Geological modeling and infiltration pattern of a karstic system based upon crossed geophysical methods and image-guided inversion

NASA Astrophysics Data System (ADS)

Duran, Lea; Jardani, Abderrahim; Fournier, Matthieu; Massei, Nicolas

2015-04-01

Karstic aquifers represent an important part of the water resources worldwide. Though they have been widely studied on many aspects, their geological and hydrogeological modeling is still complex. Geophysical methods can provide useful subsurface information for the characterization and mapping of karstic systems, especially when not accessible by speleology. The site investigated in this study is a sinkhole-spring system, with small diameter conduits that run within a chalk aquifer (Norville, in Upper Normandy, France). This site was investigated using several geophysical methods: electrical tomography, self-potential, mise-à-la-masse methods, and electromagnetic method (EM34). Coupling those results with boreholes data, a 3D geological model of the hydrogeological basin was established, including tectonic features as well as infiltration structures (sinkhole, covered dolines). The direction of the karstic conduits near the main sinkhole could be established, and the major fault was shown to be a hydraulic barrier. Also the average concentration of dolines on the basin could be estimated, as well as their depth. At last, several hypotheses could be made concerning the location of the main conduit network between the sinkhole and the spring, using previous hydrodynamic study of the site along with geophysical data. In order to validate the 3D geological model, an image-guided inversion of the apparent resistivity data was used. With this approach it is possible to use geological cross sections to constrain the inversion of apparent resistivity data, preserving both discontinuities and coherences in the inversion of the resistivity data. This method was used on the major fault, enabling to choose one geological interpretation over another (fault block structure near the fault, rather than important folding). The constrained inversion was also applied on covered dolines, to validate the interpretation of their shape and depth. Key words: Magnetic and electrical

Comparative study of inversion methods of three-dimensional NMR and sensitivity to fluids

NASA Astrophysics Data System (ADS)

Tan, Maojin; Wang, Peng; Mao, Keyu

2014-04-01

Three-dimensional nuclear magnetic resonance (3D NMR) logging can simultaneously measure transverse relaxation time (T2), longitudinal relaxation time (T1), and diffusion coefficient (D). These parameters can be used to distinguish fluids in the porous reservoirs. For 3D NMR logging, the relaxation mechanism and mathematical model, Fredholm equation, are introduced, and the inversion methods including Singular Value Decomposition (SVD), Butler-Reeds-Dawson (BRD), and Global Inversion (GI) methods are studied in detail, respectively. During one simulation test, multi-echo CPMG sequence activation is designed firstly, echo trains of the ideal fluid models are synthesized, then an inversion algorithm is carried on these synthetic echo trains, and finally T2-T1-D map is built. Futhermore, SVD, BRD, and GI methods are respectively applied into a same fluid model, and the computing speed and inversion accuracy are compared and analyzed. When the optimal inversion method and matrix dimention are applied, the inversion results are in good aggreement with the supposed fluid model, which indicates that the inversion method of 3D NMR is applieable for fluid typing of oil and gas reservoirs. Additionally, the forward modeling and inversion tests are made in oil-water and gas-water models, respectively, the sensitivity to the fluids in different magnetic field gradients is also examined in detail. The effect of magnetic gradient on fluid typing in 3D NMR logging is stuied and the optimal manetic gradient is choosen.

The application of the pilot points in groundwater numerical inversion model

NASA Astrophysics Data System (ADS)

Hu, Bin; Teng, Yanguo; Cheng, Lirong

2015-04-01

Numerical inversion simulation of groundwater has been widely applied in groundwater. Compared to traditional forward modeling, inversion model has more space to study. Zones and inversing modeling cell by cell are conventional methods. Pilot points is a method between them. The traditional inverse modeling method often uses software dividing the model into several zones with a few parameters needed to be inversed. However, distribution is usually too simple for modeler and result of simulation deviation. Inverse cell by cell will get the most actual parameter distribution in theory, but it need computational complexity greatly and quantity of survey data for geological statistical simulation areas. Compared to those methods, pilot points distribute a set of points throughout the different model domains for parameter estimation. Property values are assigned to model cells by Kriging to ensure geological units within the parameters of heterogeneity. It will reduce requirements of simulation area geological statistics and offset the gap between above methods. Pilot points can not only save calculation time, increase fitting degree, but also reduce instability of numerical model caused by numbers of parameters and other advantages. In this paper, we use pilot point in a field which structure formation heterogeneity and hydraulics parameter was unknown. We compare inversion modeling results of zones and pilot point methods. With the method of comparative analysis, we explore the characteristic of pilot point in groundwater inversion model. First, modeler generates an initial spatially correlated field given a geostatistical model by the description of the case site with the software named Groundwater Vistas 6. Defining Kriging to obtain the value of the field functions over the model domain on the basis of their values at measurement and pilot point locations (hydraulic conductivity), then we assign pilot points to the interpolated field which have been divided into 4

Hybrid Adaptive Flight Control with Model Inversion Adaptation

NASA Technical Reports Server (NTRS)

Nguyen, Nhan

2011-01-01

This study investigates a hybrid adaptive flight control method as a design possibility for a flight control system that can enable an effective adaptation strategy to deal with off-nominal flight conditions. The hybrid adaptive control blends both direct and indirect adaptive control in a model inversion flight control architecture. The blending of both direct and indirect adaptive control provides a much more flexible and effective adaptive flight control architecture than that with either direct or indirect adaptive control alone. The indirect adaptive control is used to update the model inversion controller by an on-line parameter estimation of uncertain plant dynamics based on two methods. The first parameter estimation method is an indirect adaptive law based on the Lyapunov theory, and the second method is a recursive least-squares indirect adaptive law. The model inversion controller is therefore made to adapt to changes in the plant dynamics due to uncertainty. As a result, the modeling error is reduced that directly leads to a decrease in the tracking error. In conjunction with the indirect adaptive control that updates the model inversion controller, a direct adaptive control is implemented as an augmented command to further reduce any residual tracking error that is not entirely eliminated by the indirect adaptive control.

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.

A Geophysical Inversion Model Enhancement Technique Based on the Blind Deconvolution

NASA Astrophysics Data System (ADS)

Zuo, B.; Hu, X.; Li, H.

2011-12-01

A model-enhancement technique is proposed to enhance the geophysical inversion model edges and details without introducing any additional information. Firstly, the theoretic correctness of the proposed geophysical inversion model-enhancement technique is discussed. An inversion MRM (model resolution matrix) convolution approximating PSF (Point Spread Function) method is designed to demonstrate the correctness of the deconvolution model enhancement method. Then, a total-variation regularization blind deconvolution geophysical inversion model-enhancement algorithm is proposed. In previous research, Oldenburg et al. demonstrate the connection between the PSF and the geophysical inverse solution. Alumbaugh et al. propose that more information could be provided by the PSF if we return to the idea of it behaving as an averaging or low pass filter. We consider the PSF as a low pass filter to enhance the inversion model basis on the theory of the PSF convolution approximation. Both the 1D linear and the 2D magnetotelluric inversion examples are used to analyze the validity of the theory and the algorithm. To prove the proposed PSF convolution approximation theory, the 1D linear inversion problem is considered. It shows the ratio of convolution approximation error is only 0.15%. The 2D synthetic model enhancement experiment is presented. After the deconvolution enhancement, the edges of the conductive prism and the resistive host become sharper, and the enhancement result is closer to the actual model than the original inversion model according the numerical statistic analysis. Moreover, the artifacts in the inversion model are suppressed. The overall precision of model increases 75%. All of the experiments show that the structure details and the numerical precision of inversion model are significantly improved, especially in the anomalous region. The correlation coefficient between the enhanced inversion model and the actual model are shown in Fig. 1. The figure

A model-assisted radio occultation data inversion method based on data ingestion into NeQuick

NASA Astrophysics Data System (ADS)

Shaikh, M. M.; Nava, B.; Kashcheyev, A.

2017-01-01

Inverse Abel transform is the most common method to invert radio occultation (RO) data in the ionosphere and it is based on the assumption of the spherical symmetry for the electron density distribution in the vicinity of an occultation event. It is understood that this 'spherical symmetry hypothesis' could fail, above all, in the presence of strong horizontal electron density gradients. As a consequence, in some cases wrong electron density profiles could be obtained. In this work, in order to incorporate the knowledge of horizontal gradients, we have suggested an inversion technique based on the adaption of the empirical ionospheric model, NeQuick2, to RO-derived TEC. The method relies on the minimization of a cost function involving experimental and model-derived TEC data to determine NeQuick2 input parameters (effective local ionization parameters) at specific locations and times. These parameters are then used to obtain the electron density profile along the tangent point (TP) positions associated with the relevant RO event using NeQuick2. The main focus of our research has been laid on the mitigation of spherical symmetry effects from RO data inversion without using external data such as data from global ionospheric maps (GIM). By using RO data from Constellation Observing System for Meteorology Ionosphere and Climate (FORMOSAT-3/COSMIC) mission and manually scaled peak density data from a network of ionosondes along Asian and American longitudinal sectors, we have obtained a global improvement of 5% with 7% in Asian longitudinal sector (considering the data used in this work), in the retrieval of peak electron density (NmF2) with model-assisted inversion as compared to the Abel inversion. Mean errors of NmF2 in Asian longitudinal sector are calculated to be much higher compared to American sector.

The New Method of Tsunami Source Reconstruction With r-Solution Inversion Method

NASA Astrophysics Data System (ADS)

Voronina, T. A.; Romanenko, A. A.

2016-12-01

Application of the r-solution method to reconstructing the initial tsunami waveform is discussed. This methodology is based on the inversion of remote measurements of water-level data. The wave propagation is considered within the scope of a linear shallow-water theory. The ill-posed inverse problem in question is regularized by means of a least square inversion using the truncated Singular Value Decomposition method. As a result of the numerical process, an r-solution is obtained. The method proposed allows one to control the instability of a numerical solution and to obtain an acceptable result in spite of ill posedness of the problem. Implementation of this methodology to reconstructing of the initial waveform to 2013 Solomon Islands tsunami validates the theoretical conclusion for synthetic data and a model tsunami source: the inversion result strongly depends on data noisiness, the azimuthal and temporal coverage of recording stations with respect to the source area. Furthermore, it is possible to make a preliminary selection of the most informative set of the available recording stations used in the inversion process.

Ground resistivity method and DCIP2D forward and inversion modelling to identify alteration at the Midwest uranium deposit, northern Saskatchewan, Canada

NASA Astrophysics Data System (ADS)

Long, Samuel R. M.; Smith, Richard S.; Hearst, Robert B.

2017-06-01

Resistivity methods are commonly used in mineral exploration to map lithology, structure, sulphides and alteration. In the Athabasca Basin, resistivity methods are used to detect alteration associated with uranium. At the Midwest deposit, there is an alteration zone in the Athabasca sandstones that is above a uraniferous conductive graphitic fault in the basement and below a conductive lake at surface. Previous geophysical work in this area has yielded resistivity sections that we feel are ambiguous in the area where the alteration is expected. Resolve® and TEMPEST sections yield an indistinct alteration zone, while two-dimensional (2D) inversions of the ground resistivity data show an equivocal smeared conductive feature in the expected location between the conductive graphite and the conductive lake. Forward modelling alone cannot identify features in the pseudosections that are clearly associated with alteration, as the section is dominated by the feature associated with the near-surface conductive lake; inverse modelling alone produces sections that are smeared and equivocal. We advocate an approach that uses a combination of forward and inverse modelling. We generate a forward model from a synthetic geoelectric section; this forward data is then inverse modelled and compared with the inverse model generated from the field data using the same inversion parameters. The synthetic geoelectric section is then adjusted until the synthetic inverse model closely matches the field inverse model. We found that this modelling process required a conductive alteration zone in the sandstone above the graphite, as removing the alteration zone from the sandstone created an inverse section very dissimilar to the inverse section derived from the field data. We therefore conclude that the resistivity method is able to identify conductive alteration at Midwest even though it is below a conductive lake and above a conductive graphitic fault. We also concluded that resistivity

Global inverse modeling of CH4 sources and sinks: an overview of methods

NASA Astrophysics Data System (ADS)

Houweling, Sander; Bergamaschi, Peter; Chevallier, Frederic; Heimann, Martin; Kaminski, Thomas; Krol, Maarten; Michalak, Anna M.; Patra, Prabir

2017-01-01

The aim of this paper is to present an overview of inverse modeling methods that have been developed over the years for estimating the global sources and sinks of CH4. It provides insight into how techniques and estimates have evolved over time and what the remaining shortcomings are. As such, it serves a didactical purpose of introducing apprentices to the field, but it also takes stock of developments so far and reflects on promising new directions. The main focus is on methodological aspects that are particularly relevant for CH4, such as its atmospheric oxidation, the use of methane isotopologues, and specific challenges in atmospheric transport modeling of CH4. The use of satellite retrievals receives special attention as it is an active field of methodological development, with special requirements on the sampling of the model and the treatment of data uncertainty. Regional scale flux estimation and attribution is still a grand challenge, which calls for new methods capable of combining information from multiple data streams of different measured parameters. A process model representation of sources and sinks in atmospheric transport inversion schemes allows the integrated use of such data. These new developments are needed not only to improve our understanding of the main processes driving the observed global trend but also to support international efforts to reduce greenhouse gas emissions.

Nonlinear adaptive inverse control via the unified model neural network

NASA Astrophysics Data System (ADS)

Jeng, Jin-Tsong; Lee, Tsu-Tian

1999-03-01

In this paper, we propose a new nonlinear adaptive inverse control via a unified model neural network. In order to overcome nonsystematic design and long training time in nonlinear adaptive inverse control, we propose the approximate transformable technique to obtain a Chebyshev Polynomials Based Unified Model (CPBUM) neural network for the feedforward/recurrent neural networks. It turns out that the proposed method can use less training time to get an inverse model. Finally, we apply this proposed method to control magnetic bearing system. The experimental results show that the proposed nonlinear adaptive inverse control architecture provides a greater flexibility and better performance in controlling magnetic bearing systems.

A Monte Carlo simulation based inverse propagation method for stochastic model updating

NASA Astrophysics Data System (ADS)

Bao, Nuo; Wang, Chunjie

2015-08-01

This paper presents an efficient stochastic model updating method based on statistical theory. Significant parameters have been selected implementing the F-test evaluation and design of experiments, and then the incomplete fourth-order polynomial response surface model (RSM) has been developed. Exploiting of the RSM combined with Monte Carlo simulation (MCS), reduces the calculation amount and the rapid random sampling becomes possible. The inverse uncertainty propagation is given by the equally weighted sum of mean and covariance matrix objective functions. The mean and covariance of parameters are estimated synchronously by minimizing the weighted objective function through hybrid of particle-swarm and Nelder-Mead simplex optimization method, thus the better correlation between simulation and test is achieved. Numerical examples of a three degree-of-freedom mass-spring system under different conditions and GARTEUR assembly structure validated the feasibility and effectiveness of the proposed method.

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

a method of gravity and seismic sequential inversion and its GPU implementation

NASA Astrophysics Data System (ADS)

Liu, G.; Meng, X.

2011-12-01

In this abstract, we introduce a gravity and seismic sequential inversion method to invert for density and velocity together. For the gravity inversion, we use an iterative method based on correlation imaging algorithm; for the seismic inversion, we use the full waveform inversion. The link between the density and velocity is an empirical formula called Gardner equation, for large volumes of data, we use the GPU to accelerate the computation. For the gravity inversion method , we introduce a method based on correlation imaging algorithm,it is also a interative method, first we calculate the correlation imaging of the observed gravity anomaly, it is some value between -1 and +1, then we multiply this value with a little density ,this value become the initial density model. We get a forward reuslt with this initial model and also calculate the correaltion imaging of the misfit of observed data and the forward data, also multiply the correaltion imaging result a little density and add it to the initial model, then do the same procedure above , at last ,we can get a inversion density model. For the seismic inveron method ,we use a mothod base on the linearity of acoustic wave equation written in the frequency domain,with a intial velociy model, we can get a good velocity result. In the sequential inversion of gravity and seismic , we need a link formula to convert between density and velocity ,in our method , we use the Gardner equation. Driven by the insatiable market demand for real time, high-definition 3D images, the programmable NVIDIA Graphic Processing Unit (GPU) as co-processor of CPU has been developed for high performance computing. Compute Unified Device Architecture (CUDA) is a parallel programming model and software environment provided by NVIDIA designed to overcome the challenge of using traditional general purpose GPU while maintaining a low learn curve for programmers familiar with standard programming languages such as C. In our inversion processing

Two-dimensional probabilistic inversion of plane-wave electromagnetic data: methodology, model constraints and joint inversion with electrical resistivity data

NASA Astrophysics Data System (ADS)

Rosas-Carbajal, Marina; Linde, Niklas; Kalscheuer, Thomas; Vrugt, Jasper A.

2014-03-01

Probabilistic inversion methods based on Markov chain Monte Carlo (MCMC) simulation are well suited to quantify parameter and model uncertainty of nonlinear inverse problems. Yet, application of such methods to CPU-intensive forward models can be a daunting task, particularly if the parameter space is high dimensional. Here, we present a 2-D pixel-based MCMC inversion of plane-wave electromagnetic (EM) data. Using synthetic data, we investigate how model parameter uncertainty depends on model structure constraints using different norms of the likelihood function and the model constraints, and study the added benefits of joint inversion of EM and electrical resistivity tomography (ERT) data. Our results demonstrate that model structure constraints are necessary to stabilize the MCMC inversion results of a highly discretized model. These constraints decrease model parameter uncertainty and facilitate model interpretation. A drawback is that these constraints may lead to posterior distributions that do not fully include the true underlying model, because some of its features exhibit a low sensitivity to the EM data, and hence are difficult to resolve. This problem can be partly mitigated if the plane-wave EM data is augmented with ERT observations. The hierarchical Bayesian inverse formulation introduced and used herein is able to successfully recover the probabilistic properties of the measurement data errors and a model regularization weight. Application of the proposed inversion methodology to field data from an aquifer demonstrates that the posterior mean model realization is very similar to that derived from a deterministic inversion with similar model constraints.

Bayesian Inversion of 2D Models from Airborne Transient EM Data

NASA Astrophysics Data System (ADS)

Blatter, D. B.; Key, K.; Ray, A.

2016-12-01

The inherent non-uniqueness in most geophysical inverse problems leads to an infinite number of Earth models that fit observed data to within an adequate tolerance. To resolve this ambiguity, traditional inversion methods based on optimization techniques such as the Gauss-Newton and conjugate gradient methods rely on an additional regularization constraint on the properties that an acceptable model can possess, such as having minimal roughness. While allowing such an inversion scheme to converge on a solution, regularization makes it difficult to estimate the uncertainty associated with the model parameters. This is because regularization biases the inversion process toward certain models that satisfy the regularization constraint and away from others that don't, even when both may suitably fit the data. By contrast, a Bayesian inversion framework aims to produce not a single `most acceptable' model but an estimate of the posterior likelihood of the model parameters, given the observed data. In this work, we develop a 2D Bayesian framework for the inversion of transient electromagnetic (TEM) data. Our method relies on a reversible-jump Markov Chain Monte Carlo (RJ-MCMC) Bayesian inverse method with parallel tempering. Previous gradient-based inversion work in this area used a spatially constrained scheme wherein individual (1D) soundings were inverted together and non-uniqueness was tackled by using lateral and vertical smoothness constraints. By contrast, our work uses a 2D model space of Voronoi cells whose parameterization (including number of cells) is fully data-driven. To make the problem work practically, we approximate the forward solution for each TEM sounding using a local 1D approximation where the model is obtained from the 2D model by retrieving a vertical profile through the Voronoi cells. The implicit parsimony of the Bayesian inversion process leads to the simplest models that adequately explain the data, obviating the need for explicit smoothness

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.

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

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.

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

ℓ1-Regularized full-waveform inversion with prior model information based on orthant-wise limited memory quasi-Newton method

NASA Astrophysics Data System (ADS)

Dai, Meng-Xue; Chen, Jing-Bo; Cao, Jian

2017-07-01

Full-waveform inversion (FWI) is an ill-posed optimization problem which is sensitive to noise and initial model. To alleviate the ill-posedness of the problem, regularization techniques are usually adopted. The ℓ1-norm penalty is a robust regularization method that preserves contrasts and edges. The Orthant-Wise Limited-Memory Quasi-Newton (OWL-QN) method extends the widely-used limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method to the ℓ1-regularized optimization problems and inherits the efficiency of L-BFGS. To take advantage of the ℓ1-regularized method and the prior model information obtained from sonic logs and geological information, we implement OWL-QN algorithm in ℓ1-regularized FWI with prior model information in this paper. Numerical experiments show that this method not only improve the inversion results but also has a strong anti-noise ability.

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

Lithological and Surface Geometry Joint Inversions Using Multi-Objective Global Optimization Methods

NASA Astrophysics Data System (ADS)

Lelièvre, Peter; Bijani, Rodrigo; Farquharson, Colin

2016-04-01

surfaces are set to a priori values. The inversion is tasked with calculating the geometry of the contact surfaces instead of some piecewise distribution of properties in a mesh. Again, no coupling measure is required and joint inversion is simplified. Both of these inverse problems involve high nonlinearity and discontinuous or non-obtainable derivatives. They can also involve the existence of multiple minima. Hence, one can not apply the standard descent-based local minimization methods used to solve typical minimum-structure inversions. Instead, we are applying Pareto multi-objective global optimization (PMOGO) methods, which 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. While there are definite advantages to PMOGO joint inversion approaches, the methods come with significantly increased computational requirements. We are researching various strategies to ameliorate these computational issues including parallelization and problem dimension reduction.

Inversion method applied to the rotation curves of galaxies

NASA Astrophysics Data System (ADS)

Márquez-Caicedo, L. A.; Lora-Clavijo, F. D.; Sanabria-Gómez, J. D.

2017-07-01

We used simulated annealing, Montecarlo and genetic algorithm methods for matching both numerical data of density and velocity profiles in some low surface brigthness galaxies with theoretical models of Boehmer-Harko, Navarro-Frenk-White and Pseudo Isothermal Profiles for galaxies with dark matter halos. We found that Navarro-Frenk-White model does not fit at all in contrast with the other two models which fit very well. Inversion methods have been widely used in various branches of science including astrophysics (Charbonneau 1995, ApJS, 101, 309). In this work we have used three different parametric inversion methods (MonteCarlo, Genetic Algorithm and Simmulated Annealing) in order to determine the best fit of the observed data of the density and velocity profiles of a set of low surface brigthness galaxies (De Block et al. 2001, ApJ, 122, 2396) with three models of galaxies containing dark mattter. The parameters adjusted by the inversion methods were the central density and a characteristic distance in the Boehmer-Harko BH (Boehmer & Harko 2007, JCAP, 6, 25), Navarro-Frenk-White NFW (Navarro et al. 2007, ApJ, 490, 493) and Pseudo Isothermal Profile PI (Robles & Matos 2012, MNRAS, 422, 282). The results obtained showed that the BH and PI Profile dark matter galaxies fit very well for both the density and the velocity profiles, in contrast the NFW model did not make good adjustments to the profiles in any analized galaxy.

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.

Inverse scattering theory: Inverse scattering series method for one dimensional non-compact support potential

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

Yao, Jie, E-mail: yjie2@uh.edu; Lesage, Anne-Cécile; Hussain, Fazle

2014-12-15

The reversion of the Born-Neumann series of the Lippmann-Schwinger equation is one of the standard ways to solve the inverse acoustic scattering problem. One limitation of the current inversion methods based on the reversion of the Born-Neumann series is that the velocity potential should have compact support. However, this assumption cannot be satisfied in certain cases, especially in seismic inversion. Based on the idea of distorted wave scattering, we explore an inverse scattering method for velocity potentials without compact support. The strategy is to decompose the actual medium as a known single interface reference medium, which has the same asymptoticmore » form as the actual medium and a perturbative scattering potential with compact support. After introducing the method to calculate the Green’s function for the known reference potential, the inverse scattering series and Volterra inverse scattering series are derived for the perturbative potential. Analytical and numerical examples demonstrate the feasibility and effectiveness of this method. Besides, to ensure stability of the numerical computation, the Lanczos averaging method is employed as a filter to reduce the Gibbs oscillations for the truncated discrete inverse Fourier transform of each order. Our method provides a rigorous mathematical framework for inverse acoustic scattering with a non-compact support velocity potential.« less

Sharp Boundary Inversion of 2D Magnetotelluric Data using Bayesian Method.

NASA Astrophysics Data System (ADS)

Zhou, S.; Huang, Q.

2017-12-01

Normally magnetotelluric(MT) inversion method cannot show the distribution of underground resistivity with clear boundary, even if there are obviously different blocks. Aiming to solve this problem, we develop a Bayesian structure to inverse 2D MT sharp boundary data, using boundary location and inside resistivity as the random variables. Firstly, we use other MT inversion results, like ModEM, to analyze the resistivity distribution roughly. Then, we select the suitable random variables and change its data format to traditional staggered grid parameters, which can be used to do finite difference forward part. Finally, we can shape the posterior probability density(PPD), which contains all the prior information and model-data correlation, by Markov Chain Monte Carlo(MCMC) sampling from prior distribution. The depth, resistivity and their uncertainty can be valued. It also works for sensibility estimation. We applied the method to a synthetic case, which composes two large abnormal blocks in a trivial background. We consider the boundary smooth and the near true model weight constrains that mimic joint inversion or constrained inversion, then we find that the model results a more precise and focused depth distribution. And we also test the inversion without constrains and find that the boundary could also be figured, though not as well. Both inversions have a good valuation of resistivity. The constrained result has a lower root mean square than ModEM inversion result. The data sensibility obtained via PPD shows that the resistivity is the most sensible, center depth comes second and both sides are the worst.

Inversion methods for interpretation of asteroid lightcurves

NASA Technical Reports Server (NTRS)

Kaasalainen, Mikko; Lamberg, L.; Lumme, K.

1992-01-01

We have developed methods of inversion that can be used in the determination of the three-dimensional shape or the albedo distribution of the surface of a body from disk-integrated photometry, assuming the shape to be strictly convex. In addition to the theory of inversion methods, we have studied the practical aspects of the inversion problem and applied our methods to lightcurve data of 39 Laetitia and 16 Psyche.

Inverse Monte Carlo method in a multilayered tissue model for diffuse reflectance spectroscopy

NASA Astrophysics Data System (ADS)

Fredriksson, Ingemar; Larsson, Marcus; Strömberg, Tomas

2012-04-01

Model based data analysis of diffuse reflectance spectroscopy data enables the estimation of optical and structural tissue parameters. The aim of this study was to present an inverse Monte Carlo method based on spectra from two source-detector distances (0.4 and 1.2 mm), using a multilayered tissue model. The tissue model variables include geometrical properties, light scattering properties, tissue chromophores such as melanin and hemoglobin, oxygen saturation and average vessel diameter. The method utilizes a small set of presimulated Monte Carlo data for combinations of different levels of epidermal thickness and tissue scattering. The path length distributions in the different layers are stored and the effect of the other parameters is added in the post-processing. The accuracy of the method was evaluated using Monte Carlo simulations of tissue-like models containing discrete blood vessels, evaluating blood tissue fraction and oxygenation. It was also compared to a homogeneous model. The multilayer model performed better than the homogeneous model and all tissue parameters significantly improved spectral fitting. Recorded in vivo spectra were fitted well at both distances, which we previously found was not possible with a homogeneous model. No absolute intensity calibration is needed and the algorithm is fast enough for real-time processing.

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

3D CSEM inversion based on goal-oriented adaptive finite element method

NASA Astrophysics Data System (ADS)

Zhang, Y.; Key, K.

2016-12-01

We present a parallel 3D frequency domain controlled-source electromagnetic inversion code name MARE3DEM. Non-linear inversion of observed data is performed with the Occam variant of regularized Gauss-Newton optimization. The forward operator is based on the goal-oriented finite element method that efficiently calculates the responses and sensitivity kernels in parallel using a data decomposition scheme where independent modeling tasks contain different frequencies and subsets of the transmitters and receivers. To accommodate complex 3D conductivity variation with high flexibility and precision, we adopt the dual-grid approach where the forward mesh conforms to the inversion parameter grid and is adaptively refined until the forward solution converges to the desired accuracy. This dual-grid approach is memory efficient, since the inverse parameter grid remains independent from fine meshing generated around the transmitter and receivers by the adaptive finite element method. Besides, the unstructured inverse mesh efficiently handles multiple scale structures and allows for fine-scale model parameters within the region of interest. Our mesh generation engine keeps track of the refinement hierarchy so that the map of conductivity and sensitivity kernel between the forward and inverse mesh is retained. We employ the adjoint-reciprocity method to calculate the sensitivity kernels which establish a linear relationship between changes in the conductivity model and changes in the modeled responses. Our code uses a direcy solver for the linear systems, so the adjoint problem is efficiently computed by re-using the factorization from the primary problem. Further computational efficiency and scalability is obtained in the regularized Gauss-Newton portion of the inversion using parallel dense matrix-matrix multiplication and matrix factorization routines implemented with the ScaLAPACK library. We show the scalability, reliability and the potential of the algorithm to deal with

Finite-fault source inversion using adjoint methods in 3D heterogeneous media

NASA Astrophysics Data System (ADS)

Somala, Surendra Nadh; Ampuero, Jean-Paul; Lapusta, Nadia

2018-04-01

Accounting for lateral heterogeneities in the 3D velocity structure of the crust is known to improve earthquake source inversion, compared to results based on 1D velocity models which are routinely assumed to derive finite-fault slip models. The conventional approach to include known 3D heterogeneity in source inversion involves pre-computing 3D Green's functions, which requires a number of 3D wave propagation simulations proportional to the number of stations or to the number of fault cells. The computational cost of such an approach is prohibitive for the dense datasets that could be provided by future earthquake observation systems. Here, we propose an adjoint-based optimization technique to invert for the spatio-temporal evolution of slip velocity. The approach does not require pre-computed Green's functions. The adjoint method provides the gradient of the cost function, which is used to improve the model iteratively employing an iterative gradient-based minimization method. The adjoint approach is shown to be computationally more efficient than the conventional approach based on pre-computed Green's functions in a broad range of situations. We consider data up to 1 Hz from a Haskell source scenario (a steady pulse-like rupture) on a vertical strike-slip fault embedded in an elastic 3D heterogeneous velocity model. The velocity model comprises a uniform background and a 3D stochastic perturbation with the von Karman correlation function. Source inversions based on the 3D velocity model are performed for two different station configurations, a dense and a sparse network with 1 km and 20 km station spacing, respectively. These reference inversions show that our inversion scheme adequately retrieves the rise time when the velocity model is exactly known, and illustrates how dense coverage improves the inference of peak slip velocities. We investigate the effects of uncertainties in the velocity model by performing source inversions based on an incorrect

Finite-fault source inversion using adjoint methods in 3-D heterogeneous media

NASA Astrophysics Data System (ADS)

Somala, Surendra Nadh; Ampuero, Jean-Paul; Lapusta, Nadia

2018-07-01

Accounting for lateral heterogeneities in the 3-D velocity structure of the crust is known to improve earthquake source inversion, compared to results based on 1-D velocity models which are routinely assumed to derive finite-fault slip models. The conventional approach to include known 3-D heterogeneity in source inversion involves pre-computing 3-D Green's functions, which requires a number of 3-D wave propagation simulations proportional to the number of stations or to the number of fault cells. The computational cost of such an approach is prohibitive for the dense data sets that could be provided by future earthquake observation systems. Here, we propose an adjoint-based optimization technique to invert for the spatio-temporal evolution of slip velocity. The approach does not require pre-computed Green's functions. The adjoint method provides the gradient of the cost function, which is used to improve the model iteratively employing an iterative gradient-based minimization method. The adjoint approach is shown to be computationally more efficient than the conventional approach based on pre-computed Green's functions in a broad range of situations. We consider data up to 1 Hz from a Haskell source scenario (a steady pulse-like rupture) on a vertical strike-slip fault embedded in an elastic 3-D heterogeneous velocity model. The velocity model comprises a uniform background and a 3-D stochastic perturbation with the von Karman correlation function. Source inversions based on the 3-D velocity model are performed for two different station configurations, a dense and a sparse network with 1 and 20 km station spacing, respectively. These reference inversions show that our inversion scheme adequately retrieves the rise time when the velocity model is exactly known, and illustrates how dense coverage improves the inference of peak-slip velocities. We investigate the effects of uncertainties in the velocity model by performing source inversions based on an incorrect

Two Dimensional Finite Element Based Magnetotelluric Inversion using Singular Value Decomposition Method on Transverse Electric Mode

NASA Astrophysics Data System (ADS)

Tjong, Tiffany; Yihaa’ Roodhiyah, Lisa; Nurhasan; Sutarno, Doddy

2018-04-01

In this work, an inversion scheme was performed using a vector finite element (VFE) based 2-D magnetotelluric (MT) forward modelling. We use an inversion scheme with Singular value decomposition (SVD) method toimprove the accuracy of MT inversion.The inversion scheme was applied to transverse electric (TE) mode of MT. SVD method was used in this inversion to decompose the Jacobian matrices. Singular values which obtained from the decomposition process were analyzed. This enabled us to determine the importance of data and therefore to define a threshold for truncation process. The truncation of singular value in inversion processcould improve the resulted model.

