEM and VES data

NASA Astrophysics Data System (ADS)

Martínez-Moreno, F. J.; Monteiro-Santos, F. A.; Bernardo, I.; Farzamian, M.; Nascimento, C.; Fernandes, J.; Casal, B.; Ribeiro, J. A.

2017-09-01

Seawater intrusion is an increasingly widespread problem in coastal aquifers caused by climate changes -sea-level rise, extreme phenomena like flooding and droughts- and groundwater depletion near to the coastline. To evaluate and mitigate the environmental risks of this phenomenon it is necessary to characterize the coastal aquifer and the salt intrusion. Geophysical methods are the most appropriate tool to address these researches. Among all geophysical techniques, electrical methods are able to detect seawater intrusions due to the high resistivity contrast between saltwater, freshwater and geological layers. The combination of two or more geophysical methods is recommended and they are more efficient when both data are inverted jointly because the final model encompasses the physical properties measured for each methods. In this investigation, joint inversion of vertical electric and time domain soundings has been performed to examine seawater intrusion in an area within the Ferragudo-Albufeira aquifer system (Algarve, South of Portugal). For this purpose two profiles combining electrical resistivity tomography (ERT) and time domain electromagnetic (TDEM) methods were measured and the results were compared with the information obtained from exploration drilling. Three different inversions have been carried out: single inversion of the ERT and TDEM data, 1D joint inversion and quasi-2D joint inversion. Single inversion results identify seawater intrusion, although the sedimentary layers detected in exploration drilling were not well differentiated. The models obtained with 1D joint inversion improve the previous inversion due to better detection of sedimentary layer and the seawater intrusion appear to be better defined. Finally, the quasi-2D joint inversion reveals a more realistic shape of the seawater intrusion and it is able to distinguish more sedimentary layers recognised in the exploration drilling. This study demonstrates that the quasi-2D joint inversion improves the previous inversions methods making it a powerful tool applicable to different research areas.

3-D acoustic waveform simulation and inversion at Yasur Volcano, Vanuatu

NASA Astrophysics Data System (ADS)

Iezzi, A. M.; Fee, D.; Matoza, R. S.; Austin, A.; Jolly, A. D.; Kim, K.; Christenson, B. W.; Johnson, R.; Kilgour, G.; Garaebiti, E.; Kennedy, B.; Fitzgerald, R.; Key, N.

2016-12-01

Acoustic waveform inversion shows promise for improved eruption characterization that may inform volcano monitoring. Well-constrained inversion can provide robust estimates of volume and mass flux, increasing our ability to monitor volcanic emissions (potentially in real-time). Previous studies have made assumptions about the multipole source mechanism, which can be thought of as the combination of pressure fluctuations from a volume change, directionality, and turbulence. This infrasound source could not be well constrained up to this time due to infrasound sensors only being deployed on Earth's surface, so the assumption of no vertical dipole component has been made. In this study we deploy a high-density seismo-acoustic network, including multiple acoustic sensors along a tethered balloon around Yasur Volcano, Vanuatu. Yasur has frequent strombolian eruptions from any one of its three active vents within a 400 m diameter crater. The third dimension (vertical) of pressure sensor coverage allows us to begin to constrain the acoustic source components in a profound way, primarily the horizontal and vertical components and their previously uncharted contributions to volcano infrasound. The deployment also has a geochemical and visual component, including FLIR, FTIR, two scanning FLYSPECs, and a variety of visual imagery. Our analysis employs Finite-Difference Time-Domain (FDTD) modeling to obtain the full 3D Green's functions for each propagation path. This method, following Kim et al. (2015), takes into account realistic topographic scattering based on a digital elevation model created using structure-from-motion techniques. We then invert for the source location and source-time function, constraining the contribution of the vertical sound radiation to the source. The final outcome of this inversion is an infrasound-derived volume flux as a function of time, which we then compare to those derived independently from geochemical techniques as well as the inversion of seismic data. Kim, K., Fee, D., Yokoo, A., & Lees, J. M. (2015). Acoustic source inversion to estimate volume flux from volcanic explosions. Geophysical Research Letters, 42(13), 5243-5249

Recent variability of the tropical tropopause inversion layer

NASA Astrophysics Data System (ADS)

Wang, Wuke; Matthes, Katja; Schmidt, Torsten; Neef, Lisa

2013-12-01

The recent variability of the tropopause temperature and the tropopause inversion layer (TIL) are investigated with Global Positioning System Radio Occultation data and simulations with the National Center for Atmospheric Research's Whole Atmosphere Community Climate Model (WACCM). Over the past decade (2001-2011) the data show an increase of 0.8 K in the tropopause temperature and a decrease of 0.4 K in the strength of the tropopause inversion layer in the tropics, meaning that the vertical temperature gradient has declined, and therefore that the stability above the tropopause has weakened. WACCM simulations with finer vertical resolution show a more realistic TIL structure and variability. Model simulations show that the increased tropopause temperature and the weaker tropopause inversion layer are related to weakened upwelling in the tropics. Such changes in the thermal structure of the upper troposphere and lower stratosphere may have important implications for climate, such as a possible rise in water vapor in the lower stratosphere.

Imaging the Earth's anisotropic structure with Bayesian Inversion of fundamental and higher mode surface-wave dispersion data

NASA Astrophysics Data System (ADS)

Ravenna, Matteo; Lebedev, Sergei; Celli, Nicolas

2017-04-01

We develop a Markov Chain Monte Carlo inversion of fundamental and higher mode phase-velocity curves for radially and azimuthally anisotropic structure of the crust and upper mantle. In the inversions of Rayleigh- and Love-wave dispersion curves for radially anisotropic structure, we obtain probabilistic 1D radially anisotropic shear-velocity profiles of the isotropic average Vs and anisotropy (or Vsv and Vsh) as functions of depth. In the inversions for azimuthal anisotropy, Rayleigh-wave dispersion curves at different azimuths are inverted for the vertically polarized shear-velocity structure (Vsv) and the 2-phi component of azimuthal anisotropy. The strength and originality of the method is in its fully non-linear approach. Each model realization is computed using exact forward calculations. The uncertainty of the models is a part of the output. In the inversions for azimuthal anisotropy, in particular, the computation of the forward problem is performed separately at different azimuths, with no linear approximations on the relation of the Earth's elastic parameters to surface wave phase velocities. The computations are performed in parallel in order reduce the computing time. We compare inversions of the fundamental mode phase-velocity curves alone with inversions that also include overtones. The addition of higher modes enhances the resolving power of the anisotropic structure of the deep upper mantle. We apply the inversion method to phase-velocity curves in a few regions, including the Hangai dome region in Mongolia. Our models provide constraints on the Moho depth, the Lithosphere-Asthenosphere Boundary, and the alignment of the anisotropic fabric and the direction of current and past flow, from the crust down to the deep asthenosphere.

A methodology for using borehole temperature-depth profiles under ambient, single and cross-borehole pumping conditions to estimate fracture hydraulic properties

NASA Astrophysics Data System (ADS)

Klepikova, M.; Le Borgne, T.; Bour, O.; Lavenant, N.

2011-12-01

In fractured aquifers flow generally takes place in a few fractured zones. The identification of these main flow paths is critical as it controls the transfer of fluids in the subsurface. For realistic modeling of the flow the knowledge about the spatial variability of hydraulic properties is required. Inverse problems based on hydraulic head data are generally strongly underconstrained. A possible way of reducing the uncertainty is to combine different type of data, such as flow measurements, temperature profiles or tracer test data. Here, we focus on the use of temperature, which can be seen as a natural tracer of ground water flow. Previous studies used temperature anomalies to quantify vertical or horizontal regional groundwater flow velocities. Most of these studies assume that water in the borehole is stagnant, and, thus, the temperature profile in the well is representative of the temperature in the aquifer. In fractured media, differences in hydraulic head between flow paths connected to a borehole generally create ambient vertical flow within the borehole. These differences in hydraulic head are in general due to regional flow conditions. Estimation of borehole vertical flow is of interest as it can be used to derive large scale hydraulic connections. Under a single-borehole configuration, the estimation of vertical flow can be used to estimate the local transimissivities and the hydraulic head differences driving the flow through the borehole. Under a cross-borehole set up, it can be used to characterize hydraulic connections and estimate their hydraulic properties. Using a flow and heat transfer numerical model, we find that the slope of the temperature profile is related directly to vertical borehole flow velocity. Thus, we propose a method to invert temperature measurements to derive borehole flow velocities and subsequently the fracture zone hydraulic and connectivity properties. The advantage of temperature measurements compared to flowmeter measurements is that temperature can be measured easily and very accurately, continuously in space and time. To test the methodology, we have performed a field experiment at a crystalline rocks field site, located in Ploemeur, Brittany (France). The site is composed of three 100 meters deep boreholes, located at 6-10 m distances from each other. The experiment consisted in measuring the borehole temperature profiles under all possible pumping configurations. Hence, the pumping and monitoring wells were successively changed. The thermal response in observation well induced by changes in pumping conditions is related to changes in vertical flow velocities and thus to the inter-borehole fracture connectivity. Based on this dataset, we propose a methodology to include temperature profiles in inverse problem for characterizing the spatial distribution of fracture zone hydraulic properties.

New planetary boundary layer parametrization in ECHAM5-HAM: Dynamical refinement of the vertical resolution

NASA Astrophysics Data System (ADS)

Siegenthaler-Le Drian, C.; Spichtinger, P.; Lohmann, U.

2010-09-01

Marine stratocumulus-capped boundary layers exhibit a strong net cooling impact on the Earth-Atmosphere system. Moreover, they are highly persistent over subtropical oceans. Therefore climate models need to represent them well in order to make reliable projections of future climate. One of the reasons for the absence of stratocumuli in the general circulation model ECHAM5-HAM (Roeckner et al., 2003; Stier et al., 2005) is due to the limited vertical resolution. In the current model version, no vertical sub-grid scale variability of clouds is taken into account, such that clouds occupy the full vertical layer. Around the inversion on top of the planetary boundary layer (PBL), conserved variables often have a steep gradient, which in a GCM may produce large discretization errors (Bretherton and Park, 2009). This inversion has a large diurnal cycle and varies with location around the globe, which is difficult to represent in a classical, coarse Eulerian approach. Furthermore, Lenderink and Holtslag (2000) and Lock (2001) showed that an inconsistent numerical representation between the entrainment parametrization and the other schemes, particularly with the vertical advection can lead to the occurrence of 'numerical entrainment'. The problem can be resolved by introducing a dynamical inversion as introduced by Grenier and Bretherton (2001) and Lock (2001). As these features can be seen in our version of ECHAM5-HAM, our implementation is aimed to reduce the numerical entrainment and to better represent stratocumuli in ECHAM5-HAM. To better resolve stratocumulus clouds, their inversion and the interaction between the turbulent diffusion and the vertical advection, the vertical grid is dynamically refined. The new grid is based on the reconstruction of the profiles of variables experiencing a sharp gradient (temperature, mixing ratio) applying the method presented in Grenier and Bretherton (2001). In typical stratocumulus regions, an additional grid level is thus associated with the PBL top. In case a cloud can be formed, a new level is associated with the lifting condensation level as well. The regular grid plus the two additional levels define the new dynamical grid, which varies geographically and temporally. The physical processes are computed on this new dynamical grid, Consequently, the sharp gradients and the interaction between the different processes can be better resolved. Some results of this new parametrization will be presented. On a single column model set-up, the reconstruction method accurately finds the inversion at the PBL top for the EPIC stratocumulus case. Also, on a global scale, the occurrence of a successful reconstruction, which is restricted in typical stratocumulus regions, occurs with a high frequency. The impact of the new dynamical grid on clouds and the radiation balance will be presented in the talk. References [Bretherton and Park, 2009] Bretherton, C. S. and Park, S. (2009). A new moist turbulence parametrization in the community atmosphere model. J. Climate, 22:3422-3448. [Grenier and Bretherton, 2001] Grenier, H. and Bretherton, C. S. (2001). A moist parametrization for large-scale models and its application to subtropical cloud-topped marine boundary layers. Mon. Wea. Rev., 129:357-377. [Lenderink and Holtslag, 2000] Lenderink, G. and Holtslag, A. M. (2000). Evaluation of the kinetic energy approach for modeling turbulent fluxes in stratocumulus. Mon. Wea. Rev., 128:244-258. [Lock, 2001] Lock, A. P. (2001). The numerical representation of entrainment in parametrizations of boundary layer turbulent mixing. Mon. Wea. Rev., 129:1148-1163. [Roeckner et al., 2003] Roeckner, E., Bäuml, G., Bonaventura, L. et al. (2003). The atmospheric general circulation model echam5, part I: Model description. Technical Report 349, Max-Planck-Institute for Meteorology, Hamburg,Germany. [Stier et al., 2005] Stier, P., Feichter, J., Kinne, S. et al. (2005). The aerosol-climate model ECHAM5-HAM. Atmos. Chem. Phys., 5:1125-1156.

Multicomponent pre-stack seismic waveform inversion in transversely isotropic media using a non-dominated sorting genetic algorithm

NASA Astrophysics Data System (ADS)

Padhi, Amit; Mallick, Subhashis

2014-03-01

Inversion of band- and offset-limited single component (P wave) seismic data does not provide robust estimates of subsurface elastic parameters and density. Multicomponent seismic data can, in principle, circumvent this limitation but adds to the complexity of the inversion algorithm because it requires simultaneous optimization of multiple objective functions, one for each data component. In seismology, these multiple objectives are typically handled by constructing a single objective given as a weighted sum of the objectives of individual data components and sometimes with additional regularization terms reflecting their interdependence; which is then followed by a single objective optimization. Multi-objective problems, inclusive of the multicomponent seismic inversion are however non-linear. They have non-unique solutions, known as the Pareto-optimal solutions. Therefore, casting such problems as a single objective optimization provides one out of the entire set of the Pareto-optimal solutions, which in turn, may be biased by the choice of the weights. To handle multiple objectives, it is thus appropriate to treat the objective as a vector and simultaneously optimize each of its components so that the entire Pareto-optimal set of solutions could be estimated. This paper proposes such a novel multi-objective methodology using a non-dominated sorting genetic algorithm for waveform inversion of multicomponent seismic data. The applicability of the method is demonstrated using synthetic data generated from multilayer models based on a real well log. We document that the proposed method can reliably extract subsurface elastic parameters and density from multicomponent seismic data both when the subsurface is considered isotropic and transversely isotropic with a vertical symmetry axis. We also compute approximate uncertainty values in the derived parameters. Although we restrict our inversion applications to horizontally stratified models, we outline a practical procedure of extending the method to approximately include local dips for each source-receiver offset pair. Finally, the applicability of the proposed method is not just limited to seismic inversion but it could be used to invert different data types not only requiring multiple objectives but also multiple physics to describe them.

Characterization of the groundwater aquifers at El Sadat City by joint inversion of VES and TEM data

NASA Astrophysics Data System (ADS)

Massoud, Usama; Kenawy, Abeer A.; Ragab, El-Said A.; Abbas, Abbas M.; El-Kosery, Heba M.

2014-12-01

Vertical Electrical Sounding (VES) and Transient ElectroMagnetic (TEM) survey have been applied for characterizing the groundwater aquifers at El Sadat industrial area. El-Sadat city is one of the most important industrial cities in Egypt. It has been constructed more than three decades ago at about 80 km northwest of Cairo along the Cairo-Alexandria desert road. Groundwater is the main source of water supplies required for domestic, municipal and industrial activities in this area due to the lack of surface water sources. So, it is important to maintain this vital resource in order to sustain the development plans of this city. In this study, VES and TEM data were identically measured at 24 stations along 3 profiles trending NE-SW with the elongation of the study area. The measuring points were arranged in a grid-like pattern with both inter-station spacing and line-line distance of about 2 km. After performing the necessary processing steps, the VES and TEM data sets were inverted individually to multi-layer models, followed by a joint inversion of both data sets. Joint inversion process has succeeded to overcome the model-equivalence problem encountered in the inversion of individual data set. Then, the joint models were used for the construction of a number of cross sections and contour maps showing the lateral and vertical distribution of the geoelectrical parameters in the subsurface medium. Interpretation of the obtained results and correlation with the available geological and hydrogeological information revealed TWO aquifer systems in the area. The shallow Pleistocene aquifer consists of sand and gravel saturated with fresh water and exhibits large thickness exceeding 200 m. The deep Pliocene aquifer is composed of clay and sand and shows low resistivity values. The water-bearing layer of the Pleistocene aquifer and the upper surface of Pliocene aquifer are continuous and no structural features have cut this continuity through the investigated area.

Applications of three-dimensional modeling in electromagnetic exploration

NASA Astrophysics Data System (ADS)

Pellerin, Louise Donna

Numerical modeling is used in geophysical exploration to understand physical mechanisms of a geophysical method, compare different exploration techniques, and interpret field data. Exploring the physics of a geophysical response enhances the geophysicist's insight, resulting in better survey design and interpretation. Comparing exploration methods numerically can eliminate the use of a technique that cannot resolve the exploration target. Interpreting field data to determine the structure of the earth is the ultimate goal of the exploration geophysicist. Applications of three-dimensional (3-D) electromagnetic (EM) modeling in mining, geothermal and environmental exploration demonstrate the importance of numerical modeling as a geophysical tool. Detection of a confined, conductive target with a vertical electric source (VES) can be an effective technique if properly used. The vertical magnetic field response is due solely to multi-dimensional structures, and current channeling is the dominant mechanism. A VES is deployed in a bore hole, hence the orientation of the hole is critical to the response. A deviation of more than a degree from the vertical can result in a host response that overwhelms the target response. Only the in-phase response at low frequencies can be corrected to a purely vertical response. The geothermal system studied consists of a near-surface clay cap and a deep reservoir. The magnetotelluric (MT), controlled-source audio magnetotelluric (CSAMT), long-offset time-domain electromagnetic (LOTEM) and central-loop transient electromagnetic (TEM) methods are appraised for their ability to detect the reservoir and delineate the cap. The reservoir anomaly is supported by boundary charges and therefore is detectable only with deep sounding electric field measurement MT and LOTEM. The cap is easily delineated with all techniques. For interpretation I developed an approximate 3-D inversion that refines a 1-D interpretation by removing lateral distortions. An iterative inverse procedure invokes EM reciprocity while operating on a localized portion of the survey area thereby greatly reducing the computational requirements. The scheme is illustrated with three synthetic data sets representative of problems in environmental geophysics.

Application of the L-curve in geophysical inverse problems: methodologies for the extraction of the optimal parameter

NASA Astrophysics Data System (ADS)

Bassrei, A.; Terra, F. A.; Santos, E. T.

2007-12-01

Inverse problems in Applied Geophysics are usually ill-posed. One way to reduce such deficiency is through derivative matrices, which are a particular case of a more general family that receive the name regularization. The regularization by derivative matrices has an input parameter called regularization parameter, which choice is already a problem. It was suggested in the 1970's a heuristic approach later called L-curve, with the purpose to provide the optimum regularization parameter. The L-curve is a parametric curve, where each point is associated to a λ parameter. In the horizontal axis one represents the error between the observed data and the calculated one and in the vertical axis one represents the product between the regularization matrix and the estimated model. The ideal point is the L-curve knee, where there is a balance between the quantities represented in the Cartesian axes. The L-curve has been applied to a variety of inverse problems, also in Geophysics. However, the visualization of the knee is not always an easy task, in special when the L-curve does not the L shape. In this work three methodologies are employed for the search and obtainment of the optimal regularization parameter from the L curve. The first criterion is the utilization of Hansen's tool box which extracts λ automatically. The second criterion consists in to extract visually the optimal parameter. By third criterion one understands the construction of the first derivative of the L-curve, and the posterior automatic extraction of the inflexion point. The utilization of the L-curve with the three above criteria were applied and validated in traveltime tomography and 2-D gravity inversion. After many simulations with synthetic data, noise- free as well as data corrupted with noise, with the regularization orders 0, 1, and 2, we verified that the three criteria are valid and provide satisfactory results. The third criterion presented the best performance, specially in cases where the L-curve has an irregular shape.

Comparing Vertical Distributions of Water Vapor Flux within Two Landfalling Atmospheric Rivers

NASA Astrophysics Data System (ADS)

Rutz, J. J.; Lavers, D. A.

2015-12-01

The West Coast of North America is frequently impacted by atmospheric rivers (ARs), regions of intense horizontal water vapor transport that often produce heavy rain, flooding, and landslides when they interact with near-coastal mountains. Recently, studies have shown that ARs penetrate farther inland on many occasions, with indications that the vertical distribution of vapor transport within the ARs may play a key role in this penetration (Alexander et al. 2015; Rutz et al. 2015). We hypothesize that the amount of near-coastal precipitation and the likelihood of AR penetration farther inland may be inversely linked by vertical distributions of vapor fluxes before, during, and after landfall. To explore whether differing vertical distributions of transport explain differing precipitation and penetration outcomes, we compare two landfalling ARs that had very similar spatial extents and rates of vertically integrated (total) vapor transport, but which nonetheless produced very different amounts of precipitation over northern California. The vertical distribution of water vapor flux, specific humidity, and wind speed during these two ARs are examined along several transects using cross-sectional analyses of the Climate Forecast System Reanalysis with a horizontal resolution of ~0.5° (~63 km) and a sigma-pressure hybrid coordinate at 64 vertical levels. In addition, we pursue similar analyses of forecasts from the NCEP Global Ensemble Forecast System GEFS to assess whether numerical weather prediction models accurately represent these distributions. Finally, we calculate backward trajectories from within each AR to examine whether or not the origins of their respective air parcels play a role in the resulting vertical distribution of water vapor flux. The results have major implications for two problems in weather prediction: (1) the near-coastal precipitation associated with landfalling ARs and (2) the likelihood of AR penetration farther inland.

Numerical methods for the inverse problem of density functional theory

DOE PAGES

Jensen, Daniel S.; Wasserman, Adam

2017-07-17

Here, the inverse problem of Kohn–Sham density functional theory (DFT) is often solved in an effort to benchmark and design approximate exchange-correlation potentials. The forward and inverse problems of DFT rely on the same equations but the numerical methods for solving each problem are substantially different. We examine both problems in this tutorial with a special emphasis on the algorithms and error analysis needed for solving the inverse problem. Two inversion methods based on partial differential equation constrained optimization and constrained variational ideas are introduced. We compare and contrast several different inversion methods applied to one-dimensional finite and periodic modelmore » systems.« less

Numerical methods for the inverse problem of density functional theory

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

Jensen, Daniel S.; Wasserman, Adam

Here, the inverse problem of Kohn–Sham density functional theory (DFT) is often solved in an effort to benchmark and design approximate exchange-correlation potentials. The forward and inverse problems of DFT rely on the same equations but the numerical methods for solving each problem are substantially different. We examine both problems in this tutorial with a special emphasis on the algorithms and error analysis needed for solving the inverse problem. Two inversion methods based on partial differential equation constrained optimization and constrained variational ideas are introduced. We compare and contrast several different inversion methods applied to one-dimensional finite and periodic modelmore » systems.« less

Research and application of spectral inversion technique in frequency domain to improve resolution of converted PS-wave

NASA Astrophysics Data System (ADS)

Zhang, Hua; He, Zhen-Hua; Li, Ya-Lin; Li, Rui; He, Guamg-Ming; Li, Zhong

2017-06-01

Multi-wave exploration is an effective means for improving precision in the exploration and development of complex oil and gas reservoirs that are dense and have low permeability. However, converted wave data is characterized by a low signal-to-noise ratio and low resolution, because the conventional deconvolution technology is easily affected by the frequency range limits, and there is limited scope for improving its resolution. The spectral inversion techniques is used to identify λ/8 thin layers and its breakthrough regarding band range limits has greatly improved the seismic resolution. The difficulty associated with this technology is how to use the stable inversion algorithm to obtain a high-precision reflection coefficient, and then to use this reflection coefficient to reconstruct broadband data for processing. In this paper, we focus on how to improve the vertical resolution of the converted PS-wave for multi-wave data processing. Based on previous research, we propose a least squares inversion algorithm with a total variation constraint, in which we uses the total variance as a priori information to solve under-determined problems, thereby improving the accuracy and stability of the inversion. Here, we simulate the Gaussian fitting amplitude spectrum to obtain broadband wavelet data, which we then process to obtain a higher resolution converted wave. We successfully apply the proposed inversion technology in the processing of high-resolution data from the Penglai region to obtain higher resolution converted wave data, which we then verify in a theoretical test. Improving the resolution of converted PS-wave data will provide more accurate data for subsequent velocity inversion and the extraction of reservoir reflection information.

Tunable transport gap in narrow bilayer graphene nanoribbons

PubMed Central

Yu, Woo Jong; Duan, Xiangfeng

2013-01-01

The lack of a bandgap makes bulk graphene unsuitable for room temperature transistors with a sufficient on/off current ratio. Lateral constriction of charge carriers in graphene nanostructures or vertical inversion symmetry breaking in bilayer graphene are two potential strategies to mitigate this challenge, but each alone is insufficient to consistently achieve a large enough on/off ratio (e.g. > 1000) for typical logic applications. Herein we report the combination of lateral carrier constriction and vertical inversion symmetry breaking in bilayer graphene nanoribbons (GNRs) to tune their transport gaps and improve the on/off ratio. Our studies demonstrate that the on/off current ratio of bilayer GNRs can be systematically increased upon applying a vertical electric field, to achieve a largest on/off current ratio over 3000 at room temperature. PMID:23409239

Theoretical regime diagrams for thermally driven flows in a beta-plane channel in the presence of variable gravity

NASA Technical Reports Server (NTRS)

Geisler, J. E.; Fowlis, W. W.

1980-01-01

The effect of a power law gravity field on baroclinic instability is examined, with a focus on the case of inverse fifth power gravity, since this is the power law produced when terrestrial gravity is simulated in spherical geometry by a dielectric force. Growth rates are obtained of unstable normal modes as a function of parameters of the problem by solving a second order differential equation numerically. It is concluded that over the range of parameter space explored, there is no significant change in the character of theoretical regime diagrams if the vertically averaged gravity is used as parameter.

The effects of environmental variability and spatial sampling on the three-dimensional inversion problem.

PubMed

Bender, Christopher M; Ballard, Megan S; Wilson, Preston S

2014-06-01

The overall goal of this work is to quantify the effects of environmental variability and spatial sampling on the accuracy and uncertainty of estimates of the three-dimensional ocean sound-speed field. In this work, ocean sound speed estimates are obtained with acoustic data measured by a sparse autonomous observing system using a perturbative inversion scheme [Rajan, Lynch, and Frisk, J. Acoust. Soc. Am. 82, 998-1017 (1987)]. The vertical and horizontal resolution of the solution depends on the bandwidth of acoustic data and on the quantity of sources and receivers, respectively. Thus, for a simple, range-independent ocean sound speed profile, a single source-receiver pair is sufficient to estimate the water-column sound-speed field. On the other hand, an environment with significant variability may not be fully characterized by a large number of sources and receivers, resulting in uncertainty in the solution. This work explores the interrelated effects of environmental variability and spatial sampling on the accuracy and uncertainty of the inversion solution though a set of case studies. Synthetic data representative of the ocean variability on the New Jersey shelf are used.

Circular zig-zag scan video format

DOEpatents

Peterson, C. Glen; Simmons, Charles M.

1992-01-01

A circular, ziz-zag scan for use with vidicon tubes. A sine wave is generated, rectified and its fourth root extracted. The fourth root, and its inverse, are used to generate horizontal ramp and sync signals. The fourth root is also used to generate a vertical sync signal, and the vertical sync signal, along with the horizontal sync signal, are used to generate the vertical ramp signal. Cathode blanking and preamplifier clamp signals are also obtained from the vertical sync signal.

Aerodynamic coefficients in generalized unsteady thin airfoil theory

NASA Technical Reports Server (NTRS)

Williams, M. H.

1980-01-01

Two cases are considered: (1) rigid body motion of an airfoil-flap combination consisting of vertical translation of given amplitude, rotation of given amplitude about a specified axis, and rotation of given amplitude of the control surface alone about its hinge; the upwash for this problem is defined mathematically; and (2) sinusoidal gust of given amplitude and wave number, for which the upwash is defined mathematically. Simple universal formulas are presented for the most important aerodynamic coefficients in unsteady thin airfoil theory. The lift and moment induced by a generalized gust are evaluated explicitly in terms of the gust wavelength. Similarly, in the control surface problem, the lift, moment, and hinge moments are given as explicit algebraic functions of hinge location. These results can be used together with any of the standard numerical inversion routines for the elementary loads (pitch and heave).

Remote Sensing of Precipitation from Airborne and Spaceborne Radar. Chapter 13

NASA Technical Reports Server (NTRS)

Munchak, S. Joseph

2017-01-01

Weather radar measurements from airborne or satellite platforms can be an effective remote sensing tool for examining the three-dimensional structures of clouds and precipitation. This chapter describes some fundamental properties of radar measurements and their dependence on the particle size distribution (PSD) and radar frequency. The inverse problem of solving for the vertical profile of PSD from a profile of measured reflectivity is stated as an optimal estimation problem for single- and multi-frequency measurements. Phenomena that can change the measured reflectivity Z(sub m) from its intrinsic value Z(sub e), namely attenuation, non-uniform beam filling, and multiple scattering, are described and mitigation of these effects in the context of the optimal estimation framework is discussed. Finally, some techniques involving the use of passive microwave measurements to further constrain the retrieval of the PSD are presented.

Gravitropism in leafy dicot stems

NASA Technical Reports Server (NTRS)

Salisbury, F. B.

1984-01-01

In an attempt to separate plant responses to mechanical stresses from responses to gravity compensation, six treatments were automated: (1) upright stationary controls; (2) horizontal clinostat; (3) intermittent clinostat (plants upright 3.3 minutes out of every 4 minutes, horizontal and rotated once in the remaining time); (4) inversion every ten minutes (plants upside down half the time); (5) inversion and immediate return to the vertical; and (6) vertical rotation. Epinasty appeared only on clinostated and on inverted plants, both subjected to gravity compensation. The mechanics of gravitropic stem bending and the effects of a unilateral application of ethephon of gravitropic bending were also investigated.

Final Technical Report for "Applied Mathematics Research: Simulation Based Optimization and Application to Electromagnetic Inverse Problems"

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

Haber, Eldad

2014-03-17

The focus of research was: Developing adaptive mesh for the solution of Maxwell's equations; Developing a parallel framework for time dependent inverse Maxwell's equations; Developing multilevel methods for optimization problems with inequality constraints; A new inversion code for inverse Maxwell's equations in the 0th frequency (DC resistivity); A new inversion code for inverse Maxwell's equations in low frequency regime. Although the research concentrated on electromagnetic forward and in- verse problems the results of the research was applied to the problem of image registration.

Easy way to determine quantitative spatial resolution distribution for a general inverse problem

NASA Astrophysics Data System (ADS)

An, M.; Feng, M.

2013-12-01

The spatial resolution computation of a solution was nontrivial and more difficult than solving an inverse problem. Most geophysical studies, except for tomographic studies, almost uniformly neglect the calculation of a practical spatial resolution. In seismic tomography studies, a qualitative resolution length can be indicatively given via visual inspection of the restoration of a synthetic structure (e.g., checkerboard tests). An effective strategy for obtaining quantitative resolution length is to calculate Backus-Gilbert resolution kernels (also referred to as a resolution matrix) by matrix operation. However, not all resolution matrices can provide resolution length information, and the computation of resolution matrix is often a difficult problem for very large inverse problems. A new class of resolution matrices, called the statistical resolution matrices (An, 2012, GJI), can be directly determined via a simple one-parameter nonlinear inversion performed based on limited pairs of random synthetic models and their inverse solutions. The total procedure were restricted to forward/inversion processes used in the real inverse problem and were independent of the degree of inverse skill used in the solution inversion. Spatial resolution lengths can be directly given during the inversion. Tests on 1D/2D/3D model inversion demonstrated that this simple method can be at least valid for a general linear inverse problem.

Inverse design of near unity efficiency perfectly vertical grating couplers.

PubMed

Michaels, Andrew; Yablonovitch, Eli

2018-02-19

Efficient coupling between integrated optical waveguides and optical fibers is essential to the success of silicon photonics. While many solutions exist, perfectly vertical grating couplers that scatter light out of a waveguide in the direction normal to the waveguide's top surface are an ideal candidate due to their potential to reduce packaging complexity. Designing such couplers with high efficiencies, however, has proven difficult. In this paper, we use inverse electromagnetic design techniques to optimize a high efficiency two-layer perfectly vertical silicon grating coupler. Our base design achieves a chip-to-fiber coupling efficiency of 99.2% (-0.035 dB) at 1550 nm. Using this base design as a starting point, we run subsequent constrained optimizations to realize vertical couplers with coupling efficiencies over 96% and back reflections of less than -40 dB which can be fabricated using 65 nm-resolution lithography. These results demonstrate a new path forward for designing fabrication-tolerant ultra high efficiency grating couplers.

Vertically resolved characteristics of air pollution during two severe winter haze episodes in urban Beijing, China

NASA Astrophysics Data System (ADS)

Wang, Qingqing; Sun, Yele; Xu, Weiqi; Du, Wei; Zhou, Libo; Tang, Guiqian; Chen, Chen; Cheng, Xueling; Zhao, Xiujuan; Ji, Dongsheng; Han, Tingting; Wang, Zhe; Li, Jie; Wang, Zifa

2018-02-01

We conducted the first real-time continuous vertical measurements of particle extinction (bext), gaseous NO2, and black carbon (BC) from ground level to 260 m during two severe winter haze episodes at an urban site in Beijing, China. Our results illustrated four distinct types of vertical profiles: (1) uniform vertical distributions (37 % of the time) with vertical differences less than 5 %, (2) higher values at lower altitudes (29 %), (3) higher values at higher altitudes (16 %), and (4) significant decreases at the heights of ˜ 100-150 m (14 %). Further analysis demonstrated that vertical convection as indicated by mixing layer height, temperature inversion, and local emissions are three major factors affecting the changes in vertical profiles. Particularly, the formation of type 4 was strongly associated with the stratified layer that was formed due to the interactions of different air masses and temperature inversions. Aerosol composition was substantially different below and above the transition heights with ˜ 20-30 % higher contributions of local sources (e.g., biomass burning and cooking) at lower altitudes. A more detailed evolution of vertical profiles and their relationship with the changes in source emissions, mixing layer height, and aerosol chemistry was illustrated by a case study. BC showed overall similar vertical profiles as those of bext (R2 = 0.92 and 0.69 in November and January, respectively). While NO2 was correlated with bext for most of the time, the vertical profiles of bext / NO2 varied differently for different profiles, indicating the impact of chemical transformation on vertical profiles. Our results also showed that more comprehensive vertical measurements (e.g., more aerosol and gaseous species) at higher altitudes in the megacities are needed for a better understanding of the formation mechanisms and evolution of severe haze episodes in China.

Sequential Bayesian geoacoustic inversion for mobile and compact source-receiver configuration.

PubMed

Carrière, Olivier; Hermand, Jean-Pierre

2012-04-01

Geoacoustic characterization of wide areas through inversion requires easily deployable configurations including free-drifting platforms, underwater gliders and autonomous vehicles, typically performing repeated transmissions during their course. In this paper, the inverse problem is formulated as sequential Bayesian filtering to take advantage of repeated transmission measurements. Nonlinear Kalman filters implement a random-walk model for geometry and environment and an acoustic propagation code in the measurement model. Data from MREA/BP07 sea trials are tested consisting of multitone and frequency-modulated signals (bands: 0.25-0.8 and 0.8-1.6 kHz) received on a shallow vertical array of four hydrophones 5-m spaced drifting over 0.7-1.6 km range. Space- and time-coherent processing are applied to the respective signal types. Kalman filter outputs are compared to a sequence of global optimizations performed independently on each received signal. For both signal types, the sequential approach is more accurate but also more efficient. Due to frequency diversity, the processing of modulated signals produces a more stable tracking. Although an extended Kalman filter provides comparable estimates of the tracked parameters, the ensemble Kalman filter is necessary to properly assess uncertainty. In spite of mild range dependence and simplified bottom model, all tracked geoacoustic parameters are consistent with high-resolution seismic profiling, core logging P-wave velocity, and previous inversion results with fixed geometries.

Fast, Nonlinear, Fully Probabilistic Inversion of Large Geophysical Problems

NASA Astrophysics Data System (ADS)

Curtis, A.; Shahraeeni, M.; Trampert, J.; Meier, U.; Cho, G.

2010-12-01

Almost all Geophysical inverse problems are in reality nonlinear. Fully nonlinear inversion including non-approximated physics, and solving for probability distribution functions (pdf’s) that describe the solution uncertainty, generally requires sampling-based Monte-Carlo style methods that are computationally intractable in most large problems. In order to solve such problems, physical relationships are usually linearized leading to efficiently-solved, (possibly iterated) linear inverse problems. However, it is well known that linearization can lead to erroneous solutions, and in particular to overly optimistic uncertainty estimates. What is needed across many Geophysical disciplines is a method to invert large inverse problems (or potentially tens of thousands of small inverse problems) fully probabilistically and without linearization. This talk shows how very large nonlinear inverse problems can be solved fully probabilistically and incorporating any available prior information using mixture density networks (driven by neural network banks), provided the problem can be decomposed into many small inverse problems. In this talk I will explain the methodology, compare multi-dimensional pdf inversion results to full Monte Carlo solutions, and illustrate the method with two applications: first, inverting surface wave group and phase velocities for a fully-probabilistic global tomography model of the Earth’s crust and mantle, and second inverting industrial 3D seismic data for petrophysical properties throughout and around a subsurface hydrocarbon reservoir. The latter problem is typically decomposed into 104 to 105 individual inverse problems, each solved fully probabilistically and without linearization. The results in both cases are sufficiently close to the Monte Carlo solution to exhibit realistic uncertainty, multimodality and bias. This provides far greater confidence in the results, and in decisions made on their basis.

Circular zig-zag scan video format

DOEpatents

Peterson, C.G.; Simmons, C.M.

1992-06-09

A circular, ziz-zag scan for use with vidicon tubes is disclosed. A sine wave is generated, rectified and its fourth root extracted. The fourth root, and its inverse, are used to generate horizontal ramp and sync signals. The fourth root is also used to generate a vertical sync signal, and the vertical sync signal, along with the horizontal sync signal, are used to generate the vertical ramp signal. Cathode blanking and preamplifier clamp signals are also obtained from the vertical sync signal. 10 figs.

Adults' understanding of inversion concepts: how does performance on addition and subtraction inversion problems compare to performance on multiplication and division inversion problems?

PubMed

Robinson, Katherine M; Ninowski, Jerilyn E

2003-12-01

Problems of the form a + b - b have been used to assess conceptual understanding of the relationship between addition and subtraction. No study has investigated the same relationship between multiplication and division on problems of the form d x e / e. In both types of inversion problems, no calculation is required if the inverse relationship between the operations is understood. Adult participants solved addition/subtraction and multiplication/division inversion (e.g., 9 x 22 / 22) and standard (e.g., 2 + 27 - 28) problems. Participants started to use the inversion strategy earlier and more frequently on addition/subtraction problems. Participants took longer to solve both types of multiplication/division problems. Overall, conceptual understanding of the relationship between multiplication and division was not as strong as that between addition and subtraction. One explanation for this difference in performance is that the operation of division is more weakly represented and understood than the other operations and that this weakness affects performance on problems of the form d x e / e.

External and internal facial features modulate processing of vertical but not horizontal spatial relations.

PubMed

Meinhardt, Günter; Kurbel, David; Meinhardt-Injac, Bozana; Persike, Malte

2018-03-22

Some years ago an asymmetry was reported for the inversion effect for horizontal (H) and vertical (V) relational face manipulations (Goffaux & Rossion, 2007). Subsequent research examined whether a specific disruption of long-range relations underlies the H/V inversion asymmetry (Sekunova & Barton, 2008). Here, we tested how detection of changes in interocular distance (H) and eye height (V) depends on cardinal internal features and external feature surround. Results replicated the H/V inversion asymmetry. Moreover, we found very different face cue dependencies for both change types. Performance and inversion effects did not depend on the presence of other face cues for detecting H changes. In contrast, accuracy for detecting V changes strongly depended on internal and external features, showing cumulative improvement when more cues were added. Inversion effects were generally large, and larger with external feature surround. The cue independence in detecting H relational changes indicates specialized local processing tightly tuned to the eyes region, while the strong cue dependency in detecting V relational changes indicates a global mechanism of cue integration across different face regions. These findings suggest that the H/V asymmetry of the inversion effect rests on an H/V anisotropy of face cue dependency, since only the global V mechanism suffers from disruption of cue integration as the major effect of face inversion. Copyright © 2018. Published by Elsevier Ltd.

Decomposing Large Inverse Problems with an Augmented Lagrangian Approach: Application to Joint Inversion of Body-Wave Travel Times and Surface-Wave Dispersion Measurements

NASA Astrophysics Data System (ADS)

Reiter, D. T.; Rodi, W. L.

2015-12-01

Constructing 3D Earth models through the joint inversion of large geophysical data sets presents numerous theoretical and practical challenges, especially when diverse types of data and model parameters are involved. Among the challenges are the computational complexity associated with large data and model vectors and the need to unify differing model parameterizations, forward modeling methods and regularization schemes within a common inversion framework. The challenges can be addressed in part by decomposing the inverse problem into smaller, simpler inverse problems that can be solved separately, providing one knows how to merge the separate inversion results into an optimal solution of the full problem. We have formulated an approach to the decomposition of large inverse problems based on the augmented Lagrangian technique from optimization theory. As commonly done, we define a solution to the full inverse problem as the Earth model minimizing an objective function motivated, for example, by a Bayesian inference formulation. Our decomposition approach recasts the minimization problem equivalently as the minimization of component objective functions, corresponding to specified data subsets, subject to the constraints that the minimizing models be equal. A standard optimization algorithm solves the resulting constrained minimization problems by alternating between the separate solution of the component problems and the updating of Lagrange multipliers that serve to steer the individual solution models toward a common model solving the full problem. We are applying our inversion method to the reconstruction of the·crust and upper-mantle seismic velocity structure across Eurasia.· Data for the inversion comprise a large set of P and S body-wave travel times·and fundamental and first-higher mode Rayleigh-wave group velocities.

Stochastic Inversion of InSAR Data to Assess the Probability of Pressure Penetration into the Lower Caprock at In Salah

DOE PAGES

Ramirez, Abelardo; Foxall, William

2014-05-28

Stochastic inversions of InSAR data were carried out to assess the probability that pressure perturbations resulting from CO 2 injection into well KB-502 at In Salah penetrated into the lower caprock seal above the reservoir. Inversions of synthetic data were employed to evaluate the factors that affect the vertical resolution of overpressure distributions, and to assess the impact of various sources of uncertainty in prior constraints on inverse solutions. These include alternative pressure-driven deformation modes within reservoir and caprock, the geometry of a sub-vertical fracture zone in the caprock identified in previous studies, and imperfect estimates of the rock mechanicalmore » properties. Inversions of field data indicate that there is a high probability that a pressure perturbation during the first phase of injection extended upwards along the fracture zone ~ 150 m above the reservoir, and less than 50% probability that it reached the Hot Shale unit at 1500 m depth. Within the uncertainty bounds considered, it was concluded that it is very unlikely that the pressure perturbation approached within 150 m of the top of the lower caprock at the Hercynian Unconformity. The results are consistent with previous deterministic inversion and forward modeling studies.« less

Gravity Wave Dynamics in a Mesospheric Inversion Layer: 1. Reflection, Trapping, and Instability Dynamics

PubMed Central

Laughman, Brian; Wang, Ling; Lund, Thomas S.; Collins, Richard L.

2018-01-01

Abstract An anelastic numerical model is employed to explore the dynamics of gravity waves (GWs) encountering a mesosphere inversion layer (MIL) having a moderate static stability enhancement and a layer of weaker static stability above. Instabilities occur within the MIL when the GW amplitude approaches that required for GW breaking due to compression of the vertical wavelength accompanying the increasing static stability. Thus, MILs can cause large‐amplitude GWs to yield instabilities and turbulence below the altitude where they would otherwise arise. Smaller‐amplitude GWs encountering a MIL do not lead to instability and turbulence but do exhibit partial reflection and transmission, and the transmission is a smaller fraction of the incident GW when instabilities and turbulence arise within the MIL. Additionally, greater GW transmission occurs for weaker MILs and for GWs having larger vertical wavelengths relative to the MIL depth and for lower GW intrinsic frequencies. These results imply similar dynamics for inversions due to other sources, including the tropopause inversion layer, the high stability capping the polar summer mesopause, and lower frequency GWs or tides having sufficient amplitudes to yield significant variations in stability at large and small vertical scales. MILs also imply much stronger reflections and less coherent GW propagation in environments having significant fine structure in the stability and velocity fields than in environments that are smoothly varying. PMID:29576994

Gravity Wave Dynamics in a Mesospheric Inversion Layer: 1. Reflection, Trapping, and Instability Dynamics

NASA Astrophysics Data System (ADS)

Fritts, David C.; Laughman, Brian; Wang, Ling; Lund, Thomas S.; Collins, Richard L.

2018-01-01

An anelastic numerical model is employed to explore the dynamics of gravity waves (GWs) encountering a mesosphere inversion layer (MIL) having a moderate static stability enhancement and a layer of weaker static stability above. Instabilities occur within the MIL when the GW amplitude approaches that required for GW breaking due to compression of the vertical wavelength accompanying the increasing static stability. Thus, MILs can cause large-amplitude GWs to yield instabilities and turbulence below the altitude where they would otherwise arise. Smaller-amplitude GWs encountering a MIL do not lead to instability and turbulence but do exhibit partial reflection and transmission, and the transmission is a smaller fraction of the incident GW when instabilities and turbulence arise within the MIL. Additionally, greater GW transmission occurs for weaker MILs and for GWs having larger vertical wavelengths relative to the MIL depth and for lower GW intrinsic frequencies. These results imply similar dynamics for inversions due to other sources, including the tropopause inversion layer, the high stability capping the polar summer mesopause, and lower frequency GWs or tides having sufficient amplitudes to yield significant variations in stability at large and small vertical scales. MILs also imply much stronger reflections and less coherent GW propagation in environments having significant fine structure in the stability and velocity fields than in environments that are smoothly varying.

Vertical distributions of aerosols under different weather conditions: Analysis of in-situ aircraft measurements in Beijing, China

NASA Astrophysics Data System (ADS)

Zhang, Qiang; Ma, XinCheng; Tie, Xuexi; Huang, Mengyu; Zhao, Chunsheng

In this study, aerosol vertical distributions of 17 in-situ aircraft measurements during 2005 and 2006 springs are analyzed. The 17 flights are carefully selected to exclude dust events, and the analyses are focused on the vertical distributions of aerosol particles associated with anthropogenic activities. The results show that the vertical distributions of aerosol particles are strongly affected by weather and meteorological conditions, and 3 different types of aerosol vertical distributions corresponding to different weather systems are defined in this study. The measurement with a flat vertical gradient and low surface aerosol concentrations is defined as type-1; a gradual decrease of aerosols with altitudes and modest surface aerosol concentrations is defined as type-2; a sharp vertical gradient (aerosols being strongly depressed in the PBL) with high surface aerosol concentrations is defined as type-3. The weather conditions corresponding to the 3 different aerosol types are high pressure, between two high pressures, and low pressure systems (frontal inversions), respectively. The vertical mixing and horizontal transport for the 3 different vertical distributions are analyzed. Under the type-1 condition, the vertical mixing and horizontal transport were rapid, leading to strong dilution of aerosols in both vertical and horizontal directions. As a result, the aerosol concentrations in PBL (planetary boundary layer) were very low, and the vertical distribution was flat. Under the type-2 condition, the vertical mixing was strong and there was no strong barrier at the PBL height. The horizontal transport (wind flux) was modest. As a result, the aerosol concentrations were gradually reduced with altitude, with modest surface aerosol concentrations. Under the type-3 condition, there was a cold front near the region. As a result, a frontal inversion associated with weak vertical mixing appeared at the top of the inversion layer, forming a very strong barrier to prevent aerosol particles being exchanged from the PBL height to the free troposphere. As a result, the aerosol particles were strongly depressed in the PBL height, producing high surface aerosol concentrations. The measured vertical aerosol distributions have important implications for studying the effects of aerosols on photochemistry. The J[O 3] values are reduced by 11%, 48%, and 50%, under the type-1, type-2, and type-3 conditions, respectively. This result reveals that atmospheric oxidant capacity (OH concentrations) is modestly reduced under the type-1 condition, but is significantly reduced under the type-2 and type-3 conditions. This result also suggests that the effect of aerosol particles on surface solar flux is an integrated column effect, and detailed vertical distributions of aerosol particles are very important for assessing the impacts of aerosol on photochemistry.

Aerosol Profile Retrievals from Integrated Dual Wavelengths Space Lidar ESSP3-CENA and Spectral Radiance MODIS Data

NASA Technical Reports Server (NTRS)

Kaufman, Yoram; Mattoo, Shana; Tanre, Didier; Kleidman, Richard; Lau, William K. M. (Technical Monitor)

2001-01-01

The ESSP3-CENA space mission (formally PICASSO-CENA) will provide continues global observations with a two wavelength lidar. The attenuated backscattering coefficients measured by the lidar, have valuable information about the vertical distribution of aerosol particles and their sizes. However the information cannot be mapped into unique aerosol physical properties. Infinite number of physical solutions with different attenuations through the atmosphere can reconstruct the same two wavelength backscattered profile measured from space. Spectral radiance measured by MODIS simultaneously with the ESSP3 data can constrain the problem and resolve this ambiguity to a large extent. Sensitivity study shows that inversion of the integrated MODIS+ESSP3 data can derive the vertical profiles of the fine and coarse modes mixed in the same atmospheric column in the presence of moderate calibration uncertainties and electronic noise (approx. 10%). We shall present the sensitivity study and results from application of the technique to measurements in the SAFARI-2000 and SHADE experiments.

Serial casting for neuromuscular flatfoot and vertical talus in an adolescent with hereditary spastic paraplegia.

PubMed

Sweet, Laurene A; OʼNeill, Lindsey M; Dobbs, Matthew B

2014-01-01

The purpose of this report is to explore assessment and serial casting intervention for painful rigid flatfoot deformities with vertical talus in an adolescent girl with hereditary spastic paraplegia who was nonambulatory. The participant's right foot underwent 2 phases of casting with correction first toward hindfoot inversion and then dorsiflexion. Because of a vertical talus, her left foot required an intermediate casting toward plantar flexion, inversion, and forefoot adduction prior to casting toward dorsiflexion. The patient improved despite the underlying progressive neuromuscular disorder. Pain ameliorated and she returned to supported standing and transfers. Spasticity decreased bilaterally and the flexibility of her foot deformities improved to allow orthotic fabrication in subtalar neutral. Results were maintained at 12 and 16 months. Individualized multiphase serial casting requires further investigation with patients such as those with hereditary spastic paraplegia.

Bayesian inversion of surface-wave data for radial and azimuthal shear-wave anisotropy, with applications to central Mongolia and west-central Italy

NASA Astrophysics Data System (ADS)

Ravenna, Matteo; Lebedev, Sergei

2018-04-01

Seismic anisotropy provides important information on the deformation history of the Earth's interior. Rayleigh and Love surface-waves are sensitive to and can be used to determine both radial and azimuthal shear-wave anisotropies at depth, but parameter trade-offs give rise to substantial model non-uniqueness. Here, we explore the trade-offs between isotropic and anisotropic structure parameters and present a suite of methods for the inversion of surface-wave, phase-velocity curves for radial and azimuthal anisotropies. One Markov chain Monte Carlo (McMC) implementation inverts Rayleigh and Love dispersion curves for a radially anisotropic shear velocity profile of the crust and upper mantle. Another McMC implementation inverts Rayleigh phase velocities and their azimuthal anisotropy for profiles of vertically polarized shear velocity and its depth-dependent azimuthal anisotropy. The azimuthal anisotropy inversion is fully non-linear, with the forward problem solved numerically at different azimuths for every model realization, which ensures that any linearization biases are avoided. The computations are performed in parallel, in order to reduce the computing time. The often challenging issue of data noise estimation is addressed by means of a Hierarchical Bayesian approach, with the variance of the noise treated as an unknown during the radial anisotropy inversion. In addition to the McMC inversions, we also present faster, non-linear gradient-search inversions for the same anisotropic structure. The results of the two approaches are mutually consistent; the advantage of the McMC inversions is that they provide a measure of uncertainty of the models. Applying the method to broad-band data from the Baikal-central Mongolia region, we determine radial anisotropy from the crust down to the transition-zone depths. Robust negative anisotropy (Vsh < Vsv) in the asthenosphere, at 100-300 km depths, presents strong new evidence for a vertical component of asthenospheric flow. This is consistent with an upward flow from below the thick lithosphere of the Siberian Craton to below the thinner lithosphere of central Mongolia, likely to give rise to decompression melting and the scattered, sporadic volcanism observed in the Baikal Rift area, as proposed previously. Inversion of phase-velocity data from west-central Italy for azimuthal anisotropy reveals a clear change in the shear-wave fast-propagation direction at 70-100 km depths, near the lithosphere-asthenosphere boundary. The orientation of the fabric in the lithosphere is roughly E-W, parallel to the direction of stretching over the last 10 m.y. The orientation of the fabric in the asthenosphere is NW-SE, matching the fast directions inferred from shear-wave splitting and probably indicating the direction of the asthenospheric flow.

Wake Vortex Inverse Model User's Guide

NASA Technical Reports Server (NTRS)

Lai, David; Delisi, Donald

2008-01-01

NorthWest Research Associates (NWRA) has developed an inverse model for inverting landing aircraft vortex data. The data used for the inversion are the time evolution of the lateral transport position and vertical position of both the port and starboard vortices. The inverse model performs iterative forward model runs using various estimates of vortex parameters, vertical crosswind profiles, and vortex circulation as a function of wake age. Forward model predictions of lateral transport and altitude are then compared with the observed data. Differences between the data and model predictions guide the choice of vortex parameter values, crosswind profile and circulation evolution in the next iteration. Iterations are performed until a user-defined criterion is satisfied. Currently, the inverse model is set to stop when the improvement in the rms deviation between the data and model predictions is less than 1 percent for two consecutive iterations. The forward model used in this inverse model is a modified version of the Shear-APA model. A detailed description of this forward model, the inverse model, and its validation are presented in a different report (Lai, Mellman, Robins, and Delisi, 2007). This document is a User's Guide for the Wake Vortex Inverse Model. Section 2 presents an overview of the inverse model program. Execution of the inverse model is described in Section 3. When executing the inverse model, a user is requested to provide the name of an input file which contains the inverse model parameters, the various datasets, and directories needed for the inversion. A detailed description of the list of parameters in the inversion input file is presented in Section 4. A user has an option to save the inversion results of each lidar track in a mat-file (a condensed data file in Matlab format). These saved mat-files can be used for post-inversion analysis. A description of the contents of the saved files is given in Section 5. An example of an inversion input file, with preferred parameters values, is given in Appendix A. An example of the plot generated at a normal completion of the inversion is shown in Appendix B.

Children's Understanding of the Arithmetic Concepts of Inversion and Associativity

ERIC Educational Resources Information Center

Robinson, Katherine M.; Ninowski, Jerilyn E.; Gray, Melissa L.

2006-01-01

Previous studies have shown that even preschoolers can solve inversion problems of the form a + b - b by using the knowledge that addition and subtraction are inverse operations. In this study, a new type of inversion problem of the form d x e [divided by] e was also examined. Grade 6 and 8 students solved inversion problems of both types as well…

Role of Retinocortical Processing in Spatial Vision

DTIC Science & Technology

1989-06-01

its inverse transform . These are even- symmetric functions. Odd-symmetric Gabor functions would also be required for image coding (Daugman, 1987), but...spectrum square; thus its horizontal and vertical scale factors may differ by a power of 2. Since the inverse transform undoes this distor- tion, it has...FIGURE 3 STANDARD FORM OF EVEN GABOR FILTER 7 order to inverse - transform correctly. We used Gabor functions with the standard shape of Daugman’s "polar

Face perception is tuned to horizontal orientation in the N170 time window.

PubMed

Jacques, Corentin; Schiltz, Christine; Goffaux, Valerie

2014-02-07

The specificity of face perception is thought to reside both in its dramatic vulnerability to picture-plane inversion and its strong reliance on horizontally oriented image content. Here we asked when in the visual processing stream face-specific perception is tuned to horizontal information. We measured the behavioral performance and scalp event-related potentials (ERP) when participants viewed upright and inverted images of faces and cars (and natural scenes) that were phase-randomized in a narrow orientation band centered either on vertical or horizontal orientation. For faces, the magnitude of the inversion effect (IE) on behavioral discrimination performance was significantly reduced for horizontally randomized compared to vertically or nonrandomized images, confirming the importance of horizontal information for the recruitment of face-specific processing. Inversion affected the processing of nonrandomized and vertically randomized faces early, in the N170 time window. In contrast, the magnitude of the N170 IE was much smaller for horizontally randomized faces. The present research indicates that the early face-specific neural representations are preferentially tuned to horizontal information and offers new perspectives for a description of the visual information feeding face-specific perception.

Magnetic Basement Depth Inversion in the Space Domain

NASA Astrophysics Data System (ADS)

Nunes, Tiago Mane; Barbosa, Valéria Cristina F.; Silva, João Batista C.

2008-10-01

We present a total-field anomaly inversion method to determine both the basement relief and the magnetization direction (inclination and declination) of a 2D sedimentary basin presuming negligible sediment magnetization. Our method assumes that the magnetic intensity contrast is constant and known. We use a nonspectral approach based on approximating the vertical cross section of the sedimentary basin by a polygon, whose uppermost vertices are forced to coincide with the basin outcrop, which are presumably known. For fixed values of the x coordinates our method estimates the z coordinates of the unknown polygon vertices. To obtain the magnetization direction we assume that besides the total-field anomaly, information about the basement’s outcrops at the basin borders and the basement depths at a few points is available. To obtain stable depth-to-basement estimates we impose overall smoothness and positivity constraints on the parameter estimates. Tests on synthetic data showed that the simultaneous estimation of the irregular basement relief and the magnetization direction yields good estimates for the relief despite the mild instability in the magnetization direction. The inversion of aeromagnetic data from the onshore Almada Basin, Brazil, revealed a shallow, eastward-dipping basement basin.

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

NASA Astrophysics Data System (ADS)

Clark, D.

2012-12-01

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

Comparative evolution of the inverse problems (Introduction to an interdisciplinary study of the inverse problems)

NASA Technical Reports Server (NTRS)

Sabatier, P. C.

1972-01-01

The progressive realization of the consequences of nonuniqueness imply an evolution of both the methods and the centers of interest in inverse problems. This evolution is schematically described together with the various mathematical methods used. A comparative description is given of inverse methods in scientific research, with examples taken from mathematics, quantum and classical physics, seismology, transport theory, radiative transfer, electromagnetic scattering, electrocardiology, etc. It is hoped that this paper will pave the way for an interdisciplinary study of inverse problems.

Comparisons of ionospheric electron density distributions reconstructed by GPS computerized tomography, backscatter ionograms, and vertical ionograms

NASA Astrophysics Data System (ADS)

Zhou, Chen; Lei, Yong; Li, Bofeng; An, Jiachun; Zhu, Peng; Jiang, Chunhua; Zhao, Zhengyu; Zhang, Yuannong; Ni, Binbin; Wang, Zemin; Zhou, Xuhua

2015-12-01

Global Positioning System (GPS) computerized ionosphere tomography (CIT) and ionospheric sky wave ground backscatter radar are both capable of measuring the large-scale, two-dimensional (2-D) distributions of ionospheric electron density (IED). Here we report the spatial and temporal electron density results obtained by GPS CIT and backscatter ionogram (BSI) inversion for three individual experiments. Both the GPS CIT and BSI inversion techniques demonstrate the capability and the consistency of reconstructing large-scale IED distributions. To validate the results, electron density profiles obtained from GPS CIT and BSI inversion are quantitatively compared to the vertical ionosonde data, which clearly manifests that both methods output accurate information of ionopsheric electron density and thereby provide reliable approaches to ionospheric soundings. Our study can improve current understanding of the capability and insufficiency of these two methods on the large-scale IED reconstruction.

Navier-Stokes simulation of plume/Vertical Launching System interaction flowfields

NASA Astrophysics Data System (ADS)

York, B. J.; Sinha, N.; Dash, S. M.; Anderson, L.; Gominho, L.

1992-01-01

The application of Navier-Stokes methodology to the analysis of Vertical Launching System/missile exhaust plume interactions is discussed. The complex 3D flowfields related to the Vertical Launching System are computed utilizing the PARCH/RNP Navier-Stokes code. PARCH/RNP solves the fully-coupled system of fluid, two-equation turbulence (k-epsilon) and chemical species equations via the implicit, approximately factored, Beam-Warming algorithm utilizing a block-tridiagonal inversion procedure.

Single-Column Model Simulations of Subtropical Marine Boundary-Layer Cloud Transitions Under Weakening Inversions

NASA Astrophysics Data System (ADS)

Neggers, R. A. J.; Ackerman, A. S.; Angevine, W. M.; Bazile, E.; Beau, I.; Blossey, P. N.; Boutle, I. A.; de Bruijn, C.; Cheng, A.; van der Dussen, J.; Fletcher, J.; Dal Gesso, S.; Jam, A.; Kawai, H.; Cheedela, S. K.; Larson, V. E.; Lefebvre, M.-P.; Lock, A. P.; Meyer, N. R.; de Roode, S. R.; de Rooy, W.; Sandu, I.; Xiao, H.; Xu, K.-M.

2017-10-01

Results are presented of the GASS/EUCLIPSE single-column model intercomparison study on the subtropical marine low-level cloud transition. A central goal is to establish the performance of state-of-the-art boundary-layer schemes for weather and climate models for this cloud regime, using large-eddy simulations of the same scenes as a reference. A novelty is that the comparison covers four different cases instead of one, in order to broaden the covered parameter space. Three cases are situated in the North-Eastern Pacific, while one reflects conditions in the North-Eastern Atlantic. A set of variables is considered that reflects key aspects of the transition process, making use of simple metrics to establish the model performance. Using this method, some longstanding problems in low-level cloud representation are identified. Considerable spread exists among models concerning the cloud amount, its vertical structure, and the associated impact on radiative transfer. The sign and amplitude of these biases differ somewhat per case, depending on how far the transition has progressed. After cloud breakup the ensemble median exhibits the well-known "too few too bright" problem. The boundary-layer deepening rate and its state of decoupling are both underestimated, while the representation of the thin capping cloud layer appears complicated by a lack of vertical resolution. Encouragingly, some models are successful in representing the full set of variables, in particular, the vertical structure and diurnal cycle of the cloud layer in transition. An intriguing result is that the median of the model ensemble performs best, inspiring a new approach in subgrid parameterization.

Linearized inversion of multiple scattering seismic energy

NASA Astrophysics Data System (ADS)

Aldawood, Ali; Hoteit, Ibrahim; Zuberi, Mohammad

2014-05-01

Internal multiples deteriorate the quality of the migrated image obtained conventionally by imaging single scattering energy. So, imaging seismic data with the single-scattering assumption does not locate multiple bounces events in their actual subsurface positions. However, imaging internal multiples properly has the potential to enhance the migrated image because they illuminate zones in the subsurface that are poorly illuminated by single scattering energy such as nearly vertical faults. Standard migration of these multiples provides subsurface reflectivity distributions with low spatial resolution and migration artifacts due to the limited recording aperture, coarse sources and receivers sampling, and the band-limited nature of the source wavelet. The resultant image obtained by the adjoint operator is a smoothed depiction of the true subsurface reflectivity model and is heavily masked by migration artifacts and the source wavelet fingerprint that needs to be properly deconvolved. Hence, we proposed a linearized least-square inversion scheme to mitigate the effect of the migration artifacts, enhance the spatial resolution, and provide more accurate amplitude information when imaging internal multiples. The proposed algorithm uses the least-square image based on single-scattering assumption as a constraint to invert for the part of the image that is illuminated by internal scattering energy. Then, we posed the problem of imaging double-scattering energy as a least-square minimization problem that requires solving the normal equation of the following form: GTGv = GTd, (1) where G is a linearized forward modeling operator that predicts double-scattered seismic data. Also, GT is a linearized adjoint operator that image double-scattered seismic data. Gradient-based optimization algorithms solve this linear system. Hence, we used a quasi-Newton optimization technique to find the least-square minimizer. In this approach, an estimate of the Hessian matrix that contains curvature information is modified at every iteration by a low-rank update based on gradient changes at every step. At each iteration, the data residual is imaged using GT to determine the model update. Application of the linearized inversion to synthetic data to image a vertical fault plane demonstrate the effectiveness of this methodology to properly delineate the vertical fault plane and give better amplitude information than the standard migrated image using the adjoint operator that takes into account internal multiples. Thus, least-square imaging of multiple scattering enhances the spatial resolution of the events illuminated by internal scattering energy. It also deconvolves the source signature and helps remove the fingerprint of the acquisition geometry. The final image is obtained by the superposition of the least-square solution based on single scattering assumption and the least-square solution based on double scattering assumption.

BOOK REVIEW: Inverse Problems. Activities for Undergraduates

NASA Astrophysics Data System (ADS)

Yamamoto, Masahiro

2003-06-01

This book is a valuable introduction to inverse problems. In particular, from the educational point of view, the author addresses the questions of what constitutes an inverse problem and how and why we should study them. Such an approach has been eagerly awaited for a long time. Professor Groetsch, of the University of Cincinnati, is a world-renowned specialist in inverse problems, in particular the theory of regularization. Moreover, he has made a remarkable contribution to educational activities in the field of inverse problems, which was the subject of his previous book (Groetsch C W 1993 Inverse Problems in the Mathematical Sciences (Braunschweig: Vieweg)). For this reason, he is one of the most qualified to write an introductory book on inverse problems. Without question, inverse problems are important, necessary and appear in various aspects. So it is crucial to introduce students to exercises in inverse problems. However, there are not many introductory books which are directly accessible by students in the first two undergraduate years. As a consequence, students often encounter diverse concrete inverse problems before becoming aware of their general principles. The main purpose of this book is to present activities to allow first-year undergraduates to learn inverse theory. To my knowledge, this book is a rare attempt to do this and, in my opinion, a great success. The author emphasizes that it is very important to teach inverse theory in the early years. He writes; `If students consider only the direct problem, they are not looking at the problem from all sides .... The habit of always looking at problems from the direct point of view is intellectually limiting ...' (page 21). The book is very carefully organized so that teachers will be able to use it as a textbook. After an introduction in chapter 1, sucessive chapters deal with inverse problems in precalculus, calculus, differential equations and linear algebra. In order to let one gain some insight into the nature of inverse problems and the appropriate mode of thought, chapter 1 offers historical vignettes, most of which have played an essential role in the development of natural science. These vignettes cover the first successful application of `non-destructive testing' by Archimedes (page 4) via Newton's laws of motion up to literary tomography, and readers will be able to enjoy a wide overview of inverse problems. Therefore, as the author asks, the reader should not skip this chapter. This may not be hard to do, since the headings of the sections are quite intriguing (`Archimedes' Bath', `Another World', `Got the Time?', `Head Games', etc). The author embarks on the technical approach to inverse problems in chapter 2. He has elegantly designed each section with a guide specifying course level, objective, mathematical and scientifical background and appropriate technology (e.g. types of calculators required). The guides are designed such that teachers may be able to construct effective and attractive courses by themselves. The book is not intended to offer one rigidly determined course, but should be used flexibly and independently according to the situation. Moreover, every section closes with activities which can be chosen according to the students' interests and levels of ability. Some of these exercises do not have ready solutions, but require long-term study, so readers are not required to solve all of them. After chapter 5, which contains discrete inverse problems such as the algebraic reconstruction technique and the Backus - Gilbert method, there are answers and commentaries to the activities. Finally, scripts in MATLAB are attached, although they can also be downloaded from the author's web page (http://math.uc.edu/~groetsch/). This book is aimed at students but it will be very valuable to researchers wishing to retain a wide overview of inverse problems in the midst of busy research activities. A Japanese version was published in 2002.

Smart Adaptive Socket to Improve Fit and Relieve Pain in Wounded Warriors

DTIC Science & Technology

2017-10-01

compressing the distal element may have an inverse effect on volume accommodation because it would allow the residual limb to sink further into the...connection without restricting vertical movement a custom valve was designed. The new valve can be described as an inverse duckbill. It is a rubber...valve, which is normally closed but will be deformed into an open state by pushing it into a cylindrical hole. The inverse duckbill valve, unlike

A direct application of the non-linear inverse transformation flight control system design on a STOVL aircraft

NASA Technical Reports Server (NTRS)

Chung, W. W.; Mcneill, W. E.; Stortz, M. W.

1993-01-01

The nonlinear inverse transformation flight control system design method is applied to the Lockheed Ft. Worth Company's E-7D short takeoff and vertical land (STOVL) supersonic fighter/attack aircraft design with a modified General Electric F110 engine which has augmented propulsive lift capability. The system is fully augmented to provide flight path control and velocity control, and rate command attitude hold for angular axes during the transition and hover operations. In cruise mode, the flight control system is configured to provide direct thrust command, rate command attitude hold for pitch and roll axes, and sideslip command with turn coordination. A control selector based on the nonlinear inverse transformation method is designed specifically to be compatible with the propulsion system's physical configuration which has a two dimensional convergent-divergent aft nozzle, a vectorable ventral nozzle, and a thrust augmented ejector. The nonlinear inverse transformation is used to determine the propulsive forces and nozzle deflections, which in combination with the aerodynamic forces and moments (including propulsive induced contributions), and gravitational force, are required to achieve the longitudinal and vertical acceleration commands. The longitudinal control axes are fully decoupled within the propulsion system's performance envelope. A piloted motion-base flight simulation was conducted on the Vertical Motion Simulator (VMS) at NASA Ames Research Center to examine the handling qualities of this design. Based on results of the simulation, refinements to the control system have been made and will also be covered in the report.

A Test of Maxwell's Z Model Using Inverse Modeling

NASA Technical Reports Server (NTRS)

Anderson, J. L. B.; Schultz, P. H.; Heineck, T.

2003-01-01

In modeling impact craters a small region of energy and momentum deposition, commonly called a "point source", is often assumed. This assumption implies that an impact is the same as an explosion at some depth below the surface. Maxwell's Z Model, an empirical point-source model derived from explosion cratering, has previously been compared with numerical impact craters with vertical incidence angles, leading to two main inferences. First, the flowfield center of the Z Model must be placed below the target surface in order to replicate numerical impact craters. Second, for vertical impacts, the flow-field center cannot be stationary if the value of Z is held constant; rather, the flow-field center migrates downward as the crater grows. The work presented here evaluates the utility of the Z Model for reproducing both vertical and oblique experimental impact data obtained at the NASA Ames Vertical Gun Range (AVGR). Specifically, ejection angle data obtained through Three-Dimensional Particle Image Velocimetry (3D PIV) are used to constrain the parameters of Maxwell's Z Model, including the value of Z and the depth and position of the flow-field center via inverse modeling.

Advanced Multivariate Inversion Techniques for High Resolution 3D Geophysical Modeling (Invited)

NASA Astrophysics Data System (ADS)

Maceira, M.; Zhang, H.; Rowe, C. A.

2009-12-01

We focus on the development and application of advanced multivariate inversion techniques to generate a realistic, comprehensive, and high-resolution 3D model of the seismic structure of the crust and upper mantle that satisfies several independent geophysical datasets. Building on previous efforts of joint invesion using surface wave dispersion measurements, gravity data, and receiver functions, we have added a fourth dataset, seismic body wave P and S travel times, to the simultaneous joint inversion method. We present a 3D seismic velocity model of the crust and upper mantle of northwest China resulting from the simultaneous, joint inversion of these four data types. Surface wave dispersion measurements are primarily sensitive to seismic shear-wave velocities, but at shallow depths it is difficult to obtain high-resolution velocities and to constrain the structure due to the depth-averaging of the more easily-modeled, longer-period surface waves. Gravity inversions have the greatest resolving power at shallow depths, and they provide constraints on rock density variations. Moreover, while surface wave dispersion measurements are primarily sensitive to vertical shear-wave velocity averages, body wave receiver functions are sensitive to shear-wave velocity contrasts and vertical travel-times. Addition of the fourth dataset, consisting of seismic travel-time data, helps to constrain the shear wave velocities both vertically and horizontally in the model cells crossed by the ray paths. Incorporation of both P and S body wave travel times allows us to invert for both P and S velocity structure, capitalizing on empirical relationships between both wave types’ seismic velocities with rock densities, thus eliminating the need for ad hoc assumptions regarding the Poisson ratios. Our new tomography algorithm is a modification of the Maceira and Ammon joint inversion code, in combination with the Zhang and Thurber TomoDD (double-difference tomography) program.

Boundary layer structure and scavenging effect during a typical winter haze-fog episode in a core city of BTH region, China

NASA Astrophysics Data System (ADS)

Han, Suqin; Liu, Jingle; Hao, Tianyi; Zhang, Yufen; Li, Peiyan; Yang, Jianbo; Wang, Qinliang; Cai, Ziying; Yao, Qing; Zhang, Min; Wang, Xiujun

2018-04-01

The vertical distribution of PM2.5 and meteorological parameters from ground to upper levels were observed simultaneously using meteorological tower, tethered balloons and aerosol laser radar in Dec of 2016 in the urban area of Tianjin and its southern district, Jinghai. The influence of the vertical structure of boundary layer on a typical haze-fog episode was analyzed. There existed long distance transport of PM in the high layers before the haze formed in Tianjin and the downward airflows brought the PM from the high layer to the ground. In the early stages of this episode, periodic temperature inversions occurred, leading to conspicuous diurnal variations in the vertical profile of the PM2.5. In the middle and late stages of this episode, strong inversion and thick humidity layer were sustained below 400 m, and there were no big daily changes in the vertical profiles of the PM2.5. During the rapid formation period of the fog, the inversion layer was damaged and turbulence was strengthened. During the stationary phase of the fog process, wind and turbulence in the boundary layer became weak again. Rime was the main weather-related, wet cleaning mechanism that lowered pollutants concentration during this fog episode. High concentrations of water soluble ions in the rime samples and the concentrations of those ions in ambient PM2.5 appeared significant decrease during the rime period, which illustrated the scavenging effect of rime.

Running stride peak forces inversely determine running economy in elite runners.

PubMed

Støren, Øyvind; Helgerud, Jan; Hoff, Jan

2011-01-01

The present study investigated the relationship between running economy (RE) at 15 km/h(-1) , 3.000-m race time, maximal strength, and a number of physiological, anthropometrical, and mechanical variables. The variables measured included RE, maximal oxygen consumption, heart rate, step length and frequency, contact time, and the peak horizontal and vertical forces of each step. Maximal strength was measured as the 1 repetition maximum (1RM) half-squat using a leg press machine. Eleven male elite endurance athletes with a V(O2)max of 75.8 ± 6.2 mL/kg(-1)/min(-1) participated in this study. After the anthropometric data were collected, they were tested for RE, running characteristics, and force measures on a level treadmill at 15 km/h(-1). The athletes wore contact soles, and the treadmill was placed on a force platform. Maximal oxygen consumption and 1RM were tested after the RE measurements. The sum of horizontal and vertical peak forces revealed a significant inverse correlation (p < 0.05) both with 3,000-m performance (R = 0.71) and RE (R = 0.66). Inverse correlations were also found (p < 0.05) between RE and body height (R = 0.61) and between RE and body fat percentage (R = 0.62). In conclusion, the sum of horizontal and vertical peak forces was found to be negatively correlated to running economy and 3,000-m running performance, indicating that avoiding vertical movements and high horizontal braking force is crucial for a positive development of RE.

Probabilistic numerical methods for PDE-constrained Bayesian inverse problems

NASA Astrophysics Data System (ADS)

Cockayne, Jon; Oates, Chris; Sullivan, Tim; Girolami, Mark

2017-06-01

This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for the impact of the discretisation of the forward problem. In particular, this drives statistical inferences to be more conservative in the presence of significant solver error. Theoretical results are presented describing rates of convergence for the posteriors in both the forward and inverse problems. This method is tested on a challenging inverse problem with a nonlinear forward model.

An inverse problem strategy based on forward model evaluations: Gradient-based optimization without adjoint solves

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

Aguilo Valentin, Miguel Alejandro

2016-07-01

This study presents a new nonlinear programming formulation for the solution of inverse problems. First, a general inverse problem formulation based on the compliance error functional is presented. The proposed error functional enables the computation of the Lagrange multipliers, and thus the first order derivative information, at the expense of just one model evaluation. Therefore, the calculation of the Lagrange multipliers does not require the solution of the computationally intensive adjoint problem. This leads to significant speedups for large-scale, gradient-based inverse problems.

Paleomagnetic, structural, and seismological evidence for oblique-slip deformation in fault-related folds in the Rocky Mountain Foreland, Colorado Plateau, and central Coast Ranges

NASA Astrophysics Data System (ADS)

Tetreault, Joya Liana

The two geologic questions I address in this research are: do fault-related folds accommodate oblique-slip shortening, and how is oblique-slip deformation absorbed within the folded strata? If the strata is deforming as a strike-slip shear zone, then we should be able to observe material rotations produced by strike-slip shear by measuring paleomagnetic vertical-axis rotations. I have approached these problems by applying paleomagnetic vertical-axis rotations, minor fault analyses, and focal mechanism strain inversions to identify evidence of strike-slip shear and to quantify oblique-slip deformation within fault-related folds in the Rocky Mountain Foreland, Colorado Plateau, and the central Coast Ranges. Clockwise paleomagnetic vertical-axis rotations and compressive paleostress rotations of 15-40º in the forelimb of the Grayback Monocline, northeastern Front Range Colorado, indicate that this Laramide fold is absorbing right-lateral shear from a N90E regional shortening direction. This work shows that paleomagnetic vertical-axis rotations in folded strata can be used to identify strike-slip motion on an underlying fault, and that oblique-slip deformation is localized in the forelimb of the fold. I applied the same paleomagnetic methods to identify oblique-slip on the underlying faults of the Nacimiento, East Kaibab, San Rafael, and Grand Hogback monoclines of the Colorado Plateau. The absence of paleomagnetic rotations and structural evidence for small displacements at the Nacimiento and East Kaibab monoclines indicate minor (<1km) right-lateral slip is being accommodated in these folds. Paleomagnetic vertical-axis rotations are found in the forelimbs of the San Rafael and Grand Hogback monoclines, yielding strike-slip displacements of ˜5km within these two folds. These results are consistent with a northeast Laramide compressive stress direction. In the Coalinga anticline, central Coast Ranges, California, clockwise paleomagnetic rotations and an 8º counterclockwise deflection of the maximum shortening direction (derived from focal mechanisms strain inversions of the upper 7km) are compatible with right-lateral shear. The maximum shortening direction in the area of the mainshock rupture is fold-normal, indicating that strike-slip displacement is confined to the main fault plane and not distributed to the hanging wall. The San Andreas Fault is therefore partitioning a small amount of strike-slip to the Coalinga anticline.

Physics-based Inverse Problem to Deduce Marine Atmospheric Boundary Layer Parameters

DTIC Science & Technology

2017-03-07

please find the Final Technical Report with SF 298 for Dr. Erin E. Hackett’s ONR grant entitled Physics-based Inverse Problem to Deduce Marine...From- To) 07/03/2017 Final Technica l Dec 2012- Dec 2016 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Physics-based Inverse Problem to Deduce Marine...SUPPLEMENTARY NOTES 14. ABSTRACT This report describes research results related to the development and implementation of an inverse problem approach for

Effects of Mixed Layer Shear on Vertical Heat Flux

DTIC Science & Technology

2016-12-01

correlation of ice speed to heat flux (r = .312, p < .001). Relationships between ice speed and shear (r = .107, p < .001), ice speed and inverse ...Richardson number (r = .035, p = .256), inverse Richardson number and heat flux (r = .3, p < .001), heat content and heat flux (r = .084, p < .001) were...correlation of ice speed to heat flux (r = .312, p < .001). Relationships between ice speed and shear (r = .107, p < .001), ice speed and inverse Richardson

The ZH ratio method for long-period seismic data: inversion for S-wave velocity structure

NASA Astrophysics Data System (ADS)

Yano, Tomoko; Tanimoto, T.; Rivera, L.

2009-10-01

The particle motion of surface waves, in addition to phase and group velocities, can provide useful information for S-wave velocity structure in the crust and upper mantle. In this study, we applied a new method to retrieve velocity structure using the ZH ratio, the ratio between vertical and horizontal surface amplitudes of Rayleigh waves. Analysing data from the GEOSCOPE network, we measured the ZH ratios for frequencies between 0.004 and 0.05 Hz (period between 20 and 250s) and inverted them for S-wave velocity structure beneath each station. Our analysis showed that the resolving power of the ZH ratio is limited and final solutions display dependence on starting models; in particular, the depth of the Moho in the starting model is important in order to get reliable results. Thus, initial models for the inversion need to be carefully constructed. We chose PREM and CRUST2.0 in this study as a starting model for all but one station (ECH). The eigenvalue analysis of the least-squares problem that arises for each step of the iterative process shows a few dominant eigenvalues which explains the cause of the inversion's initial-model dependence. However, the ZH ratio is unique in having high sensitivity to near-surface structure and thus provides complementary information to phase and group velocities. Application of this method to GEOSCOPE data suggest that low velocity zones may exist beneath some stations near hotspots. Our tests with different starting models show that the models with low-velocity anomalies fit better to the ZH ratio data. Such low velocity zones are seen near Hawaii (station KIP), Crozet Island (CRZF) and Djibuti (ATD) but not near Reunion Island (RER). It is also found near Echery (ECH) which is in a geothermal area. However, this method has a tendency to produce spurious low velocity zones and resolution of the low velocity zones requires further careful study. We also performed simultaneous inversions for volumetric perturbation and discontinuity-depth perturbation. While its formulation and inversion were straightforward, there seemed to be a difficult trade-off problem between volumetric perturbation and discontinuity-depth perturbation.

A Forward Glimpse into Inverse Problems through a Geology Example

ERIC Educational Resources Information Center

Winkel, Brian J.

2012-01-01

This paper describes a forward approach to an inverse problem related to detecting the nature of geological substrata which makes use of optimization techniques in a multivariable calculus setting. The true nature of the related inverse problem is highlighted. (Contains 2 figures.)

Aquifer Characterization from Surface Geo-electrical Method, western coast of Maharashtra, India

NASA Astrophysics Data System (ADS)

DAS, A.; Maiti, D. S.

2017-12-01

Knowledge of aquifer parameters are necessary for managing groundwater amenity. These parameters are evaluated through pumping tests bring off from bore wells. But it is quite expensive as well as time consuming to carry out pumping tests at various sites and sometimes it is difficult to find bore hole at every required site. Therefore, an alternate method is put forward in which the aquifer parameters are evaluated from surface geophysical method. In this method, vertical electrical sounding (VES) with Schlumberger configuration were accomplished in 85 stations over Sindhudurg district. Sindhudurg district is located in the Konkan region of Maharashtra state, India. The district is located between north latitude 15°37' and 16° 40' and east longitude 73° 19' and 74° 13'. The area is having hard rock and acute groundwater problem. In this configuration, we have taken the maximum current electrode spacing of 200 m for every vertical electrical sounding (VES). Geo-electrical sounding data (true resistivity and thickness) is interpreted through resistivity inversion approach. The required parameters are achieved through resistivity inversion technique from which the aquifer variables (D-Z parameters, mean resistivity, hydraulic conductivity, transmissivity, and coefficient of anisotropy) are calculated by using some empirical formulae. Cross-correlation investigation has been done between these parameters, which eventually used to characterize the aquifer over the study area. At the end, the contour plot for these aquifer parameters has been raised which reveals the detailed distribution of aquifer parameters throughout the study area. From contour plot, high values of longitudinal conductance, hydraulic conductivity and transmissivity are demarcate over Kelus, Vengurle, Mochemar and Shiroda villages. This may be due to intrusion of saline water from Arabian sea. From contour trends, the aquifers are characterized from which the groundwater resources could be assess and manage properly in western Maharashtra. The current method which include DC resistivity inversion could be applicable further in hydrological characterization in tangled coastal parts of India.

Bayesian approach to inverse statistical mechanics.

PubMed

Habeck, Michael

2014-05-01

Inverse statistical mechanics aims to determine particle interactions from ensemble properties. This article looks at this inverse problem from a Bayesian perspective and discusses several statistical estimators to solve it. In addition, a sequential Monte Carlo algorithm is proposed that draws the interaction parameters from their posterior probability distribution. The posterior probability involves an intractable partition function that is estimated along with the interactions. The method is illustrated for inverse problems of varying complexity, including the estimation of a temperature, the inverse Ising problem, maximum entropy fitting, and the reconstruction of molecular interaction potentials.

Bayesian approach to inverse statistical mechanics

NASA Astrophysics Data System (ADS)

Habeck, Michael

2014-05-01

Inverse statistical mechanics aims to determine particle interactions from ensemble properties. This article looks at this inverse problem from a Bayesian perspective and discusses several statistical estimators to solve it. In addition, a sequential Monte Carlo algorithm is proposed that draws the interaction parameters from their posterior probability distribution. The posterior probability involves an intractable partition function that is estimated along with the interactions. The method is illustrated for inverse problems of varying complexity, including the estimation of a temperature, the inverse Ising problem, maximum entropy fitting, and the reconstruction of molecular interaction potentials.

Inverse Modelling Problems in Linear Algebra Undergraduate Courses

ERIC Educational Resources Information Center

Martinez-Luaces, Victor E.

2013-01-01

This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different…

An inverse problem in thermal imaging

NASA Technical Reports Server (NTRS)

Bryan, Kurt; Caudill, Lester F., Jr.

1994-01-01

This paper examines uniqueness and stability results for an inverse problem in thermal imaging. The goal is to identify an unknown boundary of an object by applying a heat flux and measuring the induced temperature on the boundary of the sample. The problem is studied both in the case in which one has data at every point on the boundary of the region and the case in which only finitely many measurements are available. An inversion procedure is developed and used to study the stability of the inverse problem for various experimental configurations.

Inverse problems in quantum chemistry

NASA Astrophysics Data System (ADS)

Karwowski, Jacek

Inverse problems constitute a branch of applied mathematics with well-developed methodology and formalism. A broad family of tasks met in theoretical physics, in civil and mechanical engineering, as well as in various branches of medical and biological sciences has been formulated as specific implementations of the general theory of inverse problems. In this article, it is pointed out that a number of approaches met in quantum chemistry can (and should) be classified as inverse problems. Consequently, the methodology used in these approaches may be enriched by applying ideas and theorems developed within the general field of inverse problems. Several examples, including the RKR method for the construction of potential energy curves, determining parameter values in semiempirical methods, and finding external potentials for which the pertinent Schrödinger equation is exactly solvable, are discussed in detail.

A new inversion algorithm for HF sky-wave backscatter ionograms

NASA Astrophysics Data System (ADS)

Feng, Jing; Ni, Binbin; Lou, Peng; Wei, Na; Yang, Longquan; Liu, Wen; Zhao, Zhengyu; Li, Xue

2018-05-01

HF sky-wave backscatter sounding system is capable of measuring the large-scale, two-dimensional (2-D) distributions of ionospheric electron density. The leading edge (LE) of a backscatter ionogram (BSI) is widely used for ionospheric inversion since it is hardly affected by any factors other than ionospheric electron density. Traditional BSI inversion methods have failed to distinguish LEs associated with different ionospheric layers, and simply utilize the minimum group path of each operating frequency, which generally corresponds to the LE associated with the F2 layer. Consequently, while the inversion results can provide accurate profiles of the F region below the F2 peak, the diagnostics may not be so effective for other ionospheric layers. In order to resolve this issue, we present a new BSI inversion method using LEs associated with different layers, which can further improve the accuracy of electron density distribution, especially the profile of the ionospheric layers below the F2 region. The efficiency of the algorithm is evaluated by computing the mean and the standard deviation of the differences between inverted parameter values and true values obtained from both vertical and oblique incidence sounding. Test results clearly manifest that the method we have developed outputs more accurate electron density profiles due to improvements to acquire the profiles of the layers below the F2 region. Our study can further improve the current BSI inversion methods on the reconstruction of 2-D electron density distribution in a vertical plane aligned with the direction of sounding.

Algorithms and sensitivity analyses for Stratospheric Aerosol and Gas Experiment II water vapor retrieval

NASA Technical Reports Server (NTRS)

Chu, W. P.; Chiou, E. W.; Larsen, J. C.; Thomason, L. W.; Rind, D.; Buglia, J. J.; Oltmans, S.; Mccormick, M. P.; Mcmaster, L. M.

1993-01-01

The operational inversion algorithm used for the retrieval of the water-vapor vertical profiles from the Stratospheric Aerosol and Gas Experiment II (SAGE II) occultation data is presented. Unlike the algorithm used for the retrieval of aerosol, O3, and NO2, the water-vapor retrieval algorithm accounts for the nonlinear relationship between the concentration versus the broad-band absorption characteristics of water vapor. Problems related to the accuracy of the computational scheme, the accuracy of the removal of other interfering species, and the expected uncertainty of the retrieved profile are examined. Results are presented on the error analysis of the SAGE II water vapor retrieval, indicating that the SAGE II instrument produced good quality water vapor data.

Application of a stochastic inverse to the geophysical inverse problem

NASA Technical Reports Server (NTRS)

Jordan, T. H.; Minster, J. B.

1972-01-01

The inverse problem for gross earth data can be reduced to an undertermined linear system of integral equations of the first kind. A theory is discussed for computing particular solutions to this linear system based on the stochastic inverse theory presented by Franklin. The stochastic inverse is derived and related to the generalized inverse of Penrose and Moore. A Backus-Gilbert type tradeoff curve is constructed for the problem of estimating the solution to the linear system in the presence of noise. It is shown that the stochastic inverse represents an optimal point on this tradeoff curve. A useful form of the solution autocorrelation operator as a member of a one-parameter family of smoothing operators is derived.

Analysis of space telescope data collection system

NASA Technical Reports Server (NTRS)

Ingels, F. M.; Schoggen, W. O.

1982-01-01

An analysis of the expected performance for the Multiple Access (MA) system is provided. The analysis covers the expected bit error rate performance, the effects of synchronization loss, the problem of self-interference, and the problem of phase ambiguity. The problem of false acceptance of a command word due to data inversion is discussed. A mathematical determination of the probability of accepting an erroneous command word due to a data inversion is presented. The problem is examined for three cases: (1) a data inversion only, (2) a data inversion and a random error within the same command word, and a block (up to 256 48-bit words) containing both a data inversion and a random error.

A review on the structural styles of deformation during Late Cretaceous and Paleocene tectonic phases in the southern North Sea area

NASA Astrophysics Data System (ADS)

Deckers, Jef; van der Voet, Eva

2018-04-01

The Mesozoic rifts in the southern North Sea area were affected by Late Cretaceous to Paleocene inversion. Two main inversion phases were traditionally identified in this interval: the Sub-Hercynian and the Laramide phases. The Sub-Hercynian phase started in the early Late Cretaceous, peaked during the Campanian and ended in the late Maastrichtian, while the Laramide phase started in the late Danian and ended in the Thanetian. The Late Cretaceous Sub-Hercynian phase was strong and occurred in several pulses. These pulses led to basin-scale uplift by large reverse movements along basin-bounding faults and resulted in large amounts of erosion (up to 2 km) of Mesozoic and older sediments. The middle Paleocene Laramide phase on the other hand resulted in mild, domal uplift of some Late Cretaceous inverted basins and subsidence (into depocenters) of others. The subsequent Cenozoic inversion phases displayed similar or lower amplitudes and wavelengths of vertical surface movements as the Laramide phase. The transition from the Sub-Hercynian to the Laramide phase in the southern North Sea area therefore coincides with the overall transition from fault-controlled inversion to broad domal vertical surface movements.

Direct and inverse energy cascades in a forced rotating turbulence experiment

NASA Astrophysics Data System (ADS)

Campagne, Antoine; Gallet, Basile; Moisy, Frédéric; Cortet, Pierre-Philippe

2014-11-01

Turbulence in a rotating frame provides a remarkable system where 2D and 3D properties may coexist, with a possible tuning between direct and inverse cascades. We present here experimental evidence for a double cascade of kinetic energy in a statistically stationary rotating turbulence experiment. Turbulence is generated by a set of vertical flaps which continuously injects velocity fluctuations towards the center of a rotating water tank. The energy transfers are evaluated from two-point third-order three-component velocity structure functions, which we measure using stereoscopic PIV in the rotating frame. Without global rotation, the energy is transferred from large to small scales, as in classical 3D turbulence. For nonzero rotation rates, the horizontal kinetic energy presents a double cascade: a direct cascade at small horizontal scales and an inverse cascade at large horizontal scales. By contrast, the vertical kinetic energy is always transferred from large to small horizontal scales, a behavior reminiscent of the dynamics of a passive scalar in 2D turbulence. At the largest rotation rate, the flow is nearly 2D and a pure inverse energy cascade is found for the horizontal energy.

Fine-scale structure of the San Andreas fault zone and location of the SAFOD target earthquakes

USGS Publications Warehouse

Thurber, C.; Roecker, S.; Zhang, H.; Baher, S.; Ellsworth, W.

2004-01-01

We present results from the tomographic analysis of seismic data from the Parkfield area using three different inversion codes. The models provide a consistent view of the complex velocity structure in the vicinity of the San Andreas, including a sharp velocity contrast across the fault. We use the inversion results to assess our confidence in the absolute location accuracy of a potential target earthquake. We derive two types of accuracy estimates, one based on a consideration of the location differences from the three inversion methods, and the other based on the absolute location accuracy of "virtual earthquakes." Location differences are on the order of 100-200 m horizontally and up to 500 m vertically. Bounds on the absolute location errors based on the "virtual earthquake" relocations are ??? 50 m horizontally and vertically. The average of our locations places the target event epicenter within about 100 m of the SAF surface trace. Copyright 2004 by the American Geophysical Union.

Determination Gradients of the Earth's Magnetic Field from the Measurements of the Satellites and Inversion of the Kursk Magnetic Anomaly

NASA Technical Reports Server (NTRS)

Karoly, Kis; Taylor, Patrick T.; Geza, Wittmann

2014-01-01

We computed magnetic field gradients at satellite altitude, over Europe with emphasis on the Kursk Magnetic Anomaly (KMA). They were calculated using the CHAMP satellite total magnetic anomalies. Our computations were done to determine how the magnetic anomaly data from the new ESA/Swarm satellites could be utilized to determine the structure of the magnetization of the Earths crust, especially in the region of the KMA. Since the ten years of 2 CHAMP data could be used to simulate the Swarm data. An initial East magnetic anomaly gradient map of Europe was computed and subsequently the North, East and Vertical magnetic gradients for the KMA region were calculated. The vertical gradient of the KMA was determined using Hilbert transforms. Inversion of the total KMA was derived using Simplex and Simulated Annealing algorithms. Our resulting inversion depth model is a horizontal quadrangle with upper 300-329 km and lower 331-339 km boundaries.

Analysis of pumping tests of partially penetrating wells in an unconfined aquifer using inverse numerical optimization

NASA Astrophysics Data System (ADS)

Hvilshøj, S.; Jensen, K. H.; Barlebo, H. C.; Madsen, B.

1999-08-01

Inverse numerical modeling was applied to analyze pumping tests of partially penetrating wells carried out in three wells established in an unconfined aquifer in Vejen, Denmark, where extensive field investigations had previously been carried out, including tracer tests, mini-slug tests, and other hydraulic tests. Drawdown data from multiple piezometers located at various horizontal and vertical distances from the pumping well were included in the optimization. Horizontal and vertical hydraulic conductivities, specific storage, and specific yield were estimated, assuming that the aquifer was either a homogeneous system with vertical anisotropy or composed of two or three layers of different hydraulic properties. In two out of three cases, a more accurate interpretation was obtained for a multi-layer model defined on the basis of lithostratigraphic information obtained from geological descriptions of sediment samples, gammalogs, and flow-meter tests. Analysis of the pumping tests resulted in values for horizontal hydraulic conductivities that are in good accordance with those obtained from slug tests and mini-slug tests. Besides the horizontal hydraulic conductivity, it is possible to determine the vertical hydraulic conductivity, specific yield, and specific storage based on a pumping test of a partially penetrating well. The study demonstrates that pumping tests of partially penetrating wells can be analyzed using inverse numerical models. The model used in the study was a finite-element flow model combined with a non-linear regression model. Such a model can accommodate more geological information and complex boundary conditions, and the parameter-estimation procedure can be formalized to obtain optimum estimates of hydraulic parameters and their standard deviations.

PREFACE: The Second International Conference on Inverse Problems: Recent Theoretical Developments and Numerical Approaches

NASA Astrophysics Data System (ADS)

Cheng, Jin; Hon, Yiu-Chung; Seo, Jin Keun; Yamamoto, Masahiro

2005-01-01

The Second International Conference on Inverse Problems: Recent Theoretical Developments and Numerical Approaches was held at Fudan University, Shanghai from 16-21 June 2004. The first conference in this series was held at the City University of Hong Kong in January 2002 and it was agreed to hold the conference once every two years in a Pan-Pacific Asian country. The next conference is scheduled to be held at Hokkaido University, Sapporo, Japan in July 2006. The purpose of this series of biennial conferences is to establish and develop constant international collaboration, especially among the Pan-Pacific Asian countries. In recent decades, interest in inverse problems has been flourishing all over the globe because of both the theoretical interest and practical requirements. In particular, in Asian countries, one is witnessing remarkable new trends of research in inverse problems as well as the participation of many young talents. Considering these trends, the second conference was organized with the chairperson Professor Li Tat-tsien (Fudan University), in order to provide forums for developing research cooperation and to promote activities in the field of inverse problems. Because solutions to inverse problems are needed in various applied fields, we entertained a total of 92 participants at the second conference and arranged various talks which ranged from mathematical analyses to solutions of concrete inverse problems in the real world. This volume contains 18 selected papers, all of which have undergone peer review. The 18 papers are classified as follows: Surveys: four papers give reviews of specific inverse problems. Theoretical aspects: six papers investigate the uniqueness, stability, and reconstruction schemes. Numerical methods: four papers devise new numerical methods and their applications to inverse problems. Solutions to applied inverse problems: four papers discuss concrete inverse problems such as scattering problems and inverse problems in atmospheric sciences and oceanography. Last but not least is our gratitude. As editors we would like to express our sincere thanks to all the plenary and invited speakers, the members of the International Scientific Committee and the Advisory Board for the success of the conference, which has given rise to this present volume of selected papers. We would also like to thank Mr Wang Yanbo, Miss Wan Xiqiong and the graduate students at Fudan University for their effective work to make this conference a success. The conference was financially supported by the NFS of China, the Mathematical Center of Ministry of Education of China, E-Institutes of Shanghai Municipal Education Commission (No E03004) and Fudan University, Grant 15340027 from the Japan Society for the Promotion of Science, and Grant 15654015 from the Ministry of Education, Cultures, Sports and Technology.

Riemann–Hilbert problem approach for two-dimensional flow inverse scattering

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

Agaltsov, A. D., E-mail: agalets@gmail.com; Novikov, R. G., E-mail: novikov@cmap.polytechnique.fr; IEPT RAS, 117997 Moscow

2014-10-15

We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann–Hilbert problem approach. Comparisons with preceding results are given.

Improved Holistic Analysis of Rayleigh Waves for Single- and Multi-Offset Data: Joint Inversion of Rayleigh-Wave Particle Motion and Vertical- and Radial-Component Velocity Spectra

NASA Astrophysics Data System (ADS)

Dal Moro, Giancarlo; Moustafa, Sayed S. R.; Al-Arifi, Nassir S.

2018-01-01

Rayleigh waves often propagate according to complex mode excitation so that the proper identification and separation of specific modes can be quite difficult or, in some cases, just impossible. Furthermore, the analysis of a single component (i.e., an inversion procedure based on just one objective function) necessarily prevents solving the problems related to the non-uniqueness of the solution. To overcome these issues and define a holistic analysis of Rayleigh waves, we implemented a procedure to acquire data that are useful to define and efficiently invert the three objective functions defined from the three following "objects": the velocity spectra of the vertical- and radial-components and the Rayleigh-wave particle motion (RPM) frequency-offset data. Two possible implementations are presented. In the first case we consider classical multi-offset (and multi-component) data, while in a second possible approach we exploit the data recorded by a single three-component geophone at a fixed offset from the source. Given the simple field procedures, the method could be particularly useful for the unambiguous geotechnical exploration of large areas, where more complex acquisition procedures, based on the joint acquisition of Rayleigh and Love waves, would not be economically viable. After illustrating the different kinds of data acquisition and the data processing, the results of the proposed methodology are illustrated in a case study. Finally, a series of theoretical and practical aspects are discussed to clarify some issues involved in the overall procedure (data acquisition and processing).

The point-spread function measure of resolution for the 3-D electrical resistivity experiment

NASA Astrophysics Data System (ADS)

Oldenborger, Greg A.; Routh, Partha S.

2009-02-01

The solution appraisal component of the inverse problem involves investigation of the relationship between our estimated model and the actual model. However, full appraisal is difficult for large 3-D problems such as electrical resistivity tomography (ERT). We tackle the appraisal problem for 3-D ERT via the point-spread functions (PSFs) of the linearized resolution matrix. The PSFs represent the impulse response of the inverse solution and quantify our parameter-specific resolving capability. We implement an iterative least-squares solution of the PSF for the ERT experiment, using on-the-fly calculation of the sensitivity via an adjoint integral equation with stored Green's functions and subgrid reduction. For a synthetic example, analysis of individual PSFs demonstrates the truly 3-D character of the resolution. The PSFs for the ERT experiment are Gaussian-like in shape, with directional asymmetry and significant off-diagonal features. Computation of attributes representative of the blurring and localization of the PSF reveal significant spatial dependence of the resolution with some correlation to the electrode infrastructure. Application to a time-lapse ground-water monitoring experiment demonstrates the utility of the PSF for assessing feature discrimination, predicting artefacts and identifying model dependence of resolution. For a judicious selection of model parameters, we analyse the PSFs and their attributes to quantify the case-specific localized resolving capability and its variability over regions of interest. We observe approximate interborehole resolving capability of less than 1-1.5m in the vertical direction and less than 1-2.5m in the horizontal direction. Resolving capability deteriorates significantly outside the electrode infrastructure.

Imaging using cross-hole seismoelectric tomography

USGS Publications Warehouse

Araji, A.H.; Revil, A.; Jardani, A.; Minsley, B.

2011-01-01

We propose a new cross-hole imaging approach based on seismoelectric conversions associated with the transmission of seismic waves from seismic sources located in a borehole to receivers electrodes located in a second borehole. The seismoelectric seismic-to-electric problem is solved using Biot theory coupled with a generalized Ohm's law with an electrokinetic coupling term. The components of the displacement of the solid phase, the fluid pressure, and the electrical potential are solved using a finite element approach with PML boundary conditions for the seismic waves and boundary conditions mimicking an infinite material for the electrostatic problem. We have developed an inversion algorithm using the electrical disturbances recorded in the second borehole to localize the position of the heterogeneities responsible for the seismoelectric conversions. Because of the ill-posed nature of the inverse problem, regularization is used to constrain the solution at each time in the seismoelectric time window comprised between the time of the seismic shot and the time of the first arrival of the seismic waves in the second borehole. All the inverted volumetric current source densities are stacked to produce an image of the position of the heterogeneities between the two boreholes. Two simple synthetic case studies are presented to test this concept. The first case study corresponds to a vertical discontinuity between two homogeneous sub-domains. The second case study corresponds to a poroelastic inclusion embedded into an homogenous poroelastic formation. In both cases, the position of the heterogeneity is fairly well-recovered using only the electrical disturbances associated with the seismoelectric conversions. ?? 2011 Society of Exploration Geophysicists.

Mechanism of saline groundwater migration under the influence of deep groundwater exploitation in the North China Plain

NASA Astrophysics Data System (ADS)

Han, D.; Cao, G.; Currell, M. J.

2016-12-01

Understanding the mechanism of salt water transport in response to the exploitation of deep freshwater has long been one of the major regional environmental hydrogeological problems and scientific challenges in the North China Plain. It is also the key to a correct understanding of the sources of deep groundwater pumpage. This study will look at the Hengshui - Cangzhou region as a region with typical vertical salt water distribution, and high levels of groundwater exploitation, integrating a variety of techniques in geology, hydrogeology, geophysics, hydrodynamics, and hydrochemistry - stable isotopes. Information about the problem will be determined using multiple lines of evidence, including field surveys of drilling and water sampling, as well as laboratory experiments and physical and numerical simulations. The project will characterize and depict the migration characteristics of salt water bodies and their relationship with the geological structure and deep ground water resources. The work will reveal the freshwater-saltwater interface shape; determine the mode and mechanism of hydrodynamic transport and salt transport; estimate the vertical migration time of salt water in a thick aquitard; and develop accurate hydrogeological conceptual models. This work will utilize groundwater variable density flow- solute transport numerical models to simulate the water and salt transport processes in vertical one-dimensional (typical bore) and two-dimensional (typical cross-section) space. Both inversion of the downward movement of saltwater caused by groundwater exploitation through history, and examining future saltwater migration trends under groundwater exploitation scenarios will be conducted, to quantitatively evaluate the impact of salt water migration to the deep groundwater body in the North China Plain. The research results will provide a scientific basis for the sustainable utilization of deep groundwater resources in this area.

Subsurface solute transport with one-, two-, and three-dimensional arbitrary shape sources

NASA Astrophysics Data System (ADS)

Chen, Kewei; Zhan, Hongbin; Zhou, Renjie

2016-07-01

Solutions with one-, two-, and three-dimensional arbitrary shape source geometries will be very helpful tools for investigating a variety of contaminant transport problems in the geological media. This study proposed a general method to develop new solutions for solute transport in a saturated, homogeneous aquifer (confined or unconfined) with a constant, unilateral groundwater flow velocity. Several typical source geometries, such as arbitrary line sources, vertical and horizontal patch sources, circular and volumetric sources, were considered. The sources can sit on the upper or lower aquifer boundary to simulate light non-aqueous-phase-liquids (LNAPLs) or dense non-aqueous-phase-liquids (DNAPLs), respectively, or can be located anywhere inside the aquifer. The developed new solutions were tested against previous benchmark solutions under special circumstances and were shown to be robust and accurate. Such solutions can also be used as a starting point for the inverse problem of source zone and source geometry identification in the future. The following findings can be obtained from analyzing the solutions. The source geometry, including shape and orientation, generally played an important role for the concentration profile through the entire transport process. When comparing the inclined line sources with the horizontal line sources, the concentration contours expanded considerably along the vertical direction, and shrank considerably along the groundwater flow direction. A planar source sitting on the upper aquifer boundary (such as a LNAPL pool) would lead to significantly different concentration profiles compared to a planar source positioned in a vertical plane perpendicular to the flow direction. For a volumetric source, its dimension along the groundwater flow direction became less important compared to its other two dimensions.

A systematic linear space approach to solving partially described inverse eigenvalue problems

NASA Astrophysics Data System (ADS)

Hu, Sau-Lon James; Li, Haujun

2008-06-01

Most applications of the inverse eigenvalue problem (IEP), which concerns the reconstruction of a matrix from prescribed spectral data, are associated with special classes of structured matrices. Solving the IEP requires one to satisfy both the spectral constraint and the structural constraint. If the spectral constraint consists of only one or few prescribed eigenpairs, this kind of inverse problem has been referred to as the partially described inverse eigenvalue problem (PDIEP). This paper develops an efficient, general and systematic approach to solve the PDIEP. Basically, the approach, applicable to various structured matrices, converts the PDIEP into an ordinary inverse problem that is formulated as a set of simultaneous linear equations. While solving simultaneous linear equations for model parameters, the singular value decomposition method is applied. Because of the conversion to an ordinary inverse problem, other constraints associated with the model parameters can be easily incorporated into the solution procedure. The detailed derivation and numerical examples to implement the newly developed approach to symmetric Toeplitz and quadratic pencil (including mass, damping and stiffness matrices of a linear dynamic system) PDIEPs are presented. Excellent numerical results for both kinds of problem are achieved under the situations that have either unique or infinitely many solutions.

Convergence of Chahine's nonlinear relaxation inversion method used for limb viewing remote sensing

NASA Technical Reports Server (NTRS)

Chu, W. P.

1985-01-01

The application of Chahine's (1970) inversion technique to remote sensing problems utilizing the limb viewing geometry is discussed. The problem considered here involves occultation-type measurements and limb radiance-type measurements from either spacecraft or balloon platforms. The kernel matrix of the inversion problem is either an upper or lower triangular matrix. It is demonstrated that the Chahine inversion technique always converges, provided the diagonal elements of the kernel matrix are nonzero.

Three-Dimensional Anisotropic Acoustic and Elastic Full-Waveform Seismic Inversion

NASA Astrophysics Data System (ADS)

Warner, M.; Morgan, J. V.

2013-12-01

Three-dimensional full-waveform inversion is a high-resolution, high-fidelity, quantitative, seismic imaging technique that has advanced rapidly within the oil and gas industry. The method involves the iterative improvement of a starting model using a series of local linearized updates to solve the full non-linear inversion problem. During the inversion, forward modeling employs the full two-way three-dimensional heterogeneous anisotropic acoustic or elastic wave equation to predict the observed raw field data, wiggle-for-wiggle, trace-by-trace. The method is computationally demanding; it is highly parallelized, and runs on large multi-core multi-node clusters. Here, we demonstrate what can be achieved by applying this newly practical technique to several high-density 3D seismic datasets that were acquired to image four contrasting sedimentary targets: a gas cloud above an oil reservoir, a radially faulted dome, buried fluvial channels, and collapse structures overlying an evaporate sequence. We show that the resulting anisotropic p-wave velocity models match in situ measurements in deep boreholes, reproduce detailed structure observed independently on high-resolution seismic reflection sections, accurately predict the raw seismic data, simplify and sharpen reverse-time-migrated reflection images of deeper horizons, and flatten Kirchhoff-migrated common-image gathers. We also show that full-elastic 3D full-waveform inversion of pure pressure data can generate a reasonable shear-wave velocity model for one of these datasets. For two of the four datasets, the inclusion of significant transversely isotropic anisotropy with a vertical axis of symmetry was necessary in order to fit the kinematics of the field data properly. For the faulted dome, the full-waveform-inversion p-wave velocity model recovers the detailed structure of every fault that can be seen on coincident seismic reflection data. Some of the individual faults represent high-velocity zones, some represent low-velocity zones, some have more-complex internal structure, and some are visible merely as offsets between two regions with contrasting velocity. Although this has not yet been demonstrated quantitatively for this dataset, it seems likely that at least some of this fine structure in the recovered velocity model is related to the detailed lithology, strain history and fluid properties within the individual faults. We have here applied this technique to seismic data that were acquired by the extractive industries, however this inversion scheme is immediately scalable and applicable to a much wider range of problems given sufficient quality and density of observed data. Potential targets range from shallow magma chambers beneath active volcanoes, through whole-crustal sections across plate boundaries, to regional and whole-Earth models.

Computational inverse methods of heat source in fatigue damage problems

NASA Astrophysics Data System (ADS)

Chen, Aizhou; Li, Yuan; Yan, Bo

2018-04-01

Fatigue dissipation energy is the research focus in field of fatigue damage at present. It is a new idea to solve the problem of calculating fatigue dissipation energy by introducing inverse method of heat source into parameter identification of fatigue dissipation energy model. This paper introduces the research advances on computational inverse method of heat source and regularization technique to solve inverse problem, as well as the existing heat source solution method in fatigue process, prospects inverse method of heat source applying in fatigue damage field, lays the foundation for further improving the effectiveness of fatigue dissipation energy rapid prediction.

W17_geowave “3D full waveform geophysical models”

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

Larmat, Carene; Maceira, Monica; Roy, Corinna

2018-02-12

Performance of the MCMC inversion according to the number of cores for the computation. A) 64 cores. B) 480 cores. C) 816 cores. The true model is represented by the black line. Vsv is the wave speed of S waves polarized in the vertical plane, ξ is an anisotropy parameter. The Earth is highly anisotropics; the wavespeed of seismic waves depends on the polarization of the wave. Seismic inversion of the elastic structure is usually limited to isotropic information such as Vsv. Our research looked at the inversion of Earth anisotropy.

Joint inversion of apparent resistivity and seismic surface and body wave data

NASA Astrophysics Data System (ADS)

Garofalo, Flora; Sauvin, Guillaume; Valentina Socco, Laura; Lecomte, Isabelle

2013-04-01

A novel inversion algorithm has been implemented to jointly invert apparent resistivity curves from vertical electric soundings, surface wave dispersion curves, and P-wave travel times. The algorithm works in the case of laterally varying layered sites. Surface wave dispersion curves and P-wave travel times can be extracted from the same seismic dataset and apparent resistivity curves can be obtained from continuous vertical electric sounding acquisition. The inversion scheme is based on a series of local 1D layered models whose unknown parameters are thickness h, S-wave velocity Vs, P-wave velocity Vp, and Resistivity R of each layer. 1D models are linked to surface-wave dispersion curves and apparent resistivity curves through classical 1D forward modelling, while a 2D model is created by interpolating the 1D models and is linked to refracted P-wave hodograms. A priori information can be included in the inversion and a spatial regularization is introduced as a set of constraints between model parameters of adjacent models and layers. Both a priori information and regularization are weighted by covariance matrixes. We show the comparison of individual inversions and joint inversion for a synthetic dataset that presents smooth lateral variations. Performing individual inversions, the poor sensitivity to some model parameters leads to estimation errors up to 62.5 %, whereas for joint inversion the cooperation of different techniques reduces most of the model estimation errors below 5% with few exceptions up to 39 %, with an overall improvement. Even though the final model retrieved by joint inversion is internally consistent and more reliable, the analysis of the results evidences unacceptable values of Vp/Vs ratio for some layers, thus providing negative Poisson's ratio values. To further improve the inversion performances, an additional constraint is added imposing Poisson's ratio in the range 0-0.5. The final results are globally improved by the introduction of this constraint further reducing the maximum error to 30 %. The same test was performed on field data acquired in a landslide-prone area close by the town of Hvittingfoss, Norway. Seismic data were recorded on two 160-m long profiles in roll-along mode using a 5-kg sledgehammer as source and 24 4.5-Hz vertical geophones with 4-m separation. First-arrival travel times were picked at every shot locations and surface wave dispersion curves extracted at 8 locations for each profile. 2D resistivity measurements were carried out on the same profiles using Gradient and Dipole-Dipole arrays with 2-m electrode spacing. The apparent resistivity curves were extracted at the same location as for the dispersion curves. The data were subsequently jointly inverted and the resulting model compared to individual inversions. Although models from both, individual and joint inversions are consistent, the estimation error is smaller for joint inversion, and more especially for first-arrival travel times. The joint inversion exploits different sensitivities of the methods to model parameters and therefore mitigates solution nonuniqueness and the effects of intrinsic limitations of the different techniques. Moreover, it produces an internally consistent multi-parametric final model that can be profitably interpreted to provide a better understanding of subsurface properties.

The construction of combinatorial manifolds with prescribed sets of links of vertices

NASA Astrophysics Data System (ADS)

Gaifullin, A. A.

2008-10-01

To every oriented closed combinatorial manifold we assign the set (with repetitions) of isomorphism classes of links of its vertices. The resulting transformation \\mathcal{L} is the main object of study in this paper. We pose an inversion problem for \\mathcal{L} and show that this problem is closely related to Steenrod's problem on the realization of cycles and to the Rokhlin-Schwartz-Thom construction of combinatorial Pontryagin classes. We obtain a necessary condition for a set of isomorphism classes of combinatorial spheres to belong to the image of \\mathcal{L}. (Sets satisfying this condition are said to be balanced.) We give an explicit construction showing that every balanced set of isomorphism classes of combinatorial spheres falls into the image of \\mathcal{L} after passing to a multiple set and adding several pairs of the form (Z,-Z), where -Z is the sphere Z with the orientation reversed. Given any singular simplicial cycle \\xi of a space X, this construction enables us to find explicitly a combinatorial manifold M and a map \\varphi\\colon M\\to X such that \\varphi_* \\lbrack M \\rbrack =r[\\xi] for some positive integer r. The construction is based on resolving singularities of \\xi. We give applications of the main construction to cobordisms of manifolds with singularities and cobordisms of simple cells. In particular, we prove that every rational additive invariant of cobordisms of manifolds with singularities admits a local formula. Another application is the construction of explicit (though inefficient) local combinatorial formulae for polynomials in the rational Pontryagin classes of combinatorial manifolds.

2D Inviscid and Viscous Inverse Design Using Continuous Adjoint and Lax-Wendroff Formulation

NASA Astrophysics Data System (ADS)

Proctor, Camron Lisle

The continuous adjoint (CA) technique for optimization and/or inverse-design of aerodynamic components has seen nearly 30 years of documented success in academia. The benefits of using CA versus a direct sensitivity analysis are shown repeatedly in the literature. However, the use of CA in industry is relatively unheard-of. The sparseness of industry contributions to the field may be attributed to the tediousness of the derivation and/or to the difficulties in implementation due to the lack of well-documented adjoint numerical methods. The focus of this work has been to thoroughly document the techniques required to build a two-dimensional CA inverse-design tool. To this end, this work begins with a short background on computational fluid dynamics (CFD) and the use of optimization tools in conjunction with CFD tools to solve aerodynamic optimization problems. A thorough derivation of the continuous adjoint equations and the accompanying gradient calculations for inviscid and viscous constraining equations follows the introduction. Next, the numerical techniques used for solving the partial differential equations (PDEs) governing the flow equations and the adjoint equations are described. Numerical techniques for the supplementary equations are discussed briefly. Subsequently, a verification of the efficacy of the inverse design tool, for the inviscid adjoint equations as well as possible numerical implementation pitfalls are discussed. The NACA0012 airfoil is used as an initial airfoil and surface pressure distribution and the NACA16009 is used as the desired pressure and vice versa. Using a Savitsky-Golay gradient filter, convergence (defined as a cost function<1E-5) is reached in approximately 220 design iteration using 121 design variables. The inverse-design using inviscid adjoint equations results are followed by the discussion of the viscous inverse design results and techniques used to further the convergence of the optimizer. The relationship between limiting step-size and convergence in a line-search optimization is shown to slightly decrease the final cost function at significant computational cost. A gradient damping technique is presented and shown to increase the convergence rate for the optimization in viscous problems, at a negligible increase in computational cost, but is insufficient to converge the solution. Systematically including adjacent surface vertices in the perturbation of a design variable, also a surface vertex, is shown to affect the convergence capability of the viscous optimizer. Finally, a comparison of using inviscid adjoint equations, as opposed to viscous adjoint equations, on viscous flow is presented, and the inviscid adjoint paired with viscous flow is found to reduce the cost function further than the viscous adjoint for the presented problem.

FOREWORD: 5th International Workshop on New Computational Methods for Inverse Problems

NASA Astrophysics Data System (ADS)

Vourc'h, Eric; Rodet, Thomas

2015-11-01

This volume of Journal of Physics: Conference Series is dedicated to the scientific research presented during the 5th International Workshop on New Computational Methods for Inverse Problems, NCMIP 2015 (http://complement.farman.ens-cachan.fr/NCMIP_2015.html). This workshop took place at Ecole Normale Supérieure de Cachan, on May 29, 2015. The prior editions of NCMIP also took place in Cachan, France, firstly within the scope of ValueTools Conference, in May 2011, and secondly at the initiative of Institut Farman, in May 2012, May 2013 and May 2014. The New Computational Methods for Inverse Problems (NCMIP) workshop focused on recent advances in the resolution of inverse problems. Indeed, inverse problems appear in numerous scientific areas such as geophysics, biological and medical imaging, material and structure characterization, electrical, mechanical and civil engineering, and finances. The resolution of inverse problems consists of estimating the parameters of the observed system or structure from data collected by an instrumental sensing or imaging device. Its success firstly requires the collection of relevant observation data. It also requires accurate models describing the physical interactions between the instrumental device and the observed system, as well as the intrinsic properties of the solution itself. Finally, it requires the design of robust, accurate and efficient inversion algorithms. Advanced sensor arrays and imaging devices provide high rate and high volume data; in this context, the efficient resolution of the inverse problem requires the joint development of new models and inversion methods, taking computational and implementation aspects into account. During this one-day workshop, researchers had the opportunity to bring to light and share new techniques and results in the field of inverse problems. The topics of the workshop were: algorithms and computational aspects of inversion, Bayesian estimation, Kernel methods, learning methods, convex optimization, free discontinuity problems, metamodels, proper orthogonal decomposition, reduced models for the inversion, non-linear inverse scattering, image reconstruction and restoration, and applications (bio-medical imaging, non-destructive evaluation...). NCMIP 2015 was a one-day workshop held in May 2015 which attracted around 70 attendees. Each of the submitted papers has been reviewed by two reviewers. There have been 15 accepted papers. In addition, three international speakers were invited to present a longer talk. The workshop was supported by Institut Farman (ENS Cachan, CNRS) and endorsed by the following French research networks: GDR ISIS, GDR MIA, GDR MOA and GDR Ondes. The program committee acknowledges the following research laboratories: CMLA, LMT, LURPA and SATIE.

New Additions to the Toolkit for Forward/Inverse Problems in Electrocardiography within the SCIRun Problem Solving Environment.

PubMed

Coll-Font, Jaume; Burton, Brett M; Tate, Jess D; Erem, Burak; Swenson, Darrel J; Wang, Dafang; Brooks, Dana H; van Dam, Peter; Macleod, Rob S

2014-09-01

Cardiac electrical imaging often requires the examination of different forward and inverse problem formulations based on mathematical and numerical approximations of the underlying source and the intervening volume conductor that can generate the associated voltages on the surface of the body. If the goal is to recover the source on the heart from body surface potentials, the solution strategy must include numerical techniques that can incorporate appropriate constraints and recover useful solutions, even though the problem is badly posed. Creating complete software solutions to such problems is a daunting undertaking. In order to make such tools more accessible to a broad array of researchers, the Center for Integrative Biomedical Computing (CIBC) has made an ECG forward/inverse toolkit available within the open source SCIRun system. Here we report on three new methods added to the inverse suite of the toolkit. These new algorithms, namely a Total Variation method, a non-decreasing TMP inverse and a spline-based inverse, consist of two inverse methods that take advantage of the temporal structure of the heart potentials and one that leverages the spatial characteristics of the transmembrane potentials. These three methods further expand the possibilities of researchers in cardiology to explore and compare solutions to their particular imaging problem.

Phase and amplitude inversion of crosswell radar data

USGS Publications Warehouse

Ellefsen, Karl J.; Mazzella, Aldo T.; Horton, Robert J.; McKenna, Jason R.

2011-01-01

Phase and amplitude inversion of crosswell radar data estimates the logarithm of complex slowness for a 2.5D heterogeneous model. The inversion is formulated in the frequency domain using the vector Helmholtz equation. The objective function is minimized using a back-propagation method that is suitable for a 2.5D model and that accounts for the near-, intermediate-, and far-field regions of the antennas. The inversion is tested with crosswell radar data collected in a laboratory tank. The model anomalies are consistent with the known heterogeneity in the tank; the model’s relative dielectric permittivity, which is calculated from the real part of the estimated complex slowness, is consistent with independent laboratory measurements. The methodologies developed for this inversion can be adapted readily to inversions of seismic data (e.g., crosswell seismic and vertical seismic profiling data).

Children's Understanding of the Inverse Relation between Multiplication and Division

ERIC Educational Resources Information Center

Robinson, Katherine M.; Dube, Adam K.

2009-01-01

Children's understanding of the inversion concept in multiplication and division problems (i.e., that on problems of the form "d multiplied by e/e" no calculations are required) was investigated. Children in Grades 6, 7, and 8 completed an inversion problem-solving task, an assessment of procedures task, and a factual knowledge task of simple…

A Volunteer Computing Project for Solving Geoacoustic Inversion Problems

NASA Astrophysics Data System (ADS)

Zaikin, Oleg; Petrov, Pavel; Posypkin, Mikhail; Bulavintsev, Vadim; Kurochkin, Ilya

2017-12-01

A volunteer computing project aimed at solving computationally hard inverse problems in underwater acoustics is described. This project was used to study the possibilities of the sound speed profile reconstruction in a shallow-water waveguide using a dispersion-based geoacoustic inversion scheme. The computational capabilities provided by the project allowed us to investigate the accuracy of the inversion for different mesh sizes of the sound speed profile discretization grid. This problem suits well for volunteer computing because it can be easily decomposed into independent simpler subproblems.

Identifing Atmospheric Pollutant Sources Using Artificial Neural Networks

NASA Astrophysics Data System (ADS)

Paes, F. F.; Campos, H. F.; Luz, E. P.; Carvalho, A. R.

2008-05-01

The estimation of the area source pollutant strength is a relevant issue for atmospheric environment. This characterizes an inverse problem in the atmospheric pollution dispersion. In the inverse analysis, an area source domain is considered, where the strength of such area source term is assumed unknown. The inverse problem is solved by using a supervised artificial neural network: multi-layer perceptron. The conection weights of the neural network are computed from delta rule - learning process. The neural network inversion is compared with results from standard inverse analysis (regularized inverse solution). In the regularization method, the inverse problem is formulated as a non-linear optimization approach, whose the objective function is given by the square difference between the measured pollutant concentration and the mathematical models, associated with a regularization operator. In our numerical experiments, the forward problem is addressed by a source-receptor scheme, where a regressive Lagrangian model is applied to compute the transition matrix. The second order maximum entropy regularization is used, and the regularization parameter is calculated by the L-curve technique. The objective function is minimized employing a deterministic scheme (a quasi-Newton algorithm) [1] and a stochastic technique (PSO: particle swarm optimization) [2]. The inverse problem methodology is tested with synthetic observational data, from six measurement points in the physical domain. The best inverse solutions were obtained with neural networks. References: [1] D. R. Roberti, D. Anfossi, H. F. Campos Velho, G. A. Degrazia (2005): Estimating Emission Rate and Pollutant Source Location, Ciencia e Natura, p. 131-134. [2] E.F.P. da Luz, H.F. de Campos Velho, J.C. Becceneri, D.R. Roberti (2007): Estimating Atmospheric Area Source Strength Through Particle Swarm Optimization. Inverse Problems, Desing and Optimization Symposium IPDO-2007, April 16-18, Miami (FL), USA, vol 1, p. 354-359.

Simulation of low clouds in the Southeast Pacific by the NCEP GFS: sensitivity to vertical mixing

NASA Astrophysics Data System (ADS)

Sun, R.; Moorthi, S.; Xiao, H.; Mechoso, C. R.

2010-12-01

The NCEP Global Forecast System (GFS) model has an important systematic error shared by many other models: stratocumuli are missed over the subtropical eastern oceans. It is shown that this error can be alleviated in the GFS by introducing a consideration of the low-level inversion and making two modifications in the model's representation of vertical mixing. The modifications consist of (a) the elimination of background vertical diffusion above the inversion and (b) the incorporation of a stability parameter based on the cloud-top entrainment instability (CTEI) criterion, which limits the strength of shallow convective mixing across the inversion. A control simulation and three experiments are performed in order to examine both the individual and combined effects of modifications on the generation of the stratocumulus clouds. Individually, both modifications result in enhanced cloudiness in the Southeast Pacific (SEP) region, although the cloudiness is still low compared to the ISCCP climatology. If the modifications are applied together, however, the total cloudiness produced in the southeast Pacific has realistic values. This nonlinearity arises as the effects of both modifications reinforce each other in reducing the leakage of moisture across the inversion. Increased moisture trapped below the inversion than in the control run without modifications leads to an increase in cloud amount and cloud-top radiative cooling. Then a positive feedback due to enhanced turbulent mixing in the planetary boundary layer by cloud-top radiative cooling leads to and maintains the stratocumulus cover. Although the amount of total cloudiness obtained with both modifications has realistic values, the relative contributions of low, middle, and high layers tend to differ from the observations. These results demonstrate that it is possible to simulate realistic marine boundary clouds in large-scale models by implementing direct and physically based improvements in the model parameterizations.

Simulation of low clouds in the Southeast Pacific by the NCEP GFS: sensitivity to vertical mixing

NASA Astrophysics Data System (ADS)

Sun, R.; Moorthi, S.; Xiao, H.; Mechoso, C.-R.

2010-08-01

The NCEP Global Forecast System (GFS) model has an important systematic error shared by many other models: stratocumuli are missed over the subtropical eastern oceans. It is shown that this error can be alleviated in the GFS by introducing a consideration of the low-level inversion and making two modifications in the model's representation of vertical mixing. The modifications consist of (a) the elimination of background vertical diffusion above the inversion and (b) the incorporation of a stability parameter based on the cloud-top entrainment instability (CTEI) criterion, which limits the strength of shallow convective mixing across the inversion. A control simulation and three experiments are performed in order to examine both the individual and combined effects of modifications on the generation of the stratocumulus clouds. Individually, both modifications result in enhanced cloudiness in the Southeast Pacific (SEP) region, although the cloudiness is still low compared to the ISCCP climatology. If the modifications are applied together, however, the total cloudiness produced in the southeast Pacific has realistic values. This nonlinearity arises as the effects of both modifications reinforce each other in reducing the leakage of moisture across the inversion. Increased moisture trapped below the inversion than in the control run without modifications leads to an increase in cloud amount and cloud-top radiative cooling. Then a positive feedback due to enhanced turbulent mixing in the planetary boundary layer by cloud-top radiative cooling leads to and maintains the stratocumulus cover. Although the amount of total cloudiness obtained with both modifications has realistic values, the relative contributions of low, middle, and high layers tend to differ from the observations. These results demonstrate that it is possible to simulate realistic marine boundary clouds in large-scale models by implementing direct and physically based improvements in the model parameterizations.