Using Inverse Problem Methods with Surveillance Data in Pneumococcal Vaccination

PubMed Central

Sutton, Karyn L.; Banks, H. T.; Castillo-Chavez, Carlos

2010-01-01

The design and evaluation of epidemiological control strategies is central to public health policy. While inverse problem methods are routinely used in many applications, this remains an area in which their use is relatively rare, although their potential impact is great. We describe methods particularly relevant to epidemiological modeling at the population level. These methods are then applied to the study of pneumococcal vaccination strategies as a relevant example which poses many challenges common to other infectious diseases. We demonstrate that relevant yet typically unknown parameters may be estimated, and show that a calibrated model may used to assess implemented vaccine policies through the estimation of parameters if vaccine history is recorded along with infection and colonization information. Finally, we show how one might determine an appropriate level of refinement or aggregation in the age-structured model given age-stratified observations. These results illustrate ways in which the collection and analysis of surveillance data can be improved using inverse problem methods. PMID:20209093

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

3-D Magnetotelluric Forward Modeling And Inversion Incorporating Topography By Using Vector Finite-Element Method Combined With Divergence Corrections Based On The Magnetic Field (VFEH++)

NASA Astrophysics Data System (ADS)

Shi, X.; Utada, H.; Jiaying, W.

2009-12-01

The vector finite-element method combined with divergence corrections based on the magnetic field H, referred to as VFEH++ method, is developed to simulate the magnetotelluric (MT) responses of 3-D conductivity models. The advantages of the new VFEH++ method are the use of edge-elements to eliminate the vector parasites and the divergence corrections to explicitly guarantee the divergence-free conditions in the whole modeling domain. 3-D MT topographic responses are modeling using the new VFEH++ method, and are compared with those calculated by other numerical methods. The results show that MT responses can be modeled highly accurate using the VFEH+ +method. The VFEH++ algorithm is also employed for the 3-D MT data inversion incorporating topography. The 3-D MT inverse problem is formulated as a minimization problem of the regularized misfit function. In order to avoid the huge memory requirement and very long time for computing the Jacobian sensitivity matrix for Gauss-Newton method, we employ the conjugate gradient (CG) approach to solve the inversion equation. In each iteration of CG algorithm, the cost computation is the product of the Jacobian sensitivity matrix with a model vector x or its transpose with a data vector y, which can be transformed into two pseudo-forwarding modeling. This avoids the full explicitly Jacobian matrix calculation and storage which leads to considerable savings in the memory required by the inversion program in PC computer. The performance of CG algorithm will be illustrated by several typical 3-D models with horizontal earth surface and topographic surfaces. The results show that the VFEH++ and CG algorithms can be effectively employed to 3-D MT field data inversion.

Calculation method of water injection forward modeling and inversion process in oilfield water injection network

NASA Astrophysics Data System (ADS)

Liu, Long; Liu, Wei

2018-04-01

A forward modeling and inversion algorithm is adopted in order to determine the water injection plan in the oilfield water injection network. The main idea of the algorithm is shown as follows: firstly, the oilfield water injection network is inversely calculated. The pumping station demand flow is calculated. Then, forward modeling calculation is carried out for judging whether all water injection wells meet the requirements of injection allocation or not. If all water injection wells meet the requirements of injection allocation, calculation is stopped, otherwise the demand injection allocation flow rate of certain step size is reduced aiming at water injection wells which do not meet requirements, and next iterative operation is started. It is not necessary to list the algorithm into water injection network system algorithm, which can be realized easily. Iterative method is used, which is suitable for computer programming. Experimental result shows that the algorithm is fast and accurate.

2D Inversion of Transient Electromagnetic Method (TEM)

NASA Astrophysics Data System (ADS)

Bortolozo, Cassiano Antonio; Luís Porsani, Jorge; Acácio Monteiro dos Santos, Fernando

2017-04-01

A new methodology was developed for 2D inversion of Transient Electromagnetic Method (TEM). The methodology consists in the elaboration of a set of routines in Matlab code for modeling and inversion of TEM data and the determination of the most efficient field array for the problem. In this research, the 2D TEM modeling uses the finite differences discretization. To solve the inversion problem, were applied an algorithm based on Marquardt technique, also known as Ridge Regression. The algorithm is stable and efficient and it is widely used in geoelectrical inversion problems. The main advantage of 1D survey is the rapid data acquisition in a large area, but in regions with two-dimensional structures or that need more details, is essential to use two-dimensional interpretation methodologies. For an efficient field acquisition we used in an innovative form the fixed-loop array, with a square transmitter loop (200m x 200m) and 25m spacing between the sounding points. The TEM surveys were conducted only inside the transmitter loop, in order to not deal with negative apparent resistivity values. Although it is possible to model the negative values, it makes the inversion convergence more difficult. Therefore the methodology described above has been developed in order to achieve maximum optimization of data acquisition. Since it is necessary only one transmitter loop disposition in the surface for each series of soundings inside the loop. The algorithms were tested with synthetic data and the results were essential to the interpretation of the results with real data and will be useful in future situations. With the inversion of the real data acquired over the Paraná Sedimentary Basin (PSB) was successful realized a 2D TEM inversion. The results indicate a robust geoelectrical characterization for the sedimentary and crystalline aquifers in the PSB. Therefore, using a new and relevant approach for 2D TEM inversion, this research effectively contributed to map the most

An Improved 3D Joint Inversion Method of Potential Field Data Using Cross-Gradient Constraint and LSQR Method

NASA Astrophysics Data System (ADS)

Joulidehsar, Farshad; Moradzadeh, Ali; Doulati Ardejani, Faramarz

2018-06-01

The joint interpretation of two sets of geophysical data related to the same source is an appropriate method for decreasing non-uniqueness of the resulting models during inversion process. Among the available methods, a method based on using cross-gradient constraint combines two datasets is an efficient approach. This method, however, is time-consuming for 3D inversion and cannot provide an exact assessment of situation and extension of anomaly of interest. In this paper, the first attempt is to speed up the required calculation by substituting singular value decomposition by least-squares QR method to solve the large-scale kernel matrix of 3D inversion, more rapidly. Furthermore, to improve the accuracy of resulting models, a combination of depth-weighing matrix and compacted constraint, as automatic selection covariance of initial parameters, is used in the proposed inversion algorithm. This algorithm was developed in Matlab environment and first implemented on synthetic data. The 3D joint inversion of synthetic gravity and magnetic data shows a noticeable improvement in the results and increases the efficiency of algorithm for large-scale problems. Additionally, a real gravity and magnetic dataset of Jalalabad mine, in southeast of Iran was tested. The obtained results by the improved joint 3D inversion of cross-gradient along with compacted constraint showed a mineralised zone in depth interval of about 110-300 m which is in good agreement with the available drilling data. This is also a further confirmation on the accuracy and progress of the improved inversion algorithm.

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.

High effective inverse dynamics modelling for dual-arm robot

NASA Astrophysics Data System (ADS)

Shen, Haoyu; Liu, Yanli; Wu, Hongtao

2018-05-01

To deal with the problem of inverse dynamics modelling for dual arm robot, a recursive inverse dynamics modelling method based on decoupled natural orthogonal complement is presented. In this model, the concepts and methods of Decoupled Natural Orthogonal Complement matrices are used to eliminate the constraint forces in the Newton-Euler kinematic equations, and the screws is used to express the kinematic and dynamics variables. On this basis, the paper has developed a special simulation program with symbol software of Mathematica and conducted a simulation research on the a dual-arm robot. Simulation results show that the proposed method based on decoupled natural orthogonal complement can save an enormous amount of CPU time that was spent in computing compared with the recursive Newton-Euler kinematic equations and the results is correct and reasonable, which can verify the reliability and efficiency of the method.

Constructing inverse probability weights for continuous exposures: a comparison of methods.

PubMed

Naimi, Ashley I; Moodie, Erica E M; Auger, Nathalie; Kaufman, Jay S

2014-03-01

Inverse probability-weighted marginal structural models with binary exposures are common in epidemiology. Constructing inverse probability weights for a continuous exposure can be complicated by the presence of outliers, and the need to identify a parametric form for the exposure and account for nonconstant exposure variance. We explored the performance of various methods to construct inverse probability weights for continuous exposures using Monte Carlo simulation. We generated two continuous exposures and binary outcomes using data sampled from a large empirical cohort. The first exposure followed a normal distribution with homoscedastic variance. The second exposure followed a contaminated Poisson distribution, with heteroscedastic variance equal to the conditional mean. We assessed six methods to construct inverse probability weights using: a normal distribution, a normal distribution with heteroscedastic variance, a truncated normal distribution with heteroscedastic variance, a gamma distribution, a t distribution (1, 3, and 5 degrees of freedom), and a quantile binning approach (based on 10, 15, and 20 exposure categories). We estimated the marginal odds ratio for a single-unit increase in each simulated exposure in a regression model weighted by the inverse probability weights constructed using each approach, and then computed the bias and mean squared error for each method. For the homoscedastic exposure, the standard normal, gamma, and quantile binning approaches performed best. For the heteroscedastic exposure, the quantile binning, gamma, and heteroscedastic normal approaches performed best. Our results suggest that the quantile binning approach is a simple and versatile way to construct inverse probability weights for continuous exposures.

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

Intelligent inversion method for pre-stack seismic big data based on MapReduce

NASA Astrophysics Data System (ADS)

Yan, Xuesong; Zhu, Zhixin; Wu, Qinghua

2018-01-01

Seismic exploration is a method of oil exploration that uses seismic information; that is, according to the inversion of seismic information, the useful information of the reservoir parameters can be obtained to carry out exploration effectively. Pre-stack data are characterised by a large amount of data, abundant information, and so on, and according to its inversion, the abundant information of the reservoir parameters can be obtained. Owing to the large amount of pre-stack seismic data, existing single-machine environments have not been able to meet the computational needs of the huge amount of data; thus, the development of a method with a high efficiency and the speed to solve the inversion problem of pre-stack seismic data is urgently needed. The optimisation of the elastic parameters by using a genetic algorithm easily falls into a local optimum, which results in a non-obvious inversion effect, especially for the optimisation effect of the density. Therefore, an intelligent optimisation algorithm is proposed in this paper and used for the elastic parameter inversion of pre-stack seismic data. This algorithm improves the population initialisation strategy by using the Gardner formula and the genetic operation of the algorithm, and the improved algorithm obtains better inversion results when carrying out a model test with logging data. All of the elastic parameters obtained by inversion and the logging curve of theoretical model are fitted well, which effectively improves the inversion precision of the density. This algorithm was implemented with a MapReduce model to solve the seismic big data inversion problem. The experimental results show that the parallel model can effectively reduce the running time of the algorithm.

Part-to-itself model inversion in process compensated resonance testing

NASA Astrophysics Data System (ADS)

Mayes, Alexander; Jauriqui, Leanne; Biedermann, Eric; Heffernan, Julieanne; Livings, Richard; Aldrin, John C.; Goodlet, Brent; Mazdiyasni, Siamack

2018-04-01

Process Compensated Resonance Testing (PCRT) is a non-destructive evaluation (NDE) method involving the collection and analysis of a part's resonance spectrum to characterize its material or damage state. Prior work used the finite element method (FEM) to develop forward modeling and model inversion techniques. In many cases, the inversion problem can become confounded by multiple parameters having similar effects on a part's resonance frequencies. To reduce the influence of confounding parameters and isolate the change in a part (e.g., creep), a part-to-itself (PTI) approach can be taken. A PTI approach involves inverting only the change in resonance frequencies from the before and after states of a part. This approach reduces the possible inversion parameters to only those that change in response to in-service loads and damage mechanisms. To evaluate the effectiveness of using a PTI inversion approach, creep strain and material properties were estimated in virtual and real samples using FEM inversion. Virtual and real dog bone samples composed of nickel-based superalloy Mar-M-247 were examined. Virtual samples were modeled with typically observed variations in material properties and dimensions. Creep modeling was verified with the collected resonance spectra from an incrementally crept physical sample. All samples were inverted against a model space that allowed for change in the creep damage state and the material properties but was blind to initial part dimensions. Results quantified the capabilities of PTI inversion in evaluating creep strain and material properties, as well as its sensitivity to confounding initial dimensions.

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.

Stochastic seismic inversion based on an improved local gradual deformation method

NASA Astrophysics Data System (ADS)

Yang, Xiuwei; Zhu, Peimin

2017-12-01

A new stochastic seismic inversion method based on the local gradual deformation method is proposed, which can incorporate seismic data, well data, geology and their spatial correlations into the inversion process. Geological information, such as sedimentary facies and structures, could provide significant a priori information to constrain an inversion and arrive at reasonable solutions. The local a priori conditional cumulative distributions at each node of model to be inverted are first established by indicator cokriging, which integrates well data as hard data and geological information as soft data. Probability field simulation is used to simulate different realizations consistent with the spatial correlations and local conditional cumulative distributions. The corresponding probability field is generated by the fast Fourier transform moving average method. Then, optimization is performed to match the seismic data via an improved local gradual deformation method. Two improved strategies are proposed to be suitable for seismic inversion. The first strategy is that we select and update local areas of bad fitting between synthetic seismic data and real seismic data. The second one is that we divide each seismic trace into several parts and obtain the optimal parameters for each part individually. The applications to a synthetic example and a real case study demonstrate that our approach can effectively find fine-scale acoustic impedance models and provide uncertainty estimations.

A sparse reconstruction method for the estimation of multi-resolution emission fields via atmospheric inversion

DOE PAGES

Ray, J.; Lee, J.; Yadav, V.; ...

2015-04-29

Atmospheric inversions are frequently used to estimate fluxes of atmospheric greenhouse gases (e.g., biospheric CO 2 flux fields) at Earth's surface. These inversions typically assume that flux departures from a prior model are spatially smoothly varying, which are then modeled using a multi-variate Gaussian. When the field being estimated is spatially rough, multi-variate Gaussian models are difficult to construct and a wavelet-based field model may be more suitable. Unfortunately, such models are very high dimensional and are most conveniently used when the estimation method can simultaneously perform data-driven model simplification (removal of model parameters that cannot be reliably estimated) andmore » fitting. Such sparse reconstruction methods are typically not used in atmospheric inversions. In this work, we devise a sparse reconstruction method, and illustrate it in an idealized atmospheric inversion problem for the estimation of fossil fuel CO 2 (ffCO 2) emissions in the lower 48 states of the USA. Our new method is based on stagewise orthogonal matching pursuit (StOMP), a method used to reconstruct compressively sensed images. Our adaptations bestow three properties to the sparse reconstruction procedure which are useful in atmospheric inversions. We have modified StOMP to incorporate prior information on the emission field being estimated and to enforce non-negativity on the estimated field. Finally, though based on wavelets, our method allows for the estimation of fields in non-rectangular geometries, e.g., emission fields inside geographical and political boundaries. Our idealized inversions use a recently developed multi-resolution (i.e., wavelet-based) random field model developed for ffCO 2 emissions and synthetic observations of ffCO 2 concentrations from a limited set of measurement sites. We find that our method for limiting the estimated field within an irregularly shaped region is about a factor of 10 faster than conventional approaches. It

A sparse reconstruction method for the estimation of multi-resolution emission fields via atmospheric inversion

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

Ray, J.; Lee, J.; Yadav, V.

Atmospheric inversions are frequently used to estimate fluxes of atmospheric greenhouse gases (e.g., biospheric CO 2 flux fields) at Earth's surface. These inversions typically assume that flux departures from a prior model are spatially smoothly varying, which are then modeled using a multi-variate Gaussian. When the field being estimated is spatially rough, multi-variate Gaussian models are difficult to construct and a wavelet-based field model may be more suitable. Unfortunately, such models are very high dimensional and are most conveniently used when the estimation method can simultaneously perform data-driven model simplification (removal of model parameters that cannot be reliably estimated) andmore » fitting. Such sparse reconstruction methods are typically not used in atmospheric inversions. In this work, we devise a sparse reconstruction method, and illustrate it in an idealized atmospheric inversion problem for the estimation of fossil fuel CO 2 (ffCO 2) emissions in the lower 48 states of the USA. Our new method is based on stagewise orthogonal matching pursuit (StOMP), a method used to reconstruct compressively sensed images. Our adaptations bestow three properties to the sparse reconstruction procedure which are useful in atmospheric inversions. We have modified StOMP to incorporate prior information on the emission field being estimated and to enforce non-negativity on the estimated field. Finally, though based on wavelets, our method allows for the estimation of fields in non-rectangular geometries, e.g., emission fields inside geographical and political boundaries. Our idealized inversions use a recently developed multi-resolution (i.e., wavelet-based) random field model developed for ffCO 2 emissions and synthetic observations of ffCO 2 concentrations from a limited set of measurement sites. We find that our method for limiting the estimated field within an irregularly shaped region is about a factor of 10 faster than conventional approaches. It

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.

pyGIMLi: An open-source library for modelling and inversion in geophysics

NASA Astrophysics Data System (ADS)

Rücker, Carsten; Günther, Thomas; Wagner, Florian M.

2017-12-01

Many tasks in applied geosciences cannot be solved by single measurements, but require the integration of geophysical, geotechnical and hydrological methods. Numerical simulation techniques are essential both for planning and interpretation, as well as for the process understanding of modern geophysical methods. These trends encourage open, simple, and modern software architectures aiming at a uniform interface for interdisciplinary and flexible modelling and inversion approaches. We present pyGIMLi (Python Library for Inversion and Modelling in Geophysics), an open-source framework that provides tools for modelling and inversion of various geophysical but also hydrological methods. The modelling component supplies discretization management and the numerical basis for finite-element and finite-volume solvers in 1D, 2D and 3D on arbitrarily structured meshes. The generalized inversion framework solves the minimization problem with a Gauss-Newton algorithm for any physical forward operator and provides opportunities for uncertainty and resolution analyses. More general requirements, such as flexible regularization strategies, time-lapse processing and different sorts of coupling individual methods are provided independently of the actual methods used. The usage of pyGIMLi is first demonstrated by solving the steady-state heat equation, followed by a demonstration of more complex capabilities for the combination of different geophysical data sets. A fully coupled hydrogeophysical inversion of electrical resistivity tomography (ERT) data of a simulated tracer experiment is presented that allows to directly reconstruct the underlying hydraulic conductivity distribution of the aquifer. Another example demonstrates the improvement of jointly inverting ERT and ultrasonic data with respect to saturation by a new approach that incorporates petrophysical relations in the inversion. Potential applications of the presented framework are manifold and include time

Efficient Stochastic Inversion Using Adjoint Models and Kernel-PCA

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

Thimmisetty, Charanraj A.; Zhao, Wenju; Chen, Xiao

2017-10-18

Performing stochastic inversion on a computationally expensive forward simulation model with a high-dimensional uncertain parameter space (e.g. a spatial random field) is computationally prohibitive even when gradient information can be computed efficiently. Moreover, the ‘nonlinear’ mapping from parameters to observables generally gives rise to non-Gaussian posteriors even with Gaussian priors, thus hampering the use of efficient inversion algorithms designed for models with Gaussian assumptions. In this paper, we propose a novel Bayesian stochastic inversion methodology, which is characterized by a tight coupling between the gradient-based Langevin Markov Chain Monte Carlo (LMCMC) method and a kernel principal component analysis (KPCA). Thismore » approach addresses the ‘curse-of-dimensionality’ via KPCA to identify a low-dimensional feature space within the high-dimensional and nonlinearly correlated parameter space. In addition, non-Gaussian posterior distributions are estimated via an efficient LMCMC method on the projected low-dimensional feature space. We will demonstrate this computational framework by integrating and adapting our recent data-driven statistics-on-manifolds constructions and reduction-through-projection techniques to a linear elasticity model.« less

[Study of inversion and classification of particle size distribution under dependent model algorithm].

PubMed

Sun, Xiao-Gang; Tang, Hong; Yuan, Gui-Bin

2008-05-01

For the total light scattering particle sizing technique, an inversion and classification method was proposed with the dependent model algorithm. The measured particle system was inversed simultaneously by different particle distribution functions whose mathematic model was known in advance, and then classified according to the inversion errors. The simulation experiments illustrated that it is feasible to use the inversion errors to determine the particle size distribution. The particle size distribution function was obtained accurately at only three wavelengths in the visible light range with the genetic algorithm, and the inversion results were steady and reliable, which decreased the number of multi wavelengths to the greatest extent and increased the selectivity of light source. The single peak distribution inversion error was less than 5% and the bimodal distribution inversion error was less than 10% when 5% stochastic noise was put in the transmission extinction measurement values at two wavelengths. The running time of this method was less than 2 s. The method has advantages of simplicity, rapidity, and suitability for on-line particle size measurement.

Inverse methods-based estimation of plate coupling in a plate motion model governed by mantle flow

NASA Astrophysics Data System (ADS)

Ratnaswamy, V.; Stadler, G.; Gurnis, M.

2013-12-01

Plate motion is primarily controlled by buoyancy (slab pull) which occurs at convergent plate margins where oceanic plates undergo deformation near the seismogenic zone. Yielding within subducting plates, lateral variations in viscosity, and the strength of seismic coupling between plate margins likely have an important control on plate motion. Here, we wish to infer the inter-plate coupling for different subduction zones, and develop a method for inferring it as a PDE-constrained optimization problem, where the cost functional is the misfit in plate velocities and is constrained by the nonlinear Stokes equation. The inverse models have well resolved slabs, plates, and plate margins in addition to a power law rheology with yielding in the upper mantle. Additionally, a Newton method is used to solve the nonlinear Stokes equation with viscosity bounds. We infer plate boundary strength using an inexact Gauss-Newton method with line search for backtracking. Each inverse model is applied to two simple 2-D scenarios (each with three subduction zones), one with back-arc spreading and one without. For each case we examine the sensitivity of the inversion to the amount of surface velocity used: 1) full surface velocity data and 2) surface velocity data simplified using a single scalar average (2-D equivalent to an Euler pole) for each plate. We can recover plate boundary strength in each case, even in the presence of highly nonlinear flow with extreme variations in viscosity. Additionally, we ascribe an uncertainty in each plate's velocity and perform an uncertainty quantification (UQ) through the Hessian of the misfit in plate velocities. We find that as plate boundaries become strongly coupled, the uncertainty in the inferred plate boundary strength decreases. For very weak, uncoupled subduction zones, the uncertainty of inferred plate margin strength increases since there is little sensitivity between plate margin strength and plate velocity. This result is significant

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).

Multiple estimation channel decoupling and optimization method based on inverse system

NASA Astrophysics Data System (ADS)

Wu, Peng; Mu, Rongjun; Zhang, Xin; Deng, Yanpeng

2018-03-01

This paper addressed the intelligent autonomous navigation request of intelligent deformation missile, based on the intelligent deformation missile dynamics and kinematics modeling, navigation subsystem solution method and error modeling, and then focuses on the corresponding data fusion and decision fusion technology, decouples the sensitive channel of the filter input through the inverse system of design dynamics to reduce the influence of sudden change of the measurement information on the filter input. Then carrying out a series of simulation experiments, which verified the feasibility of the inverse system decoupling algorithm effectiveness.

2.5D complex resistivity modeling and inversion using unstructured grids

NASA Astrophysics Data System (ADS)

Xu, Kaijun; Sun, Jie

2016-04-01

The characteristic of complex resistivity on rock and ore has been recognized by people for a long time. Generally we have used the Cole-Cole Model(CCM) to describe complex resistivity. It has been proved that the electrical anomaly of geologic body can be quantitative estimated by CCM parameters such as direct resistivity(ρ0), chargeability(m), time constant(τ) and frequency dependence(c). Thus it is very important to obtain the complex parameters of geologic body. It is difficult to approximate complex structures and terrain using traditional rectangular grid. In order to enhance the numerical accuracy and rationality of modeling and inversion, we use an adaptive finite-element algorithm for forward modeling of the frequency-domain 2.5D complex resistivity and implement the conjugate gradient algorithm in the inversion of 2.5D complex resistivity. An adaptive finite element method is applied for solving the 2.5D complex resistivity forward modeling of horizontal electric dipole source. First of all, the CCM is introduced into the Maxwell's equations to calculate the complex resistivity electromagnetic fields. Next, the pseudo delta function is used to distribute electric dipole source. Then the electromagnetic fields can be expressed in terms of the primary fields caused by layered structure and the secondary fields caused by inhomogeneities anomalous conductivity. At last, we calculated the electromagnetic fields response of complex geoelectric structures such as anticline, syncline, fault. The modeling results show that adaptive finite-element methods can automatically improve mesh generation and simulate complex geoelectric models using unstructured grids. The 2.5D complex resistivity invertion is implemented based the conjugate gradient algorithm.The conjugate gradient algorithm doesn't need to compute the sensitivity matrix but directly computes the sensitivity matrix or its transpose multiplying vector. In addition, the inversion target zones are

A comparison of different radiative transfer model inversion methods for canopy water content retrieval

NASA Astrophysics Data System (ADS)

Boren, E. J.; Boschetti, L.; Johnson, D.

2016-12-01

With near-future droughts predicted to become both more frequent and more intense (Allen et al. 2015, Diffenbaugh et al. 2015), the estimation of satellite-derived vegetation water content would benefit a wide range of environmental applications including agricultural, vegetation, and fire risk monitoring. No vegetation water content thematic product is currently available (Yebra et al. 2013), but the successful launch of the Landsat 8 OLI and Sentinel 2A satellites, and the forthcoming Sentinel 2B, provide the opportunity for monitoring biophysical variables at a scale (10-30m) and temporal resolution (5 days) needed by most applications. Radiative transfer models (RTM) use a set of biophysical parameters to produce an estimated spectral response and - when used in inverse mode - provide a way to use satellite spectral data to estimate vegetation biophysical parameters, including water content (Zarco-Tejada et al. 2003). Using the coupled leaf and canopy level model PROSAIL5, and Landsat 8 OLI and Sentinel 2A MSI optical satellite data, the present research compares the results of three model inversion techniques: iterative optimization (OPT), look-up table (LUT), and artificial neural network (ANN) training. Ancillary biophysical data, needed for constraining the inversion process, were collected from various crop species grown in a controlled setting and under different water stress conditions. The measurements included fresh weight, dry weight, leaf area, and spectral leaf transmittance and reflectance in the 350-2500 nm range. Plot-level data, collected coincidently with satellite overpasses during three summer field campaigns in northern Idaho (2014 to 2016), are used to evaluate the results of the model inversion. Field measurements included fresh weight, dry weight, leaf area index, plant height, and top of canopy reflectance in the 350-2500 nm range. The results of the model inversion intercomparison exercised are used to characterize the uncertainties of

A matrix-inversion method for gamma-source mapping from gamma-count data

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

Adsley, Ian; Burgess, Claire; Bull, Richard K

In a previous paper it was proposed that a simple matrix inversion method could be used to extract source distributions from gamma-count maps, using simple models to calculate the response matrix. The method was tested using numerically generated count maps. In the present work a 100 kBq Co{sup 60} source has been placed on a gridded surface and the count rate measured using a NaI scintillation detector. The resulting map of gamma counts was used as input to the matrix inversion procedure and the source position recovered. A multi-source array was simulated by superposition of several single-source count maps andmore » the source distribution was again recovered using matrix inversion. The measurements were performed for several detector heights. The effects of uncertainties in source-detector distances on the matrix inversion method are also examined. The results from this work give confidence in the application of the method to practical applications, such as the segregation of highly active objects amongst fuel-element debris. (authors)« less

Non-cavitating propeller noise modeling and inversion

NASA Astrophysics Data System (ADS)

Kim, Dongho; Lee, Keunhwa; Seong, Woojae

2014-12-01

Marine propeller is the dominant exciter of the hull surface above it causing high level of noise and vibration in the ship structure. Recent successful developments have led to non-cavitating propeller designs and thus present focus is the non-cavitating characteristics of propeller such as hydrodynamic noise and its induced hull excitation. In this paper, analytic source model of propeller non-cavitating noise, described by longitudinal quadrupoles and dipoles, is suggested based on the propeller hydrodynamics. To find the source unknown parameters, the multi-parameter inversion technique is adopted using the pressure data obtained from the model scale experiment and pressure field replicas calculated by boundary element method. The inversion results show that the proposed source model is appropriate in modeling non-cavitating propeller noise. The result of this study can be utilized in the prediction of propeller non-cavitating noise and hull excitation at various stages in design and analysis.

Multi-scale signed envelope inversion

NASA Astrophysics Data System (ADS)

Chen, Guo-Xin; Wu, Ru-Shan; Wang, Yu-Qing; Chen, Sheng-Chang

2018-06-01

Envelope inversion based on modulation signal mode was proposed to reconstruct large-scale structures of underground media. In order to solve the shortcomings of conventional envelope inversion, multi-scale envelope inversion was proposed using new envelope Fréchet derivative and multi-scale inversion strategy to invert strong contrast models. In multi-scale envelope inversion, amplitude demodulation was used to extract the low frequency information from envelope data. However, only to use amplitude demodulation method will cause the loss of wavefield polarity information, thus increasing the possibility of inversion to obtain multiple solutions. In this paper we proposed a new demodulation method which can contain both the amplitude and polarity information of the envelope data. Then we introduced this demodulation method into multi-scale envelope inversion, and proposed a new misfit functional: multi-scale signed envelope inversion. In the numerical tests, we applied the new inversion method to the salt layer model and SEG/EAGE 2-D Salt model using low-cut source (frequency components below 4 Hz were truncated). The results of numerical test demonstrated the effectiveness of this method.

Electromagnetic Inverse Methods and Applications for Inhomogeneous Media Probing and Synthesis.

NASA Astrophysics Data System (ADS)

Xia, Jake Jiqing

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.).

Time-lapse joint AVO inversion using generalized linear method based on exact Zoeppritz equations

NASA Astrophysics Data System (ADS)

Zhi, Longxiao; Gu, Hanming

2018-03-01

The conventional method of time-lapse AVO (Amplitude Versus Offset) inversion is mainly based on the approximate expression of Zoeppritz equations. Though the approximate expression is concise and convenient to use, it has certain limitations. For example, its application condition is that the difference of elastic parameters between the upper medium and lower medium is little and the incident angle is small. In addition, the inversion of density is not stable. Therefore, we develop the method of time-lapse joint AVO inversion based on exact Zoeppritz equations. In this method, we apply exact Zoeppritz equations to calculate the reflection coefficient of PP wave. And in the construction of objective function for inversion, we use Taylor series expansion to linearize the inversion problem. Through the joint AVO inversion of seismic data in baseline survey and monitor survey, we can obtain the P-wave velocity, S-wave velocity, density in baseline survey and their time-lapse changes simultaneously. We can also estimate the oil saturation change according to inversion results. Compared with the time-lapse difference inversion, the joint inversion doesn't need certain assumptions and can estimate more parameters simultaneously. It has a better applicability. Meanwhile, by using the generalized linear method, the inversion is easily implemented and its calculation cost is small. We use the theoretical model to generate synthetic seismic records to test and analyze the influence of random noise. The results can prove the availability and anti-noise-interference ability of our method. We also apply the inversion to actual field data and prove the feasibility of our method in actual situation.

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.

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.

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

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.

A Stochastic Inversion Method for Potential Field Data: Ant Colony Optimization

NASA Astrophysics Data System (ADS)

Liu, Shuang; Hu, Xiangyun; Liu, Tianyou

2014-07-01

Simulating natural ants' foraging behavior, the ant colony optimization (ACO) algorithm performs excellently in combinational optimization problems, for example the traveling salesman problem and the quadratic assignment problem. However, the ACO is seldom used to inverted for gravitational and magnetic data. On the basis of the continuous and multi-dimensional objective function for potential field data optimization inversion, we present the node partition strategy ACO (NP-ACO) algorithm for inversion of model variables of fixed shape and recovery of physical property distributions of complicated shape models. We divide the continuous variables into discrete nodes and ants directionally tour the nodes by use of transition probabilities. We update the pheromone trails by use of Gaussian mapping between the objective function value and the quantity of pheromone. It can analyze the search results in real time and promote the rate of convergence and precision of inversion. Traditional mapping, including the ant-cycle system, weaken the differences between ant individuals and lead to premature convergence. We tested our method by use of synthetic data and real data from scenarios involving gravity and magnetic anomalies. The inverted model variables and recovered physical property distributions were in good agreement with the true values. The ACO algorithm for binary representation imaging and full imaging can recover sharper physical property distributions than traditional linear inversion methods. The ACO has good optimization capability and some excellent characteristics, for example robustness, parallel implementation, and portability, compared with other stochastic metaheuristics.

Core flow inversion tested with numerical dynamo models

NASA Astrophysics Data System (ADS)

Rau, Steffen; Christensen, Ulrich; Jackson, Andrew; Wicht, Johannes

2000-05-01

We test inversion methods of geomagnetic secular variation data for the pattern of fluid flow near the surface of the core with synthetic data. These are taken from self-consistent 3-D models of convection-driven magnetohydrodynamic dynamos in rotating spherical shells, which generate dipole-dominated magnetic fields with an Earth-like morphology. We find that the frozen-flux approximation, which is fundamental to all inversion schemes, is satisfied to a fair degree in the models. In order to alleviate the non-uniqueness of the inversion, usually a priori conditions are imposed on the flow; for example, it is required to be purely toroidal or geostrophic. Either condition is nearly satisfied by our model flows near the outer surface. However, most of the surface velocity field lies in the nullspace of the inversion problem. Nonetheless, the a priori constraints reduce the nullspace, and by inverting the magnetic data with either one of them we recover a significant part of the flow. With the geostrophic condition the correlation coefficient between the inverted and the true velocity field can reach values of up to 0.65, depending on the choice of the damping parameter. The correlation is significant at the 95 per cent level for most spherical harmonic degrees up to l=26. However, it degrades substantially, even at long wavelengths, when we truncate the magnetic data sets to l <= 14, that is, to the resolution of core-field models. In some of the latter inversions prominent zonal currents, similar to those seen in core-flow models derived from geomagnetic data, occur in the equatorial region. However, the true flow does not contain this flow component. The results suggest that some meaningful information on the core-flow pattern can be retrieved from secular variation data, but also that the limited resolution of the magnetic core field could produce serious artefacts.

Adjoint Sensitivity Method to Determine Optimal Set of Stations for Tsunami Source Inversion

NASA Astrophysics Data System (ADS)

Gusman, A. R.; Hossen, M. J.; Cummins, P. R.; Satake, K.

2017-12-01

We applied the adjoint sensitivity technique in tsunami science for the first time to determine an optimal set of stations for a tsunami source inversion. The adjoint sensitivity (AS) method has been used in numerical weather prediction to find optimal locations for adaptive observations. We implemented this technique to Green's Function based Time Reverse Imaging (GFTRI), which is recently used in tsunami source inversion in order to reconstruct the initial sea surface displacement, known as tsunami source model. This method has the same source representation as the traditional least square (LSQ) source inversion method where a tsunami source is represented by dividing the source region into a regular grid of "point" sources. For each of these, Green's function (GF) is computed using a basis function for initial sea surface displacement whose amplitude is concentrated near the grid point. We applied the AS method to the 2009 Samoa earthquake tsunami that occurred on 29 September 2009 in the southwest Pacific, near the Tonga trench. Many studies show that this earthquake is a doublet associated with both normal faulting in the outer-rise region and thrust faulting in the subduction interface. To estimate the tsunami source model for this complex event, we initially considered 11 observations consisting of 5 tide gauges and 6 DART bouys. After implementing AS method, we found the optimal set of observations consisting with 8 stations. Inversion with this optimal set provides better result in terms of waveform fitting and source model that shows both sub-events associated with normal and thrust faulting.

Evaluation of the inverse dispersion modelling method for estimating ammonia multi-source emissions using low-cost long time averaging sensor

NASA Astrophysics Data System (ADS)

Loubet, Benjamin; Carozzi, Marco

2015-04-01

Tropospheric ammonia (NH3) is a key player in atmospheric chemistry and its deposition is a threat for the environment (ecosystem eutrophication, soil acidification and reduction in species biodiversity). Most of the NH3 global emissions derive from agriculture, mainly from livestock manure (storage and field application) but also from nitrogen-based fertilisers. Inverse dispersion modelling has been widely used to infer emission sources from a homogeneous source of known geometry. When the emission derives from different sources inside of the measured footprint, the emission should be treated as multi-source problem. This work aims at estimating whether multi-source inverse dispersion modelling can be used to infer NH3 emissions from different agronomic treatment, composed of small fields (typically squares of 25 m side) located near to each other, using low-cost NH3 measurements (diffusion samplers). To do that, a numerical experiment was designed with a combination of 3 x 3 square field sources (625 m2), and a set of sensors placed at the centre of each field at several heights as well as at 200 m away from the sources in each cardinal directions. The concentration at each sensor location was simulated with a forward Lagrangian Stochastic (WindTrax) and a Gaussian-like (FIDES) dispersion model. The concentrations were averaged over various integration times (3 hours to 28 days), to mimic the diffusion sampler behaviour with several sampling strategy. The sources were then inferred by inverse modelling using the averaged concentration and the same models in backward mode. The sources patterns were evaluated using a soil-vegetation-atmosphere model (SurfAtm-NH3) that incorporates the response of the NH3 emissions to surface temperature. A combination emission patterns (constant, linear decreasing, exponential decreasing and Gaussian type) and strengths were used to evaluate the uncertainty of the inversion method. Each numerical experiment covered a period of 28

Estimating surface acoustic impedance with the inverse method.

PubMed

Piechowicz, Janusz

2011-01-01

Sound field parameters are predicted with numerical methods in sound control systems, in acoustic designs of building and in sound field simulations. Those methods define the acoustic properties of surfaces, such as sound absorption coefficients or acoustic impedance, to determine boundary conditions. Several in situ measurement techniques were developed; one of them uses 2 microphones to measure direct and reflected sound over a planar test surface. Another approach is used in the inverse boundary elements method, in which estimating acoustic impedance of a surface is expressed as an inverse boundary problem. The boundary values can be found from multipoint sound pressure measurements in the interior of a room. This method can be applied to arbitrarily-shaped surfaces. This investigation is part of a research programme on using inverse methods in industrial room acoustics.

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

PubMed

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

2004-06-01

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

A Hybrid Seismic Inversion Method for V P/V S Ratio and Its Application to Gas Identification

NASA Astrophysics Data System (ADS)

Guo, Qiang; Zhang, Hongbing; Han, Feilong; Xiao, Wei; Shang, Zuoping

2018-03-01

The ratio of compressional wave velocity to shear wave velocity (V P/V S ratio) has established itself as one of the most important parameters in identifying gas reservoirs. However, considering that seismic inversion process is highly non-linear and geological conditions encountered may be complex, a direct estimation of V P/V S ratio from pre-stack seismic data remains a challenging task. In this paper, we propose a hybrid seismic inversion method to estimate V P/V S ratio directly. In this method, post- and pre-stack inversions are combined in which the pre-stack inversion for V P/V S ratio is driven by the post-stack inversion results (i.e., V P and density). In particular, the V P/V S ratio is considered as a model parameter and is directly inverted from the pre-stack inversion based on the exact Zoeppritz equation. Moreover, anisotropic Markov random field is employed in order to regularise the inversion process as well as taking care of geological structures (boundaries) information. Aided by the proposed hybrid inversion strategy, the directional weighting coefficients incorporated in the anisotropic Markov random field neighbourhoods are quantitatively calculated by the anisotropic diffusion method. The synthetic test demonstrates the effectiveness of the proposed inversion method. In particular, given low quality of the pre-stack data and high heterogeneity of the target layers in the field data, the proposed inversion method reveals the detailed model of V P/V S ratio that can successfully identify the gas-bearing zones.

Significance of the model considering mixed grain-size for inverse analysis of turbidites

NASA Astrophysics Data System (ADS)

Nakao, K.; Naruse, H.; Tokuhashi, S., Sr.

2016-12-01

A method for inverse analysis of turbidity currents is proposed for application to field observations. Estimation of initial condition of the catastrophic events from field observations has been important for sedimentological researches. For instance, there are various inverse analyses to estimate hydraulic conditions from topography observations of pyroclastic flows (Rossano et al., 1996), real-time monitored debris-flow events (Fraccarollo and Papa, 2000), tsunami deposits (Jaffe and Gelfenbaum, 2007) and ancient turbidites (Falcini et al., 2009). These inverse analyses need forward models and the most turbidity current models employ uniform grain-size particles. The turbidity currents, however, are the best characterized by variation of grain-size distribution. Though there are numerical models of mixed grain-sized particles, the models have difficulty in feasibility of application to natural examples because of calculating costs (Lesshaft et al., 2011). Here we expand the turbidity current model based on the non-steady 1D shallow-water equation at low calculation costs for mixed grain-size particles and applied the model to the inverse analysis. In this study, we compared two forward models considering uniform and mixed grain-size particles respectively. We adopted inverse analysis based on the Simplex method that optimizes the initial conditions (thickness, depth-averaged velocity and depth-averaged volumetric concentration of a turbidity current) with multi-point start and employed the result of the forward model [h: 2.0 m, U: 5.0 m/s, C: 0.01%] as reference data. The result shows that inverse analysis using the mixed grain-size model found the known initial condition of reference data even if the condition where the optimization started is deviated from the true solution, whereas the inverse analysis using the uniform grain-size model requires the condition in which the starting parameters for optimization must be in quite narrow range near the solution. The

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

Micro-seismic imaging using a source function independent full waveform inversion method

NASA Astrophysics Data System (ADS)

Wang, Hanchen; Alkhalifah, Tariq

2018-03-01

At the heart of micro-seismic event measurements is the task to estimate the location of the source micro-seismic events, as well as their ignition times. The accuracy of locating the sources is highly dependent on the velocity model. On the other hand, the conventional micro-seismic source locating methods require, in many cases manual picking of traveltime arrivals, which do not only lead to manual effort and human interaction, but also prone to errors. Using full waveform inversion (FWI) to locate and image micro-seismic events allows for an automatic process (free of picking) that utilizes the full wavefield. However, full waveform inversion of micro-seismic events faces incredible nonlinearity due to the unknown source locations (space) and functions (time). We developed a source function independent full waveform inversion of micro-seismic events to invert for the source image, source function and the velocity model. It is based on convolving reference traces with these observed and modeled to mitigate the effect of an unknown source ignition time. The adjoint-state method is used to derive the gradient for the source image, source function and velocity updates. The extended image for the source wavelet in Z axis is extracted to check the accuracy of the inverted source image and velocity model. Also, angle gathers is calculated to assess the quality of the long wavelength component of the velocity model. By inverting for the source image, source wavelet and the velocity model simultaneously, the proposed method produces good estimates of the source location, ignition time and the background velocity for synthetic examples used here, like those corresponding to the Marmousi model and the SEG/EAGE overthrust model.

Time-lapse joint AVO inversion using generalized linear method based on exact Zoeppritz equations

NASA Astrophysics Data System (ADS)

Zhi, L.; Gu, H.

2017-12-01

The conventional method of time-lapse AVO (Amplitude Versus Offset) inversion is mainly based on the approximate expression of Zoeppritz equations. Though the approximate expression is concise and convenient to use, it has certain limitations. For example, its application condition is that the difference of elastic parameters between the upper medium and lower medium is little and the incident angle is small. In addition, the inversion of density is not stable. Therefore, we develop the method of time-lapse joint AVO inversion based on exact Zoeppritz equations. In this method, we apply exact Zoeppritz equations to calculate the reflection coefficient of PP wave. And in the construction of objective function for inversion, we use Taylor expansion to linearize the inversion problem. Through the joint AVO inversion of seismic data in baseline survey and monitor survey, we can obtain P-wave velocity, S-wave velocity, density in baseline survey and their time-lapse changes simultaneously. We can also estimate the oil saturation change according to inversion results. Compared with the time-lapse difference inversion, the joint inversion has a better applicability. It doesn't need some assumptions and can estimate more parameters simultaneously. Meanwhile, by using the generalized linear method, the inversion is easily realized and its calculation amount is small. We use the Marmousi model to generate synthetic seismic records to test and analyze the influence of random noise. Without noise, all estimation results are relatively accurate. With the increase of noise, P-wave velocity change and oil saturation change are stable and less affected by noise. S-wave velocity change is most affected by noise. Finally we use the actual field data of time-lapse seismic prospecting to process and the results can prove the availability and feasibility of our method in actual situation.

3D CSEM data inversion using Newton and Halley class methods

NASA Astrophysics Data System (ADS)

Amaya, M.; Hansen, K. R.; Morten, J. P.

2016-05-01

For the first time in 3D controlled source electromagnetic data inversion, we explore the use of the Newton and the Halley optimization methods, which may show their potential when the cost function has a complex topology. The inversion is formulated as a constrained nonlinear least-squares problem which is solved by iterative optimization. These methods require the derivatives up to second order of the residuals with respect to model parameters. We show how Green's functions determine the high-order derivatives, and develop a diagrammatical representation of the residual derivatives. The Green's functions are efficiently calculated on-the-fly, making use of a finite-difference frequency-domain forward modelling code based on a multi-frontal sparse direct solver. This allow us to build the second-order derivatives of the residuals keeping the memory cost in the same order as in a Gauss-Newton (GN) scheme. Model updates are computed with a trust-region based conjugate-gradient solver which does not require the computation of a stabilizer. We present inversion results for a synthetic survey and compare the GN, Newton, and super-Halley optimization schemes, and consider two different approaches to set the initial trust-region radius. Our analysis shows that the Newton and super-Halley schemes, using the same regularization configuration, add significant information to the inversion so that the convergence is reached by different paths. In our simple resistivity model examples, the convergence speed of the Newton and the super-Halley schemes are either similar or slightly superior with respect to the convergence speed of the GN scheme, close to the minimum of the cost function. Due to the current noise levels and other measurement inaccuracies in geophysical investigations, this advantageous behaviour is at present of low consequence, but may, with the further improvement of geophysical data acquisition, be an argument for more accurate higher-order methods like those

Parallelized Three-Dimensional Resistivity Inversion Using Finite Elements And Adjoint State Methods

NASA Astrophysics Data System (ADS)

Schaa, Ralf; Gross, Lutz; Du Plessis, Jaco

2015-04-01

The resistivity method is one of the oldest geophysical exploration methods, which employs one pair of electrodes to inject current into the ground and one or more pairs of electrodes to measure the electrical potential difference. The potential difference is a non-linear function of the subsurface resistivity distribution described by an elliptic partial differential equation (PDE) of the Poisson type. Inversion of measured potentials solves for the subsurface resistivity represented by PDE coefficients. With increasing advances in multichannel resistivity acquisition systems (systems with more than 60 channels and full waveform recording are now emerging), inversion software require efficient storage and solver algorithms. We developed the finite element solver Escript, which provides a user-friendly programming environment in Python to solve large-scale PDE-based problems (see https://launchpad.net/escript-finley). Using finite elements, highly irregular shaped geology and topography can readily be taken into account. For the 3D resistivity problem, we have implemented the secondary potential approach, where the PDE is decomposed into a primary potential caused by the source current and the secondary potential caused by changes in subsurface resistivity. The primary potential is calculated analytically, and the boundary value problem for the secondary potential is solved using nodal finite elements. This approach removes the singularity caused by the source currents and provides more accurate 3D resistivity models. To solve the inversion problem we apply a 'first optimize then discretize' approach using the quasi-Newton scheme in form of the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method (see Gross & Kemp 2013). The evaluation of the cost function requires the solution of the secondary potential PDE for each source current and the solution of the corresponding adjoint-state PDE for the cost function gradients with respect to the subsurface

A full potential inverse method based on a density linearization scheme for wing design

NASA Technical Reports Server (NTRS)

Shankar, V.

1982-01-01

A mixed analysis inverse procedure based on the full potential equation in conservation form was developed to recontour a given base wing to produce density linearization scheme in applying the pressure boundary condition in terms of the velocity potential. The FL030 finite volume analysis code was modified to include the inverse option. The new surface shape information, associated with the modified pressure boundary condition, is calculated at a constant span station based on a mass flux integration. The inverse method is shown to recover the original shape when the analysis pressure is not altered. Inverse calculations for weakening of a strong shock system and for a laminar flow control (LFC) pressure distribution are presented. Two methods for a trailing edge closure model are proposed for further study.

Inverse Modeling of Texas NOx Emissions Using Space-Based and Ground-Based NO2 Observations

NASA Technical Reports Server (NTRS)

Tang, Wei; Cohan, D.; Lamsal, L. N.; Xiao, X.; Zhou, W.

2013-01-01

Inverse modeling of nitrogen oxide (NOx) emissions using satellite-based NO2 observations has become more prevalent in recent years, but has rarely been applied to regulatory modeling at regional scales. In this study, OMI satellite observations of NO2 column densities are used to conduct inverse modeling of NOx emission inventories for two Texas State Implementation Plan (SIP) modeling episodes. Addition of lightning, aircraft, and soil NOx emissions to the regulatory inventory narrowed but did not close the gap between modeled and satellite observed NO2 over rural regions. Satellitebased top-down emission inventories are created with the regional Comprehensive Air Quality Model with extensions (CAMx) using two techniques: the direct scaling method and discrete Kalman filter (DKF) with Decoupled Direct Method (DDM) sensitivity analysis. The simulations with satellite-inverted inventories are compared to the modeling results using the a priori inventory as well as an inventory created by a ground-level NO2 based DKF inversion. The DKF inversions yield conflicting results: the satellite based inversion scales up the a priori NOx emissions in most regions by factors of 1.02 to 1.84, leading to 3-55% increase in modeled NO2 column densities and 1-7 ppb increase in ground 8 h ozone concentrations, while the ground-based inversion indicates the a priori NOx emissions should be scaled by factors of 0.34 to 0.57 in each region. However, none of the inversions improve the model performance in simulating aircraft-observed NO2 or ground-level ozone (O3) concentrations.

Inverse modeling of Texas NOx emissions using space-based and ground-based NO2 observations

NASA Astrophysics Data System (ADS)

Tang, W.; Cohan, D. S.; Lamsal, L. N.; Xiao, X.; Zhou, W.

2013-11-01

Inverse modeling of nitrogen oxide (NOx) emissions using satellite-based NO2 observations has become more prevalent in recent years, but has rarely been applied to regulatory modeling at regional scales. In this study, OMI satellite observations of NO2 column densities are used to conduct inverse modeling of NOx emission inventories for two Texas State Implementation Plan (SIP) modeling episodes. Addition of lightning, aircraft, and soil NOx emissions to the regulatory inventory narrowed but did not close the gap between modeled and satellite-observed NO2 over rural regions. Satellite-based top-down emission inventories are created with the regional Comprehensive Air Quality Model with extensions (CAMx) using two techniques: the direct scaling method and discrete Kalman filter (DKF) with decoupled direct method (DDM) sensitivity analysis. The simulations with satellite-inverted inventories are compared to the modeling results using the a priori inventory as well as an inventory created by a ground-level NO2-based DKF inversion. The DKF inversions yield conflicting results: the satellite-based inversion scales up the a priori NOx emissions in most regions by factors of 1.02 to 1.84, leading to 3-55% increase in modeled NO2 column densities and 1-7 ppb increase in ground 8 h ozone concentrations, while the ground-based inversion indicates the a priori NOx emissions should be scaled by factors of 0.34 to 0.57 in each region. However, none of the inversions improve the model performance in simulating aircraft-observed NO2 or ground-level ozone (O3) concentrations.

Inverse modeling of Texas NOx emissions using space-based and ground-based NO2 observations

NASA Astrophysics Data System (ADS)

Tang, W.; Cohan, D.; Lamsal, L. N.; Xiao, X.; Zhou, W.

2013-07-01

Inverse modeling of nitrogen oxide (NOx) emissions using satellite-based NO2 observations has become more prevalent in recent years, but has rarely been applied to regulatory modeling at regional scales. In this study, OMI satellite observations of NO2 column densities are used to conduct inverse modeling of NOx emission inventories for two Texas State Implementation Plan (SIP) modeling episodes. Addition of lightning, aircraft, and soil NOx emissions to the regulatory inventory narrowed but did not close the gap between modeled and satellite observed NO2 over rural regions. Satellite-based top-down emission inventories are created with the regional Comprehensive Air Quality Model with extensions (CAMx) using two techniques: the direct scaling method and discrete Kalman filter (DKF) with Decoupled Direct Method (DDM) sensitivity analysis. The simulations with satellite-inverted inventories are compared to the modeling results using the a priori inventory as well as an inventory created by a ground-level NO2 based DKF inversion. The DKF inversions yield conflicting results: the satellite-based inversion scales up the a priori NOx emissions in most regions by factors of 1.02 to 1.84, leading to 3-55% increase in modeled NO2 column densities and 1-7 ppb increase in ground 8 h ozone concentrations, while the ground-based inversion indicates the a priori NOx emissions should be scaled by factors of 0.34 to 0.57 in each region. However, none of the inversions improve the model performance in simulating aircraft-observed NO2 or ground-level ozone (O3) concentrations.

An Inversion Method for Reconstructing Hall Thruster Plume Parameters from the Line Integrated Measurements (Preprint)

DTIC Science & Technology

2007-06-05

From - To) 05-06-2007 Technical Paper 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER An Inversion Method for Reconstructing Hall Thruster Plume...239.18 An Inversion Method for Reconstructing Hall Thruster Plume Parameters from Line Integrated Measurements (Preprint) Taylor S. Matlock∗ Jackson...dimensional estimate of the plume electron temperature using a published xenon collisional radiative model. I. Introduction The Hall thruster is a high

Voxel inversion of airborne electromagnetic data for improved model integration

NASA Astrophysics Data System (ADS)

Fiandaca, Gianluca; Auken, Esben; Kirkegaard, Casper; Vest Christiansen, Anders

2014-05-01

Inversion of electromagnetic data has migrated from single site interpretations to inversions including entire surveys using spatial constraints to obtain geologically reasonable results. Though, the model space is usually linked to the actual observation points. For airborne electromagnetic (AEM) surveys the spatial discretization of the model space reflects the flight lines. On the contrary, geological and groundwater models most often refer to a regular voxel grid, not correlated to the geophysical model space, and the geophysical information has to be relocated for integration in (hydro)geological models. We have developed a new geophysical inversion algorithm working directly in a voxel grid disconnected from the actual measuring points, which then allows for informing directly geological/hydrogeological models. The new voxel model space defines the soil properties (like resistivity) on a set of nodes, and the distribution of the soil properties is computed everywhere by means of an interpolation function (e.g. inverse distance or kriging). Given this definition of the voxel model space, the 1D forward responses of the AEM data are computed as follows: 1) a 1D model subdivision, in terms of model thicknesses, is defined for each 1D data set, creating "virtual" layers. 2) the "virtual" 1D models at the sounding positions are finalized by interpolating the soil properties (the resistivity) in the center of the "virtual" layers. 3) the forward response is computed in 1D for each "virtual" model. We tested the new inversion scheme on an AEM survey carried out with the SkyTEM system close to Odder, in Denmark. The survey comprises 106054 dual mode AEM soundings, and covers an area of approximately 13 km X 16 km. The voxel inversion was carried out on a structured grid of 260 X 325 X 29 xyz nodes (50 m xy spacing), for a total of 2450500 inversion parameters. A classical spatially constrained inversion (SCI) was carried out on the same data set, using 106054

Comparison of Optimal Design Methods in Inverse Problems

PubMed Central

Banks, H. T.; Holm, Kathleen; Kappel, Franz

2011-01-01

Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher Information Matrix (FIM). A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criteria with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst-Pearl logistic population model [13], the standard harmonic oscillator model [13] and a popular glucose regulation model [16, 19, 29]. PMID:21857762

On the Development of Multi-Step Inverse FEM with Shell Model

NASA Astrophysics Data System (ADS)

Huang, Y.; Du, R.

2005-08-01

The inverse or one-step finite element approach is increasingly used in the sheet metal stamping industry to predict strain distribution and the initial blank shape in the preliminary design stage. Based on the existing theory, there are two types of method: one is based on the principle of virtual work and the other is based on the principle of extreme work. Much research has been conducted to improve the accuracy of simulation results. For example, based on the virtual work principle, Batoz et al. developed a new method using triangular DKT shell elements. In this new method, the bending and unbending effects are considered. Based on the principle of extreme work, Majlessi and et al. proposed the multi-step inverse approach with membrane elements and applied it to an axis-symmetric part. Lee and et al. presented an axis-symmetric shell element model to solve the similar problem. In this paper, a new multi-step inverse method is introduced with no limitation on the workpiece shape. It is a shell element model based on the virtual work principle. The new method is validated by means of comparing to the commercial software system (PAMSTAMP®). The comparison results indicate that the accuracy is good.

Inverse modelling of European CH4 emissions during 2006-2012 using different inverse models and reassessed atmospheric observations

NASA Astrophysics Data System (ADS)

Bergamaschi, Peter; Karstens, Ute; Manning, Alistair J.; Saunois, Marielle; Tsuruta, Aki; Berchet, Antoine; Vermeulen, Alexander T.; Arnold, Tim; Janssens-Maenhout, Greet; Hammer, Samuel; Levin, Ingeborg; Schmidt, Martina; Ramonet, Michel; Lopez, Morgan; Lavric, Jost; Aalto, Tuula; Chen, Huilin; Feist, Dietrich G.; Gerbig, Christoph; Haszpra, László; Hermansen, Ove; Manca, Giovanni; Moncrieff, John; Meinhardt, Frank; Necki, Jaroslaw; Galkowski, Michal; O'Doherty, Simon; Paramonova, Nina; Scheeren, Hubertus A.; Steinbacher, Martin; Dlugokencky, Ed

2018-01-01

We present inverse modelling (top down) estimates of European methane (CH4) emissions for 2006-2012 based on a new quality-controlled and harmonised in situ data set from 18 European atmospheric monitoring stations. We applied an ensemble of seven inverse models and performed four inversion experiments, investigating the impact of different sets of stations and the use of a priori information on emissions. The inverse models infer total CH4 emissions of 26.8 (20.2-29.7) Tg CH4 yr-1 (mean, 10th and 90th percentiles from all inversions) for the EU-28 for 2006-2012 from the four inversion experiments. For comparison, total anthropogenic CH4 emissions reported to UNFCCC (bottom up, based on statistical data and emissions factors) amount to only 21.3 Tg CH4 yr-1 (2006) to 18.8 Tg CH4 yr-1 (2012). A potential explanation for the higher range of top-down estimates compared to bottom-up inventories could be the contribution from natural sources, such as peatlands, wetlands, and wet soils. Based on seven different wetland inventories from the Wetland and Wetland CH4 Inter-comparison of Models Project (WETCHIMP), total wetland emissions of 4.3 (2.3-8.2) Tg CH4 yr-1 from the EU-28 are estimated. The hypothesis of significant natural emissions is supported by the finding that several inverse models yield significant seasonal cycles of derived CH4 emissions with maxima in summer, while anthropogenic CH4 emissions are assumed to have much lower seasonal variability. Taking into account the wetland emissions from the WETCHIMP ensemble, the top-down estimates are broadly consistent with the sum of anthropogenic and natural bottom-up inventories. However, the contribution of natural sources and their regional distribution remain rather uncertain. Furthermore, we investigate potential biases in the inverse models by comparison with regular aircraft profiles at four European sites and with vertical profiles obtained during the Infrastructure for Measurement of the European Carbon

A high-order 3-D spectral-element method for the forward modelling and inversion of gravimetric data—Application to the western Pyrenees

NASA Astrophysics Data System (ADS)

Martin, Roland; Chevrot, Sébastien; Komatitsch, Dimitri; Seoane, Lucia; Spangenberg, Hannah; Wang, Yi; Dufréchou, Grégory; Bonvalot, Sylvain; Bruinsma, Sean

2017-04-01

We image the internal density structure of the Pyrenees by inverting gravity data using an a priori density model derived by scaling a Vp model obtained by full waveform inversion of teleseismic P-waves. Gravity anomalies are computed via a 3-D high-order finite-element integration in the same high-order spectral-element grid as the one used to solve the wave equation and thus to obtain the velocity model. The curvature of the Earth and surface topography are taken into account in order to obtain a density model as accurate as possible. The method is validated through comparisons with exact semi-analytical solutions. We show that the spectral-element method drastically accelerates the computations when compared to other more classical methods. Different scaling relations between compressional velocity and density are tested, and the Nafe-Drake relation is the one that leads to the best agreement between computed and observed gravity anomalies. Gravity data inversion is then performed and the results allow us to put more constraints on the density structure of the shallow crust and on the deep architecture of the mountain range.