Estimation of the vertical profile of sulfur dioxide injection into the atmosphere by a volcanic eruption using satellite column measurements and inverse transport modeling

NASA Astrophysics Data System (ADS)

Eckhardt, S.; Prata, A. J.; Seibert, P.; Stebel, K.; Stohl, A.

2008-07-01

An analytical inversion method has been developed to estimate the vertical profile of SO2 emissions from volcanic eruptions. The method uses satellite-observed total SO2 columns and an atmospheric transport model (FLEXPART) to exploit the fact that winds change with altitude thus, the position and shape of the volcanic plume bear information on its emission altitude. The method finds the vertical emission distribution which minimizes the total difference between simulated and observed SO2 columns while also considering a priori information. We have tested the method with the eruption of Jebel at Tair, Yemen, on 30 September 2007 for which a comprehensive observational data set from various satellite instruments (AIRS, OMI, SEVIRI, CALIPSO) is available. Using satellite data from the first 24 h after the eruption for the inversion, we found an emission maximum near 16 km above sea level (a.s.l.), and secondary maxima near 5, 9, 12 and 14 km a.s.l. 60% of the emission occurred above the tropopause. The emission profile obtained in the inversion was then used to simulate the transport of the plume over the following week. The modeled plume agrees very well with SO2 total columns observed by OMI, and its altitude agrees with CALIPSO aerosol observations to within 1 2 km. The inversion result is robust against various changes in both the a priori and the observations. Even when using only SEVIRI data from the first 15 h after the eruption, the emission profile was reasonably well estimated. The method is computationally very fast. It is therefore suitable for implementation within an operational environment, such as the Volcanic Ash Advisory Centers, to predict the threat posed by volcanic ash for air traffic. It could also be helpful for assessing the sulfur input into the stratosphere, be it in the context of volcanic processes or also for proposed geo-engineering techniques to counteract global warming.

Inversion of Magnetic Measurements of the CHAMP Satellite Over the Pannonian Basin

NASA Technical Reports Server (NTRS)

Kis, K. I.; Taylor, P. T.; Wittmann, G.; Toronyi, B.; Puszta, S.

2011-01-01

The Pannonian Basin is a deep intra-continental basin that formed as part of the Alpine orogeny. In order to study the nature of the crustal basement we used the long-wavelength magnetic anomalies acquired by the CHAMP satellite. The anomalies were distributed in a spherical shell, some 107,927 data recorded between January 1 and December 31 of 2008. They covered the Pannonian Basin and its vicinity. These anomaly data were interpolated into a spherical grid of 0.5 x 0.5, at the elevation of 324 km by the Gaussian weight function. The vertical gradient of these total magnetic anomalies was also computed and mapped to the surface of a sphere at 324 km elevation. The former spherical anomaly data at 425 km altitude were downward continued to 324 km. To interpret these data at the elevation of 324 km we used an inversion method. A polygonal prism forward model was used for the inversion. The minimum problem was solved numerically by the Simplex and Simulated annealing methods; a L2 norm in the case of Gaussian distribution parameters and a L1 norm was used in the case of Laplace distribution parameters. We INTERPRET THAT the magnetic anomaly WAS produced by several sources and the effect of the sable magnetization of the exsolution of hemo-ilmenite minerals in the upper crustal metamorphic rocks.

Joint inversion of seismic refraction and resistivity data using layered models - applications to hydrogeology

NASA Astrophysics Data System (ADS)

Juhojuntti, N. G.; Kamm, J.

2010-12-01

We present a layered-model approach to joint inversion of shallow seismic refraction and resistivity (DC) data, which we believe is a seldom tested method of addressing the problem. This method has been developed as we believe that for shallow sedimentary environments (roughly <100 m depth) a model with a few layers and sharp layer boundaries better represents the subsurface than a smooth minimum-structure (grid) model. Due to the strong assumption our model parameterization implies on the subsurface, only a low number of well resolved model parameters has to be estimated, and provided that this assumptions holds our method can also be applied to other environments. We are using a least-squares inversion, with lateral smoothness constraints, allowing lateral variations in the seismic velocity and the resistivity but no vertical variations. One exception is a positive gradient in the seismic velocity in the uppermost layer in order to get diving rays (the refractions in the deeper layers are modeled as head waves). We assume no connection between seismic velocity and resistivity, and these parameters are allowed to vary individually within the layers. The layer boundaries are, however, common for both parameters. During the inversion lateral smoothing can be applied to the layer boundaries as well as to the seismic velocity and the resistivity. The number of layers is specified before the inversion, and typically we use models with three layers. Depending on the type of environment it is possible to apply smoothing either to the depth of the layer boundaries or to the thickness of the layers, although normally the former is used for shallow sedimentary environments. The smoothing parameters can be chosen independently for each layer. For the DC data we use a finite-difference algorithm to perform the forward modeling and to calculate the Jacobian matrix, while for the seismic data the corresponding entities are retrieved via ray-tracing, using components from the RAYINVR package. The modular layout of the code makes it straightforward to include other types of geophysical data, i.e. gravity. The code has been tested using synthetic examples with fairly simple 2D geometries, mainly for checking the validity of the calculations. The inversion generally converges towards the correct solution, although there could be stability problems if the starting model is too erroneous. We have also applied the code to field data from seismic refraction and multi-electrode resistivity measurements at typical sand-gravel groundwater reservoirs. The tests are promising, as the calculated depths agree fairly well with information from drilling and the velocity and resistivity values appear reasonable. Current work includes better regularization of the inversion as well as defining individual weight factors for the different datasets, as the present algorithm tends to constrain the depths mainly by using the seismic data. More complex synthetic examples will also be tested, including models addressing the seismic hidden-layer problem.

Implement Method for Automated Testing of Markov Chain Convergence into INVERSE for ORNL12-RS-108J: Advanced Multi-Dimensional Forward and Inverse Modeling

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

Bledsoe, Keith C.

2015-04-01

The DiffeRential Evolution Adaptive Metropolis (DREAM) method is a powerful optimization/uncertainty quantification tool used to solve inverse transport problems in Los Alamos National Laboratory’s INVERSE code system. The DREAM method has been shown to be adept at accurate uncertainty quantification, but it can be very computationally demanding. Previously, the DREAM method in INVERSE performed a user-defined number of particle transport calculations. This placed a burden on the user to guess the number of calculations that would be required to accurately solve any given problem. This report discusses a new approach that has been implemented into INVERSE, the Gelman-Rubin convergence metric.more » This metric automatically detects when an appropriate number of transport calculations have been completed and the uncertainty in the inverse problem has been accurately calculated. In a test problem with a spherical geometry, this method was found to decrease the number of transport calculations (and thus time required) to solve a problem by an average of over 90%. In a cylindrical test geometry, a 75% decrease was obtained.« less

Numerical Modeling of the Vertical Heat Transport Through the Diffusive Layer of the Arctic Ocean

DTIC Science & Technology

2013-03-01

vertical heat transport through Arctic thermohaline staircases over time . Re-engaging in the inverse modeling technique that was started by Chaplin ...reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instruction, searching...function. ........................................42 Figure 23. Temperature—Salinity plots for ITPs 1-6 (After Chaplin 2009

Improved Abel transform inversion: First application to COSMIC/FORMOSAT-3

NASA Astrophysics Data System (ADS)

Aragon-Angel, A.; Hernandez-Pajares, M.; Juan, J.; Sanz, J.

2007-05-01

In this paper the first results of Ionospheric Tomographic inversion are presented, using the Improved Abel Transform on the COSMIC/FORMOSAT-3 constellation of 6 LEO satellites, carrying on-board GPS receivers.[- 4mm] The Abel transform inversion is a wide used technique which in the ionospheric context makes it possible to retrieve electron densities as a function of height based of STEC (Slant Total Electron Content) data gathered from GPS receivers on board of LEO (Low Earth Orbit) satellites. Within this precise use, the classical approach of the Abel inversion is based on the assumption of spherical symmetry of the electron density in the vicinity of an occultation, meaning that the electron content varies in height but not horizontally. In particular, one implication of this assumption is that the VTEC (Vertical Total Electron Content) is a constant value for the occultation region. This assumption may not always be valid since horizontal ionospheric gradients (a very frequent feature in some ionosphere problematic areas such as the Equatorial region) could significantly affect the electron profiles. [- 4mm] In order to overcome this limitation/problem of the classical Abel inversion, a studied improvement of this technique can be obtained by assuming separability in the electron density (see Hernández-Pajares et al. 2000). This means that the electron density can be expressed by the multiplication of VTEC data and a shape function which assumes all the height dependency in it while the VTEC data keeps the horizontal dependency. Actually, it is more realistic to assume that this shape fuction depends only on the height and to use VTEC information to take into account the horizontal variation rather than considering spherical symmetry in the electron density function as it has been carried out in the classical approach of the Abel inversion.[-4mm] Since the above mentioned improved Abel inversion technique has already been tested and proven to be a useful tool to obtain a vertical description of the ionospheric electron density (see García-Fernández et al. 2003), a natural following step would be to extend the use of this technique to the recently available COSMIC data. The COSMIC satellite constellation, formed by 6 micro-satellites, is being deployed since April 2006 in circular orbit around the Earth, with a final altitude of about 700-800 kilometers. Its global and almost uniform coverage will overcome one of the main limitations of this technique which is the sparcity of data, related to lack of GPS receivers in some regions. This can significantly stimulate the development of radio occultation techniques with the use of the huge volume of data provided by the COSMIC constellation to be processed and analysed updating the current knowledge of the Ionospheres nature and behaviour. In this context a summary of the Improvel Abel transform inversion technique and the first results based on COSMIC constellation data will be presented. Moreover, future improvements, taking into account the higher temporal and global spatial coverage, will be discussed. [-4mm] References:M. Hernández-Pajares, J. M. Juan and J. Sanz, Improving the Abel inversion by adding ground GPS data to LEO radio occultations in ionospheric sounding, GEOPHYSICAL RESEARCH LETTERS, VOL. 27, NO. 16, PAGES 2473-2476, AUGUST 15, 2000.M. Garcia-Fernández, M. Hernández-Pajares, M. Juan, and J. Sanz, Improvement of ionospheric electron density estimation with GPSMET occultations using Abel inversion and VTEC Information, JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. A9, 1338, doi:10.1029/2003JA009952, 2003

The role of military footwear and workload on ground reaction forces during a simulated lateral ankle sprain mechanism.

PubMed

Simpson, Jeffrey D; DeBusk, Hunter; Hill, Christopher; Knight, Adam; Chander, Harish

2018-03-01

Ankle sprains are a common orthopedic injury in military populations, which may be attributed to occupational demands and footwear. Minimalist military boots have become popular, but their influence on ground reaction force (GRF) attenuation capabilities during an ankle inversion perturbation are unknown. Therefore, the purpose of this study was to examine potential differences in GRFs during an ankle inversion perturbation in a standard issue (STN) and minimalist military boot (MIN) before and after a simulated military workload. Twenty-one healthy adult males completed an ankle inversion perturbation protocol in each footwear condition before and after an incremental treadmill exercise protocol to volitional exhaustion while wearing a 16kg rucksack. The ankle inversion perturbation protocol consisted of stepping down from a 27cm box onto a force platform with a fulcrum (FUL), which created 25° of inversion upon landing, or flat (FLT) outer sole attached to the plantar aspect of the participants' footwear in random order. Peak vertical, anterior/posterior, and medial/lateral components of the GRF during FUL and FLT conditions were assessed, normalized to multiples of body weight in each footwear. Dependent variables were then analyzed using separate 2 (footwear)×2 (time) repeated measures ANOVA (p<0.05). The MIN footwear demonstrated significantly greater vertical GRF and significantly less medial GRF during the FUL condition. These results indicate that various mechanical and design characteristics of military footwear may influence GRF attenuation capabilities and ankle joint loading when the foot/ankle complex is forced into inversion. Copyright © 2017 Elsevier Ltd. All rights reserved.

Inverse Scattering Problem For The Schrödinger Equation With An Additional Quadratic Potential On The Entire Axis

NASA Astrophysics Data System (ADS)

Guseinov, I. M.; Khanmamedov, A. Kh.; Mamedova, A. F.

2018-04-01

We consider the Schrödinger equation with an additional quadratic potential on the entire axis and use the transformation operator method to study the direct and inverse problems of the scattering theory. We obtain the main integral equations of the inverse problem and prove that the basic equations are uniquely solvable.

Assessing non-uniqueness: An algebraic approach

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

Vasco, Don W.

Geophysical inverse problems are endowed with a rich mathematical structure. When discretized, most differential and integral equations of interest are algebraic (polynomial) in form. Techniques from algebraic geometry and computational algebra provide a means to address questions of existence and uniqueness for both linear and non-linear inverse problem. In a sense, the methods extend ideas which have proven fruitful in treating linear inverse problems.

Relationship between strong-motion array parameters and the accuracy of source inversion and physical waves

USGS Publications Warehouse

Iida, M.; Miyatake, T.; Shimazaki, K.

1990-01-01

We develop general rules for a strong-motion array layout on the basis of our method of applying a prediction analysis to a source inversion scheme. A systematic analysis is done to obtain a relationship between fault-array parameters and the accuracy of a source inversion. Our study of the effects of various physical waves indicates that surface waves at distant stations contribute significantly to the inversion accuracy for the inclined fault plane, whereas only far-field body waves at both small and large distances contribute to the inversion accuracy for the vertical fault, which produces more phase interference. These observations imply the adequacy of the half-space approximation used throughout our present study and suggest rules for actual array designs. -from Authors

Small-scale Scheimpflug lidar for aerosol extinction coefficient and vertical atmospheric transmittance detection.

PubMed

Sun, Guodong; Qin, Laian; Hou, Zaihong; Jing, Xu; He, Feng; Tan, Fengfu; Zhang, Silong

2018-03-19

In this paper, a new prototypical Scheimpflug lidar capable of detecting the aerosol extinction coefficient and vertical atmospheric transmittance at 1 km above the ground is described. The lidar system operates at 532 nm and can be used to detect aerosol extinction coefficients throughout an entire day. Then, the vertical atmospheric transmittance can be determined from the extinction coefficients with the equation of numerical integration in this area. CCD flat fielding of the image data is used to mitigate the effects of pixel sensitivity variation. An efficient method of two-dimensional wavelet transform according to a local threshold value has been proposed to reduce the Gaussian white noise in the lidar signal. Furthermore, a new iteration method of backscattering ratio based on genetic algorithm is presented to calculate the aerosol extinction coefficient and vertical atmospheric transmittance. Some simulations are performed to reduce the different levels of noise in the simulated signal in order to test the precision of the de-noising method and inversion algorithm. The simulation result shows that the root-mean-square errors of extinction coefficients are all less than 0.02 km -1 , and that the relative errors of the atmospheric transmittance between the model and inversion data are below 0.56% for all cases. The feasibility of the instrument and the inversion algorithm have also been verified by an optical experiment. The average relative errors of aerosol extinction coefficients between the Scheimpflug lidar and the conventional backscattering elastic lidar are 3.54% and 2.79% in the full overlap heights of two time points, respectively. This work opens up new possibilities of using a small-scale Scheimpflug lidar system for the remote sensing of atmospheric aerosols.

Microtremor exploration for shallow S-wave velocity structure in Bandung Basin, Indonesia

NASA Astrophysics Data System (ADS)

Pramatadie, Andi Muhamad; Yamanaka, Hiroaki; Chimoto, Kosuke; Afnimar Collaboration; Koketsu, Kazuki; Sakaue, Minoru; Miyake, Hiroe; Sengara, I. Wayan; Sadisun, Imam A.

2017-05-01

We have conducted a microtremor survey for shallow S-wave velocity profiles to be used for seismic hazard evaluation in the Bandung Basin, Indonesia. In the survey, two arrays were deployed temporarily at each of 29 sites, by installing seven vertical sensors in triangular configurations with side lengths from 1 to 16 m. Records of vertical microtremors from each array were used to estimate Rayleigh wave phase velocity spectra using the spatial autocorrelation method, as well as the horizontal-to-vertical spectral ratio obtained at the centre of the arrays. Phase velocities at sites on the basin margin exhibit higher values than those obtained in the central part of the basin, in a frequency range of 7 to 30 Hz. The phase velocity data were used to deduce S-wave velocity profiles of shallow soil using a hybrid heuristic inversion method. We validated our inversion models by comparing observed horizontal-to-vertical spectral ratios with ellipticities of the fundamental mode of Rayleigh waves, calculated for the inversion models. The S-wave velocity profiles in the area can be characterised by two soft layers over a firm engineering basement that has an S-wave velocity of 500 m/s. The S-wave velocities of the two layers are 120 and 280 m/s on average. The distribution of the averaged S-wave velocity in the top 30 m clearly indicates low values in the eastern central part and high values in the edge of the basin. The amplification is large in the areas with low velocity layers. In addition, we have proposed an empirical relation between the amplification factor and the topographical slope in the area.

Effect of bird maneuver on frequency-domain helicopter EM response

USGS Publications Warehouse

Fitterman, D.V.; Yin, C.

2004-01-01

Bird maneuver, the rotation of the coil-carrying instrument pod used for frequency-domain helicopter electromagnetic surveys, changes the nominal geometric relationship between the bird-coil system and the ground. These changes affect electromagnetic coupling and can introduce errors in helicopter electromagnetic, (HEM) data. We analyze these effects for a layered half-space for three coil configurations: vertical coaxial, vertical coplanar, and horizontal coplanar. Maneuver effect is shown to have two components: one that is purely geometric and another that is inductive in nature. The geometric component is significantly larger. A correction procedure is developed using an iterative approach that uses standard HEM inversion routines. The maneuver effect correction reduces inversion misfit error and produces laterally smoother cross sections than obtained from uncorrected data. ?? 2004 Society of Exploration Geophysicists. All rights reserved.

The inverse problem of refraction travel times, part I: Types of Geophysical Nonuniqueness through Minimization

USGS Publications Warehouse

Ivanov, J.; Miller, R.D.; Xia, J.; Steeples, D.; Park, C.B.

2005-01-01

In a set of two papers we study the inverse problem of refraction travel times. The purpose of this work is to use the study as a basis for development of more sophisticated methods for finding more reliable solutions to the inverse problem of refraction travel times, which is known to be nonunique. The first paper, "Types of Geophysical Nonuniqueness through Minimization," emphasizes the existence of different forms of nonuniqueness in the realm of inverse geophysical problems. Each type of nonuniqueness requires a different type and amount of a priori information to acquire a reliable solution. Based on such coupling, a nonuniqueness classification is designed. Therefore, since most inverse geophysical problems are nonunique, each inverse problem must be studied to define what type of nonuniqueness it belongs to and thus determine what type of a priori information is necessary to find a realistic solution. The second paper, "Quantifying Refraction Nonuniqueness Using a Three-layer Model," serves as an example of such an approach. However, its main purpose is to provide a better understanding of the inverse refraction problem by studying the type of nonuniqueness it possesses. An approach for obtaining a realistic solution to the inverse refraction problem is planned to be offered in a third paper that is in preparation. The main goal of this paper is to redefine the existing generalized notion of nonuniqueness and a priori information by offering a classified, discriminate structure. Nonuniqueness is often encountered when trying to solve inverse problems. However, possible nonuniqueness diversity is typically neglected and nonuniqueness is regarded as a whole, as an unpleasant "black box" and is approached in the same manner by applying smoothing constraints, damping constraints with respect to the solution increment and, rarely, damping constraints with respect to some sparse reference information about the true parameters. In practice, when solving geophysical problems different types of nonuniqueness exist, and thus there are different ways to solve the problems. Nonuniqueness is usually regarded as due to data error, assuming the true geology is acceptably approximated by simple mathematical models. Compounding the nonlinear problems, geophysical applications routinely exhibit exact-data nonuniqueness even for models with very few parameters adding to the nonuniqueness due to data error. While nonuniqueness variations have been defined earlier, they have not been linked to specific use of a priori information necessary to resolve each case. Four types of nonuniqueness, typical for minimization problems are defined with the corresponding methods for inclusion of a priori information to find a realistic solution without resorting to a non-discriminative approach. The above-developed stand-alone classification is expected to be helpful when solving any geophysical inverse problems. ?? Birkha??user Verlag, Basel, 2005.

Computational methods for inverse problems in geophysics: inversion of travel time observations

USGS Publications Warehouse

Pereyra, V.; Keller, H.B.; Lee, W.H.K.

1980-01-01

General ways of solving various inverse problems are studied for given travel time observations between sources and receivers. These problems are separated into three components: (a) the representation of the unknown quantities appearing in the model; (b) the nonlinear least-squares problem; (c) the direct, two-point ray-tracing problem used to compute travel time once the model parameters are given. Novel software is described for (b) and (c), and some ideas given on (a). Numerical results obtained with artificial data and an implementation of the algorithm are also presented. ?? 1980.

A fixed energy fixed angle inverse scattering in interior transmission problem

NASA Astrophysics Data System (ADS)

Chen, Lung-Hui

2017-06-01

We study the inverse acoustic scattering problem in mathematical physics. The problem is to recover the index of refraction in an inhomogeneous medium by measuring the scattered wave fields in the far field. We transform the problem to the interior transmission problem in the study of the Helmholtz equation. We find an inverse uniqueness on the scatterer with a knowledge of a fixed interior transmission eigenvalue. By examining the solution in a series of spherical harmonics in the far field, we can determine uniquely the perturbation source for the radially symmetric perturbations.

Total-variation based velocity inversion with Bregmanized operator splitting algorithm

NASA Astrophysics Data System (ADS)

Zand, Toktam; Gholami, Ali

2018-04-01

Many problems in applied geophysics can be formulated as a linear inverse problem. The associated problems, however, are large-scale and ill-conditioned. Therefore, regularization techniques are needed to be employed for solving them and generating a stable and acceptable solution. We consider numerical methods for solving such problems in this paper. In order to tackle the ill-conditioning of the problem we use blockiness as a prior information of the subsurface parameters and formulate the problem as a constrained total variation (TV) regularization. The Bregmanized operator splitting (BOS) algorithm as a combination of the Bregman iteration and the proximal forward backward operator splitting method is developed to solve the arranged problem. Two main advantages of this new algorithm are that no matrix inversion is required and that a discrepancy stopping criterion is used to stop the iterations, which allow efficient solution of large-scale problems. The high performance of the proposed TV regularization method is demonstrated using two different experiments: 1) velocity inversion from (synthetic) seismic data which is based on Born approximation, 2) computing interval velocities from RMS velocities via Dix formula. Numerical examples are presented to verify the feasibility of the proposed method for high-resolution velocity inversion.

Analytical and numerical analysis of inverse optimization problems: conditions of uniqueness and computational methods

PubMed Central

Zatsiorsky, Vladimir M.

2011-01-01

One of the key problems of motor control is the redundancy problem, in particular how the central nervous system (CNS) chooses an action out of infinitely many possible. A promising way to address this question is to assume that the choice is made based on optimization of a certain cost function. A number of cost functions have been proposed in the literature to explain performance in different motor tasks: from force sharing in grasping to path planning in walking. However, the problem of uniqueness of the cost function(s) was not addressed until recently. In this article, we analyze two methods of finding additive cost functions in inverse optimization problems with linear constraints, so-called linear-additive inverse optimization problems. These methods are based on the Uniqueness Theorem for inverse optimization problems that we proved recently (Terekhov et al., J Math Biol 61(3):423–453, 2010). Using synthetic data, we show that both methods allow for determining the cost function. We analyze the influence of noise on the both methods. Finally, we show how a violation of the conditions of the Uniqueness Theorem may lead to incorrect solutions of the inverse optimization problem. PMID:21311907

The neural network approximation method for solving multidimensional nonlinear inverse problems of geophysics

NASA Astrophysics Data System (ADS)

Shimelevich, M. I.; Obornev, E. A.; Obornev, I. E.; Rodionov, E. A.

2017-07-01

The iterative approximation neural network method for solving conditionally well-posed nonlinear inverse problems of geophysics is presented. The method is based on the neural network approximation of the inverse operator. The inverse problem is solved in the class of grid (block) models of the medium on a regularized parameterization grid. The construction principle of this grid relies on using the calculated values of the continuity modulus of the inverse operator and its modifications determining the degree of ambiguity of the solutions. The method provides approximate solutions of inverse problems with the maximal degree of detail given the specified degree of ambiguity with the total number of the sought parameters n × 103 of the medium. The a priori and a posteriori estimates of the degree of ambiguity of the approximated solutions are calculated. The work of the method is illustrated by the example of the three-dimensional (3D) inversion of the synthesized 2D areal geoelectrical (audio magnetotelluric sounding, AMTS) data corresponding to the schematic model of a kimberlite pipe.

Geostatistical regularization operators for geophysical inverse problems on irregular meshes

NASA Astrophysics Data System (ADS)

Jordi, C.; Doetsch, J.; Günther, T.; Schmelzbach, C.; Robertsson, J. OA

2018-05-01

Irregular meshes allow to include complicated subsurface structures into geophysical modelling and inverse problems. The non-uniqueness of these inverse problems requires appropriate regularization that can incorporate a priori information. However, defining regularization operators for irregular discretizations is not trivial. Different schemes for calculating smoothness operators on irregular meshes have been proposed. In contrast to classical regularization constraints that are only defined using the nearest neighbours of a cell, geostatistical operators include a larger neighbourhood around a particular cell. A correlation model defines the extent of the neighbourhood and allows to incorporate information about geological structures. We propose an approach to calculate geostatistical operators for inverse problems on irregular meshes by eigendecomposition of a covariance matrix that contains the a priori geological information. Using our approach, the calculation of the operator matrix becomes tractable for 3-D inverse problems on irregular meshes. We tested the performance of the geostatistical regularization operators and compared them against the results of anisotropic smoothing in inversions of 2-D surface synthetic electrical resistivity tomography (ERT) data as well as in the inversion of a realistic 3-D cross-well synthetic ERT scenario. The inversions of 2-D ERT and seismic traveltime field data with geostatistical regularization provide results that are in good accordance with the expected geology and thus facilitate their interpretation. In particular, for layered structures the geostatistical regularization provides geologically more plausible results compared to the anisotropic smoothness constraints.

FOREWORD: 4th International Workshop on New Computational Methods for Inverse Problems (NCMIP2014)

NASA Astrophysics Data System (ADS)

2014-10-01

This volume of Journal of Physics: Conference Series is dedicated to the scientific contributions presented during the 4th International Workshop on New Computational Methods for Inverse Problems, NCMIP 2014 (http://www.farman.ens-cachan.fr/NCMIP_2014.html). This workshop took place at Ecole Normale Supérieure de Cachan, on May 23, 2014. The prior editions of NCMIP also took place in Cachan, France, firstly within the scope of ValueTools Conference, in May 2011 (http://www.ncmip.org/2011/), and secondly at the initiative of Institut Farman, in May 2012 and May 2013, (http://www.farman.ens-cachan.fr/NCMIP_2012.html), (http://www.farman.ens-cachan.fr/NCMIP_2013.html). The New Computational Methods for Inverse Problems (NCMIP) Workshop focused on recent advances in the resolution of inverse problems. Indeed, inverse problems appear in numerous scientific areas such as geophysics, biological and medical imaging, material and structure characterization, electrical, mechanical and civil engineering, and finances. The resolution of inverse problems consists of estimating the parameters of the observed system or structure from data collected by an instrumental sensing or imaging device. Its success firstly requires the collection of relevant observation data. It also requires accurate models describing the physical interactions between the instrumental device and the observed system, as well as the intrinsic properties of the solution itself. Finally, it requires the design of robust, accurate and efficient inversion algorithms. Advanced sensor arrays and imaging devices provide high rate and high volume data; in this context, the efficient resolution of the inverse problem requires the joint development of new models and inversion methods, taking computational and implementation aspects into account. During this one-day workshop, researchers had the opportunity to bring to light and share new techniques and results in the field of inverse problems. The topics of the workshop were: algorithms and computational aspects of inversion, Bayesian estimation, Kernel methods, learning methods, convex optimization, free discontinuity problems, metamodels, proper orthogonal decomposition, reduced models for the inversion, non-linear inverse scattering, image reconstruction and restoration, and applications (bio-medical imaging, non-destructive evaluation...). NCMIP 2014 was a one-day workshop held in May 2014 which attracted around sixty attendees. Each of the submitted papers has been reviewed by two reviewers. There have been nine accepted papers. In addition, three international speakers were invited to present a longer talk. The workshop was supported by Institut Farman (ENS Cachan, CNRS) and endorsed by the following French research networks (GDR ISIS, GDR MIA, GDR MOA, GDR Ondes). The program committee acknowledges the following research laboratories: CMLA, LMT, LURPA, SATIE. Eric Vourc'h and Thomas Rodet

Inverse problems in the design, modeling and testing of engineering systems

NASA Technical Reports Server (NTRS)

Alifanov, Oleg M.

1991-01-01

Formulations, classification, areas of application, and approaches to solving different inverse problems are considered for the design of structures, modeling, and experimental data processing. Problems in the practical implementation of theoretical-experimental methods based on solving inverse problems are analyzed in order to identify mathematical models of physical processes, aid in input data preparation for design parameter optimization, help in design parameter optimization itself, and to model experiments, large-scale tests, and real tests of engineering systems.

Determining the near-surface current profile from measurements of the wave dispersion relation

NASA Astrophysics Data System (ADS)

Smeltzer, Benjamin; Maxwell, Peter; Aesøy, Eirik; Ellingsen, Simen

2017-11-01

The current-induced Doppler shifts of waves can yield information about the background mean flow, providing an attractive method of inferring the current profile in the upper layer of the ocean. We present measurements of waves propagating on shear currents in a laboratory water channel, as well as theoretical investigations of inversion techniques for determining the vertical current structure. Spatial and temporal measurements of the free surface profile obtained using a synthetic Schlieren method are analyzed to determine the wave dispersion relation and Doppler shifts as a function of wavelength. The vertical current profile can then be inferred from the Doppler shifts using an inversion algorithm. Most existing algorithms rely on a priori assumptions of the shape of the current profile, and developing a method that uses less stringent assumptions is a focus of this study, allowing for measurement of more general current profiles. The accuracy of current inversion algorithms are evaluated by comparison to measurements of the mean flow profile from particle image velocimetry (PIV), and a discussion of the sensitivity to errors in the Doppler shifts is presented.

A computationally efficient parallel Levenberg-Marquardt algorithm for highly parameterized inverse model analyses

NASA Astrophysics Data System (ADS)

Lin, Youzuo; O'Malley, Daniel; Vesselinov, Velimir V.

2016-09-01

Inverse modeling seeks model parameters given a set of observations. However, for practical problems because the number of measurements is often large and the model parameters are also numerous, conventional methods for inverse modeling can be computationally expensive. We have developed a new, computationally efficient parallel Levenberg-Marquardt method for solving inverse modeling problems with a highly parameterized model space. Levenberg-Marquardt methods require the solution of a linear system of equations which can be prohibitively expensive to compute for moderate to large-scale problems. Our novel method projects the original linear problem down to a Krylov subspace such that the dimensionality of the problem can be significantly reduced. Furthermore, we store the Krylov subspace computed when using the first damping parameter and recycle the subspace for the subsequent damping parameters. The efficiency of our new inverse modeling algorithm is significantly improved using these computational techniques. We apply this new inverse modeling method to invert for random transmissivity fields in 2-D and a random hydraulic conductivity field in 3-D. Our algorithm is fast enough to solve for the distributed model parameters (transmissivity) in the model domain. The algorithm is coded in Julia and implemented in the MADS computational framework (http://mads.lanl.gov). By comparing with Levenberg-Marquardt methods using standard linear inversion techniques such as QR or SVD methods, our Levenberg-Marquardt method yields a speed-up ratio on the order of ˜101 to ˜102 in a multicore computational environment. Therefore, our new inverse modeling method is a powerful tool for characterizing subsurface heterogeneity for moderate to large-scale problems.

Effects of multiple scattering and surface albedo on the photochemistry of the troposphere

NASA Technical Reports Server (NTRS)

Augustsson, T. R.; Tiwari, S. N.

1981-01-01

The effect of treatment of incoming solar radiation on the photochemistry of the troposphere is discussed. A one dimensional photochemical model of the troposphere containing the species of the nitrogen, oxygen, carbon, hydrogen, and sulfur families was developed. The vertical flux is simulated by use of the parameterized eddy diffusion coefficients. The photochemical model is coupled to a radiative transfer model that calculates the radiation field due to the incoming solar radiation which initiates much of the photochemistry of the troposphere. Vertical profiles of tropospheric species were compared with the Leighton approximation, radiative transfer, matrix inversion model. The radiative transfer code includes the effects of multiple scattering due to molecules and aerosols, pure absorption, and surface albedo on the transfer of incoming solar radiation. It is indicated that significant differences exist for several key photolysis frequencies and species number density profiles between the Leighton approximation and the profiles generated with, radiative transfer, matrix inversion technique. Most species show enhanced vertical profiles when the more realistic treatment of the incoming solar radiation field is included

Effects of multiple scattering and surface albedo on the photochemistry of the troposphere. Final report, period ending 30 Nov 1981

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

Augustsson, T.R.; Tiwari, S.N.

The effect of treatment of incoming solar radiation on the photochemistry of the troposphere is discussed. A one dimensional photochemical model of the troposphere containing the species of the nitrogen, oxygen, carbon, hydrogen, and sulfur families was developed. The vertical flux is simulated by use of the parameterized eddy diffusion coefficients. The photochemical model is coupled to a radiative transfer model that calculates the radiation field due to the incoming solar radiation which initiates much of the photochemistry of the troposphere. Vertical profiles of tropospheric species were compared with the Leighton approximation, radiative transfer, matrix inversion model. The radiative transfermore » code includes the effects of multiple scattering due to molecules and aerosols, pure absorption, and surface albedo on the transfer of incoming solar radiation. It is indicated that significant differences exist for several key photolysis frequencies and species number density profiles between the Leighton approximation and the profiles generated with, radiative transfer, matrix inversion technique. Most species show enhanced vertical profiles when the more realistic treatment of the incoming solar radiation field is included« less

Solving geosteering inverse problems by stochastic Hybrid Monte Carlo method

DOE PAGES

Shen, Qiuyang; Wu, Xuqing; Chen, Jiefu; ...

2017-11-20

The inverse problems arise in almost all fields of science where the real-world parameters are extracted from a set of measured data. The geosteering inversion plays an essential role in the accurate prediction of oncoming strata as well as a reliable guidance to adjust the borehole position on the fly to reach one or more geological targets. This mathematical treatment is not easy to solve, which requires finding an optimum solution among a large solution space, especially when the problem is non-linear and non-convex. Nowadays, a new generation of logging-while-drilling (LWD) tools has emerged on the market. The so-called azimuthalmore » resistivity LWD tools have azimuthal sensitivity and a large depth of investigation. Hence, the associated inverse problems become much more difficult since the earth model to be inverted will have more detailed structures. The conventional deterministic methods are incapable to solve such a complicated inverse problem, where they suffer from the local minimum trap. Alternatively, stochastic optimizations are in general better at finding global optimal solutions and handling uncertainty quantification. In this article, we investigate the Hybrid Monte Carlo (HMC) based statistical inversion approach and suggest that HMC based inference is more efficient in dealing with the increased complexity and uncertainty faced by the geosteering problems.« less

Using a derivative-free optimization method for multiple solutions of inverse transport problems

DOE PAGES

Armstrong, Jerawan C.; Favorite, Jeffrey A.

2016-01-14

Identifying unknown components of an object that emits radiation is an important problem for national and global security. Radiation signatures measured from an object of interest can be used to infer object parameter values that are not known. This problem is called an inverse transport problem. An inverse transport problem may have multiple solutions and the most widely used approach for its solution is an iterative optimization method. This paper proposes a stochastic derivative-free global optimization algorithm to find multiple solutions of inverse transport problems. The algorithm is an extension of a multilevel single linkage (MLSL) method where a meshmore » adaptive direct search (MADS) algorithm is incorporated into the local phase. Furthermore, numerical test cases using uncollided fluxes of discrete gamma-ray lines are presented to show the performance of this new algorithm.« less

A novel and generalized approach in the inversion of geoelectrical resistivity data using Artificial Neural Networks (ANN)

NASA Astrophysics Data System (ADS)

Raj, A. Stanley; Srinivas, Y.; Oliver, D. Hudson; Muthuraj, D.

2014-03-01

The non-linear apparent resistivity problem in the subsurface study of the earth takes into account the model parameters in terms of resistivity and thickness of individual subsurface layers using the trained synthetic data by means of Artificial Neural Networks (ANN). Here we used a single layer feed-forward neural network with fast back propagation learning algorithm. So on proper training of back propagation networks it tends to give the resistivity and thickness of the subsurface layer model of the field resistivity data with reference to the synthetic data trained in the appropriate network. During training, the weights and biases of the network are iteratively adjusted to make network performance function level more efficient. On adequate training, errors are minimized and the best result is obtained using the artificial neural networks. The network is trained with more number of VES data and this trained network is demonstrated by the field data. The accuracy of inversion depends upon the number of data trained. In this novel and specially designed algorithm, the interpretation of the vertical electrical sounding has been done successfully with the more accurate layer model.

Frnakenstein: multiple target inverse RNA folding.

PubMed

Lyngsø, Rune B; Anderson, James W J; Sizikova, Elena; Badugu, Amarendra; Hyland, Tomas; Hein, Jotun

2012-10-09

RNA secondary structure prediction, or folding, is a classic problem in bioinformatics: given a sequence of nucleotides, the aim is to predict the base pairs formed in its three dimensional conformation. The inverse problem of designing a sequence folding into a particular target structure has only more recently received notable interest. With a growing appreciation and understanding of the functional and structural properties of RNA motifs, and a growing interest in utilising biomolecules in nano-scale designs, the interest in the inverse RNA folding problem is bound to increase. However, whereas the RNA folding problem from an algorithmic viewpoint has an elegant and efficient solution, the inverse RNA folding problem appears to be hard. In this paper we present a genetic algorithm approach to solve the inverse folding problem. The main aims of the development was to address the hitherto mostly ignored extension of solving the inverse folding problem, the multi-target inverse folding problem, while simultaneously designing a method with superior performance when measured on the quality of designed sequences. The genetic algorithm has been implemented as a Python program called Frnakenstein. It was benchmarked against four existing methods and several data sets totalling 769 real and predicted single structure targets, and on 292 two structure targets. It performed as well as or better at finding sequences which folded in silico into the target structure than all existing methods, without the heavy bias towards CG base pairs that was observed for all other top performing methods. On the two structure targets it also performed well, generating a perfect design for about 80% of the targets. Our method illustrates that successful designs for the inverse RNA folding problem does not necessarily have to rely on heavy biases in base pair and unpaired base distributions. The design problem seems to become more difficult on larger structures when the target structures are real structures, while no deterioration was observed for predicted structures. Design for two structure targets is considerably more difficult, but far from impossible, demonstrating the feasibility of automated design of artificial riboswitches. The Python implementation is available at http://www.stats.ox.ac.uk/research/genome/software/frnakenstein.

Frnakenstein: multiple target inverse RNA folding

PubMed Central

2012-01-01

Background RNA secondary structure prediction, or folding, is a classic problem in bioinformatics: given a sequence of nucleotides, the aim is to predict the base pairs formed in its three dimensional conformation. The inverse problem of designing a sequence folding into a particular target structure has only more recently received notable interest. With a growing appreciation and understanding of the functional and structural properties of RNA motifs, and a growing interest in utilising biomolecules in nano-scale designs, the interest in the inverse RNA folding problem is bound to increase. However, whereas the RNA folding problem from an algorithmic viewpoint has an elegant and efficient solution, the inverse RNA folding problem appears to be hard. Results In this paper we present a genetic algorithm approach to solve the inverse folding problem. The main aims of the development was to address the hitherto mostly ignored extension of solving the inverse folding problem, the multi-target inverse folding problem, while simultaneously designing a method with superior performance when measured on the quality of designed sequences. The genetic algorithm has been implemented as a Python program called Frnakenstein. It was benchmarked against four existing methods and several data sets totalling 769 real and predicted single structure targets, and on 292 two structure targets. It performed as well as or better at finding sequences which folded in silico into the target structure than all existing methods, without the heavy bias towards CG base pairs that was observed for all other top performing methods. On the two structure targets it also performed well, generating a perfect design for about 80% of the targets. Conclusions Our method illustrates that successful designs for the inverse RNA folding problem does not necessarily have to rely on heavy biases in base pair and unpaired base distributions. The design problem seems to become more difficult on larger structures when the target structures are real structures, while no deterioration was observed for predicted structures. Design for two structure targets is considerably more difficult, but far from impossible, demonstrating the feasibility of automated design of artificial riboswitches. The Python implementation is available at http://www.stats.ox.ac.uk/research/genome/software/frnakenstein. PMID:23043260

A multi-resolution approach to electromagnetic modeling.

NASA Astrophysics Data System (ADS)

Cherevatova, M.; Egbert, G. D.; Smirnov, M. Yu

2018-04-01

We present a multi-resolution approach for three-dimensional magnetotelluric forward modeling. Our approach is motivated by the fact that fine grid resolution is typically required at shallow levels to adequately represent near surface inhomogeneities, topography, and bathymetry, while a much coarser grid may be adequate at depth where the diffusively propagating electromagnetic fields are much smoother. This is especially true for forward modeling required in regularized inversion, where conductivity variations at depth are generally very smooth. With a conventional structured finite-difference grid the fine discretization required to adequately represent rapid variations near the surface are continued to all depths, resulting in higher computational costs. Increasing the computational efficiency of the forward modeling is especially important for solving regularized inversion problems. We implement a multi-resolution finite-difference scheme that allows us to decrease the horizontal grid resolution with depth, as is done with vertical discretization. In our implementation, the multi-resolution grid is represented as a vertical stack of sub-grids, with each sub-grid being a standard Cartesian tensor product staggered grid. Thus, our approach is similar to the octree discretization previously used for electromagnetic modeling, but simpler in that we allow refinement only with depth. The major difficulty arose in deriving the forward modeling operators on interfaces between adjacent sub-grids. We considered three ways of handling the interface layers and suggest a preferable one, which results in similar accuracy as the staggered grid solution, while retaining the symmetry of coefficient matrix. A comparison between multi-resolution and staggered solvers for various models show that multi-resolution approach improves on computational efficiency without compromising the accuracy of the solution.

First Calderón Prize

NASA Astrophysics Data System (ADS)

Rundell, William; Somersalo, Erkki

2008-07-01

The Inverse Problems International Association (IPIA) awarded the first Calderón Prize to Matti Lassas for his outstanding contributions to the field of inverse problems, especially in geometric inverse problems. The Calderón Prize is given to a researcher under the age of 40 who has made distinguished contributions to the field of inverse problems broadly defined. The first Calderón Prize Committee consisted of Professors Adrian Nachman, Lassi Päivärinta, William Rundell (chair), and Michael Vogelius. William Rundell For the Calderón Prize Committee Prize ceremony The ceremony awarding the Calderón Prize. Matti Lassas is on the left. He and William Rundell are on the right. Photos by P Stefanov. Brief Biography of Matti Lassas Matti Lassas was born in 1969 in Helsinki, Finland, and studied at the University of Helsinki. He finished his Master's studies in 1992 in three years and earned his PhD in 1996. His PhD thesis, written under the supervision of Professor Erkki Somersalo was entitled `Non-selfadjoint inverse spectral problems and their applications to random bodies'. Already in his thesis, Matti demonstrated a remarkable command of different fields of mathematics, bringing together the spectral theory of operators, geometry of Riemannian surfaces, Maxwell's equations and stochastic analysis. He has continued to develop all of these branches in the framework of inverse problems, the most remarkable results perhaps being in the field of differential geometry and inverse problems. Matti has always been a very generous researcher, sharing his ideas with his numerous collaborators. He has authored over sixty scientific articles, among which a monograph on inverse boundary spectral problems with Alexander Kachalov and Yaroslav Kurylev and over forty articles in peer reviewed journals of the highest standards. To get an idea of the wide range of Matti's interests, it is enough to say that he also has three US patents on medical imaging applications. Matti is currently professor of mathematics at Helsinki University of Technology, where he has created his own line of research with young talented researchers around him. He is a central person in the Centre of Excellence in Inverse Problems Research of the Academy of Finland. Previously, Matti Lassas has won several awards in his home country, including the prestigious Vaisala price of the Finnish Academy of Science and Letters in 2004. He is a highly esteemed colleague, teacher and friend, and the Great Diving Beetle of the Finnish Inverse Problems Society (http://venda.uku.fi/research/FIPS/), an honorary title for a person who has no fear of the deep. Erkki Somersalo

Adaptive eigenspace method for inverse scattering problems in the frequency domain

NASA Astrophysics Data System (ADS)

Grote, Marcus J.; Kray, Marie; Nahum, Uri

2017-02-01

A nonlinear optimization method is proposed for the solution of inverse scattering problems in the frequency domain, when the scattered field is governed by the Helmholtz equation. The time-harmonic inverse medium problem is formulated as a PDE-constrained optimization problem and solved by an inexact truncated Newton-type iteration. Instead of a grid-based discrete representation, the unknown wave speed is projected to a particular finite-dimensional basis of eigenfunctions, which is iteratively adapted during the optimization. Truncating the adaptive eigenspace (AE) basis at a (small and slowly increasing) finite number of eigenfunctions effectively introduces regularization into the inversion and thus avoids the need for standard Tikhonov-type regularization. Both analytical and numerical evidence underpins the accuracy of the AE representation. Numerical experiments demonstrate the efficiency and robustness to missing or noisy data of the resulting adaptive eigenspace inversion method.

Integration of Gravitational Torques in Cerebellar Pathways Allows for the Dynamic Inverse Computation of Vertical Pointing Movements of a Robot Arm

PubMed Central

Gentili, Rodolphe J.; Papaxanthis, Charalambos; Ebadzadeh, Mehdi; Eskiizmirliler, Selim; Ouanezar, Sofiane; Darlot, Christian

2009-01-01

Background Several authors suggested that gravitational forces are centrally represented in the brain for planning, control and sensorimotor predictions of movements. Furthermore, some studies proposed that the cerebellum computes the inverse dynamics (internal inverse model) whereas others suggested that it computes sensorimotor predictions (internal forward model). Methodology/Principal Findings This study proposes a model of cerebellar pathways deduced from both biological and physical constraints. The model learns the dynamic inverse computation of the effect of gravitational torques from its sensorimotor predictions without calculating an explicit inverse computation. By using supervised learning, this model learns to control an anthropomorphic robot arm actuated by two antagonists McKibben artificial muscles. This was achieved by using internal parallel feedback loops containing neural networks which anticipate the sensorimotor consequences of the neural commands. The artificial neural networks architecture was similar to the large-scale connectivity of the cerebellar cortex. Movements in the sagittal plane were performed during three sessions combining different initial positions, amplitudes and directions of movements to vary the effects of the gravitational torques applied to the robotic arm. The results show that this model acquired an internal representation of the gravitational effects during vertical arm pointing movements. Conclusions/Significance This is consistent with the proposal that the cerebellar cortex contains an internal representation of gravitational torques which is encoded through a learning process. Furthermore, this model suggests that the cerebellum performs the inverse dynamics computation based on sensorimotor predictions. This highlights the importance of sensorimotor predictions of gravitational torques acting on upper limb movements performed in the gravitational field. PMID:19384420

PREFACE: Inverse Problems in Applied Sciences—towards breakthrough

NASA Astrophysics Data System (ADS)

Cheng, Jin; Iso, Yuusuke; Nakamura, Gen; Yamamoto, Masahiro

2007-06-01

These are the proceedings of the international conference `Inverse Problems in Applied Sciences—towards breakthrough' which was held at Hokkaido University, Sapporo, Japan on 3-7 July 2006 (http://coe.math.sci.hokudai.ac.jp/sympo/inverse/). There were 88 presentations and more than 100 participants, and we are proud to say that the conference was very successful. Nowadays, many new activities on inverse problems are flourishing at many centers of research around the world, and the conference has successfully gathered a world-wide variety of researchers. We believe that this volume contains not only main papers, but also conveys the general status of current research into inverse problems. This conference was the third biennial international conference on inverse problems, the core of which is the Pan-Pacific Asian area. The purpose of this series of conferences is to establish and develop constant international collaboration, especially among the Pan-Pacific Asian countries, and to lead the organization of activities concerning inverse problems centered in East Asia. The first conference was held at City University of Hong Kong in January 2002 and the second was held at Fudan University in June 2004. Following the preceding two successes, the third conference was organized in order to extend the scope of activities and build useful bridges to the next conference in Seoul in 2008. Therefore this third biennial conference was intended not only to establish collaboration and links between researchers in Asia and leading researchers worldwide in inverse problems but also to nurture interdisciplinary collaboration in theoretical fields such as mathematics, applied fields and evolving aspects of inverse problems. For these purposes, we organized tutorial lectures, serial lectures and a panel discussion as well as conference research presentations. This volume contains three lecture notes from the tutorial and serial lectures, and 22 papers. Especially at this flourishing time, it is necessary to carefully analyse the current status of inverse problems for further development. Thus we have opened with the panel discussion entitled `Future of Inverse Problems' with panelists: Professors J Cheng, H W Engl, V Isakov, R Kress, J-K Seo, G Uhlmann and the commentator: Elaine Longden-Chapman from IOP Publishing. The aims of the panel discussion were to examine the current research status from various viewpoints, to discuss how we can overcome any difficulties and how we can promote young researchers and open new possibilities for inverse problems such as industrial linkages. As one output, the panel discussion has triggered the organization of the Inverse Problems International Association (IPIA) which has led to its first international congress in the summer of 2007. Another remarkable outcome of the conference is, of course, the present volume: this is the very high quality online proceedings volume of Journal of Physics: Conference Series. Readers can see in these proceedings very well written tutorial lecture notes, and very high quality original research and review papers all of which show what was achieved by the time the conference was held. The electronic publication of the proceedings is a new way of publicizing the achievement of the conference. It has the advantage of wide circulation and cost reduction. We believe this is a most efficient method for our needs and purposes. We would like to take this opportunity to acknowledge all the people who helped to organize the conference. Guest Editors Jin Cheng, Fudan University, Shanghai, China Yuusuke Iso, Kyoto University, Kyoto, Japan Gen Nakamura, Hokkaido University, Sapporo, Japan Masahiro Yamamoto, University of Tokyo, Tokyo, Japan

Solvability of the electrocardiology inverse problem for a moving dipole.

PubMed

Tolkachev, V; Bershadsky, B; Nemirko, A

1993-01-01

New formulations of the direct and inverse problems for the moving dipole are offered. It has been suggested to limit the study by a small area on the chest surface. This lowers the role of the medium inhomogeneity. When formulating the direct problem, irregular components are considered. The algorithm of simultaneous determination of the dipole and regular noise parameters has been described and analytically investigated. It is shown that temporal overdetermination of the equations offers a single solution of the inverse problem for the four leads.

A computationally efficient parallel Levenberg-Marquardt algorithm for highly parameterized inverse model analyses

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

Lin, Youzuo; O'Malley, Daniel; Vesselinov, Velimir V.

Inverse modeling seeks model parameters given a set of observations. However, for practical problems because the number of measurements is often large and the model parameters are also numerous, conventional methods for inverse modeling can be computationally expensive. We have developed a new, computationally-efficient parallel Levenberg-Marquardt method for solving inverse modeling problems with a highly parameterized model space. Levenberg-Marquardt methods require the solution of a linear system of equations which can be prohibitively expensive to compute for moderate to large-scale problems. Our novel method projects the original linear problem down to a Krylov subspace, such that the dimensionality of themore » problem can be significantly reduced. Furthermore, we store the Krylov subspace computed when using the first damping parameter and recycle the subspace for the subsequent damping parameters. The efficiency of our new inverse modeling algorithm is significantly improved using these computational techniques. We apply this new inverse modeling method to invert for random transmissivity fields in 2D and a random hydraulic conductivity field in 3D. Our algorithm is fast enough to solve for the distributed model parameters (transmissivity) in the model domain. The algorithm is coded in Julia and implemented in the MADS computational framework (http://mads.lanl.gov). By comparing with Levenberg-Marquardt methods using standard linear inversion techniques such as QR or SVD methods, our Levenberg-Marquardt method yields a speed-up ratio on the order of ~10 1 to ~10 2 in a multi-core computational environment. Furthermore, our new inverse modeling method is a powerful tool for characterizing subsurface heterogeneity for moderate- to large-scale problems.« less

A computationally efficient parallel Levenberg-Marquardt algorithm for highly parameterized inverse model analyses

DOE PAGES

Lin, Youzuo; O'Malley, Daniel; Vesselinov, Velimir V.

2016-09-01

Inverse modeling seeks model parameters given a set of observations. However, for practical problems because the number of measurements is often large and the model parameters are also numerous, conventional methods for inverse modeling can be computationally expensive. We have developed a new, computationally-efficient parallel Levenberg-Marquardt method for solving inverse modeling problems with a highly parameterized model space. Levenberg-Marquardt methods require the solution of a linear system of equations which can be prohibitively expensive to compute for moderate to large-scale problems. Our novel method projects the original linear problem down to a Krylov subspace, such that the dimensionality of themore » problem can be significantly reduced. Furthermore, we store the Krylov subspace computed when using the first damping parameter and recycle the subspace for the subsequent damping parameters. The efficiency of our new inverse modeling algorithm is significantly improved using these computational techniques. We apply this new inverse modeling method to invert for random transmissivity fields in 2D and a random hydraulic conductivity field in 3D. Our algorithm is fast enough to solve for the distributed model parameters (transmissivity) in the model domain. The algorithm is coded in Julia and implemented in the MADS computational framework (http://mads.lanl.gov). By comparing with Levenberg-Marquardt methods using standard linear inversion techniques such as QR or SVD methods, our Levenberg-Marquardt method yields a speed-up ratio on the order of ~10 1 to ~10 2 in a multi-core computational environment. Furthermore, our new inverse modeling method is a powerful tool for characterizing subsurface heterogeneity for moderate- to large-scale problems.« less

Inverse modeling of flow tomography experiments in fractured media

NASA Astrophysics Data System (ADS)

Klepikova, Maria; Le Borgne, Tanguy; Bour, Olivier; de Dreuzy, Jean-Raynald

2014-05-01

Inverse modeling of fracture hydraulic properties and connectivity is a very challenging objective due to the strong heterogeneity of the medium at multiple scales and the scarcity of data. Cross-borehole flowmeter tests, which consist of measuring changes in vertical borehole flows when pumping a neighboring borehole, were shown to be an efficient technique to provide information on the properties of the flow zones that connect borehole pairs (Paillet, 1998, Le Borgne et al., 2007). The interpretation of such experiments may, however, be quite uncertain when multiple connections exist. We propose the flow tomography approach (i.e., sequential cross-borehole flowmeter tests) to characterize the connectivity and transmissivity of preferential permeable flow paths in fractured aquifers (Klepikova et al., 2013). An inverse model approach is developed to estimate log-transformed transmissivity values of hydraulically active fractures between the pumping and observation wells by inverting cross-borehole flow and water level data. Here a simplified discrete fracture network approach that highlights main connectivity structures is used. This conceptual model attempts to reproduce fracture network connectivity without taking fracture geometry (length, orientation, dip) into account. We demonstrate that successively exchanging the roles of pumping and observation boreholes improves the quality of available information and reduces the under-determination of the problem. The inverse method is validated for several synthetic flow scenarios. It is shown to provide a good estimation of connectivity patterns and transmissivities of main flow paths. It also allows the estimation of the transmissivity of fractures that connect the flow paths but do not cross the boreholes, although the associated uncertainty may be high for some geometries. The results of this investigation encourage the application of flow tomography to natural fractured aquifers.

Development of a new semi-analytical model for cross-borehole flow experiments in fractured media

USGS Publications Warehouse

Roubinet, Delphine; Irving, James; Day-Lewis, Frederick D.

2015-01-01

Analysis of borehole flow logs is a valuable technique for identifying the presence of fractures in the subsurface and estimating properties such as fracture connectivity, transmissivity and storativity. However, such estimation requires the development of analytical and/or numerical modeling tools that are well adapted to the complexity of the problem. In this paper, we present a new semi-analytical formulation for cross-borehole flow in fractured media that links transient vertical-flow velocities measured in one or a series of observation wells during hydraulic forcing to the transmissivity and storativity of the fractures intersected by these wells. In comparison with existing models, our approach presents major improvements in terms of computational expense and potential adaptation to a variety of fracture and experimental configurations. After derivation of the formulation, we demonstrate its application in the context of sensitivity analysis for a relatively simple two-fracture synthetic problem, as well as for field-data analysis to investigate fracture connectivity and estimate fracture hydraulic properties. These applications provide important insights regarding (i) the strong sensitivity of fracture property estimates to the overall connectivity of the system; and (ii) the non-uniqueness of the corresponding inverse problem for realistic fracture configurations.

MAP Estimators for Piecewise Continuous Inversion

DTIC Science & Technology

2016-08-08

MAP estimators for piecewise continuous inversion M M Dunlop1 and A M Stuart Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK E...Published 8 August 2016 Abstract We study the inverse problem of estimating a field ua from data comprising a finite set of nonlinear functionals of ua...then natural to study maximum a posterior (MAP) estimators. Recently (Dashti et al 2013 Inverse Problems 29 095017) it has been shown that MAP

Time-domain full waveform inversion using instantaneous phase information with damping

NASA Astrophysics Data System (ADS)

Luo, Jingrui; Wu, Ru-Shan; Gao, Fuchun

2018-06-01

In time domain, the instantaneous phase can be obtained from the complex seismic trace using Hilbert transform. The instantaneous phase information has great potential in overcoming the local minima problem and improving the result of full waveform inversion. However, the phase wrapping problem, which comes from numerical calculation, prevents its application. In order to avoid the phase wrapping problem, we choose to use the exponential phase combined with the damping method, which gives instantaneous phase-based multi-stage inversion. We construct the objective functions based on the exponential instantaneous phase, and also derive the corresponding gradient operators. Conventional full waveform inversion and the instantaneous phase-based inversion are compared with numerical examples, which indicates that in the case without low frequency information in seismic data, our method is an effective and efficient approach for initial model construction for full waveform inversion.

Improving the Automatic Inversion of Digital ISIS-2 Ionogram Reflection Traces into Topside Vertical Electron-Density Profiles

NASA Technical Reports Server (NTRS)

Benson, R. F.; Truhlik, V.; Huang, X.; Wang, Y.; Bilitza, D.

2011-01-01

The topside-sounders on the four satellites of the International Satellites for Ionospheric Studies (ISIS) program were designed as analog systems. The resulting ionograms were displayed on 35-mm film for analysis by visual inspection. Each of these satellites, launched between 1962 and 1971, produced data for 10 to 20 years. A number of the original telemetry tapes from this large data set have been converted directly into digital records. Software, known as the TOPside Ionogram Scalar with True-height (TOPIST) algorithm has been produced that enables the automatic inversion of ISIS-2 ionogram reflection traces into topside vertical electron-density profiles Ne(h). More than million digital Alouette/ISIS topside ionograms have been produced and over 300,000 are from ISIS 2. Many of these ISIS-2 ionograms correspond to a passive mode of operation for the detection of natural radio emissions and thus do not contain ionospheric reflection traces. TOPIST, however, is not able to produce Ne(h) profiles from all of the ISIS-2 ionograms with reflection traces because some of them did not contain frequency information. This information was missing due to difficulties encountered during the analog-to-digital conversion process in the detection of the ionogram frame-sync pulse and/or the frequency markers. Of the many digital topside ionograms that TOPIST was able to process, over 200 were found where direct comparisons could be made with Ne(h) profiles that were produced by manual scaling in the early days of the ISIS program. While many of these comparisons indicated excellent agreement (<10% average difference over the entire profile) there were also many cases with large differences (more than a factor of two). Here we will report on two approaches to improve the automatic inversion process: (1) improve the quality of the digital ionogram database by remedying the missing frequency-information problem when possible, and (2) using the above-mentioned comparisons as teaching examples of how to improve the original TOPIST software.

Flowing partially penetrating well: solution to a mixed-type boundary value problem

NASA Astrophysics Data System (ADS)

Cassiani, G.; Kabala, Z. J.; Medina, M. A.

A new semi-analytic solution to the mixed-type boundary value problem for a flowing partially penetrating well with infinitesimal skin situated in an anisotropic aquifer is developed. The solution is suited to aquifers having a semi-infinite vertical extent or to packer tests with aquifer horizontal boundaries far enough from the tested area. The problem reduces to a system of dual integral equations (DE) and further to a deconvolution problem. Unlike the analogous Dagan's steady-state solution [Water Resour. Res. 1978; 14:929-34], our DE solution does not suffer from numerical oscillations. The new solution is validated by matching the corresponding finite-difference solution and is computationally much more efficient. An automated (Newton-Raphson) parameter identification algorithm is proposed for field test inversion, utilizing the DE solution for the forward model. The procedure is computationally efficient and converges to correct parameter values. A solution for the partially penetrating flowing well with no skin and a drawdown-drawdown discontinuous boundary condition, analogous to that by Novakowski [Can. Geotech. J. 1993; 30:600-6], is compared to the DE solution. The D-D solution leads to physically inconsistent infinite total flow rate to the well, when no skin effect is considered. The DE solution, on the other hand, produces accurate results.

Imaging Faults in Carbonate Reservoir using Full Waveform Inversion and Reverse Time Migration of Walkaway VSP Data

NASA Astrophysics Data System (ADS)

Takam Takougang, E. M.; Bouzidi, Y.

2016-12-01

Multi-offset Vertical Seismic Profile (walkaway VSP) data were collected in an oil field located in a shallow water environment dominated by carbonate rocks, offshore the United Arab Emirates. The purpose of the survey was to provide structural information of the reservoir, around and away from the borehole. Five parallel lines were collected using an air gun at 25 m shot interval and 4 m source depth. A typical recording tool with 20 receivers spaced every 15.1 m, and located in a deviated borehole with an angle varying between 0 and 24 degree from the vertical direction, was used to record the data. The recording tool was deployed at different depths for each line, from 521 m to 2742 m depth. Smaller offsets were used for shallow receivers and larger offsets for deeper receivers. The lines merged to form the input dataset for waveform tomography. The total length of the combined lines was 9 km, containing 1344 shots and 100 receivers in the borehole located half-way down. Acoustic full waveform inversion was applied in the frequency domain to derive a high resolution velocity model. The final velocity model derived after the inversion using the frequencies 5-40 Hz, showed good correlation with velocities estimated from vertical incidence VSP and sonic log, confirming the success of the inversion. The velocity model showed anomalous low values in areas that correlate with known location of hydrocarbon reservoir. Pre-stack depth Reverse time migration was then applied using the final velocity model from waveform inversion and the up-going wavefield from the input data. The final estimated source signature from waveform inversion was used as input source for reverse time migration. To save computational memory and time, every 3 shots were used during reverse time migration and the data were low-pass filtered to 30 Hz. Migration artifacts were attenuated using a second order derivative filter. The final migration image shows a good correlation with the waveform tomography velocity model, and highlights a complex network of faults in the reservoir, that could be useful in understanding fluid and hydrocarbon movements. This study shows that the combination of full waveform tomography and reverse time migration can provide high resolution images that can enhance interpretation and characterization of oil reservoirs.

Solutions to inverse plume in a crosswind problem using a predictor - corrector method

NASA Astrophysics Data System (ADS)

Vanderveer, Joseph; Jaluria, Yogesh

2013-11-01

Investigation for minimalist solutions to the inverse convection problem of a plume in a crosswind has developed a predictor - corrector method. The inverse problem is to predict the strength and location of the plume with respect to a select few downstream sampling points. This is accomplished with the help of two numerical simulations of the domain at differing source strengths, allowing the generation of two inverse interpolation functions. These functions in turn are utilized by the predictor step to acquire the plume strength. Finally, the same interpolation functions with the corrections from the plume strength are used to solve for the plume location. Through optimization of the relative location of the sampling points, the minimum number of samples for accurate predictions is reduced to two for the plume strength and three for the plume location. After the optimization, the predictor-corrector method demonstrates global uniqueness of the inverse solution for all test cases. The solution error is less than 1% for both plume strength and plume location. The basic approach could be extended to other inverse convection transport problems, particularly those encountered in environmental flows.

Infrasound data inversion for atmospheric sounding

NASA Astrophysics Data System (ADS)

Lalande, J.-M.; Sèbe, O.; Landès, M.; Blanc-Benon, Ph.; Matoza, R. S.; Le Pichon, A.; Blanc, E.