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.

Neural-Based Compensation of Nonlinearities in an Airplane Longitudinal Model with Dynamic-Inversion Control

PubMed Central

Li, YuHui; Jin, FeiTeng

2017-01-01

The inversion design approach is a very useful tool for the complex multiple-input-multiple-output nonlinear systems to implement the decoupling control goal, such as the airplane model and spacecraft model. In this work, the flight control law is proposed using the neural-based inversion design method associated with the nonlinear compensation for a general longitudinal model of the airplane. First, the nonlinear mathematic model is converted to the equivalent linear model based on the feedback linearization theory. Then, the flight control law integrated with this inversion model is developed to stabilize the nonlinear system and relieve the coupling effect. Afterwards, the inversion control combined with the neural network and nonlinear portion is presented to improve the transient performance and attenuate the uncertain effects on both external disturbances and model errors. Finally, the simulation results demonstrate the effectiveness of this controller. PMID:29410680

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

NASA Astrophysics Data System (ADS)

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

2016-04-01

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

Modeling and inversion Matlab algorithms for resistivity, induced polarization and seismic data

NASA Astrophysics Data System (ADS)

Karaoulis, M.; Revil, A.; Minsley, B. J.; Werkema, D. D.

2011-12-01

M. Karaoulis (1), D.D. Werkema (3), A. Revil (1,2), A., B. Minsley (4), (1) Colorado School of Mines, Dept. of Geophysics, Golden, CO, USA. (2) ISTerre, CNRS, UMR 5559, Université de Savoie, Equipe Volcan, Le Bourget du Lac, France. (3) U.S. EPA, ORD, NERL, ESD, CMB, Las Vegas, Nevada, USA . (4) USGS, Federal Center, Lakewood, 10, 80225-0046, CO. Abstract We propose 2D and 3D forward modeling and inversion package for DC resistivity, time domain induced polarization (IP), frequency-domain IP, and seismic refraction data. For the resistivity and IP case, discretization is based on rectangular cells, where each cell has as unknown resistivity in the case of DC modelling, resistivity and chargeability in the time domain IP modelling, and complex resistivity in the spectral IP modelling. The governing partial-differential equations are solved with the finite element method, which can be applied to both real and complex variables that are solved for. For the seismic case, forward modeling is based on solving the eikonal equation using a second-order fast marching method. The wavepaths are materialized by Fresnel volumes rather than by conventional rays. This approach accounts for complicated velocity models and is advantageous because it considers frequency effects on the velocity resolution. The inversion can accommodate data at a single time step, or as a time-lapse dataset if the geophysical data are gathered for monitoring purposes. The aim of time-lapse inversion is to find the change in the velocities or resistivities of each model cell as a function of time. Different time-lapse algorithms can be applied such as independent inversion, difference inversion, 4D inversion, and 4D active time constraint inversion. The forward algorithms are benchmarked against analytical solutions and inversion results are compared with existing ones. The algorithms are packaged as Matlab codes with a simple Graphical User Interface. Although the code is parallelized for multi

On the joint inversion of geophysical data for models of the coupled core-mantle system

NASA Technical Reports Server (NTRS)

Voorhies, Coerte V.

1991-01-01

Joint inversion of magnetic, earth rotation, geoid, and seismic data for a unified model of the coupled core-mantle system is proposed and shown to be possible. A sample objective function is offered and simplified by targeting results from independent inversions and summary travel time residuals instead of original observations. These data are parameterized in terms of a very simple, closed model of the topographically coupled core-mantle system. Minimization of the simplified objective function leads to a nonlinear inverse problem; an iterative method for solution is presented. Parameterization and method are emphasized; numerical results are not presented.

Mixed linear-nonlinear fault slip inversion: Bayesian inference of model, weighting, and smoothing parameters

NASA Astrophysics Data System (ADS)

Fukuda, J.; Johnson, K. M.

2009-12-01

Studies utilizing inversions of geodetic data for the spatial distribution of coseismic slip on faults typically present the result as a single fault plane and slip distribution. Commonly the geometry of the fault plane is assumed to be known a priori and the data are inverted for slip. However, sometimes there is not strong a priori information on the geometry of the fault that produced the earthquake and the data is not always strong enough to completely resolve the fault geometry. We develop a method to solve for the full posterior probability distribution of fault slip and fault geometry parameters in a Bayesian framework using Monte Carlo methods. The slip inversion problem is particularly challenging because it often involves multiple data sets with unknown relative weights (e.g. InSAR, GPS), model parameters that are related linearly (slip) and nonlinearly (fault geometry) through the theoretical model to surface observations, prior information on model parameters, and a regularization prior to stabilize the inversion. We present the theoretical framework and solution method for a Bayesian inversion that can handle all of these aspects of the problem. The method handles the mixed linear/nonlinear nature of the problem through combination of both analytical least-squares solutions and Monte Carlo methods. We first illustrate and validate the inversion scheme using synthetic data sets. We then apply the method to inversion of geodetic data from the 2003 M6.6 San Simeon, California earthquake. We show that the uncertainty in strike and dip of the fault plane is over 20 degrees. We characterize the uncertainty in the slip estimate with a volume around the mean fault solution in which the slip most likely occurred. Slip likely occurred somewhere in a volume that extends 5-10 km in either direction normal to the fault plane. We implement slip inversions with both traditional, kinematic smoothing constraints on slip and a simple physical condition of uniform stress

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.

Inverse Optimization: A New Perspective on the Black-Litterman Model.

PubMed

Bertsimas, Dimitris; Gupta, Vishal; Paschalidis, Ioannis Ch

2012-12-11

The Black-Litterman (BL) model is a widely used asset allocation model in the financial industry. In this paper, we provide a new perspective. The key insight is to replace the statistical framework in the original approach with ideas from inverse optimization. This insight allows us to significantly expand the scope and applicability of the BL model. We provide a richer formulation that, unlike the original model, is flexible enough to incorporate investor information on volatility and market dynamics. Equally importantly, our approach allows us to move beyond the traditional mean-variance paradigm of the original model and construct "BL"-type estimators for more general notions of risk such as coherent risk measures. Computationally, we introduce and study two new "BL"-type estimators and their corresponding portfolios: a Mean Variance Inverse Optimization (MV-IO) portfolio and a Robust Mean Variance Inverse Optimization (RMV-IO) portfolio. These two approaches are motivated by ideas from arbitrage pricing theory and volatility uncertainty. Using numerical simulation and historical backtesting, we show that both methods often demonstrate a better risk-reward tradeoff than their BL counterparts and are more robust to incorrect investor views.

Inverse Optimization: A New Perspective on the Black-Litterman Model

PubMed Central

Bertsimas, Dimitris; Gupta, Vishal; Paschalidis, Ioannis Ch.

2014-01-01

The Black-Litterman (BL) model is a widely used asset allocation model in the financial industry. In this paper, we provide a new perspective. The key insight is to replace the statistical framework in the original approach with ideas from inverse optimization. This insight allows us to significantly expand the scope and applicability of the BL model. We provide a richer formulation that, unlike the original model, is flexible enough to incorporate investor information on volatility and market dynamics. Equally importantly, our approach allows us to move beyond the traditional mean-variance paradigm of the original model and construct “BL”-type estimators for more general notions of risk such as coherent risk measures. Computationally, we introduce and study two new “BL”-type estimators and their corresponding portfolios: a Mean Variance Inverse Optimization (MV-IO) portfolio and a Robust Mean Variance Inverse Optimization (RMV-IO) portfolio. These two approaches are motivated by ideas from arbitrage pricing theory and volatility uncertainty. Using numerical simulation and historical backtesting, we show that both methods often demonstrate a better risk-reward tradeoff than their BL counterparts and are more robust to incorrect investor views. PMID:25382873

Convergence analysis of surrogate-based methods for Bayesian inverse problems

NASA Astrophysics Data System (ADS)

Yan, Liang; Zhang, Yuan-Xiang

2017-12-01

The major challenges in the Bayesian inverse problems arise from the need for repeated evaluations of the forward model, as required by Markov chain Monte Carlo (MCMC) methods for posterior sampling. Many attempts at accelerating Bayesian inference have relied on surrogates for the forward model, typically constructed through repeated forward simulations that are performed in an offline phase. Although such approaches can be quite effective at reducing computation cost, there has been little analysis of the approximation on posterior inference. In this work, we prove error bounds on the Kullback-Leibler (KL) distance between the true posterior distribution and the approximation based on surrogate models. Our rigorous error analysis show that if the forward model approximation converges at certain rate in the prior-weighted L 2 norm, then the posterior distribution generated by the approximation converges to the true posterior at least two times faster in the KL sense. The error bound on the Hellinger distance is also provided. To provide concrete examples focusing on the use of the surrogate model based methods, we present an efficient technique for constructing stochastic surrogate models to accelerate the Bayesian inference approach. The Christoffel least squares algorithms, based on generalized polynomial chaos, are used to construct a polynomial approximation of the forward solution over the support of the prior distribution. The numerical strategy and the predicted convergence rates are then demonstrated on the nonlinear inverse problems, involving the inference of parameters appearing in partial differential equations.

Iterative Inverse Modeling for Reconciliation of Emission Inventories during the 2006 TexAQS Intensive Field Campaign

NASA Astrophysics Data System (ADS)

Xiao, X.; Cohan, D. S.

2009-12-01

Substantial uncertainties in current emission inventories have been detected by the Texas Air Quality Study 2006 (TexAQS 2006) intensive field program. These emission uncertainties have caused large inaccuracies in model simulations of air quality and its responses to management strategies. To improve the quantitative understanding of the temporal, spatial, and categorized distributions of primary pollutant emissions by utilizing the corresponding measurements collected during TexAQS 2006, we implemented both the recursive Kalman filter and a batch matrix inversion 4-D data assimilation (FDDA) method in an iterative inverse modeling framework of the CMAQ-DDM model. Equipped with the decoupled direct method, CMAQ-DDM enables simultaneous calculation of the sensitivity coefficients of pollutant concentrations to emissions to be used in the inversions. Primary pollutant concentrations measured by the multiple platforms (TCEQ ground-based, NOAA WP-3D aircraft and Ronald H. Brown vessel, and UH Moody Tower) during TexAQS 2006 have been integrated for the use in the inverse modeling. Firstly pseudo-data analyses have been conducted to assess the two methods, taking a coarse spatial resolution emission inventory as a case. Model base case concentrations of isoprene and ozone at arbitrarily selected ground grid cells were perturbed to generate pseudo measurements with different assumed Gaussian uncertainties expressed by 1-sigma standard deviations. Single-species inversions have been conducted with both methods for isoprene and NOx surface emissions from eight states in the Southeastern United States by using the pseudo measurements of isoprene and ozone, respectively. Utilization of ozone pseudo data to invert for NOx emissions serves only for the purpose of method assessment. Both the Kalman filter and FDDA methods show good performance in tuning arbitrarily shifted a priori emissions to the base case “true” values within 3-4 iterations even for the nonlinear

Locally refined block-centred finite-difference groundwater models: Evaluation of parameter sensitivity and the consequences for inverse modelling

USGS Publications Warehouse

Mehl, S.; Hill, M.C.

2002-01-01

Models with local grid refinement, as often required in groundwater models, pose special problems for model calibration. This work investigates the calculation of sensitivities and the performance of regression methods using two existing and one new method of grid refinement. The existing local grid refinement methods considered are: (a) a variably spaced grid in which the grid spacing becomes smaller near the area of interest and larger where such detail is not needed, and (b) telescopic mesh refinement (TMR), which uses the hydraulic heads or fluxes of a regional model to provide the boundary conditions for a locally refined model. The new method has a feedback between the regional and local grids using shared nodes, and thereby, unlike the TMR methods, balances heads and fluxes at the interfacing boundary. Results for sensitivities are compared for the three methods and the effect of the accuracy of sensitivity calculations are evaluated by comparing inverse modelling results. For the cases tested, results indicate that the inaccuracies of the sensitivities calculated using the TMR approach can cause the inverse model to converge to an incorrect solution.

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.

Strategies to Enhance the Model Update in Regions of Weak Sensitivities for Use in Full Waveform Inversion

NASA Astrophysics Data System (ADS)

Nuber, André; Manukyan, Edgar; Maurer, Hansruedi

2014-05-01

Conventional methods of interpreting seismic data rely on filtering and processing limited portions of the recorded wavefield. Typically, either reflections, refractions or surface waves are considered in isolation. Particularly in near-surface engineering and environmental investigations (depths less than, say 100 m), these wave types often overlap in time and are difficult to separate. Full waveform inversion is a technique that seeks to exploit and interpret the full information content of the seismic records without the need for separating events first; it yields models of the subsurface at sub-wavelength resolution. We use a finite element modelling code to solve the 2D elastic isotropic wave equation in the frequency domain. This code is part of a Gauss-Newton inversion scheme which we employ to invert for the P- and S-wave velocities as well as for density in the subsurface. For shallow surface data the use of an elastic forward solver is essential because surface waves often dominate the seismograms. This leads to high sensitivities (partial derivatives contained in the Jacobian matrix of the Gauss-Newton inversion scheme) and thus large model updates close to the surface. Reflections from deeper structures may also include useful information, but the large sensitivities of the surface waves often preclude this information from being fully exploited. We have developed two methods that balance the sensitivity distributions and thus may help resolve the deeper structures. The first method includes equilibrating the columns of the Jacobian matrix prior to every inversion step by multiplying them with individual scaling factors. This is expected to also balance the model updates throughout the entire subsurface model. It can be shown that this procedure is mathematically equivalent to balancing the regularization weights of the individual model parameters. A proper choice of the scaling factors required to balance the Jacobian matrix is critical. We decided to

Obtaining source current density related to irregularly structured electromagnetic target field inside human body using hybrid inverse/FDTD method.

PubMed

Han, Jijun; Yang, Deqiang; Sun, Houjun; Xin, Sherman Xuegang

2017-01-01

Inverse method is inherently suitable for calculating the distribution of source current density related with an irregularly structured electromagnetic target field. However, the present form of inverse method cannot calculate complex field-tissue interactions. A novel hybrid inverse/finite-difference time domain (FDTD) method that can calculate the complex field-tissue interactions for the inverse design of source current density related with an irregularly structured electromagnetic target field is proposed. A Huygens' equivalent surface is established as a bridge to combine the inverse and FDTD method. Distribution of the radiofrequency (RF) magnetic field on the Huygens' equivalent surface is obtained using the FDTD method by considering the complex field-tissue interactions within the human body model. The obtained magnetic field distributed on the Huygens' equivalent surface is regarded as the next target. The current density on the designated source surface is derived using the inverse method. The homogeneity of target magnetic field and specific energy absorption rate are calculated to verify the proposed method.

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

Data-resolution matrix and model-resolution matrix for Rayleigh-wave inversion using a damped least-squares method

USGS Publications Warehouse

Xia, J.; Miller, R.D.; Xu, Y.

2008-01-01

Inversion of multimode surface-wave data is of increasing interest in the near-surface geophysics community. For a given near-surface geophysical problem, it is essential to understand how well the data, calculated according to a layered-earth model, might match the observed data. A data-resolution matrix is a function of the data kernel (determined by a geophysical model and a priori information applied to the problem), not the data. A data-resolution matrix of high-frequency (>2 Hz) Rayleigh-wave phase velocities, therefore, offers a quantitative tool for designing field surveys and predicting the match between calculated and observed data. We employed a data-resolution matrix to select data that would be well predicted and we find that there are advantages of incorporating higher modes in inversion. The resulting discussion using the data-resolution matrix provides insight into the process of inverting Rayleigh-wave phase velocities with higher-mode data to estimate S-wave velocity structure. Discussion also suggested that each near-surface geophysical target can only be resolved using Rayleigh-wave phase velocities within specific frequency ranges, and higher-mode data are normally more accurately predicted than fundamental-mode data because of restrictions on the data kernel for the inversion system. We used synthetic and real-world examples to demonstrate that selected data with the data-resolution matrix can provide better inversion results and to explain with the data-resolution matrix why incorporating higher-mode data in inversion can provide better results. We also calculated model-resolution matrices in these examples to show the potential of increasing model resolution with selected surface-wave data. ?? Birkhaueser 2008.

Modeling the 16 September 2015 Chile tsunami source with the inversion of deep-ocean tsunami records by means of the r - solution method

NASA Astrophysics Data System (ADS)

Voronina, Tatyana; Romanenko, Alexey; Loskutov, Artem

2017-04-01

The key point in the state-of-the-art in the tsunami forecasting is constructing a reliable tsunami source. In this study, we present an application of the original numerical inversion technique to modeling the tsunami sources of the 16 September 2015 Chile tsunami. The problem of recovering a tsunami source from remote measurements of the incoming wave in the deep-water tsunameters is considered as an inverse problem of mathematical physics in the class of ill-posed problems. This approach is based on the least squares and the truncated singular value decomposition techniques. The tsunami wave propagation is considered within the scope of the linear shallow-water theory. As in inverse seismic problem, the numerical solutions obtained by mathematical methods become unstable due to the presence of noise in real data. A method of r-solutions makes it possible to avoid instability in the solution to the ill-posed problem under study. This method seems to be attractive from the computational point of view since the main efforts are required only once for calculating the matrix whose columns consist of computed waveforms for each harmonic as a source (an unknown tsunami source is represented as a part of a spatial harmonics series in the source area). Furthermore, analyzing the singular spectra of the matrix obtained in the course of numerical calculations one can estimate the future inversion by a certain observational system that will allow offering a more effective disposition for the tsunameters with the help of precomputations. In other words, the results obtained allow finding a way to improve the inversion by selecting the most informative set of available recording stations. The case study of the 6 February 2013 Solomon Islands tsunami highlights a critical role of arranging deep-water tsunameters for obtaining the inversion results. Implementation of the proposed methodology to the 16 September 2015 Chile tsunami has successfully produced tsunami source model

Large-scale 3D inversion of marine controlled source electromagnetic data using the integral equation method

NASA Astrophysics Data System (ADS)

Zhdanov, M. S.; Cuma, M.; Black, N.; Wilson, G. A.

2009-12-01

The marine controlled source electromagnetic (MCSEM) method has become widely used in offshore oil and gas exploration. Interpretation of MCSEM data is still a very challenging problem, especially if one would like to take into account the realistic 3D structure of the subsurface. The inversion of MCSEM data is complicated by the fact that the EM response of a hydrocarbon-bearing reservoir is very weak in comparison with the background EM fields generated by an electric dipole transmitter in complex geoelectrical structures formed by a conductive sea-water layer and the terranes beneath it. In this paper, we present a review of the recent developments in the area of large-scale 3D EM forward modeling and inversion. Our approach is based on using a new integral form of Maxwell’s equations allowing for an inhomogeneous background conductivity, which results in a numerically effective integral representation for 3D EM field. This representation provides an efficient tool for the solution of 3D EM inverse problems. To obtain a robust inverse model of the conductivity distribution, we apply regularization based on a focusing stabilizing functional which allows for the recovery of models with both smooth and sharp geoelectrical boundaries. The method is implemented in a fully parallel computer code, which makes it possible to run large-scale 3D inversions on grids with millions of inversion cells. This new technique can be effectively used for active EM detection and monitoring of the subsurface targets.

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

NASA Astrophysics Data System (ADS)

Alkharji, Mohammed N.

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

3D Magnetization Vector Inversion of Magnetic Data: Improving and Comparing Methods

NASA Astrophysics Data System (ADS)

Liu, Shuang; Hu, Xiangyun; Zhang, Henglei; Geng, Meixia; Zuo, Boxin

2017-12-01

Magnetization vector inversion is an useful approach to invert for magnetic anomaly in the presence of significant remanent magnetization and self-demagnetization. However, magnetizations are usually obtained in many different directions under the influences of geophysical non-uniqueness. We propose an iteration algorithm of magnetization vector inversion (M-IDI) that one couple of magnetization direction is iteratively computed after the magnetization intensity is recovered from the magnitude magnetic anomaly. And we compare it with previous methods of (1) three orthogonal components inversion of total magnetization vector at Cartesian framework (MMM), (2) intensity, inclination and declination inversion at spherical framework (MID), (3) directly recovering the magnetization inclination and declination (M-IDCG) and (4) estimating the magnetization direction using correlation method (M-IDC) at the sequential inversion frameworks. The synthetic examples indicate that MMM returns multiply magnetization directions and MID results are strongly dependent on initial model and parameter weights. M-IDI computes faster than M-IDC and achieves a constant magnetization direction compared with M-IDCG. Additional priori information constraints can improve the results of MMM, MID and M-IDCG. Obtaining one magnetization direction, M-IDC and M-IDI are suitable for single and isolated anomaly. Finally, M-IDI and M-IDC are used to invert and interpret the magnetic anomaly of the Galinge iron-ore deposit (NW China) and the results are verified by information from drillholes and physical properties measurements of ore and rock samples. Magnetization vector inversion provides a comprehensive way to evaluate and investigate the remanent magnetization and self-demagnetization.

Efficient Storage Scheme of Covariance Matrix during Inverse Modeling

NASA Astrophysics Data System (ADS)

Mao, D.; Yeh, T. J.

2013-12-01

During stochastic inverse modeling, the covariance matrix of geostatistical based methods carries the information about the geologic structure. Its update during iterations reflects the decrease of uncertainty with the incorporation of observed data. For large scale problem, its storage and update cost too much memory and computational resources. In this study, we propose a new efficient storage scheme for storage and update. Compressed Sparse Column (CSC) format is utilized to storage the covariance matrix, and users can assign how many data they prefer to store based on correlation scales since the data beyond several correlation scales are usually not very informative for inverse modeling. After every iteration, only the diagonal terms of the covariance matrix are updated. The off diagonal terms are calculated and updated based on shortened correlation scales with a pre-assigned exponential model. The correlation scales are shortened by a coefficient, i.e. 0.95, every iteration to show the decrease of uncertainty. There is no universal coefficient for all the problems and users are encouraged to try several times. This new scheme is tested with 1D examples first. The estimated results and uncertainty are compared with the traditional full storage method. In the end, a large scale numerical model is utilized to validate this new scheme.

Aerosol Models for the CALIPSO Lidar Inversion Algorithms

NASA Technical Reports Server (NTRS)

Omar, Ali H.; Winker, David M.; Won, Jae-Gwang

2003-01-01

We use measurements and models to develop aerosol models for use in the inversion algorithms for the Cloud Aerosol Lidar and Imager Pathfinder Spaceborne Observations (CALIPSO). Radiance measurements and inversions of the AErosol RObotic NETwork (AERONET1, 2) are used to group global atmospheric aerosols using optical and microphysical parameters. This study uses more than 105 records of radiance measurements, aerosol size distributions, and complex refractive indices to generate the optical properties of the aerosol at more 200 sites worldwide. These properties together with the radiance measurements are then classified using classical clustering methods to group the sites according to the type of aerosol with the greatest frequency of occurrence at each site. Six significant clusters are identified: desert dust, biomass burning, urban industrial pollution, rural background, marine, and dirty pollution. Three of these are used in the CALIPSO aerosol models to characterize desert dust, biomass burning, and polluted continental aerosols. The CALIPSO aerosol model also uses the coarse mode of desert dust and the fine mode of biomass burning to build a polluted dust model. For marine aerosol, the CALIPSO aerosol model uses measurements from the SEAS experiment 3. In addition to categorizing the aerosol types, the cluster analysis provides all the column optical and microphysical properties for each cluster.

TOPEX/POSEIDON tides estimated using a global inverse model

NASA Technical Reports Server (NTRS)

Egbert, Gary D.; Bennett, Andrew F.; Foreman, Michael G. G.

1994-01-01

Altimetric data from the TOPEX/POSEIDON mission will be used for studies of global ocean circulation and marine geophysics. However, it is first necessary to remove the ocean tides, which are aliased in the raw data. The tides are constrained by the two distinct types of information: the hydrodynamic equations which the tidal fields of elevations and velocities must satisfy, and direct observational data from tide gauges and satellite altimetry. Here we develop and apply a generalized inverse method, which allows us to combine rationally all of this information into global tidal fields best fitting both the data and the dynamics, in a least squares sense. The resulting inverse solution is a sum of the direct solution to the astronomically forced Laplace tidal equations and a linear combination of the representers for the data functionals. The representer functions (one for each datum) are determined by the dynamical equations, and by our prior estimates of the statistics or errors in these equations. Our major task is a direct numerical calculation of these representers. This task is computationally intensive, but well suited to massively parallel processing. By calculating the representers we reduce the full (infinite dimensional) problem to a relatively low-dimensional problem at the outset, allowing full control over the conditioning and hence the stability of the inverse solution. With the representers calculated we can easily update our model as additional TOPEX/POSEIDON data become available. As an initial illustration we invert harmonic constants from a set of 80 open-ocean tide gauges. We then present a practical scheme for direct inversion of TOPEX/POSEIDON crossover data. We apply this method to 38 cycles of geophysical data records (GDR) data, computing preliminary global estimates of the four principal tidal constituents, M(sub 2), S(sub 2), K(sub 1) and O(sub 1). The inverse solution yields tidal fields which are simultaneously smoother, and in better

Study on Fault Diagnostics of a Turboprop Engine Using Inverse Performance Model and Artificial Intelligent Methods

NASA Astrophysics Data System (ADS)

Kong, Changduk; Lim, Semyeong

2011-12-01

Recently, the health monitoring system of major gas path components of gas turbine uses mostly the model based method like the Gas Path Analysis (GPA). This method is to find quantity changes of component performance characteristic parameters such as isentropic efficiency and mass flow parameter by comparing between measured engine performance parameters such as temperatures, pressures, rotational speeds, fuel consumption, etc. and clean engine performance parameters without any engine faults which are calculated by the base engine performance model. Currently, the expert engine diagnostic systems using the artificial intelligent methods such as Neural Networks (NNs), Fuzzy Logic and Genetic Algorithms (GAs) have been studied to improve the model based method. Among them the NNs are mostly used to the engine fault diagnostic system due to its good learning performance, but it has a drawback due to low accuracy and long learning time to build learning data base if there are large amount of learning data. In addition, it has a very complex structure for finding effectively single type faults or multiple type faults of gas path components. This work builds inversely a base performance model of a turboprop engine to be used for a high altitude operation UAV using measured performance data, and proposes a fault diagnostic system using the base engine performance model and the artificial intelligent methods such as Fuzzy logic and Neural Network. The proposed diagnostic system isolates firstly the faulted components using Fuzzy Logic, then quantifies faults of the identified components using the NN leaned by fault learning data base, which are obtained from the developed base performance model. In leaning the NN, the Feed Forward Back Propagation (FFBP) method is used. Finally, it is verified through several test examples that the component faults implanted arbitrarily in the engine are well isolated and quantified by the proposed diagnostic system.

Comparison result of inversion of gravity data of a fault by particle swarm optimization and Levenberg-Marquardt methods.

PubMed

Toushmalani, Reza

2013-01-01

The purpose of this study was to compare the performance of two methods for gravity inversion of a fault. First method [Particle swarm optimization (PSO)] 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. Second method [The Levenberg-Marquardt algorithm (LM)] is an approximation to the Newton method used also for training ANNs. In this paper first we discussed the gravity field of a fault, then describes the algorithms of PSO and LM And presents application of Levenberg-Marquardt algorithm, and a particle swarm algorithm in solving inverse problem of a fault. Most importantly the parameters for the algorithms are given for the individual tests. Inverse solution reveals that fault model parameters are agree quite well with the known results. A more agreement has been found between the predicted model anomaly and the observed gravity anomaly in PSO method rather than LM method.

Joining direct and indirect inverse calibration methods to characterize karst, coastal aquifers

NASA Astrophysics Data System (ADS)

De Filippis, Giovanna; Foglia, Laura; Giudici, Mauro; Mehl, Steffen; Margiotta, Stefano; Negri, Sergio

2016-04-01

Parameter estimation is extremely relevant for accurate simulation of groundwater flow. Parameter values for models of large-scale catchments are usually derived from a limited set of field observations, which can rarely be obtained in a straightforward way from field tests or laboratory measurements on samples, due to a number of factors, including measurement errors and inadequate sampling density. Indeed, a wide gap exists between the local scale, at which most of the observations are taken, and the regional or basin scale, at which the planning and management decisions are usually made. For this reason, the use of geologic information and field data is generally made by zoning the parameter fields. However, pure zoning does not perform well in the case of fairly complex aquifers and this is particularly true for karst aquifers. In fact, the support of the hydraulic conductivity measured in the field is normally much smaller than the cell size of the numerical model, so it should be upscaled to a scale consistent with that of the numerical model discretization. Automatic inverse calibration is a valuable procedure to identify model parameter values by conditioning on observed, available data, limiting the subjective evaluations introduced with the trial-and-error technique. Many approaches have been proposed to solve the inverse problem. Generally speaking, inverse methods fall into two groups: direct and indirect methods. Direct methods allow determination of hydraulic conductivities from the groundwater flow equations which relate the conductivity and head fields. Indirect methods, instead, can handle any type of parameters, independently from the mathematical equations that govern the process, and condition parameter values and model construction on measurements of model output quantities, compared with the available observation data, through the minimization of an objective function. Both approaches have pros and cons, depending also on model complexity. For

Study of multilayer thermal insulation by inverse problems method

NASA Astrophysics Data System (ADS)

Alifanov, O. M.; Nenarokomov, A. V.; Gonzalez, V. M.

2009-11-01

The purpose of this paper is to introduce a new method in the research of radiative and thermal properties of materials with further applications in the design of thermal control systems (TCS) of spacecrafts. In this paper the radiative and thermal properties (emissivity and thermal conductance) of a multilayered thermal-insulating blanket (MLI), which is a screen-vacuum thermal insulation as a part of the TCS for perspective spacecrafts, are estimated. Properties of the materials under study are determined in the result of temperature and heat flux measurement data processing based on the solution of the inverse heat transfer problem (IHTP) technique. Given are physical and mathematical models of heat transfer processes in a specimen of the multilayered thermal-insulating blanket located in the experimental facility. A mathematical formulation of the inverse heat conduction problem is presented as well. The practical approves were made for specimen of the real MLI.