2012-07-01

The International Monitoring System (IMS) of the Comprehensive Nuclear-Test-Ban Treaty (CTBT) continuously records acoustic waves in the 0.01-10 Hz frequency band, known as infrasound. These waves propagate through the layered structure of the atmosphere. Coherent infrasonic waves are produced by a variety of anthropogenic and natural sources and their propagation is controlled by spatiotemporal variations of temperature and wind velocity. Natural stratification of atmospheric properties (e.g. temperature, density and winds) forms waveguides, allowing long-range propagation of infrasound waves. However, atmospheric specifications used in infrasound propagation modelling suffer from lack and sparsity of available data above an altitude of 50 km. As infrasound can propagate in the upper atmosphere up to 120 km, we assume that infrasonic data could be used for sounding the atmosphere, analogous to the use of seismic data to infer solid Earth structure and the use of hydroacoustic data to infer oceanic structure. We therefore develop an inversion scheme for vertical atmospheric wind profiles in the framework of an iterative linear inversion. The forward problem is treated in the high-frequency approximation using a Hamiltonian formulation and complete first-order ray perturbation theory is developed to construct the Fréchet derivatives matrix. We introduce a specific parametrization for the unknown model parameters based on Principal Component Analysis. Finally, our algorithm is tested on synthetic data cases spanning different seasonal periods and network configurations. The results show that our approach is suitable for infrasound atmospheric sounding on a regional scale.

Acoustic Inversion in Optoacoustic Tomography: A Review

PubMed Central

Rosenthal, Amir; Ntziachristos, Vasilis; Razansky, Daniel

2013-01-01

Optoacoustic tomography enables volumetric imaging with optical contrast in biological tissue at depths beyond the optical mean free path by the use of optical excitation and acoustic detection. The hybrid nature of optoacoustic tomography gives rise to two distinct inverse problems: The optical inverse problem, related to the propagation of the excitation light in tissue, and the acoustic inverse problem, which deals with the propagation and detection of the generated acoustic waves. Since the two inverse problems have different physical underpinnings and are governed by different types of equations, they are often treated independently as unrelated problems. From an imaging standpoint, the acoustic inverse problem relates to forming an image from the measured acoustic data, whereas the optical inverse problem relates to quantifying the formed image. This review focuses on the acoustic aspects of optoacoustic tomography, specifically acoustic reconstruction algorithms and imaging-system practicalities. As these two aspects are intimately linked, and no silver bullet exists in the path towards high-performance imaging, we adopt a holistic approach in our review and discuss the many links between the two aspects. Four classes of reconstruction algorithms are reviewed: time-domain (so called back-projection) formulae, frequency-domain formulae, time-reversal algorithms, and model-based algorithms. These algorithms are discussed in the context of the various acoustic detectors and detection surfaces which are commonly used in experimental studies. We further discuss the effects of non-ideal imaging scenarios on the quality of reconstruction and review methods that can mitigate these effects. Namely, we consider the cases of finite detector aperture, limited-view tomography, spatial under-sampling of the acoustic signals, and acoustic heterogeneities and losses. PMID:24772060

INTRODUCTION Introduction to the conference proceeding of the Workshop on Electromagnetic Inverse ProblemsThe University of Manchester, UK, 15-18 June, 2009

NASA Astrophysics Data System (ADS)

Dorn, Oliver; Lionheart, Bill

2010-11-01

This proceeding combines selected contributions from participants of the Workshop on Electromagnetic Inverse Problems which was hosted by the University of Manchester in June 2009. The workshop was organized by the two guest editors of this conference proceeding and ran in parallel to the 10th International Conference on Electrical Impedance Tomography, which was guided by Bill Lionheart, Richard Bayford, and Eung Je Woo. Both events shared plenary talks and several selected sessions. One reason for combining these two events was the goal of bringing together scientists from various related disciplines who normally might not attend the same conferences, and to enhance discussions between these different groups. So, for example, one day of the workshop was dedicated to the broader area of geophysical inverse problems (including inverse problems in petroleum engineering), where participants from the EIT community and from the medical imaging community were also encouraged to participate, with great success. Other sessions concentrated on microwave medical imaging, on inverse scattering, or on eddy current imaging, with active feedback also from geophysically oriented scientists. Furthermore, several talks addressed such diverse topics as optical tomography, photoacoustic tomography, time reversal, or electrosensing fish. As a result of the workshop, speakers were invited to contribute extended papers to this conference proceeding. All submissions were thoroughly reviewed and, after a thoughtful revision by the authors, combined in this proceeding. The resulting set of six papers presenting the work of in total 22 authors from 5 different countries provides a very interesting overview of several of the themes which were represented at the workshop. These can be divided into two important categories, namely (i) modelling and (ii) data inversion. The first three papers of this selection, as outlined below, focus more on modelling aspects, being an essential component of any successful inversion, whereas the other three papers discuss novel inversion techniques for specific applications. In the first contribution, with the title A Novel Simplified Mathematical Model for Antennas used in Medical Imaging Applications, the authors M J Fernando, M Elsdon, K Busawon and D Smith discuss a new technique for modelling the current across a monopole antenna from which the radiation fields of the antenna can be calculated very efficiently in specific medical imaging applications. This new technique is then tested on two examples, a quarter wavelength and a three quarter wavelength monopole antenna. The next contribution, with the title An investigation into the use of a mixture model for simulating the electrical properties of soil with varying effective saturation levels for sub-soil imaging using ECT by R R Hayes, P A Newill, F J W Podd, T A York, B D Grieve and O Dorn, considers the development of a new visualization tool for monitoring soil moisture content surrounding certain seed breeder plants. An electrical capacitance tomography technique is employed for verifying how efficiently each plant utilises the water and nutrients available in the surrounding soil. The goal of this study is to help in developing and identifying new drought tolerant food crops. In the third contribution Combination of Maximin and Kriging Prediction Methods for Eddy-Current Testing Database Generation by S Bilicz, M Lambert, E Vazquez and S Gyimóthy, a novel database generation technique is proposed for its use in solving inverse eddy-current testing problems. For avoiding expensive repeated forward simulations during the creation of this database, a kriging interpolation technique is employed for filling uniformly the data output space with sample points. Mathematically this is achieved by using a maximin formalism. The paper 2.5D inversion of CSEM data in a vertically anisotropic earth by C Ramananjaona and L MacGregor considers controlled-source electromagnetic techniques for imaging the earth in a marine environment. It focuses in particular on taking into account anisotropy effects in the inversion. Results of this technique are demonstrated from simulated and from real field data. Furthermore, in the contribution Multiple level-sets for elliptic Cauchy problems in three-dimensional domains by A Leitão and M Marques Alves the authors consider a TV-H1regularization technique for multiple level-set inversion of elliptic Cauchy problems. Generalized minimizers are defined and convergence and stability results are provided for this method, in addition to several numerical experiments. Finally, in the paper Development of in-vivo fluorescence imaging with the matrix-free method, the authors A Zacharopoulos, A Garofalakis, J Ripoll and S Arridge address a recently developed non-contact fluorescence molecular tomography technique where the use of non-contact acquisition systems poses new challenges on computational efficiency during data processing. The matrix-free method is designed to reduce computational cost and memory requirements during the inversion. Reconstructions from a simulated mouse phantom are provided for demonstrating the performance of the proposed technique in realistic scenarios. We hope that this selection of strong and thought-provoking papers will help stimulating further cross-disciplinary research in the spirit of the workshop. We thank all authors for providing us with this excellent set of high-quality contributions. We also thank EPSRC for having provided funding for the workshop under grant EP/G065047/1. Oliver Dorn, Bill Lionheart School of Mathematics, University of Manchester, Alan Turing Building, Oxford Rd Manchester, M13 9PL, UK E-mail: oliver.dorn@manchester.ac.uk, bill.lionheart@manchester.ac.uk Guest Editors

Review of the inverse scattering problem at fixed energy in quantum mechanics

NASA Technical Reports Server (NTRS)

Sabatier, P. C.

1972-01-01

Methods of solution of the inverse scattering problem at fixed energy in quantum mechanics are presented. Scattering experiments of a beam of particles at a nonrelativisitic energy by a target made up of particles are analyzed. The Schroedinger equation is used to develop the quantum mechanical description of the system and one of several functions depending on the relative distance of the particles. The inverse problem is the construction of the potentials from experimental measurements.

Estimation of the vertical profile of sulfur dioxide injection into the atmosphere by a volcanic eruption using satellite column measurements and inverse transport modeling

NASA Astrophysics Data System (ADS)

Eckhardt, S.; Prata, A. J.; Seibert, P.; Stebel, K.; Stohl, A.

2008-02-01

An analytical inversion method has been developed to estimate the vertical profile of SO2 emissions from volcanic eruptions. The method uses satellite-observed total SO2 columns and an atmospheric transport model (FLEXPART) to exploit the fact that winds change with altitude - thus, the position and shape of the volcanic plume bear information on its emission altitude. The method finds the vertical emission distribution which minimizes the total difference between simulated and observed SO2 columns while also considering a priori information. We have tested the method with the eruption of Jebel at Tair on 30 September 2007 for which a comprehensive observational data set from various satellite instruments (AIRS, OMI, SEVIRI, CALIPSO) is available. Using satellite data from the first 24 h after the eruption for the inversion, we found an emission maximum near 16 km above sea level (asl), and secondary maxima near 5, 9, 12 and 14 km a.s.l. 60% of the emission occurred above the tropopause. The emission profile obtained in the inversion was then used to simulate the transport of the plume over the following week. The modeled plume agrees very well with SO2 total columns observed by OMI, and its altitude and width agree mostly within 1-2 km with CALIPSO observations of stratospheric aerosol produced from the SO2. The inversion result is robust against various changes in both the a priori and the observations. Even when using only SEVIRI data from the first 15 h after the eruption, the emission profile was reasonably well estimated. The method is computationally very fast. It is therefore suitable for implementation within an operational environment, such as the Volcanic Ash Advisory Centers, to predict the threat posed by volcanic ash for air traffic. It could also be helpful for assessing the sulfur input into the stratosphere, be it in the context of volcanic processes or also for proposed geo-engineering techniques to counteract global warming.

Efficient Inversion of Mult-frequency and Multi-Source Electromagnetic Data

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

Gary D. Egbert

2007-03-22

The project covered by this report focused on development of efficient but robust non-linear inversion algorithms for electromagnetic induction data, in particular for data collected with multiple receivers, and multiple transmitters, a situation extremely common in eophysical EM subsurface imaging methods. A key observation is that for such multi-transmitter problems each step in commonly used linearized iterative limited memory search schemes such as conjugate gradients (CG) requires solution of forward and adjoint EM problems for each of the N frequencies or sources, essentially generating data sensitivities for an N dimensional data-subspace. These multiple sensitivities allow a good approximation to themore » full Jacobian of the data mapping to be built up in many fewer search steps than would be required by application of textbook optimization methods, which take no account of the multiplicity of forward problems that must be solved for each search step. We have applied this idea to a develop a hybrid inversion scheme that combines features of the iterative limited memory type methods with a Newton-type approach using a partial calculation of the Jacobian. Initial tests on 2D problems show that the new approach produces results essentially identical to a Newton type Occam minimum structure inversion, while running more rapidly than an iterative (fixed regularization parameter) CG style inversion. Memory requirements, while greater than for something like CG, are modest enough that even in 3D the scheme should allow 3D inverse problems to be solved on a common desktop PC, at least for modest (~ 100 sites, 15-20 frequencies) data sets. A secondary focus of the research has been development of a modular system for EM inversion, using an object oriented approach. This system has proven useful for more rapid prototyping of inversion algorithms, in particular allowing initial development and testing to be conducted with two-dimensional example problems, before approaching more computationally cumbersome three-dimensional problems.« less

Three-dimensional full waveform inversion of short-period teleseismic wavefields based upon the SEM-DSM hybrid method

NASA Astrophysics Data System (ADS)

Monteiller, Vadim; Chevrot, Sébastien; Komatitsch, Dimitri; Wang, Yi

2015-08-01

We present a method for high-resolution imaging of lithospheric structures based on full waveform inversion of teleseismic waveforms. We model the propagation of seismic waves using our recently developed direct solution method/spectral-element method hybrid technique, which allows us to simulate the propagation of short-period teleseismic waves through a regional 3-D model. We implement an iterative quasi-Newton method based upon the L-BFGS algorithm, where the gradient of the misfit function is computed using the adjoint-state method. Compared to gradient or conjugate-gradient methods, the L-BFGS algorithm has a much faster convergence rate. We illustrate the potential of this method on a synthetic test case that consists of a crustal model with a crustal discontinuity at 25 km depth and a sharp Moho jump. This model contains short- and long-wavelength heterogeneities along the lateral and vertical directions. The iterative inversion starts from a smooth 1-D model derived from the IASP91 reference Earth model. We invert both radial and vertical component waveforms, starting from long-period signals filtered at 10 s and gradually decreasing the cut-off period down to 1.25 s. This multiscale algorithm quickly converges towards a model that is very close to the true model, in contrast to inversions involving short-period waveforms only, which always get trapped into a local minimum of the cost function.

Definition and solution of a stochastic inverse problem for the Manning's n parameter field in hydrodynamic models.

PubMed

Butler, T; Graham, L; Estep, D; Dawson, C; Westerink, J J

2015-04-01

The uncertainty in spatially heterogeneous Manning's n fields is quantified using a novel formulation and numerical solution of stochastic inverse problems for physics-based models. The uncertainty is quantified in terms of a probability measure and the physics-based model considered here is the state-of-the-art ADCIRC model although the presented methodology applies to other hydrodynamic models. An accessible overview of the formulation and solution of the stochastic inverse problem in a mathematically rigorous framework based on measure theory is presented. Technical details that arise in practice by applying the framework to determine the Manning's n parameter field in a shallow water equation model used for coastal hydrodynamics are presented and an efficient computational algorithm and open source software package are developed. A new notion of "condition" for the stochastic inverse problem is defined and analyzed as it relates to the computation of probabilities. This notion of condition is investigated to determine effective output quantities of interest of maximum water elevations to use for the inverse problem for the Manning's n parameter and the effect on model predictions is analyzed.

Definition and solution of a stochastic inverse problem for the Manning's n parameter field in hydrodynamic models

NASA Astrophysics Data System (ADS)

Butler, T.; Graham, L.; Estep, D.; Dawson, C.; Westerink, J. J.

2015-04-01

The uncertainty in spatially heterogeneous Manning's n fields is quantified using a novel formulation and numerical solution of stochastic inverse problems for physics-based models. The uncertainty is quantified in terms of a probability measure and the physics-based model considered here is the state-of-the-art ADCIRC model although the presented methodology applies to other hydrodynamic models. An accessible overview of the formulation and solution of the stochastic inverse problem in a mathematically rigorous framework based on measure theory is presented. Technical details that arise in practice by applying the framework to determine the Manning's n parameter field in a shallow water equation model used for coastal hydrodynamics are presented and an efficient computational algorithm and open source software package are developed. A new notion of "condition" for the stochastic inverse problem is defined and analyzed as it relates to the computation of probabilities. This notion of condition is investigated to determine effective output quantities of interest of maximum water elevations to use for the inverse problem for the Manning's n parameter and the effect on model predictions is analyzed.

Inverse models: A necessary next step in ground-water modeling

USGS Publications Warehouse

Poeter, E.P.; Hill, M.C.

1997-01-01

Inverse models using, for example, nonlinear least-squares regression, provide capabilities that help modelers take full advantage of the insight available from ground-water models. However, lack of information about the requirements and benefits of inverse models is an obstacle to their widespread use. This paper presents a simple ground-water flow problem to illustrate the requirements and benefits of the nonlinear least-squares repression method of inverse modeling and discusses how these attributes apply to field problems. The benefits of inverse modeling include: (1) expedited determination of best fit parameter values; (2) quantification of the (a) quality of calibration, (b) data shortcomings and needs, and (c) confidence limits on parameter estimates and predictions; and (3) identification of issues that are easily overlooked during nonautomated calibration.Inverse models using, for example, nonlinear least-squares regression, provide capabilities that help modelers take full advantage of the insight available from ground-water models. However, lack of information about the requirements and benefits of inverse models is an obstacle to their widespread use. This paper presents a simple ground-water flow problem to illustrate the requirements and benefits of the nonlinear least-squares regression method of inverse modeling and discusses how these attributes apply to field problems. The benefits of inverse modeling include: (1) expedited determination of best fit parameter values; (2) quantification of the (a) quality of calibration, (b) data shortcomings and needs, and (c) confidence limits on parameter estimates and predictions; and (3) identification of issues that are easily overlooked during nonautomated calibration.

Inverse modeling of CO2 sources and sinks using satellite observations of CO2 from TES and surface flask measurements

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

Nassar, Ray; Jones, DBA; Kulawik, SS

2011-01-01

We infer CO2 surface fluxes using satellite observations of mid-tropospheric CO2 from the Tropospheric Emission Spectrometer (TES) and measurements of CO2 from surface flasks in a time-independent inversion analysis based on the GEOS-Chem model. Using TES CO2 observations over oceans, spanning 40 S 40 N, we find that the horizontal and vertical coverage of the TES and flask data are complementary. This complementarity is demonstrated by combining the datasets in a joint inversion, which provides better constraints than from either dataset alone, when a posteriori CO2 distributions are evaluated against independent ship and aircraft CO2 data. In particular, the jointmore » inversion offers improved constraints in the tropics where surface measurements are sparse, such as the tropical forests of South America. Aggregating the annual surface-to-atmosphere fluxes from the joint inversion for the year 2006 yields 1.13 0.21 PgC for the global ocean, 2.77 0.20 PgC for the global land biosphere and 3.90 0.29 PgC for the total global natural flux (defined as the sum of all biospheric, oceanic, and biomass burning contributions but excluding CO2 emissions from fossil fuel combustion). These global ocean and global land fluxes are shown to be near the median of the broad range of values from other inversion results for 2006. To achieve these results, a bias in TES CO2 in the Southern Hemisphere was assessed and corrected using aircraft flask data, and we demonstrate that our results have low sensitivity to variations in the bias correction approach. Overall, this analysis suggests that future carbon data assimilation systems can benefit by integrating in situ and satellite observations of CO2 and that the vertical information provided by satellite observations of mid-tropospheric CO2 combined with measurements of surface CO2, provides an important additional constraint for flux inversions.« less

Iterative algorithms for a non-linear inverse problem in atmospheric lidar

NASA Astrophysics Data System (ADS)

Denevi, Giulia; Garbarino, Sara; Sorrentino, Alberto

2017-08-01

We consider the inverse problem of retrieving aerosol extinction coefficients from Raman lidar measurements. In this problem the unknown and the data are related through the exponential of a linear operator, the unknown is non-negative and the data follow the Poisson distribution. Standard methods work on the log-transformed data and solve the resulting linear inverse problem, but neglect to take into account the noise statistics. In this study we show that proper modelling of the noise distribution can improve substantially the quality of the reconstructed extinction profiles. To achieve this goal, we consider the non-linear inverse problem with non-negativity constraint, and propose two iterative algorithms derived using the Karush-Kuhn-Tucker conditions. We validate the algorithms with synthetic and experimental data. As expected, the proposed algorithms out-perform standard methods in terms of sensitivity to noise and reliability of the estimated profile.

Efficient Monte Carlo sampling of inverse problems using a neural network-based forward—applied to GPR crosshole traveltime inversion

NASA Astrophysics Data System (ADS)

Hansen, T. M.; Cordua, K. S.

2017-12-01

Probabilistically formulated inverse problems can be solved using Monte Carlo-based sampling methods. In principle, both advanced prior information, based on for example, complex geostatistical models and non-linear forward models can be considered using such methods. However, Monte Carlo methods may be associated with huge computational costs that, in practice, limit their application. This is not least due to the computational requirements related to solving the forward problem, where the physical forward response of some earth model has to be evaluated. Here, it is suggested to replace a numerical complex evaluation of the forward problem, with a trained neural network that can be evaluated very fast. This will introduce a modeling error that is quantified probabilistically such that it can be accounted for during inversion. This allows a very fast and efficient Monte Carlo sampling of the solution to an inverse problem. We demonstrate the methodology for first arrival traveltime inversion of crosshole ground penetrating radar data. An accurate forward model, based on 2-D full-waveform modeling followed by automatic traveltime picking, is replaced by a fast neural network. This provides a sampling algorithm three orders of magnitude faster than using the accurate and computationally expensive forward model, and also considerably faster and more accurate (i.e. with better resolution), than commonly used approximate forward models. The methodology has the potential to dramatically change the complexity of non-linear and non-Gaussian inverse problems that have to be solved using Monte Carlo sampling techniques.

Ocular manifestations of gravity inversion.

PubMed

Friberg, T R; Weinreb, R N

To determine the ocular manifestations of inverting the human body into a head-down vertical position, we evaluated normal volunteers with applanation tonometry, fundus photography, fluorescein angiography, and ophthalmodynamometry. Compared with data obtained in the sitting position, the intraocular pressure more than doubled on inversion (35.6 +/- 4 v 14.1 +/- 2.8 mm Hg, n = 16), increasing to levels well within the glaucomatous range. Pressures in the central retinal artery underwent similar increases, while the caliber of the retinal arterioles decreased substantially. External ocular findings associated with gravity inversion included orbital congestion, conjunctival hyperemia, petechiae of the eyelids, excessive tearing (epiphora), and subconjunctival hemorrhage. We suggest that patients with retinal vascular abnormalities, macular degeneration, ocular hypertension, glaucoma, and similar disorders refrain from inversion altogether. Whether normal individuals will suffer irreversible damage from inversion is uncertain, but it seems prudent to recommend that prolonged periods of inverted posturing be avoided.

The incomplete inverse and its applications to the linear least squares problem

NASA Technical Reports Server (NTRS)

Morduch, G. E.

1977-01-01

A modified matrix product is explained, and it is shown that this product defiles a group whose inverse is called the incomplete inverse. It was proven that the incomplete inverse of an augmented normal matrix includes all the quantities associated with the least squares solution. An answer is provided to the problem that occurs when the data residuals are too large and when insufficient data to justify augmenting the model are available.

Analytic semigroups: Applications to inverse problems for flexible structures

NASA Technical Reports Server (NTRS)

Banks, H. T.; Rebnord, D. A.

1990-01-01

Convergence and stability results for least squares inverse problems involving systems described by analytic semigroups are presented. The practical importance of these results is demonstrated by application to several examples from problems of estimation of material parameters in flexible structures using accelerometer data.

A direct method for nonlinear ill-posed problems

NASA Astrophysics Data System (ADS)

Lakhal, A.

2018-02-01

We propose a direct method for solving nonlinear ill-posed problems in Banach-spaces. The method is based on a stable inversion formula we explicitly compute by applying techniques for analytic functions. Furthermore, we investigate the convergence and stability of the method and prove that the derived noniterative algorithm is a regularization. The inversion formula provides a systematic sensitivity analysis. The approach is applicable to a wide range of nonlinear ill-posed problems. We test the algorithm on a nonlinear problem of travel-time inversion in seismic tomography. Numerical results illustrate the robustness and efficiency of the algorithm.

A gradient based algorithm to solve inverse plane bimodular problems of identification

NASA Astrophysics Data System (ADS)

Ran, Chunjiang; Yang, Haitian; Zhang, Guoqing

2018-02-01

This paper presents a gradient based algorithm to solve inverse plane bimodular problems of identifying constitutive parameters, including tensile/compressive moduli and tensile/compressive Poisson's ratios. For the forward bimodular problem, a FE tangent stiffness matrix is derived facilitating the implementation of gradient based algorithms, for the inverse bimodular problem of identification, a two-level sensitivity analysis based strategy is proposed. Numerical verification in term of accuracy and efficiency is provided, and the impacts of initial guess, number of measurement points, regional inhomogeneity, and noisy data on the identification are taken into accounts.

Gravity inversion of a fault by Particle swarm optimization (PSO).

PubMed

Toushmalani, Reza

2013-01-01

Particle swarm optimization is a heuristic global optimization method and also an optimization algorithm, which is based on swarm intelligence. It comes from the research on the bird and fish flock movement behavior. In this paper we introduce and use this method in gravity inverse problem. We discuss the solution for the inverse problem of determining the shape of a fault whose gravity anomaly is known. Application of the proposed algorithm to this problem has proven its capability to deal with difficult optimization problems. The technique proved to work efficiently when tested to a number of models.

The Inverse Problem in Jet Acoustics

NASA Technical Reports Server (NTRS)

Wooddruff, S. L.; Hussaini, M. Y.

2001-01-01

The inverse problem for jet acoustics, or the determination of noise sources from far-field pressure information, is proposed as a tool for understanding the generation of noise by turbulence and for the improved prediction of jet noise. An idealized version of the problem is investigated first to establish the extent to which information about the noise sources may be determined from far-field pressure data and to determine how a well-posed inverse problem may be set up. Then a version of the industry-standard MGB code is used to predict a jet noise source spectrum from experimental noise data.

Seismic-geodynamic constraints on three-dimensional structure, vertical flow, and heat transfer in the mantle

USGS Publications Warehouse

Forte, A.M.; Woodward, R.L.

1997-01-01

Joint inversions of seismic and geodynamic data are carried out in which we simultaneously constrain global-scale seismic heterogeneity in the mantle as well as the amplitude of vertical mantle flow across the 670 km seismic discontinuity. These inversions reveal the existence of a family of three-dimensional (3-D) mantle models that satisfy the data while at the same time yielding predictions of layered mantle flow. The new 3-D mantle models we obtain demonstrate that the buoyancy forces due to the undulations of the 670 km phase-change boundary strongly inhibit the vertical flow between the upper and lower mantle. The strong stabilizing effect of the 670 km topography also has an important impact on the predicted dynamic topography of the Earth's solid surface and on the surface gravity anomalies. The new 3-D models that predict strongly or partially layered mantle flow provide essentially identical fits to the global seismic data as previous models that have, until now, predicted only whole-mantle flow. The convective vertical transport of heat across the mantle predicted on the basis of the new 3-D models shows that the heat flow is a minimum at 1000 km depth. This suggests the presence at this depth of a globally defined horizon across which the pattern of lateral heterogeneity changes rapidly. Copyright 1997 by the American Geophysical Union.

Inverse kinematics problem in robotics using neural networks

NASA Technical Reports Server (NTRS)

Choi, Benjamin B.; Lawrence, Charles

1992-01-01

In this paper, Multilayer Feedforward Networks are applied to the robot inverse kinematic problem. The networks are trained with endeffector position and joint angles. After training, performance is measured by having the network generate joint angles for arbitrary endeffector trajectories. A 3-degree-of-freedom (DOF) spatial manipulator is used for the study. It is found that neural networks provide a simple and effective way to both model the manipulator inverse kinematics and circumvent the problems associated with algorithmic solution methods.

EDITORIAL: Inverse Problems in Engineering

NASA Astrophysics Data System (ADS)

West, Robert M.; Lesnic, Daniel

2007-01-01

Presented here are 11 noteworthy papers selected from the Fifth International Conference on Inverse Problems in Engineering: Theory and Practice held in Cambridge, UK during 11-15 July 2005. The papers have been peer-reviewed to the usual high standards of this journal and the contributions of reviewers are much appreciated. The conference featured a good balance of the fundamental mathematical concepts of inverse problems with a diverse range of important and interesting applications, which are represented here by the selected papers. Aspects of finite-element modelling and the performance of inverse algorithms are investigated by Autrique et al and Leduc et al. Statistical aspects are considered by Emery et al and Watzenig et al with regard to Bayesian parameter estimation and inversion using particle filters. Electrostatic applications are demonstrated by van Berkel and Lionheart and also Nakatani et al. Contributions to the applications of electrical techniques and specifically electrical tomographies are provided by Wakatsuki and Kagawa, Kim et al and Kortschak et al. Aspects of inversion in optical tomography are investigated by Wright et al and Douiri et al. The authors are representative of the worldwide interest in inverse problems relating to engineering applications and their efforts in producing these excellent papers will be appreciated by many readers of this journal.

Inverse problem for multispecies ferromagneticlike mean-field models in phase space with many states

NASA Astrophysics Data System (ADS)

Fedele, Micaela; Vernia, Cecilia

2017-10-01

In this paper we solve the inverse problem for the Curie-Weiss model and its multispecies version when multiple thermodynamic states are present as in the low temperature phase where the phase space is clustered. The inverse problem consists of reconstructing the model parameters starting from configuration data generated according to the distribution of the model. We demonstrate that, without taking into account the presence of many states, the application of the inversion procedure produces very poor inference results. To overcome this problem, we use the clustering algorithm. When the system has two symmetric states of positive and negative magnetizations, the parameter reconstruction can also be obtained with smaller computational effort simply by flipping the sign of the magnetizations from positive to negative (or vice versa). The parameter reconstruction fails when the system undergoes a phase transition: In that case we give the correct inversion formulas for the Curie-Weiss model and we show that they can be used to measure how close the system gets to being critical.

Research on inverse, hybrid and optimization problems in engineering sciences with emphasis on turbomachine aerodynamics: Review of Chinese advances

NASA Technical Reports Server (NTRS)

Liu, Gao-Lian

1991-01-01

Advances in inverse design and optimization theory in engineering fields in China are presented. Two original approaches, the image-space approach and the variational approach, are discussed in terms of turbomachine aerodynamic inverse design. Other areas of research in turbomachine aerodynamic inverse design include the improved mean-streamline (stream surface) method and optimization theory based on optimal control. Among the additional engineering fields discussed are the following: the inverse problem of heat conduction, free-surface flow, variational cogeneration of optimal grid and flow field, and optimal meshing theory of gears.

Domain identification in impedance computed tomography by spline collocation method

NASA Technical Reports Server (NTRS)

Kojima, Fumio

1990-01-01

A method for estimating an unknown domain in elliptic boundary value problems is considered. The problem is formulated as an inverse problem of integral equations of the second kind. A computational method is developed using a splice collocation scheme. The results can be applied to the inverse problem of impedance computed tomography (ICT) for image reconstruction.

Direct-current vertical electrical-resistivity soundings in the Lower Peninsula of Michigan

USGS Publications Warehouse

Westjohn, D.B.; Carter, P.J.

1989-01-01

Ninety-three direct-current vertical electrical-resistivity soundings were conducted in the Lower Peninsula of Michigan from June through October 1987. These soundings were made to assist in mapping the depth to brine in areas where borehole resistivity logs and water-quality data are sparse or lacking. The Schlumberger array for placement of current and potential electrodes was used for each sounding. Vertical electrical-resistivity sounding field data, shifted and smoothed sounding data, and electric layers calculated using inverse modeling techniques are presented. Also included is a summary of the near-surface conditions and depths to conductors and resistors for each sounding location.

Correlation-based regularization and gradient operators for (joint) inversion on unstructured meshes

NASA Astrophysics Data System (ADS)

Jordi, Claudio; Doetsch, Joseph; Günther, Thomas; Schmelzbach, Cedric; Robertsson, Johan

2017-04-01

When working with unstructured meshes for geophysical inversions, special attention should be paid to the design of the operators that are used for regularizing the inverse problem and coupling of different property models in joint inversions. Regularization constraints for inversions on unstructured meshes are often defined in a rather ad-hoc manner and usually only involve the cell to which the operator is applied and its direct neighbours. Similarly, most structural coupling operators for joint inversion, such as the popular cross-gradients operator, are only defined in the direct neighbourhood of a cell. As a result, the regularization and coupling length scales and strength of these operators depend on the discretization as well as cell sizes and shape. Especially for unstructured meshes, where the cell sizes vary throughout the model domain, the dependency of the operator on the discretization may lead to artefacts. Designing operators that are based on a spatial correlation model allows to define correlation length scales over which an operator acts (called footprint), reducing the dependency on the discretization and the effects of variable cell sizes. Moreover, correlation-based operators can accommodate for expected anisotropy by using different length scales in horizontal and vertical directions. Correlation-based regularization operators also known as stochastic regularization operators have already been successfully applied to inversions on regular grids. Here, we formulate stochastic operators for unstructured meshes and apply them in 2D surface and 3D cross-well electrical resistivity tomography data inversion examples of layered media. Especially for the synthetic cross-well example, improved inversion results are achieved when stochastic regularization is used instead of a classical smoothness constraint. For the case of cross-gradients operators for joint inversion, the correlation model is used to define the footprint of the operator and weigh the contributions of the property values that are used to calculate the cross-gradients. In a first series of synthetic-data tests, we examined the mesh dependency of the cross-gradients operators. Compared to operators that are only defined in the direct neighbourhood of a cell, the dependency on the cell size of the cross-gradients calculation is markedly reduced when using operators with larger footprints. A second test with synthetic models focussed on the effect of small-scale variabilities of the parameter value on the cross-gradients calculation. Small-scale variabilities that are superimposed on a global trend of the property value can potentially degrade the cross-gradients calculation and destabilize joint inversion. We observe that the cross-gradients from operators with footprints larger than the length scale of the variabilities are less affected compared to operators with a small footprint. In joint inversions on unstructured meshes, we thus expect the correlation-based coupling operators to ensure robust coupling on a physically meaningful scale.

Light hydrocarbons vertical profiles and fluxes in a french rural area

NASA Astrophysics Data System (ADS)

Kanakidou, M.; Bonsang, B.; Lambert, G.

By means of manned hot air balloon flights, in July 1986, an experiment was conducted in a rural area of southwest France in order to determine the production at ground level of non-methane hydrocarbons in the C 2-C 6 range. Flux determinations were based on vertical profiles before and after the development of a temperature inversion layer which allowed the measurement of the NMHC accumulation close to ground level. The main species produced in the late afternoon were acetylene, propane, ethene, propene and ethane with production rates of the order of 0.5 to 2 × 10 -4g of C m -2 h -1. Isoprene was found to be the main other unsaturated species also produced. The fluxes and the atmospheric content of the air column before the inversion are consistent with an average OH radical concentration of 2 × 10 6 cm -3.

Vertical directivities of seismic arrays on the ground surface

NASA Astrophysics Data System (ADS)

Shiraishi, H.; Asanuma, H.

2012-12-01

Microtremor survey method (MSM) is a technique to estimate subsurface velocity structures by inverting phase velocities of the surface waves in the microtremors. We can explorer the S-wave velocity structures at significantly lower expenses by the MSM than the conventional geophysical techniques because of its passive nature. Coherent waves across an array are identified in the MSM, and, therefore, all the existing velocity inversion methods have been deduced under an implicit assumption of horizontal velocity structure. However, it is expected that the development of the 3D inversion theory would drastically enhance applicability and reliability of the MSM. We, hence, investigated the characteristics of vertical directivities of the arrays deployed on the ground surface as an initial step for deriving the 3D MSM. We have firstly examined the response of an elemental two sensor array to which plane waves propagates from the deep crust with a certain angle of incident, and then examined the characteristics of several types of arrays, including triangular and circular arrays to clarify the characteristics of practical arrays. Real part of the complex coherence function, which has been derived to evaluate coherence of the Rayleigh wave between sensors for plane waves (Shiraishi et al., 2006), has been applied for this investigation. Our results showed that the directivity varies according to a parameter kr ( k : wave number, r : separation of the sensors ). A vertical directivity of two sensor array at kr = π shows a rotationally-symmetrical shape (Figure (a)). In contrast, an equilateral triangle array has a conspicuous directivity toward the vertical direction (cf. Figure (b)). This divergence suggests that the shape of the vertical directivity significantly depend on the geometry, and a sharp directivity toward just beneath the array can be realized by designing the vertical directivity. We concluded from this study that 3D MSM is feasible and further study to investigate measurement and processing theories will be made by the authors. An example of the vertical directivity at kr=π. Red circles represent the sensors.

Computational structures for robotic computations

NASA Technical Reports Server (NTRS)

Lee, C. S. G.; Chang, P. R.

1987-01-01

The computational problem of inverse kinematics and inverse dynamics of robot manipulators by taking advantage of parallelism and pipelining architectures is discussed. For the computation of inverse kinematic position solution, a maximum pipelined CORDIC architecture has been designed based on a functional decomposition of the closed-form joint equations. For the inverse dynamics computation, an efficient p-fold parallel algorithm to overcome the recurrence problem of the Newton-Euler equations of motion to achieve the time lower bound of O(log sub 2 n) has also been developed.

A Toolkit for Forward/Inverse Problems in Electrocardiography within the SCIRun Problem Solving Environment

PubMed Central

Burton, Brett M; Tate, Jess D; Erem, Burak; Swenson, Darrell J; Wang, Dafang F; Steffen, Michael; Brooks, Dana H; van Dam, Peter M; Macleod, Rob S

2012-01-01

Computational modeling in electrocardiography often requires the examination of cardiac forward and inverse problems in order to non-invasively analyze physiological events that are otherwise inaccessible or unethical to explore. The study of these models can be performed in the open-source SCIRun problem solving environment developed at the Center for Integrative Biomedical Computing (CIBC). A new toolkit within SCIRun provides researchers with essential frameworks for constructing and manipulating electrocardiographic forward and inverse models in a highly efficient and interactive way. The toolkit contains sample networks, tutorials and documentation which direct users through SCIRun-specific approaches in the assembly and execution of these specific problems. PMID:22254301

Geoelectric Characterization of Thermal Water Aquifers Using 2.5D Inversion of VES Measurements

NASA Astrophysics Data System (ADS)

Gyulai, Á.; Szűcs, P.; Turai, E.; Baracza, M. K.; Fejes, Z.

2017-03-01

This paper presents a short theoretical summary of the series expansion-based 2.5D combined geoelectric weighted inversion (CGWI) method and highlights the advantageous way with which the number of unknowns can be decreased due to the simultaneous characteristic of this inversion. 2.5D CGWI is an approximate inversion method for the determination of 3D structures, which uses the joint 2D forward modeling of dip and strike direction data. In the inversion procedure, the Steiner's most frequent value method is applied to the automatic separation of dip and strike direction data and outliers. The workflow of inversion and its practical application are presented in the study. For conventional vertical electrical sounding (VES) measurements, this method can determine the parameters of complex structures more accurately than the single inversion method. Field data show that the 2.5D CGWI which was developed can determine the optimal location for drilling an exploratory thermal water prospecting well. The novelty of this research is that the measured VES data in dip and strike direction are jointly inverted by the 2.5D CGWI method.

Physical Activity Producing Low, but Not Medium or Higher, Vertical Impacts Is Inversely Related to BMI in Older Adults: Findings From a Multicohort Study

PubMed Central

Elhakeem, Ahmed; Hannam, Kimberly; Deere, Kevin C; Hartley, April; Clark, Emma M; Moss, Charlotte; Edwards, Mark H; Dennison, Elaine; Gaysin, Tim; Kuh, Diana; Wong, Andrew; Cooper, Cyrus; Cooper, Rachel; Tobias, Jon H

2018-01-01

Abstract Background High impact physical activity (PA) is thought to improve skeletal health, but its relation to other health outcomes are unclear. We investigated associations between PA impact magnitude and body mass index (BMI) in older adults. Methods Data were taken from the Cohort for Skeletal Health in Bristol and Avon (COSHIBA), Hertfordshire Cohort Study, and MRC National Survey of Health and Development. Vertical acceleration peaks from 7-day hip-worn accelerometer recordings were used to classify PA as low (0.5 < g < 1.0g), medium (1 < g < 1.5g), or higher (≥1.5g) impact. Cohort-specific associations of low, medium, and higher impact PA with BMI were examined using linear regressions and estimates combined using random-effects meta-analysis. Results A total of 1182 participants (mean age = 72.7 years, 68% female) were included. Low, medium, and higher impact PA were inversely related to BMI in initial models. After adjustment for confounders and other impacts, low, but not medium or higher, impacts were inversely related to BMI (−0.31, p < .001: overall combined standard deviation change in BMI per doubling in the number of low impacts). In adjusted analyses of body composition measured by dual-energy X-ray absorptiometry in COSHIBA, low, but not medium or higher, impacts were inversely related to total body fat mass (−0.19, p < .001) and android:gynoid fat mass ratio (−0.16, p = .01), whereas high impact PA was weakly and positively associated with lean mass (0.05, p = .06). Conclusions Greater exposure to PA producing low magnitude vertical impacts was associated with lower BMI and fat mass at older age. Low impact PA may help reduce obesity risk in older adults. PMID:29028919

Sensitivity of Ocean Reflectance Inversion Models for Identifying and Discriminating Between Phytoplankton Functional Groups

NASA Technical Reports Server (NTRS)

Werdell, P. Jeremy; Ooesler, Collin S.

2012-01-01

The daily, synoptic images provided by satellite ocean color instruments provide viable data streams for observing changes in the biogeochemistrY of marine ecosystems. Ocean reflectance inversion models (ORMs) provide a common mechanism for inverting the "color" of the water observed a satellite into marine inherent optical properties (lOPs) through a combination of empiricism and radiative transfer theory. lOPs, namely the spectral absorption and scattering characteristics of ocean water and its dissolved and particulate constituents, describe the contents of the upper ocean, information critical for furthering scientific understanding of biogeochemical oceanic processes. Many recent studies inferred marine particle sizes and discriminated between phytoplankton functional groups using remotely-sensed lOPs. While all demonstrated the viability of their approaches, few described the vertical distributions of the water column constituents under consideration and, thus, failed to report the biophysical conditions under which their model performed (e.g., the depth and thickness of the phytoplankton bloom(s)). We developed an ORM to remotely identifY Noctiluca miliaris and other phytoplankton functional types using satellite ocean color data records collected in the northern Arabian Sea. Here, we present results from analyses designed to evaluate the applicability and sensitivity of the ORM to varied biophysical conditions. Specifically, we: (1) synthesized a series of vertical profiles of spectral inherent optical properties that represent a wide variety of bio-optical conditions for the northern Arabian Sea under aN Miliaris bloom; (2) generated spectral remote-sensing reflectances from these profiles using Hydrolight; and, (3) applied the ORM to the synthesized reflectances to estimate the relative concentrations of diatoms and N Miliaris for each example. By comparing the estimates from the inversion model to those from synthesized vertical profiles, we were able to identifY those bio-optical conditions under which the inversion model performs both well and poorly.

The role of simulated small-scale ocean variability in inverse computations for ocean acoustic tomography.

PubMed

Dushaw, Brian D; Sagen, Hanne

2017-12-01

Ocean acoustic tomography depends on a suitable reference ocean environment with which to set the basic parameters of the inverse problem. Some inverse problems may require a reference ocean that includes the small-scale variations from internal waves, small mesoscale, or spice. Tomographic inversions that employ data of stable shadow zone arrivals, such as those that have been observed in the North Pacific and Canary Basin, are an example. Estimating temperature from the unique acoustic data that have been obtained in Fram Strait is another example. The addition of small-scale variability to augment a smooth reference ocean is essential to understanding the acoustic forward problem in these cases. Rather than a hindrance, the stochastic influences of the small scale can be exploited to obtain accurate inverse estimates. Inverse solutions are readily obtained, and they give computed arrival patterns that matched the observations. The approach is not ad hoc, but universal, and it has allowed inverse estimates for ocean temperature variations in Fram Strait to be readily computed on several acoustic paths for which tomographic data were obtained.

Joint Geophysical Inversion With Multi-Objective Global Optimization Methods

NASA Astrophysics Data System (ADS)

Lelievre, P. G.; Bijani, R.; Farquharson, C. G.

2015-12-01

Pareto multi-objective global optimization (PMOGO) methods generate a suite of solutions that minimize multiple objectives (e.g. data misfits and regularization terms) in a Pareto-optimal sense. Providing a suite of models, as opposed to a single model that minimizes a weighted sum of objectives, allows a more complete assessment of the possibilities and avoids the often difficult choice of how to weight each objective. We are applying PMOGO methods to three classes of inverse problems. The first class are standard mesh-based problems where the physical property values in each cell are treated as continuous variables. The second class of problems are also mesh-based but cells can only take discrete physical property values corresponding to known or assumed rock units. In the third class we consider a fundamentally different type of inversion in which a model comprises wireframe surfaces representing contacts between rock units; the physical properties of each rock unit remain fixed while the inversion controls the position of the contact surfaces via control nodes. This third class of problem 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. Joint inversion is greatly simplified for the latter two problem classes because no additional mathematical coupling measure is required in the objective function. PMOGO methods can solve numerically complicated problems that could not be solved with standard descent-based local minimization methods. This includes the latter two classes of problems mentioned above. There are significant increases in the computational requirements when PMOGO methods are used but these can be ameliorated using parallelization and problem dimension reduction strategies.

An inverse dynamics approach to trajectory optimization and guidance for an aerospace plane

NASA Technical Reports Server (NTRS)

Lu, Ping

1992-01-01

The optimal ascent problem for an aerospace planes is formulated as an optimal inverse dynamic problem. Both minimum-fuel and minimax type of performance indices are considered. Some important features of the optimal trajectory and controls are used to construct a nonlinear feedback midcourse controller, which not only greatly simplifies the difficult constrained optimization problem and yields improved solutions, but is also suited for onboard implementation. Robust ascent guidance is obtained by using combination of feedback compensation and onboard generation of control through the inverse dynamics approach. Accurate orbital insertion can be achieved with near-optimal control of the rocket through inverse dynamics even in the presence of disturbances.

Time-reversal and Bayesian inversion

NASA Astrophysics Data System (ADS)

Debski, Wojciech

2017-04-01

Probabilistic inversion technique is superior to the classical optimization-based approach in all but one aspects. It requires quite exhaustive computations which prohibit its use in huge size inverse problems like global seismic tomography or waveform inversion to name a few. The advantages of the approach are, however, so appealing that there is an ongoing continuous afford to make the large inverse task as mentioned above manageable with the probabilistic inverse approach. One of the perspective possibility to achieve this goal relays on exploring the internal symmetry of the seismological modeling problems in hand - a time reversal and reciprocity invariance. This two basic properties of the elastic wave equation when incorporating into the probabilistic inversion schemata open a new horizons for Bayesian inversion. In this presentation we discuss the time reversal symmetry property, its mathematical aspects and propose how to combine it with the probabilistic inverse theory into a compact, fast inversion algorithm. We illustrate the proposed idea with the newly developed location algorithm TRMLOC and discuss its efficiency when applied to mining induced seismic data.

Inverse random source scattering for the Helmholtz equation in inhomogeneous media

NASA Astrophysics Data System (ADS)

Li, Ming; Chen, Chuchu; Li, Peijun

2018-01-01

This paper is concerned with an inverse random source scattering problem in an inhomogeneous background medium. The wave propagation is modeled by the stochastic Helmholtz equation with the source driven by additive white noise. The goal is to reconstruct the statistical properties of the random source such as the mean and variance from the boundary measurement of the radiated random wave field at multiple frequencies. Both the direct and inverse problems are considered. We show that the direct problem has a unique mild solution by a constructive proof. For the inverse problem, we derive Fredholm integral equations, which connect the boundary measurement of the radiated wave field with the unknown source function. A regularized block Kaczmarz method is developed to solve the ill-posed integral equations. Numerical experiments are included to demonstrate the effectiveness of the proposed method.

The inverse Numerical Computer Program FLUX-BOT for estimating Vertical Water Fluxes from Temperature Time-Series.

NASA Astrophysics Data System (ADS)

Trauth, N.; Schmidt, C.; Munz, M.

2016-12-01

Heat as a natural tracer to quantify water fluxes between groundwater and surface water has evolved to a standard hydrological method. Typically, time series of temperatures in the surface water and in the sediment are observed and are subsequently evaluated by a vertical 1D representation of heat transport by advection and dispersion. Several analytical solutions as well as their implementation into user-friendly software exist in order to estimate water fluxes from the observed temperatures. Analytical solutions can be easily implemented but assumptions on the boundary conditions have to be made a priori, e.g. sinusoidal upper temperature boundary. Numerical models offer more flexibility and can handle temperature data which is characterized by irregular variations such as storm-event induced temperature changes and thus cannot readily be incorporated in analytical solutions. This also reduced the effort of data preprocessing such as the extraction of the diurnal temperature variation. We developed a software to estimate water FLUXes Based On Temperatures- FLUX-BOT. FLUX-BOT is a numerical code written in MATLAB which is intended to calculate vertical water fluxes in saturated sediments, based on the inversion of measured temperature time series observed at multiple depths. It applies a cell-centered Crank-Nicolson implicit finite difference scheme to solve the one-dimensional heat advection-conduction equation. Besides its core inverse numerical routines, FLUX-BOT includes functions visualizing the results and functions for performing uncertainty analysis. We provide applications of FLUX-BOT to generic as well as to measured temperature data to demonstrate its performance.

Synoptic-Scale Behavior of the Extratropical Tropopause Inversion Layer

NASA Astrophysics Data System (ADS)

Pilch Kedzierski, Robin; Matthes, Katja; Bumke, Karl

2015-04-01

The Tropopause Inversion Layer (TIL) is a climatological feature of the tropopause region, characterized by enhanced static stability and strong temperature inversion in a thin layer (about 1km deep) right above the tropopause. It was discovered recently via tropopause-based averaging [Birner 2002]. The sharp static stability, temperature and wind shear gradients of the TIL theoretically shall inhibit stratosphere-troposphere exchange and influence the vertical propagation of planetary scale Rossby and small-scale gravity waves. High vertically resolved radiosonde and GPS radio occultation measurements show that the strength of the TIL is positively correlated with the tropopause height and anticyclonic conditions, and that it reaches its maximum strength in polar regions during summer [Birner 2006] [Randel and Wu, 2007 and 2010]. Our study takes advantage of the high density of vertical profiles (~2000 measurements per day, globally) measured by the COSMIC satellites (2007-present), in order to describe the synoptic-scale structures of the TIL and the differences between the seasonal climatologies from earlier studies and the real-time TIL. Also, using ERA-Interim reanalysis wind fields, we split relative vorticity into shear and curl terms and study separately their relation to TIL strength in cyclonic-anticyclonic conditions. We find that the TIL has a rich zonal structure, especially in midlatitude winter, and that its strength is instantly adjusted to the synoptic situation at near-tropopause level. The peaks of strongest TIL at midlatitude ridges in winter are stronger and much more frequent than any peaks found in polar summer. The roles of shear and curl vorticity differ substantially towards higher values of relative vorticity (both cyclonic and anticyclonic).

The double tropopause and its dynamical relationship to the tropopause inversion layer in storm track regions

NASA Astrophysics Data System (ADS)

Peevey, T. R.; Gille, J. C.; Homeyer, C. R.; Manney, G. L.

2014-09-01

Using High Resolution Dynamic Limb Sounder observations and ERA-Interim reanalysis this study demonstrates that the warm conveyor belt (WCB) is a mechanism responsible for the relationship between the double tropopause (DT) and the tropopause inversion layer (TIL), a relationship recently suggested in the literature based on idealized model simulations of baroclinic disturbances. Using these data sets, spatial and temporal characteristics of the DT-TIL relationship are examined over a 3 year period, 2005-2008. In the extratropics, results from satellite data show that as the TIL increases in strength, so does the frequency of the DT, regardless of season or hemisphere. The inverse relationship is found in the tropics. Using only DT profiles, zonal composites of wind, relative vorticity, and temperature from reanalysis data show that as the TIL increases in strength, the upper tropospheric circulation switches from cyclonic to anticyclonic, and the upward vertical motion increases. This result suggests the WCB as a mechanism since it is on the anticyclonic side of the jet and is characterized by the movement of tropical air poleward and upward from the surface. To verify this relationship, the vertical and horizontal development of a synoptic-scale baroclinic system is analyzed over a 4 day period. Results show the equatorward extension of the polar tropopause, and thus the formation of the DT, due to the strengthening of the TIL in the region of vertical motion associated with the WCB. Moreover, this result suggests that air movement within the DT could originate from high latitudes when associated with a baroclinic disturbance.

Rapid processing of data based on high-performance algorithms for solving inverse problems and 3D-simulation of the tsunami and earthquakes

NASA Astrophysics Data System (ADS)

Marinin, I. V.; Kabanikhin, S. I.; Krivorotko, O. I.; Karas, A.; Khidasheli, D. G.

2012-04-01

We consider new techniques and methods for earthquake and tsunami related problems, particularly - inverse problems for the determination of tsunami source parameters, numerical simulation of long wave propagation in soil and water and tsunami risk estimations. In addition, we will touch upon the issue of database management and destruction scenario visualization. New approaches and strategies, as well as mathematical tools and software are to be shown. The long joint investigations by researchers of the Institute of Mathematical Geophysics and Computational Mathematics SB RAS and specialists from WAPMERR and Informap have produced special theoretical approaches, numerical methods, and software tsunami and earthquake modeling (modeling of propagation and run-up of tsunami waves on coastal areas), visualization, risk estimation of tsunami, and earthquakes. Algorithms are developed for the operational definition of the origin and forms of the tsunami source. The system TSS numerically simulates the source of tsunami and/or earthquakes and includes the possibility to solve the direct and the inverse problem. It becomes possible to involve advanced mathematical results to improve models and to increase the resolution of inverse problems. Via TSS one can construct maps of risks, the online scenario of disasters, estimation of potential damage to buildings and roads. One of the main tools for the numerical modeling is the finite volume method (FVM), which allows us to achieve stability with respect to possible input errors, as well as to achieve optimum computing speed. Our approach to the inverse problem of tsunami and earthquake determination is based on recent theoretical results concerning the Dirichlet problem for the wave equation. This problem is intrinsically ill-posed. We use the optimization approach to solve this problem and SVD-analysis to estimate the degree of ill-posedness and to find the quasi-solution. The software system we developed is intended to create technology «no frost», realizing a steady stream of direct and inverse problems: solving the direct problem, the visualization and comparison with observed data, to solve the inverse problem (correction of the model parameters). The main objective of further work is the creation of a workstation operating emergency tool that could be used by an emergency duty person in real time.

PREFACE: First International Congress of the International Association of Inverse Problems (IPIA): Applied Inverse Problems 2007: Theoretical and Computational Aspects

NASA Astrophysics Data System (ADS)

Uhlmann, Gunther

2008-07-01

This volume represents the proceedings of the fourth Applied Inverse Problems (AIP) international conference and the first congress of the Inverse Problems International Association (IPIA) which was held in Vancouver, Canada, June 25 29, 2007. The organizing committee was formed by Uri Ascher, University of British Columbia, Richard Froese, University of British Columbia, Gary Margrave, University of Calgary, and Gunther Uhlmann, University of Washington, chair. The conference was part of the activities of the Pacific Institute of Mathematical Sciences (PIMS) Collaborative Research Group on inverse problems (http://www.pims.math.ca/scientific/collaborative-research-groups/past-crgs). This event was also supported by grants from NSF and MITACS. Inverse Problems (IP) are problems where causes for a desired or an observed effect are to be determined. They lie at the heart of scientific inquiry and technological development. The enormous increase in computing power and the development of powerful algorithms have made it possible to apply the techniques of IP to real-world problems of growing complexity. Applications include a number of medical as well as other imaging techniques, location of oil and mineral deposits in the earth's substructure, creation of astrophysical images from telescope data, finding cracks and interfaces within materials, shape optimization, model identification in growth processes and, more recently, modelling in the life sciences. The series of Applied Inverse Problems (AIP) Conferences aims to provide a primary international forum for academic and industrial researchers working on all aspects of inverse problems, such as mathematical modelling, functional analytic methods, computational approaches, numerical algorithms etc. The steering committee of the AIP conferences consists of Heinz Engl (Johannes Kepler Universität, Austria), Joyce McLaughlin (RPI, USA), William Rundell (Texas A&M, USA), Erkki Somersalo (Helsinki University of Technology, Finland), Masahiro Yamamoto (University of Tokyo, Japan), Gunther Uhlmann (University of Washington) and Jun Zou (Chinese University of Hong Kong). IPIA is a recently formed organization that intends to promote the field of inverse problem at all levels. See http://www.inverse-problems.net/. IPIA awarded the first Calderón prize at the opening of the conference to Matti Lassas (see first article in the Proceedings). There was also a general meeting of IPIA during the workshop. This was probably the largest conference ever on IP with 350 registered participants. The program consisted of 18 invited speakers and the Calderón Prize Lecture given by Matti Lassas. Another integral part of the program was the more than 60 mini-symposia that covered a broad spectrum of the theory and applications of inverse problems, focusing on recent developments in medical imaging, seismic exploration, remote sensing, industrial applications, numerical and regularization methods in inverse problems. Another important related topic was image processing in particular the advances which have allowed for significant enhancement of widely used imaging techniques. For more details on the program see the web page: http://www.pims.math.ca/science/2007/07aip. These proceedings reflect the broad spectrum of topics covered in AIP 2007. The conference and these proceedings would not have happened without the contributions of many people. I thank all my fellow organizers, the invited speakers, the speakers and organizers of mini-symposia for making this an exciting and vibrant event. I also thank PIMS, NSF and MITACS for their generous financial support. I take this opportunity to thank the PIMS staff, particularly Ken Leung, for making the local arrangements. Also thanks are due to Stephen McDowall for his help in preparing the schedule of the conference and Xiaosheng Li for the help in preparing these proceedings. I also would like to thank the contributors of this volume and the referees. Finally, many thanks are due to Graham Douglas and Elaine Longden-Chapman for suggesting publication in Journal of Physics: Conference Series.

Modular Approaches to Earth Science Scientific Computing: 3D Electromagnetic Induction Modeling as an Example

NASA Astrophysics Data System (ADS)

Tandon, K.; Egbert, G.; Siripunvaraporn, W.

2003-12-01

We are developing a modular system for three-dimensional inversion of electromagnetic (EM) induction data, using an object oriented programming approach. This approach allows us to modify the individual components of the inversion scheme proposed, and also reuse the components for variety of problems in earth science computing howsoever diverse they might be. In particular, the modularity allows us to (a) change modeling codes independently of inversion algorithm details; (b) experiment with new inversion algorithms; and (c) modify the way prior information is imposed in the inversion to test competing hypothesis and techniques required to solve an earth science problem. Our initial code development is for EM induction equations on a staggered grid, using iterative solution techniques in 3D. An example illustrated here is an experiment with the sensitivity of 3D magnetotelluric inversion to uncertainties in the boundary conditions required for regional induction problems. These boundary conditions should reflect the large-scale geoelectric structure of the study area, which is usually poorly constrained. In general for inversion of MT data, one fixes boundary conditions at the edge of the model domain, and adjusts the earth?s conductivity structure within the modeling domain. Allowing for errors in specification of the open boundary values is simple in principle, but no existing inversion codes that we are aware of have this feature. Adding a feature such as this is straightforward within the context of the modular approach. More generally, a modular approach provides an efficient methodology for setting up earth science computing problems to test various ideas. As a concrete illustration relevant to EM induction problems, we investigate the sensitivity of MT data near San Andreas Fault at Parkfield (California) to uncertainties in the regional geoelectric structure.

Definition and solution of a stochastic inverse problem for the Manning’s n parameter field in hydrodynamic models

DOE PAGES

Butler, Troy; Graham, L.; Estep, D.; ...

2015-02-03

The uncertainty in spatially heterogeneous Manning’s n fields is quantified using a novel formulation and numerical solution of stochastic inverse problems for physics-based models. The uncertainty is quantified in terms of a probability measure and the physics-based model considered here is the state-of-the-art ADCIRC model although the presented methodology applies to other hydrodynamic models. An accessible overview of the formulation and solution of the stochastic inverse problem in a mathematically rigorous framework based on measure theory is presented in this paper. Technical details that arise in practice by applying the framework to determine the Manning’s n parameter field in amore » shallow water equation model used for coastal hydrodynamics are presented and an efficient computational algorithm and open source software package are developed. A new notion of “condition” for the stochastic inverse problem is defined and analyzed as it relates to the computation of probabilities. Finally, this notion of condition is investigated to determine effective output quantities of interest of maximum water elevations to use for the inverse problem for the Manning’s n parameter and the effect on model predictions is analyzed.« less

A Riemann-Hilbert approach to the inverse problem for the Stark operator on the line

NASA Astrophysics Data System (ADS)

Its, A.; Sukhanov, V.

2016-05-01

The paper is concerned with the inverse scattering problem for the Stark operator on the line with a potential from the Schwartz class. In our study of the inverse problem, we use the Riemann-Hilbert formalism. This allows us to overcome the principal technical difficulties which arise in the more traditional approaches based on the Gel’fand-Levitan-Marchenko equations, and indeed solve the problem. We also produce a complete description of the relevant scattering data (which have not been obtained in the previous works on the Stark operator) and establish the bijection between the Schwartz class potentials and the scattering data.

Track monitoring from the dynamic response of a passing train: A sparse approach

NASA Astrophysics Data System (ADS)

Lederman, George; Chen, Siheng; Garrett, James H.; Kovačević, Jelena; Noh, Hae Young; Bielak, Jacobo

2017-06-01

Collecting vibration data from revenue service trains could be a low-cost way to more frequently monitor railroad tracks, yet operational variability makes robust analysis a challenge. We propose a novel analysis technique for track monitoring that exploits the sparsity inherent in train-vibration data. This sparsity is based on the observation that large vertical train vibrations typically involve the excitation of the train's fundamental mode due to track joints, switchgear, or other discrete hardware. Rather than try to model the entire rail profile, in this study we examine a sparse approach to solving an inverse problem where (1) the roughness is constrained to a discrete and limited set of "bumps"; and (2) the train system is idealized as a simple damped oscillator that models the train's vibration in the fundamental mode. We use an expectation maximization (EM) approach to iteratively solve for the track profile and the train system properties, using orthogonal matching pursuit (OMP) to find the sparse approximation within each step. By enforcing sparsity, the inverse problem is well posed and the train's position can be found relative to the sparse bumps, thus reducing the uncertainty in the GPS data. We validate the sparse approach on two sections of track monitored from an operational train over a 16 month period of time, one where track changes did not occur during this period and another where changes did occur. We show that this approach can not only detect when track changes occur, but also offers insight into the type of such changes.

Iterative electromagnetic Born inversion applied to earth conductivity imaging

NASA Astrophysics Data System (ADS)

Alumbaugh, D. L.

1993-08-01

This thesis investigates the use of a fast imaging technique to deduce the spatial conductivity distribution in the earth from low frequency (less than 1 MHz), cross well electromagnetic (EM) measurements. The theory embodied in this work is the extension of previous strategies and is based on the Born series approximation to solve both the forward and inverse problem. Nonlinear integral equations are employed to derive the series expansion which accounts for the scattered magnetic fields that are generated by inhomogeneities embedded in either a homogenous or a layered earth. A sinusoidally oscillating, vertically oriented magnetic dipole is employed as a source, and it is assumed that the scattering bodies are azimuthally symmetric about the source dipole axis. The use of this model geometry reduces the 3-D vector problem to a more manageable 2-D scalar form. The validity of the cross well EM method is tested by applying the imaging scheme to two sets of field data. Images of the data collected at the Devine, Texas test site show excellent correlation with the well logs. Unfortunately there is a drift error present in the data that limits the accuracy of the results. A more complete set of data collected at the Richmond field station in Richmond, California demonstrates that cross well EM can be successfully employed to monitor the position of an injected mass of salt water. Both the data and the resulting images clearly indicate the plume migrates toward the north-northwest. The plausibility of these conclusions is verified by applying the imaging code to synthetic data generated by a 3-D sheet model.

Inverse energy cascade and emergence of large coherent vortices in turbulence driven by Faraday waves.

PubMed

Francois, N; Xia, H; Punzmann, H; Shats, M

2013-05-10

We report the generation of large coherent vortices via inverse energy cascade in Faraday wave driven turbulence. The motion of floaters in the Faraday waves is three dimensional, but its horizontal velocity fluctuations show unexpected similarity with two-dimensional turbulence. The inverse cascade is detected by measuring frequency spectra of the Lagrangian velocity, and it is confirmed by computing the third moment of the horizontal velocity fluctuations. This is observed in deep water in a broad range of wavelengths and vertical accelerations. The results broaden the scope of recent findings on Faraday waves in thin layers [A. von Kameke et al., Phys. Rev. Lett. 107, 074502 (2011)].

Development of a Preventive HIV Vaccine Requires Solving Inverse Problems Which Is Unattainable by Rational Vaccine Design

PubMed Central

Van Regenmortel, Marc H. V.

2018-01-01

Hypotheses and theories are essential constituents of the scientific method. Many vaccinologists are unaware that the problems they try to solve are mostly inverse problems that consist in imagining what could bring about a desired outcome. An inverse problem starts with the result and tries to guess what are the multiple causes that could have produced it. Compared to the usual direct scientific problems that start with the causes and derive or calculate the results using deductive reasoning and known mechanisms, solving an inverse problem uses a less reliable inductive approach and requires the development of a theoretical model that may have different solutions or none at all. Unsuccessful attempts to solve inverse problems in HIV vaccinology by reductionist methods, systems biology and structure-based reverse vaccinology are described. The popular strategy known as rational vaccine design is unable to solve the multiple inverse problems faced by HIV vaccine developers. The term “rational” is derived from “rational drug design” which uses the 3D structure of a biological target for designing molecules that will selectively bind to it and inhibit its biological activity. In vaccine design, however, the word “rational” simply means that the investigator is concentrating on parts of the system for which molecular information is available. The economist and Nobel laureate Herbert Simon introduced the concept of “bounded rationality” to explain why the complexity of the world economic system makes it impossible, for instance, to predict an event like the financial crash of 2007–2008. Humans always operate under unavoidable constraints such as insufficient information, a limited capacity to process huge amounts of data and a limited amount of time available to reach a decision. Such limitations always prevent us from achieving the complete understanding and optimization of a complex system that would be needed to achieve a truly rational design process. This is why the complexity of the human immune system prevents us from rationally designing an HIV vaccine by solving inverse problems. PMID:29387066

The importance of coherence in inverse problems in optics

NASA Astrophysics Data System (ADS)

Ferwerda, H. A.; Baltes, H. P.; Glass, A. S.; Steinle, B.