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…

Three-dimensional magnetotelluric axial anisotropic forward modeling and inversion

NASA Astrophysics Data System (ADS)

Cao, Hui; Wang, Kunpeng; Wang, Tao; Hua, Boguang

2018-06-01

Magnetotelluric (MT) data has been widely used to image underground electrical structural. However, when the significant axial resistivity anisotropy presents, how this influences three-dimensional MT data has not been resolved clearly yet. We here propose a scheme for three-dimensional modeling of MT data in presence of axial anisotropic resistivity, where the electromagnetic fields are decomposed into primary and secondary components. A 3D staggered-grid finite difference method is then used to resolve the resulting 3D governing equations. Numerical tests have completed to validate the correctness and accuracy of the present algorithm. A limited-memory Broyden-Fletcher-Goldfarb-Shanno method is then utilized to realize the 3D MT axial anisotropic inversion. The testing results show that, compared to the results of isotropic resistivity inversion, taking account the axial anisotropy can much improve the inverted results.

Balancing aggregation and smoothing errors in inverse models

DOE PAGES

Turner, A. J.; Jacob, D. J.

2015-06-30

Inverse models use observations of a system (observation vector) to quantify the variables driving that system (state vector) by statistical optimization. When the observation vector is large, such as with satellite data, selecting a suitable dimension for the state vector is a challenge. A state vector that is too large cannot be effectively constrained by the observations, leading to smoothing error. However, reducing the dimension of the state vector leads to aggregation error as prior relationships between state vector elements are imposed rather than optimized. Here we present a method for quantifying aggregation and smoothing errors as a function ofmore » state vector dimension, so that a suitable dimension can be selected by minimizing the combined error. Reducing the state vector within the aggregation error constraints can have the added advantage of enabling analytical solution to the inverse problem with full error characterization. We compare three methods for reducing the dimension of the state vector from its native resolution: (1) merging adjacent elements (grid coarsening), (2) clustering with principal component analysis (PCA), and (3) applying a Gaussian mixture model (GMM) with Gaussian pdfs as state vector elements on which the native-resolution state vector elements are projected using radial basis functions (RBFs). The GMM method leads to somewhat lower aggregation error than the other methods, but more importantly it retains resolution of major local features in the state vector while smoothing weak and broad features.« less

Balancing aggregation and smoothing errors in inverse models

NASA Astrophysics Data System (ADS)

Turner, A. J.; Jacob, D. J.

2015-01-01

Inverse models use observations of a system (observation vector) to quantify the variables driving that system (state vector) by statistical optimization. When the observation vector is large, such as with satellite data, selecting a suitable dimension for the state vector is a challenge. A state vector that is too large cannot be effectively constrained by the observations, leading to smoothing error. However, reducing the dimension of the state vector leads to aggregation error as prior relationships between state vector elements are imposed rather than optimized. Here we present a method for quantifying aggregation and smoothing errors as a function of state vector dimension, so that a suitable dimension can be selected by minimizing the combined error. Reducing the state vector within the aggregation error constraints can have the added advantage of enabling analytical solution to the inverse problem with full error characterization. We compare three methods for reducing the dimension of the state vector from its native resolution: (1) merging adjacent elements (grid coarsening), (2) clustering with principal component analysis (PCA), and (3) applying a Gaussian mixture model (GMM) with Gaussian pdfs as state vector elements on which the native-resolution state vector elements are projected using radial basis functions (RBFs). The GMM method leads to somewhat lower aggregation error than the other methods, but more importantly it retains resolution of major local features in the state vector while smoothing weak and broad features.

Balancing aggregation and smoothing errors in inverse models

NASA Astrophysics Data System (ADS)

Turner, A. J.; Jacob, D. J.

2015-06-01

Inverse models use observations of a system (observation vector) to quantify the variables driving that system (state vector) by statistical optimization. When the observation vector is large, such as with satellite data, selecting a suitable dimension for the state vector is a challenge. A state vector that is too large cannot be effectively constrained by the observations, leading to smoothing error. However, reducing the dimension of the state vector leads to aggregation error as prior relationships between state vector elements are imposed rather than optimized. Here we present a method for quantifying aggregation and smoothing errors as a function of state vector dimension, so that a suitable dimension can be selected by minimizing the combined error. Reducing the state vector within the aggregation error constraints can have the added advantage of enabling analytical solution to the inverse problem with full error characterization. We compare three methods for reducing the dimension of the state vector from its native resolution: (1) merging adjacent elements (grid coarsening), (2) clustering with principal component analysis (PCA), and (3) applying a Gaussian mixture model (GMM) with Gaussian pdfs as state vector elements on which the native-resolution state vector elements are projected using radial basis functions (RBFs). The GMM method leads to somewhat lower aggregation error than the other methods, but more importantly it retains resolution of major local features in the state vector while smoothing weak and broad features.

Angle-domain inverse scattering migration/inversion in isotropic media

NASA Astrophysics Data System (ADS)

Li, Wuqun; Mao, Weijian; Li, Xuelei; Ouyang, Wei; Liang, Quan

2018-07-01

The classical seismic asymptotic inversion can be transformed into a problem of inversion of generalized Radon transform (GRT). In such methods, the combined parameters are linearly attached to the scattered wave-field by Born approximation and recovered by applying an inverse GRT operator to the scattered wave-field data. Typical GRT-style true-amplitude inversion procedure contains an amplitude compensation process after the weighted migration via dividing an illumination associated matrix whose elements are integrals of scattering angles. It is intuitional to some extent that performs the generalized linear inversion and the inversion of GRT together by this process for direct inversion. However, it is imprecise to carry out such operation when the illumination at the image point is limited, which easily leads to the inaccuracy and instability of the matrix. This paper formulates the GRT true-amplitude inversion framework in an angle-domain version, which naturally degrades the external integral term related to the illumination in the conventional case. We solve the linearized integral equation for combined parameters of different fixed scattering angle values. With this step, we obtain high-quality angle-domain common-image gathers (CIGs) in the migration loop which provide correct amplitude-versus-angle (AVA) behavior and reasonable illumination range for subsurface image points. Then we deal with the over-determined problem to solve each parameter in the combination by a standard optimization operation. The angle-domain GRT inversion method keeps away from calculating the inaccurate and unstable illumination matrix. Compared with the conventional method, the angle-domain method can obtain more accurate amplitude information and wider amplitude-preserved range. Several model tests demonstrate the effectiveness and practicability.

A model reduction approach to numerical inversion for a parabolic partial differential equation

NASA Astrophysics Data System (ADS)

Borcea, Liliana; Druskin, Vladimir; Mamonov, Alexander V.; Zaslavsky, Mikhail

2014-12-01

We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where the unknown is the subsurface electrical resistivity and the data are time resolved surface measurements of the magnetic field. The algorithm presented in this paper considers inversion in one and two dimensions. The reduced model is obtained with rational interpolation in the frequency (Laplace) domain and a rational Krylov subspace projection method. It amounts to a nonlinear mapping from the function space of the unknown resistivity to the small dimensional space of the parameters of the reduced model. We use this mapping as a nonlinear preconditioner for the Gauss-Newton iterative solution of the inverse problem. The advantage of the inversion algorithm is twofold. First, the nonlinear preconditioner resolves most of the nonlinearity of the problem. Thus the iterations are less likely to get stuck in local minima and the convergence is fast. Second, the inversion is computationally efficient because it avoids repeated accurate simulations of the time-domain response. We study the stability of the inversion algorithm for various rational Krylov subspaces, and assess its performance with numerical experiments.

2 + 1 Toda chain. I. Inverse scattering method

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

Lipovskii, V.D.; Shirokov, A.V.

A formal scheme of the inverse scattering method is constructed for the2 + 1 Toda chain in the class of rapidly decreasing Cauchy data. Application of the inverse scattering method to the two-dimensional infinite Toda chain was made difficult by the circumstance that this system is a (2 + 1)-dimensional object, i.e., possesses time and two spatial variables, the role of one of these being played by the chain site number. Because of this, our information about the 2 + 1 Toda chain was limited to a rich set of particular solutions of soliton type obtained in the cycle ofmore » studies by the Darboux transformation method.« less

Computer Model Inversion and Uncertainty Quantification in the Geosciences

NASA Astrophysics Data System (ADS)

White, Jeremy T.

The subject of this dissertation is use of computer models as data analysis tools in several different geoscience settings, including integrated surface water/groundwater modeling, tephra fallout modeling, geophysical inversion, and hydrothermal groundwater modeling. The dissertation is organized into three chapters, which correspond to three individual publication manuscripts. In the first chapter, a linear framework is developed to identify and estimate the potential predictive consequences of using a simple computer model as a data analysis tool. The framework is applied to a complex integrated surface-water/groundwater numerical model with thousands of parameters. Several types of predictions are evaluated, including particle travel time and surface-water/groundwater exchange volume. The analysis suggests that model simplifications have the potential to corrupt many types of predictions. The implementation of the inversion, including how the objective function is formulated, what minimum of the objective function value is acceptable, and how expert knowledge is enforced on parameters, can greatly influence the manifestation of model simplification. Depending on the prediction, failure to specifically address each of these important issues during inversion is shown to degrade the reliability of some predictions. In some instances, inversion is shown to increase, rather than decrease, the uncertainty of a prediction, which defeats the purpose of using a model as a data analysis tool. In the second chapter, an efficient inversion and uncertainty quantification approach is applied to a computer model of volcanic tephra transport and deposition. The computer model simulates many physical processes related to tephra transport and fallout. The utility of the approach is demonstrated for two eruption events. In both cases, the importance of uncertainty quantification is highlighted by exposing the variability in the conditioning provided by the observations used for

Propeller sheet cavitation noise source modeling and inversion

NASA Astrophysics Data System (ADS)

Lee, Keunhwa; Lee, Jaehyuk; Kim, Dongho; Kim, Kyungseop; Seong, Woojae

2014-02-01

Propeller sheet cavitation is the main contributor to high level of noise and vibration in the after body of a ship. Full measurement of the cavitation-induced hull pressure over the entire surface of the affected area is desired but not practical. Therefore, using a few measurements on the outer hull above the propeller in a cavitation tunnel, empirical or semi-empirical techniques based on physical model have been used to predict the hull-induced pressure (or hull-induced force). In this paper, with the analytic source model for sheet cavitation, a multi-parameter inversion scheme to find the positions of noise sources and their strengths is suggested. The inversion is posed as a nonlinear optimization problem, which is solved by the optimization algorithm based on the adaptive simplex simulated annealing algorithm. Then, the resulting hull pressure can be modeled with boundary element method from the inverted cavitation noise sources. The suggested approach is applied to the hull pressure data measured in a cavitation tunnel of the Samsung Heavy Industry. Two monopole sources are adequate to model the propeller sheet cavitation noise. The inverted source information is reasonable with the cavitation dynamics of the propeller and the modeled hull pressure shows good agreement with cavitation tunnel experimental data.

Structural Health Monitoring Using High-Density Fiber Optic Strain Sensor and Inverse Finite Element Methods

NASA Technical Reports Server (NTRS)

Vazquez, Sixto L.; Tessler, Alexander; Quach, Cuong C.; Cooper, Eric G.; Parks, Jeffrey; Spangler, Jan L.

2005-01-01

In an effort to mitigate accidents due to system and component failure, NASA s Aviation Safety has partnered with industry, academia, and other governmental organizations to develop real-time, on-board monitoring capabilities and system performance models for early detection of airframe structure degradation. NASA Langley is investigating a structural health monitoring capability that uses a distributed fiber optic strain system and an inverse finite element method for measuring and modeling structural deformations. This report describes the constituent systems that enable this structural monitoring function and discusses results from laboratory tests using the fiber strain sensor system and the inverse finite element method to demonstrate structural deformation estimation on an instrumented test article

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

NASA Astrophysics Data System (ADS)

Yagi, Y.; Okuwaki, R.

2017-12-01

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

Inverse estimation of parameters for an estuarine eutrophication model

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

Shen, J.; Kuo, A.Y.

1996-11-01

An inverse model of an estuarine eutrophication model with eight state variables is developed. It provides a framework to estimate parameter values of the eutrophication model by assimilation of concentration data of these state variables. The inverse model using the variational technique in conjunction with a vertical two-dimensional eutrophication model is general enough to be applicable to aid model calibration. The formulation is illustrated by conducting a series of numerical experiments for the tidal Rappahannock River, a western shore tributary of the Chesapeake Bay. The numerical experiments of short-period model simulations with different hypothetical data sets and long-period model simulationsmore » with limited hypothetical data sets demonstrated that the inverse model can be satisfactorily used to estimate parameter values of the eutrophication model. The experiments also showed that the inverse model is useful to address some important questions, such as uniqueness of the parameter estimation and data requirements for model calibration. Because of the complexity of the eutrophication system, degrading of speed of convergence may occur. Two major factors which cause degradation of speed of convergence are cross effects among parameters and the multiple scales involved in the parameter system.« less

Nonlinear inversion of resistivity sounding data for 1-D earth models using the Neighbourhood Algorithm

NASA Astrophysics Data System (ADS)

Ojo, A. O.; Xie, Jun; Olorunfemi, M. O.

2018-01-01

To reduce ambiguity related to nonlinearities in the resistivity model-data relationships, an efficient direct-search scheme employing the Neighbourhood Algorithm (NA) was implemented to solve the 1-D resistivity problem. In addition to finding a range of best-fit models which are more likely to be global minimums, this method investigates the entire multi-dimensional model space and provides additional information about the posterior model covariance matrix, marginal probability density function and an ensemble of acceptable models. This provides new insights into how well the model parameters are constrained and make assessing trade-offs between them possible, thus avoiding some common interpretation pitfalls. The efficacy of the newly developed program is tested by inverting both synthetic (noisy and noise-free) data and field data from other authors employing different inversion methods so as to provide a good base for comparative performance. In all cases, the inverted model parameters were in good agreement with the true and recovered model parameters from other methods and remarkably correlate with the available borehole litho-log and known geology for the field dataset. The NA method has proven to be useful whilst a good starting model is not available and the reduced number of unknowns in the 1-D resistivity inverse problem makes it an attractive alternative to the linearized methods. Hence, it is concluded that the newly developed program offers an excellent complementary tool for the global inversion of the layered resistivity structure.

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.

Issues in the inverse modeling of a soil infiltration process

NASA Astrophysics Data System (ADS)

Kuraz, Michal; Jacka, Lukas; Leps, Matej

2017-04-01

This contribution addresses issues in evaluation of the soil hydraulic parameters (SHP) from the Richards equation based inverse model. The inverse model was representing single ring infiltration experiment on mountainous podzolic soil profile, and was searching for the SHP parameters of the top soil layer. Since the thickness of the top soil layer is often much lower than the depth required to embed the single ring or Guelph permeameter device, the SHPs for the top soil layer are very difficult to measure directly. The SHPs for the top soil layer were therefore identified here by inverse modeling of the single ring infiltration process, where, especially, the initial unsteady part of the experiment is expected to provide very useful data for evaluating the retention curve parameters (excluding the residual water content) and the saturated hydraulic conductivity. The main issue, which is addressed in this contribution, is the uniqueness of the Richards equation inverse model. We tried to answer the question whether is it possible to characterize the unsteady infiltration experiment with a unique set of SHPs values, and whether are all SHP parameters vulnerable with the non-uniqueness. Which is an important issue, since we could further conclude whether the popular gradient methods are appropriate here. Further the issues in assigning the initial and boundary condition setup, the influence of spatial and temporal discretization on the values of the identified SHPs, and the convergence issues with the Richards equation nonlinear operator during automatic calibration procedure are also covered here.

Model-based elastography: a survey of approaches to the inverse elasticity problem

PubMed Central

Doyley, M M

2012-01-01

Elastography is emerging as an imaging modality that can distinguish normal versus diseased tissues via their biomechanical properties. This article reviews current approaches to elastography in three areas — quasi-static, harmonic, and transient — and describes inversion schemes for each elastographic imaging approach. Approaches include: first-order approximation methods; direct and iterative inversion schemes for linear elastic; isotropic materials; and advanced reconstruction methods for recovering parameters that characterize complex mechanical behavior. The paper’s objective is to document efforts to develop elastography within the framework of solving an inverse problem, so that elastography may provide reliable estimates of shear modulus and other mechanical parameters. We discuss issues that must be addressed if model-based elastography is to become the prevailing approach to quasi-static, harmonic, and transient elastography: (1) developing practical techniques to transform the ill-posed problem with a well-posed one; (2) devising better forward models to capture the transient behavior of soft tissue; and (3) developing better test procedures to evaluate the performance of modulus elastograms. PMID:22222839

Inversion of Surface-wave Dispersion Curves due to Low-velocity-layer Models

NASA Astrophysics Data System (ADS)

Shen, C.; Xia, J.; Mi, B.

2016-12-01

A successful inversion relies on exact forward modeling methods. It is a key step to accurately calculate multi-mode dispersion curves of a given model in high-frequency surface-wave (Rayleigh wave and Love wave) methods. For normal models (shear (S)-wave velocity increasing with depth), their theoretical dispersion curves completely match the dispersion spectrum that is generated based on wave equation. For models containing a low-velocity-layer, however, phase velocities calculated by existing forward-modeling algorithms (e.g. Thomson-Haskell algorithm, Knopoff algorithm, fast vector-transfer algorithm and so on) fail to be consistent with the dispersion spectrum at a high frequency range. They will approach a value that close to the surface-wave velocity of the low-velocity-layer under the surface layer, rather than that of the surface layer when their corresponding wavelengths are short enough. This phenomenon conflicts with the characteristics of surface waves, which results in an erroneous inverted model. By comparing the theoretical dispersion curves with simulated dispersion energy, we proposed a direct and essential solution to accurately compute surface-wave phase velocities due to low-velocity-layer models. Based on the proposed forward modeling technique, we can achieve correct inversion for these types of models. Several synthetic data proved the effectiveness of our method.

Locally refined block-centered finite-difference groundwater models: Evaluation of parameter sensitivity and the consequences for inverse modelling and predictions

USGS Publications Warehouse

Mehl, S.; Hill, M.C.

2002-01-01

Models with local grid refinement, as often required in groundwater models, pose special problems for model calibration. This work investigates the calculation of sensitivities and performance of regression methods using two existing and one new method of grid refinement. The existing local grid refinement methods considered are (1) a variably spaced grid in which the grid spacing becomes smaller near the area of interest and larger where such detail is not needed and (2) telescopic mesh refinement (TMR), which uses the hydraulic heads or fluxes of a regional model to provide the boundary conditions for a locally refined model. The new method has a feedback between the regional and local grids using shared nodes, and thereby, unlike the TMR methods, balances heads and fluxes at the interfacing boundary. Results for sensitivities are compared for the three methods and the effect of the accuracy of sensitivity calculations are evaluated by comparing inverse modelling results. For the cases tested, results indicate that the inaccuracies of the sensitivities calculated using the TMR approach can cause the inverse model to converge to an incorrect solution.

A direct-inverse method for transonic and separated flows about airfoils

NASA Technical Reports Server (NTRS)

Carlson, K. D.

1985-01-01

A direct-inverse technique and computer program called TAMSEP that can be sued for the analysis of the flow about airfoils at subsonic and low transonic freestream velocities is presented. The method is based upon a direct-inverse nonconservative full potential inviscid method, a Thwaites laminar boundary layer technique, and the Barnwell turbulent momentum integral scheme; and it is formulated using Cartesian coordinates. Since the method utilizes inverse boundary conditions in regions of separated flow, it is suitable for predicing the flowfield about airfoils having trailing edge separated flow under high lift conditions. Comparisons with experimental data indicate that the method should be a useful tool for applied aerodynamic analyses.

A direct-inverse method for transonic and separated flows about airfoils

NASA Technical Reports Server (NTRS)

Carlson, Leland A.

1990-01-01

A direct-inverse technique and computer program called TAMSEP that can be used for the analysis of the flow about airfoils at subsonic and low transonic freestream velocities is presented. The method is based upon a direct-inverse nonconservative full potential inviscid method, a Thwaites laminar boundary layer technique, and the Barnwell turbulent momentum integral scheme; and it is formulated using Cartesian coordinates. Since the method utilizes inverse boundary conditions in regions of separated flow, it is suitable for predicting the flow field about airfoils having trailing edge separated flow under high lift conditions. Comparisons with experimental data indicate that the method should be a useful tool for applied aerodynamic analyses.

3-D linear inversion of gravity data: method and application to Basse-Terre volcanic island, Guadeloupe, Lesser Antilles

NASA Astrophysics Data System (ADS)

Barnoud, Anne; Coutant, Olivier; Bouligand, Claire; Gunawan, Hendra; Deroussi, Sébastien

2016-04-01

We use a Bayesian formalism combined with a grid node discretization for the linear inversion of gravimetric data in terms of 3-D density distribution. The forward modelling and the inversion method are derived from seismological inversion techniques in order to facilitate joint inversion or interpretation of density and seismic velocity models. The Bayesian formulation introduces covariance matrices on model parameters to regularize the ill-posed problem and reduce the non-uniqueness of the solution. This formalism favours smooth solutions and allows us to specify a spatial correlation length and to perform inversions at multiple scales. We also extract resolution parameters from the resolution matrix to discuss how well our density models are resolved. This method is applied to the inversion of data from the volcanic island of Basse-Terre in Guadeloupe, Lesser Antilles. A series of synthetic tests are performed to investigate advantages and limitations of the methodology in this context. This study results in the first 3-D density models of the island of Basse-Terre for which we identify: (i) a southward decrease of densities parallel to the migration of volcanic activity within the island, (ii) three dense anomalies beneath Petite Plaine Valley, Beaugendre Valley and the Grande-Découverte-Carmichaël-Soufrière Complex that may reflect the trace of former major volcanic feeding systems, (iii) shallow low-density anomalies in the southern part of Basse-Terre, especially around La Soufrière active volcano, Piton de Bouillante edifice and along the western coast, reflecting the presence of hydrothermal systems and fractured and altered rocks.

Laterally constrained inversion for CSAMT data interpretation

NASA Astrophysics Data System (ADS)

Wang, Ruo; Yin, Changchun; Wang, Miaoyue; Di, Qingyun

2015-10-01

Laterally constrained inversion (LCI) has been successfully applied to the inversion of dc resistivity, TEM and airborne EM data. However, it hasn't been yet applied to the interpretation of controlled-source audio-frequency magnetotelluric (CSAMT) data. In this paper, we apply the LCI method for CSAMT data inversion by preconditioning the Jacobian matrix. We apply a weighting matrix to Jacobian to balance the sensitivity of model parameters, so that the resolution with respect to different model parameters becomes more uniform. Numerical experiments confirm that this can improve the convergence of the inversion. We first invert a synthetic dataset with and without noise to investigate the effect of LCI applications to CSAMT data, for the noise free data, the results show that the LCI method can recover the true model better compared to the traditional single-station inversion; and for the noisy data, the true model is recovered even with a noise level of 8%, indicating that LCI inversions are to some extent noise insensitive. Then, we re-invert two CSAMT datasets collected respectively in a watershed and a coal mine area in Northern China and compare our results with those from previous inversions. The comparison with the previous inversion in a coal mine shows that LCI method delivers smoother layer interfaces that well correlate to seismic data, while comparison with a global searching algorithm of simulated annealing (SA) in a watershed shows that though both methods deliver very similar good results, however, LCI algorithm presented in this paper runs much faster. The inversion results for the coal mine CSAMT survey show that a conductive water-bearing zone that was not revealed by the previous inversions has been identified by the LCI. This further demonstrates that the method presented in this paper works for CSAMT data inversion.

Total variation regularization for seismic waveform inversion using an adaptive primal dual hybrid gradient method

NASA Astrophysics Data System (ADS)

Yong, Peng; Liao, Wenyuan; Huang, Jianping; Li, Zhenchuan

2018-04-01

Full waveform inversion is an effective tool for recovering the properties of the Earth from seismograms. However, it suffers from local minima caused mainly by the limited accuracy of the starting model and the lack of a low-frequency component in the seismic data. Because of the high velocity contrast between salt and sediment, the relation between the waveform and velocity perturbation is strongly nonlinear. Therefore, salt inversion can easily get trapped in the local minima. Since the velocity of salt is nearly constant, we can make the most of this characteristic with total variation regularization to mitigate the local minima. In this paper, we develop an adaptive primal dual hybrid gradient method to implement total variation regularization by projecting the solution onto a total variation norm constrained convex set, through which the total variation norm constraint is satisfied at every model iteration. The smooth background velocities are first inverted and the perturbations are gradually obtained by successively relaxing the total variation norm constraints. Numerical experiment of the projection of the BP model onto the intersection of the total variation norm and box constraints has demonstrated the accuracy and efficiency of our adaptive primal dual hybrid gradient method. A workflow is designed to recover complex salt structures in the BP 2004 model and the 2D SEG/EAGE salt model, starting from a linear gradient model without using low-frequency data below 3 Hz. The salt inversion processes demonstrate that wavefield reconstruction inversion with a total variation norm and box constraints is able to overcome local minima and inverts the complex salt velocity layer by layer.

Saturation-inversion-recovery: A method for T1 measurement

NASA Astrophysics Data System (ADS)

Wang, Hongzhi; Zhao, Ming; Ackerman, Jerome L.; Song, Yiqiao

2017-01-01

Spin-lattice relaxation (T1) has always been measured by inversion-recovery (IR), saturation-recovery (SR), or related methods. These existing methods share a common behavior in that the function describing T1 sensitivity is the exponential, e.g., exp(- τ /T1), where τ is the recovery time. In this paper, we describe a saturation-inversion-recovery (SIR) sequence for T1 measurement with considerably sharper T1-dependence than those of the IR and SR sequences, and demonstrate it experimentally. The SIR method could be useful in improving the contrast between regions of differing T1 in T1-weighted MRI.

Understanding the Day Cent model: Calibration, sensitivity, and identifiability through inverse modeling

USGS Publications Warehouse

Necpálová, Magdalena; Anex, Robert P.; Fienen, Michael N.; Del Grosso, Stephen J.; Castellano, Michael J.; Sawyer, John E.; Iqbal, Javed; Pantoja, Jose L.; Barker, Daniel W.

2015-01-01

The ability of biogeochemical ecosystem models to represent agro-ecosystems depends on their correct integration with field observations. We report simultaneous calibration of 67 DayCent model parameters using multiple observation types through inverse modeling using the PEST parameter estimation software. Parameter estimation reduced the total sum of weighted squared residuals by 56% and improved model fit to crop productivity, soil carbon, volumetric soil water content, soil temperature, N2O, and soil3NO− compared to the default simulation. Inverse modeling substantially reduced predictive model error relative to the default model for all model predictions, except for soil 3NO− and 4NH+. Post-processing analyses provided insights into parameter–observation relationships based on parameter correlations, sensitivity and identifiability. Inverse modeling tools are shown to be a powerful way to systematize and accelerate the process of biogeochemical model interrogation, improving our understanding of model function and the underlying ecosystem biogeochemical processes that they represent.

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.

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

NASA Astrophysics Data System (ADS)

Jahandari, H.; Farquharson, C. G.

2017-11-01

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

3-D Modeling of Irregular Volcanic Sources Using Sparsity-Promoting Inversions of Geodetic Data and Boundary Element Method

NASA Astrophysics Data System (ADS)

Zhai, Guang; Shirzaei, Manoochehr

2017-12-01

Geodetic observations of surface deformation associated with volcanic activities can be used to constrain volcanic source parameters and their kinematics. Simple analytical models, such as point and spherical sources, are widely used to model deformation data. The inherent nature of oversimplified model geometries makes them unable to explain fine details of surface deformation. Current nonparametric, geometry-free inversion approaches resolve the distributed volume change, assuming it varies smoothly in space, which may detect artificial volume change outside magmatic source regions. To obtain a physically meaningful representation of an irregular volcanic source, we devise a new sparsity-promoting modeling scheme assuming active magma bodies are well-localized melt accumulations, namely, outliers in the background crust. First, surface deformation data are inverted using a hybrid L1- and L2-norm regularization scheme to solve for sparse volume change distributions. Next, a boundary element method is implemented to solve for the displacement discontinuity distribution of the reservoir, which satisfies a uniform pressure boundary condition. The inversion approach is thoroughly validated using benchmark and synthetic tests, of which the results show that source dimension, depth, and shape can be recovered appropriately. We apply this modeling scheme to deformation observed at Kilauea summit for periods of uplift and subsidence leading to and following the 2007 Father's Day event. We find that the magmatic source geometries for these periods are statistically distinct, which may be an indicator that magma is released from isolated compartments due to large differential pressure leading to the rift intrusion.

Simultaneous inversion of seismic velocity and moment tensor using elastic-waveform inversion of microseismic data: Application to the Aneth CO2-EOR field

NASA Astrophysics Data System (ADS)

Chen, Y.; Huang, L.

2017-12-01

Moment tensors are key parameters for characterizing CO2-injection-induced microseismic events. Elastic-waveform inversion has the potential to providing accurate results of moment tensors. Microseismic waveforms contains information of source moment tensors and the wave propagation velocity along the wavepaths. We develop an elastic-waveform inversion method to jointly invert the seismic velocity model and moment tensor. We first use our adaptive moment-tensor joint inversion method to estimate moment tensors of microseismic events. Our adaptive moment-tensor inversion method jointly inverts multiple microseismic events with similar waveforms within a cluster to reduce inversion uncertainty for microseismic data recorded using a single borehole geophone array. We use this inversion result as the initial model for our elastic-waveform inversion to minimize the cross-correlated-based data misfit between observed data and synthetic data. We verify our method using synthetic microseismic data and obtain improved results of both moment tensors and seismic velocity model. We apply our new inversion method to microseismic data acquired at a CO2-enhanced oil recovery field in Aneth, Utah, using a single borehole geophone array. The results demonstrate that our new inversion method significantly reduces the data misfit compared to the conventional ray-theory-based moment-tensor inversion.

A Comparison between Model Base Hardconstrain, Bandlimited, and Sparse-Spike Seismic Inversion: New Insights for CBM Reservoir Modelling on Muara Enim Formation, South Sumatra

NASA Astrophysics Data System (ADS)

Mohamad Noor, Faris; Adipta, Agra

2018-03-01

Coal Bed Methane (CBM) as a newly developed resource in Indonesia is one of the alternatives to relieve Indonesia’s dependencies on conventional energies. Coal resource of Muara Enim Formation is known as one of the prolific reservoirs in South Sumatra Basin. Seismic inversion and well analysis are done to determine the coal seam characteristics of Muara Enim Formation. This research uses three inversion methods, which are: model base hard- constrain, bandlimited, and sparse-spike inversion. Each type of seismic inversion has its own advantages to display the coal seam and its characteristic. Interpretation result from the analysis data shows that the Muara Enim coal seam has 20 (API) gamma ray value, 1 (gr/cc) – 1.4 (gr/cc) from density log, and low AI cutoff value range between 5000-6400 (m/s)*(g/cc). The distribution of coal seam is laterally thinning northwest to southeast. Coal seam is seen biasedly on model base hard constraint inversion and discontinued on band-limited inversion which isn’t similar to the geological model. The appropriate AI inversion is sparse spike inversion which has 0.884757 value from cross plot inversion as the best correlation value among the chosen inversion methods. Sparse Spike inversion its self-has high amplitude as a proper tool to identify coal seam continuity which commonly appears as a thin layer. Cross-sectional sparse spike inversion shows that there are possible new boreholes in CDP 3662-3722, CDP 3586-3622, and CDP 4004-4148 which is seen in seismic data as a thick coal seam.

A sparse reconstruction method for the estimation of multiresolution emission fields via atmospheric inversion

DOE PAGES

Ray, J.; Lee, J.; Yadav, V.; ...

2014-08-20

We present a sparse reconstruction scheme that can also be used to ensure non-negativity when fitting wavelet-based random field models to limited observations in non-rectangular geometries. The method is relevant when multiresolution fields are estimated using linear inverse problems. Examples include the estimation of emission fields for many anthropogenic pollutants using atmospheric inversion or hydraulic conductivity in aquifers from flow measurements. The scheme is based on three new developments. Firstly, we extend an existing sparse reconstruction method, Stagewise Orthogonal Matching Pursuit (StOMP), to incorporate prior information on the target field. Secondly, we develop an iterative method that uses StOMP tomore » impose non-negativity on the estimated field. Finally, we devise a method, based on compressive sensing, to limit the estimated field within an irregularly shaped domain. We demonstrate the method on the estimation of fossil-fuel CO 2 (ffCO 2) emissions in the lower 48 states of the US. The application uses a recently developed multiresolution random field model and synthetic observations of ffCO 2 concentrations from a limited set of measurement sites. We find that our method for limiting the estimated field within an irregularly shaped region is about a factor of 10 faster than conventional approaches. It also reduces the overall computational cost by a factor of two. Further, the sparse reconstruction scheme imposes non-negativity without introducing strong nonlinearities, such as those introduced by employing log-transformed fields, and thus reaps the benefits of simplicity and computational speed that are characteristic of linear inverse problems.« less

Refractive index inversion based on Mueller matrix method

NASA Astrophysics Data System (ADS)

Fan, Huaxi; Wu, Wenyuan; Huang, Yanhua; Li, Zhaozhao

2016-03-01

Based on Stokes vector and Jones vector, the correlation between Mueller matrix elements and refractive index was studied with the result simplified, and through Mueller matrix way, the expression of refractive index inversion was deduced. The Mueller matrix elements, under different incident angle, are simulated through the expression of specular reflection so as to analyze the influence of the angle of incidence and refractive index on it, which is verified through the measure of the Mueller matrix elements of polished metal surface. Research shows that, under the condition of specular reflection, the result of Mueller matrix inversion is consistent with the experiment and can be used as an index of refraction of inversion method, and it provides a new way for target detection and recognition technology.

Inverse Problems in Complex Models and Applications to Earth Sciences

NASA Astrophysics Data System (ADS)

Bosch, M. E.

2015-12-01

The inference of the subsurface earth structure and properties requires the integration of different types of data, information and knowledge, by combined processes of analysis and synthesis. To support the process of integrating information, the regular concept of data inversion is evolving to expand its application to models with multiple inner components (properties, scales, structural parameters) that explain multiple data (geophysical survey data, well-logs, core data). The probabilistic inference methods provide the natural framework for the formulation of these problems, considering a posterior probability density function (PDF) that combines the information from a prior information PDF and the new sets of observations. To formulate the posterior PDF in the context of multiple datasets, the data likelihood functions are factorized assuming independence of uncertainties for data originating across different surveys. A realistic description of the earth medium requires modeling several properties and structural parameters, which relate to each other according to dependency and independency notions. Thus, conditional probabilities across model components also factorize. A common setting proceeds by structuring the model parameter space in hierarchical layers. A primary layer (e.g. lithology) conditions a secondary layer (e.g. physical medium properties), which conditions a third layer (e.g. geophysical data). In general, less structured relations within model components and data emerge from the analysis of other inverse problems. They can be described with flexibility via direct acyclic graphs, which are graphs that map dependency relations between the model components. Examples of inverse problems in complex models can be shown at various scales. At local scale, for example, the distribution of gas saturation is inferred from pre-stack seismic data and a calibrated rock-physics model. At regional scale, joint inversion of gravity and magnetic data is applied

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Effects of induced stress on seismic forward modelling and inversion

NASA Astrophysics Data System (ADS)

Tromp, Jeroen; Trampert, Jeannot

2018-05-01

We demonstrate how effects of induced stress may be incorporated in seismic modelling and inversion. Our approach is motivated by the accommodation of pre-stress in global seismology. Induced stress modifies both the equation of motion and the constitutive relationship. The theory predicts that induced pressure linearly affects the unstressed isotropic moduli with a slope determined by their adiabatic pressure derivatives. The induced deviatoric stress produces anisotropic compressional and shear wave speeds; the latter result in shear wave splitting. For forward modelling purposes, we determine the weak form of the equation of motion under induced stress. In the context of the inverse problem, we determine induced stress sensitivity kernels, which may be used for adjoint tomography. The theory is illustrated by considering 2-D propagation of SH waves and related Fréchet derivatives based on a spectral-element method.

Lebedev acceleration and comparison of different photometric models in the inversion of lightcurves for asteroids

NASA Astrophysics Data System (ADS)

Lu, Xiao-Ping; Huang, Xiang-Jie; Ip, Wing-Huen; Hsia, Chi-Hao

2018-04-01

In the lightcurve inversion process where asteroid's physical parameters such as rotational period, pole orientation and overall shape are searched, the numerical calculations of the synthetic photometric brightness based on different shape models are frequently implemented. Lebedev quadrature is an efficient method to numerically calculate the surface integral on the unit sphere. By transforming the surface integral on the Cellinoid shape model to that on the unit sphere, the lightcurve inversion process based on the Cellinoid shape model can be remarkably accelerated. Furthermore, Matlab codes of the lightcurve inversion process based on the Cellinoid shape model are available on Github for free downloading. The photometric models, i.e., the scattering laws, also play an important role in the lightcurve inversion process, although the shape variations of asteroids dominate the morphologies of the lightcurves. Derived from the radiative transfer theory, the Hapke model can describe the light reflectance behaviors from the viewpoint of physics, while there are also many empirical models in numerical applications. Numerical simulations are implemented for the comparison of the Hapke model with the other three numerical models, including the Lommel-Seeliger, Minnaert, and Kaasalainen models. The results show that the numerical models with simple function expressions can fit well with the synthetic lightcurves generated based on the Hapke model; this good fit implies that they can be adopted in the lightcurve inversion process for asteroids to improve the numerical efficiency and derive similar results to those of the Hapke model.

Kinematic inversion of the 2008 Mw7 Iwate-Miyagi (Japan) earthquake by two independent methods: Sensitivity and resolution analysis

NASA Astrophysics Data System (ADS)

Gallovic, Frantisek; Cirella, Antonella; Plicka, Vladimir; Piatanesi, Alessio

2013-04-01

On 14 June 2008, UTC 23:43, the border of Iwate and Miyagi prefectures was hit by an Mw7 reverse-fault type crustal earthquake. The event is known to have the largest ground acceleration observed to date (~4g), which was recorded at station IWTH25. We analyze observed strong motion data with the objective to image the event rupture process and the associated uncertainties. Two different slip inversion approaches are used, the difference between the two methods being only in the parameterization of the source model. To minimize mismodeling of the propagation effects we use crustal model obtained by full waveform inversion of aftershock records in the frequency range between 0.05-0.3 Hz. In the first method, based on linear formulation, the parameters are represented by samples of slip velocity functions along the (finely discretized) fault in a time window spanning the whole rupture duration. Such a source description is very general with no prior constraint on the nucleation point, rupture velocity, shape of the velocity function. Thus the inversion could resolve very general (unexpected) features of the rupture evolution, such as multiple rupturing, rupture-propagation reversals, etc. On the other hand, due to the relatively large number of model parameters, the inversion result is highly non-unique, with possibility of obtaining a biased solution. The second method is a non-linear global inversion technique, where each point on the fault can slip only once, following a prescribed functional form of the source time function. We invert simultaneously for peak slip velocity, slip angle, rise time and rupture time by allowing a given range of variability for each kinematic model parameter. For this reason, unlike to the linear inversion approach, the rupture process needs a smaller number of parameters to be retrieved, and is more constrained with a proper control on the allowed range of parameter values. In order to test the resolution and reliability of the

INVERSE MODEL ESTIMATION AND EVALUATION OF SEASONAL NH 3 EMISSIONS

EPA Science Inventory

The presentation topic is inverse modeling for estimate and evaluation of emissions. The case study presented is the need for seasonal estimates of NH₃ emissions for air quality modeling. The inverse modeling application approach is first described, and then the NH

Localization of incipient tip vortex cavitation using ray based matched field inversion method

NASA Astrophysics Data System (ADS)

Kim, Dongho; Seong, Woojae; Choo, Youngmin; Lee, Jeunghoon

2015-10-01

Cavitation of marine propeller is one of the main contributing factors of broadband radiated ship noise. In this research, an algorithm for the source localization of incipient vortex cavitation is suggested. Incipient cavitation is modeled as monopole type source and matched-field inversion method is applied to find the source position by comparing the spatial correlation between measured and replicated pressure fields at the receiver array. The accuracy of source localization is improved by broadband matched-field inversion technique that enhances correlation by incoherently averaging correlations of individual frequencies. Suggested localization algorithm is verified through known virtual source and model test conducted in Samsung ship model basin cavitation tunnel. It is found that suggested localization algorithm enables efficient localization of incipient tip vortex cavitation using a few pressure data measured on the outer hull above the propeller and practically applicable to the typically performed model scale experiment in a cavitation tunnel at the early design stage.

Application of a Numerical Inverse Laplace Integration Method to Surface Loading on a Viscoelastic Compressible Earth Model

NASA Astrophysics Data System (ADS)

Tanaka, Yoshiyuki; Klemann, Volker; Okuno, Jun'ichi

2009-09-01

Normal mode approaches for calculating viscoelastic responses of self-gravitating and compressible spherical earth models have an intrinsic problem of determining the roots of the secular equation and the associated residues in the Laplace domain. To bypass this problem, a method based on numerical inverse Laplace integration was developed by T anaka et al. (2006, 2007) for computations of viscoelastic deformation caused by an internal dislocation. The advantage of this approach is that the root-finding problem is avoided without imposing additional constraints on the governing equations and earth models. In this study, we apply the same algorithm to computations of viscoelastic responses to a surface load and show that the results obtained by this approach agree well with those obtained by a time-domain approach that does not need determinations of the normal modes in the Laplace domain. Using the elastic earth model PREM and a convex viscosity profile, we calculate viscoelastic load Love numbers ( h, l, k) for compressible and incompressible models. Comparisons between the results show that effects due to compressibility are consistent with results obtained by previous studies and that the rate differences between the two models total 10-40%. This will serve as an independent method to confirm results obtained by time-domain approaches and will usefully increase the reliability when modeling postglacial rebound.

A Higher Order Iterative Method for Computing the Drazin Inverse

PubMed Central

Soleymani, F.; Stanimirović, Predrag S.

2013-01-01

A method with high convergence rate for finding approximate inverses of nonsingular matrices is suggested and established analytically. An extension of the introduced computational scheme to general square matrices is defined. The extended method could be used for finding the Drazin inverse. The application of the scheme on large sparse test matrices alongside the use in preconditioning of linear system of equations will be presented to clarify the contribution of the paper. PMID:24222747

Model based inversion of ultrasound data in composites

NASA Astrophysics Data System (ADS)

Roberts, R. A.

2018-04-01

Work is reported on model-based defect characterization in CFRP composites. The work utilizes computational models of ultrasound interaction with defects in composites, to determine 1) the measured signal dependence on material and defect properties (forward problem), and 2) an assessment of defect properties from analysis of measured ultrasound signals (inverse problem). Work is reported on model implementation for inspection of CFRP laminates containing multi-ply impact-induced delamination, in laminates displaying irregular surface geometry (roughness), as well as internal elastic heterogeneity (varying fiber density, porosity). Inversion of ultrasound data is demonstrated showing the quantitative extraction of delamination geometry and surface transmissivity. Additionally, data inversion is demonstrated for determination of surface roughness and internal heterogeneity, and the influence of these features on delamination characterization is examined. Estimation of porosity volume fraction is demonstrated when internal heterogeneity is attributed to porosity.

Application of random seismic inversion method based on tectonic model in thin sand body research

NASA Astrophysics Data System (ADS)

Dianju, W.; Jianghai, L.; Qingkai, F.

2017-12-01

The oil and gas exploitation at Songliao Basin, Northeast China have already progressed to the period with high water production. The previous detailed reservoir description that based on seismic image, sediment core, borehole logging has great limitations in small scale structural interpretation and thin sand body characterization. Thus, precise guidance for petroleum exploration is badly in need of a more advanced method. To do so, we derived the method of random seismic inversion constrained by tectonic model.It can effectively improve the depicting ability of thin sand bodies, combining numerical simulation techniques, which can credibly reducing the blindness of reservoir analysis from the whole to the local and from the macroscopic to the microscopic. At the same time, this can reduce the limitations of the study under the constraints of different geological conditions of the reservoir, accomplish probably the exact estimation for the effective reservoir. Based on the research, this paper has optimized the regional effective reservoir evaluation and the productive location adjustment of applicability, combined with the practical exploration and development in Aonan oil field.

Comparison of optimal design methods in inverse problems

NASA Astrophysics Data System (ADS)

Banks, H. T.; Holm, K.; Kappel, F.

2011-07-01

Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric-based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher information matrix. A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criterion with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst-Pearl logistic population model (Banks H T and Tran H T 2009 Mathematical and Experimental Modeling of Physical and Biological Processes (Boca Raton, FL: Chapman and Hall/CRC)), the standard harmonic oscillator model (Banks H T and Tran H T 2009) and a popular glucose regulation model (Bergman R N, Ider Y Z, Bowden C R and Cobelli C 1979 Am. J. Physiol. 236 E667-77 De Gaetano A and Arino O 2000 J. Math. Biol. 40 136-68 Toffolo G, Bergman R N, Finegood D T, Bowden C R and Cobelli C 1980 Diabetes 29 979-90).

A MATLAB based 3D modeling and inversion code for MT data

NASA Astrophysics Data System (ADS)

Singh, Arun; Dehiya, Rahul; Gupta, Pravin K.; Israil, M.

2017-07-01

The development of a MATLAB based computer code, AP3DMT, for modeling and inversion of 3D Magnetotelluric (MT) data is presented. The code comprises two independent components: grid generator code and modeling/inversion code. The grid generator code performs model discretization and acts as an interface by generating various I/O files. The inversion code performs core computations in modular form - forward modeling, data functionals, sensitivity computations and regularization. These modules can be readily extended to other similar inverse problems like Controlled-Source EM (CSEM). The modular structure of the code provides a framework useful for implementation of new applications and inversion algorithms. The use of MATLAB and its libraries makes it more compact and user friendly. The code has been validated on several published models. To demonstrate its versatility and capabilities the results of inversion for two complex models are presented.

Inverse Modeling Using Markov Chain Monte Carlo Aided by Adaptive Stochastic Collocation Method with Transformation

NASA Astrophysics Data System (ADS)

Zhang, D.; Liao, Q.

2016-12-01

The Bayesian inference provides a convenient framework to solve statistical inverse problems. In this method, the parameters to be identified are treated as random variables. The prior knowledge, the system nonlinearity, and the measurement errors can be directly incorporated in the posterior probability density function (PDF) of the parameters. The Markov chain Monte Carlo (MCMC) method is a powerful tool to generate samples from the posterior PDF. However, since the MCMC usually requires thousands or even millions of forward simulations, it can be a computationally intensive endeavor, particularly when faced with large-scale flow and transport models. To address this issue, we construct a surrogate system for the model responses in the form of polynomials by the stochastic collocation method. In addition, we employ interpolation based on the nested sparse grids and takes into account the different importance of the parameters, under the condition of high random dimensions in the stochastic space. Furthermore, in case of low regularity such as discontinuous or unsmooth relation between the input parameters and the output responses, we introduce an additional transform process to improve the accuracy of the surrogate model. Once we build the surrogate system, we may evaluate the likelihood with very little computational cost. We analyzed the convergence rate of the forward solution and the surrogate posterior by Kullback-Leibler divergence, which quantifies the difference between probability distributions. The fast convergence of the forward solution implies fast convergence of the surrogate posterior to the true posterior. We also tested the proposed algorithm on water-flooding two-phase flow reservoir examples. The posterior PDF calculated from a very long chain with direct forward simulation is assumed to be accurate. The posterior PDF calculated using the surrogate model is in reasonable agreement with the reference, revealing a great improvement in terms of

A Generic 1D Forward Modeling and Inversion Algorithm for TEM Sounding with an Arbitrary Horizontal Loop

NASA Astrophysics Data System (ADS)

Li, Zhanhui; Huang, Qinghua; Xie, Xingbing; Tang, Xingong; Chang, Liao

2016-08-01

We present a generic 1D forward modeling and inversion algorithm for transient electromagnetic (TEM) data with an arbitrary horizontal transmitting loop and receivers at any depth in a layered earth. Both the Hankel and sine transforms required in the forward algorithm are calculated using the filter method. The adjoint-equation method is used to derive the formulation of data sensitivity at any depth in non-permeable media. The inversion algorithm based on this forward modeling algorithm and sensitivity formulation is developed using the Gauss-Newton iteration method combined with the Tikhonov regularization. We propose a new data-weighting method to minimize the initial model dependence that enhances the convergence stability. On a laptop with a CPU of i7-5700HQ@3.5 GHz, the inversion iteration of a 200 layered input model with a single receiver takes only 0.34 s, while it increases to only 0.53 s for the data from four receivers at a same depth. For the case of four receivers at different depths, the inversion iteration runtime increases to 1.3 s. Modeling the data with an irregular loop and an equal-area square loop indicates that the effect of the loop geometry is significant at early times and vanishes gradually along the diffusion of TEM field. For a stratified earth, inversion of data from more than one receiver is useful in noise reducing to get a more credible layered earth. However, for a resistive layer shielded below a conductive layer, increasing the number of receivers on the ground does not have significant improvement in recovering the resistive layer. Even with a down-hole TEM sounding, the shielded resistive layer cannot be recovered if all receivers are above the shielded resistive layer. However, our modeling demonstrates remarkable improvement in detecting the resistive layer with receivers in or under this layer.

Forward and inverse models of electromagnetic scattering from layered media with rough interfaces

NASA Astrophysics Data System (ADS)

Tabatabaeenejad, Seyed Alireza

This work addresses the problem of electromagnetic scattering from layered dielectric structures with rough boundaries and the associated inverse problem of retrieving the subsurface parameters of the structure using the scattered field. To this end, a forward scattering model based on the Small Perturbation Method (SPM) is developed to calculate the first-order spectral-domain bistatic scattering coefficients of a two-layer rough surface structure. SPM requires the boundaries to be slightly rough compared to the wavelength, but to understand the range of applicability of this method in scattering from two-layer rough surfaces, its region of validity is investigated by comparing its output with that of a first principle solver that does not impose roughness restrictions. The Method of Moments (MoM) is used for this purpose. Finally, for retrieval of the model parameters of the layered structure using scattered field, an inversion scheme based on the Simulated Annealing method is investigated and a strategy is proposed to address convergence to local minimum.

Large Airborne Full Tensor Gradient Data Inversion Based on a Non-Monotone Gradient Method

NASA Astrophysics Data System (ADS)

Sun, Yong; Meng, Zhaohai; Li, Fengting

2018-03-01

Following the development of gravity gradiometer instrument technology, the full tensor gravity (FTG) data can be acquired on airborne and marine platforms. Large-scale geophysical data can be obtained using these methods, making such data sets a number of the "big data" category. Therefore, a fast and effective inversion method is developed to solve the large-scale FTG data inversion problem. Many algorithms are available to accelerate the FTG data inversion, such as conjugate gradient method. However, the conventional conjugate gradient method takes a long time to complete data processing. Thus, a fast and effective iterative algorithm is necessary to improve the utilization of FTG data. Generally, inversion processing is formulated by incorporating regularizing constraints, followed by the introduction of a non-monotone gradient-descent method to accelerate the convergence rate of FTG data inversion. Compared with the conventional gradient method, the steepest descent gradient algorithm, and the conjugate gradient algorithm, there are clear advantages of the non-monotone iterative gradient-descent algorithm. Simulated and field FTG data were applied to show the application value of this new fast inversion method.

An inverse method for determining the spatially resolved properties of viscoelastic–viscoplastic three-dimensional printed materials

PubMed Central

Chen, X.; Ashcroft, I. A.; Wildman, R. D.; Tuck, C. J.

2015-01-01

A method using experimental nanoindentation and inverse finite-element analysis (FEA) has been developed that enables the spatial variation of material constitutive properties to be accurately determined. The method was used to measure property variation in a three-dimensional printed (3DP) polymeric material. The accuracy of the method is dependent on the applicability of the constitutive model used in the inverse FEA, hence four potential material models: viscoelastic, viscoelastic–viscoplastic, nonlinear viscoelastic and nonlinear viscoelastic–viscoplastic were evaluated, with the latter enabling the best fit to experimental data. Significant changes in material properties were seen in the depth direction of the 3DP sample, which could be linked to the degree of cross-linking within the material, a feature inherent in a UV-cured layer-by-layer construction method. It is proposed that the method is a powerful tool in the analysis of manufacturing processes with potential spatial property variation that will also enable the accurate prediction of final manufactured part performance. PMID:26730216

An inverse method for determining the spatially resolved properties of viscoelastic-viscoplastic three-dimensional printed materials.

PubMed

Chen, X; Ashcroft, I A; Wildman, R D; Tuck, C J

2015-11-08

A method using experimental nanoindentation and inverse finite-element analysis (FEA) has been developed that enables the spatial variation of material constitutive properties to be accurately determined. The method was used to measure property variation in a three-dimensional printed (3DP) polymeric material. The accuracy of the method is dependent on the applicability of the constitutive model used in the inverse FEA, hence four potential material models: viscoelastic, viscoelastic-viscoplastic, nonlinear viscoelastic and nonlinear viscoelastic-viscoplastic were evaluated, with the latter enabling the best fit to experimental data. Significant changes in material properties were seen in the depth direction of the 3DP sample, which could be linked to the degree of cross-linking within the material, a feature inherent in a UV-cured layer-by-layer construction method. It is proposed that the method is a powerful tool in the analysis of manufacturing processes with potential spatial property variation that will also enable the accurate prediction of final manufactured part performance.

Dynamic inverse models in human-cyber-physical systems

NASA Astrophysics Data System (ADS)

Robinson, Ryan M.; Scobee, Dexter R. R.; Burden, Samuel A.; Sastry, S. Shankar

2016-05-01

Human interaction with the physical world is increasingly mediated by automation. This interaction is characterized by dynamic coupling between robotic (i.e. cyber) and neuromechanical (i.e. human) decision-making agents. Guaranteeing performance of such human-cyber-physical systems will require predictive mathematical models of this dynamic coupling. Toward this end, we propose a rapprochement between robotics and neuromechanics premised on the existence of internal forward and inverse models in the human agent. We hypothesize that, in tele-robotic applications of interest, a human operator learns to invert automation dynamics, directly translating from desired task to required control input. By formulating the model inversion problem in the context of a tracking task for a nonlinear control system in control-a_ne form, we derive criteria for exponential tracking and show that the resulting dynamic inverse model generally renders a portion of the physical system state (i.e., the internal dynamics) unobservable from the human operator's perspective. Under stability conditions, we show that the human can achieve exponential tracking without formulating an estimate of the system's state so long as they possess an accurate model of the system's dynamics. These theoretical results are illustrated using a planar quadrotor example. We then demonstrate that the automation can intervene to improve performance of the tracking task by solving an optimal control problem. Performance is guaranteed to improve under the assumption that the human learns and inverts the dynamic model of the altered system. We conclude with a discussion of practical limitations that may hinder exact dynamic model inversion.

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

. 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.

Preliminary gravity inversion model of Frenchman Flat Basin, Nevada Test Site, Nevada

USGS Publications Warehouse

Phelps, Geoffrey A.; Graham, Scott E.

2002-01-01

The depth of the basin beneath Frenchman Flat is estimated using a gravity inversion method. Gamma-gamma density logs from two wells in Frenchman Flat constrained the density profiles used to create the gravity inversion model. Three initial models were considered using data from one well, then a final model is proposed based on new information from the second well. The preferred model indicates that a northeast-trending oval-shaped basin underlies Frenchman Flat at least 2,100 m deep, with a maximum depth of 2,400 m at its northeast end. No major horst and graben structures are predicted. Sensitivity analysis of the model indicates that each parameter contributes the same magnitude change to the model, up to 30 meters change in depth for a 1% change in density, but some parameters affect a broader area of the basin. The horizontal resolution of the model was determined by examining the spacing between data stations, and was set to 500 square meters.

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

Dynamic Shape Reconstruction of Three-Dimensional Frame Structures Using the Inverse Finite Element Method

NASA Technical Reports Server (NTRS)

Gherlone, Marco; Cerracchio, Priscilla; Mattone, Massimiliano; Di Sciuva, Marco; Tessler, Alexander

2011-01-01

A robust and efficient computational method for reconstructing the three-dimensional displacement field of truss, beam, and frame structures, using measured surface-strain data, is presented. Known as shape sensing , this inverse problem has important implications for real-time actuation and control of smart structures, and for monitoring of structural integrity. The present formulation, based on the inverse Finite Element Method (iFEM), uses a least-squares variational principle involving strain measures of Timoshenko theory for stretching, torsion, bending, and transverse shear. Two inverse-frame finite elements are derived using interdependent interpolations whose interior degrees-of-freedom are condensed out at the element level. In addition, relationships between the order of kinematic-element interpolations and the number of required strain gauges are established. As an example problem, a thin-walled, circular cross-section cantilevered beam subjected to harmonic excitations in the presence of structural damping is modeled using iFEM; where, to simulate strain-gauge values and to provide reference displacements, a high-fidelity MSC/NASTRAN shell finite element model is used. Examples of low and high-frequency dynamic motion are analyzed and the solution accuracy examined with respect to various levels of discretization and the number of strain gauges.

Computer modeling of inversion layer MOS solar cells and arrays

NASA Technical Reports Server (NTRS)

Ho, Fat Duen

1991-01-01

A two dimensional numerical model of the inversion layer metal insulator semiconductor (IL/MIS) solar cell is proposed by using the finite element method. The two-dimensional current flow in the device is taken into account in this model. The electrostatic potential distribution, the electron concentration distribution, and the hole concentration distribution for different terminal voltages are simulated. The results of simple calculation are presented. The existing problems for this model are addressed. Future work is proposed. The MIS structures are studied and some of the results are reported.

`Inverse Crime' and Model Integrity in Lightcurve Inversion applied to unresolved Space Object Identification

NASA Astrophysics Data System (ADS)

Henderson, Laura S.; Subbarao, Kamesh

2017-12-01

This work presents a case wherein the selection of models when producing synthetic light curves affects the estimation of the size of unresolved space objects. Through this case, "inverse crime" (using the same model for the generation of synthetic data and data inversion), is illustrated. This is done by using two models to produce the synthetic light curve and later invert it. It is shown here that the choice of model indeed affects the estimation of the shape/size parameters. When a higher fidelity model (henceforth the one that results in the smallest error residuals after the crime is committed) is used to both create, and invert the light curve model the estimates of the shape/size parameters are significantly better than those obtained when a lower fidelity model (in comparison) is implemented for the estimation. It is therefore of utmost importance to consider the choice of models when producing synthetic data, which later will be inverted, as the results might be misleadingly optimistic.

Estimating Emissions of Ammonia and Methane from an Anaerobic Livestock Lagoon Using Micrometeorological Methods and Inverse Modeling

NASA Astrophysics Data System (ADS)

Shonkwiler, K. B.; Ham, J. M.; Williams, C.

2012-12-01

Development Initiative. Food and Agriculture Organization of the United Nations, Rome, Italy. [2] Loubet, B., Génermont, S., Ferrara, R., Bedos, C., Decuq, C., Personne, E., Fanucci, O., Durand, B., Rana, G., Cellier, P., 2010. An inverse model to estimate ammonia emissions from fields. Eur. J. Soil Sci. 61: 793-805. Panorama of a weather station (left) utilizing micrometeorological methods to aid in estimating emissions of methane and ammonia from an anaerobic livestock lagoon (center) at a commercial dairy in Northern Colorado, USA.

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.

Prediction and assimilation of surf-zone processes using a Bayesian network: Part II: Inverse models

USGS Publications Warehouse

Plant, Nathaniel G.; Holland, K. Todd

2011-01-01

A Bayesian network model has been developed to simulate a relatively simple problem of wave propagation in the surf zone (detailed in Part I). Here, we demonstrate that this Bayesian model can provide both inverse modeling and data-assimilation solutions for predicting offshore wave heights and depth estimates given limited wave-height and depth information from an onshore location. The inverse method is extended to allow data assimilation using observational inputs that are not compatible with deterministic solutions of the problem. These inputs include sand bar positions (instead of bathymetry) and estimates of the intensity of wave breaking (instead of wave-height observations). Our results indicate that wave breaking information is essential to reduce prediction errors. In many practical situations, this information could be provided from a shore-based observer or from remote-sensing systems. We show that various combinations of the assimilated inputs significantly reduce the uncertainty in the estimates of water depths and wave heights in the model domain. Application of the Bayesian network model to new field data demonstrated significant predictive skill (R2 = 0.7) for the inverse estimate of a month-long time series of offshore wave heights. The Bayesian inverse results include uncertainty estimates that were shown to be most accurate when given uncertainty in the inputs (e.g., depth and tuning parameters). Furthermore, the inverse modeling was extended to directly estimate tuning parameters associated with the underlying wave-process model. The inverse estimates of the model parameters not only showed an offshore wave height dependence consistent with results of previous studies but the uncertainty estimates of the tuning parameters also explain previously reported variations in the model parameters.