1981-12-01

Current inverse problems of statistical optics are presented with a guide to relevant literature. The inverse problems are categorized into four groups, and the Van Cittert-Zernike theorem and its generalization are discussed. The retrieval of structural information from the far-zone degree of coherence and the time-averaged intensity distribution of radiation scattered by a superposition of random and periodic scatterers are also discussed. In addition, formulas for the calculation of far-zone properties are derived within the framework of scalar optics, and results are applied to two examples.

Comparison of iterative inverse coarse-graining methods

NASA Astrophysics Data System (ADS)

Rosenberger, David; Hanke, Martin; van der Vegt, Nico F. A.

2016-10-01

Deriving potentials for coarse-grained Molecular Dynamics (MD) simulations is frequently done by solving an inverse problem. Methods like Iterative Boltzmann Inversion (IBI) or Inverse Monte Carlo (IMC) have been widely used to solve this problem. The solution obtained by application of these methods guarantees a match in the radial distribution function (RDF) between the underlying fine-grained system and the derived coarse-grained system. However, these methods often fail in reproducing thermodynamic properties. To overcome this deficiency, additional thermodynamic constraints such as pressure or Kirkwood-Buff integrals (KBI) may be added to these methods. In this communication we test the ability of these methods to converge to a known solution of the inverse problem. With this goal in mind we have studied a binary mixture of two simple Lennard-Jones (LJ) fluids, in which no actual coarse-graining is performed. We further discuss whether full convergence is actually needed to achieve thermodynamic representability.

Atmospheric inverse modeling via sparse reconstruction

NASA Astrophysics Data System (ADS)

Hase, Nils; Miller, Scot M.; Maaß, Peter; Notholt, Justus; Palm, Mathias; Warneke, Thorsten

2017-10-01

Many applications in atmospheric science involve ill-posed inverse problems. A crucial component of many inverse problems is the proper formulation of a priori knowledge about the unknown parameters. In most cases, this knowledge is expressed as a Gaussian prior. This formulation often performs well at capturing smoothed, large-scale processes but is often ill equipped to capture localized structures like large point sources or localized hot spots. Over the last decade, scientists from a diverse array of applied mathematics and engineering fields have developed sparse reconstruction techniques to identify localized structures. In this study, we present a new regularization approach for ill-posed inverse problems in atmospheric science. It is based on Tikhonov regularization with sparsity constraint and allows bounds on the parameters. We enforce sparsity using a dictionary representation system. We analyze its performance in an atmospheric inverse modeling scenario by estimating anthropogenic US methane (CH4) emissions from simulated atmospheric measurements. Different measures indicate that our sparse reconstruction approach is better able to capture large point sources or localized hot spots than other methods commonly used in atmospheric inversions. It captures the overall signal equally well but adds details on the grid scale. This feature can be of value for any inverse problem with point or spatially discrete sources. We show an example for source estimation of synthetic methane emissions from the Barnett shale formation.

The role of gravity in apical dominance: effects of clinostating on shoot inversion-induced ethylene production, shoot elongation and lateral bud growth

NASA Technical Reports Server (NTRS)

Prasad, T. K.; Cline, M. G.

1987-01-01

Shoot inversion-induced release of apical dominance in Pharbitis nil is inhibited by rotating the plant at 0.42 revolutions per minute in a vertical plane perpendicular to the axis of rotation of a horizontal clinostat. Clinostating prevented lateral bud outgrowth, apparently by negating the restriction of the shoot elongation via reduction of ethylene production in the inverted shoot. Radial stem expansion was also decreased. Data from experiments with intact tissue and isolated segments indicated that shoot-inversion stimulates ethylene production by increasing the activity of 1-aminocyclopropane-1-carboxylic acid synthase. The results support the hypothesis that shoot inversion-induced release of apical dominance in Pharbitis nil is due to gravity stress and is mediated by ethylene-induced retardation of the elongation of the inverted shoot.

Variable-permittivity linear inverse problem for the H(sub z)-polarized case

NASA Technical Reports Server (NTRS)

Moghaddam, M.; Chew, W. C.

1993-01-01

The H(sub z)-polarized inverse problem has rarely been studied before due to the complicated way in which the unknown permittivity appears in the wave equation. This problem is equivalent to the acoustic inverse problem with variable density. We have recently reported the solution to the nonlinear variable-permittivity H(sub z)-polarized inverse problem using the Born iterative method. Here, the linear inverse problem is solved for permittivity (epsilon) and permeability (mu) using a different approach which is an extension of the basic ideas of diffraction tomography (DT). The key to solving this problem is to utilize frequency diversity to obtain the required independent measurements. The receivers are assumed to be in the far field of the object, and plane wave incidence is also assumed. It is assumed that the scatterer is weak, so that the Born approximation can be used to arrive at a relationship between the measured pressure field and two terms related to the spatial Fourier transform of the two unknowns, epsilon and mu. The term involving permeability corresponds to monopole scattering and that for permittivity to dipole scattering. Measurements at several frequencies are used and a least squares problem is solved to reconstruct epsilon and mu. It is observed that the low spatial frequencies in the spectra of epsilon and mu produce inaccuracies in the results. Hence, a regularization method is devised to remove this problem. Several results are shown. Low contrast objects for which the above analysis holds are used to show that good reconstructions are obtained for both permittivity and permeability after regularization is applied.

On computational experiments in some inverse problems of heat and mass transfer

NASA Astrophysics Data System (ADS)

Bilchenko, G. G.; Bilchenko, N. G.

2016-11-01

The results of mathematical modeling of effective heat and mass transfer on hypersonic aircraft permeable surfaces are considered. The physic-chemical processes (the dissociation and the ionization) in laminar boundary layer of compressible gas are appreciated. Some algorithms of control restoration are suggested for the interpolation and approximation statements of heat and mass transfer inverse problems. The differences between the methods applied for the problem solutions search for these statements are discussed. Both the algorithms are realized as programs. Many computational experiments were accomplished with the use of these programs. The parameters of boundary layer obtained by means of the A.A.Dorodnicyn's generalized integral relations method from solving the direct problems have been used to obtain the inverse problems solutions. Two types of blowing laws restoration for the inverse problem in interpolation statement are presented as the examples. The influence of the temperature factor on the blowing restoration is investigated. The different character of sensitivity of controllable parameters (the local heat flow and local tangent friction) respectively to step (discrete) changing of control (the blowing) and the switching point position is studied.

On size-constrained minimum s–t cut problems and size-constrained dense subgraph problems

DOE PAGES

Chen, Wenbin; Samatova, Nagiza F.; Stallmann, Matthias F.; ...

2015-10-30

In some application cases, the solutions of combinatorial optimization problems on graphs should satisfy an additional vertex size constraint. In this paper, we consider size-constrained minimum s–t cut problems and size-constrained dense subgraph problems. We introduce the minimum s–t cut with at-least-k vertices problem, the minimum s–t cut with at-most-k vertices problem, and the minimum s–t cut with exactly k vertices problem. We prove that they are NP-complete. Thus, they are not polynomially solvable unless P = NP. On the other hand, we also study the densest at-least-k-subgraph problem (DalkS) and the densest at-most-k-subgraph problem (DamkS) introduced by Andersen andmore » Chellapilla [1]. We present a polynomial time algorithm for DalkS when k is bounded by some constant c. We also present two approximation algorithms for DamkS. In conclusion, the first approximation algorithm for DamkS has an approximation ratio of n-1/k-1, where n is the number of vertices in the input graph. The second approximation algorithm for DamkS has an approximation ratio of O (n δ), for some δ < 1/3.« less

Surface Gravity Data Contribution to the Puerto Rico and U.S. Virgin Islands Geoid Model

NASA Astrophysics Data System (ADS)

Li, X.; Gerhards, C.; Holmes, S. A.; Saleh, J.; Shaw, B.

2015-12-01

The Gravity for the Redefinition of the American Vertical Datum (GRAV-D) project provides updated local gravity field information for the XGEOID15 models. In particular, its airborne gravity data in the area of Puerto Rico and U.S. Virgin Islands (PRVI) made substantial improvements (~60%) on the precision of the geoid models at the local GNSS/Leveling bench marks in the target area. Fortunately, PRVI is free of the huge systematic error in the North American Vertical Datum of 1988 (NAVD88). Thus, the airborne contribution was evaluated more realistically. In addition, the airborne data picked up more detailed gravity field information in the medium wavelength band (spherical harmonic degree 200 to 600) that are largely beyond the resolution of the current satellite missions, especially along the nearby ocean trench areas. Under this circumstance (significant airborne contributions in the medium band), local surface gravity data need to be examined more carefully than before during merging with the satellite and airborne information for local geoid improvement, especially considering the well-known systematic problems in the NGS historical gravity holdings (Saleh et al 2013 JoG). Initial tests showed that it is very important to maintain high consistency between the surface data sets and the airborne enhanced reference model. In addition, a new aggregation method (Gerhards 2014, Inverse Problems) will also be tested to optimally combine the local surface data with the reference model. The data cleaning and combining procedures in the target area will be summarized here as reference for future applications.

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Regularization Reconstruction Method for Imaging Problems in Electrical Capacitance Tomography

NASA Astrophysics Data System (ADS)

Chu, Pan; Lei, Jing

2017-11-01

The electrical capacitance tomography (ECT) is deemed to be a powerful visualization measurement technique for the parametric measurement in a multiphase flow system. The inversion task in the ECT technology is an ill-posed inverse problem, and seeking for an efficient numerical method to improve the precision of the reconstruction images is important for practical measurements. By the introduction of the Tikhonov regularization (TR) methodology, in this paper a loss function that emphasizes the robustness of the estimation and the low rank property of the imaging targets is put forward to convert the solution of the inverse problem in the ECT reconstruction task into a minimization problem. Inspired by the split Bregman (SB) algorithm, an iteration scheme is developed for solving the proposed loss function. Numerical experiment results validate that the proposed inversion method not only reconstructs the fine structures of the imaging targets, but also improves the robustness.

Termination Proofs for String Rewriting Systems via Inverse Match-Bounds

NASA Technical Reports Server (NTRS)

Butler, Ricky (Technical Monitor); Geser, Alfons; Hofbauer, Dieter; Waldmann, Johannes

2004-01-01

Annotating a letter by a number, one can record information about its history during a reduction. A string rewriting system is called match-bounded if there is a global upper bound to these numbers. In earlier papers we established match-boundedness as a strong sufficient criterion for both termination and preservation of regular languages. We show now that the string rewriting system whose inverse (left and right hand sides exchanged) is match-bounded, also have exceptional properties, but slightly different ones. Inverse match-bounded systems effectively preserve context-free languages; their sets of normalized strings and their sets of immortal strings are effectively regular. These sets of strings can be used to decide the normalization, the termination and the uniform termination problems of inverse match-bounded systems. We also show that the termination problem is decidable in linear time, and that a certain strong reachability problem is deciable, thus solving two open problems of McNaughton's.

Assimilating data into open ocean tidal models

NASA Astrophysics Data System (ADS)

Kivman, Gennady A.

The problem of deriving tidal fields from observations by reason of incompleteness and imperfectness of every data set practically available has an infinitely large number of allowable solutions fitting the data within measurement errors and hence can be treated as ill-posed. Therefore, interpolating the data always relies on some a priori assumptions concerning the tides, which provide a rule of sampling or, in other words, a regularization of the ill-posed problem. Data assimilation procedures used in large scale tide modeling are viewed in a common mathematical framework as such regularizations. It is shown that they all (basis functions expansion, parameter estimation, nudging, objective analysis, general inversion, and extended general inversion), including those (objective analysis and general inversion) originally formulated in stochastic terms, may be considered as utilizations of one of the three general methods suggested by the theory of ill-posed problems. The problem of grid refinement critical for inverse methods and nudging is discussed.

Inversion of azimuthally dependent NMO velocity in transversely isotropic media with a tilted axis of symmetry

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

Grechka, V.; Tsvankin, I.

2000-02-01

Just as the transversely isotropic model with a vertical symmetry axis (VTI media) is typical for describing horizontally layered sediments, transverse isotropy with a tilted symmetry axis (TTI) describes dipping TI layers (such as tilted shale beds near salt domes) or crack systems. P-wave kinematic signatures in TTI media are controlled by the velocity V{sub PO} in the symmetry direction, Thomsen's anisotropic coefficients {xi} and {delta}, and the orientation (tilt {nu} and azimuth {beta}) of the symmetry axis. Here, the authors show that all five parameters can be obtained from azimuthally varying P-wave NMO velocities measured for two reflectors withmore » different dips and/or azimuths (one of the reflectors can be horizontal). The shear-wave velocity V{sub SO} in the symmetry direction, which has negligible influence on P-wave kinematic signatures, can be found only from the moveout of shear waves. Using the exact NMO equation, the authors examine the propagation of errors in observed moveout velocities into estimated values of the anisotropic parameters and establish the necessary conditions for a stable inversion procedure. Since the azimuthal variation of the NMO velocity is elliptical, each reflection event provides them with up to three constraints on the model parameters. Generally, the five parameters responsible for P-wave velocity can be obtained from two P-wave ellipses, but the feasibility of the moveout inversion strongly depends on the tilt {nu}. While most of the analysis is carried out for a single layer, the authors also extend the inversion algorithm to vertically heterogeneous TTI media above a dipping reflector using the generalized Dix equation. A synthetic example for a strongly anisotropic, stratified TTI medium demonstrates a high accuracy of the inversion.« less

A Tower-based Prototype VHF/UHF Radar for Subsurface Sensing: System Description and Data Inversion Results

NASA Technical Reports Server (NTRS)

Moghaddam, Mahta; Pierce, Leland; Tabatabaeenejad, Alireza; Rodriguez, Ernesto

2005-01-01

Knowledge of subsurface characteristics such as permittivity variations and layering structure could provide a breakthrough in many terrestrial and planetary science disciplines. For Earth science, knowledge of subsurface and subcanopy soil moisture layers can enable the estimation of vertical flow in the soil column linking surface hydrologic processes with that in the subsurface. For planetary science, determining the existence of subsurface water and ice is regarded as one of the most critical information needs for the study of the origins of the solar system. The subsurface in general can be described as several near-parallel layers with rough interfaces. Each homogenous rough layer can be defined by its average thickness, permittivity, and rms interface roughness assuming a known surface spectral distribution. As the number and depth of layers increase, the number of measurements needed to invert for the layer unknowns also increases, and deeper penetration capability would be required. To nondestructively calculate the characteristics of the rough layers, a multifrequency polarimetric radar backscattering approach can be used. One such system is that we have developed for data prototyping of the Microwave Observatory of Subcanopy and Subsurface (MOSS) mission concept. A tower-mounted radar makes backscattering measurements at VHF, UHF, and L-band frequencies. The radar is a pulsed CW system, which uses the same wideband antenna to transmit and receive the signals at all three frequencies. To focus the beam at various incidence angles within the beamwidth of the antenna, the tower is moved vertically and measurements made at each position. The signals are coherently summed to achieve focusing and image formation in the subsurface. This requires an estimate of wave velocity profiles. To solve the inverse scattering problem for subsurface velocity profile simultaneously with radar focusing, we use an iterative technique based on a forward numerical solution of the layered rough surface problem. The layers are each defined in terms of a small number of unknown distributions as given above. An a priori estimate of the solution is first assumed, based on which the forward problem is solved for the backscattered measurements. This is compared with the measured data and using iterative techniques an update to the solution for the unknowns is calculated. The process continues until convergence is achieved. Numerical results will be shown using actual radar data acquired with the MOSS tower radar system in Arizona in Fall 2003, and compared with in-situ measurements.

Density-to-Potential Inversions to Guide Development of Exchange-Correlation Approximations at Finite Temperature

NASA Astrophysics Data System (ADS)

Jensen, Daniel; Wasserman, Adam; Baczewski, Andrew

The construction of approximations to the exchange-correlation potential for warm dense matter (WDM) is a topic of significant recent interest. In this work, we study the inverse problem of Kohn-Sham (KS) DFT as a means of guiding functional design at zero temperature and in WDM. Whereas the forward problem solves the KS equations to produce a density from a specified exchange-correlation potential, the inverse problem seeks to construct the exchange-correlation potential from specified densities. These two problems require different computational methods and convergence criteria despite sharing the same mathematical equations. We present two new inversion methods based on constrained variational and PDE-constrained optimization methods. We adapt these methods to finite temperature calculations to reveal the exchange-correlation potential's temperature dependence in WDM-relevant conditions. The different inversion methods presented are applied to both non-interacting and interacting model systems for comparison. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Security Administration under contract DE-AC04-94.

Performance impact of mutation operators of a subpopulation-based genetic algorithm for multi-robot task allocation problems.

PubMed

Liu, Chun; Kroll, Andreas

2016-01-01

Multi-robot task allocation determines the task sequence and distribution for a group of robots in multi-robot systems, which is one of constrained combinatorial optimization problems and more complex in case of cooperative tasks because they introduce additional spatial and temporal constraints. To solve multi-robot task allocation problems with cooperative tasks efficiently, a subpopulation-based genetic algorithm, a crossover-free genetic algorithm employing mutation operators and elitism selection in each subpopulation, is developed in this paper. Moreover, the impact of mutation operators (swap, insertion, inversion, displacement, and their various combinations) is analyzed when solving several industrial plant inspection problems. The experimental results show that: (1) the proposed genetic algorithm can obtain better solutions than the tested binary tournament genetic algorithm with partially mapped crossover; (2) inversion mutation performs better than other tested mutation operators when solving problems without cooperative tasks, and the swap-inversion combination performs better than other tested mutation operators/combinations when solving problems with cooperative tasks. As it is difficult to produce all desired effects with a single mutation operator, using multiple mutation operators (including both inversion and swap) is suggested when solving similar combinatorial optimization problems.

A function space framework for structural total variation regularization with applications in inverse problems

NASA Astrophysics Data System (ADS)

Hintermüller, Michael; Holler, Martin; Papafitsoros, Kostas

2018-06-01

In this work, we introduce a function space setting for a wide class of structural/weighted total variation (TV) regularization methods motivated by their applications in inverse problems. In particular, we consider a regularizer that is the appropriate lower semi-continuous envelope (relaxation) of a suitable TV type functional initially defined for sufficiently smooth functions. We study examples where this relaxation can be expressed explicitly, and we also provide refinements for weighted TV for a wide range of weights. Since an integral characterization of the relaxation in function space is, in general, not always available, we show that, for a rather general linear inverse problems setting, instead of the classical Tikhonov regularization problem, one can equivalently solve a saddle-point problem where no a priori knowledge of an explicit formulation of the structural TV functional is needed. In particular, motivated by concrete applications, we deduce corresponding results for linear inverse problems with norm and Poisson log-likelihood data discrepancy terms. Finally, we provide proof-of-concept numerical examples where we solve the saddle-point problem for weighted TV denoising as well as for MR guided PET image reconstruction.

Convex blind image deconvolution with inverse filtering

NASA Astrophysics Data System (ADS)

Lv, Xiao-Guang; Li, Fang; Zeng, Tieyong

2018-03-01

Blind image deconvolution is the process of estimating both the original image and the blur kernel from the degraded image with only partial or no information about degradation and the imaging system. It is a bilinear ill-posed inverse problem corresponding to the direct problem of convolution. Regularization methods are used to handle the ill-posedness of blind deconvolution and get meaningful solutions. In this paper, we investigate a convex regularized inverse filtering method for blind deconvolution of images. We assume that the support region of the blur object is known, as has been done in a few existing works. By studying the inverse filters of signal and image restoration problems, we observe the oscillation structure of the inverse filters. Inspired by the oscillation structure of the inverse filters, we propose to use the star norm to regularize the inverse filter. Meanwhile, we use the total variation to regularize the resulting image obtained by convolving the inverse filter with the degraded image. The proposed minimization model is shown to be convex. We employ the first-order primal-dual method for the solution of the proposed minimization model. Numerical examples for blind image restoration are given to show that the proposed method outperforms some existing methods in terms of peak signal-to-noise ratio (PSNR), structural similarity (SSIM), visual quality and time consumption.

Parana Basin Structure from Multi-Objective Inversion of Surface Wave and Receiver Function by Competent Genetic Algorithm

NASA Astrophysics Data System (ADS)

An, M.; Assumpcao, M.

2003-12-01

The joint inversion of receiver function and surface wave is an effective way to diminish the influences of the strong tradeoff among parameters and the different sensitivity to the model parameters in their respective inversions, but the inversion problem becomes more complex. Multi-objective problems can be much more complicated than single-objective inversion in the model selection and optimization. If objectives are involved and conflicting, models can be ordered only partially. In this case, Pareto-optimal preference should be used to select solutions. On the other hand, the inversion to get only a few optimal solutions can not deal properly with the strong tradeoff between parameters, the uncertainties in the observation, the geophysical complexities and even the incompetency of the inversion technique. The effective way is to retrieve the geophysical information statistically from many acceptable solutions, which requires more competent global algorithms. Competent genetic algorithms recently proposed are far superior to the conventional genetic algorithm and can solve hard problems quickly, reliably and accurately. In this work we used one of competent genetic algorithms, Bayesian Optimization Algorithm as the main inverse procedure. This algorithm uses Bayesian networks to draw out inherited information and can use Pareto-optimal preference in the inversion. With this algorithm, the lithospheric structure of Paran"› basin is inverted to fit both the observations of inter-station surface wave dispersion and receiver function.

A restricted Steiner tree problem is solved by Geometric Method II

NASA Astrophysics Data System (ADS)

Lin, Dazhi; Zhang, Youlin; Lu, Xiaoxu

2013-03-01

The minimum Steiner tree problem has wide application background, such as transportation system, communication network, pipeline design and VISL, etc. It is unfortunately that the computational complexity of the problem is NP-hard. People are common to find some special problems to consider. In this paper, we first put forward a restricted Steiner tree problem, which the fixed vertices are in the same side of one line L and we find a vertex on L such the length of the tree is minimal. By the definition and the complexity of the Steiner tree problem, we know that the complexity of this problem is also Np-complete. In the part one, we have considered there are two fixed vertices to find the restricted Steiner tree problem. Naturally, we consider there are three fixed vertices to find the restricted Steiner tree problem. And we also use the geometric method to solve such the problem.

Estimation of biological parameters of marine organisms using linear and nonlinear acoustic scattering model-based inversion methods.

PubMed

Chu, Dezhang; Lawson, Gareth L; Wiebe, Peter H

2016-05-01

The linear inversion commonly used in fisheries and zooplankton acoustics assumes a constant inversion kernel and ignores the uncertainties associated with the shape and behavior of the scattering targets, as well as other relevant animal parameters. Here, errors of the linear inversion due to uncertainty associated with the inversion kernel are quantified. A scattering model-based nonlinear inversion method is presented that takes into account the nonlinearity of the inverse problem and is able to estimate simultaneously animal abundance and the parameters associated with the scattering model inherent to the kernel. It uses sophisticated scattering models to estimate first, the abundance, and second, the relevant shape and behavioral parameters of the target organisms. Numerical simulations demonstrate that the abundance, size, and behavior (tilt angle) parameters of marine animals (fish or zooplankton) can be accurately inferred from the inversion by using multi-frequency acoustic data. The influence of the singularity and uncertainty in the inversion kernel on the inversion results can be mitigated by examining the singular values for linear inverse problems and employing a non-linear inversion involving a scattering model-based kernel.

An ambiguity of information content and error in an ill-posed satellite inversion

NASA Astrophysics Data System (ADS)

Koner, Prabhat

According to Rodgers (2000, stochastic approach), the averaging kernel (AK) is the representational matrix to understand the information content in a scholastic inversion. On the other hand, in deterministic approach this is referred to as model resolution matrix (MRM, Menke 1989). The analysis of AK/MRM can only give some understanding of how much regularization is imposed on the inverse problem. The trace of the AK/MRM matrix, which is the so-called degree of freedom from signal (DFS; stochastic) or degree of freedom in retrieval (DFR; deterministic). There are no physical/mathematical explanations in the literature: why the trace of the matrix is a valid form to calculate this quantity? We will present an ambiguity between information and error using a real life problem of SST retrieval from GOES13. The stochastic information content calculation is based on the linear assumption. The validity of such mathematics in satellite inversion will be questioned because it is based on the nonlinear radiative transfer and ill-conditioned inverse problems. References: Menke, W., 1989: Geophysical data analysis: discrete inverse theory. San Diego academic press. Rodgers, C.D., 2000: Inverse methods for atmospheric soundings: theory and practice. Singapore :World Scientific.

The inverse electroencephalography pipeline

NASA Astrophysics Data System (ADS)

Weinstein, David Michael

The inverse electroencephalography (EEG) problem is defined as determining which regions of the brain are active based on remote measurements recorded with scalp EEG electrodes. An accurate solution to this problem would benefit both fundamental neuroscience research and clinical neuroscience applications. However, constructing accurate patient-specific inverse EEG solutions requires complex modeling, simulation, and visualization algorithms, and to date only a few systems have been developed that provide such capabilities. In this dissertation, a computational system for generating and investigating patient-specific inverse EEG solutions is introduced, and the requirements for each stage of this Inverse EEG Pipeline are defined and discussed. While the requirements of many of the stages are satisfied with existing algorithms, others have motivated research into novel modeling and simulation methods. The principal technical results of this work include novel surface-based volume modeling techniques, an efficient construction for the EEG lead field, and the Open Source release of the Inverse EEG Pipeline software for use by the bioelectric field research community. In this work, the Inverse EEG Pipeline is applied to three research problems in neurology: comparing focal and distributed source imaging algorithms; separating measurements into independent activation components for multifocal epilepsy; and localizing the cortical activity that produces the P300 effect in schizophrenia.

IPDO-2007: Inverse Problems, Design and Optimization Symposium

DTIC Science & Technology

2007-08-01

Kanevce, G. H., Kanevce, Lj. P., and Mitrevski , V. B.), International Symposium on Inverse Problems, Design and Optimization (IPDO-2007), (eds...107 Gligor Kanevce Ljubica Kanevce Vangelce Mitrevski George Dulikravich 108 Gligor Kanevce Ljubica Kanevce Igor Andreevski George Dulikravich

Four dimensional data assimilation (FDDA) impacts on WRF performance in simulating inversion layer structure and distributions of CMAQ-simulated winter ozone concentrations in Uintah Basin

NASA Astrophysics Data System (ADS)

Tran, Trang; Tran, Huy; Mansfield, Marc; Lyman, Seth; Crosman, Erik

2018-03-01

Four-dimensional data assimilation (FDDA) was applied in WRF-CMAQ model sensitivity tests to study the impact of observational and analysis nudging on model performance in simulating inversion layers and O3 concentration distributions within the Uintah Basin, Utah, U.S.A. in winter 2013. Observational nudging substantially improved WRF model performance in simulating surface wind fields, correcting a 10 °C warm surface temperature bias, correcting overestimation of the planetary boundary layer height (PBLH) and correcting underestimation of inversion strengths produced by regular WRF model physics without nudging. However, the combined effects of poor performance of WRF meteorological model physical parameterization schemes in simulating low clouds, and warm and moist biases in the temperature and moisture initialization and subsequent simulation fields, likely amplified the overestimation of warm clouds during inversion days when observational nudging was applied, impacting the resulting O3 photochemical formation in the chemistry model. To reduce the impact of a moist bias in the simulations on warm cloud formation, nudging with the analysis water mixing ratio above the planetary boundary layer (PBL) was applied. However, due to poor analysis vertical temperature profiles, applying analysis nudging also increased the errors in the modeled inversion layer vertical structure compared to observational nudging. Combining both observational and analysis nudging methods resulted in unrealistically extreme stratified stability that trapped pollutants at the lowest elevations at the center of the Uintah Basin and yielded the worst WRF performance in simulating inversion layer structure among the four sensitivity tests. The results of this study illustrate the importance of carefully considering the representativeness and quality of the observational and model analysis data sets when applying nudging techniques within stable PBLs, and the need to evaluate model results on a basin-wide scale.

Geometric Hitting Set for Segments of Few Orientations

DOE PAGES

Fekete, Sandor P.; Huang, Kan; Mitchell, Joseph S. B.; ...

2016-01-13

Here we study several natural instances of the geometric hitting set problem for input consisting of sets of line segments (and rays, lines) having a small number of distinct slopes. These problems model path monitoring (e.g., on road networks) using the fewest sensors (the \\hitting points"). We give approximation algorithms for cases including (i) lines of 3 slopes in the plane, (ii) vertical lines and horizontal segments, (iii) pairs of horizontal/vertical segments. Lastly, we give hardness and hardness of approximation results for these problems. We prove that the hitting set problem for vertical lines and horizontal rays is polynomially solvable.

Altitude Differentiated Aerosol Extinction Over Tenerife (North Atlantic Coast) During ACE-2 by Means of Ground and Airborne Photometry and Lidar Measurements

NASA Technical Reports Server (NTRS)

Formenti, P.; Elias, T.; Welton, J.; Diaz, J. P.; Exposito, F.; Schmid, B.; Powell, D.; Holben, B. N.; Smirnov, A.; Andreae, M. O.;

Almost but not quite 2D, Non-linear Bayesian Inversion of CSEM Data

NASA Astrophysics Data System (ADS)

Ray, A.; Key, K.; Bodin, T.

2013-12-01

The geophysical inverse problem can be elegantly stated in a Bayesian framework where a probability distribution can be viewed as a statement of information regarding a random variable. After all, the goal of geophysical inversion is to provide information on the random variables of interest - physical properties of the earth's subsurface. However, though it may be simple to postulate, a practical difficulty of fully non-linear Bayesian inversion is the computer time required to adequately sample the model space and extract the information we seek. As a consequence, in geophysical problems where evaluation of a full 2D/3D forward model is computationally expensive, such as marine controlled source electromagnetic (CSEM) mapping of the resistivity of seafloor oil and gas reservoirs, Bayesian studies have largely been conducted with 1D forward models. While the 1D approximation is indeed appropriate for exploration targets with planar geometry and geological stratification, it only provides a limited, site-specific idea of uncertainty in resistivity with depth. In this work, we extend our fully non-linear 1D Bayesian inversion to a 2D model framework, without requiring the usual regularization of model resistivities in the horizontal or vertical directions used to stabilize quasi-2D inversions. In our approach, we use the reversible jump Markov-chain Monte-Carlo (RJ-MCMC) or trans-dimensional method and parameterize the subsurface in a 2D plane with Voronoi cells. The method is trans-dimensional in that the number of cells required to parameterize the subsurface is variable, and the cells dynamically move around and multiply or combine as demanded by the data being inverted. This approach allows us to expand our uncertainty analysis of resistivity at depth to more than a single site location, allowing for interactions between model resistivities at different horizontal locations along a traverse over an exploration target. While the model is parameterized in 2D, we efficiently evaluate the forward response using 1D profiles extracted from the model at the common-midpoints of the EM source-receiver pairs. Since the 1D approximation is locally valid at different midpoint locations, the computation time is far lower than is required by a full 2D or 3D simulation. We have applied this method to both synthetic and real CSEM survey data from the Scarborough gas field on the Northwest shelf of Australia, resulting in a spatially variable quantification of resistivity and its uncertainty in 2D. This Bayesian approach results in a large database of 2D models that comprise a posterior probability distribution, which we can subset to test various hypotheses about the range of model structures compatible with the data. For example, we can subset the model distributions to examine the hypothesis that a resistive reservoir extends overs a certain spatial extent. Depending on how this conditions other parts of the model space, light can be shed on the geological viability of the hypothesis. Since tackling spatially variable uncertainty and trade-offs in 2D and 3D is a challenging research problem, the insights gained from this work may prove valuable for subsequent full 2D and 3D Bayesian inversions.

Nonlinear inversion of tilt-affected very long period records of explosive eruptions at Fuego volcano

NASA Astrophysics Data System (ADS)

Waite, Gregory P.; Lanza, Federica

2016-10-01

Magmatic processes produce a rich variety of volcano seismic signals, ranging over several orders of magnitude in frequency and over a wide range of mechanism types. We examined signals from 400 to 10 s period associated with explosive eruptions at Fuego volcano, Guatemala, that were recorded over 19 days in 2009 on broadband stations with 30 s and 60 s corner periods. The raw data from the closest stations include tilt effects on the horizontal components but also have significant signal at periods below the instrument corners on the vertical components, where tilt effects should be negligible. We address the problems of tilt-affected horizontal waveforms through a joint waveform inversion of translation and rotation, which allows for an investigation of the varying influence of tilt with period. Using a phase-weighted stack of six similar events, we invert for source moment tensor using multiple bands. We use a grid search for source type and constrained inversions, which provides a quantitative measure of source mechanism reliability. The 30-10 s band-pass results are consistent with previous work that modeled data with a combined two crack or crack and pipe model. At the longest-period band examined, 400-60 s, the source mechanism is like a pipe that could represent the shallowest portion of the conduit. On the other hand, source mechanisms in some bands are unconstrained, presumably due to the combined tilt-dominated and translation-dominated signals, which are not coincident in space and have different time spans.

A preprocessing strategy for helioseismic inversions

NASA Astrophysics Data System (ADS)

Christensen-Dalsgaard, J.; Thompson, M. J.

1993-05-01

Helioseismic inversion in general involves considerable computational expense, due to the large number of modes that is typically considered. This is true in particular of the widely used optimally localized averages (OLA) inversion methods, which require the inversion of one or more matrices whose order is the number of modes in the set. However, the number of practically independent pieces of information that a large helioseismic mode set contains is very much less than the number of modes, suggesting that the set might first be reduced before the expensive inversion is performed. We demonstrate with a model problem that by first performing a singular value decomposition the original problem may be transformed into a much smaller one, reducing considerably the cost of the OLA inversion and with no significant loss of information.

Weak unique continuation property and a related inverse source problem for time-fractional diffusion-advection equations

NASA Astrophysics Data System (ADS)

Jiang, Daijun; Li, Zhiyuan; Liu, Yikan; Yamamoto, Masahiro

2017-05-01

In this paper, we first establish a weak unique continuation property for time-fractional diffusion-advection equations. The proof is mainly based on the Laplace transform and the unique continuation properties for elliptic and parabolic equations. The result is weaker than its parabolic counterpart in the sense that we additionally impose the homogeneous boundary condition. As a direct application, we prove the uniqueness for an inverse problem on determining the spatial component in the source term by interior measurements. Numerically, we reformulate our inverse source problem as an optimization problem, and propose an iterative thresholding algorithm. Finally, several numerical experiments are presented to show the accuracy and efficiency of the algorithm.

Energy distribution from vertical impact of a three-dimensional solid body onto the flat free surface of an ideal fluid

NASA Astrophysics Data System (ADS)

Scolan, Y.-M.; Korobkin, A. A.

2003-02-01

Hydrodynamic impact phenomena are three dimensional in nature and naval architects need more advanced tools than a simple strip theory to calculate impact loads at the preliminary design stage. Three-dimensional analytical solutions have been obtained with the help of the so-called inverse Wagner problem as discussed by Scolan and Korobkin in 2001. The approach by Wagner provides a consistent way to evaluate the flow caused by a blunt body entering liquid through its free surface. However, this approach does not account for the spray jets and gives no idea regarding the energy evacuated from the main flow by the jets. Clear insight into the jet formation is required. Wagner provided certain elements of the answer for two-dimensional configurations. On the basis of those results, the energy distribution pattern is analysed for three-dimensional configurations in the present paper.

Jet formation at the interaction of localized waves on the free surface of dielectric liquid in a tangential electric field

NASA Astrophysics Data System (ADS)

Kochurin, E. A.; Zubarev, N. M.

2018-01-01

Nonlinear dynamics of the free surface of finite depth non-conducting fluid with high dielectric constant subjected to a strong horizontal electric field is considered. Using the conformal transformation of the region occupied by the fluid into a strip, the process of interaction of counter-propagating waves is numerically simulated. The nonlinear solitary waves on the surface can separately propagate along or against the direction of electric field without distortion. At the same time, the shape of the oppositely traveling waves can be distorted as the result of their interaction. In the problem under study, the nonlinearity leads to increasing the wave amplitudes and the duration of their interaction. This effect is inversely proportional to the fluid depth. In the shallow water limit, the tendency to the formation of a vertical liquid jet is observed.

Multiscale estimation of excess mass from gravity data

NASA Astrophysics Data System (ADS)

Castaldo, Raffaele; Fedi, Maurizio; Florio, Giovanni

2014-06-01

We describe a multiscale method to estimate the excess mass of gravity anomaly sources, based on the theory of source moments. Using a multipole expansion of the potential field and considering only the data along the vertical direction, a system of linear equations is obtained. The choice of inverting data along a vertical profile can help us to reduce the interference effects due to nearby anomalies and will allow a local estimate of the source parameters. A criterion is established allowing the selection of the optimal highest altitude of the vertical profile data and truncation order of the series expansion. The inversion provides an estimate of the total anomalous mass and of the depth to the centre of mass. The method has several advantages with respect to classical methods, such as the Gauss' method: (i) we need just a 1-D inversion to obtain our estimates, being the inverted data sampled along a single vertical profile; (ii) the resolution may be straightforward enhanced by using vertical derivatives; (iii) the centre of mass is also estimated, besides the excess mass; (iv) the method is very robust versus noise; (v) the profile may be chosen in such a way to minimize the effects from interfering anomalies or from side effects due to the a limited area extension. The multiscale estimation of excess mass method can be successfully used in various fields of application. Here, we analyse the gravity anomaly generated by a sulphide body in the Skelleftea ore district, North Sweden, obtaining source mass and volume estimates in agreement with the known information. We show also that these estimates are substantially improved with respect to those obtained with the classical approach.

[Simulation of CO2 exchange between forest canopy and atmosphere].

PubMed

Diao, Yiwei; Wang, Anzhi; Jin, Changjie; Guan, Dexin; Pei, Tiefan

2006-12-01

Estimating the scalar source/sink distribution of CO2 and its vertical fluxes within and above forest canopy continues to be a critical research problem in biosphere-atmosphere exchange processes and plant ecology. With broad-leaved Korean pine forest in Changbai Mountains as test object, and based on Raupach's localized near field theory, the source/sink and vertical flux distribution of CO2 within and above forest canopy were modeled through an inverse Lagrangian dispersion analysis. This model correctly predicted a strong positive CO2 source strength in the deeper layers of the canopy due to soil-plant respiration, and a strong CO2 sink in the upper layers of the canopy due to the assimilation by sunlit foliage. The foliage in the top layer of canopy changed from a CO2 source in the morning to a CO2 sink in the afternoon, while the soil constituted a strong CO2 source all the day. The simulation results accorded well with the eddy covariance CO2 flux measurements within and above the canopy, and the average precision was 89%. The CO2 exchange predicted by the analysis was averagely 15% higher than that of the eddy correlation, but exhibited identical temporal trend. Atmospheric stability remarkably affected the CO2 exchange between forest canopy and atmosphere.

Site characterization at Groningen gas field area through joint surface-borehole H/V analysis

NASA Astrophysics Data System (ADS)

Spica, Zack J.; Perton, Mathieu; Nakata, Nori; Liu, Xin; Beroza, Gregory C.

2018-01-01

A new interpretation of the horizontal to vertical (H/V) spectral ratio in terms of the Diffuse Field Assumption (DFA) has fuelled a resurgence of interest in that approach. The DFA links H/V measurements to Green's function retrieval through autocorrelation of the ambient seismic field. This naturally allows for estimation of layered velocity structure. In this contribution, we further explore the potential of H/V analysis. Our study is facilitated by a distributed array of surface and co-located borehole stations deployed at multiple depths, and by detailed prior information on velocity structure that is available due to development of the Groningen gas field. We use the vertical distribution of H/V spectra recorded at discrete depths inside boreholes to obtain shear wave velocity models of the shallow subsurface. We combine both joint H/V inversion and borehole interferometry to reduce the non-uniqueness of the problem and to allow faster convergence towards a reliable velocity model. The good agreement between our results and velocity models from an independent study validates the methodology, demonstrates the power of the method, but more importantly provides further constraints on the shallow velocity structure, which is an essential component of integrated hazard assessment in the area.

Higher order total variation regularization for EIT reconstruction.

PubMed

Gong, Bo; Schullcke, Benjamin; Krueger-Ziolek, Sabine; Zhang, Fan; Mueller-Lisse, Ullrich; Moeller, Knut

2018-01-08

Electrical impedance tomography (EIT) attempts to reveal the conductivity distribution of a domain based on the electrical boundary condition. This is an ill-posed inverse problem; its solution is very unstable. Total variation (TV) regularization is one of the techniques commonly employed to stabilize reconstructions. However, it is well known that TV regularization induces staircase effects, which are not realistic in clinical applications. To reduce such artifacts, modified TV regularization terms considering a higher order differential operator were developed in several previous studies. One of them is called total generalized variation (TGV) regularization. TGV regularization has been successively applied in image processing in a regular grid context. In this study, we adapted TGV regularization to the finite element model (FEM) framework for EIT reconstruction. Reconstructions using simulation and clinical data were performed. First results indicate that, in comparison to TV regularization, TGV regularization promotes more realistic images. Graphical abstract Reconstructed conductivity changes located on selected vertical lines. For each of the reconstructed images as well as the ground truth image, conductivity changes located along the selected left and right vertical lines are plotted. In these plots, the notation GT in the legend stands for ground truth, TV stands for total variation method, and TGV stands for total generalized variation method. Reconstructed conductivity distributions from the GREIT algorithm are also demonstrated.

Comparing multiple statistical methods for inverse prediction in nuclear forensics applications

DOE PAGES

Lewis, John R.; Zhang, Adah; Anderson-Cook, Christine Michaela

2017-10-29

Forensic science seeks to predict source characteristics using measured observables. Statistically, this objective can be thought of as an inverse problem where interest is in the unknown source characteristics or factors ( X) of some underlying causal model producing the observables or responses (Y = g ( X) + error). Here, this paper reviews several statistical methods for use in inverse problems and demonstrates that comparing results from multiple methods can be used to assess predictive capability. Motivation for assessing inverse predictions comes from the desired application to historical and future experiments involving nuclear material production for forensics research inmore » which inverse predictions, along with an assessment of predictive capability, are desired.« less

Comparing multiple statistical methods for inverse prediction in nuclear forensics applications

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

Lewis, John R.; Zhang, Adah; Anderson-Cook, Christine Michaela

Forensic science seeks to predict source characteristics using measured observables. Statistically, this objective can be thought of as an inverse problem where interest is in the unknown source characteristics or factors ( X) of some underlying causal model producing the observables or responses (Y = g ( X) + error). Here, this paper reviews several statistical methods for use in inverse problems and demonstrates that comparing results from multiple methods can be used to assess predictive capability. Motivation for assessing inverse predictions comes from the desired application to historical and future experiments involving nuclear material production for forensics research inmore » which inverse predictions, along with an assessment of predictive capability, are desired.« less

Final Report: Resolving and Discriminating Overlapping Anomalies from Multiple Objects in Cluttered Environments

DTIC Science & Technology

2015-12-15

UXO community . NAME Total Number: PERCENT_SUPPORTEDNAME FTE Equivalent: Total Number: Irma Shamatava 0.50 0.50 1 Resolving and Discriminating...Distinguishing an object of interest from innocuous items is the main problem that the UXO community is facing currently. This inverse problem...innocuous items is the main problem that the UXO community is facing currently. This inverse problem demands fast and accurate representation of

Regularized inversion of controlled source audio-frequency magnetotelluric data in horizontally layered transversely isotropic media

NASA Astrophysics Data System (ADS)

Zhou, Jianmei; Wang, Jianxun; Shang, Qinglong; Wang, Hongnian; Yin, Changchun

2014-04-01

We present an algorithm for inverting controlled source audio-frequency magnetotelluric (CSAMT) data in horizontally layered transversely isotropic (TI) media. The popular inversion method parameterizes the media into a large number of layers which have fixed thickness and only reconstruct the conductivities (e.g. Occam's inversion), which does not enable the recovery of the sharp interfaces between layers. In this paper, we simultaneously reconstruct all the model parameters, including both the horizontal and vertical conductivities and layer depths. Applying the perturbation principle and the dyadic Green's function in TI media, we derive the analytic expression of Fréchet derivatives of CSAMT responses with respect to all the model parameters in the form of Sommerfeld integrals. A regularized iterative inversion method is established to simultaneously reconstruct all the model parameters. Numerical results show that the inverse algorithm, including the depths of the layer interfaces, can significantly improve the inverse results. It can not only reconstruct the sharp interfaces between layers, but also can obtain conductivities close to the true value.

Objective function analysis for electric soundings (VES), transient electromagnetic soundings (TEM) and joint inversion VES/TEM

NASA Astrophysics Data System (ADS)

Bortolozo, Cassiano Antonio; Bokhonok, Oleg; Porsani, Jorge Luís; Monteiro dos Santos, Fernando Acácio; Diogo, Liliana Alcazar; Slob, Evert

2017-11-01

Ambiguities in geophysical inversion results are always present. How these ambiguities appear in most cases open to interpretation. It is interesting to investigate ambiguities with regard to the parameters of the models under study. Residual Function Dispersion Map (RFDM) can be used to differentiate between global ambiguities and local minima in the objective function. We apply RFDM to Vertical Electrical Sounding (VES) and TEM Sounding inversion results. Through topographic analysis of the objective function we evaluate the advantages and limitations of electrical sounding data compared with TEM sounding data, and the benefits of joint inversion in comparison with the individual methods. The RFDM analysis proved to be a very interesting tool for understanding the joint inversion method of VES/TEM. Also the advantage of the applicability of the RFDM analyses in real data is explored in this paper to demonstrate not only how the objective function of real data behaves but the applicability of the RFDM approach in real cases. With the analysis of the results, it is possible to understand how the joint inversion can reduce the ambiguity of the methods.

Cross hole GPR traveltime inversion using a fast and accurate neural network as a forward model

NASA Astrophysics Data System (ADS)

Mejer Hansen, Thomas

2017-04-01

Probabilistic formulated inverse problems can be solved using Monte Carlo based sampling methods. In principle both advanced prior information, such as based on geostatistics, and complex non-linear forward physical models can be considered. However, in practice these methods can be associated with huge computational costs that in practice limit their application. This is not least due to the computational requirements related to solving the forward problem, where the physical response of some earth model has to be evaluated. Here, it is suggested to replace a numerical complex evaluation of the forward problem, with a trained neural network that can be evaluated very fast. This will introduce a modeling error, that is quantified probabilistically such that it can be accounted for during inversion. This allows a very fast and efficient Monte Carlo sampling of the solution to an inverse problem. We demonstrate the methodology for first arrival travel time inversion of cross hole ground-penetrating radar (GPR) data. An accurate forward model, based on 2D full-waveform modeling followed by automatic travel time picking, is replaced by a fast neural network. This provides a sampling algorithm three orders of magnitude faster than using the full forward model, and considerably faster, and more accurate, than commonly used approximate forward models. The methodology has the potential to dramatically change the complexity of the types of inverse problems that can be solved using non-linear Monte Carlo sampling techniques.

A multi-frequency iterative imaging method for discontinuous inverse medium problem

NASA Astrophysics Data System (ADS)

Zhang, Lei; Feng, Lixin

2018-06-01

The inverse medium problem with discontinuous refractive index is a kind of challenging inverse problem. We employ the primal dual theory and fast solution of integral equations, and propose a new iterative imaging method. The selection criteria of regularization parameter is given by the method of generalized cross-validation. Based on multi-frequency measurements of the scattered field, a recursive linearization algorithm has been presented with respect to the frequency from low to high. We also discuss the initial guess selection strategy by semi-analytical approaches. Numerical experiments are presented to show the effectiveness of the proposed method.

Effective one-dimensional approach to the source reconstruction problem of three-dimensional inverse optoacoustics

NASA Astrophysics Data System (ADS)

Stritzel, J.; Melchert, O.; Wollweber, M.; Roth, B.

2017-09-01

The direct problem of optoacoustic signal generation in biological media consists of solving an inhomogeneous three-dimensional (3D) wave equation for an initial acoustic stress profile. In contrast, the more defiant inverse problem requires the reconstruction of the initial stress profile from a proper set of observed signals. In this article, we consider an effectively 1D approach, based on the assumption of a Gaussian transverse irradiation source profile and plane acoustic waves, in which the effects of acoustic diffraction are described in terms of a linear integral equation. The respective inverse problem along the beam axis can be cast into a Volterra integral equation of the second kind for which we explore here efficient numerical schemes in order to reconstruct initial stress profiles from observed signals, constituting a methodical progress of computational aspects of optoacoustics. In this regard, we explore the validity as well as the limits of the inversion scheme via numerical experiments, with parameters geared toward actual optoacoustic problem instances. The considered inversion input consists of synthetic data, obtained in terms of the effectively 1D approach, and, more generally, a solution of the 3D optoacoustic wave equation. Finally, we also analyze the effect of noise and different detector-to-sample distances on the optoacoustic signal and the reconstructed pressure profiles.

The inverse problem of sensing the mass and force induced by an adsorbate on a beam nanomechanical resonator

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

Liu, Yun; Zhang, Yin

2016-06-08

The mass sensing superiority of a micro/nanomechanical resonator sensor over conventional mass spectrometry has been, or at least, is being firmly established. Because the sensing mechanism of a mechanical resonator sensor is the shifts of resonant frequencies, how to link the shifts of resonant frequencies with the material properties of an analyte formulates an inverse problem. Besides the analyte/adsorbate mass, many other factors such as position and axial force can also cause the shifts of resonant frequencies. The in-situ measurement of the adsorbate position and axial force is extremely difficult if not impossible, especially when an adsorbate is as smallmore » as a molecule or an atom. Extra instruments are also required. In this study, an inverse problem of using three resonant frequencies to determine the mass, position and axial force is formulated and solved. The accuracy of the inverse problem solving method is demonstrated and how the method can be used in the real application of a nanomechanical resonator is also discussed. Solving the inverse problem is helpful to the development and application of mechanical resonator sensor on two things: reducing extra experimental equipments and achieving better mass sensing by considering more factors.« less

Importance of closely spaced vertical sampling in delineating chemical and microbiological gradients in groundwater studies

USGS Publications Warehouse

Smith, R.L.; Harvey, R.W.; LeBlanc, D.R.

1991-01-01

Vertical gradients of selected chemical constituents, bacterial populations, bacterial activity and electron acceptors were investigated for an unconfined aquifer contaminated with nitrate and organic compounds on Cape Cod, Massachusetts, U.S.A. Fifteen-port multilevel sampling devices (MLS's) were installed within the contaminant plume at the source of the contamination, and at 250 and 2100 m downgradient from the source. Depth profiles of specific conductance and dissolved oxygen at the downgradient sites exhibited vertical gradients that were both steep and inversely related. Narrow zones (2-4 m thick) of high N2O and NH4+ concentrations were also detected within the contaminant plume. A 27-fold change in bacterial abundance; a 35-fold change in frequency of dividing cells (FDC), an indicator of bacterial growth; a 23-fold change in 3H-glucose uptake, a measure of heterotrophic activity; and substantial changes in overall cell morphology were evident within a 9-m vertical interval at 250 m downgradient. The existence of these gradients argues for the need for closely spaced vertical sampling in groundwater studies because small differences in the vertical placement of a well screen can lead to incorrect conclusions about the chemical and microbiological processes within an aquifer.Vertical gradients of selected chemical constituents, bacterial populations, bacterial activity and electron acceptors were investigated for an unconfined aquifer contaminated with nitrate and organic compounds on Cape Cod, Massachusetts, USA. Fifteen-port multilevel sampling devices (MLS's) were installed within the contaminant plume at the source of the contamination, and at 250 and 2100 m downgradient from the source. Depth profiles of specific conductance and dissolved oxygen at the downgradient sites exhibited vertical gradients that were both steep and inversely related. Narrow zones (2-4 m thick) of high N2O and NH4+ concentrations were also detected within the contaminant plume. A 27-fold change in bacterial abundance; a 35-fold change in frequency of dividing cells (FDC), an indicator of bacterial growth; a 23-fold change in 3H-glucose uptake, a measure of heterotrophic activity; and substantial changes in overall cell morphology were evident within a 9-m vertical interval at 250 m downgradient. The existence of these gradients argues for the need for closely spaced vertical sampling in ground-water studies because small differences in the vertical placement of a well screen can lead to incorrect conclusions about the chemical and microbiological processes within an aquifer.

Distorted Born iterative T-matrix method for inversion of CSEM data in anisotropic media

NASA Astrophysics Data System (ADS)

Jakobsen, Morten; Tveit, Svenn

2018-05-01

We present a direct iterative solutions to the nonlinear controlled-source electromagnetic (CSEM) inversion problem in the frequency domain, which is based on a volume integral equation formulation of the forward modelling problem in anisotropic conductive media. Our vectorial nonlinear inverse scattering approach effectively replaces an ill-posed nonlinear inverse problem with a series of linear ill-posed inverse problems, for which there already exist efficient (regularized) solution methods. The solution update the dyadic Green's function's from the source to the scattering-volume and from the scattering-volume to the receivers, after each iteration. The T-matrix approach of multiple scattering theory is used for efficient updating of all dyadic Green's functions after each linearized inversion step. This means that we have developed a T-matrix variant of the Distorted Born Iterative (DBI) method, which is often used in the acoustic and electromagnetic (medical) imaging communities as an alternative to contrast-source inversion. The main advantage of using the T-matrix approach in this context, is that it eliminates the need to perform a full forward simulation at each iteration of the DBI method, which is known to be consistent with the Gauss-Newton method. The T-matrix allows for a natural domain decomposition, since in the sense that a large model can be decomposed into an arbitrary number of domains that can be treated independently and in parallel. The T-matrix we use for efficient model updating is also independent of the source-receiver configuration, which could be an advantage when performing fast-repeat modelling and time-lapse inversion. The T-matrix is also compatible with the use of modern renormalization methods that can potentially help us to reduce the sensitivity of the CSEM inversion results on the starting model. To illustrate the performance and potential of our T-matrix variant of the DBI method for CSEM inversion, we performed a numerical experiments based on synthetic CSEM data associated with 2D VTI and 3D orthorombic model inversions. The results of our numerical experiment suggest that the DBIT method for inversion of CSEM data in anisotropic media is both accurate and efficient.

Fracture characterization from near-offset VSP inversion

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

Horne, S.; MacBeth, C.; Queen, J.

1997-01-01

A global optimization method incorporating a ray-tracing scheme is used to invert observations of shear-wave splitting from two near-offset VSPs recorded at the Conoco Borehole Test Facility, Kay County, Oklahoma. Inversion results suggest that the seismic anisotropy is due to a non-vertical fracture system. This interpretation is constrained by the VSP acquisition geometry for which two sources are employed along near diametrically opposite azimuths about the well heads. A correlation is noted between the time-delay variations between the fast and slow split shear waves and the sandstone formations.

Utilization of high-frequency Rayleigh waves in near-surface geophysics

USGS Publications Warehouse

Xia, J.; Miller, R.D.; Park, C.B.; Ivanov, J.; Tian, G.; Chen, C.

2004-01-01

Shear-wave velocities can be derived from inverting the dispersive phase velocity of the surface. The multichannel analysis of surface waves (MASW) is one technique for inverting high-frequency Rayleigh waves. The process includes acquisition of high-frequency broad-band Rayleigh waves, efficient and accurate algorithms designed to extract Rayleigh-wave dispersion curves from Rayleigh waves, and stable and efficient inversion algorithms to obtain near-surface S-wave velocity profiles. MASW estimates S-wave velocity from multichannel vertical compoent data and consists of data acquisition, dispersion-curve picking, and inversion.

Direct and inverse energy cascades in a forced rotating turbulence experiment

NASA Astrophysics Data System (ADS)

Campagne, Antoine; Gallet, Basile; Moisy, Frédéric; Cortet, Pierre-Philippe

2014-12-01

We present experimental evidence for a double cascade of kinetic energy in a statistically stationary rotating turbulence experiment. Turbulence is generated by a set of vertical flaps, which continuously injects velocity fluctuations towards the center of a rotating water tank. The energy transfers are evaluated from two-point third-order three-component velocity structure functions, which we measure using stereoscopic particle image velocimetry in the rotating frame. Without global rotation, the energy is transferred from large to small scales, as in classical three-dimensional turbulence. For nonzero rotation rates, the horizontal kinetic energy presents a double cascade: a direct cascade at small horizontal scales and an inverse cascade at large horizontal scales. By contrast, the vertical kinetic energy is always transferred from large to small horizontal scales, a behavior reminiscent of the dynamics of a passive scalar in two-dimensional turbulence. At the largest rotation rate, the flow is nearly two-dimensional, and a pure inverse energy cascade is found for the horizontal energy. To describe the scale-by-scale energy budget, we consider a generalization of the Kármán-Howarth-Monin equation to inhomogeneous turbulent flows, in which the energy input is explicitly described as the advection of turbulent energy from the flaps through the surface of the control volume where the measurements are performed.

Lidar-Radiometer Inversion Code (LIRIC) for the Retrieval of Vertical Aerosol Properties from Combined Lidar Radiometer Data: Development and Distribution in EARLINET

NASA Technical Reports Server (NTRS)

Chaikovsky, A.; Dubovik, O.; Holben, Brent N.; Bril, A.; Goloub, P.; Tanre, D.; Pappalardo, G.; Wandinger, U.; Chaikovskaya, L.; Denisov, S.;

An attempt to estimate isotropic and anisotropic lateral structure of the Earth by spectral inversion incorporating mixed coupling

NASA Astrophysics Data System (ADS)

Oda, Hitoshi

2005-02-01

We present a way to calculate free oscillation spectra for an aspherical earth model, which is constructed by adding isotropic and anisotropic velocity perturbations to the seismic velocity parameters of a reference earth model, and examine the effect of the velocity perturbations on the free oscillation spectrum. Lateral variations of the velocity perturbations are parametrized as an expansion in generalized spherical harmonics. We assume weak hexagonal anisotropy for the seismic wave anisotropy in the upper mantle, where the hexagonal symmetry axes are horizontally distributed. The synthetic spectra show that the velocity perturbations cause not only strong self-coupling among singlets of a multiplet but also mixed coupling between toroidal and spheroidal multiplets. Both the couplings give rise to an amplitude anomaly on the vertical component spectrum. In this study, we identify the amplitude anomaly resulting from the mixed coupling as quasi-toroidal mode. Excitation of the quasi-toroidal mode by a vertical strike-slip fault is largest on nodal lines of the Rayleigh wave, decreases with increasing azimuth angle and becomes smallest on loop lines. This azimuthal dependence of the spectral amplitude is quite similar to the Love wave radiation pattern. In addition, the amplitude spectrum of the quasi-toroidal mode is more sensitive to the anisotropic velocity perturbation than to the isotropic velocity perturbation. This means that the mode spectrum allowing for the mixed-coupling effect may provide constraints on the anisotropic lateral structure as well as the isotropic lateral structure. An inversion method, called mixed-coupling spectral inversion, is devised to retrieve the isotropic and anisotropic velocity perturbations from the free oscillation spectra incorporating the quasi-toroidal mode. We confirm that the spectral inversion method correctly recovers the isotropic and anisotropic lateral structure. Moreover introducing the mixed-coupling effect in the spectral inversion makes it possible to estimate the odd-order lateral structure, which cannot be determined by the conventional spectral inversion, which takes no account of the mixed coupling. Higher order structure is biased by the mixed coupling when the conventional spectral inversion is applied to the amplitude spectra incorporating the mixed coupling.

Viscoelastic material inversion using Sierra-SD and ROL

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

Walsh, Timothy; Aquino, Wilkins; Ridzal, Denis

2014-11-01

In this report we derive frequency-domain methods for inverse characterization of the constitutive parameters of viscoelastic materials. The inverse problem is cast in a PDE-constrained optimization framework with efficient computation of gradients and Hessian vector products through matrix free operations. The abstract optimization operators for first and second derivatives are derived from first principles. Various methods from the Rapid Optimization Library (ROL) are tested on the viscoelastic inversion problem. The methods described herein are applied to compute the viscoelastic bulk and shear moduli of a foam block model, which was recently used in experimental testing for viscoelastic property characterization.

Impact of spatial inhomogeneities on stratospheric species vertical profiles from remote-sensing balloon-borne instruments

NASA Astrophysics Data System (ADS)

Berthet, Gwenael; Renard, Jean-Baptiste; Catoire, Valery; Huret, Nathalie; Lefevre, Franck; Hauchecorne, Alain; Chartier, Michel; Robert, Claude

Remote-sensing balloon observations have recurrently revealed high concentrations of polar stratospheric NO2 in particular in the lower stratosphere as can be seen in various published vertical profiles. A balloon campaign dedicated to the investigation of this problem through comparisons between remote-sensing (SALOMON) and in situ (SPIRALE) measurements of NO2 inside the polar vortex was conducted in January 2006. The published results show unexpected strong enhancements in the slant column densities of NO2 with respect to the elevation angle and displacement of the balloon. These fluctuations result from NO2 spatial inhomogeneities located above the balloon float altitude resulting from mid-latitude air intrusion as revealed by Potential Vorticity (PV) maps. The retrieval of the NO2 vertical profile is subsequently biased in the form of artificial excesses of NO2 concentrations. A direct implication is that the differences previously observed between measurements of NO2 and OClO and model results are probably mostly due to the improper inversion of NO2 in presence of either perturbed dynamical conditions or when mesospheric production events occur as recently highlighted from ENVISAT data. Through the occurrence of such events, we propose to re-examine formerly published high-latitude profiles from the remote-sensing instruments AMON and SALOMON using in parallel PV maps from the MIMOSA advection contour model and the REPROBUS CTM outputs. Mid-latitude profiles of NO2 will also be investigated since they are likely to be biased if presence of air from other latitudes was present at the time of the observations.

An optimization method for the problems of thermal cloaking of material bodies

NASA Astrophysics Data System (ADS)

Alekseev, G. V.; Levin, V. A.

2016-11-01

Inverse heat-transfer problems related to constructing special thermal devices such as cloaking shells, thermal-illusion or thermal-camouflage devices, and heat-flux concentrators are studied. The heatdiffusion equation with a variable heat-conductivity coefficient is used as the initial heat-transfer model. An optimization method is used to reduce the above inverse problems to the respective control problem. The solvability of the above control problem is proved, an optimality system that describes necessary extremum conditions is derived, and a numerical algorithm for solving the control problem is proposed.

Geodynamic inversion to constrain the non-linear rheology of the lithosphere

NASA Astrophysics Data System (ADS)

Baumann, T. S.; Kaus, Boris J. P.

2015-08-01

One of the main methods to determine the strength of the lithosphere is by estimating it's effective elastic thickness. This method assumes that the lithosphere is a thin elastic plate that floats on the mantle and uses both topography and gravity anomalies to estimate the plate thickness. Whereas this seems to work well for oceanic plates, it has given controversial results in continental collision zones. For most of these locations, additional geophysical data sets such as receiver functions and seismic tomography exist that constrain the geometry of the lithosphere and often show that it is rather complex. Yet, lithospheric geometry by itself is insufficient to understand the dynamics of the lithosphere as this also requires knowledge of the rheology of the lithosphere. Laboratory experiments suggest that rocks deform in a viscous manner if temperatures are high and stresses low, or in a plastic/brittle manner if the yield stress is exceeded. Yet, the experimental results show significant variability between various rock types and there are large uncertainties in extrapolating laboratory values to nature, which leaves room for speculation. An independent method is thus required to better understand the rheology and dynamics of the lithosphere in collision zones. The goal of this paper is to discuss such an approach. Our method relies on performing numerical thermomechanical forward models of the present-day lithosphere with an initial geometry that is constructed from geophysical data sets. We employ experimentally determined creep-laws for the various parts of the lithosphere, but assume that the parameters of these creep-laws as well as the temperature structure of the lithosphere are uncertain. This is used as a priori information to formulate a Bayesian inverse problem that employs topography, gravity, horizontal and vertical surface velocities to invert for the unknown material parameters and temperature structure. In order to test the general methodology, we first perform a geodynamic inversion of a synthetic forward model of intraoceanic subduction with known parameters. This requires solving an inverse problem with 14-16 parameters, depending on whether temperature is assumed to be known or not. With the help of a massively parallel direct-search combined with a Markov Chain Monte Carlo method, solving the inverse problem becomes feasible. Results show that the rheological parameters and particularly the effective viscosity structure of the lithosphere can be reconstructed in a probabilistic sense. This also holds, with somewhat larger uncertainties, for the case where the temperature distribution is parametrized. Finally, we apply the method to a cross-section of the India-Asia collision system. In this case, the number of parameters is larger, which requires solving around 1.9 × 106 forward models. The resulting models fit the data within their respective uncertainty bounds, and show that the Indian mantle lithosphere must have a high viscosity. Results for the Tibetan plateau are less clear, and both models with a weak Asian mantle lithosphere and with a weak Asian lower crust fit the data nearly equally well.

Complete Sets of Radiating and Nonradiating Parts of a Source and Their Fields with Applications in Inverse Scattering Limited-Angle Problems

PubMed Central

Louis, A. K.