Variational methods for direct/inverse problems of atmospheric dynamics and chemistry

NASA Astrophysics Data System (ADS)

Penenko, Vladimir; Penenko, Alexey; Tsvetova, Elena

2013-04-01

We present a variational approach for solving direct and inverse problems of atmospheric hydrodynamics and chemistry. It is important that the accurate matching of numerical schemes has to be provided in the chain of objects: direct/adjoint problems - sensitivity relations - inverse problems, including assimilation of all available measurement data. To solve the problems we have developed a new enhanced set of cost-effective algorithms. The matched description of the multi-scale processes is provided by a specific choice of the variational principle functionals for the whole set of integrated models. Then all functionals of variational principle are approximated in space and time by splitting and decomposition methods. Such approach allows us to separately consider, for example, the space-time problems of atmospheric chemistry in the frames of decomposition schemes for the integral identity sum analogs of the variational principle at each time step and in each of 3D finite-volumes. To enhance the realization efficiency, the set of chemical reactions is divided on the subsets related to the operators of production and destruction. Then the idea of the Euler's integrating factors is applied in the frames of the local adjoint problem technique [1]-[3]. The analytical solutions of such adjoint problems play the role of integrating factors for differential equations describing atmospheric chemistry. With their help, the system of differential equations is transformed to the equivalent system of integral equations. As a result we avoid the construction and inversion of preconditioning operators containing the Jacobi matrixes which arise in traditional implicit schemes for ODE solution. This is the main advantage of our schemes. At the same time step but on the different stages of the "global" splitting scheme, the system of atmospheric dynamic equations is solved. For convection - diffusion equations for all state functions in the integrated models we have developed the

An inverse method to estimate the flow through a levee breach

NASA Astrophysics Data System (ADS)

D'Oria, Marco; Mignosa, Paolo; Tanda, Maria Giovanna

2015-08-01

We propose a procedure to estimate the flow through a levee breach based on water levels recorded in river stations downstream and/or upstream of the failure site. The inverse problem is solved using a Bayesian approach and requires the execution of several forward unsteady flow simulations. For this purpose, we have used the well-known 1-D HEC-RAS model, but any unsteady flow model could be adopted in the same way. The procedure has been tested using four synthetic examples. Levee breaches with different characteristics (free flow, flow with tailwater effects, etc.) have been simulated to collect the synthetic level data used at a later stage in the inverse procedure. The method was able to accurately reproduce the flow through the breach in all cases. The practicability of the procedure was then confirmed applying it to the inundation of the Polesine Region (Northern Italy) which occurred in 1951 and was caused by three contiguous and almost simultaneous breaches on the left embankment of the Po River.

Model based Inverse Methods for Sizing Cracks of Varying Shape and Location in Bolt hole Eddy Current (BHEC) Inspections (Postprint)

DTIC Science & Technology

2016-02-10

using bolt hole eddy current (BHEC) techniques. Data was acquired for a wide range of crack sizes and shapes, including mid- bore , corner and through...to select the most appropriate VIC-3D surrogate model for subsequent crack sizing inversion step. Inversion results for select mid- bore , through and...the flaw. 15. SUBJECT TERMS Bolt hole eddy current (BHEC); mid- bore , corner and through-thickness crack types; VIC-3D generated surrogate models

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.

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

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

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.

Erlang circular model motivated by inverse stereographic projection

NASA Astrophysics Data System (ADS)

Pramesti, G.

2018-05-01

The Erlang distribution is a special case of the Gamma distribution with the shape parameter is an integer. This paper proposed a new circular model used inverse stereographic projection. The inverse stereographic projection which is a mapping that projects a random variable from a real line onto a circle can be used in circular statistics to construct a distribution on the circle from real domain. From the circular model, then can be derived the characteristics of the Erlang circular model such as the mean resultant length, mean direction, circular variance and trigonometric moments of the distribution.

A stochastic approach for model reduction and memory function design in hydrogeophysical inversion

NASA Astrophysics Data System (ADS)

Hou, Z.; Kellogg, A.; Terry, N.

2009-12-01

Geophysical (e.g., seismic, electromagnetic, radar) techniques and statistical methods are essential for research related to subsurface characterization, including monitoring subsurface flow and transport processes, oil/gas reservoir identification, etc. For deep subsurface characterization such as reservoir petroleum exploration, seismic methods have been widely used. Recently, electromagnetic (EM) methods have drawn great attention in the area of reservoir characterization. However, considering the enormous computational demand corresponding to seismic and EM forward modeling, it is usually a big problem to have too many unknown parameters in the modeling domain. For shallow subsurface applications, the characterization can be very complicated considering the complexity and nonlinearity of flow and transport processes in the unsaturated zone. It is warranted to reduce the dimension of parameter space to a reasonable level. Another common concern is how to make the best use of time-lapse data with spatial-temporal correlations. This is even more critical when we try to monitor subsurface processes using geophysical data collected at different times. The normal practice is to get the inverse images individually. These images are not necessarily continuous or even reasonably related, because of the non-uniqueness of hydrogeophysical inversion. We propose to use a stochastic framework by integrating minimum-relative-entropy concept, quasi Monto Carlo sampling techniques, and statistical tests. The approach allows efficient and sufficient exploration of all possibilities of model parameters and evaluation of their significances to geophysical responses. The analyses enable us to reduce the parameter space significantly. The approach can be combined with Bayesian updating, allowing us to treat the updated ‘posterior’ pdf as a memory function, which stores all the information up to date about the distributions of soil/field attributes/properties, then consider the

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.

A Comparison of Land Surface Model Soil Hydraulic Properties Estimated by Inverse Modeling and Pedotransfer Functions

NASA Technical Reports Server (NTRS)

Gutmann, Ethan D.; Small, Eric E.

2007-01-01

Soil hydraulic properties (SHPs) regulate the movement of water in the soil. This in turn plays an important role in the water and energy cycles at the land surface. At present, SHPS are commonly defined by a simple pedotransfer function from soil texture class, but SHPs vary more within a texture class than between classes. To examine the impact of using soil texture class to predict SHPS, we run the Noah land surface model for a wide variety of measured SHPs. We find that across a range of vegetation cover (5 - 80% cover) and climates (250 - 900 mm mean annual precipitation), soil texture class only explains 5% of the variance expected from the real distribution of SHPs. We then show that modifying SHPs can drastically improve model performance. We compare two methods of estimating SHPs: (1) inverse method, and (2) soil texture class. Compared to texture class, inverse modeling reduces errors between measured and modeled latent heat flux from 88 to 28 w/m(exp 2). Additionally we find that with increasing vegetation cover the importance of SHPs decreases and that the van Genuchten m parameter becomes less important, while the saturated conductivity becomes more important.

Hybrid Weighted Minimum Norm Method A new method based LORETA to solve EEG inverse problem.

PubMed

Song, C; Zhuang, T; Wu, Q

2005-01-01

This Paper brings forward a new method to solve EEG inverse problem. Based on following physiological characteristic of neural electrical activity source: first, the neighboring neurons are prone to active synchronously; second, the distribution of source space is sparse; third, the active intensity of the sources are high centralized, we take these prior knowledge as prerequisite condition to develop the inverse solution of EEG, and not assume other characteristic of inverse solution to realize the most commonly 3D EEG reconstruction map. The proposed algorithm takes advantage of LORETA's low resolution method which emphasizes particularly on 'localization' and FOCUSS's high resolution method which emphasizes particularly on 'separability'. The method is still under the frame of the weighted minimum norm method. The keystone is to construct a weighted matrix which takes reference from the existing smoothness operator, competition mechanism and study algorithm. The basic processing is to obtain an initial solution's estimation firstly, then construct a new estimation using the initial solution's information, repeat this process until the solutions under last two estimate processing is keeping unchanged.

The Earthquake‐Source Inversion Validation (SIV) Project

USGS Publications Warehouse

Mai, P. Martin; Schorlemmer, Danijel; Page, Morgan T.; Ampuero, Jean-Paul; Asano, Kimiyuki; Causse, Mathieu; Custodio, Susana; Fan, Wenyuan; Festa, Gaetano; Galis, Martin; Gallovic, Frantisek; Imperatori, Walter; Käser, Martin; Malytskyy, Dmytro; Okuwaki, Ryo; Pollitz, Fred; Passone, Luca; Razafindrakoto, Hoby N. T.; Sekiguchi, Haruko; Song, Seok Goo; Somala, Surendra N.; Thingbaijam, Kiran K. S.; Twardzik, Cedric; van Driel, Martin; Vyas, Jagdish C.; Wang, Rongjiang; Yagi, Yuji; Zielke, Olaf

2016-01-01

Finite‐fault earthquake source inversions infer the (time‐dependent) displacement on the rupture surface from geophysical data. The resulting earthquake source models document the complexity of the rupture process. However, multiple source models for the same earthquake, obtained by different research teams, often exhibit remarkable dissimilarities. To address the uncertainties in earthquake‐source inversion methods and to understand strengths and weaknesses of the various approaches used, the Source Inversion Validation (SIV) project conducts a set of forward‐modeling exercises and inversion benchmarks. In this article, we describe the SIV strategy, the initial benchmarks, and current SIV results. Furthermore, we apply statistical tools for quantitative waveform comparison and for investigating source‐model (dis)similarities that enable us to rank the solutions, and to identify particularly promising source inversion approaches. All SIV exercises (with related data and descriptions) and statistical comparison tools are available via an online collaboration platform, and we encourage source modelers to use the SIV benchmarks for developing and testing new methods. We envision that the SIV efforts will lead to new developments for tackling the earthquake‐source imaging problem.

Development of a coupled FLEXPART-TM5 CO2 inverse modeling system

NASA Astrophysics Data System (ADS)

Monteil, Guillaume; Scholze, Marko

2017-04-01

Inverse modeling techniques are used to derive information on surface CO2 fluxes from measurements of atmospheric CO2 concentrations. The principle is to use an atmospheric transport model to compute the CO2 concentrations corresponding to a prior estimate of the surface CO2 fluxes. From the mismatches between observed and modeled concentrations, a correction of the flux estimate is computed, that represents the best statistical compromise between the prior knowledge and the new information brought in by the observations. Such "top-down" CO2 flux estimates are useful for a number of applications, such as the verification of CO2 emission inventories reported by countries in the framework of international greenhouse gas emission reduction treaties (Paris agreement), or for the validation and improvement of the bottom-up models used in future climate predictions. Inverse modeling CO2 flux estimates are limited in resolution (spatial and temporal) by the lack of observational constraints and by the very heavy computational cost of high-resolution inversions. The observational limitation is however being lifted, with the expansion of regional surface networks such as ICOS in Europe, and with the launch of new satellite instruments to measure tropospheric CO2 concentrations. To make an efficient use of these new observations, it is necessary to step up the resolution of atmospheric inversions. We have developed an inverse modeling system, based on a coupling between the TM5 and the FLEXPART transport models. The coupling follows the approach described in Rodenbeck et al., 2009: a first global, coarse resolution, inversion is performed using TM5-4DVAR, and is used to provide background constraints to a second, regional, fine resolution inversion, using FLEXPART as a transport model. The inversion algorithm is adapted from the 4DVAR algorithm used by TM5, but has been developed to be model-agnostic: it would be straightforward to replace TM5 and/or FLEXPART by other

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.

Impact of transport model errors on the global and regional methane emissions estimated by inverse modelling

DOE PAGES

Locatelli, R.; Bousquet, P.; Chevallier, F.; ...

2013-10-08

A modelling experiment has been conceived to assess the impact of transport model errors on methane emissions estimated in an atmospheric inversion system. Synthetic methane observations, obtained from 10 different model outputs from the international TransCom-CH4 model inter-comparison exercise, are combined with a prior scenario of methane emissions and sinks, and integrated into the three-component PYVAR-LMDZ-SACS (PYthon VARiational-Laboratoire de Météorologie Dynamique model with Zooming capability-Simplified Atmospheric Chemistry System) inversion system to produce 10 different methane emission estimates at the global scale for the year 2005. The same methane sinks, emissions and initial conditions have been applied to produce the 10more » synthetic observation datasets. The same inversion set-up (statistical errors, prior emissions, inverse procedure) is then applied to derive flux estimates by inverse modelling. Consequently, only differences in the modelling of atmospheric transport may cause differences in the estimated fluxes. Here in our framework, we show that transport model errors lead to a discrepancy of 27 Tg yr -1 at the global scale, representing 5% of total methane emissions. At continental and annual scales, transport model errors are proportionally larger than at the global scale, with errors ranging from 36 Tg yr -1 in North America to 7 Tg yr -1 in Boreal Eurasia (from 23 to 48%, respectively). At the model grid-scale, the spread of inverse estimates can reach 150% of the prior flux. Therefore, transport model errors contribute significantly to overall uncertainties in emission estimates by inverse modelling, especially when small spatial scales are examined. Sensitivity tests have been carried out to estimate the impact of the measurement network and the advantage of higher horizontal resolution in transport models. The large differences found between methane flux estimates inferred in these different configurations highly question the

Comparison of the convolution quadrature method and enhanced inverse FFT with application in elastodynamic boundary element method

NASA Astrophysics Data System (ADS)

Schanz, Martin; Ye, Wenjing; Xiao, Jinyou

2016-04-01

Transient problems can often be solved with transformation methods, where the inverse transformation is usually performed numerically. Here, the discrete Fourier transform in combination with the exponential window method is compared with the convolution quadrature method formulated as inverse transformation. Both are inverse Laplace transforms, which are formally identical but use different complex frequencies. A numerical study is performed, first with simple convolution integrals and, second, with a boundary element method (BEM) for elastodynamics. Essentially, when combined with the BEM, the discrete Fourier transform needs less frequency calculations, but finer mesh compared to the convolution quadrature method to obtain the same level of accuracy. If further fast methods like the fast multipole method are used to accelerate the boundary element method the convolution quadrature method is better, because the iterative solver needs much less iterations to converge. This is caused by the larger real part of the complex frequencies necessary for the calculation, which improves the conditions of system matrix.

Forward and Inverse Predictive Model for the Trajectory Tracking Control of a Lower Limb Exoskeleton for Gait Rehabilitation: Simulation modelling analysis

NASA Astrophysics Data System (ADS)

Zakaria, M. A.; Majeed, A. P. P. A.; Taha, Z.; Alim, M. M.; Baarath, K.

2018-03-01

The movement of a lower limb exoskeleton requires a reasonably accurate control method to allow for an effective gait therapy session to transpire. Trajectory tracking is a nontrivial means of passive rehabilitation technique to correct the motion of the patients’ impaired limb. This paper proposes an inverse predictive model that is coupled together with the forward kinematics of the exoskeleton to estimate the behaviour of the system. A conventional PID control system is used to converge the required joint angles based on the desired input from the inverse predictive model. It was demonstrated through the present study, that the inverse predictive model is capable of meeting the trajectory demand with acceptable error tolerance. The findings further suggest the ability of the predictive model of the exoskeleton to predict a correct joint angle command to the system.

An inverse radiation model for optical determination of temperature and species concentration: Development and validation

NASA Astrophysics Data System (ADS)

Ren, Tao; Modest, Michael F.; Fateev, Alexander; Clausen, Sønnik

2015-01-01

In this study, we present an inverse calculation model based on the Levenberg-Marquardt optimization method to reconstruct temperature and species concentration from measured line-of-sight spectral transmissivity data for homogeneous gaseous media. The high temperature gas property database HITEMP 2010 (Rothman et al. (2010) [1]), which contains line-by-line (LBL) information for several combustion gas species, such as CO2 and H2O, was used to predict gas spectral transmissivities. The model was validated by retrieving temperatures and species concentrations from experimental CO2 and H2O transmissivity measurements. Optimal wavenumber ranges for CO2 and H2O transmissivity measured across a wide range of temperatures and concentrations were determined according to the performance of inverse calculations. Results indicate that the inverse radiation model shows good feasibility for measurements of temperature and gas concentration.

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.

Using informative priors in facies inversion: The case of C-ISR method

NASA Astrophysics Data System (ADS)

Valakas, G.; Modis, K.

2016-08-01

Inverse problems involving the characterization of hydraulic properties of groundwater flow systems by conditioning on observations of the state variables are mathematically ill-posed because they have multiple solutions and are sensitive to small changes in the data. In the framework of McMC methods for nonlinear optimization and under an iterative spatial resampling transition kernel, we present an algorithm for narrowing the prior and thus producing improved proposal realizations. To achieve this goal, we cosimulate the facies distribution conditionally to facies observations and normal scores transformed hydrologic response measurements, assuming a linear coregionalization model. The approach works by creating an importance sampling effect that steers the process to selected areas of the prior. The effectiveness of our approach is demonstrated by an example application on a synthetic underdetermined inverse problem in aquifer characterization.

Identification of polymorphic inversions from genotypes

PubMed Central

2012-01-01

Background Polymorphic inversions are a source of genetic variability with a direct impact on recombination frequencies. Given the difficulty of their experimental study, computational methods have been developed to infer their existence in a large number of individuals using genome-wide data of nucleotide variation. Methods based on haplotype tagging of known inversions attempt to classify individuals as having a normal or inverted allele. Other methods that measure differences between linkage disequilibrium attempt to identify regions with inversions but unable to classify subjects accurately, an essential requirement for association studies. Results We present a novel method to both identify polymorphic inversions from genome-wide genotype data and classify individuals as containing a normal or inverted allele. Our method, a generalization of a published method for haplotype data [1], utilizes linkage between groups of SNPs to partition a set of individuals into normal and inverted subpopulations. We employ a sliding window scan to identify regions likely to have an inversion, and accumulation of evidence from neighboring SNPs is used to accurately determine the inversion status of each subject. Further, our approach detects inversions directly from genotype data, thus increasing its usability to current genome-wide association studies (GWAS). Conclusions We demonstrate the accuracy of our method to detect inversions and classify individuals on principled-simulated genotypes, produced by the evolution of an inversion event within a coalescent model [2]. We applied our method to real genotype data from HapMap Phase III to characterize the inversion status of two known inversions within the regions 17q21 and 8p23 across 1184 individuals. Finally, we scan the full genomes of the European Origin (CEU) and Yoruba (YRI) HapMap samples. We find population-based evidence for 9 out of 15 well-established autosomic inversions, and for 52 regions previously predicted by

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

Sensitivity analyses of acoustic impedance inversion with full-waveform inversion

NASA Astrophysics Data System (ADS)

Yao, Gang; da Silva, Nuno V.; Wu, Di

2018-04-01

Acoustic impedance estimation has a significant importance to seismic exploration. In this paper, we use full-waveform inversion to recover the impedance from seismic data, and analyze the sensitivity of the acoustic impedance with respect to the source-receiver offset of seismic data and to the initial velocity model. We parameterize the acoustic wave equation with velocity and impedance, and demonstrate three key aspects of acoustic impedance inversion. First, short-offset data are most suitable for acoustic impedance inversion. Second, acoustic impedance inversion is more compatible with the data generated by density contrasts than velocity contrasts. Finally, acoustic impedance inversion requires the starting velocity model to be very accurate for achieving a high-quality inversion. Based upon these observations, we propose a workflow for acoustic impedance inversion as: (1) building a background velocity model with travel-time tomography or reflection waveform inversion; (2) recovering the intermediate wavelength components of the velocity model with full-waveform inversion constrained by Gardner’s relation; (3) inverting the high-resolution acoustic impedance model with short-offset data through full-waveform inversion. We verify this workflow by the synthetic tests based on the Marmousi model.

Methodes entropiques appliquees au probleme inverse en magnetoencephalographie

NASA Astrophysics Data System (ADS)

Lapalme, Ervig

2005-07-01

This thesis is devoted to biomagnetic source localization using magnetoencephalography. This problem is known to have an infinite number of solutions. So methods are required to take into account anatomical and functional information on the solution. The work presented in this thesis uses the maximum entropy on the mean method to constrain the solution. This method originates from statistical mechanics and information theory. This thesis is divided into two main parts containing three chapters each. The first part reviews the magnetoencephalographic inverse problem: the theory needed to understand its context and the hypotheses for simplifying the problem. In the last chapter of this first part, the maximum entropy on the mean method is presented: its origins are explained and also how it is applied to our problem. The second part is the original work of this thesis presenting three articles; one of them already published and two others submitted for publication. In the first article, a biomagnetic source model is developed and applied in a theoretical con text but still demonstrating the efficiency of the method. In the second article, we go one step further towards a realistic modelization of the cerebral activation. The main priors are estimated using the magnetoencephalographic data. This method proved to be very efficient in realistic simulations. In the third article, the previous method is extended to deal with time signals thus exploiting the excellent time resolution offered by magnetoencephalography. Compared with our previous work, the temporal method is applied to real magnetoencephalographic data coming from a somatotopy experience and results agree with previous physiological knowledge about this kind of cognitive process.

Thermal Diagnostics with the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory: A Validated Method for Differential Emission Measure Inversions

NASA Astrophysics Data System (ADS)

Cheung, Mark C. M.; Boerner, P.; Schrijver, C. J.; Testa, P.; Chen, F.; Peter, H.; Malanushenko, A.

2015-07-01

We present a new method for performing differential emission measure (DEM) inversions on narrow-band EUV images from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory. The method yields positive definite DEM solutions by solving a linear program. This method has been validated against a diverse set of thermal models of varying complexity and realism. These include (1) idealized Gaussian DEM distributions, (2) 3D models of NOAA Active Region 11158 comprising quasi-steady loop atmospheres in a nonlinear force-free field, and (3) thermodynamic models from a fully compressible, 3D MHD simulation of active region (AR) corona formation following magnetic flux emergence. We then present results from the application of the method to AIA observations of Active Region 11158, comparing the region's thermal structure on two successive solar rotations. Additionally, we show how the DEM inversion method can be adapted to simultaneously invert AIA and Hinode X-ray Telescope data, and how supplementing AIA data with the latter improves the inversion result. The speed of the method allows for routine production of DEM maps, thus facilitating science studies that require tracking of the thermal structure of the solar corona in time and space.

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.

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.

A method of inversion of satellite magnetic anomaly data

NASA Technical Reports Server (NTRS)

Mayhew, M. A.

1977-01-01

A method of finding a first approximation to a crustal magnetization distribution from inversion of satellite magnetic anomaly data is described. Magnetization is expressed as a Fourier Series in a segment of spherical shell. Input to this procedure is an equivalent source representation of the observed anomaly field. Instability of the inversion occurs when high frequency noise is present in the input data, or when the series is carried to an excessively high wave number. Preliminary results are given for the United States and adjacent areas.

Inverse modelling of radionuclide release rates using gamma dose rate observations

NASA Astrophysics Data System (ADS)

Hamburger, Thomas; Evangeliou, Nikolaos; Stohl, Andreas; von Haustein, Christoph; Thummerer, Severin; Wallner, Christian

2015-04-01

Severe accidents in nuclear power plants such as the historical accident in Chernobyl 1986 or the more recent disaster in the Fukushima Dai-ichi nuclear power plant in 2011 have drastic impacts on the population and environment. Observations and dispersion modelling of the released radionuclides help to assess the regional impact of such nuclear accidents. Modelling the increase of regional radionuclide activity concentrations, which results from nuclear accidents, underlies a multiplicity of uncertainties. One of the most significant uncertainties is the estimation of the source term. That is, the time dependent quantification of the released spectrum of radionuclides during the course of the nuclear accident. The quantification of the source term may either remain uncertain (e.g. Chernobyl, Devell et al., 1995) or rely on estimates given by the operators of the nuclear power plant. Precise measurements are mostly missing due to practical limitations during the accident. The release rates of radionuclides at the accident site can be estimated using inverse modelling (Davoine and Bocquet, 2007). The accuracy of the method depends amongst others on the availability, reliability and the resolution in time and space of the used observations. Radionuclide activity concentrations are observed on a relatively sparse grid and the temporal resolution of available data may be low within the order of hours or a day. Gamma dose rates, on the other hand, are observed routinely on a much denser grid and higher temporal resolution and provide therefore a wider basis for inverse modelling (Saunier et al., 2013). We present a new inversion approach, which combines an atmospheric dispersion model and observations of radionuclide activity concentrations and gamma dose rates to obtain the source term of radionuclides. We use the Lagrangian particle dispersion model FLEXPART (Stohl et al., 1998; Stohl et al., 2005) to model the atmospheric transport of the released radionuclides. The

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

Surface defects evaluation system based on electromagnetic model simulation and inverse-recognition calibration method

NASA Astrophysics Data System (ADS)

Yang, Yongying; Chai, Huiting; Li, Chen; Zhang, Yihui; Wu, Fan; Bai, Jian; Shen, Yibing

2017-05-01

Digitized evaluation of micro sparse defects on large fine optical surfaces is one of the challenges in the field of optical manufacturing and inspection. The surface defects evaluation system (SDES) for large fine optical surfaces is developed based on our previously reported work. In this paper, the electromagnetic simulation model based on Finite-Difference Time-Domain (FDTD) for vector diffraction theory is firstly established to study the law of microscopic scattering dark-field imaging. Given the aberration in actual optical systems, point spread function (PSF) approximated by a Gaussian function is introduced in the extrapolation from the near field to the far field and the scatter intensity distribution in the image plane is deduced. Analysis shows that both diffraction-broadening imaging and geometrical imaging should be considered in precise size evaluation of defects. Thus, a novel inverse-recognition calibration method is put forward to avoid confusion caused by diffraction-broadening effect. The evaluation method is applied to quantitative evaluation of defects information. The evaluation results of samples of many materials by SDES are compared with those by OLYMPUS microscope to verify the micron-scale resolution and precision. The established system has been applied to inspect defects on large fine optical surfaces and can achieve defects inspection of surfaces as large as 850 mm×500 mm with the resolution of 0.5 μm.

FOREWORD: 3rd International Workshop on New Computational Methods for Inverse Problems (NCMIP 2013)

NASA Astrophysics Data System (ADS)

Blanc-Féraud, Laure; Joubert, Pierre-Yves

2013-10-01

Conference logo This volume of Journal of Physics: Conference Series is dedicated to the scientific contributions presented during the 3rd International Workshop on New Computational Methods for Inverse Problems, NCMIP 2013 (http://www.farman.ens-cachan.fr/NCMIP_2013.html). This workshop took place at Ecole Normale Supérieure de Cachan, in Cachan, France, on 22 May 2013, at the initiative of Institut Farman. The prior editions of NCMIP also took place in Cachan, France, firstly within the scope of the ValueTools Conference, in May 2011 (http://www.ncmip.org/2011/), and secondly at the initiative of Institut Farman, in May 2012 (http://www.farman.ens-cachan.fr/NCMIP_2012.html). The 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

FOREWORD: 2nd International Workshop on New Computational Methods for Inverse Problems (NCMIP 2012)

NASA Astrophysics Data System (ADS)

Blanc-Féraud, Laure; Joubert, Pierre-Yves

2012-09-01

Conference logo This volume of Journal of Physics: Conference Series is dedicated to the scientific contributions presented during the 2nd International Workshop on New Computational Methods for Inverse Problems, (NCMIP 2012). This workshop took place at Ecole Normale Supérieure de Cachan, in Cachan, France, on 15 May 2012, at the initiative of Institut Farman. The first edition of NCMIP also took place in Cachan, France, within the scope of the ValueTools Conference, in May 2011 (http://www.ncmip.org/2011/). The 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 finance. 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

Parallel three-dimensional magnetotelluric inversion using adaptive finite-element method. Part I: theory and synthetic study

NASA Astrophysics Data System (ADS)

Grayver, Alexander V.

2015-07-01

This paper presents a distributed magnetotelluric inversion scheme based on adaptive finite-element method (FEM). The key novel aspect of the introduced algorithm is the use of automatic mesh refinement techniques for both forward and inverse modelling. These techniques alleviate tedious and subjective procedure of choosing a suitable model parametrization. To avoid overparametrization, meshes for forward and inverse problems were decoupled. For calculation of accurate electromagnetic (EM) responses, automatic mesh refinement algorithm based on a goal-oriented error estimator has been adopted. For further efficiency gain, EM fields for each frequency were calculated using independent meshes in order to account for substantially different spatial behaviour of the fields over a wide range of frequencies. An automatic approach for efficient initial mesh design in inverse problems based on linearized model resolution matrix was developed. To make this algorithm suitable for large-scale problems, it was proposed to use a low-rank approximation of the linearized model resolution matrix. In order to fill a gap between initial and true model complexities and resolve emerging 3-D structures better, an algorithm for adaptive inverse mesh refinement was derived. Within this algorithm, spatial variations of the imaged parameter are calculated and mesh is refined in the neighborhoods of points with the largest variations. A series of numerical tests were performed to demonstrate the utility of the presented algorithms. Adaptive mesh refinement based on the model resolution estimates provides an efficient tool to derive initial meshes which account for arbitrary survey layouts, data types, frequency content and measurement uncertainties. Furthermore, the algorithm is capable to deliver meshes suitable to resolve features on multiple scales while keeping number of unknowns low. However, such meshes exhibit dependency on an initial model guess. Additionally, it is demonstrated

Inverse modelling of radionuclide release rates using gamma dose rate observations

NASA Astrophysics Data System (ADS)

Hamburger, Thomas; Stohl, Andreas; von Haustein, Christoph; Thummerer, Severin; Wallner, Christian

2014-05-01

Severe accidents in nuclear power plants such as the historical accident in Chernobyl 1986 or the more recent disaster in the Fukushima Dai-ichi nuclear power plant in 2011 have drastic impacts on the population and environment. The hazardous consequences reach out on a national and continental scale. Environmental measurements and methods to model the transport and dispersion of the released radionuclides serve as a platform to assess the regional impact of nuclear accidents - both, for research purposes and, more important, to determine the immediate threat to the population. However, the assessments of the regional radionuclide activity concentrations and the individual exposure to radiation dose underlie several uncertainties. For example, the accurate model representation of wet and dry deposition. One of the most significant uncertainty, however, results from the estimation of the source term. That is, the time dependent quantification of the released spectrum of radionuclides during the course of the nuclear accident. The quantification of the source terms of severe nuclear accidents may either remain uncertain (e.g. Chernobyl, Devell et al., 1995) or rely on rather rough estimates of released key radionuclides given by the operators. Precise measurements are mostly missing due to practical limitations during the accident. Inverse modelling can be used to realise a feasible estimation of the source term (Davoine and Bocquet, 2007). Existing point measurements of radionuclide activity concentrations are therefore combined with atmospheric transport models. The release rates of radionuclides at the accident site are then obtained by improving the agreement between the modelled and observed concentrations (Stohl et al., 2012). The accuracy of the method and hence of the resulting source term depends amongst others on the availability, reliability and the resolution in time and space of the observations. Radionuclide activity concentrations are observed on a

Marine Controlled-Source Electromagnetic 2D Inversion for synthetic models.

NASA Astrophysics Data System (ADS)

Liu, Y.; Li, Y.