2006-01-01

Many algorithms applied in inverse scattering problems use source-field systems instead of the direct computation of the unknown scatterer. It is well known that the resulting source problem does not have a unique solution, since certain parts of the source totally vanish outside of the reconstruction area. This paper provides for the two-dimensional case special sets of functions, which include all radiating and all nonradiating parts of the source. These sets are used to solve an acoustic inverse problem in two steps. The problem under discussion consists of determining an inhomogeneous obstacle supported in a part of a disc, from data, known for a subset of a two-dimensional circle. In a first step, the radiating parts are computed by solving a linear problem. The second step is nonlinear and consists of determining the nonradiating parts. PMID:23165060

Reconstruction of local perturbations in periodic surfaces

NASA Astrophysics Data System (ADS)

Lechleiter, Armin; Zhang, Ruming

2018-03-01

This paper concerns the inverse scattering problem to reconstruct a local perturbation in a periodic structure. Unlike the periodic problems, the periodicity for the scattered field no longer holds, thus classical methods, which reduce quasi-periodic fields in one periodic cell, are no longer available. Based on the Floquet-Bloch transform, a numerical method has been developed to solve the direct problem, that leads to a possibility to design an algorithm for the inverse problem. The numerical method introduced in this paper contains two steps. The first step is initialization, that is to locate the support of the perturbation by a simple method. This step reduces the inverse problem in an infinite domain into one periodic cell. The second step is to apply the Newton-CG method to solve the associated optimization problem. The perturbation is then approximated by a finite spline basis. Numerical examples are given at the end of this paper, showing the efficiency of the numerical method.

Linear System of Equations, Matrix Inversion, and Linear Programming Using MS Excel

ERIC Educational Resources Information Center

El-Gebeily, M.; Yushau, B.

2008-01-01

In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…

Accounting for model error in Bayesian solutions to hydrogeophysical inverse problems using a local basis approach

NASA Astrophysics Data System (ADS)

Irving, J.; Koepke, C.; Elsheikh, A. H.

2017-12-01

Bayesian solutions to geophysical and hydrological inverse problems are dependent upon a forward process model linking subsurface parameters to measured data, which is typically assumed to be known perfectly in the inversion procedure. However, in order to make the stochastic solution of the inverse problem computationally tractable using, for example, Markov-chain-Monte-Carlo (MCMC) methods, fast approximations of the forward model are commonly employed. This introduces model error into the problem, which has the potential to significantly bias posterior statistics and hamper data integration efforts if not properly accounted for. Here, we present a new methodology for addressing the issue of model error in Bayesian solutions to hydrogeophysical inverse problems that is geared towards the common case where these errors cannot be effectively characterized globally through some parametric statistical distribution or locally based on interpolation between a small number of computed realizations. Rather than focusing on the construction of a global or local error model, we instead work towards identification of the model-error component of the residual through a projection-based approach. In this regard, pairs of approximate and detailed model runs are stored in a dictionary that grows at a specified rate during the MCMC inversion procedure. At each iteration, a local model-error basis is constructed for the current test set of model parameters using the K-nearest neighbour entries in the dictionary, which is then used to separate the model error from the other error sources before computing the likelihood of the proposed set of model parameters. We demonstrate the performance of our technique on the inversion of synthetic crosshole ground-penetrating radar traveltime data for three different subsurface parameterizations of varying complexity. The synthetic data are generated using the eikonal equation, whereas a straight-ray forward model is assumed in the inversion procedure. In each case, the developed model-error approach enables to remove posterior bias and obtain a more realistic characterization of uncertainty.

Identification of groundwater flow parameters using reciprocal data from hydraulic interference tests

NASA Astrophysics Data System (ADS)

Marinoni, Marianna; Delay, Frederick; Ackerer, Philippe; Riva, Monica; Guadagnini, Alberto

2016-08-01

We investigate the effect of considering reciprocal drawdown curves for the characterization of hydraulic properties of aquifer systems through inverse modeling based on interference well testing. Reciprocity implies that drawdown observed in a well B when pumping takes place from well A should strictly coincide with the drawdown observed in A when pumping in B with the same flow rate as in A. In this context, a critical point related to applications of hydraulic tomography is the assessment of the number of available independent drawdown data and their impact on the solution of the inverse problem. The issue arises when inverse modeling relies upon mathematical formulations of the classical single-continuum approach to flow in porous media grounded on Darcy's law. In these cases, introducing reciprocal drawdown curves in the database of an inverse problem is equivalent to duplicate some information, to a certain extent. We present a theoretical analysis of the way a Least-Square objective function and a Levenberg-Marquardt minimization algorithm are affected by the introduction of reciprocal information in the inverse problem. We also investigate the way these reciprocal data, eventually corrupted by measurement errors, influence model parameter identification in terms of: (a) the convergence of the inverse model, (b) the optimal values of parameter estimates, and (c) the associated estimation uncertainty. Our theoretical findings are exemplified through a suite of computational examples focused on block-heterogeneous systems with increased complexity level. We find that the introduction of noisy reciprocal information in the objective function of the inverse problem has a very limited influence on the optimal parameter estimates. Convergence of the inverse problem improves when adding diverse (nonreciprocal) drawdown series, but does not improve when reciprocal information is added to condition the flow model. The uncertainty on optimal parameter estimates is influenced by the strength of measurement errors and it is not significantly diminished or increased by adding noisy reciprocal information.

Enhanced photochemical catalysis of TiO2 inverse opals by modification with ZnO or Fe2O3 using ALD and the hydrothermal method

NASA Astrophysics Data System (ADS)

Liu, Jiatong; Sun, Cuifeng; Fu, Ming; Long, Jie; He, Dawei; Wang, Yongsheng

2018-02-01

The development of porous materials exhibiting photon regulation abilities for improved photoelectrochemical catalysis performance is always one of the important goals of solar energy harvesting. In this study, methods to improve the photocatalytic activity of TiO2 inverse opals were discussed. TiO2 inverse opals were prepared by atomic layer deposition (ALD) using colloidal crystal templates. In addition, TiO2 inverse opal heterostructures were fabricated using colloidal heterocrystals by repeated vertical deposition using different colloidal spheres. The hydrothermal method and ALD were used to prepare ZnO- or Fe2O3-modified TiO2 inverse opals on the internal surfaces of the TiO2 porous structures. Although the photonic reflection band was not significantly varied by oxide modification, the presence of Fe2O3 in the TiO2 inverse opals enhanced their visible absorption. The conformally modified oxides on the TiO2 inverse opals could also form energy barriers and avoid the recombination of electrons and holes. The fabrication of the TiO2 photonic crystal heterostructures and modification with ZnO or Fe2O3 can enhance the photocatalytic activity of TiO2 inverse opals.

Effects of blurring and vertical misalignment on visual fatigue of stereoscopic displays

NASA Astrophysics Data System (ADS)

Baek, Sangwook; Lee, Chulhee

2015-03-01

In this paper, we investigate two error issues in stereo images, which may produce visual fatigue. When two cameras are used to produce 3D video sequences, vertical misalignment can be a problem. Although this problem may not occur in professionally produced 3D programs, it is still a major issue in many low-cost 3D programs. Recently, efforts have been made to produce 3D video programs using smart phones or tablets, which may present the vertical alignment problem. Also, in 2D-3D conversion techniques, the simulated frame may have blur effects, which can also introduce visual fatigue in 3D programs. In this paper, to investigate the relationship between these two errors (vertical misalignment and blurring in one image), we performed a subjective test using simulated 3D video sequences that include stereo video sequences with various vertical misalignments and blurring in a stereo image. We present some analyses along with objective models to predict the degree of visual fatigue from vertical misalignment and blurring.

The Potential of The Synergy of Sunphotometer and Lidar Data to Validate Vertical Profiles of The Aerosol Mass Concentration Estimated by An Air Quality Model

NASA Astrophysics Data System (ADS)

Siomos, N.; Filioglou, M.; Poupkou, A.; Liora, N.; Dimopoulos, S.; Melas, D.; Chaikovsky, A.; Balis, D. S.

2016-06-01

Vertical profiles of the aerosol mass concentration derived by the Lidar/Radiometer Inversion Code (LIRIC), that uses combined sunphotometer and lidar data, were used in order to validate the aerosol mass concentration profiles estimated by the air quality model CAMx. Lidar and CIMEL measurements performed at the Laboratory of Atmospheric Physics of the Aristotle University of Thessaloniki, Greece (40.5N, 22.9E) from the period 2013-2014 were used in this study.

An approach to quantum-computational hydrologic inverse analysis

DOE PAGES

O'Malley, Daniel

2018-05-02

Making predictions about flow and transport in an aquifer requires knowledge of the heterogeneous properties of the aquifer such as permeability. Computational methods for inverse analysis are commonly used to infer these properties from quantities that are more readily observable such as hydraulic head. We present a method for computational inverse analysis that utilizes a type of quantum computer called a quantum annealer. While quantum computing is in an early stage compared to classical computing, we demonstrate that it is sufficiently developed that it can be used to solve certain subsurface flow problems. We utilize a D-Wave 2X quantum annealermore » to solve 1D and 2D hydrologic inverse problems that, while small by modern standards, are similar in size and sometimes larger than hydrologic inverse problems that were solved with early classical computers. Our results and the rapid progress being made with quantum computing hardware indicate that the era of quantum-computational hydrology may not be too far in the future.« less

An approach to quantum-computational hydrologic inverse analysis.

PubMed

O'Malley, Daniel

2018-05-02

Making predictions about flow and transport in an aquifer requires knowledge of the heterogeneous properties of the aquifer such as permeability. Computational methods for inverse analysis are commonly used to infer these properties from quantities that are more readily observable such as hydraulic head. We present a method for computational inverse analysis that utilizes a type of quantum computer called a quantum annealer. While quantum computing is in an early stage compared to classical computing, we demonstrate that it is sufficiently developed that it can be used to solve certain subsurface flow problems. We utilize a D-Wave 2X quantum annealer to solve 1D and 2D hydrologic inverse problems that, while small by modern standards, are similar in size and sometimes larger than hydrologic inverse problems that were solved with early classical computers. Our results and the rapid progress being made with quantum computing hardware indicate that the era of quantum-computational hydrology may not be too far in the future.

Coupling of Large Amplitude Inversion with Other States

NASA Astrophysics Data System (ADS)

Pearson, John; Yu, Shanshan

2016-06-01

The coupling of a large amplitude motion with a small amplitude vibration remains one of the least well characterized problems in molecular physics. Molecular inversion poses a few unique and not intuitively obvious challenges to the large amplitude motion problem. In spite of several decades of theoretical work numerous challenges in calculation of transition frequencies and more importantly intensities persist. The most challenging aspect of this problem is that the inversion coordinate is a unique function of the overall vibrational state including both the large and small amplitude modes. As a result, the r-axis system and the meaning of the K-quantum number in the rotational basis set are unique to each vibrational state of large or small amplitude motion. This unfortunate reality has profound consequences to calculation of intensities and the coupling of nearly degenerate vibrational states. The case of NH3 inversion and inversion through a plane of symmetry in alcohols will be examined to find a general path forward.

An approach to quantum-computational hydrologic inverse analysis

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

O'Malley, Daniel

Making predictions about flow and transport in an aquifer requires knowledge of the heterogeneous properties of the aquifer such as permeability. Computational methods for inverse analysis are commonly used to infer these properties from quantities that are more readily observable such as hydraulic head. We present a method for computational inverse analysis that utilizes a type of quantum computer called a quantum annealer. While quantum computing is in an early stage compared to classical computing, we demonstrate that it is sufficiently developed that it can be used to solve certain subsurface flow problems. We utilize a D-Wave 2X quantum annealermore » to solve 1D and 2D hydrologic inverse problems that, while small by modern standards, are similar in size and sometimes larger than hydrologic inverse problems that were solved with early classical computers. Our results and the rapid progress being made with quantum computing hardware indicate that the era of quantum-computational hydrology may not be too far in the future.« less

Reconstruction of 3D Shapes of Opaque Cumulus Clouds from Airborne Multiangle Imaging: A Proof-of-Concept

NASA Astrophysics Data System (ADS)

Davis, A. B.; Bal, G.; Chen, J.

2015-12-01

Operational remote sensing of microphysical and optical cloud properties is invariably predicated on the assumption of plane-parallel slab geometry for the targeted cloud. The sole benefit of this often-questionable assumption about the cloud is that it leads to one-dimensional (1D) radiative transfer (RT)---a textbook, computationally tractable model. We present new results as evidence that, thanks to converging advances in 3D RT, inverse problem theory, algorithm implementation, and computer hardware, we are at the dawn of a new era in cloud remote sensing where we can finally go beyond the plane-parallel paradigm. Granted, the plane-parallel/1D RT assumption is reasonable for spatially extended stratiform cloud layers, as well as the smoothly distributed background aerosol layers. However, these 1D RT-friendly scenarios exclude cases that are critically important for climate physics. 1D RT---whence operational cloud remote sensing---fails catastrophically for cumuliform clouds that have fully 3D outer shapes and internal structures driven by shallow or deep convection. For these situations, the first order of business in a robust characterization by remote sensing is to abandon the slab geometry framework and determine the 3D geometry of the cloud, as a first step toward bone fide 3D cloud tomography. With this specific goal in mind, we deliver a proof-of-concept for an entirely new kind of remote sensing applicable to 3D clouds. It is based on highly simplified 3D RT and exploits multi-angular suites of cloud images at high spatial resolution. Airborne sensors like AirMSPI readily acquire such data. The key element of the reconstruction algorithm is a sophisticated solution of the nonlinear inverse problem via linearization of the forward model and an iteration scheme supported, where necessary, by adaptive regularization. Currently, the demo uses a 2D setting to show how either vertical profiles or horizontal slices of the cloud can be accurately reconstructed. Extension to 3D volumes is straightforward but the next challenge is to accommodate images at lower spatial resolution, e.g., from MISR/Terra. G. Bal, J. Chen, and A.B. Davis (2015). Reconstruction of cloud geometry from multi-angle images, Inverse Problems in Imaging (submitted).

Mixed linear-non-linear inversion of crustal deformation data: Bayesian inference of model, weighting and regularization parameters

NASA Astrophysics Data System (ADS)

Fukuda, Jun'ichi; Johnson, Kaj M.

2010-06-01

We present a unified theoretical framework and solution method for probabilistic, Bayesian inversions of crustal deformation data. The inversions involve multiple data sets with unknown relative weights, model parameters that are related linearly or non-linearly through theoretic models to observations, prior information on model parameters and regularization priors to stabilize underdetermined problems. To efficiently handle non-linear inversions in which some of the model parameters are linearly related to the observations, this method combines both analytical least-squares solutions and a Monte Carlo sampling technique. In this method, model parameters that are linearly and non-linearly related to observations, relative weights of multiple data sets and relative weights of prior information and regularization priors are determined in a unified Bayesian framework. In this paper, we define the mixed linear-non-linear inverse problem, outline the theoretical basis for the method, provide a step-by-step algorithm for the inversion, validate the inversion method using synthetic data and apply the method to two real data sets. We apply the method to inversions of multiple geodetic data sets with unknown relative data weights for interseismic fault slip and locking depth. We also apply the method to the problem of estimating the spatial distribution of coseismic slip on faults with unknown fault geometry, relative data weights and smoothing regularization weight.

Air Pollution and Weather: Activities and Demonstrations for Science Classes

ERIC Educational Resources Information Center

Cole, Henry S.

1973-01-01

Discusses a number of concepts (turbulence, dispersion, vertical temperature distribution, atmospheric stability and instability, and inversions) which are prerequisite to understanding how weather affects air quality. Describes classroom demonstrations effective in introducing these concepts to students at the elementary, secondary and college…

Pattern formation of Rayleigh-Bénard convection of cold water near its density maximum in a vertical cylindrical container.

PubMed

Li, You-Rong; Ouyang, Yu-Qing; Hu, Yu-Peng

2012-10-01

In order to understand the onset of convective instability and multiple stable convection patterns of buoyancy-driven convection of cold water near its density maximum in a vertical cylindrical container heated from below, a series of three-dimensional numerical simulations were performed. The aspect ratio of the container was 2 and Prandtl number of cold water was 11.57. The sidewall was considered to be perfectly adiabatic, and the density inversion parameter was fixed at 0.3. The result shows that the density inversion phenomenon in cold water has an important effect on the critical Rayleigh number for the onset of convection and the pattern formation at higher Rayleigh numbers. When the Rayleigh number varies from 3×10(3) to 1.2×10(5), eight stable, steady convection patterns are obtained under different initial conditions. The coexistence of multiple stable steady flow patterns is also observed within some specific ranges of the Rayleigh number.

Direct and inverse problems of studying the properties of multilayer nanostructures based on a two-dimensional model of X-ray reflection and scattering

NASA Astrophysics Data System (ADS)

Khachaturov, R. V.

2014-06-01

A mathematical model of X-ray reflection and scattering by multilayered nanostructures in the quasi-optical approximation is proposed. X-ray propagation and the electric field distribution inside the multilayered structure are considered with allowance for refraction, which is taken into account via the second derivative with respect to the depth of the structure. This model is used to demonstrate the possibility of solving inverse problems in order to determine the characteristics of irregularities not only over the depth (as in the one-dimensional problem) but also over the length of the structure. An approximate combinatorial method for system decomposition and composition is proposed for solving the inverse problems.

a Novel Discrete Optimal Transport Method for Bayesian Inverse Problems

NASA Astrophysics Data System (ADS)

Bui-Thanh, T.; Myers, A.; Wang, K.; Thiery, A.

2017-12-01

We present the Augmented Ensemble Transform (AET) method for generating approximate samples from a high-dimensional posterior distribution as a solution to Bayesian inverse problems. Solving large-scale inverse problems is critical for some of the most relevant and impactful scientific endeavors of our time. Therefore, constructing novel methods for solving the Bayesian inverse problem in more computationally efficient ways can have a profound impact on the science community. This research derives the novel AET method for exploring a posterior by solving a sequence of linear programming problems, resulting in a series of transport maps which map prior samples to posterior samples, allowing for the computation of moments of the posterior. We show both theoretical and numerical results, indicating this method can offer superior computational efficiency when compared to other SMC methods. Most of this efficiency is derived from matrix scaling methods to solve the linear programming problem and derivative-free optimization for particle movement. We use this method to determine inter-well connectivity in a reservoir and the associated uncertainty related to certain parameters. The attached file shows the difference between the true parameter and the AET parameter in an example 3D reservoir problem. The error is within the Morozov discrepancy allowance with lower computational cost than other particle methods.

Seismic waveform inversion best practices: regional, global and exploration test cases

NASA Astrophysics Data System (ADS)

Modrak, Ryan; Tromp, Jeroen

2016-09-01

Reaching the global minimum of a waveform misfit function requires careful choices about the nonlinear optimization, preconditioning and regularization methods underlying an inversion. Because waveform inversion problems are susceptible to erratic convergence associated with strong nonlinearity, one or two test cases are not enough to reliably inform such decisions. We identify best practices, instead, using four seismic near-surface problems, one regional problem and two global problems. To make meaningful quantitative comparisons between methods, we carry out hundreds of inversions, varying one aspect of the implementation at a time. Comparing nonlinear optimization algorithms, we find that limited-memory BFGS provides computational savings over nonlinear conjugate gradient methods in a wide range of test cases. Comparing preconditioners, we show that a new diagonal scaling derived from the adjoint of the forward operator provides better performance than two conventional preconditioning schemes. Comparing regularization strategies, we find that projection, convolution, Tikhonov regularization and total variation regularization are effective in different contexts. Besides questions of one strategy or another, reliability and efficiency in waveform inversion depend on close numerical attention and care. Implementation details involving the line search and restart conditions have a strong effect on computational cost, regardless of the chosen nonlinear optimization algorithm.

Accounting for model error in Bayesian solutions to hydrogeophysical inverse problems using a local basis approach

NASA Astrophysics Data System (ADS)

Köpke, Corinna; Irving, James; Elsheikh, Ahmed H.

2018-06-01

Bayesian solutions to geophysical and hydrological inverse problems are dependent upon a forward model linking subsurface physical properties to measured data, which is typically assumed to be perfectly known in the inversion procedure. However, to make the stochastic solution of the inverse problem computationally tractable using methods such as Markov-chain-Monte-Carlo (MCMC), fast approximations of the forward model are commonly employed. This gives rise to model error, which has the potential to significantly bias posterior statistics if not properly accounted for. Here, we present a new methodology for dealing with the model error arising from the use of approximate forward solvers in Bayesian solutions to hydrogeophysical inverse problems. Our approach is geared towards the common case where this error cannot be (i) effectively characterized through some parametric statistical distribution; or (ii) estimated by interpolating between a small number of computed model-error realizations. To this end, we focus on identification and removal of the model-error component of the residual during MCMC using a projection-based approach, whereby the orthogonal basis employed for the projection is derived in each iteration from the K-nearest-neighboring entries in a model-error dictionary. The latter is constructed during the inversion and grows at a specified rate as the iterations proceed. We demonstrate the performance of our technique on the inversion of synthetic crosshole ground-penetrating radar travel-time data considering three different subsurface parameterizations of varying complexity. Synthetic data are generated using the eikonal equation, whereas a straight-ray forward model is assumed for their inversion. In each case, our developed approach enables us to remove posterior bias and obtain a more realistic characterization of uncertainty.

Control and System Theory, Optimization, Inverse and Ill-Posed Problems

DTIC Science & Technology

1988-09-14

Justlfleatlen Distribut ion/ Availability Codes # AFOSR-87-0350 Avat’ and/or1987-1988 Dist Special *CONTROL AND SYSTEM THEORY , ~ * OPTIMIZATION, * INVERSE...considerable va- riety of research investigations within the grant areas (Control and system theory , Optimization, and Ill-posed problems]. The

Bayesian ionospheric multi-instrument 3D tomography

NASA Astrophysics Data System (ADS)

Norberg, Johannes; Vierinen, Juha; Roininen, Lassi

2017-04-01

The tomographic reconstruction of ionospheric electron densities is an inverse problem that cannot be solved without relatively strong regularising additional information. % Especially the vertical electron density profile is determined predominantly by the regularisation. % %Often utilised regularisations in ionospheric tomography include smoothness constraints and iterative methods with initial ionospheric models. % Despite its crucial role, the regularisation is often hidden in the algorithm as a numerical procedure without physical understanding. % % The Bayesian methodology provides an interpretative approach for the problem, as the regularisation can be given in a physically meaningful and quantifiable prior probability distribution. % The prior distribution can be based on ionospheric physics, other available ionospheric measurements and their statistics. % Updating the prior with measurements results as the posterior distribution that carries all the available information combined. % From the posterior distribution, the most probable state of the ionosphere can then be solved with the corresponding probability intervals. % Altogether, the Bayesian methodology provides understanding on how strong the given regularisation is, what is the information gained with the measurements and how reliable the final result is. % In addition, the combination of different measurements and temporal development can be taken into account in a very intuitive way. However, a direct implementation of the Bayesian approach requires inversion of large covariance matrices resulting in computational infeasibility. % In the presented method, Gaussian Markov random fields are used to form a sparse matrix approximations for the covariances. % The approach makes the problem computationally feasible while retaining the probabilistic and physical interpretation. Here, the Bayesian method with Gaussian Markov random fields is applied for ionospheric 3D tomography over Northern Europe. % Multi-instrument measurements are utilised from TomoScand receiver network for Low Earth orbit beacon satellite signals, GNSS receiver networks, as well as from EISCAT ionosondes and incoherent scatter radars. % %The performance is demonstrated in three-dimensional spatial domain with temporal development also taken into account.

Ozone height profiles using laser heterodyne radiometer

NASA Technical Reports Server (NTRS)

Jain, S. L.

1994-01-01

The monitoring of vertical profiles of ozone and related minor constituents in the atmosphere are of great significance to understanding the complex interaction between atmospheric dynamics, chemistry and radiation budget. An ultra high spectral resolution tunable CO2 laser heterodyne radiometer has been designed, developed and set up at the National Physical Laboratory, New Delhi to obtain vertical profiles of various minor constituents the characteristic absorption lines in 9 to 11 micron spectral range. Due to its high spectral resolution the lines can be resolved completely and data obtained are inverted to get vertical profiles using an inversion technique developed by the author. In the present communication the salient features of the laser heterodyne system and the results obtained are discussed in detail.

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

NASA Astrophysics Data System (ADS)

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

2014-09-01

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

Deconvolution using a neural network

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

Lehman, S.K.

1990-11-15

Viewing one dimensional deconvolution as a matrix inversion problem, we compare a neural network backpropagation matrix inverse with LMS, and pseudo-inverse. This is a largely an exercise in understanding how our neural network code works. 1 ref.

Genetics Home Reference: Koolen-de Vries syndrome

MedlinePlus

... of Koolen-de Vries syndrome , has undergone an inversion . An inversion involves two breaks in a chromosome; the resulting ... lineage have no health problems related to the inversion. However, genetic material can be lost or duplicated ...

Inverse modeling of the hydraulic properties of fractured media : development of a flow tomography approach

NASA Astrophysics Data System (ADS)

Bour, O.; Klepikova, M.; Le Borgne, T.; De Dreuzy, J.

2013-12-01

Inverse modeling of hydraulic and geometrical properties of fractured media is a very challenging objective due to the spatial heterogeneity of the medium and the scarcity of data. Here we present a flow tomography approach that permits to characterize the location, the connectivity and the hydraulic properties of main flow paths in fractured media. The accurate characterization of the location, hydraulic properties and connectivity of major fracture zones is essential to model flow and solute transport in fractured media. Cross-borehole flowmeter tests, which consist of measuring changes in vertical borehole flows when pumping a neighboring borehole, were shown to be an efficient technique to provide information on the properties of the flow zones that connect borehole pairs [Paillet, 1998; Le Borgne et al., 2006]. The interpretation of such experiments may however be quite uncertain when multiple connections exist. In this study, we explore the potential of flow tomography (i.e., sequential cross-borehole flowmeter tests) for characterizing aquifer heterogeneity. We first propose a framework for inverting flow and drawdown data to infer fracture connectivity and transmissivities. Here we use a simplified discrete fracture network approach that highlights main connectivity structures. This conceptual model attempts to reproduce fracture network connectivity without taking fracture geometry (length, orientation, dip) into account. We then explore the potential of the method for simplified synthetic fracture network models and quantify the sensitivity of drawdown and borehole flow velocities to the transmissivity of the connecting flowpaths. Flow tomography is expected to be most effective if cross-borehole pumping induces large changes in vertical borehole velocities. The uncertainty of the transmissivity estimates increases for small borehole flow velocities. The uncertainty about the transmissivity of fractures that connect the main flowpath but not the boreholes is generally higher. We demonstrate that successively changing pumping and observation boreholes improves the quality of available information and reduces the indetermination of the problem. The inverse method is validated for different synthetic flow scenarios. It is shown to provide a good estimation of connectivity patterns and transmissivities of main flowpaths. Although the chosen fracture network geometry has been simplified, flow tomography appears to be a promising approach for characterizing connectivity patterns and transmissivities of fractured media.

Numerical Representation of Wintertime Near-Surface Inversions in the Arctic with a 2.5-km Version of the Global Environmental Multiscale (GEM) Model

NASA Astrophysics Data System (ADS)

Dehghan, A.; Mariani, Z.; Gascon, G.; Bélair, S.; Milbrandt, J.; Joe, P. I.; Crawford, R.; Melo, S.

2017-12-01

Environment and Climate Change Canada (ECCC) is implementing a 2.5-km resolution version of the Global Environmental Multiscale (GEM) model over the Canadian Arctic. Radiosonde observations were used to evaluate the numerical representation of surface-based temperature inversion which is a major feature in the Arctic region. Arctic surface-based inversions are often created by imbalance between radiative cooling processes at surface and warm air advection above. This can have a significant effect on vertical mixing of pollutants and moisture, and ultimately, on cloud formation. It is therefore important to correctly predict the existence of surface inversions along with their characteristics (i.e., intensity and depth). Previous climatological studies showed that the frequency and intensity of surface-based inversions are larger during colder months in the Arctic. Therefore, surface-based inversions were estimated using radiosonde measurements during winter (December 2015 to February 2016) at Iqaluit (Nunavut, Canada). Results show that the inversion intensity can exceed 10 K with depths as large as 1 km. Preliminary evaluation of GEM outputs reveals that the model tends to underestimate the intensity of near-surface inversions, and in some cases, the model failed to predict an inversion. This study presents the factors contributing to this bias including surface temperature and snow cover.

Three-dimensional inversion of multisource array electromagnetic data

NASA Astrophysics Data System (ADS)

Tartaras, Efthimios

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

Sensitivity computation of the ell1 minimization problem and its application to dictionary design of ill-posed problems

NASA Astrophysics Data System (ADS)

Horesh, L.; Haber, E.

2009-09-01

The ell1 minimization problem has been studied extensively in the past few years. Recently, there has been a growing interest in its application for inverse problems. Most studies have concentrated in devising ways for sparse representation of a solution using a given prototype dictionary. Very few studies have addressed the more challenging problem of optimal dictionary construction, and even these were primarily devoted to the simplistic sparse coding application. In this paper, sensitivity analysis of the inverse solution with respect to the dictionary is presented. This analysis reveals some of the salient features and intrinsic difficulties which are associated with the dictionary design problem. Equipped with these insights, we propose an optimization strategy that alleviates these hurdles while utilizing the derived sensitivity relations for the design of a locally optimal dictionary. Our optimality criterion is based on local minimization of the Bayesian risk, given a set of training models. We present a mathematical formulation and an algorithmic framework to achieve this goal. The proposed framework offers the design of dictionaries for inverse problems that incorporate non-trivial, non-injective observation operators, where the data and the recovered parameters may reside in different spaces. We test our algorithm and show that it yields improved dictionaries for a diverse set of inverse problems in geophysics and medical imaging.

Inverse scattering transform and soliton classification of the coupled modified Korteweg-de Vries equation

NASA Astrophysics Data System (ADS)

Wu, Jianping; Geng, Xianguo

2017-12-01

The inverse scattering transform of the coupled modified Korteweg-de Vries equation is studied by the Riemann-Hilbert approach. In the direct scattering process, the spectral analysis of the Lax pair is performed, from which a Riemann-Hilbert problem is established for the equation. In the inverse scattering process, by solving Riemann-Hilbert problems corresponding to the reflectionless cases, three types of multi-soliton solutions are obtained. The multi-soliton classification is based on the zero structures of the Riemann-Hilbert problem. In addition, some figures are given to illustrate the soliton characteristics of the coupled modified Korteweg-de Vries equation.

Minimum Altitude-Loss Soaring in a Specified Vertical Wind Distribution

NASA Technical Reports Server (NTRS)

Pierson, B. L.; Chen, I.

1979-01-01

Minimum altitude-loss flight of a sailplane through a given vertical wind distribution is discussed. The problem is posed as an optimal control problem, and several numerical solutions are obtained for a sinusoidal wind distribution.

Individual differences in children's understanding of inversion and arithmetical skill.

PubMed

Gilmore, Camilla K; Bryant, Peter

2006-06-01

Background and aims. In order to develop arithmetic expertise, children must understand arithmetic principles, such as the inverse relationship between addition and subtraction, in addition to learning calculation skills. We report two experiments that investigate children's understanding of the principle of inversion and the relationship between their conceptual understanding and arithmetical skills. A group of 127 children from primary schools took part in the study. The children were from 2 age groups (6-7 and 8-9 years). Children's accuracy on inverse and control problems in a variety of presentation formats and in canonical and non-canonical forms was measured. Tests of general arithmetic ability were also administered. Children consistently performed better on inverse than control problems, which indicates that they could make use of the inverse principle. Presentation format affected performance: picture presentation allowed children to apply their conceptual understanding flexibly regardless of the problem type, while word problems restricted their ability to use their conceptual knowledge. Cluster analyses revealed three subgroups with different profiles of conceptual understanding and arithmetical skill. Children in the 'high ability' and 'low ability' groups showed conceptual understanding that was in-line with their arithmetical skill, whilst a 3rd group of children had more advanced conceptual understanding than arithmetical skill. The three subgroups may represent different points along a single developmental path or distinct developmental paths. The discovery of the existence of the three groups has important consequences for education. It demonstrates the importance of considering the pattern of individual children's conceptual understanding and problem-solving skills.

On stability of the solutions of inverse problem for determining the right-hand side of a degenerate parabolic equation with two independent variables

NASA Astrophysics Data System (ADS)

Kamynin, V. L.; Bukharova, T. I.

2017-01-01

We prove the estimates of stability with respect to perturbations of input data for the solutions of inverse problems for degenerate parabolic equations with unbounded coefficients. An important feature of these estimates is that the constants in these estimates are written out explicitly by the input data of the problem.

THE SUCCESSIVE LINEAR ESTIMATOR: A REVISIT. (R827114)

EPA Science Inventory

This paper examines the theoretical basis of the successive linear estimator (SLE) that has been developed for the inverse problem in subsurface hydrology. We show that the SLE algorithm is a non-linear iterative estimator to the inverse problem. The weights used in the SLE al...

ON THE GEOSTATISTICAL APPROACH TO THE INVERSE PROBLEM. (R825689C037)

EPA Science Inventory

Abstract

The geostatistical approach to the inverse problem is discussed with emphasis on the importance of structural analysis. Although the geostatistical approach is occasionally misconstrued as mere cokriging, in fact it consists of two steps: estimation of statist...

On a local solvability and stability of the inverse transmission eigenvalue problem

NASA Astrophysics Data System (ADS)

Bondarenko, Natalia; Buterin, Sergey

2017-11-01

We prove a local solvability and stability of the inverse transmission eigenvalue problem posed by McLaughlin and Polyakov (1994 J. Diff. Equ. 107 351-82). In particular, this result establishes the minimality of the data used therein. The proof is constructive.

Retrievals of Profiles of Fine And Coarse Aerosols Using Lidar And Radiometric Space Measurements

NASA Technical Reports Server (NTRS)

Kaufman, Yoram; Tanre, Didier; Leon, Jean-Francois; Pelon, Jacques; Lau, William K. M. (Technical Monitor)

2002-01-01

In couple of years we expect the launch of the CALIPSO lidar spaceborne mission designed to observe aerosols and clouds. CALIPSO will collect profiles of the lidar attenuated backscattering coefficients in two spectral wavelengths (0.53 and 1.06 microns). Observations are provided along the track of the satellite around the globe from pole to pole. The attenuated backscattering coefficients are sensitive to the vertical distribution of aerosol particles, their shape and size. However the information is insufficient to be mapped into unique aerosol physical properties and vertical distribution. Infinite number of physical solutions can reconstruct the same two wavelength backscattered profile measured from space. CALIPSO will fly in formation with the Aqua satellite and the MODIS spectro-radiometer on board. Spectral radiances measured by MODIS in six channels between 0.55 and 2.13 microns simultaneously with the CALIPSO observations can constrain the solutions and resolve this ambiguity, albeit under some assumptions. In this paper we describe the inversion method and apply it to aircraft lidar and MODIS data collected over a dust storm off the coast of West Africa during the SHADE experiment. It is shown that the product of the single scattering albedo, omega, and the phase function, P, for backscattering can be retrieved from the synergism between measurements avoiding a priori hypotheses required for inverting lidar measurements alone. The resultant value of (omega)P(180 deg.) = 0.016/sr are significantly different from what is expected using Mie theory, but are in good agreement with recent results obtained from lidar observations of dust episodes. The inversion is robust in the presence of noise of 10% and 20% in the lidar signal in the 0.53 and 1.06 pm channels respectively. Calibration errors of the lidar of 5 to 10% can cause an error in optical thickness of 20 to 40% respectively in the tested cases. The lidar calibration errors cause degradation in the ability to fit the MODIS data. Therefore the MODIS measurements can be used to identify the calibration problem and correct for it. The CALIPSO-MODIS measurements of the profiles of fine and coarse aerosols, together with CALIPSO measurements of clouds vertical distribution, is expected to be critically important in understanding aerosol transport across continents and political boundaries, and to study aerosol-cloud interaction and its effect on precipitation and global forcing of climate.

Testing joint inversion techniques of gravity data and cosmic ray muon flux at a well-characterized site for use in the detection of subsurface density structures beneath volcanoes.

NASA Astrophysics Data System (ADS)

Cosburn, K.; Roy, M.; Rowe, C. A.; Guardincerri, E.

2017-12-01

Obtaining accurate static and time-dependent shallow subsurface density structure beneath volcanic, hydrogeologic, and tectonic targets can help illuminate active processes of fluid flow and magma transport. A limitation of using surface gravity measurements for such imaging is that these observations are vastly underdetermined and non-unique. In order to hone in on a more accurate solution, other data sets are needed to provide constraints, typically seismic or borehole observations. The spatial resolution of these techniques, however, is relatively poor, and a novel solution to this problem in recent years has been to use attenuation of the cosmic ray muon flux, which provides an independent constraint on density. In this study we present a joint inversion of gravity and cosmic ray muon flux observations to infer the density structure of a target rock volume at a well-characterized site near Los Alamos, New Mexico, USA. We investigate the shallow structure of a mesa formed by the Quaternary ash-flow tuffs on the Pajarito Plateau, flanking the Jemez volcano in New Mexico. Gravity measurements were made using a Lacoste and Romberg D meter on the surface of the mesa and inside a tunnel beneath the mesa. Muon flux measurements were also made at the mesa surface and at various points within the same tunnel using a muon detector having an acceptance region of 45 degrees from the vertical and a track resolution of several milliradians. We expect the combination of muon and gravity data to provide us with enhanced resolution as well as the ability to sense deeper structures in our region of interest. We use Bayesian joint inversion techniques on the gravity-muon dataset to test these ideas, building upon previous work using gravity inversion alone to resolve density structure in our study area. Both the regional geology and geometry of our study area is well-known and we assess the inferred density structure from our gravity-muon joint inversion within this known geologic framework.

RF Tomography for Tunnel Detection: Principles and Inversion Schemes

NASA Astrophysics Data System (ADS)

Lo Monte, L.; Erricolo, D.; Inan, U. S.; Wicks, M. C.

2008-12-01

We propose a novel way to detect underground tunnels based on classical seismic tomography, Ground Penetrating Radar (GPR), inverse scattering principles, and the deployment of distributed sensors, which we call "Distributed RF Tomography". Tunnel detection has been a critical problem that cannot be considered fully solved. Presently, tunnel detection is performed by methods that include seismic sensors, electrical impedance, microgravity, boreholes, and GPR. All of these methods have drawbacks that make them not applicable for use in unfriendly environments, such as battlefields. Specifically, they do not cover wide surface areas, they are generally shallow, they are limited to vertical prospecting, and require the user to be in situ, which may jeopardize one's safety. Additional application of the proposed distributed RF tomography include monitoring sensitive areas, (e.g. banks, power plants, military bases, prisons, national borders) and civil applications (e.g. environmental engineering, mine safety, search and rescue, speleology, archaeology and geophysics). The novelty of a Distributed RF tomography system consists of the following. 1) Sensors are scattered randomly above the ground, thus saving time and money compared to the use of boreholes. 2) The use of lower operating frequency (around HF), which allows for deeper penetration. 3) The use of CW diffraction tomography, which increases the resolution to sub-wavelength values, independently from the sensor displacement, and increases the SNR. 4) Use of linear inversion schemes that are suited for tunnel detection. 5) The use of modulation schemes and signal processing algorithms to mitigate interferences and noise. This presentation will cover: 1. Current physical limits of existing techniques for tunnel detection. 2. Concept of Distributed RF Tomography. 3. Inversion theories and strategies a. Proper forward model for voids buried into an homogeneous medium b. Extended matched filtering inversion c. Near field formulation : Dyadic representation d. Fourier approach: principles and techniques aimed at improving the reconstructed image. e. Theoretical Limits f. Super-Resolution : Singular Values Decomposition and MUSIC 4. Propagation Model and theoretical limitations. 5. Transmitting and Receiving design, with signal processing and modulation. 6. Numerical Simulations using FDTD tools.

Geoelectrical characterization with 1D VES/TDEM joint inversion in Urupês-SP region, Paraná Basin: Applications to hydrogeology

NASA Astrophysics Data System (ADS)

Leite, David Nakamura; Bortolozo, Cassiano Antonio; Porsani, Jorge Luís; Couto, Marco Antonio; Campaña, Julian David Realpe; dos Santos, Fernando Acácio Monteiro; Rangel, Rodrigo Corrêa; Hamada, Luiz Rodrigo; Sifontes, Rimary Valera; Serejo de Oliveira, Gabriela; Stangari, Marcelo César

2018-04-01

Although Brazil is well known by the large rivers and the Amazon Rain Forest most cities do not have access to sufficient quantities of surface water to supply the population. Because of this 61% of Brazilian population (IBGE, 2003) depends on groundwater resources. In order to help the conscious exploration of this resource in Urupês city (São Paulo State) which is characterized by problems of lack of water, this research applied the transient electromagnetic method (TDEM) and Vertical Electrical Sounding (VES) for the geoelectrical characterization of the interest region. So, the objective of this work was increase the hydrogeological basis for groundwater exploitation of Bauru sedimentary aquifer and Serra Geral fractured aquifer (Paraná Basin). A total of 23 TDEM and 15 VES soundings were conducted during the years of 2009, 2011 and 2012. In addition, 10 pairs of VES/TDEM soundings were acquired with coincident centers to be able to perform the joint inversion. The joint inversion technique is a promising tool, which enables to get the best of both methods, where the VES add the shallow information and TDEM the deeper one. In this work, the individual and joint inversions were performed using the "Curupira" software. After data process and inversion, the results were interpreted based on geological well information provided by the Department of Water and Electrical Power (DAEE) and the Brazilian Geological Survey (CPRM) which enabled to estimate favorable places to exploitation of water in Bauru and Serra Geral aquifers. For the Bauru aquifer, the results suggest areas where thickness exceeds 100 m. In these areas, the resistivity calculated was about 20 Ω·m. Therefore, the sediments have been interpreted as saturated sandy clay. In the basalt layer of Serra Geral Formation, the suggested locations present resistivity values <100 Ω·m at 200 m depth. The indicated places in sedimentary aquifer and the locations in the fractured aquifer will may show alternative sources for groundwater exploitation and water supply for Urupês city.

Discrimination of Mirror-Image shapes by Young Children

ERIC Educational Resources Information Center

Thompson, G. Brian

1975-01-01

Conducted two experiments which employed discrimination learning methods to test predictions related to the difficulty of discrimination of lateral reversals and of inversions when shapes are presented: (1) successively, (2) simultaneously in lateral alignment, and (3) simultaneously in vertical alignment. Subjects were 6-year-old children. (SDH)

NLSE: Parameter-Based Inversion Algorithm

NASA Astrophysics Data System (ADS)

Sabbagh, Harold A.; Murphy, R. Kim; Sabbagh, Elias H.; Aldrin, John C.; Knopp, Jeremy S.

Chapter 11 introduced us to the notion of an inverse problem and gave us some examples of the value of this idea to the solution of realistic industrial problems. The basic inversion algorithm described in Chap. 11 was based upon the Gauss-Newton theory of nonlinear least-squares estimation and is called NLSE in this book. In this chapter we will develop the mathematical background of this theory more fully, because this algorithm will be the foundation of inverse methods and their applications during the remainder of this book. We hope, thereby, to introduce the reader to the application of sophisticated mathematical concepts to engineering practice without introducing excessive mathematical sophistication.

Solution of some types of differential equations: operational calculus and inverse differential operators.

PubMed

Zhukovsky, K

2014-01-01

We present a general method of operational nature to analyze and obtain solutions for a variety of equations of mathematical physics and related mathematical problems. We construct inverse differential operators and produce operational identities, involving inverse derivatives and families of generalised orthogonal polynomials, such as Hermite and Laguerre polynomial families. We develop the methodology of inverse and exponential operators, employing them for the study of partial differential equations. Advantages of the operational technique, combined with the use of integral transforms, generating functions with exponentials and their integrals, for solving a wide class of partial derivative equations, related to heat, wave, and transport problems, are demonstrated.

Optimal estimation retrievals of the atmospheric structure and composition of HD 189733b from secondary eclipse spectroscopy

NASA Astrophysics Data System (ADS)

Lee, J.-M.; Fletcher, L. N.; Irwin, P. G. J.

2012-02-01

Recent spectroscopic observations of transiting hot Jupiters have permitted the derivation of the thermal structure and molecular abundances of H2O, CO2, CO and CH4 in these extreme atmospheres. Here, for the first time, we apply the technique of optimal estimation to determine the thermal structure and composition of an exoplanet by solving the inverse problem. The development of a suite of radiative transfer and retrieval tools for exoplanet atmospheres is described, building upon a retrieval algorithm which is extensively used in the study of our own Solar system. First, we discuss the plausibility of detection of different molecules in the dayside atmosphere of HD 189733b and the best-fitting spectrum retrieved from all publicly available sets of secondary eclipse observations between 1.45 and 24 μm. Additionally, we use contribution functions to assess the vertical sensitivity of the emission spectrum to temperatures and molecular composition. Over the altitudes probed by the contribution functions, the retrieved thermal structure shows an isothermal upper atmosphere overlying a deeper adiabatic layer (temperature decreasing with altitude), which is consistent with previously reported dynamical and observational results. The formal uncertainties on retrieved parameters are estimated conservatively using an analysis of the cross-correlation functions and the degeneracy between different atmospheric properties. The formal solution of the inverse problem suggests that the uncertainties on retrieved parameters are larger than suggested in previous studies, and that the presence of CO and CH4 is only marginally supported by the available data. Nevertheless, by including as broad a wavelength range as possible in the retrieval, we demonstrate that available spectra of HD 189733b can constrain a family of potential solutions for the atmospheric structure.

The atmospheric boundary layer in the CSIRO global climate model: simulations versus observations

NASA Astrophysics Data System (ADS)

Garratt, J. R.; Rotstayn, L. D.; Krummel, P. B.

2002-07-01

A 5-year simulation of the atmospheric boundary layer in the CSIRO global climate model (GCM) is compared with detailed boundary-layer observations at six locations, two over the ocean and four over land. Field observations, in the form of surface fluxes and vertical profiles of wind, temperature and humidity, are generally available for each hour over periods of one month or more in a single year. GCM simulations are for specific months corresponding to the field observations, for each of five years. At three of the four land sites (two in Australia, one in south-eastern France), modelled rainfall was close to the observed climatological values, but was significantly in deficit at the fourth (Kansas, USA). Observed rainfall during the field expeditions was close to climatology at all four sites. At the Kansas site, modelled screen temperatures (Tsc), diurnal temperature amplitude and sensible heat flux (H) were significantly higher than observed, with modelled evaporation (E) much lower. At the other three land sites, there is excellent correspondence between the diurnal amplitude and phase and absolute values of each variable (Tsc, H, E). Mean monthly vertical profiles for specific times of the day show strong similarities: over land and ocean in vertical shape and absolute values of variables, and in the mixed-layer and nocturnal-inversion depths (over land) and the height of the elevated inversion or height of the cloud layer (over the sea). Of special interest is the presence climatologically of early morning humidity inversions related to dewfall and of nocturnal low-level jets; such features are found in the GCM simulations. The observed day-to-day variability in vertical structure is captured well in the model for most sites, including, over a whole month, the temperature range at all levels in the boundary layer, and the mix of shallow and deep mixed layers. Weaknesses or unrealistic structure include the following, (a) unrealistic model mixed-layer temperature profiles over land in clear skies, related to use of a simple local first-order turbulence closure, (b) a tendency to overpredict cloud liquid water near the surface.

Solving inversion problems with neural networks

NASA Technical Reports Server (NTRS)

Kamgar-Parsi, Behzad; Gualtieri, J. A.

1990-01-01

A class of inverse problems in remote sensing can be characterized by Q = F(x), where F is a nonlinear and noninvertible (or hard to invert) operator, and the objective is to infer the unknowns, x, from the observed quantities, Q. Since the number of observations is usually greater than the number of unknowns, these problems are formulated as optimization problems, which can be solved by a variety of techniques. The feasibility of neural networks for solving such problems is presently investigated. As an example, the problem of finding the atmospheric ozone profile from measured ultraviolet radiances is studied.

Approximation of the ruin probability using the scaled Laplace transform inversion

PubMed Central

Mnatsakanov, Robert M.; Sarkisian, Khachatur; Hakobyan, Artak

2015-01-01

The problem of recovering the ruin probability in the classical risk model based on the scaled Laplace transform inversion is studied. It is shown how to overcome the problem of evaluating the ruin probability at large values of an initial surplus process. Comparisons of proposed approximations with the ones based on the Laplace transform inversions using a fixed Talbot algorithm as well as on the ones using the Trefethen–Weideman–Schmelzer and maximum entropy methods are presented via a simulation study. PMID:26752796

Inverse problems and coherence

NASA Astrophysics Data System (ADS)

Baltes, H. P.; Ferwerda, H. A.

1981-03-01

A summary of current inverse problems of statistical optics is presented together with a short guide to the pertinent review-type literature. The retrieval of structural information from the far-zone degree of coherence and the average intensity distribution of radiation scattered by a superposition of random and periodic scatterers is discussed.

Inverse transport problems in quantitative PAT for molecular imaging

NASA Astrophysics Data System (ADS)

Ren, Kui; Zhang, Rongting; Zhong, Yimin

2015-12-01

Fluorescence photoacoustic tomography (fPAT) is a molecular imaging modality that combines photoacoustic tomography with fluorescence imaging to obtain high-resolution imaging of fluorescence distributions inside heterogeneous media. The objective of this work is to study inverse problems in the quantitative step of fPAT where we intend to reconstruct physical coefficients in a coupled system of radiative transport equations using internal data recovered from ultrasound measurements. We derive uniqueness and stability results on the inverse problems and develop some efficient algorithms for image reconstructions. Numerical simulations based on synthetic data are presented to validate the theoretical analysis. The results we present here complement these in Ren K and Zhao H (2013 SIAM J. Imaging Sci. 6 2024-49) on the same problem but in the diffusive regime.

Application of quasi-distributions for solving inverse problems of neutron and {gamma}-ray transport

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

Pogosbekyan, L.R.; Lysov, D.A.

The considered inverse problems deal with the calculation of the unknown values of nuclear installations by means of the known (goal) functionals of neutron/{gamma}-ray distributions. The example of these problems might be the calculation of the automatic control rods position as function of neutron sensors reading, or the calculation of experimentally-corrected values of cross-sections, isotopes concentration, fuel enrichment via the measured functional. The authors have developed the new method to solve inverse problem. It finds flux density as quasi-solution of the particles conservation linear system adjointed to equalities for functionals. The method is more effective compared to the one basedmore » on the classical perturbation theory. It is suitable for vectorization and it can be used successfully in optimization codes.« less

SIAM conference on inverse problems: Geophysical applications. Final technical report

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

NONE

1995-12-31

This conference was the second in a series devoted to a particular area of inverse problems. The theme of this series is to discuss problems of major scientific importance in a specific area from a mathematical perspective. The theme of this symposium was geophysical applications. In putting together the program we tried to include a wide range of mathematical scientists and to interpret geophysics in as broad a sense as possible. Our speaker came from industry, government laboratories, and diverse departments in academia. We managed to attract a geographically diverse audience with participation from five continents. There were talks devotedmore » to seismology, hydrology, determination of the earth`s interior on a global scale as well as oceanographic and atmospheric inverse problems.« less

Inverse problems and optimal experiment design in unsteady heat transfer processes identification

NASA Technical Reports Server (NTRS)

Artyukhin, Eugene A.

1991-01-01

Experimental-computational methods for estimating characteristics of unsteady heat transfer processes are analyzed. The methods are based on the principles of distributed parameter system identification. The theoretical basis of such methods is the numerical solution of nonlinear ill-posed inverse heat transfer problems and optimal experiment design problems. Numerical techniques for solving problems are briefly reviewed. The results of the practical application of identification methods are demonstrated when estimating effective thermophysical characteristics of composite materials and thermal contact resistance in two-layer systems.

Inverse problem of the vibrational band gap of periodically supported beam

NASA Astrophysics Data System (ADS)

Shi, Xiaona; Shu, Haisheng; Dong, Fuzhen; Zhao, Lei

2017-04-01

The researches of periodic structures have a long history with the main contents confined in the field of forward problem. In this paper, the inverse problem is considered and an overall frame is proposed which includes two main stages, i.e., the band gap criterion and its optimization. As a preliminary investigation, the inverse problem of the flexural vibrational band gap of a periodically supported beam is analyzed. According to existing knowledge of its forward problem, the band gap criterion is given in implicit form. Then, two cases with three independent parameters, namely the double supported case and the triple one, are studied in detail and the explicit expressions of the feasible domain are constructed by numerical fitting. Finally, the parameter optimization of the double supported case with three variables is conducted using genetic algorithm aiming for the best mean attenuation within specified frequency band.

Evaluating Heat Pipe Performance in 1/6 g Acceleration: Problems and Prospects

NASA Technical Reports Server (NTRS)

Jaworske, Donald A.; McCollum, Timothy A.; Gibson, Marc A.; Sanzi, James L.; Sechkar, Edward A.

2011-01-01

Heat pipes composed of titanium and water are being considered for use in the heat rejection system of a fission power system option for lunar exploration. Placed vertically on the lunar surface, the heat pipes would operate as thermosyphons in the 1/6 g environment. The design of thermosyphons for such an application is determined, in part, by the flooding limit. Flooding is composed of two components, the thickness of the fluid film on the walls of the thermosyphon and the interaction of the fluid flow with the concurrent vapor counter flow. Both the fluid thickness contribution and interfacial shear contribution are inversely proportional to gravity. Hence, evaluating the performance of a thermosyphon in a 1 g environment on Earth may inadvertently lead to overestimating the performance of the same thermosyphon as experienced in the 1/6 g environment on the moon. Several concepts of varying complexity have been proposed for evaluating thermosyphon performance in reduced gravity, ranging from tilting the thermosyphons on Earth based on a cosine function, to flying heat pipes on a low-g aircraft. This paper summarizes the problems and prospects for evaluating thermosyphon performance in 1/6 g.

Single-Column Model Simulations of Subtropical Marine Boundary-Layer Cloud Transitions Under Weakening Inversions: SCM SIMULATIONS OF CLOUD TRANSITIONS

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

Neggers, R. A. J.; Ackerman, A. S.; Angevine, W. M.

Results are presented of the GASS/EUCLIPSE single-column model inter-comparison study on the subtropical marine low-level cloud transition. A central goal is to establish the performance of state-of-the-art boundary-layer schemes for weather and climate mod- els for this cloud regime, using large-eddy simulations of the same scenes as a reference. A novelty is that the comparison covers four different cases instead of one, in order to broaden the covered parameter space. Three cases are situated in the North-Eastern Pa- cific, while one reflects conditions in the North-Eastern Atlantic. A set of variables is considered that reflects key aspects of the transitionmore » process, making use of simple met- rics to establish the model performance. Using this method some longstanding problems in low level cloud representation are identified. Considerable spread exists among models concerning the cloud amount, its vertical structure and the associated impact on radia- tive transfer. The sign and amplitude of these biases differ somewhat per case, depending on how far the transition has progressed. After cloud breakup the ensemble median ex- hibits the well-known “too few too bright” problem. The boundary layer deepening rate and its state of decoupling are both underestimated, while the representation of the thin capping cloud layer appears complicated by a lack of vertical resolution. Encouragingly, some models are successful in representing the full set of variables, in particular the verti- cal structure and diurnal cycle of the cloud layer in transition. An intriguing result is that the median of the model ensemble performs best, inspiring a new approach in subgrid pa- rameterization.« less

Electromagnetic Inverse Methods and Applications for Inhomogeneous Media Probing and Synthesis.

NASA Astrophysics Data System (ADS)

Xia, Jake Jiqing

The electromagnetic inverse scattering problems concerned in this thesis are to find unknown inhomogeneous permittivity and conductivity profiles in a medium from the scattering data. Both analytical and numerical methods are studied in the thesis. The inverse methods can be applied to geophysical medium probing, non-destructive testing, medical imaging, optical waveguide synthesis and material characterization. An introduction is given in Chapter 1. The first part of the thesis presents inhomogeneous media probing. The Riccati equation approach is discussed in Chapter 2 for a one-dimensional planar profile inversion problem. Two types of the Riccati equations are derived and distinguished. New renormalized formulae based inverting one specific type of the Riccati equation are derived. Relations between the inverse methods of Green's function, the Riccati equation and the Gel'fand-Levitan-Marchenko (GLM) theory are studied. In Chapter 3, the renormalized source-type integral equation (STIE) approach is formulated for inversion of cylindrically inhomogeneous permittivity and conductivity profiles. The advantages of the renormalized STIE approach are demonstrated in numerical examples. The cylindrical profile inversion problem has an application for borehole inversion. In Chapter 4 the renormalized STIE approach is extended to a planar case where the two background media are different. Numerical results have shown fast convergence. This formulation is applied to inversion of the underground soil moisture profiles in remote sensing. The second part of the thesis presents the synthesis problem of inhomogeneous dielectric waveguides using the electromagnetic inverse methods. As a particular example, the rational function representation of reflection coefficients in the GLM theory is used. The GLM method is reviewed in Chapter 5. Relations between modal structures and transverse reflection coefficients of an inhomogeneous medium are established in Chapter 6. A stratified medium model is used to derive the guidance condition and the reflection coefficient. Results obtained in Chapter 6 provide the physical foundation for applying the inverse methods for the waveguide design problem. In Chapter 7, a global guidance condition for continuously varying medium is derived using the Riccati equation. It is further shown that the discrete modes in an inhomogeneous medium have the same wave vectors as the poles of the transverse reflection coefficient. An example of synthesizing an inhomogeneous dielectric waveguide using a rational reflection coefficient is presented. A summary of the thesis is given in Chapter 8. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.).

Large-scale inverse model analyses employing fast randomized data reduction

NASA Astrophysics Data System (ADS)

Lin, Youzuo; Le, Ellen B.; O'Malley, Daniel; Vesselinov, Velimir V.; Bui-Thanh, Tan

2017-08-01

When the number of observations is large, it is computationally challenging to apply classical inverse modeling techniques. We have developed a new computationally efficient technique for solving inverse problems with a large number of observations (e.g., on the order of 107 or greater). Our method, which we call the randomized geostatistical approach (RGA), is built upon the principal component geostatistical approach (PCGA). We employ a data reduction technique combined with the PCGA to improve the computational efficiency and reduce the memory usage. Specifically, we employ a randomized numerical linear algebra technique based on a so-called "sketching" matrix to effectively reduce the dimension of the observations without losing the information content needed for the inverse analysis. In this way, the computational and memory costs for RGA scale with the information content rather than the size of the calibration data. Our algorithm is coded in Julia and implemented in the MADS open-source high-performance computational framework (http://mads.lanl.gov). We apply our new inverse modeling method to invert for a synthetic transmissivity field. Compared to a standard geostatistical approach (GA), our method is more efficient when the number of observations is large. Most importantly, our method is capable of solving larger inverse problems than the standard GA and PCGA approaches. Therefore, our new model inversion method is a powerful tool for solving large-scale inverse problems. The method can be applied in any field and is not limited to hydrogeological applications such as the characterization of aquifer heterogeneity.

Misalignment tolerant efficient inverse taper coupler for silicon waveguide

NASA Astrophysics Data System (ADS)

Wang, Peng; Michael, Aron; Kwok, Chee Yee; Chen, Ssu-Han

2015-12-01

This paper describes an efficient fiber to submicron silicon waveguide coupling based on an inversely tapered silicon waveguide embedded in a SiO2 waveguide that is suspended in air. The inverse taper waveguide consist of a 50um long and 240nm thick silicon that linearly taper in width from 500nm to 120nm, which is embedded in SiO2. The SiO2 waveguide is 6um wide and 10um long. The simulation results show that the coupling loss of this new approach is 2.7dB including the interface loss at the input and output. The tolerance to fiber misalignment at the input of the coupler is 2um in both horizontal and vertical directions for only 1.5dB additional loss.

Error analysis applied to several inversion techniques used for the retrieval of middle atmospheric constituents from limb-scanning MM-wave spectroscopic measurements

NASA Technical Reports Server (NTRS)

Puliafito, E.; Bevilacqua, R.; Olivero, J.; Degenhardt, W.

1992-01-01

The formal retrieval error analysis of Rodgers (1990) allows the quantitative determination of such retrieval properties as measurement error sensitivity, resolution, and inversion bias. This technique was applied to five numerical inversion techniques and two nonlinear iterative techniques used for the retrieval of middle atmospheric constituent concentrations from limb-scanning millimeter-wave spectroscopic measurements. It is found that the iterative methods have better vertical resolution, but are slightly more sensitive to measurement error than constrained matrix methods. The iterative methods converge to the exact solution, whereas two of the matrix methods under consideration have an explicit constraint, the sensitivity of the solution to the a priori profile. Tradeoffs of these retrieval characteristics are presented.

Geophysical approaches to inverse problems: A methodological comparison. Part 1: A Posteriori approach

NASA Technical Reports Server (NTRS)

Seidman, T. I.; Munteanu, M. J.

1979-01-01

The relationships of a variety of general computational methods (and variances) for treating illposed problems such as geophysical inverse problems are considered. Differences in approach and interpretation based on varying assumptions as to, e.g., the nature of measurement uncertainties are discussed along with the factors to be considered in selecting an approach. The reliability of the results of such computation is addressed.

Layer Stripping Solutions of Inverse Seismic Problems.

DTIC Science & Technology

1985-03-21

problems--more so than has generally been recognized. The subject of this thesis is the theoretical development of the . layer-stripping methodology , and...medium varies sharply at each interface, which would be expected to cause difficulties for the algorithm, since it was designed for a smoothy varying... methodology was applied in a novel way. The inverse problem considered in this chapter was that of reconstructing a layered medium from measurement of its

Hydromagnetic conditions near the core-mantle boundary

NASA Technical Reports Server (NTRS)

Backus, George E.

1995-01-01

The main results of the grant were (1) finishing the manuscript of a proof of completeness of the Poincare modes in an incompressible nonviscous fluid corotating with a rigid ellipsoidal boundary, (2) partial completion of a manuscript describing a definition of helicity that resolved questions in the literature about calculating the helicities of vector fields with complicated topologies, and (3) the beginning of a reexamination of the inverse problem of inferring properties of the geomagnetic field B just outside the core-mantle boundary (CMB) from measurements of elements of B at and above the earth's surface. This last work has led to a simple general formalism for linear and nonlinear inverse problems that appears to include all the inversion schemes so far considered for the uniqueness problem in geomagnetic inversion. The technique suggests some new methods for error estimation that form part of this report.

Reconstruction of Vertical Profile of Permittivity of Layered Media which is Probed Using Vertical Differential Antenna

NASA Astrophysics Data System (ADS)

Pochanin, Gennadiy P.; Poyedinchuk, Anatoliy Y.; Varianytsia-Roshchupkina, Liudmyla A.; Pochanina, Iryna Ye.

2016-04-01

Results of this research are intended to use at GPR investigations of layered media (for example, at roads' inspection) for the processing of collected data and reconstruction of dependence of permittivity on the depth. Recently, an antenna system with a vertical differential configuration of receiving module (Patent UA81652) for GPR was suggested and developed The main advantage of the differential antennas in comparison with bistatic antennas is a high electromagnetic decoupling between the transmitting and receiving modules. The new vertical differential configuration has an additional advantage because it allows collecting GPR data reflected by layered media without any losses of information about these layers [1] and, potentially, it is a more accurate instrument for the layers thickness measurements [2]. The developed antenna system is tested in practice with the GPR at asphalt thickness measurements [3] and shown an accuracy which is better than 0.5 cm. Since this antenna system is good for sounding from above the surface (air coupled technique), the mobile laboratory was equipped with the developed GPR [3]. In order to process big set of GPR data that collected during probing at long routes of the roads, for the data processing it was tested new algorithm of the inverse problem solution. It uses a fast algorithm for calculation of electromagnetic wave diffraction by non-uniform anisotropic layers [4]. The algorithm is based on constructing a special case solution to the Riccati equation for the Cauchy problem and enables a qualitative description of the wave diffraction by the electromagnetic structure of the type within a unitary framework. At this stage as initial data we used synthetic GPR data that were obtained as results of the FDTD simulation of the problem of UWB electromagnetic impulse diffraction on layered media. Differential and bistatic antenna configurations were tested at several different profiles of permittivity. Meanings of permittivity of each of layers were reconstructed successfully. Corresponding results are given in the presentation. Acknowledgement The authors acknowledge COST for funding Action TU1208 "Civil Engineering Applications of Ground Penetrating Radar", supporting this work. References 1. L. Gurel, and U. Oguz, "Three-Dimensional FDTD modeling of a ground penetrating radar" IEEE Trans. Geosci. Remote Sensing, vol. 38, no. 4, pp. 1513-1521, 2000. 2. L. Varianytsia-Roshchupkina, Pochanin G., Pochanina I., Masalov Proc. of the 8th Int. Workshop on Advanced Ground Penetrating Radar (IWAGPR 15), Florence, Italy, July 2015. 3. Pochanin, G. P., Ruban, V. P., Kholod, P. V., Shuba, A. A., Pochanin, A. G., Orlenko, A.A., Batrakov, D. O., and Batrakova, A. G. GPR for pavement monitoring., Journal of Radio Electronics. No.1. 2013, Moscow, http://jre.cplire.ru/alt/jan13/8/text.pdf. 4. A. V. Brovenko, P. N. Melezhik, A. Y. Poyedinchuk A numerical analytical method for solving problems of electromagnetic wave diffraction by non-uniform anisotropic layers. Radiophysics and Electronics, Vol.19, No. 4. 2014. pp.12-20.

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

NASA Astrophysics Data System (ADS)

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

2016-04-01

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

2D magnetotelluric inversion using reflection seismic images as constraints and application in the COSC project

NASA Astrophysics Data System (ADS)

Kalscheuer, Thomas; Yan, Ping; Hedin, Peter; Garcia Juanatey, Maria d. l. A.

2017-04-01

We introduce a new constrained 2D magnetotelluric (MT) inversion scheme, in which the local weights of the regularization operator with smoothness constraints are based directly on the envelope attribute of a reflection seismic image. The weights resemble those of a previously published seismic modification of the minimum gradient support method introducing a global stabilization parameter. We measure the directional gradients of the seismic envelope to modify the horizontal and vertical smoothness constraints separately. An appropriate choice of the new stabilization parameter is based on a simple trial-and-error procedure. Our proposed constrained inversion scheme was easily implemented in an existing Gauss-Newton inversion package. From a theoretical perspective, we compare our new constrained inversion to similar constrained inversion methods, which are based on image theory and seismic attributes. Successful application of the proposed inversion scheme to the MT field data of the Collisional Orogeny in the Scandinavian Caledonides (COSC) project using constraints from the envelope attribute of the COSC reflection seismic profile (CSP) helped to reduce the uncertainty of the interpretation of the main décollement. Thus, the new model gave support to the proposed location of a future borehole COSC-2 which is supposed to penetrate the main décollement and the underlying Precambrian basement.

The Relationship Between Non-Symbolic Multiplication and Division in Childhood

PubMed Central

McCrink, Koleen; Shafto, Patrick; Barth, Hilary

2016-01-01

Children without formal education in addition and subtraction are able to perform multi-step operations over an approximate number of objects. Further, their performance improves when solving approximate (but not exact) addition and subtraction problems that allow for inversion as a shortcut (e.g., a + b − b = a). The current study examines children’s ability to perform multi-step operations, and the potential for an inversion benefit, for the operations of approximate, non-symbolic multiplication and division. Children were trained to compute a multiplication and division scaling factor (*2 or /2, *4 or /4), and then tested on problems that combined two of these factors in a way that either allowed for an inversion shortcut (e.g., 8 * 4 / 4) or did not (e.g., 8 * 4 / 2). Children’s performance was significantly better than chance for all scaling factors during training, and they successfully computed the outcomes of the multi-step testing problems. They did not exhibit a performance benefit for problems with the a * b / b structure, suggesting they did not draw upon inversion reasoning as a logical shortcut to help them solve the multi-step test problems. PMID:26880261

Comparison of micrometeorological techniques in measuring gas emissions from waste lagoons

USDA-ARS?s Scientific Manuscript database

In this study, we evaluated and compared the accuracies of two micrometeorological methods using open-path tunable diode laser absorption spectrometers; vertical radial plume mapping method and the inverse dispersion model method. The accuracy of these two methods was evaluated using a 45m x 45m p...

Comparison of micrometeorological techniques in measuring gas emissions from waste lagoons

USDA-ARS?s Scientific Manuscript database

In this study, we evaluated and compared the accuracies of two micrometeorological methods using open-path tunable diode laser absorption spectrometers; vertical radial plume mapping method (US EPA OTM-10) and the inverse dispersion model method. The accuracy of these two methods was evaluated usin...

Effects of adaptive refinement on the inverse EEG solution

NASA Astrophysics Data System (ADS)

Weinstein, David M.; Johnson, Christopher R.; Schmidt, John A.

1995-10-01

One of the fundamental problems in electroencephalography can be characterized by an inverse problem. Given a subset of electrostatic potentials measured on the surface of the scalp and the geometry and conductivity properties within the head, calculate the current vectors and potential fields within the cerebrum. Mathematically the generalized EEG problem can be stated as solving Poisson's equation of electrical conduction for the primary current sources. The resulting problem is mathematically ill-posed i.e., the solution does not depend continuously on the data, such that small errors in the measurement of the voltages on the scalp can yield unbounded errors in the solution, and, for the general treatment of a solution of Poisson's equation, the solution is non-unique. However, if accurate solutions the general treatment of a solution of Poisson's equation, the solution is non-unique. However, if accurate solutions to such problems could be obtained, neurologists would gain noninvasive accesss to patient-specific cortical activity. Access to such data would ultimately increase the number of patients who could be effectively treated for pathological cortical conditions such as temporal lobe epilepsy. In this paper, we present the effects of spatial adaptive refinement on the inverse EEG problem and show that the use of adaptive methods allow for significantly better estimates of electric and potential fileds within the brain through an inverse procedure. To test these methods, we have constructed several finite element head models from magneteic resonance images of a patient. The finite element meshes ranged in size from 2724 nodes and 12,812 elements to 5224 nodes and 29,135 tetrahedral elements, depending on the level of discretization. We show that an adaptive meshing algorithm minimizes the error in the forward problem due to spatial discretization and thus increases the accuracy of the inverse solution.

Transient well flow in vertically heterogeneous aquifers

NASA Astrophysics Data System (ADS)

Hemker, C. J.

1999-11-01

A solution for the general problem of computing well flow in vertically heterogeneous aquifers is found by an integration of both analytical and numerical techniques. The radial component of flow is treated analytically; the drawdown is a continuous function of the distance to the well. The finite-difference technique is used for the vertical flow component only. The aquifer is discretized in the vertical dimension and the heterogeneous aquifer is considered to be a layered (stratified) formation with a finite number of homogeneous sublayers, where each sublayer may have different properties. The transient part of the differential equation is solved with Stehfest's algorithm, a numerical inversion technique of the Laplace transform. The well is of constant discharge and penetrates one or more of the sublayers. The effect of wellbore storage on early drawdown data is taken into account. In this way drawdowns are found for a finite number of sublayers as a continuous function of radial distance to the well and of time since the pumping started. The model is verified by comparing results with published analytical and numerical solutions for well flow in homogeneous and heterogeneous, confined and unconfined aquifers. Instantaneous and delayed drainage of water from above the water table are considered, combined with the effects of partially penetrating and finite-diameter wells. The model is applied to demonstrate that the transient effects of wellbore storage in unconfined aquifers are less pronounced than previous numerical experiments suggest. Other applications of the presented solution technique are given for partially penetrating wells in heterogeneous formations, including a demonstration of the effect of decreasing specific storage values with depth in an otherwise homogeneous aquifer. The presented solution can be a powerful tool for the analysis of drawdown from pumping tests, because hydraulic properties of layered heterogeneous aquifer systems with partially penetrating wells may be estimated without the need to construct transient numerical models. A computer program based on the hybrid analytical-numerical technique is available from the author.

Two-dimensional modeling of thermal inversion layers in the middle atmosphere of Mars

NASA Technical Reports Server (NTRS)

Theodore, B.; Chassefiere, E.

1993-01-01

There is some evidence that the thermal structure of the martian middle atmosphere may be altered in a significant way by the general circulation motions. Indeed, while it is well known that the circulation in the meridional plane is responsible for the reversal of the latitudinal thermal gradient at the solstice through the adiabatic heating due to sinking motions above the winter pole, here we want to emphasize that a likely by-product effect could be the formation of warm layers, mainly located in the winter hemisphere, and exhibiting an inversion of the vertical thermal gradient.

Optimal landing of a helicopter in autorotation

NASA Technical Reports Server (NTRS)

Lee, A. Y. N.

1985-01-01

Gliding descent in autorotation is a maneuver used by helicopter pilots in case of engine failure. The landing of a helicopter in autorotation is formulated as a nonlinear optimal control problem. The OH-58A helicopter was used. Helicopter vertical and horizontal velocities, vertical and horizontal displacement, and the rotor angle speed were modeled. An empirical approximation for the induced veloctiy in the vortex-ring state were provided. The cost function of the optimal control problem is a weighted sum of the squared horizontal and vertical components of the helicopter velocity at touchdown. Optimal trajectories are calculated for entry conditions well within the horizontal-vertical restriction curve, with the helicopter initially in hover or forwared flight. The resultant two-point boundary value problem with path equality constraints was successfully solved using the Sequential Gradient Restoration Technique.

Determination of unknown coefficient in a non-linear elliptic problem related to the elastoplastic torsion of a bar

NASA Astrophysics Data System (ADS)

Hasanov, Alemdar; Erdem, Arzu

2008-08-01

The inverse problem of determining the unknown coefficient of the non-linear differential equation of torsional creep is studied. The unknown coefficient g = g({xi}2) depends on the gradient{xi} : = |{nabla}u| of the solution u(x), x [isin] {Omega} [sub] Rn, of the direct problem. It is proved that this gradient is bounded in C-norm. This permits one to choose the natural class of admissible coefficients for the considered inverse problem. The continuity in the norm of the Sobolev space H1({Omega}) of the solution u(x;g) of the direct problem with respect to the unknown coefficient g = g({xi}2) is obtained in the following sense: ||u(x;g) - u(x;gm)||1 [->] 0 when gm({eta}) [->] g({eta}) point-wise as m [->] {infty}. Based on these results, the existence of a quasi-solution of the inverse problem in the considered class of admissible coefficients is obtained. Numerical examples related to determination of the unknown coefficient are presented.

Solving an inverse eigenvalue problem with triple constraints on eigenvalues, singular values, and diagonal elements

NASA Astrophysics Data System (ADS)

Wu, Sheng-Jhih; Chu, Moody T.

2017-08-01

An inverse eigenvalue problem usually entails two constraints, one conditioned upon the spectrum and the other on the structure. This paper investigates the problem where triple constraints of eigenvalues, singular values, and diagonal entries are imposed simultaneously. An approach combining an eclectic mix of skills from differential geometry, optimization theory, and analytic gradient flow is employed to prove the solvability of such a problem. The result generalizes the classical Mirsky, Sing-Thompson, and Weyl-Horn theorems concerning the respective majorization relationships between any two of the arrays of main diagonal entries, eigenvalues, and singular values. The existence theory fills a gap in the classical matrix theory. The problem might find applications in wireless communication and quantum information science. The technique employed can be implemented as a first-step numerical method for constructing the matrix. With slight modification, the approach might be used to explore similar types of inverse problems where the prescribed entries are at general locations.

A quasi-spectral method for Cauchy problem of 2/D Laplace equation on an annulus

NASA Astrophysics Data System (ADS)

Saito, Katsuyoshi; Nakada, Manabu; Iijima, Kentaro; Onishi, Kazuei

2005-01-01

Real numbers are usually represented in the computer as a finite number of digits hexa-decimal floating point numbers. Accordingly the numerical analysis is often suffered from rounding errors. The rounding errors particularly deteriorate the precision of numerical solution in inverse and ill-posed problems. We attempt to use a multi-precision arithmetic for reducing the rounding error evil. The use of the multi-precision arithmetic system is by the courtesy of Dr Fujiwara of Kyoto University. In this paper we try to show effectiveness of the multi-precision arithmetic by taking two typical examples; the Cauchy problem of the Laplace equation in two dimensions and the shape identification problem by inverse scattering in three dimensions. It is concluded from a few numerical examples that the multi-precision arithmetic works well on the resolution of those numerical solutions, as it is combined with the high order finite difference method for the Cauchy problem and with the eigenfunction expansion method for the inverse scattering problem.

Inverse problems with nonnegative and sparse solutions: algorithms and application to the phase retrieval problem

NASA Astrophysics Data System (ADS)

Quy Muoi, Pham; Nho Hào, Dinh; Sahoo, Sujit Kumar; Tang, Dongliang; Cong, Nguyen Huu; Dang, Cuong

2018-05-01

In this paper, we study a gradient-type method and a semismooth Newton method for minimization problems in regularizing inverse problems with nonnegative and sparse solutions. We propose a special penalty functional forcing the minimizers of regularized minimization problems to be nonnegative and sparse, and then we apply the proposed algorithms in a practical the problem. The strong convergence of the gradient-type method and the local superlinear convergence of the semismooth Newton method are proven. Then, we use these algorithms for the phase retrieval problem and illustrate their efficiency in numerical examples, particularly in the practical problem of optical imaging through scattering media where all the noises from experiment are presented.

Redox potential distribution of an organic-rich contaminated site obtained by the inversion of self-potential data

NASA Astrophysics Data System (ADS)

Abbas, M.; Jardani, A.; Soueid Ahmed, A.; Revil, A.; Brigaud, L.; Bégassat, Ph.; Dupont, J. P.

2017-11-01

Mapping the redox potential of shallow aquifers impacted by hydrocarbon contaminant plumes is important for the characterization and remediation of such contaminated sites. The redox potential of groundwater is indicative of the biodegradation of hydrocarbons and is important in delineating the shapes of contaminant plumes. The self-potential method was used to reconstruct the redox potential of groundwater associated with an organic-rich contaminant plume in northern France. The self-potential technique is a passive technique consisting in recording the electrical potential distribution at the surface of the Earth. A self-potential map is essentially the sum of two contributions, one associated with groundwater flow referred to as the electrokinetic component, and one associated with redox potential anomalies referred to as the electroredox component (thermoelectric and diffusion potentials are generally negligible). A groundwater flow model was first used to remove the electrokinetic component from the observed self-potential data. Then, a residual self-potential map was obtained. The source current density generating the residual self-potential signals is assumed to be associated with the position of the water table, an interface characterized by a change in both the electrical conductivity and the redox potential. The source current density was obtained through an inverse problem by minimizing a cost function including a data misfit contribution and a regularizer. This inversion algorithm allows the determination of the vertical and horizontal components of the source current density taking into account the electrical conductivity distribution of the saturated and non-saturated zones obtained independently by electrical resistivity tomography. The redox potential distribution was finally determined from the inverted residual source current density. A redox map was successfully built and the estimated redox potential values correlated well with in-situ measurements.

Inverse scattering transform for the nonlocal nonlinear Schrödinger equation with nonzero boundary conditions

NASA Astrophysics Data System (ADS)

Ablowitz, Mark J.; Luo, Xu-Dan; Musslimani, Ziad H.

2018-01-01

In 2013, a new nonlocal symmetry reduction of the well-known AKNS (an integrable system of partial differential equations, introduced by and named after Mark J. Ablowitz, David J. Kaup, and Alan C. Newell et al. (1974)) scattering problem was found. It was shown to give rise to a new nonlocal PT symmetric and integrable Hamiltonian nonlinear Schrödinger (NLS) equation. Subsequently, the inverse scattering transform was constructed for the case of rapidly decaying initial data and a family of spatially localized, time periodic one-soliton solutions was found. In this paper, the inverse scattering transform for the nonlocal NLS equation with nonzero boundary conditions at infinity is presented in four different cases when the data at infinity have constant amplitudes. The direct and inverse scattering problems are analyzed. Specifically, the direct problem is formulated, the analytic properties of the eigenfunctions and scattering data and their symmetries are obtained. The inverse scattering problem, which arises from a novel nonlocal system, is developed via a left-right Riemann-Hilbert problem in terms of a suitable uniformization variable and the time dependence of the scattering data is obtained. This leads to a method to linearize/solve the Cauchy problem. Pure soliton solutions are discussed, and explicit 1-soliton solution and two 2-soliton solutions are provided for three of the four different cases corresponding to two different signs of nonlinearity and two different values of the phase difference between plus and minus infinity. In another case, there are no solitons.

Fast Component Pursuit for Large-Scale Inverse Covariance Estimation.

PubMed

Han, Lei; Zhang, Yu; Zhang, Tong

2016-08-01

The maximum likelihood estimation (MLE) for the Gaussian graphical model, which is also known as the inverse covariance estimation problem, has gained increasing interest recently. Most existing works assume that inverse covariance estimators contain sparse structure and then construct models with the ℓ 1 regularization. In this paper, different from existing works, we study the inverse covariance estimation problem from another perspective by efficiently modeling the low-rank structure in the inverse covariance, which is assumed to be a combination of a low-rank part and a diagonal matrix. One motivation for this assumption is that the low-rank structure is common in many applications including the climate and financial analysis, and another one is that such assumption can reduce the computational complexity when computing its inverse. Specifically, we propose an efficient COmponent Pursuit (COP) method to obtain the low-rank part, where each component can be sparse. For optimization, the COP method greedily learns a rank-one component in each iteration by maximizing the log-likelihood. Moreover, the COP algorithm enjoys several appealing properties including the existence of an efficient solution in each iteration and the theoretical guarantee on the convergence of this greedy approach. Experiments on large-scale synthetic and real-world datasets including thousands of millions variables show that the COP method is faster than the state-of-the-art techniques for the inverse covariance estimation problem when achieving comparable log-likelihood on test data.

Absolute mass scale calibration in the inverse problem of the physical theory of fireballs.

NASA Astrophysics Data System (ADS)

Kalenichenko, V. V.

A method of the absolute mass scale calibration is suggested for solving the inverse problem of the physical theory of fireballs. The method is based on the data on the masses of the fallen meteorites whose fireballs have been photographed in their flight. The method may be applied to those fireballs whose bodies have not experienced considerable fragmentation during their destruction in the atmosphere and have kept their form well enough. Statistical analysis of the inverse problem solution for a sufficiently representative sample makes it possible to separate a subsample of such fireballs. The data on the Lost City and Innisfree meteorites are used to obtain calibration coefficients.

Inverse problems in the modeling of vibrations of flexible beams

NASA Technical Reports Server (NTRS)

Banks, H. T.; Powers, R. K.; Rosen, I. G.

1987-01-01

The formulation and solution of inverse problems for the estimation of parameters which describe damping and other dynamic properties in distributed models for the vibration of flexible structures is considered. Motivated by a slewing beam experiment, the identification of a nonlinear velocity dependent term which models air drag damping in the Euler-Bernoulli equation is investigated. Galerkin techniques are used to generate finite dimensional approximations. Convergence estimates and numerical results are given. The modeling of, and related inverse problems for the dynamics of a high pressure hose line feeding a gas thruster actuator at the tip of a cantilevered beam are then considered. Approximation and convergence are discussed and numerical results involving experimental data are presented.

An inverse finance problem for estimation of the volatility

NASA Astrophysics Data System (ADS)

Neisy, A.; Salmani, K.

2013-01-01

Black-Scholes model, as a base model for pricing in derivatives markets has some deficiencies, such as ignoring market jumps, and considering market volatility as a constant factor. In this article, we introduce a pricing model for European-Options under jump-diffusion underlying asset. Then, using some appropriate numerical methods we try to solve this model with integral term, and terms including derivative. Finally, considering volatility as an unknown parameter, we try to estimate it by using our proposed model. For the purpose of estimating volatility, in this article, we utilize inverse problem, in which inverse problem model is first defined, and then volatility is estimated using minimization function with Tikhonov regularization.

Real Variable Inversion of Laplace Transforms: An Application in Plasma Physics.

ERIC Educational Resources Information Center

Bohn, C. L.; Flynn, R. W.

1978-01-01

Discusses the nature of Laplace transform techniques and explains an alternative to them: the Widder's real inversion. To illustrate the power of this new technique, it is applied to a difficult inversion: the problem of Landau damping. (GA)

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

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

Zhu, Hongyu; Petra, Noemi; Stadler, Georg

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection–diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations andmore » model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov–Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems – i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian – we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. Here, we show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.« less

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

DOE PAGES

Zhu, Hongyu; Petra, Noemi; Stadler, Georg; ...

2016-07-13

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection–diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations andmore » model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov–Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems – i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian – we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. Here, we show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.« less

Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model

NASA Astrophysics Data System (ADS)

Zhu, Hongyu; Petra, Noemi; Stadler, Georg; Isaac, Tobin; Hughes, Thomas J. R.; Ghattas, Omar

2016-07-01

We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection-diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov-Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems - i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian - we study the effect on the inversion of a one-way coupling of the adjoint energy and Stokes equations. We show that taking such a one-way coupled approach for the adjoint equations can lead to an incorrect gradient and premature termination of optimization iterations. This is due to loss of a descent direction stemming from inconsistency of the gradient with the contours of the cost functional. Nevertheless, one may still obtain a reasonable approximate inverse solution particularly if important features of the reconstructed solution emerge early in optimization iterations, before the premature termination.

A refined model of sedimentary rock cover in the southeastern part of the Congo basin from GOCE gravity and vertical gravity gradient observations

NASA Astrophysics Data System (ADS)

Martinec, Zdeněk; Fullea, Javier

2015-03-01

We aim to interpret the vertical gravity and vertical gravity gradient of the GOCE-GRACE combined gravity model over the southeastern part of the Congo basin to refine the published model of sedimentary rock cover. We use the GOCO03S gravity model and evaluate its spherical harmonic representation at or near the Earth's surface. In this case, the gradiometry signals are enhanced as compared to the original measured GOCE gradients at satellite height and better emphasize the spatial pattern of sedimentary geology. To avoid aliasing, the omission error of the modelled gravity induced by the sedimentary rocks is adjusted to that of the GOCO03S gravity model. The mass-density Green's functions derived for the a priori structure of the sediments show a slightly greater sensitivity to the GOCO03S vertical gravity gradient than to the vertical gravity. Hence, the refinement of the sedimentary model is carried out for the vertical gravity gradient over the basin, such that a few anomalous values of the GOCO03S-derived vertical gravity gradient are adjusted by refining the model. We apply the 5-parameter Helmert's transformation, defined by 2 translations, 1 rotation and 2 scale parameters that are searched for by the steepest descent method. The refined sedimentary model is only slightly changed with respect to the original map, but it significantly improves the fit of the vertical gravity and vertical gravity gradient over the basin. However, there are still spatial features in the gravity and gradiometric data that remain unfitted by the refined model. These may be due to lateral density variation that is not contained in the model, a density contrast at the Moho discontinuity, lithospheric density stratifications or mantle convection. In a second step, the refined sedimentary model is used to find the vertical density stratification of sedimentary rocks. Although the gravity data can be interpreted by a constant sedimentary density, such a model does not correspond to the gravitational compaction of sedimentary rocks. Therefore, the density model is extended by including a linear increase in density with depth. Subsequent L2 and L∞ norm minimization procedures are applied to find the density parameters by adjusting both the vertical gravity and the vertical gravity gradient. We found that including the vertical gravity gradient in the interpretation of the GOCO03S-derived data reduces the non-uniqueness of the inverse gradiometric problem for density determination. The density structure of the sedimentary formations that provide the optimum predictions of the GOCO03S-derived gravity and vertical gradient of gravity consists of a surface density contrast with respect to surrounding rocks of 0.24-0.28 g/cm3 and its decrease with depth of 0.05-0.25 g/cm3 per 10 km. Moreover, the case where the sedimentary rocks are gravitationally completely compacted in the deepest parts of the basin is supported by L∞ norm minimization. However, this minimization also allows a remaining density contrast at the deepest parts of the sedimentary basin of about 0.1 g/cm3.

The Modularized Software Package ASKI - Full Waveform Inversion Based on Waveform Sensitivity Kernels Utilizing External Seismic Wave Propagation Codes

NASA Astrophysics Data System (ADS)

Schumacher, F.; Friederich, W.

2015-12-01

We present the modularized software package ASKI which is a flexible and extendable toolbox for seismic full waveform inversion (FWI) as well as sensitivity or resolution analysis operating on the sensitivity matrix. It utilizes established wave propagation codes for solving the forward problem and offers an alternative to the monolithic, unflexible and hard-to-modify codes that have typically been written for solving inverse problems. It is available under the GPL at www.rub.de/aski. The Gauss-Newton FWI method for 3D-heterogeneous elastic earth models is based on waveform sensitivity kernels and can be applied to inverse problems at various spatial scales in both Cartesian and spherical geometries. The kernels are derived in the frequency domain from Born scattering theory as the Fréchet derivatives of linearized full waveform data functionals, quantifying the influence of elastic earth model parameters on the particular waveform data values. As an important innovation, we keep two independent spatial descriptions of the earth model - one for solving the forward problem and one representing the inverted model updates. Thereby we account for the independent needs of spatial model resolution of forward and inverse problem, respectively. Due to pre-integration of the kernels over the (in general much coarser) inversion grid, storage requirements for the sensitivity kernels are dramatically reduced.ASKI can be flexibly extended to other forward codes by providing it with specific interface routines that contain knowledge about forward code-specific file formats and auxiliary information provided by the new forward code. In order to sustain flexibility, the ASKI tools must communicate via file output/input, thus large storage capacities need to be accessible in a convenient way. Storing the complete sensitivity matrix to file, however, permits the scientist full manual control over each step in a customized procedure of sensitivity/resolution analysis and full waveform inversion.

On the Ramsey numbers for complete distance graphs with vertices in {l_brace}0,1{r_brace}{sup n}

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

Mikhailov, Kirill A; Raigorodskii, Andrei M

2009-12-31

A new problem of Ramsey type is posed for complete distance graphs in R{sup n} with vertices in the Boolean cube. This problem is closely related to the classical Nelson-Erdos-Hadwiger problem on the chromatic number of a space. Several quite sharp estimates are obtained for certain numerical characteristics that appear in the framework of the problem. Bibliography: 15 titles.

On Making a Distinguished Vertex Minimum Degree by Vertex Deletion

NASA Astrophysics Data System (ADS)

Betzler, Nadja; Bredereck, Robert; Niedermeier, Rolf; Uhlmann, Johannes

For directed and undirected graphs, we study the problem to make a distinguished vertex the unique minimum-(in)degree vertex through deletion of a minimum number of vertices. The corresponding NP-hard optimization problems are motivated by applications concerning control in elections and social network analysis. Continuing previous work for the directed case, we show that the problem is W[2]-hard when parameterized by the graph's feedback arc set number, whereas it becomes fixed-parameter tractable when combining the parameters "feedback vertex set number" and "number of vertices to delete". For the so far unstudied undirected case, we show that the problem is NP-hard and W[1]-hard when parameterized by the "number of vertices to delete". On the positive side, we show fixed-parameter tractability for several parameterizations measuring tree-likeness, including a vertex-linear problem kernel with respect to the parameter "feedback edge set number". On the contrary, we show a non-existence result concerning polynomial-size problem kernels for the combined parameter "vertex cover number and number of vertices to delete", implying corresponding nonexistence results when replacing vertex cover number by treewidth or feedback vertex set number.

An Adjoint-Based Analysis of the Sampling Footprints of Tall Tower, Aircraft and Potential Future Lidar Observations of CO2

NASA Technical Reports Server (NTRS)

Andrews, Arlyn; Kawa, Randy; Zhu, Zhengxin; Burris, John; Abshire, Jim

2004-01-01

A detailed mechanistic understanding of the sources and sinks of CO2 will be required to reliably predict future CO2 levels and climate. A commonly used technique for deriving information about CO2 exchange with surface reservoirs is to solve an 'inverse problem', where CO2 observations are used with an atmospheric transport model to find the optimal distribution of sources and sinks. Synthesis inversion methods are powerful tools for addressing this question, but the results are disturbingly sensitive to the details of the calculation. Studies done using different atmospheric transport models and combinations of surface station data have produced substantially different distributions of surface fluxes. Adjoint methods are now being developed that will more effectively incorporate diverse datasets in estimates of surface fluxes of CO2. In an adjoint framework, it will be possible to combine CO2 concentration data from longterm surface and aircraft monitoring stations with data from intensive field campaigns and with proposed future satellite observations. We have recently developed an adjoint for the GSFC 3-D Parameterized Chemistry and Transport Model (PCTM). Here, we will present results from a PCTM Adjoint study comparing the sampling footprints of tall tower, aircraft and potential future lidar observations of CO2. The vertical resolution and extent of the profiles and the observation frequency will be considered for several sites in North America.

Development of a GNSS water vapour tomography system using algebraic reconstruction techniques

NASA Astrophysics Data System (ADS)

Bender, Michael; Dick, Galina; Ge, Maorong; Deng, Zhiguo; Wickert, Jens; Kahle, Hans-Gert; Raabe, Armin; Tetzlaff, Gerd

2011-05-01

A GNSS water vapour tomography system developed to reconstruct spatially resolved humidity fields in the troposphere is described. The tomography system was designed to process the slant path delays of about 270 German GNSS stations in near real-time with a temporal resolution of 30 min, a horizontal resolution of 40 km and a vertical resolution of 500 m or better. After a short introduction to the GPS slant delay processing the framework of the GNSS tomography is described in detail. Different implementations of the iterative algebraic reconstruction techniques (ART) used to invert the linear inverse problem are discussed. It was found that the multiplicative techniques (MART) provide the best results with least processing time, i.e., a tomographic reconstruction of about 26,000 slant delays on a 8280 cell grid can be obtained in less than 10 min. Different iterative reconstruction techniques are compared with respect to their convergence behaviour and some numerical parameters. The inversion can be considerably stabilized by using additional non-GNSS observations and implementing various constraints. Different strategies for initialising the tomography and utilizing extra information are discussed. At last an example of a reconstructed field of the wet refractivity is presented and compared to the corresponding distribution of the integrated water vapour, an analysis of a numerical weather model (COSMO-DE) and some radiosonde profiles.

Tropospheric characteristics over sea ice during N-ICE2015

NASA Astrophysics Data System (ADS)

Kayser, Markus; Maturilli, Marion; Graham, Robert; Hudson, Stephen; Cohen, Lana; Rinke, Annette; Kim, Joo-Hong; Park, Sang-Jong; Moon, Woosok; Granskog, Mats

2017-04-01

Over recent years, the Arctic Ocean region has shifted towards a younger and thinner sea-ice regime. The Norwegian young sea ICE (N-ICE2015) expedition was designed to investigate the atmosphere-snow-ice-ocean interactions in this new ice regime north of Svalbard. Here we analyze upper-air measurements made by radiosondes launched twice daily together with surface meteorology observations during N-ICE2015 from January to June 2015. We study the multiple cyclonic events observed during N-ICE2015 with respect to changes in the vertical thermodynamic structure, sudden increases in moisture content and temperature, temperature inversions and boundary layer dynamics. The influence of synoptic cyclones is strongest under polar night conditions, when radiative cooling is most effective and the moisture content is low. We find that transitions between the radiatively clear and opaque state are the largest drivers of changes to temperature inversion and stability characteristics in the boundary layer during winter. In spring radiative fluxes warm the surface leading to lifted temperature inversions and a statically unstable boundary layer. The unique N-ICE2015 dataset is used for case studies investigating changes in the vertical structure of the atmosphere under varying synoptic conditions. The goal is to deepen our understanding of synoptic interactions within the Arctic climate system, to improve model performance, as well as to identify gaps in instrumentation, which precludes further investigations.

Estimating uncertainty of Full Waveform Inversion with Ensemble-based methods

NASA Astrophysics Data System (ADS)

Thurin, J.; Brossier, R.; Métivier, L.

2017-12-01

Uncertainty estimation is one key feature of tomographic applications for robust interpretation. However, this information is often missing in the frame of large scale linearized inversions, and only the results at convergence are shown, despite the ill-posed nature of the problem. This issue is common in the Full Waveform Inversion community.While few methodologies have already been proposed in the literature, standard FWI workflows do not include any systematic uncertainty quantifications methods yet, but often try to assess the result's quality through cross-comparison with other results from seismic or comparison with other geophysical data. With the development of large seismic networks/surveys, the increase in computational power and the more and more systematic application of FWI, it is crucial to tackle this problem and to propose robust and affordable workflows, in order to address the uncertainty quantification problem faced for near surface targets, crustal exploration, as well as regional and global scales.In this work (Thurin et al., 2017a,b), we propose an approach which takes advantage of the Ensemble Transform Kalman Filter (ETKF) proposed by Bishop et al., (2001), in order to estimate a low-rank approximation of the posterior covariance matrix of the FWI problem, allowing us to evaluate some uncertainty information of the solution. Instead of solving the FWI problem through a Bayesian inversion with the ETKF, we chose to combine a conventional FWI, based on local optimization, and the ETKF strategies. This scheme allows combining the efficiency of local optimization for solving large scale inverse problems and make the sampling of the local solution space possible thanks to its embarrassingly parallel property. References:Bishop, C. H., Etherton, B. J. and Majumdar, S. J., 2001. Adaptive sampling with the ensemble transform Kalman filter. Part I: Theoretical aspects. Monthly weather review, 129(3), 420-436.Thurin, J., Brossier, R. and Métivier, L. 2017,a.: Ensemble-Based Uncertainty Estimation in Full Waveform Inversion. 79th EAGE Conference and Exhibition 2017, (12 - 15 June, 2017)Thurin, J., Brossier, R. and Métivier, L. 2017,b.: An Ensemble-Transform Kalman Filter - Full Waveform Inversion scheme for Uncertainty estimation; SEG Technical Program Expanded Abstracts 2012

A Non-linear Geodetic Data Inversion Using ABIC for Slip Distribution on a Fault With an Unknown dip Angle

NASA Astrophysics Data System (ADS)

Fukahata, Y.; Wright, T. J.

2006-12-01

We developed a method of geodetic data inversion for slip distribution on a fault with an unknown dip angle. When fault geometry is unknown, the problem of geodetic data inversion is non-linear. A common strategy for obtaining slip distribution is to first determine the fault geometry by minimizing the square misfit under the assumption of a uniform slip on a rectangular fault, and then apply the usual linear inversion technique to estimate a slip distribution on the determined fault. It is not guaranteed, however, that the fault determined under the assumption of a uniform slip gives the best fault geometry for a spatially variable slip distribution. In addition, in obtaining a uniform slip fault model, we have to simultaneously determine the values of the nine mutually dependent parameters, which is a highly non-linear, complicated process. Although the inverse problem is non-linear for cases with unknown fault geometries, the non-linearity of the problems is actually weak, when we can assume the fault surface to be flat. In particular, when a clear fault trace is observed on the EarthOs surface after an earthquake, we can precisely estimate the strike and the location of the fault. In this case only the dip angle has large ambiguity. In geodetic data inversion we usually need to introduce smoothness constraints in order to compromise reciprocal requirements for model resolution and estimation errors in a natural way. Strictly speaking, the inverse problem with smoothness constraints is also non-linear, even if the fault geometry is known. The non-linearity has been dissolved by introducing AkaikeOs Bayesian Information Criterion (ABIC), with which the optimal value of the relative weight of observed data to smoothness constraints is objectively determined. In this study, using ABIC in determining the optimal dip angle, we dissolved the non-linearity of the inverse problem. We applied the method to the InSAR data of the 1995 Dinar, Turkey earthquake and obtained a much shallower dip angle than before.

The inverse resonance problem for CMV operators

NASA Astrophysics Data System (ADS)

Weikard, Rudi; Zinchenko, Maxim

2010-05-01

We consider the class of CMV operators with super-exponentially decaying Verblunsky coefficients. For these we define the concept of a resonance. Then we prove the existence of Jost solutions and a uniqueness theorem for the inverse resonance problem: given the location of all resonances, taking multiplicities into account, the Verblunsky coefficients are uniquely determined.

An inverse problem for a semilinear parabolic equation arising from cardiac electrophysiology

NASA Astrophysics Data System (ADS)

Beretta, Elena; Cavaterra, Cecilia; Cerutti, M. Cristina; Manzoni, Andrea; Ratti, Luca

2017-10-01

In this paper we develop theoretical analysis and numerical reconstruction techniques for the solution of an inverse boundary value problem dealing with the nonlinear, time-dependent monodomain equation, which models the evolution of the electric potential in the myocardial tissue. The goal is the detection of an inhomogeneity \

Analysis of the Hessian for Inverse Scattering Problems. Part 1: Inverse Shape Scattering of Acoustic Waves

DTIC Science & Technology

2011-06-01

in giving us of a copy of his habilitation thesis, without which this article would not have been possible. We also thank Prof. Karsten Eppler for...John Wiley & Sons, 1983. [19] Andreas Kirsch. Generalized boundary value- and control problems for the Helmholtz equation. Habilitation thesis, 1984

A posteriori error estimates in voice source recovery

NASA Astrophysics Data System (ADS)

Leonov, A. S.; Sorokin, V. N.

2017-12-01

The inverse problem of voice source pulse recovery from a segment of a speech signal is under consideration. A special mathematical model is used for the solution that relates these quantities. A variational method of solving inverse problem of voice source recovery for a new parametric class of sources, that is for piecewise-linear sources (PWL-sources), is proposed. Also, a technique for a posteriori numerical error estimation for obtained solutions is presented. A computer study of the adequacy of adopted speech production model with PWL-sources is performed in solving the inverse problems for various types of voice signals, as well as corresponding study of a posteriori error estimates. Numerical experiments for speech signals show satisfactory properties of proposed a posteriori error estimates, which represent the upper bounds of possible errors in solving the inverse problem. The estimate of the most probable error in determining the source-pulse shapes is about 7-8% for the investigated speech material. It is noted that a posteriori error estimates can be used as a criterion of the quality for obtained voice source pulses in application to speaker recognition.

Solving ill-posed inverse problems using iterative deep neural networks

NASA Astrophysics Data System (ADS)

Adler, Jonas; Öktem, Ozan

2017-12-01

We propose a partially learned approach for the solution of ill-posed inverse problems with not necessarily linear forward operators. The method builds on ideas from classical regularisation theory and recent advances in deep learning to perform learning while making use of prior information about the inverse problem encoded in the forward operator, noise model and a regularising functional. The method results in a gradient-like iterative scheme, where the ‘gradient’ component is learned using a convolutional network that includes the gradients of the data discrepancy and regulariser as input in each iteration. We present results of such a partially learned gradient scheme on a non-linear tomographic inversion problem with simulated data from both the Sheep-Logan phantom as well as a head CT. The outcome is compared against filtered backprojection and total variation reconstruction and the proposed method provides a 5.4 dB PSNR improvement over the total variation reconstruction while being significantly faster, giving reconstructions of 512 × 512 pixel images in about 0.4 s using a single graphics processing unit (GPU).

Full Waveform Inversion for Seismic Velocity And Anelastic Losses in Heterogeneous Structures

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

Askan, A.; /Carnegie Mellon U.; Akcelik, V.

2009-04-30

We present a least-squares optimization method for solving the nonlinear full waveform inverse problem of determining the crustal velocity and intrinsic attenuation properties of sedimentary valleys in earthquake-prone regions. Given a known earthquake source and a set of seismograms generated by the source, the inverse problem is to reconstruct the anelastic properties of a heterogeneous medium with possibly discontinuous wave velocities. The inverse problem is formulated as a constrained optimization problem, where the constraints are the partial and ordinary differential equations governing the anelastic wave propagation from the source to the receivers in the time domain. This leads to amore » variational formulation in terms of the material model plus the state variables and their adjoints. We employ a wave propagation model in which the intrinsic energy-dissipating nature of the soil medium is modeled by a set of standard linear solids. The least-squares optimization approach to inverse wave propagation presents the well-known difficulties of ill posedness and multiple minima. To overcome ill posedness, we include a total variation regularization functional in the objective function, which annihilates highly oscillatory material property components while preserving discontinuities in the medium. To treat multiple minima, we use a multilevel algorithm that solves a sequence of subproblems on increasingly finer grids with increasingly higher frequency source components to remain within the basin of attraction of the global minimum. We illustrate the methodology with high-resolution inversions for two-dimensional sedimentary models of the San Fernando Valley, under SH-wave excitation. We perform inversions for both the seismic velocity and the intrinsic attenuation using synthetic waveforms at the observer locations as pseudoobserved data.« less

Trimming and procrastination as inversion techniques

NASA Astrophysics Data System (ADS)

Backus, George E.

1996-12-01

By examining the processes of truncating and approximating the model space (trimming it), and by committing to neither the objectivist nor the subjectivist interpretation of probability (procrastinating), we construct a formal scheme for solving linear and non-linear geophysical inverse problems. The necessary prior information about the correct model xE can be either a collection of inequalities or a probability measure describing where xE was likely to be in the model space X before the data vector y0 was measured. The results of the inversion are (1) a vector z0 that estimates some numerical properties zE of xE; (2) an estimate of the error δz = z0 - zE. As y0 is finite dimensional, so is z0, and hence in principle inversion cannot describe all of xE. The error δz is studied under successively more specialized assumptions about the inverse problem, culminating in a complete analysis of the linear inverse problem with a prior quadratic bound on xE. Our formalism appears to encompass and provide error estimates for many of the inversion schemes current in geomagnetism, and would be equally applicable in geodesy and seismology if adequate prior information were available there. As an idealized example we study the magnetic field at the core-mantle boundary, using satellite measurements of field elements at sites assumed to be almost uniformly distributed on a single spherical surface. Magnetospheric currents are neglected and the crustal field is idealized as a random process with rotationally invariant statistics. We find that an appropriate data compression diagonalizes the variance matrix of the crustal signal and permits an analytic trimming of the idealized problem.

Integrated Tsunami Database: simulation and identification of seismic tsunami sources, 3D visualization and post-disaster assessment on the shore

NASA Astrophysics Data System (ADS)

Krivorot'ko, Olga; Kabanikhin, Sergey; Marinin, Igor; Karas, Adel; Khidasheli, David

2013-04-01

One of the most important problems of tsunami investigation is the problem of seismic tsunami source reconstruction. Non-profit organization WAPMERR (http://wapmerr.org) has provided a historical database of alleged tsunami sources around the world that obtained with the help of information about seaquakes. WAPMERR also has a database of observations of the tsunami waves in coastal areas. The main idea of presentation consists of determining of the tsunami source parameters using seismic data and observations of the tsunami waves on the shore, and the expansion and refinement of the database of presupposed tsunami sources for operative and accurate prediction of hazards and assessment of risks and consequences. Also we present 3D visualization of real-time tsunami wave propagation and loss assessment, characterizing the nature of the building stock in cities at risk, and monitoring by satellite images using modern GIS technology ITRIS (Integrated Tsunami Research and Information System) developed by WAPMERR and Informap Ltd. The special scientific plug-in components are embedded in a specially developed GIS-type graphic shell for easy data retrieval, visualization and processing. The most suitable physical models related to simulation of tsunamis are based on shallow water equations. We consider the initial-boundary value problem in Ω := {(x,y) ?R2 : x ?(0,Lx ), y ?(0,Ly ), Lx,Ly > 0} for the well-known linear shallow water equations in the Cartesian coordinate system in terms of the liquid flow components in dimensional form Here ?(x,y,t) defines the free water surface vertical displacement, i.e. amplitude of a tsunami wave, q(x,y) is the initial amplitude of a tsunami wave. The lateral boundary is assumed to be a non-reflecting boundary of the domain, that is, it allows the free passage of the propagating waves. Assume that the free surface oscillation data at points (xm, ym) are given as a measured output data from tsunami records: fm(t) := ? (xm, ym,t), (xm,ym ) ?Ω, t ?(Tm1, Tm2), m = 1,2,...,M, M ?N (2) The problem of tsunami source reconstruction (inverse tsunami problem) consists of determining the unknown initial perturbation q(x,y) of the free surface defied in (1) from knowledge of the free surface oscillation data fm(t) given by (2). We present a numerical method to determine the tsunami source using measurements of the height of a passing tsunami wave. Proposed approach based on the weak solution theory for hyperbolic PDEs and adjoint problem method for minimization of the corresponding cost functional 2 J(q) = ?Aq - F? , F = (f1,...,fM ). (3) The adjoint problem is defined to obtain an explicit gradient formula for the cost functional (3). Different numerical algorithms (finite-difference approach and finite volume method) are proposed for the direct as well as adjoint problem. Conjugate gradient algorithm based on explicit gradient formula is used for numerical solution of the inverse problem (1)-(2). This work was partially supported by the Russian Foundation for Basic Research (project No. 12-01-00773) and by SB RAS interdisciplinary project 14 "Inverse Problems and Applications: Theory, Algorithms, Software".

A general approach to regularizing inverse problems with regional data using Slepian wavelets

NASA Astrophysics Data System (ADS)

Michel, Volker; Simons, Frederik J.

2017-12-01

Slepian functions are orthogonal function systems that live on subdomains (for example, geographical regions on the Earth’s surface, or bandlimited portions of the entire spectrum). They have been firmly established as a useful tool for the synthesis and analysis of localized (concentrated or confined) signals, and for the modeling and inversion of noise-contaminated data that are only regionally available or only of regional interest. In this paper, we consider a general abstract setup for inverse problems represented by a linear and compact operator between Hilbert spaces with a known singular-value decomposition (svd). In practice, such an svd is often only given for the case of a global expansion of the data (e.g. on the whole sphere) but not for regional data distributions. We show that, in either case, Slepian functions (associated to an arbitrarily prescribed region and the given compact operator) can be determined and applied to construct a regularization for the ill-posed regional inverse problem. Moreover, we describe an algorithm for constructing the Slepian basis via an algebraic eigenvalue problem. The obtained Slepian functions can be used to derive an svd for the combination of the regionalizing projection and the compact operator. As a result, standard regularization techniques relying on a known svd become applicable also to those inverse problems where the data are regionally given only. In particular, wavelet-based multiscale techniques can be used. An example for the latter case is elaborated theoretically and tested on two synthetic numerical examples.

Bayesian parameter estimation in spectral quantitative photoacoustic tomography

NASA Astrophysics Data System (ADS)

Pulkkinen, Aki; Cox, Ben T.; Arridge, Simon R.; Kaipio, Jari P.; Tarvainen, Tanja

2016-03-01

Photoacoustic tomography (PAT) is an imaging technique combining strong contrast of optical imaging to high spatial resolution of ultrasound imaging. These strengths are achieved via photoacoustic effect, where a spatial absorption of light pulse is converted into a measurable propagating ultrasound wave. The method is seen as a potential tool for small animal imaging, pre-clinical investigations, study of blood vessels and vasculature, as well as for cancer imaging. The goal in PAT is to form an image of the absorbed optical energy density field via acoustic inverse problem approaches from the measured ultrasound data. Quantitative PAT (QPAT) proceeds from these images and forms quantitative estimates of the optical properties of the target. This optical inverse problem of QPAT is illposed. To alleviate the issue, spectral QPAT (SQPAT) utilizes PAT data formed at multiple optical wavelengths simultaneously with optical parameter models of tissue to form quantitative estimates of the parameters of interest. In this work, the inverse problem of SQPAT is investigated. Light propagation is modelled using the diffusion equation. Optical absorption is described with chromophore concentration weighted sum of known chromophore absorption spectra. Scattering is described by Mie scattering theory with an exponential power law. In the inverse problem, the spatially varying unknown parameters of interest are the chromophore concentrations, the Mie scattering parameters (power law factor and the exponent), and Gruneisen parameter. The inverse problem is approached with a Bayesian method. It is numerically demonstrated, that estimation of all parameters of interest is possible with the approach.

A geostatistical approach to the change-of-support problem and variable-support data fusion in spatial analysis

NASA Astrophysics Data System (ADS)

Wang, Jun; Wang, Yang; Zeng, Hui

2016-01-01

A key issue to address in synthesizing spatial data with variable-support in spatial analysis and modeling is the change-of-support problem. We present an approach for solving the change-of-support and variable-support data fusion problems. This approach is based on geostatistical inverse modeling that explicitly accounts for differences in spatial support. The inverse model is applied here to produce both the best predictions of a target support and prediction uncertainties, based on one or more measurements, while honoring measurements. Spatial data covering large geographic areas often exhibit spatial nonstationarity and can lead to computational challenge due to the large data size. We developed a local-window geostatistical inverse modeling approach to accommodate these issues of spatial nonstationarity and alleviate computational burden. We conducted experiments using synthetic and real-world raster data. Synthetic data were generated and aggregated to multiple supports and downscaled back to the original support to analyze the accuracy of spatial predictions and the correctness of prediction uncertainties. Similar experiments were conducted for real-world raster data. Real-world data with variable-support were statistically fused to produce single-support predictions and associated uncertainties. The modeling results demonstrate that geostatistical inverse modeling can produce accurate predictions and associated prediction uncertainties. It is shown that the local-window geostatistical inverse modeling approach suggested offers a practical way to solve the well-known change-of-support problem and variable-support data fusion problem in spatial analysis and modeling.

Inversion of Robin coefficient by a spectral stochastic finite element approach

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

Jin Bangti; Zou Jun

2008-03-01

This paper investigates a variational approach to the nonlinear stochastic inverse problem of probabilistically calibrating the Robin coefficient from boundary measurements for the steady-state heat conduction. The problem is formulated into an optimization problem, and mathematical properties relevant to its numerical computations are investigated. The spectral stochastic finite element method using polynomial chaos is utilized for the discretization of the optimization problem, and its convergence is analyzed. The nonlinear conjugate gradient method is derived for the optimization system. Numerical results for several two-dimensional problems are presented to illustrate the accuracy and efficiency of the stochastic finite element method.

Restart Operator Meta-heuristics for a Problem-Oriented Evolutionary Strategies Algorithm in Inverse Mathematical MISO Modelling Problem Solving

NASA Astrophysics Data System (ADS)

Ryzhikov, I. S.; Semenkin, E. S.

2017-02-01

This study is focused on solving an inverse mathematical modelling problem for dynamical systems based on observation data and control inputs. The mathematical model is being searched in the form of a linear differential equation, which determines the system with multiple inputs and a single output, and a vector of the initial point coordinates. The described problem is complex and multimodal and for this reason the proposed evolutionary-based optimization technique, which is oriented on a dynamical system identification problem, was applied. To improve its performance an algorithm restart operator was implemented.

An Inverse Problem for a Class of Conditional Probability Measure-Dependent Evolution Equations

PubMed Central

Mirzaev, Inom; Byrne, Erin C.; Bortz, David M.

2016-01-01

We investigate the inverse problem of identifying a conditional probability measure in measure-dependent evolution equations arising in size-structured population modeling. We formulate the inverse problem as a least squares problem for the probability measure estimation. Using the Prohorov metric framework, we prove existence and consistency of the least squares estimates and outline a discretization scheme for approximating a conditional probability measure. For this scheme, we prove general method stability. The work is motivated by Partial Differential Equation (PDE) models of flocculation for which the shape of the post-fragmentation conditional probability measure greatly impacts the solution dynamics. To illustrate our methodology, we apply the theory to a particular PDE model that arises in the study of population dynamics for flocculating bacterial aggregates in suspension, and provide numerical evidence for the utility of the approach. PMID:28316360

Bayesian inference in geomagnetism

NASA Technical Reports Server (NTRS)

Backus, George E.

1988-01-01

The inverse problem in empirical geomagnetic modeling is investigated, with critical examination of recently published studies. Particular attention is given to the use of Bayesian inference (BI) to select the damping parameter lambda in the uniqueness portion of the inverse problem. The mathematical bases of BI and stochastic inversion are explored, with consideration of bound-softening problems and resolution in linear Gaussian BI. The problem of estimating the radial magnetic field B(r) at the earth core-mantle boundary from surface and satellite measurements is then analyzed in detail, with specific attention to the selection of lambda in the studies of Gubbins (1983) and Gubbins and Bloxham (1985). It is argued that the selection method is inappropriate and leads to lambda values much larger than those that would result if a reasonable bound on the heat flow at the CMB were assumed.

Solving Inverse Kinematics of Robot Manipulators by Means of Meta-Heuristic Optimisation

NASA Astrophysics Data System (ADS)

Wichapong, Kritsada; Bureerat, Sujin; Pholdee, Nantiwat

2018-05-01

This paper presents the use of meta-heuristic algorithms (MHs) for solving inverse kinematics of robot manipulators based on using forward kinematic. Design variables are joint angular displacements used to move a robot end-effector to the target in the Cartesian space while the design problem is posed to minimize error between target points and the positions of the robot end-effector. The problem is said to be a dynamic problem as the target points always changed by a robot user. Several well established MHs are used to solve the problem and the results obtained from using different meta-heuristics are compared based on the end-effector error and searching speed of the algorithms. From the study, the best performer will be obtained for setting as the baseline for future development of MH-based inverse kinematic solving.

Total variation regularization of the 3-D gravity inverse problem using a randomized generalized singular value decomposition

NASA Astrophysics Data System (ADS)

Vatankhah, Saeed; Renaut, Rosemary A.; Ardestani, Vahid E.

2018-04-01

We present a fast algorithm for the total variation regularization of the 3-D gravity inverse problem. Through imposition of the total variation regularization, subsurface structures presenting with sharp discontinuities are preserved better than when using a conventional minimum-structure inversion. The associated problem formulation for the regularization is nonlinear but can be solved using an iteratively reweighted least-squares algorithm. For small-scale problems the regularized least-squares problem at each iteration can be solved using the generalized singular value decomposition. This is not feasible for large-scale, or even moderate-scale, problems. Instead we introduce the use of a randomized generalized singular value decomposition in order to reduce the dimensions of the problem and provide an effective and efficient solution technique. For further efficiency an alternating direction algorithm is used to implement the total variation weighting operator within the iteratively reweighted least-squares algorithm. Presented results for synthetic examples demonstrate that the novel randomized decomposition provides good accuracy for reduced computational and memory demands as compared to use of classical approaches.

ANNIT - An Efficient Inversion Algorithm based on Prediction Principles

NASA Astrophysics Data System (ADS)

Růžek, B.; Kolář, P.

2009-04-01

Solution of inverse problems represents meaningful job in geophysics. The amount of data is continuously increasing, methods of modeling are being improved and the computer facilities are also advancing great technical progress. Therefore the development of new and efficient algorithms and computer codes for both forward and inverse modeling is still up to date. ANNIT is contributing to this stream since it is a tool for efficient solution of a set of non-linear equations. Typical geophysical problems are based on parametric approach. The system is characterized by a vector of parameters p, the response of the system is characterized by a vector of data d. The forward problem is usually represented by unique mapping F(p)=d. The inverse problem is much more complex and the inverse mapping p=G(d) is available in an analytical or closed form only exceptionally and generally it may not exist at all. Technically, both forward and inverse mapping F and G are sets of non-linear equations. ANNIT solves such situation as follows: (i) joint subspaces {pD, pM} of original data and model spaces D, M, resp. are searched for, within which the forward mapping F is sufficiently smooth that the inverse mapping G does exist, (ii) numerical approximation of G in subspaces {pD, pM} is found, (iii) candidate solution is predicted by using this numerical approximation. ANNIT is working in an iterative way in cycles. The subspaces {pD, pM} are searched for by generating suitable populations of individuals (models) covering data and model spaces. The approximation of the inverse mapping is made by using three methods: (a) linear regression, (b) Radial Basis Function Network technique, (c) linear prediction (also known as "Kriging"). The ANNIT algorithm has built in also an archive of already evaluated models. Archive models are re-used in a suitable way and thus the number of forward evaluations is minimized. ANNIT is now implemented both in MATLAB and SCILAB. Numerical tests show good performance of the algorithm. Both versions and documentation are available on Internet and anybody can download them. The goal of this presentation is to offer the algorithm and computer codes for anybody interested in the solution to inverse problems.

Trajectory optimization for lunar rover performing vertical takeoff vertical landing maneuvers in the presence of terrain

NASA Astrophysics Data System (ADS)

Ma, Lin; Wang, Kexin; Xu, Zuhua; Shao, Zhijiang; Song, Zhengyu; Biegler, Lorenz T.

2018-05-01

This study presents a trajectory optimization framework for lunar rover performing vertical takeoff vertical landing (VTVL) maneuvers in the presence of terrain using variable-thrust propulsion. First, a VTVL trajectory optimization problem with three-dimensional kinematics and dynamics model, boundary conditions, and path constraints is formulated. Then, a finite-element approach transcribes the formulated trajectory optimization problem into a nonlinear programming (NLP) problem solved by a highly efficient NLP solver. A homotopy-based backtracking strategy is applied to enhance the convergence in solving the formulated VTVL trajectory optimization problem. The optimal thrust solution typically has a "bang-bang" profile considering that bounds are imposed on the magnitude of engine thrust. An adaptive mesh refinement strategy based on a constant Hamiltonian profile is designed to address the difficulty in locating the breakpoints in the thrust profile. Four scenarios are simulated. Simulation results indicate that the proposed trajectory optimization framework has sufficient adaptability to handle VTVL missions efficiently.

Putting atomic diffusion theory of magnetic ApBp stars to the test: evaluation of the predictions of time-dependent diffusion models

NASA Astrophysics Data System (ADS)

Kochukhov, O.; Ryabchikova, T. A.

2018-02-01

A series of recent theoretical atomic diffusion studies has address the challenging problem of predicting inhomogeneous vertical and horizontal chemical element distributions in the atmospheres of magnetic ApBp stars. Here we critically assess the most sophisticated of such diffusion models - based on a time-dependent treatment of the atomic diffusion in a magnetized stellar atmosphere - by direct comparison with observations as well by testing the widely used surface mapping tools with the spectral line profiles predicted by this theory. We show that the mean abundances of Fe and Cr are grossly underestimated by the time-dependent theoretical diffusion model, with discrepancies reaching a factor of 1000 for Cr. We also demonstrate that Doppler imaging inversion codes, based either on modelling of individual metal lines or line-averaged profiles simulated according to theoretical three-dimensional abundance distribution, are able to reconstruct correct horizontal chemical spot maps despite ignoring the vertical abundance variation. These numerical experiments justify a direct comparison of the empirical two-dimensional Doppler maps with theoretical diffusion calculations. This comparison is generally unfavourable for the current diffusion theory, as very few chemical elements are observed to form overabundance rings in the horizontal field regions as predicted by the theory and there are numerous examples of element accumulations in the vicinity of radial field zones, which cannot be explained by diffusion calculations.

Inverse kinematics of a dual linear actuator pitch/roll heliostat

NASA Astrophysics Data System (ADS)

Freeman, Joshua; Shankar, Balakrishnan; Sundaram, Ganesh

2017-06-01

This work presents a simple, computationally efficient inverse kinematics solution for a pitch/roll heliostat using two linear actuators. The heliostat design and kinematics have been developed, modeled and tested using computer simulation software. A physical heliostat prototype was fabricated to validate the theoretical computations and data. Pitch/roll heliostats have numerous advantages including reduced cost potential and reduced space requirements, with a primary disadvantage being the significantly more complicated kinematics, which are solved here. Novel methods are applied to simplify the inverse kinematics problem which could be applied to other similar problems.

Two-dimensional magnetotelluric inversion using reflection seismic data as constraints and application in the COSC project

NASA Astrophysics Data System (ADS)

Yan, Ping; Kalscheuer, Thomas; Hedin, Peter; Garcia Juanatey, Maria A.

2017-04-01

We present a novel 2-D magnetotelluric (MT) inversion scheme, in which the local weights of the regularizing smoothness constraints are based on the envelope attribute of a reflection seismic image. The weights resemble those of a previously published seismic modification of the minimum gradient support method. We measure the directional gradients of the seismic envelope to modify the horizontal and vertical smoothness constraints separately. Successful application of the inversion to MT field data of the Collisional Orogeny in the Scandinavian Caledonides (COSC) project using the envelope attribute of the COSC reflection seismic profile helped to reduce the uncertainty of the interpretation of the main décollement by demonstrating that the associated alum shales may be much thinner than suggested by a previous inversion model. Thus, the new model supports the proposed location of a future borehole COSC-2 which is hoped to penetrate the main décollement and the underlying Precambrian basement.

Solving Large-Scale Inverse Magnetostatic Problems using the Adjoint Method

PubMed Central

Bruckner, Florian; Abert, Claas; Wautischer, Gregor; Huber, Christian; Vogler, Christoph; Hinze, Michael; Suess, Dieter

2017-01-01

An efficient algorithm for the reconstruction of the magnetization state within magnetic components is presented. The occurring inverse magnetostatic problem is solved by means of an adjoint approach, based on the Fredkin-Koehler method for the solution of the forward problem. Due to the use of hybrid FEM-BEM coupling combined with matrix compression techniques the resulting algorithm is well suited for large-scale problems. Furthermore the reconstruction of the magnetization state within a permanent magnet as well as an optimal design application are demonstrated. PMID:28098851

Group-theoretic models of the inversion process in bacterial genomes.

PubMed

Egri-Nagy, Attila; Gebhardt, Volker; Tanaka, Mark M; Francis, Andrew R

2014-07-01

The variation in genome arrangements among bacterial taxa is largely due to the process of inversion. Recent studies indicate that not all inversions are equally probable, suggesting, for instance, that shorter inversions are more frequent than longer, and those that move the terminus of replication are less probable than those that do not. Current methods for establishing the inversion distance between two bacterial genomes are unable to incorporate such information. In this paper we suggest a group-theoretic framework that in principle can take these constraints into account. In particular, we show that by lifting the problem from circular permutations to the affine symmetric group, the inversion distance can be found in polynomial time for a model in which inversions are restricted to acting on two regions. This requires the proof of new results in group theory, and suggests a vein of new combinatorial problems concerning permutation groups on which group theorists will be needed to collaborate with biologists. We apply the new method to inferring distances and phylogenies for published Yersinia pestis data.

Query-based learning for aerospace applications.

PubMed

Saad, E W; Choi, J J; Vian, J L; Wunsch, D C Ii

2003-01-01

Models of real-world applications often include a large number of parameters with a wide dynamic range, which contributes to the difficulties of neural network training. Creating the training data set for such applications becomes costly, if not impossible. In order to overcome the challenge, one can employ an active learning technique known as query-based learning (QBL) to add performance-critical data to the training set during the learning phase, thereby efficiently improving the overall learning/generalization. The performance-critical data can be obtained using an inverse mapping called network inversion (discrete network inversion and continuous network inversion) followed by oracle query. This paper investigates the use of both inversion techniques for QBL learning, and introduces an original heuristic to select the inversion target values for continuous network inversion method. Efficiency and generalization was further enhanced by employing node decoupled extended Kalman filter (NDEKF) training and a causality index (CI) as a means to reduce the input search dimensionality. The benefits of the overall QBL approach are experimentally demonstrated in two aerospace applications: a classification problem with large input space and a control distribution problem.

Towards a Millennial Time-scale Vertical Deformation Field in Taiwan

NASA Astrophysics Data System (ADS)

Bordovaos, P. A.; Johnson, K. M.

2015-12-01

Pete Bordovalos and Kaj M. Johnson To better understand the feedbacks between erosion and deformation in Taiwan, we need constraints on the millennial time-scale vertical field. Dense GPS and leveling data sets in Taiwan provide measurements of the present-day vertical deformation field over the entire Taiwan island. However, it is unclear how much of this vertical field is transient (varies over earthquake cycle) or steady (over millennial time scale). A deformation model is required to decouple transient from steady deformation. This study takes a look at how the 82 mm/yr of convergence motion between the Eurasian plate and the Philippine Sea plate is distributed across the faults on Taiwan. We build a plate flexure model that consists of all known active faults and subduction zones cutting through an elastic plate supported by buoyancy. We use horizontal and vertical GPS data, leveling data, and geologic surface uplift rates with a Monte Carlo probabilistic inversion method to infer fault slip rates and locking depths on all faults. Using our model we examine how different fault geometries influence the estimates of distribution of slip along faults and deformation patterns.

A practical method to assess model sensitivity and parameter uncertainty in C cycle models

NASA Astrophysics Data System (ADS)

Delahaies, Sylvain; Roulstone, Ian; Nichols, Nancy

2015-04-01

The carbon cycle combines multiple spatial and temporal scales, from minutes to hours for the chemical processes occurring in plant cells to several hundred of years for the exchange between the atmosphere and the deep ocean and finally to millennia for the formation of fossil fuels. Together with our knowledge of the transformation processes involved in the carbon cycle, many Earth Observation systems are now available to help improving models and predictions using inverse modelling techniques. A generic inverse problem consists in finding a n-dimensional state vector x such that h(x) = y, for a given N-dimensional observation vector y, including random noise, and a given model h. The problem is well posed if the three following conditions hold: 1) there exists a solution, 2) the solution is unique and 3) the solution depends continuously on the input data. If at least one of these conditions is violated the problem is said ill-posed. The inverse problem is often ill-posed, a regularization method is required to replace the original problem with a well posed problem and then a solution strategy amounts to 1) constructing a solution x, 2) assessing the validity of the solution, 3) characterizing its uncertainty. The data assimilation linked ecosystem carbon (DALEC) model is a simple box model simulating the carbon budget allocation for terrestrial ecosystems. Intercomparison experiments have demonstrated the relative merit of various inverse modelling strategies (MCMC, ENKF) to estimate model parameters and initial carbon stocks for DALEC using eddy covariance measurements of net ecosystem exchange of CO2 and leaf area index observations. Most results agreed on the fact that parameters and initial stocks directly related to fast processes were best estimated with narrow confidence intervals, whereas those related to slow processes were poorly estimated with very large uncertainties. While other studies have tried to overcome this difficulty by adding complementary data streams or by considering longer observation windows no systematic analysis has been carried out so far to explain the large differences among results. We consider adjoint based methods to investigate inverse problems using DALEC and various data streams. Using resolution matrices we study the nature of the inverse problems (solution existence, uniqueness and stability) and show how standard regularization techniques affect resolution and stability properties. Instead of using standard prior information as a penalty term in the cost function to regularize the problems we constraint the parameter space using ecological balance conditions and inequality constraints. The efficiency and rapidity of this approach allows us to compute ensembles of solutions to the inverse problems from which we can establish the robustness of the variational method and obtain non Gaussian posterior distributions for the model parameters and initial carbon stocks.

Linkage disequilibrium network analysis (LDna) gives a global view of chromosomal inversions, local adaptation and geographic structure.

PubMed

Kemppainen, Petri; Knight, Christopher G; Sarma, Devojit K; Hlaing, Thaung; Prakash, Anil; Maung Maung, Yan Naung; Somboon, Pradya; Mahanta, Jagadish; Walton, Catherine

2015-09-01

Recent advances in sequencing allow population-genomic data to be generated for virtually any species. However, approaches to analyse such data lag behind the ability to generate it, particularly in nonmodel species. Linkage disequilibrium (LD, the nonrandom association of alleles from different loci) is a highly sensitive indicator of many evolutionary phenomena including chromosomal inversions, local adaptation and geographical structure. Here, we present linkage disequilibrium network analysis (LDna), which accesses information on LD shared between multiple loci genomewide. In LD networks, vertices represent loci, and connections between vertices represent the LD between them. We analysed such networks in two test cases: a new restriction-site-associated DNA sequence (RAD-seq) data set for Anopheles baimaii, a Southeast Asian malaria vector; and a well-characterized single nucleotide polymorphism (SNP) data set from 21 three-spined stickleback individuals. In each case, we readily identified five distinct LD network clusters (single-outlier clusters, SOCs), each comprising many loci connected by high LD. In A. baimaii, further population-genetic analyses supported the inference that each SOC corresponds to a large inversion, consistent with previous cytological studies. For sticklebacks, we inferred that each SOC was associated with a distinct evolutionary phenomenon: two chromosomal inversions, local adaptation, population-demographic history and geographic structure. LDna is thus a useful exploratory tool, able to give a global overview of LD associated with diverse evolutionary phenomena and identify loci potentially involved. LDna does not require a linkage map or reference genome, so it is applicable to any population-genomic data set, making it especially valuable for nonmodel species. © 2015 The Authors. Molecular Ecology Resources Published by John Wiley & Sons Ltd.

Recovery of surface mass redistribution from a joint inversion of GPS and GRACE data - A methodology and results from the Australian and other continents

NASA Astrophysics Data System (ADS)

Han, S. C.; Tangdamrongsub, N.; Razeghi, S. M.

2017-12-01

We present a methodology to invert a regional set of vertical displacement data from Global Positioning System (GPS) to determine surface mass redistribution. It is assumed that GPS deformation is a result of the Earth's elastic response to the surface mass load of hydrology, atmosphere, and ocean. The identical assumption is made when global geopotential change data from Gravity Recovery And Climate Experiment (GRACE) are used to determine surface mass changes. We developed an algorithm to estimate the spectral information of displacements from "regional" GPS data through regional spherical (Slepian) basis functions and apply the load Love numbers to estimate the mass load. We rigorously examine all systematic errors caused by various truncations (spherical harmonic series and Slepian series) and the smoothing constraint applied to the GPS-only inversion. We demonstrate the technique by processing 16 years of daily vertical motions determined from 114 GPS stations in Australia. The GPS inverted surface mass changes are validated against GRACE data, atmosphere and ocean models, and a land surface model. Seasonal and inter-annual terrestrial mass variations from GPS are in good agreement with GRACE data and the water storage models. The GPS recovery compares better with the water storage model around the smaller coastal basins of Australia than two different GRACE solutions. The sub-monthly mass changes from GPS provide meaningful results agreeing with atmospheric mass changes in central Australia. Finally, we integrate GPS data from different continents with GRACE in the least-square normal equations and solve for the global surface mass changes by jointly inverting GPS and GRACE data. We present the results of surface mass changes from the GPS-only inversion and from the joint GPS-GRACE inversion.

Multichannel analysis of surface-waves and integration of downhole acoustic televiewer imaging, ultrasonic Vs and Vp, and vertical seismic profiling in an NEHRP-standard classification, South of Concordia, Kansas, USA

NASA Astrophysics Data System (ADS)

Raef, Abdelmoneam; Gad, Sabreen; Tucker-Kulesza, Stacey

2015-10-01

Seismic site characteristics, as pertaining to earthquake hazard reduction, are a function of the subsurface elastic moduli and the geologic structures. This study explores how multiscale (surface, downhole, and laboratory) datasets can be utilized to improve "constrained" average Vs30 (shear-wave velocity to a 30-meter depth). We integrate borehole, surface and laboratory measurements for a seismic site classification based on the standards of the National Earthquake Hazard Reduction Program (NEHRP). The seismic shear-wave velocity (Vs30) was derived from a geophysical inversion workflow that utilized multichannel analysis of surface-waves (MASW) and downhole acoustic televiewer imaging (DATI). P-wave and S-wave velocities, based on laboratory measurements of arrival times of ultrasonic-frequency signals, supported the workflow by enabling us to calculate Poisson's ratio, which was incorporated in building an initial model for the geophysical inversion of MASW. Extraction of core samples from two boreholes provided lithology and thickness calibration of the amplitudes of the acoustic televiewer imaging for each layer. The MASW inversion, for calculating Vs sections, was constrained with both ultrasonic laboratory measurements (from first arrivals of Vs and Vp waveforms at simulated in situ overburden stress conditions) and the downhole acoustic televiewer (DATV) amplitude logs. The Vs30 calculations enabled categorizing the studied site as NEHRP-class "C" - very dense soil and soft rock. Unlike shallow fractured carbonates in the studied area, S-wave and P-wave velocities at ultrasonic frequency for the deeper intact shale core-samples from two boreholes were in better agreement with the corresponding velocities from both a zero-offset vertical seismic profiling (VSP) and inversion of Rayleigh-wave velocity dispersion curves.

Turbulent premixed combustion in V-shaped flames: Characteristics of flame front

NASA Astrophysics Data System (ADS)

Kheirkhah, S.; Gülder, Ö. L.

2013-05-01

Flame front characteristics of turbulent premixed V-shaped flames were investigated experimentally using the Mie scattering and the particle image velocimetry techniques. The experiments were performed at mean streamwise exit velocities of 4.0, 6.2, and 8.6 m/s, along with fuel-air equivalence ratios of 0.7, 0.8, and 0.9. Effects of vertical distance from the flame-holder, mean streamwise exit velocity, and fuel-air equivalence ratio on statistics of the distance between the flame front and the vertical axis, flame brush thickness, flame front curvature, and angle between tangent to the flame front and the horizontal axis were studied. The results show that increasing the vertical distance from the flame-holder and the fuel-air equivalence ratio increase the mean and root-mean-square (RMS) of the distance between the flame front and the vertical axis; however, increasing the mean streamwise exit velocity decreases these statistics. Spectral analysis of the fluctuations of the flame front position depicts that the normalized and averaged power-spectrum-densities collapse and show a power-law relation with the normalized wave number. The flame brush thickness is linearly correlated with RMS of the distance between the flame front and the vertical axis. Analysis of the curvature of the flame front data shows that the mean curvature is independent of the experimental conditions tested and equals to zero. Values of the inverse of the RMS of flame front curvature are similar to those of the integral length scale, suggesting that the large eddies in the flow make a significant contribution in wrinkling of the flame front. Spectral analyses of the flame front curvature as well as the angle between tangent to the flame front and the horizontal axis show that the power-spectrum-densities feature a peak. Value of the inverse of the wave number pertaining to the peak is larger than that of the integral length scale.

Sulfur dioxide in the Venus atmosphere: I. Vertical distribution and variability

NASA Astrophysics Data System (ADS)

Vandaele, A. C.; Korablev, O.; Belyaev, D.; Chamberlain, S.; Evdokimova, D.; Encrenaz, Th.; Esposito, L.; Jessup, K. L.; Lefèvre, F.; Limaye, S.; Mahieux, A.; Marcq, E.; Mills, F. P.; Montmessin, F.; Parkinson, C. D.; Robert, S.; Roman, T.; Sandor, B.; Stolzenbach, A.; Wilson, C.; Wilquet, V.

2017-10-01

Recent observations of sulfur containing species (SO2, SO, OCS, and H2SO4) in Venus' mesosphere have generated controversy and great interest in the scientific community. These observations revealed unexpected spatial patterns and spatial/temporal variability that have not been satisfactorily explained by models. Sulfur oxide chemistry on Venus is closely linked to the global-scale cloud and haze layers, which are composed primarily of concentrated sulfuric acid. Sulfur oxide observations provide therefore important insight into the on-going chemical evolution of Venus' atmosphere, atmospheric dynamics, and possible volcanism. This paper is the first of a series of two investigating the SO2 and SO variability in the Venus atmosphere. This first part of the study will focus on the vertical distribution of SO2, considering mostly observations performed by instruments and techniques providing accurate vertical information. This comprises instruments in space (SPICAV/SOIR suite on board Venus Express) and Earth-based instruments (JCMT). The most noticeable feature of the vertical profile of the SO2 abundance in the Venus atmosphere is the presence of an inversion layer located at about 70-75 km, with VMRs increasing above. The observations presented in this compilation indicate that at least one other significant sulfur reservoir (in addition to SO2 and SO) must be present throughout the 70-100 km altitude region to explain the inversion in the SO2 vertical profile. No photochemical model has an explanation for this behaviour. GCM modelling indicates that dynamics may play an important role in generating an inflection point at 75 km altitude but does not provide a definitive explanation of the source of the inflection at all local times or latitudes The current study has been carried out within the frame of the International Space Science Institute (ISSI) International Team entitled 'SO2 variability in the Venus atmosphere'.

Model Order Reduction for the fast solution of 3D Stokes problems and its application in geophysical inversion

NASA Astrophysics Data System (ADS)

Ortega Gelabert, Olga; Zlotnik, Sergio; Afonso, Juan Carlos; Díez, Pedro

2017-04-01

The determination of the present-day physical state of the thermal and compositional structure of the Earth's lithosphere and sub-lithospheric mantle is one of the main goals in modern lithospheric research. All this data is essential to build Earth's evolution models and to reproduce many geophysical observables (e.g. elevation, gravity anomalies, travel time data, heat flow, etc) together with understanding the relationship between them. Determining the lithospheric state involves the solution of high-resolution inverse problems and, consequently, the solution of many direct models is required. The main objective of this work is to contribute to the existing inversion techniques in terms of improving the estimation of the elevation (topography) by including a dynamic component arising from sub-lithospheric mantle flow. In order to do so, we implement an efficient Reduced Order Method (ROM) built upon classic Finite Elements. ROM allows to reduce significantly the computational cost of solving a family of problems, for example all the direct models that are required in the solution of the inverse problem. The strategy of the method consists in creating a (reduced) basis of solutions, so that when a new problem has to be solved, its solution is sought within the basis instead of attempting to solve the problem itself. In order to check the Reduced Basis approach, we implemented the method in a 3D domain reproducing a portion of Earth that covers up to 400 km depth. Within the domain the Stokes equation is solved with realistic viscosities and densities. The different realizations (the family of problems) is created by varying viscosities and densities in a similar way as it would happen in an inversion problem. The Reduced Basis method is shown to be an extremely efficiently solver for the Stokes equation in this context.

Inverse modeling for seawater intrusion in coastal aquifers: Insights about parameter sensitivities, variances, correlations and estimation procedures derived from the Henry problem

USGS Publications Warehouse

Sanz, E.; Voss, C.I.

2006-01-01

Inverse modeling studies employing data collected from the classic Henry seawater intrusion problem give insight into several important aspects of inverse modeling of seawater intrusion problems and effective measurement strategies for estimation of parameters for seawater intrusion. Despite the simplicity of the Henry problem, it embodies the behavior of a typical seawater intrusion situation in a single aquifer. Data collected from the numerical problem solution are employed without added noise in order to focus on the aspects of inverse modeling strategies dictated by the physics of variable-density flow and solute transport during seawater intrusion. Covariances of model parameters that can be estimated are strongly dependent on the physics. The insights gained from this type of analysis may be directly applied to field problems in the presence of data errors, using standard inverse modeling approaches to deal with uncertainty in data. Covariance analysis of the Henry problem indicates that in order to generally reduce variance of parameter estimates, the ideal places to measure pressure are as far away from the coast as possible, at any depth, and the ideal places to measure concentration are near the bottom of the aquifer between the center of the transition zone and its inland fringe. These observations are located in and near high-sensitivity regions of system parameters, which may be identified in a sensitivity analysis with respect to several parameters. However, both the form of error distribution in the observations and the observation weights impact the spatial sensitivity distributions, and different choices for error distributions or weights can result in significantly different regions of high sensitivity. Thus, in order to design effective sampling networks, the error form and weights must be carefully considered. For the Henry problem, permeability and freshwater inflow can be estimated with low estimation variance from only pressure or only concentration observations. Permeability, freshwater inflow, solute molecular diffusivity, and porosity can be estimated with roughly equivalent confidence using observations of only the logarithm of concentration. Furthermore, covariance analysis allows a logical reduction of the number of estimated parameters for ill-posed inverse seawater intrusion problems. Ill-posed problems may exhibit poor estimation convergence, have a non-unique solution, have multiple minima, or require excessive computational effort, and the condition often occurs when estimating too many or co-dependent parameters. For the Henry problem, such analysis allows selection of the two parameters that control system physics from among all possible system parameters. ?? 2005 Elsevier Ltd. All rights reserved.

Solving the Inverse-Square Problem with Complex Variables

ERIC Educational Resources Information Center

Gauthier, N.

2005-01-01

The equation of motion for a mass that moves under the influence of a central, inverse-square force is formulated and solved as a problem in complex variables. To find the solution, the constancy of angular momentum is first established using complex variables. Next, the complex position coordinate and complex velocity of the particle are assumed…

Backus-Gilbert inversion of travel time data

NASA Technical Reports Server (NTRS)

Johnson, L. E.

1972-01-01

Application of the Backus-Gilbert theory for geophysical inverse problems to the seismic body wave travel-time problem is described. In particular, it is shown how to generate earth models that fit travel-time data to within one standard error and having generated such models how to describe their degree of uniqueness. An example is given to illustrate the process.

Determination of thermophysical characteristics of solid materials by electrical modelling of the solutions to the inverse problems in nonsteady heat conduction

NASA Technical Reports Server (NTRS)

Kozdoba, L. A.; Krivoshei, F. A.

1985-01-01

The solution of the inverse problem of nonsteady heat conduction is discussed, based on finding the coefficient of the heat conduction and the coefficient of specific volumetric heat capacity. These findings are included in the equation used for the electrical model of this phenomenon.

Performance evaluation of the inverse dynamics method for optimal spacecraft reorientation

NASA Astrophysics Data System (ADS)

Ventura, Jacopo; Romano, Marcello; Walter, Ulrich

2015-05-01

This paper investigates the application of the inverse dynamics in the virtual domain method to Euler angles, quaternions, and modified Rodrigues parameters for rapid optimal attitude trajectory generation for spacecraft reorientation maneuvers. The impact of the virtual domain and attitude representation is numerically investigated for both minimum time and minimum energy problems. Owing to the nature of the inverse dynamics method, it yields sub-optimal solutions for minimum time problems. Furthermore, the virtual domain improves the optimality of the solution, but at the cost of more computational time. The attitude representation also affects solution quality and computational speed. For minimum energy problems, the optimal solution can be obtained without the virtual domain with any considered attitude representation.

Nonsteady Problem for an Elastic Half-Plane with Mixed Boundary Conditions

NASA Astrophysics Data System (ADS)

Kubenko, V. D.

2016-03-01

An approach to studying nonstationary wave processes in an elastic half-plane with mixed boundary conditions of the fourth boundary-value problem of elasticity is proposed. The Laplace and Fourier transforms are used. The sequential inversion of these transforms or the inversion of the joint transform by the Cagniard method allows obtaining the required solution (stresses, displacements) in a closed analytic form. With this approach, the problem can be solved for various types of loads

Music algorithm for imaging of a sound-hard arc in limited-view inverse scattering problem

NASA Astrophysics Data System (ADS)

Park, Won-Kwang

2017-07-01

MUltiple SIgnal Classification (MUSIC) algorithm for a non-iterative imaging of sound-hard arc in limited-view inverse scattering problem is considered. In order to discover mathematical structure of MUSIC, we derive a relationship between MUSIC and an infinite series of Bessel functions of integer order. This structure enables us to examine some properties of MUSIC in limited-view problem. Numerical simulations are performed to support the identified structure of MUSIC.

Application of the Kano-Hamilton multiangle inversion method in clear atmospheres

Treesearch

Mariana Adam; Vladimir A. Kovalev; Cyle Wold; Jenny Newton; Markus Pahlow; Wei M. Hao; Marc B. Parlange

2007-01-01

An improved measurement methodology and a data-processing technique for multiangle data obtained with an elastic scanning lidar in clear atmospheres are introduced. Azimuthal and slope scans are combined to reduce the atmospheric heterogeneity. Vertical profiles of optical depth and intercept (proportional to the logarithm of the backscatter coefficient) are determined...

An Evaluation of the Naval Oceanic Vertical Aerosol Model During Key90

DTIC Science & Technology

1991-06-01

regions with extensive aerosol content (such as were caused by the intentional burning of oil rigs). Many military devices operate in the visible to...that aerosol extinction above the second inversion is essentil y zero when the air mass parameter is calculated to be approximately equal to one do : s

Real-time monitoring of the structure of ultrathin Fe3O4 films during growth on Nb-doped SrTiO3(001)

NASA Astrophysics Data System (ADS)

Kuschel, O.; Spiess, W.; Schemme, T.; Rubio-Zuazo, J.; Kuepper, K.; Wollschläger, J.

2017-07-01

In this work, thin magnetite films were deposited on SrTiO3 via reactive molecular beam epitaxy at different substrate temperatures. The growth process was monitored in-situ during deposition by means of x-ray diffraction. While the magnetite film grown at 400 °C shows a fully relaxed vertical lattice constant already in the early growth stages, the film deposited at 270 °C exhibits a strong vertical compressive strain and relaxes towards the bulk value with increasing film thickness. Furthermore, a lateral tensile strain was observed under these growth conditions although the inverse behavior is expected due to the lattice mismatch of -7.5%. Additionally, the occupancy of the A and B sublattices of magnetite with tetrahedral and octahedral sites was investigated showing a lower occupancy of the A sites compared to an ideal inverse spinel structure. The occupation of A sites decreases for a higher growth temperature. Thus, we assume a relocation of the iron ions from tetrahedral sites to octahedral vacancies forming a deficient rock salt lattice.

Genetic algorithms and their use in Geophysical Problems

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

Parker, Paul B.

1999-04-01

Genetic algorithms (GAs), global optimization methods that mimic Darwinian evolution are well suited to the nonlinear inverse problems of geophysics. A standard genetic algorithm selects the best or ''fittest'' models from a ''population'' and then applies operators such as crossover and mutation in order to combine the most successful characteristics of each model and produce fitter models. More sophisticated operators have been developed, but the standard GA usually provides a robust and efficient search. Although the choice of parameter settings such as crossover and mutation rate may depend largely on the type of problem being solved, numerous results show thatmore » certain parameter settings produce optimal performance for a wide range of problems and difficulties. In particular, a low (about half of the inverse of the population size) mutation rate is crucial for optimal results, but the choice of crossover method and rate do not seem to affect performance appreciably. Optimal efficiency is usually achieved with smaller (< 50) populations. Lastly, tournament selection appears to be the best choice of selection methods due to its simplicity and its autoscaling properties. However, if a proportional selection method is used such as roulette wheel selection, fitness scaling is a necessity, and a high scaling factor (> 2.0) should be used for the best performance. Three case studies are presented in which genetic algorithms are used to invert for crustal parameters. The first is an inversion for basement depth at Yucca mountain using gravity data, the second an inversion for velocity structure in the crust of the south island of New Zealand using receiver functions derived from teleseismic events, and the third is a similar receiver function inversion for crustal velocities beneath the Mendocino Triple Junction region of Northern California. The inversions demonstrate that genetic algorithms are effective in solving problems with reasonably large numbers of free parameters and with computationally expensive objective function calculations. More sophisticated techniques are presented for special problems. Niching and island model algorithms are introduced as methods to find multiple, distinct solutions to the nonunique problems that are typically seen in geophysics. Finally, hybrid algorithms are investigated as a way to improve the efficiency of the standard genetic algorithm.« less

Genetic algorithms and their use in geophysical problems

NASA Astrophysics Data System (ADS)

Parker, Paul Bradley

Genetic algorithms (GAs), global optimization methods that mimic Darwinian evolution are well suited to the nonlinear inverse problems of geophysics. A standard genetic algorithm selects the best or "fittest" models from a "population" and then applies operators such as crossover and mutation in order to combine the most successful characteristics of each model and produce fitter models. More sophisticated operators have been developed, but the standard GA usually provides a robust and efficient search. Although the choice of parameter settings such as crossover and mutation rate may depend largely on the type of problem being solved, numerous results show that certain parameter settings produce optimal performance for a wide range of problems and difficulties. In particular, a low (about half of the inverse of the population size) mutation rate is crucial for optimal results, but the choice of crossover method and rate do not seem to affect performance appreciably. Also, optimal efficiency is usually achieved with smaller (<50) populations. Lastly, tournament selection appears to be the best choice of selection methods due to its simplicity and its autoscaling properties. However, if a proportional selection method is used such as roulette wheel selection, fitness scaling is a necessity, and a high scaling factor (>2.0) should be used for the best performance. Three case studies are presented in which genetic algorithms are used to invert for crustal parameters. The first is an inversion for basement depth at Yucca mountain using gravity data, the second an inversion for velocity structure in the crust of the south island of New Zealand using receiver functions derived from teleseismic events, and the third is a similar receiver function inversion for crustal velocities beneath the Mendocino Triple Junction region of Northern California. The inversions demonstrate that genetic algorithms are effective in solving problems with reasonably large numbers of free parameters and with computationally expensive objective function calculations. More sophisticated techniques are presented for special problems. Niching and island model algorithms are introduced as methods to find multiple, distinct solutions to the nonunique problems that are typically seen in geophysics. Finally, hybrid algorithms are investigated as a way to improve the efficiency of the standard genetic algorithm.

Effect of screw threading dislocations and inverse domain boundaries in GaN on the shape of reciprocal-space maps.

PubMed

Barchuk, Mykhailo; Motylenko, Mykhaylo; Lukin, Gleb; Pätzold, Olf; Rafaja, David

2017-04-01

The microstructure of polar GaN layers, grown by upgraded high-temperature vapour phase epitaxy on [001]-oriented sapphire substrates, was studied by means of high-resolution X-ray diffraction and transmission electron microscopy. Systematic differences between reciprocal-space maps measured by X-ray diffraction and those which were simulated for different densities of threading dislocations revealed that threading dislocations are not the only microstructure defect in these GaN layers. Conventional dark-field transmission electron microscopy and convergent-beam electron diffraction detected vertical inversion domains as an additional microstructure feature. On a series of polar GaN layers with different proportions of threading dislocations and inversion domain boundaries, this contribution illustrates the capability and limitations of coplanar reciprocal-space mapping by X-ray diffraction to distinguish between these microstructure features.

Differences between radiosonde and dropsonde temperature profiles over the Arctic Ocean

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

Skony, S.M.; Kahl, J.D.W.; Zaitseva, N.A.

1994-10-01

The boundary layer structure measured by 402 pairs of approximately collocated radiosonde and dropsonde temperature profiles over the Arctic Ocean during the period 1957-1961 is examined. The radiosonde profiles were obtained at the Russian drifting ice camps `North Pole 7` and `North Pole 8,` and the dropsonde profiles were measured during the United States Air Force `Ptarmigan` series of weather reconnaissance flights. The boundary layer structure is characterized by the features of the low-level tropospheric temperature inversion. The results indicate that the dropsonde soundings, although containing relatively few measurement levels, contain sufficient vertical resolution to characterize the temperature inversion. Systematicmore » differences were noted in wintertime inversion features and near-surface temperatures as measured by dropsondes and radiosondes. These differences are attributed to contrasting temperature lag errors accompanying ascending and descending sensors.« less

Vertical Distribution of Non-Methane Hydrocarbons During Winter Ozone Production Events in the Uintah Basin

NASA Astrophysics Data System (ADS)

Stephens, C. R.; Helmig, D.; Evans, J.; Hueber, J.; Park, J.; Boylan, P.

2013-12-01

Emissions of non-methane hydrocarbons (NMHC) are primarily linked to anthropogenic fossil fuel activities, such as oil and natural gas extraction and distribution, and are important tropospheric ozone precursors. The Uintah Basin, Utah, is a region of heavy oil and natural gas development where high winter-time ozone production events have been observed during strong inversions when there is snow cover present. In the winters of 2012 and 2013, we conducted measurements of methane and NMHC during the Uintah Basin Winter Ozone Study. NMHC were monitored along a vertical gradient up to 150 m using a flux tower and tethered balloon. In 2013, measurements of NMHC were also conducted from within the snowpack. In 2012, no high ozone events were observed. In contrast, during the 2013 study, several periods of high ozone occurred concurrently with strong increases in ambient NMHC. Here, we present vertical profile measurements of C2-C5 alkanes, benzene and toluene comparing 2012 and 2013. Data from 2013 show strong vertical gradients with build-up of NMHC and ozone near the surface during inversion events, with wash out of both ozone and ozone precursors during low pressure front passage from the west. The NOAA/INSTAAR global flask network provides a useful comparison for expected regional background values of NMHC, and we find up to a 570-fold enhancement in Uintah, providing evidence for the importance of local emissions sources. Investigation of NMHC ratios reveals distinctly different values in the ambient air and within the snowpack, suggesting active radical chemistry occurring in the snow. Analysis of butane and pentane isomer ratios points towards the presence of chlorine radicals, indicating that the snow may serve as a reactive chlorine reservoir that may enhance ozone production chemistry.

Resolution enhancement of robust Bayesian pre-stack inversion in the frequency domain

NASA Astrophysics Data System (ADS)

Yin, Xingyao; Li, Kun; Zong, Zhaoyun

2016-10-01

AVO/AVA (amplitude variation with an offset or angle) inversion is one of the most practical and useful approaches to estimating model parameters. So far, publications on AVO inversion in the Fourier domain have been quite limited in view of its poor stability and sensitivity to noise compared with time-domain inversion. For the resolution and stability of AVO inversion in the Fourier domain, a novel robust Bayesian pre-stack AVO inversion based on the mixed domain formulation of stationary convolution is proposed which could solve the instability and achieve superior resolution. The Fourier operator will be integrated into the objective equation and it avoids the Fourier inverse transform in our inversion process. Furthermore, the background constraints of model parameters are taken into consideration to improve the stability and reliability of inversion which could compensate for the low-frequency components of seismic signals. Besides, the different frequency components of seismic signals can realize decoupling automatically. This will help us to solve the inverse problem by means of multi-component successive iterations and the convergence precision of the inverse problem could be improved. So, superior resolution compared with the conventional time-domain pre-stack inversion could be achieved easily. Synthetic tests illustrate that the proposed method could achieve high-resolution results with a high degree of agreement with the theoretical model and verify the quality of anti-noise. Finally, applications on a field data case demonstrate that the proposed method could obtain stable inversion results of elastic parameters from pre-stack seismic data in conformity with the real logging data.

The 2-D magnetotelluric inverse problem solved with optimization

NASA Astrophysics Data System (ADS)

van Beusekom, Ashley E.; Parker, Robert L.; Bank, Randolph E.; Gill, Philip E.; Constable, Steven

2011-02-01

The practical 2-D magnetotelluric inverse problem seeks to determine the shallow-Earth conductivity structure using finite and uncertain data collected on the ground surface. We present an approach based on using PLTMG (Piecewise Linear Triangular MultiGrid), a special-purpose code for optimization with second-order partial differential equation (PDE) constraints. At each frequency, the electromagnetic field and conductivity are treated as unknowns in an optimization problem in which the data misfit is minimized subject to constraints that include Maxwell's equations and the boundary conditions. Within this framework it is straightforward to accommodate upper and lower bounds or other conditions on the conductivity. In addition, as the underlying inverse problem is ill-posed, constraints may be used to apply various kinds of regularization. We discuss some of the advantages and difficulties associated with using PDE-constrained optimization as the basis for solving large-scale nonlinear geophysical inverse problems. Combined transverse electric and transverse magnetic complex admittances from the COPROD2 data are inverted. First, we invert penalizing size and roughness giving solutions that are similar to those found previously. In a second example, conventional regularization is replaced by a technique that imposes upper and lower bounds on the model. In both examples the data misfit is better than that obtained previously, without any increase in model complexity.

Sparsity-promoting and edge-preserving maximum a posteriori estimators in non-parametric Bayesian inverse problems

NASA Astrophysics Data System (ADS)

Agapiou, Sergios; Burger, Martin; Dashti, Masoumeh; Helin, Tapio

2018-04-01

We consider the inverse problem of recovering an unknown functional parameter u in a separable Banach space, from a noisy observation vector y of its image through a known possibly non-linear map {{\\mathcal G}} . We adopt a Bayesian approach to the problem and consider Besov space priors (see Lassas et al (2009 Inverse Problems Imaging 3 87-122)), which are well-known for their edge-preserving and sparsity-promoting properties and have recently attracted wide attention especially in the medical imaging community. Our key result is to show that in this non-parametric setup the maximum a posteriori (MAP) estimates are characterized by the minimizers of a generalized Onsager-Machlup functional of the posterior. This is done independently for the so-called weak and strong MAP estimates, which as we show coincide in our context. In addition, we prove a form of weak consistency for the MAP estimators in the infinitely informative data limit. Our results are remarkable for two reasons: first, the prior distribution is non-Gaussian and does not meet the smoothness conditions required in previous research on non-parametric MAP estimates. Second, the result analytically justifies existing uses of the MAP estimate in finite but high dimensional discretizations of Bayesian inverse problems with the considered Besov priors.

Joint inversion of geophysical data using petrophysical clustering and facies deformation wth the level set technique

NASA Astrophysics Data System (ADS)

Revil, A.

2015-12-01

Geological expertise and petrophysical relationships can be brought together to provide prior information while inverting multiple geophysical datasets. The merging of such information can result in more realistic solution in the distribution of the model parameters, reducing ipse facto the non-uniqueness of the inverse problem. We consider two level of heterogeneities: facies, described by facies boundaries and heteroegenities inside each facies determined by a correlogram. In this presentation, we pose the geophysical inverse problem in terms of Gaussian random fields with mean functions controlled by petrophysical relationships and covariance functions controlled by a prior geological cross-section, including the definition of spatial boundaries for the geological facies. The petrophysical relationship problem is formulated as a regression problem upon each facies. The inversion of the geophysical data is performed in a Bayesian framework. We demonstrate the usefulness of this strategy using a first synthetic case for which we perform a joint inversion of gravity and galvanometric resistivity data with the stations located at the ground surface. The joint inversion is used to recover the density and resistivity distributions of the subsurface. In a second step, we consider the possibility that the facies boundaries are deformable and their shapes are inverted as well. We use the level set approach to perform such deformation preserving prior topological properties of the facies throughout the inversion. With the help of prior facies petrophysical relationships and topological characteristic of each facies, we make posterior inference about multiple geophysical tomograms based on their corresponding geophysical data misfits. The method is applied to a second synthetic case showing that we can recover the heterogeneities inside the facies, the mean values for the petrophysical properties, and, to some extent, the facies boundaries using the 2D joint inversion of gravity and galvanometric resistivity data. For this 2D synthetic example, we note that the position of the facies are well-recovered except far from the ground surfce where the sensitivity is too low. The figure shows the evolution of the shape of the facies during the inversion itertion by iteration.

Black hole algorithm for determining model parameter in self-potential data

NASA Astrophysics Data System (ADS)

Sungkono; Warnana, Dwa Desa

2018-01-01

Analysis of self-potential (SP) data is increasingly popular in geophysical method due to its relevance in many cases. However, the inversion of SP data is often highly nonlinear. Consequently, local search algorithms commonly based on gradient approaches have often failed to find the global optimum solution in nonlinear problems. Black hole algorithm (BHA) was proposed as a solution to such problems. As the name suggests, the algorithm was constructed based on the black hole phenomena. This paper investigates the application of BHA to solve inversions of field and synthetic self-potential (SP) data. The inversion results show that BHA accurately determines model parameters and model uncertainty. This indicates that BHA is highly potential as an innovative approach for SP data inversion.

EIT image reconstruction based on a hybrid FE-EFG forward method and the complete-electrode model.

PubMed

Hadinia, M; Jafari, R; Soleimani, M

2016-06-01

This paper presents the application of the hybrid finite element-element free Galerkin (FE-EFG) method for the forward and inverse problems of electrical impedance tomography (EIT). The proposed method is based on the complete electrode model. Finite element (FE) and element-free Galerkin (EFG) methods are accurate numerical techniques. However, the FE technique has meshing task problems and the EFG method is computationally expensive. In this paper, the hybrid FE-EFG method is applied to take both advantages of FE and EFG methods, the complete electrode model of the forward problem is solved, and an iterative regularized Gauss-Newton method is adopted to solve the inverse problem. The proposed method is applied to compute Jacobian in the inverse problem. Utilizing 2D circular homogenous models, the numerical results are validated with analytical and experimental results and the performance of the hybrid FE-EFG method compared with the FE method is illustrated. Results of image reconstruction are presented for a human chest experimental phantom.

M-matrices with prescribed elementary divisors

NASA Astrophysics Data System (ADS)

Soto, Ricardo L.; Díaz, Roberto C.; Salas, Mario; Rojo, Oscar

2017-09-01

A real matrix A is said to be an M-matrix if it is of the form A=α I-B, where B is a nonnegative matrix with Perron eigenvalue ρ (B), and α ≥slant ρ (B) . This paper provides sufficient conditions for the existence and construction of an M-matrix A with prescribed elementary divisors, which are the characteristic polynomials of the Jordan blocks of the Jordan canonical form of A. This inverse problem on M-matrices has not been treated until now. We solve the inverse elementary divisors problem for diagonalizable M-matrices and the symmetric generalized doubly stochastic inverse M-matrix problem for lists of real numbers and for lists of complex numbers of the form Λ =\\{λ 1, a+/- bi, \\ldots, a+/- bi\\} . The constructive nature of our results allows for the computation of a solution matrix. The paper also discusses an application of M-matrices to a capacity problem in wireless communications.

Force sensing using 3D displacement measurements in linear elastic bodies

NASA Astrophysics Data System (ADS)

Feng, Xinzeng; Hui, Chung-Yuen

2016-07-01

In cell traction microscopy, the mechanical forces exerted by a cell on its environment is usually determined from experimentally measured displacement by solving an inverse problem in elasticity. In this paper, an innovative numerical method is proposed which finds the "optimal" traction to the inverse problem. When sufficient regularization is applied, we demonstrate that the proposed method significantly improves the widely used approach using Green's functions. Motivated by real cell experiments, the equilibrium condition of a slowly migrating cell is imposed as a set of equality constraints on the unknown traction. Our validation benchmarks demonstrate that the numeric solution to the constrained inverse problem well recovers the actual traction when the optimal regularization parameter is used. The proposed method can thus be applied to study general force sensing problems, which utilize displacement measurements to sense inaccessible forces in linear elastic bodies with a priori constraints.

A MATLAB implementation of the minimum relative entropy method for linear inverse problems

NASA Astrophysics Data System (ADS)

Neupauer, Roseanna M.; Borchers, Brian

2001-08-01

The minimum relative entropy (MRE) method can be used to solve linear inverse problems of the form Gm= d, where m is a vector of unknown model parameters and d is a vector of measured data. The MRE method treats the elements of m as random variables, and obtains a multivariate probability density function for m. The probability density function is constrained by prior information about the upper and lower bounds of m, a prior expected value of m, and the measured data. The solution of the inverse problem is the expected value of m, based on the derived probability density function. We present a MATLAB implementation of the MRE method. Several numerical issues arise in the implementation of the MRE method and are discussed here. We present the source history reconstruction problem from groundwater hydrology as an example of the MRE implementation.

EDITORIAL: Introduction to the special issue on electromagnetic inverse problems: emerging methods and novel applications Introduction to the special issue on electromagnetic inverse problems: emerging methods and novel applications

NASA Astrophysics Data System (ADS)

Dorn, O.; Lesselier, D.

2010-07-01

Inverse problems in electromagnetics have a long history and have stimulated exciting research over many decades. New applications and solution methods are still emerging, providing a rich source of challenging topics for further investigation. The purpose of this special issue is to combine descriptions of several such developments that are expected to have the potential to fundamentally fuel new research, and to provide an overview of novel methods and applications for electromagnetic inverse problems. There have been several special sections published in Inverse Problems over the last decade addressing fully, or partly, electromagnetic inverse problems. Examples are: Electromagnetic imaging and inversion of the Earth's subsurface (Guest Editors: D Lesselier and T Habashy) October 2000 Testing inversion algorithms against experimental data (Guest Editors: K Belkebir and M Saillard) December 2001 Electromagnetic and ultrasonic nondestructive evaluation (Guest Editors: D Lesselier and J Bowler) December 2002 Electromagnetic characterization of buried obstacles (Guest Editors: D Lesselier and W C Chew) December 2004 Testing inversion algorithms against experimental data: inhomogeneous targets (Guest Editors: K Belkebir and M Saillard) December 2005 Testing inversion algorithms against experimental data: 3D targets (Guest Editors: A Litman and L Crocco) February 2009 In a certain sense, the current issue can be understood as a continuation of this series of special sections on electromagnetic inverse problems. On the other hand, its focus is intended to be more general than previous ones. Instead of trying to cover a well-defined, somewhat specialized research topic as completely as possible, this issue aims to show the broad range of techniques and applications that are relevant to electromagnetic imaging nowadays, which may serve as a source of inspiration and encouragement for all those entering this active and rapidly developing research area. Also, the construction of this special issue is likely to have been different from preceding ones. In addition to the invitations sent to specific research groups involved in electromagnetic inverse problems, the Guest Editors also solicited recommendations, from a large number of experts, of potential authors who were thereupon encouraged to contribute. Moreover, an open call for contributions was published on the homepage of Inverse Problems in order to attract as wide a scope of contributions as possible. This special issue's attempt at generality might also define its limitations: by no means could this collection of papers be exhaustive or complete, and as Guest Editors we are well aware that many exciting topics and potential contributions will be missing. This, however, also determines its very special flavor: besides addressing electromagnetic inverse problems in a broad sense, there were only a few restrictions on the contributions considered for this section. One requirement was plausible evidence of either novelty or the emergent nature of the technique or application described, judged mainly by the referees, and in some cases by the Guest Editors. The technical quality of the contributions always remained a stringent condition of acceptance, final adjudication (possibly questionable either way, not always positive) being made in most cases once a thorough revision process had been carried out. Therefore, we hope that the final result presented here constitutes an interesting collection of novel ideas and applications, properly refereed and edited, which will find its own readership and which can stimulate significant new research in the topics represented. Overall, as Guest Editors, we feel quite fortunate to have obtained such a strong response to the call for this issue and to have a really wide-ranging collection of high-quality contributions which, indeed, can be read from the first to the last page with sustained enthusiasm. A large number of applications and techniques is represented, overall via 16 contributions with 45 authors in total. This shows, in our opinion, that electromagnetic imaging and inversion remain amongst the most challenging and active research areas in applied inverse problems today. Below, we give a brief overview of the contributions included in this issue, ordered alphabetically by the surname of the leading author. 1. The complexity of handling potential randomness of the source in an inverse scattering problem is not minor, and the literature is far from being replete in this configuration. The contribution by G Bao, S N Chow, P Li and H Zhou, `Numerical solution of an inverse medium scattering problem with a stochastic source', exemplifies how to hybridize Wiener chaos expansion with a recursive linearization method in order to solve the stochastic problem as a set of decoupled deterministic ones. 2. In cases where the forward problem is expensive to evaluate, database methods might become a reliable method of choice, while enabling one to deliver more information on the inversion itself. The contribution by S Bilicz, M Lambert and Sz Gyimóthy, `Kriging-based generation of optimal databases as forward and inverse surrogate models', describes such a technique which uses kriging for constructing an efficient database with the goal of achieving an equidistant distribution of points in the measurement space. 3. Anisotropy remains a considerable challenge in electromagnetic imaging, which is tackled in the contribution by F Cakoni, D Colton, P Monk and J Sun, `The inverse electromagnetic scattering problem for anisotropic media', via the fact that transmission eigenvalues can be retrieved from a far-field scattering pattern, yielding, in particular, lower and upper bounds of the index of refraction of the unknown (dielectric anisotropic) scatterer. 4. So-called subspace optimization methods (SOM) have attracted a lot of interest recently in many fields. The contribution by X Chen, `Subspace-based optimization method for inverse scattering problems with an inhomogeneous background medium', illustrates how to address a realistic situation in which the medium containing the unknown obstacles is not homogeneous, via blending a properly developed SOM with a finite-element approach to the required Green's functions. 5. H Egger, M Hanke, C Schneider, J Schöberl and S Zaglmayr, in their contribution `Adjoint-based sampling methods for electromagnetic scattering', show how to efficiently develop sampling methods without explicit knowledge of the dyadic Green's function once an adjoint problem has been solved at much lower computational cost. This is demonstrated by examples in demanding propagative and diffusive situations. 6. Passive sensor arrays can be employed to image reflectors from ambient noise via proper migration of cross-correlation matrices into their embedding medium. This is investigated, and resolution, in particular, is considered in detail, as a function of the characteristics of the sensor array and those of the noise, in the contribution by J Garnier and G Papanicolaou, `Resolution analysis for imaging with noise'. 7. A direct reconstruction technique based on the conformal mapping theorem is proposed and investigated in depth in the contribution by H Haddar and R Kress, `Conformal mapping and impedance tomography'. This paper expands on previous work, with inclusions in homogeneous media, convergence results, and numerical illustrations. 8. The contribution by T Hohage and S Langer, `Acceleration techniques for regularized Newton methods applied to electromagnetic inverse medium scattering problems', focuses on a spectral preconditioner intended to accelerate regularized Newton methods as employed for the retrieval of a local inhomogeneity in a three-dimensional vector electromagnetic case, while also illustrating the implementation of a Lepskiĭ-type stopping rule outsmarting a traditional discrepancy principle. 9. Geophysical applications are a rich source of practically relevant inverse problems. The contribution by M Li, A Abubakar and T Habashy, `Application of a two-and-a-half dimensional model-based algorithm to crosswell electromagnetic data inversion', deals with a model-based inversion technique for electromagnetic imaging which addresses novel challenges such as multi-physics inversion, and incorporation of prior knowledge, such as in hydrocarbon recovery. 10. Non-stationary inverse problems, considered as a special class of Bayesian inverse problems, are framed via an orthogonal decomposition representation in the contribution by A Lipponen, A Seppänen and J P Kaipio, `Reduced order estimation of nonstationary flows with electrical impedance tomography'. The goal is to simultaneously estimate, from electrical impedance tomography data, certain characteristics of the Navier--Stokes fluid flow model together with time-varying concentration distribution. 11. Non-iterative imaging methods of thin, penetrable cracks, based on asymptotic expansion of the scattering amplitude and analysis of the multi-static response matrix, are discussed in the contribution by W-K Park, `On the imaging of thin dielectric inclusions buried within a half-space', completing, for a shallow burial case at multiple frequencies, the direct imaging of small obstacles (here, along their transverse dimension), MUSIC and non-MUSIC type indicator functions being used for that purpose. 12. The contribution by R Potthast, `A study on orthogonality sampling' envisages quick localization and shaping of obstacles from (portions of) far-field scattering patterns collected at one or more time-harmonic frequencies, via the simple calculation (and summation) of scalar products between those patterns and a test function. This is numerically exemplified for Neumann/Dirichlet boundary conditions and homogeneous/heterogeneous embedding media. 13. The contribution by J D Shea, P Kosmas, B D Van Veen and S C Hagness, `Contrast-enhanced microwave imaging of breast tumors: a computational study using 3D realistic numerical phantoms', aims at microwave medical imaging, namely the early detection of breast cancer. The use of contrast enhancing agents is discussed in detail and a number of reconstructions in three-dimensional geometry of realistic numerical breast phantoms are presented. 14. The contribution by D A Subbarayappa and V Isakov, `Increasing stability of the continuation for the Maxwell system', discusses enhanced log-type stability results for continuation of solutions of the time-harmonic Maxwell system, adding a fresh chapter to the interesting story of the study of the Cauchy problem for PDE. 15. In their contribution, `Recent developments of a monotonicity imaging method for magnetic induction tomography in the small skin-depth regime', A Tamburrino, S Ventre and G Rubinacci extend the recently developed monotonicity method toward the application of magnetic induction tomography in order to map surface-breaking defects affecting a damaged metal component. 16. The contribution by F Viani, P Rocca, M Benedetti, G Oliveri and A Massa, `Electromagnetic passive localization and tracking of moving targets in a WSN-infrastructured environment', contributes to what could still be seen as a niche problem, yet both useful in terms of applications, e.g., security, and challenging in terms of methodologies and experiments, in particular, in view of the complexity of environments in which this endeavor is to take place and the variability of the wireless sensor networks employed. To conclude, we would like to thank the able and tireless work of Kate Watt and Zoë Crossman, as past and present Publishers of the Journal, on what was definitely a long and exciting journey (sometimes a little discouraging when reports were not arriving, or authors were late, or Guest Editors overwhelmed) that started from a thorough discussion at the `Manchester workshop on electromagnetic inverse problems' held mid-June 2009, between Kate Watt and the Guest Editors. We gratefully acknowledge the fact that W W Symes gave us his full backing to carry out this special issue and that A K Louis completed it successfully. Last, but not least, the staff of Inverse Problems should be thanked, since they work together to make it a premier journal.

A note on convergence of solutions of total variation regularized linear inverse problems

NASA Astrophysics Data System (ADS)

Iglesias, José A.; Mercier, Gwenael; Scherzer, Otmar

2018-05-01

In a recent paper by Chambolle et al (2017 Inverse Problems 33 015002) it was proven that if the subgradient of the total variation at the noise free data is not empty, the level-sets of the total variation denoised solutions converge to the level-sets of the noise free data with respect to the Hausdorff distance. The condition on the subgradient corresponds to the source condition introduced by Burger and Osher (2007 Multiscale Model. Simul. 6 365–95), who proved convergence rates results with respect to the Bregman distance under this condition. We generalize the result of Chambolle et al to total variation regularization of general linear inverse problems under such a source condition. As particular applications we present denoising in bounded and unbounded, convex and non convex domains, deblurring and inversion of the circular Radon transform. In all these examples the convergence result applies. Moreover, we illustrate the convergence behavior through numerical examples.

Round-off errors in cutting plane algorithms based on the revised simplex procedure

NASA Technical Reports Server (NTRS)

Moore, J. E.

1973-01-01

This report statistically analyzes computational round-off errors associated with the cutting plane approach to solving linear integer programming problems. Cutting plane methods require that the inverse of a sequence of matrices be computed. The problem basically reduces to one of minimizing round-off errors in the sequence of inverses. Two procedures for minimizing this problem are presented, and their influence on error accumulation is statistically analyzed. One procedure employs a very small tolerance factor to round computed values to zero. The other procedure is a numerical analysis technique for reinverting or improving the approximate inverse of a matrix. The results indicated that round-off accumulation can be effectively minimized by employing a tolerance factor which reflects the number of significant digits carried for each calculation and by applying the reinversion procedure once to each computed inverse. If 18 significant digits plus an exponent are carried for each variable during computations, then a tolerance value of 0.1 x 10 to the minus 12th power is reasonable.

Simultaneous source and attenuation reconstruction in SPECT using ballistic and single scattering data

NASA Astrophysics Data System (ADS)

Courdurier, M.; Monard, F.; Osses, A.; Romero, F.

2015-09-01

In medical single-photon emission computed tomography (SPECT) imaging, we seek to simultaneously obtain the internal radioactive sources and the attenuation map using not only ballistic measurements but also first-order scattering measurements and assuming a very specific scattering regime. The problem is modeled using the radiative transfer equation by means of an explicit non-linear operator that gives the ballistic and scattering measurements as a function of the radioactive source and attenuation distributions. First, by differentiating this non-linear operator we obtain a linearized inverse problem. Then, under regularity hypothesis for the source distribution and attenuation map and considering small attenuations, we rigorously prove that the linear operator is invertible and we compute its inverse explicitly. This allows proof of local uniqueness for the non-linear inverse problem. Finally, using the previous inversion result for the linear operator, we propose a new type of iterative algorithm for simultaneous source and attenuation recovery for SPECT based on the Neumann series and a Newton-Raphson algorithm.

Inverse dynamics of a 3 degree of freedom spatial flexible manipulator

NASA Technical Reports Server (NTRS)

Bayo, Eduardo; Serna, M.

1989-01-01

A technique is presented for solving the inverse dynamics and kinematics of 3 degree of freedom spatial flexible manipulator. The proposed method finds the joint torques necessary to produce a specified end effector motion. Since the inverse dynamic problem in elastic manipulators is closely coupled to the inverse kinematic problem, the solution of the first also renders the displacements and rotations at any point of the manipulator, including the joints. Furthermore the formulation is complete in the sense that it includes all the nonlinear terms due to the large rotation of the links. The Timoshenko beam theory is used to model the elastic characteristics, and the resulting equations of motion are discretized using the finite element method. An iterative solution scheme is proposed that relies on local linearization of the problem. The solution of each linearization is carried out in the frequency domain. The performance and capabilities of this technique are tested through simulation analysis. Results show the potential use of this method for the smooth motion control of space telerobots.

Exact solution for an optimal impermeable parachute problem

NASA Astrophysics Data System (ADS)

Lupu, Mircea; Scheiber, Ernest

2002-10-01

In the paper there are solved direct and inverse boundary problems and analytical solutions are obtained for optimization problems in the case of some nonlinear integral operators. It is modeled the plane potential flow of an inviscid, incompressible and nonlimited fluid jet, witch encounters a symmetrical, curvilinear obstacle--the deflector of maximal drag. There are derived integral singular equations, for direct and inverse problems and the movement in the auxiliary canonical half-plane is obtained. Next, the optimization problem is solved in an analytical manner. The design of the optimal airfoil is performed and finally, numerical computations concerning the drag coefficient and other geometrical and aerodynamical parameters are carried out. This model corresponds to the Helmholtz impermeable parachute problem.

Doppler-Zeeman mapping of the magnetic CP star HD 215441

NASA Astrophysics Data System (ADS)

Khokhlova, V. L.; Vasilchenko, D. V.; Stepanov, V. V.; Tsymbal, V. V.

1997-07-01

The method of Vasilchenko et al. (1996) is used to obtain a Doppler-Zeeman map of the magnetic CP star HD 215441. The magnetic field is approximated by a magnetic dipole that is arbitrarily shifted from the star center. The solution of the inverse problem yields the dipole parameters and the maps of Si, Ti, Cr, and Fe abundance anomalies; the coordinates of local magnetic vectors on the star surface are computed. A comparison of the distribution of abundance anomalies and the magnetic-field configuration reveals that in the region where the magnetic-field lines are vertical (near the magnetic pole), Si, Ti and Cr are highly deficient, while the Fe enhancement is strongest. In the regions where the magnetic-field lines are horizontal (near the magnetic equator), Si, Ti and Cr show the greatest overabundance. In these regions, the Fe abundance is also slightly enhanced and exhibits, as it were, a secondary maximum. The factors that limit the accuracy of Doppler-Zeeman mapping are reviewed.

The attitude inversion method of geostationary satellites based on unscented particle filter

NASA Astrophysics Data System (ADS)

Du, Xiaoping; Wang, Yang; Hu, Heng; Gou, Ruixin; Liu, Hao

2018-04-01

The attitude information of geostationary satellites is difficult to be obtained since they are presented in non-resolved images on the ground observation equipment in space object surveillance. In this paper, an attitude inversion method for geostationary satellite based on Unscented Particle Filter (UPF) and ground photometric data is presented. The inversion algorithm based on UPF is proposed aiming at the strong non-linear feature in the photometric data inversion for satellite attitude, which combines the advantage of Unscented Kalman Filter (UKF) and Particle Filter (PF). This update method improves the particle selection based on the idea of UKF to redesign the importance density function. Moreover, it uses the RMS-UKF to partially correct the prediction covariance matrix, which improves the applicability of the attitude inversion method in view of UKF and the particle degradation and dilution of the attitude inversion method based on PF. This paper describes the main principles and steps of algorithm in detail, correctness, accuracy, stability and applicability of the method are verified by simulation experiment and scaling experiment in the end. The results show that the proposed method can effectively solve the problem of particle degradation and depletion in the attitude inversion method on account of PF, and the problem that UKF is not suitable for the strong non-linear attitude inversion. However, the inversion accuracy is obviously superior to UKF and PF, in addition, in the case of the inversion with large attitude error that can inverse the attitude with small particles and high precision.

A Computationally Efficient Parallel Levenberg-Marquardt Algorithm for Large-Scale Big-Data Inversion

NASA Astrophysics Data System (ADS)

Lin, Y.; O'Malley, D.; Vesselinov, V. V.

2015-12-01

Inverse modeling seeks model parameters given a set of observed state variables. However, for many practical problems due to the facts that the observed data sets are often large and model parameters are often numerous, conventional methods for solving the inverse modeling can be computationally expensive. We have developed a new, computationally-efficient Levenberg-Marquardt method for solving large-scale inverse modeling. Levenberg-Marquardt methods require the solution of a dense linear system of equations which can be prohibitively expensive to compute for large-scale inverse problems. Our novel method projects the original large-scale linear problem down to a Krylov subspace, such that the dimensionality of the measurements can be significantly reduced. Furthermore, instead of solving the linear system for every Levenberg-Marquardt damping parameter, we store the Krylov subspace computed when solving the first damping parameter and recycle it for all the following damping parameters. The efficiency of our new inverse modeling algorithm is significantly improved by using these computational techniques. We apply this new inverse modeling method to invert for a random transitivity field. Our algorithm is fast enough to solve for the distributed model parameters (transitivity) at each computational node in the model domain. The inversion is also aided by the use regularization techniques. The algorithm is coded in Julia and implemented in the MADS computational framework (http://mads.lanl.gov). Julia is an advanced high-level scientific programing language that allows for efficient memory management and utilization of high-performance computational resources. By comparing with a Levenberg-Marquardt method using standard linear inversion techniques, our Levenberg-Marquardt method yields speed-up ratio of 15 in a multi-core computational environment and a speed-up ratio of 45 in a single-core computational environment. Therefore, our new inverse modeling method is a powerful tool for large-scale applications.

Inverse solutions for electrical impedance tomography based on conjugate gradients methods

NASA Astrophysics Data System (ADS)

Wang, M.

2002-01-01

A multistep inverse solution for two-dimensional electric field distribution is developed to deal with the nonlinear inverse problem of electric field distribution in relation to its boundary condition and the problem of divergence due to errors introduced by the ill-conditioned sensitivity matrix and the noise produced by electrode modelling and instruments. This solution is based on a normalized linear approximation method where the change in mutual impedance is derived from the sensitivity theorem and a method of error vector decomposition. This paper presents an algebraic solution of the linear equations at each inverse step, using a generalized conjugate gradients method. Limiting the number of iterations in the generalized conjugate gradients method controls the artificial errors introduced by the assumption of linearity and the ill-conditioned sensitivity matrix. The solution of the nonlinear problem is approached using a multistep inversion. This paper also reviews the mathematical and physical definitions of the sensitivity back-projection algorithm based on the sensitivity theorem. Simulations and discussion based on the multistep algorithm, the sensitivity coefficient back-projection method and the Newton-Raphson method are given. Examples of imaging gas-liquid mixing and a human hand in brine are presented.

Combining Earthquake Focal Mechanism Inversion and Coulomb Friction Law to Yield Tectonic Stress Magnitudes in Strike-slip Faulting Regime

NASA Astrophysics Data System (ADS)

Soh, I.; Chang, C.

2017-12-01

The techniques for estimating present-day stress states by inverting multiple earthquake focal mechanism solutions (FMS) provide orientations of the three principal stresses and their relative magnitudes. In order to estimate absolute magnitudes of the stresses that are generally required to analyze faulting mechanics, we combine the relative stress magnitude parameter (R-value) derived from the inversion process and the concept of frictional equilibrium of stress state defined by Coulomb friction law. The stress inversion in Korean Peninsula using 152 FMS data (magnitude≥2.5) conducted at regularly spaced grid points yields a consistent strike-slip faulting regime in which the maximum (S1) and the minimum (S3) principal stresses act in horizontal planes (with an S1 azimuth in ENE-WSW) and the intermediate principal stress (S2) close to vertical. However, R-value varies from 0.28 to 0.75 depending on locations, systematically increasing eastward. Based on the assumptions that the vertical stress is lithostatic, pore pressure is hydrostatic, and the maximum differential stress (S1-S3) is limited by Byerlee's friction of optimally oriented faults for slip, we estimate absolute magnitudes of the two horizontal principal stresses using R-value. As R-value increases, so do the magnitudes of the horizontal stresses. Our estimation of the stress magnitudes shows that the maximum horizontal principal stress (S1) normalized by vertical stress tends to increase from 1.3 in the west to 1.8 in the east. The estimated variation of stress magnitudes is compatible with distinct clustering of faulting types in different regions. Normal faulting events are densely populated in the west region where the horizontal stress is relatively low, whereas numerous reverse faulting events prevail in the east offshore where the horizontal stress is relatively high. Such a characteristic distribution of distinct faulting types in different regions can only be explained in terms of stress magnitude variation.

Acoustic sounding in the planetary boundary layer

NASA Technical Reports Server (NTRS)

Kelly, E. H.

1974-01-01

Three case studies are presented involving data from an acoustic radar. The first two cases examine data collected during the passage of a mesoscale cold-air intrusion, probably thunderstorm outflow, and a synoptic-scale cold front. In these studies the radar data are compared to conventional meteorological data obtained from the WKY tower facility for the purpose of radar data interpretation. It is shown that the acoustic radar echoes reveal the boundary between warm and cold air and other areas of turbulent mixing, regions of strong vertical temperature gradients, and areas of weak or no wind shear. The third case study examines the relationship between the nocturnal radiation inversion and the low-level wind maximum or jet in the light of conclusions presented by Blackadar (1957). The low-level jet is seen forming well above the top of the inversion. Sudden rapid growth of the inversion occurs which brings the top of the inversion to a height equal that of the jet. Coincident with the rapid growth of the inversion is a sudden decrease in the intensity of the acoustic radar echoes in the inversion layer. It is suggested that the decrease in echo intensity reveals a decrease in turbulent mixing in the inversion layer as predicted by Blackadar. It is concluded that the acoustic radar can be a valuable tool for study in the lower atmosphere.

Effects of the measurement configuration in GPR prospecting

NASA Astrophysics Data System (ADS)

Persico, Raffaele; Soldovieri, Francesco

2017-04-01

The measurement configuration is an issue of great interest in problems of inverse scattering in general, and in particular in problems regarding GPR data. In particular, the measurement configuration has an influence on the amount of retrievable information [1-2] and can be a way to achieve an intrinsic two dimensional filtering of the data [3], possibly accounting for the characteristics of the exploited antennas too [4]. However, no filter is able to erase exactly the undesired contribution to the comprehensive signal while leaving unperturbed the useful part of the gathered datum. In other word, any filtering of the data (included those implicitly imposed through the measurement configuration) has some price in terms of loss or distortion of the received information, and therefore it has to be applied only when needed and only at the right degree of intensity. In particular, differential measurement configurations have been introduced in the last few years, especially with interest in the field of detection of UXO [5-6]. The filtering effects in some differential configuration are not immediately understood, but need some deep reasoning. In particular, the theory of the diffraction tomography, allows to quantify the retrievable spatial frequencies under the measurement configuration at hand, and so allows to quantify the filtering effect of the differential configurations. Examples will be shown at the conference, regarding both a horizontal and a vertical differential configuration. References [1] R. Persico, R. Bernini, F. Soldovieri, "The role of the measurement configuration in inverse scattering from buried objects under the Born approximation", IEEE Trans. On Antennas and Prop., vol. 53, n. 6, pp. 1875-1886, June 2005. [2] R. Persico, "On the role of measurement Configuration in Contactless GPR data Processing by Means of Linear Inverse Scattering, IEEE Trans. On Antennas and Prop AP, Vol. 54 n. 7 p. 2062-2071, July 2006. [3] R. Persico, F. Soldovieri, Effects of the Background Removal in Linear Inverse Scattering, IEEE Trans. on Geos. and Rem. Sens., vol. 46, n. 4, pp. 1104-1114, April 2008. [4] F. Soldovieri, R. Persico and G. Leone, "Effect of source and receiver radiation characteristics in subsurface prospecting within the DBA", Radio Science, vol. 40, RS3006, May 2005. [5] R. Persico, F. Soldovieri, A Microwave Tomography approach for a Differential Configuration in GPR Prospecting, IEEE Trans. On Antennas and Prop AP, vol. 54, n. 11, pp. 3541-3548, November 2006. [6] R. Persico, G. Pochanin, V. Ruban, I. Catapano, F. Soldovieri, Performances of a Microwave Tomographic Algorithm for GPR Systems Working in Differential Configuration, IEEE Jstars, vol. 9, n. 4, pp. 1343-1356, April 2016.

Joint Stochastic Inversion of Pre-Stack 3D Seismic Data and Well Logs for High Resolution Hydrocarbon Reservoir Characterization

NASA Astrophysics Data System (ADS)

Torres-Verdin, C.

2007-05-01

This paper describes the successful implementation of a new 3D AVA stochastic inversion algorithm to quantitatively integrate pre-stack seismic amplitude data and well logs. The stochastic inversion algorithm is used to characterize flow units of a deepwater reservoir located in the central Gulf of Mexico. Conventional fluid/lithology sensitivity analysis indicates that the shale/sand interface represented by the top of the hydrocarbon-bearing turbidite deposits generates typical Class III AVA responses. On the other hand, layer- dependent Biot-Gassmann analysis shows significant sensitivity of the P-wave velocity and density to fluid substitution. Accordingly, AVA stochastic inversion, which combines the advantages of AVA analysis with those of geostatistical inversion, provided quantitative information about the lateral continuity of the turbidite reservoirs based on the interpretation of inverted acoustic properties (P-velocity, S-velocity, density), and lithotype (sand- shale) distributions. The quantitative use of rock/fluid information through AVA seismic amplitude data, coupled with the implementation of co-simulation via lithotype-dependent multidimensional joint probability distributions of acoustic/petrophysical properties, yields accurate 3D models of petrophysical properties such as porosity and permeability. Finally, by fully integrating pre-stack seismic amplitude data and well logs, the vertical resolution of inverted products is higher than that of deterministic inversions methods.

Rayleigh lidar observation of tropical mesospheric inversion layer: a comparison between dynamics and chemistry

NASA Astrophysics Data System (ADS)

Ramesh, K.; Sridharan, S.; Raghunath, K.

2018-04-01

The Rayleigh lidar at National Atmospheric Research Laboratory, Gadanki (13.5°N, 79.2°E), India operates at 532 nm green laser with 600 mJ/pulse since 2007. The vertical temperature profiles are derived above 30 km by assuming the atmosphere is in hydrostatic equilibrium and obeys ideal gas law. A large mesospheric inversion layer (MIL) is observed at 77.4-84.6 km on the night of 22 March 2007 over Gadanki. Although dynamics and chemistry play vital role, both the mechanisms are compared for the occurrence of the MIL in the present study.

Optimization of the Inverse Algorithm for Estimating the Optical Properties of Biological Materials Using Spatially-resolved Diffuse Reflectance Technique

USDA-ARS?s Scientific Manuscript database

Determination of the optical properties from intact biological materials based on diffusion approximation theory is a complicated inverse problem, and it requires proper implementation of inverse algorithm, instrumentation, and experiment. This work was aimed at optimizing the procedure of estimatin...

Decision rules for allocation of finances to health systems strengthening

PubMed Central

Morton, Alec; Thomas, Ranjeeta; Smith, Peter C.

2017-01-01

A key dilemma in global health is how to allocate funds between disease-specific “vertical projects” on the one hand and “horizontal programmes” which aim to strengthen the entire health system on the other. While economic evaluation provides a way of approaching the prioritisation of vertical projects, it provides less guidance on how to prioritise between horizontal and vertical spending. We approach this problem by formulating a mathematical program which captures the complementary benefits of funding both vertical projects and horizontal programmes. We show that our solution to this math program has an appealing intuitive structure. We illustrate our model by computationally solving two specialised versions of this problem, with illustrations based on the problem of allocating funding for infectious diseases in sub-Saharan Africa. We conclude by reflecting on how such a model may be developed in the future and used to guide empirical data collection and theory development. PMID:27394006

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

NASA Astrophysics Data System (ADS)

Tietze, Kristina; Ritter, Oliver

2013-10-01

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