2016-12-01

We present a 2D inverse algorithm for frequency domain marine controlled-source electromagnetic (CSEM) data, which is based on the regularized Gauss-Newton approach. As a forward solver, our parallel adaptive finite element forward modeling program is employed. It is a self-adaptive, goal-oriented grid refinement algorithm in which a finite element analysis is performed on a sequence of refined meshes. The mesh refinement process is guided by a dual error estimate weighting to bias refinement towards elements that affect the solution at the EM receiver locations. With the use of the direct solver (MUMPS), we can effectively compute the electromagnetic fields for multi-sources and parametric sensitivities. We also implement the parallel data domain decomposition approach of Key and Ovall (2011), with the goal of being able to compute accurate responses in parallel for complicated models and a full suite of data parameters typical of offshore CSEM surveys. All minimizations are carried out by using the Gauss-Newton algorithm and model perturbations at each iteration step are obtained by using the Inexact Conjugate Gradient iteration method. Synthetic test inversions are presented.

Diagnostic methods for atmospheric inversions of long-lived greenhouse gases

NASA Astrophysics Data System (ADS)

Michalak, Anna M.; Randazzo, Nina A.; Chevallier, Frédéric

2017-06-01

The ability to predict the trajectory of climate change requires a clear understanding of the emissions and uptake (i.e., surface fluxes) of long-lived greenhouse gases (GHGs). Furthermore, the development of climate policies is driving a need to constrain the budgets of anthropogenic GHG emissions. Inverse problems that couple atmospheric observations of GHG concentrations with an atmospheric chemistry and transport model have increasingly been used to gain insights into surface fluxes. Given the inherent technical challenges associated with their solution, it is imperative that objective approaches exist for the evaluation of such inverse problems. Because direct observation of fluxes at compatible spatiotemporal scales is rarely possible, diagnostics tools must rely on indirect measures. Here we review diagnostics that have been implemented in recent studies and discuss their use in informing adjustments to model setup. We group the diagnostics along a continuum starting with those that are most closely related to the scientific question being targeted, and ending with those most closely tied to the statistical and computational setup of the inversion. We thus begin with diagnostics based on assessments against independent information (e.g., unused atmospheric observations, large-scale scientific constraints), followed by statistical diagnostics of inversion results, diagnostics based on sensitivity tests, and analyses of robustness (e.g., tests focusing on the chemistry and transport model, the atmospheric observations, or the statistical and computational framework), and close with the use of synthetic data experiments (i.e., observing system simulation experiments, OSSEs). We find that existing diagnostics provide a crucial toolbox for evaluating and improving flux estimates but, not surprisingly, cannot overcome the fundamental challenges associated with limited atmospheric observations or the lack of direct flux measurements at compatible scales. As

Inversion of chlorophyll contents by use of hyperspectral CHRIS data based on radiative transfer model

NASA Astrophysics Data System (ADS)

Wang, M. C.; Niu, X. F.; Chen, S. B.; Guo, P. J.; Yang, Q.; Wang, Z. J.

2014-03-01

Chlorophyll content, the most important pigment related to photosynthesis, is the key parameter for vegetation growth. The continuous spectrum characteristics of ground objects can be captured through hyperspectral remotely sensed data. In this study, based on the coniferous forest radiative transfer model, chlorophyll contents were inverted by use of hyperspectral CHRIS data in the coniferous forest coverage of Changbai Mountain Area. In addition, the sensitivity of LIBERTY model was analyzed. The experimental results validated that the reflectance simulation of different chlorophyll contents was coincided with that of the field measurement, and hyperspectral vegetation indices applied to the quantitative inversion of chlorophyll contents was feasible and accurate. This study presents a reasonable method of chlorophyll inversion for the coniferous forest, promotes the inversion precision, is of significance in coniferous forest monitoring.

Linear functional minimization for inverse modeling

DOE PAGES

Barajas-Solano, David A.; Wohlberg, Brendt Egon; Vesselinov, Velimir Valentinov; ...

2015-06-01

In this paper, we present a novel inverse modeling strategy to estimate spatially distributed parameters of nonlinear models. The maximum a posteriori (MAP) estimators of these parameters are based on a likelihood functional, which contains spatially discrete measurements of the system parameters and spatiotemporally discrete measurements of the transient system states. The piecewise continuity prior for the parameters is expressed via Total Variation (TV) regularization. The MAP estimator is computed by minimizing a nonquadratic objective equipped with the TV operator. We apply this inversion algorithm to estimate hydraulic conductivity of a synthetic confined aquifer from measurements of conductivity and hydraulicmore » head. The synthetic conductivity field is composed of a low-conductivity heterogeneous intrusion into a high-conductivity heterogeneous medium. Our algorithm accurately reconstructs the location, orientation, and extent of the intrusion from the steady-state data only. Finally, addition of transient measurements of hydraulic head improves the parameter estimation, accurately reconstructing the conductivity field in the vicinity of observation locations.« less

Identifying Flow Networks in a Karstified Aquifer by Application of the Cellular Automata-Based Deterministic Inversion Method (Lez Aquifer, France)

NASA Astrophysics Data System (ADS)

Fischer, P.; Jardani, A.; Wang, X.; Jourde, H.; Lecoq, N.

2017-12-01

The distributed modeling of flow paths within karstic and fractured fields remains a complex task because of the high dependence of the hydraulic responses to the relative locations between observational boreholes and interconnected fractures and karstic conduits that control the main flow of the hydrosystem. The inverse problem in a distributed model is one alternative approach to interpret the hydraulic test data by mapping the karstic networks and fractured areas. In this work, we developed a Bayesian inversion approach, the Cellular Automata-based Deterministic Inversion (CADI) algorithm to infer the spatial distribution of hydraulic properties in a structurally constrained model. This method distributes hydraulic properties along linear structures (i.e., flow conduits) and iteratively modifies the structural geometry of this conduit network to progressively match the observed hydraulic data to the modeled ones. As a result, this method produces a conductivity model that is composed of a discrete conduit network embedded in the background matrix, capable of producing the same flow behavior as the investigated hydrologic system. The method is applied to invert a set of multiborehole hydraulic tests collected from a hydraulic tomography experiment conducted at the Terrieu field site in the Lez aquifer, Southern France. The emergent model shows a high consistency to field observation of hydraulic connections between boreholes. Furthermore, it provides a geologically realistic pattern of flow conduits. This method is therefore of considerable value toward an enhanced distributed modeling of the fractured and karstified aquifers.

Inverse analysis of aerodynamic loads from strain information using structural models and neural networks

NASA Astrophysics Data System (ADS)

Wada, Daichi; Sugimoto, Yohei

2017-04-01

Aerodynamic loads on aircraft wings are one of the key parameters to be monitored for reliable and effective aircraft operations and management. Flight data of the aerodynamic loads would be used onboard to control the aircraft and accumulated data would be used for the condition-based maintenance and the feedback for the fatigue and critical load modeling. The effective sensing techniques such as fiber optic distributed sensing have been developed and demonstrated promising capability of monitoring structural responses, i.e., strains on the surface of the aircraft wings. By using the developed techniques, load identification methods for structural health monitoring are expected to be established. The typical inverse analysis for load identification using strains calculates the loads in a discrete form of concentrated forces, however, the distributed form of the loads is essential for the accurate and reliable estimation of the critical stress at structural parts. In this study, we demonstrate an inverse analysis to identify the distributed loads from measured strain information. The introduced inverse analysis technique calculates aerodynamic loads not in a discrete but in a distributed manner based on a finite element model. In order to verify the technique through numerical simulations, we apply static aerodynamic loads on a flat panel model, and conduct the inverse identification of the load distributions. We take two approaches to build the inverse system between loads and strains. The first one uses structural models and the second one uses neural networks. We compare the performance of the two approaches, and discuss the effect of the amount of the strain sensing information.

Three dimensional lithospheric magnetization structures beneath Australia derived by inverse modeling of CHAMP satellite magnetic field model

NASA Astrophysics Data System (ADS)

Du, Jinsong; Chen, Chao; Lesur, Vincent; Li, Yaoguo; Lane, Richard; Liang, Qing; Wang, Haoran

2014-05-01

We present an inversion algorithm for magnetic anomaly data in spherical coordinates to image the three dimensional (3-D) susceptibility distributions in the lithosphere. The method assumes that remanent magnetization is absent and that the magnetic anomalies are solely the result of lateral variations in magnetic susceptibility. To take into account the curvature of the Earth, the 3-D model is comprised of a set of spherical prisms (referred to as tesseroids), each of which has a constant isotropic susceptibility. The inversion method is formulated with a specifically designed model objective function and radial weighting function in spherical coordinates. A Tikhonov regularization technique is used to obtain an optimal solution with data misfit consistent with the estimated error level. Results for regional synthetic models with different magnetized inclinations and declinations are presented to demonstrate the capability of the method to recover large scale lithospheric magnetic structures. We have applied the algoithm to study the lithospheric susceptibility structures in the Australia region using magnetic anomaly data from the GRIMM_L120v0.0 model, which is based on ten years of CHAMP satellite data. As a self-constrained inversion, the maximum depths variation of magnetization layer is estimated first and then incorporated to the three dimensional (3-D) inversion. Results showed that the susceptibility anomalies concentrate in the depth range from 25 km to 45 km, i.e., focused in the lower crust. In addition, the results showed that the susceptibilities in continental lithosphere are higher than those in oceanic lithosphere. The inverted 3-D susceptibility distribution in the region of Australia reveals significant features related to tectonics, surface heat-flux, crustal thickness and Curie isotherm depths. In general, the higher susceptibility anomalies correlate with Precambrian rocks, and the lower susceptibility anomalies correlate with younger orogenic

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.

Modeling analysis of pulsed magnetization process of magnetic core based on inverse Jiles-Atherton model

NASA Astrophysics Data System (ADS)

Liu, Yi; Zhang, He; Liu, Siwei; Lin, Fuchang

2018-05-01

The J-A (Jiles-Atherton) model is widely used to describe the magnetization characteristics of magnetic cores in a low-frequency alternating field. However, this model is deficient in the quantitative analysis of the eddy current loss and residual loss in a high-frequency magnetic field. Based on the decomposition of magnetization intensity, an inverse J-A model is established which uses magnetic flux density B as an input variable. Static and dynamic core losses under high frequency excitation are separated based on the inverse J-A model. Optimized parameters of the inverse J-A model are obtained based on particle swarm optimization. The platform for the pulsed magnetization characteristic test is designed and constructed. The hysteresis curves of ferrite and Fe-based nanocrystalline cores at high magnetization rates are measured. The simulated and measured hysteresis curves are presented and compared. It is found that the inverse J-A model can be used to describe the magnetization characteristics at high magnetization rates and to separate the static loss and dynamic loss accurately.

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

GePb Alloy Growth Using Layer Inversion Method

NASA Astrophysics Data System (ADS)

Alahmad, Hakimah; Mosleh, Aboozar; Alher, Murtadha; Banihashemian, Seyedeh Fahimeh; Ghetmiri, Seyed Amir; Al-Kabi, Sattar; Du, Wei; Li, Bauhoa; Yu, Shui-Qing; Naseem, Hameed A.

2018-04-01

Germanium-lead films have been investigated as a new direct-bandgap group IV alloy. GePb films were deposited on Si via thermal evaporation of Ge and Pb solid sources using the layer inversion metal-induced crystallization method for comparison with the current laser-induced recrystallization method. Material characterization of the films using x-ray diffraction analysis revealed highly oriented crystallinity and Pb incorporation as high as 13.5% before and 5.2% after annealing. Transmission electron microscopy, scanning electron microscopy, and energy-dispersive x-ray mapping of the samples revealed uniform incorporation of elements and complete layer inversion. Optical characterization of the GePb films by Raman spectroscopy and photoluminescence techniques showed that annealing the samples resulted in higher crystalline quality as well as bandgap reduction. The bandgap reduction from 0.67 eV to 0.547 eV observed for the highest-quality material confirms the achievement of a direct-bandgap material.

GePb Alloy Growth Using Layer Inversion Method

NASA Astrophysics Data System (ADS)

Alahmad, Hakimah; Mosleh, Aboozar; Alher, Murtadha; Banihashemian, Seyedeh Fahimeh; Ghetmiri, Seyed Amir; Al-Kabi, Sattar; Du, Wei; Li, Bauhoa; Yu, Shui-Qing; Naseem, Hameed A.

2018-07-01

Germanium-lead films have been investigated as a new direct-bandgap group IV alloy. GePb films were deposited on Si via thermal evaporation of Ge and Pb solid sources using the layer inversion metal-induced crystallization method for comparison with the current laser-induced recrystallization method. Material characterization of the films using x-ray diffraction analysis revealed highly oriented crystallinity and Pb incorporation as high as 13.5% before and 5.2% after annealing. Transmission electron microscopy, scanning electron microscopy, and energy-dispersive x-ray mapping of the samples revealed uniform incorporation of elements and complete layer inversion. Optical characterization of the GePb films by Raman spectroscopy and photoluminescence techniques showed that annealing the samples resulted in higher crystalline quality as well as bandgap reduction. The bandgap reduction from 0.67 eV to 0.547 eV observed for the highest-quality material confirms the achievement of a direct-bandgap material.

In search of best fitted composite model to the ALAE data set with transformed Gamma and inversed transformed Gamma families

NASA Astrophysics Data System (ADS)

Maghsoudi, Mastoureh; Bakar, Shaiful Anuar Abu

2017-05-01

In this paper, a recent novel approach is applied to estimate the threshold parameter of a composite model. Several composite models from Transformed Gamma and Inverse Transformed Gamma families are constructed based on this approach and their parameters are estimated by the maximum likelihood method. These composite models are fitted to allocated loss adjustment expenses (ALAE). In comparison to all composite models studied, the composite Weibull-Inverse Transformed Gamma model is proved to be a competitor candidate as it best fit the loss data. The final part considers the backtesting method to verify the validation of VaR and CTE risk measures.

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.

Ellipsoidal head model for fetal magnetoencephalography: forward and inverse solutions

NASA Astrophysics Data System (ADS)

Gutiérrez, David; Nehorai, Arye; Preissl, Hubert

2005-05-01

Fetal magnetoencephalography (fMEG) is a non-invasive technique where measurements of the magnetic field outside the maternal abdomen are used to infer the source location and signals of the fetus' neural activity. There are a number of aspects related to fMEG modelling that must be addressed, such as the conductor volume, fetal position and orientation, gestation period, etc. We propose a solution to the forward problem of fMEG based on an ellipsoidal head geometry. This model has the advantage of highlighting special characteristics of the field that are inherent to the anisotropy of the human head, such as the spread and orientation of the field in relationship with the localization and position of the fetal head. Our forward solution is presented in the form of a kernel matrix that facilitates the solution of the inverse problem through decoupling of the dipole localization parameters from the source signals. Then, we use this model and the maximum likelihood technique to solve the inverse problem assuming the availability of measurements from multiple trials. The applicability and performance of our methods are illustrated through numerical examples based on a real 151-channel SQUID fMEG measurement system (SARA). SARA is an MEG system especially designed for fetal assessment and is currently used for heart and brain studies. Finally, since our model requires knowledge of the best-fitting ellipsoid's centre location and semiaxes lengths, we propose a method for estimating these parameters through a least-squares fit on anatomical information obtained from three-dimensional ultrasound images.

A new full-Stokes model as a tool for basal inversions.

NASA Astrophysics Data System (ADS)

Kyrke-Smith, Teresa M.; Hilmar Gudmundsson, G.; Farrell, Patrick E.

2016-04-01

High resolution models of ice sheet dynamics are required to make accurate predictions of the future mass balance of ice sheets. These require knowledge of flow conditions at the bed of the ice, however, the inaccessibility of the bed means there exist few observational constraints. Inverse methods are therefore commonly used to obtain information about the nature of basal control using given surface observations. We present a new 3D Stokes solver written using FEniCS with the potential to carry out second-order inversions for basal slipperiness. We will be applying the model to Pine Island Glacier, Antarctica. Pine Island Glacier is one of the fastest flowing and most rapidly changing ice streams in Antarctica, and is currently contributing to sea-level rise at an increasing rate. Recent field seasons as part of the iSTAR project have acquired high-resolution in-situ geophysical measurements; results from our model will be compared with these to try and increase understanding about the conditions at the bed of Pine Island Glacier.

Fully three-dimensional and viscous semi-inverse method for axial/radial turbomachine blade design

NASA Astrophysics Data System (ADS)

Ji, Min

2008-10-01

A fully three-dimensional viscous semi-inverse method for the design of turbomachine blades is presented in this work. Built on a time marching Reynolds-Averaged Navier-Stokes solver, the inverse scheme is capable of designing axial/radial turbomachinery blades in flow regimes ranging from very low Mach number to transonic/supersonic flows. In order to solve flow at all-speed conditions, the preconditioning technique is incorporated into the basic JST time-marching scheme. The accuracy of the resulting flow solver is verified with documented experimental data and commercial CFD codes. The level of accuracy of the flow solver exhibited in those verification cases is typical of CFD analysis employed in the design process in industry. The inverse method described in the present work takes pressure loading and blade thickness as prescribed quantities and computes the corresponding three-dimensional blade camber surface. In order to have the option of imposing geometrical constraints on the designed blade shapes, a new inverse algorithm is developed to solve the camber surface at specified spanwise pseudo stream-tubes (i.e. along grid lines), while the blade geometry is constructed through ruling (e.g. straight-line element) at the remaining spanwise stations. The new inverse algorithm involves re-formulating the boundary condition on the blade surfaces as a hybrid inverse/analysis boundary condition, preserving the full three-dimensional nature of the flow. The new design procedure can be interpreted as a fully three-dimensional viscous semi-inverse method. The ruled surface design ensures the blade surface smoothness and mechanical integrity as well as achieves cost reduction for the manufacturing process. A numerical target shooting experiment for a mixed flow impeller shows that the semi-inverse method is able to accurately recover the target blade composed of straightline element from a different initial blade. The semi-inverse method is proved to work well with

The Source Inversion Validation (SIV) Initiative: A Collaborative Study on Uncertainty Quantification in Earthquake Source Inversions

NASA Astrophysics Data System (ADS)

Mai, P. M.; Schorlemmer, D.; Page, M.

2012-04-01

Earthquake source inversions image the spatio-temporal rupture evolution on one or more fault planes using seismic and/or geodetic data. Such studies are critically important for earthquake seismology in general, and for advancing seismic hazard analysis in particular, as they reveal earthquake source complexity and help (i) to investigate earthquake mechanics; (ii) to develop spontaneous dynamic rupture models; (iii) to build models for generating rupture realizations for ground-motion simulations. In applications (i - iii), the underlying finite-fault source models are regarded as "data" (input information), but their uncertainties are essentially unknown. After all, source models are obtained from solving an inherently ill-posed inverse problem to which many a priori assumptions and uncertain observations are applied. The Source Inversion Validation (SIV) project is a collaborative effort to better understand the variability between rupture models for a single earthquake (as manifested in the finite-source rupture model database) and to develop robust uncertainty quantification for earthquake source inversions. The SIV project highlights the need to develop a long-standing and rigorous testing platform to examine the current state-of-the-art in earthquake source inversion, and to develop and test novel source inversion approaches. We will review the current status of the SIV project, and report the findings and conclusions of the recent workshops. We will briefly discuss several source-inversion methods, how they treat uncertainties in data, and assess the posterior model uncertainty. Case studies include initial forward-modeling tests on Green's function calculations, and inversion results for synthetic data from spontaneous dynamic crack-like strike-slip earthquake on steeply dipping fault, embedded in a layered crustal velocity-density structure.

Numerical modeling of axi-symmetrical cold forging process by ``Pseudo Inverse Approach''

NASA Astrophysics Data System (ADS)

Halouani, A.; Li, Y. M.; Abbes, B.; Guo, Y. Q.

2011-05-01

The incremental approach is widely used for the forging process modeling, it gives good strain and stress estimation, but it is time consuming. A fast Inverse Approach (IA) has been developed for the axi-symmetric cold forging modeling [1-2]. This approach exploits maximum the knowledge of the final part's shape and the assumptions of proportional loading and simplified tool actions make the IA simulation very fast. The IA is proved very useful for the tool design and optimization because of its rapidity and good strain estimation. However, the assumptions mentioned above cannot provide good stress estimation because of neglecting the loading history. A new approach called "Pseudo Inverse Approach" (PIA) was proposed by Batoz, Guo et al.. [3] for the sheet forming modeling, which keeps the IA's advantages but gives good stress estimation by taking into consideration the loading history. Our aim is to adapt the PIA for the cold forging modeling in this paper. The main developments in PIA are resumed as follows: A few intermediate configurations are generated for the given tools' positions to consider the deformation history; the strain increment is calculated by the inverse method between the previous and actual configurations. An incremental algorithm of the plastic integration is used in PIA instead of the total constitutive law used in the IA. An example is used to show the effectiveness and limitations of the PIA for the cold forging process modeling.

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

NASA Astrophysics Data System (ADS)

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

2007-12-01

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

Frequency domain, waveform inversion of laboratory crosswell radar data

USGS Publications Warehouse

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

2010-01-01

A new waveform inversion for crosswell radar is formulated in the frequency-domain for a 2.5D model. The inversion simulates radar waves using the vector Helmholtz equation for electromagnetic waves. The objective function is minimized using a backpropagation method suitable for a 2.5D model. The inversion is tested by processing crosswell radar data collected in a laboratory tank. The estimated model is consistent with the known electromagnetic properties of the tank. The formulation for the 2.5D model can be extended to inversions of acoustic and elastic data.

THERMAL DIAGNOSTICS WITH THE ATMOSPHERIC IMAGING ASSEMBLY ON BOARD THE SOLAR DYNAMICS OBSERVATORY: A VALIDATED METHOD FOR DIFFERENTIAL EMISSION MEASURE INVERSIONS

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

Cheung, Mark C. M.; Boerner, P.; Schrijver, C. J.

We present a new method for performing differential emission measure (DEM) inversions on narrow-band EUV images from the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory. The method yields positive definite DEM solutions by solving a linear program. This method has been validated against a diverse set of thermal models of varying complexity and realism. These include (1) idealized Gaussian DEM distributions, (2) 3D models of NOAA Active Region 11158 comprising quasi-steady loop atmospheres in a nonlinear force-free field, and (3) thermodynamic models from a fully compressible, 3D MHD simulation of active region (AR) corona formation following magneticmore » flux emergence. We then present results from the application of the method to AIA observations of Active Region 11158, comparing the region's thermal structure on two successive solar rotations. Additionally, we show how the DEM inversion method can be adapted to simultaneously invert AIA and Hinode X-ray Telescope data, and how supplementing AIA data with the latter improves the inversion result. The speed of the method allows for routine production of DEM maps, thus facilitating science studies that require tracking of the thermal structure of the solar corona in time and space.« less

A trade-off solution between model resolution and covariance in surface-wave inversion

USGS Publications Warehouse

Xia, J.; Xu, Y.; Miller, R.D.; Zeng, C.

2010-01-01

Regularization is necessary for inversion of ill-posed geophysical problems. Appraisal of inverse models is essential for meaningful interpretation of these models. Because uncertainties are associated with regularization parameters, extra conditions are usually required to determine proper parameters for assessing inverse models. Commonly used techniques for assessment of a geophysical inverse model derived (generally iteratively) from a linear system are based on calculating the model resolution and the model covariance matrices. Because the model resolution and the model covariance matrices of the regularized solutions are controlled by the regularization parameter, direct assessment of inverse models using only the covariance matrix may provide incorrect results. To assess an inverted model, we use the concept of a trade-off between model resolution and covariance to find a proper regularization parameter with singular values calculated in the last iteration. We plot the singular values from large to small to form a singular value plot. A proper regularization parameter is normally the first singular value that approaches zero in the plot. With this regularization parameter, we obtain a trade-off solution between model resolution and model covariance in the vicinity of a regularized solution. The unit covariance matrix can then be used to calculate error bars of the inverse model at a resolution level determined by the regularization parameter. We demonstrate this approach with both synthetic and real surface-wave data. ?? 2010 Birkh??user / Springer Basel AG.

On the calibration process of film dosimetry: OLS inverse regression versus WLS inverse prediction.

PubMed

Crop, F; Van Rompaye, B; Paelinck, L; Vakaet, L; Thierens, H; De Wagter, C

2008-07-21

The purpose of this study was both putting forward a statistically correct model for film calibration and the optimization of this process. A reliable calibration is needed in order to perform accurate reference dosimetry with radiographic (Gafchromic) film. Sometimes, an ordinary least squares simple linear (in the parameters) regression is applied to the dose-optical-density (OD) curve with the dose as a function of OD (inverse regression) or sometimes OD as a function of dose (inverse prediction). The application of a simple linear regression fit is an invalid method because heteroscedasticity of the data is not taken into account. This could lead to erroneous results originating from the calibration process itself and thus to a lower accuracy. In this work, we compare the ordinary least squares (OLS) inverse regression method with the correct weighted least squares (WLS) inverse prediction method to create calibration curves. We found that the OLS inverse regression method could lead to a prediction bias of up to 7.3 cGy at 300 cGy and total prediction errors of 3% or more for Gafchromic EBT film. Application of the WLS inverse prediction method resulted in a maximum prediction bias of 1.4 cGy and total prediction errors below 2% in a 0-400 cGy range. We developed a Monte-Carlo-based process to optimize calibrations, depending on the needs of the experiment. This type of thorough analysis can lead to a higher accuracy for film dosimetry.

Design optimization of axial flow hydraulic turbine runner: Part I - an improved Q3D inverse method

NASA Astrophysics Data System (ADS)

Peng, Guoyi; Cao, Shuliang; Ishizuka, Masaru; Hayama, Shinji

2002-06-01

With the aim of constructing a comprehensive design optimization procedure of axial flow hydraulic turbine, an improved quasi-three-dimensional inverse method has been proposed from the viewpoint of system and a set of rotational flow governing equations as well as a blade geometry design equation has been derived. The computation domain is firstly taken from the inlet of guide vane to the far outlet of runner blade in the inverse method and flows in different regions are solved simultaneously. So the influence of wicket gate parameters on the runner blade design can be considered and the difficulty to define the flow condition at the runner blade inlet is surmounted. As a pre-computation of initial blade design on S2m surface is newly adopted, the iteration of S1 and S2m surfaces has been reduced greatly and the convergence of inverse computation has been improved. The present model has been applied to the inverse computation of a Kaplan turbine runner. Experimental results and the direct flow analysis have proved the validation of inverse computation. Numerical investigations show that a proper enlargement of guide vane distribution diameter is advantageous to improve the performance of axial hydraulic turbine runner. Copyright

Earthquake source tensor inversion with the gCAP method and 3D Green's functions

NASA Astrophysics Data System (ADS)

Zheng, J.; Ben-Zion, Y.; Zhu, L.; Ross, Z.

2013-12-01

We develop and apply a method to invert earthquake seismograms for source properties using a general tensor representation and 3D Green's functions. The method employs (i) a general representation of earthquake potency/moment tensors with double couple (DC), compensated linear vector dipole (CLVD), and isotropic (ISO) components, and (ii) a corresponding generalized CAP (gCap) scheme where the continuous wave trains are broken into Pnl and surface waves (Zhu & Ben-Zion, 2013). For comparison, we also use the waveform inversion method of Zheng & Chen (2012) and Ammon et al. (1998). Sets of 3D Green's functions are calculated on a grid of 1 km3 using the 3-D community velocity model CVM-4 (Kohler et al. 2003). A bootstrap technique is adopted to establish robustness of the inversion results using the gCap method (Ross & Ben-Zion, 2013). Synthetic tests with 1-D and 3-D waveform calculations show that the source tensor inversion procedure is reasonably reliable and robust. As initial application, the method is used to investigate source properties of the March 11, 2013, Mw=4.7 earthquake on the San Jacinto fault using recordings of ~45 stations up to ~0.2Hz. Both the best fitting and most probable solutions include ISO component of ~1% and CLVD component of ~0%. The obtained ISO component, while small, is found to be a non-negligible positive value that can have significant implications for the physics of the failure process. Work on using higher frequency data for this and other earthquakes is in progress.

Comparative Study of Three Data Assimilation Methods for Ice Sheet Model Initialisation

NASA Astrophysics Data System (ADS)

Mosbeux, Cyrille; Gillet-Chaulet, Fabien; Gagliardini, Olivier

2015-04-01

The current global warming has direct consequences on ice-sheet mass loss contributing to sea level rise. This loss is generally driven by an acceleration of some coastal outlet glaciers and reproducing these mechanisms is one of the major issues in ice-sheet and ice flow modelling. The construction of an initial state, as close as possible to current observations, is required as a prerequisite before producing any reliable projection of the evolution of ice-sheets. For this step, inverse methods are often used to infer badly known or unknown parameters. For instance, the adjoint inverse method has been implemented and applied with success by different authors in different ice flow models in order to infer the basal drag [ Schafer et al., 2012; Gillet-chauletet al., 2012; Morlighem et al., 2010]. Others data fields, such as ice surface and bedrock topography, are easily measurable with more or less uncertainty but only locally along tracks and interpolated on finer model grid. All these approximations lead to errors on the data elevation model and give rise to an ill-posed problem inducing non-physical anomalies in flux divergence [Seroussi et al, 2011]. A solution to dissipate these divergences of flux is to conduct a surface relaxation step at the expense of the accuracy of the modelled surface [Gillet-Chaulet et al., 2012]. Other solutions, based on the inversion of ice thickness and basal drag were proposed [Perego et al., 2014; Pralong & Gudmundsson, 2011]. In this study, we create a twin experiment to compare three different assimilation algorithms based on inverse methods and nudging to constrain the bedrock friction and the bedrock elevation: (i) cyclic inversion of friction parameter and bedrock topography using adjoint method, (ii) cycles coupling inversion of friction parameter using adjoint method and nudging of bedrock topography, (iii) one step inversion of both parameters with adjoint method. The three methods show a clear improvement in parameters

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.

Use of Inverse-Modeling Methods to Improve Ground-Water-Model Calibration and Evaluate Model-Prediction Uncertainty, Camp Edwards, Cape Cod, Massachusetts

USGS Publications Warehouse

Walter, Donald A.; LeBlanc, Denis R.

2008-01-01

Historical weapons testing and disposal activities at Camp Edwards, which is located on the Massachusetts Military Reservation, western Cape Cod, have resulted in the release of contaminants into an underlying sand and gravel aquifer that is the sole source of potable water to surrounding communities. Ground-water models have been used at the site to simulate advective transport in the aquifer in support of field investigations. Reasonable models developed by different groups and calibrated by trial and error often yield different predictions of advective transport, and the predictions lack quantitative measures of uncertainty. A recently (2004) developed regional model of western Cape Cod, modified to include the sensitivity and parameter-estimation capabilities of MODFLOW-2000, was used in this report to evaluate the utility of inverse (statistical) methods to (1) improve model calibration and (2) assess model-prediction uncertainty. Simulated heads and flows were most sensitive to recharge and to the horizontal hydraulic conductivity of the Buzzards Bay and Sandwich Moraines and the Buzzards Bay and northern parts of the Mashpee outwash plains. Conversely, simulated heads and flows were much less sensitive to vertical hydraulic conductivity. Parameter estimation (inverse calibration) improved the match to observed heads and flows; the absolute mean residual for heads improved by 0.32 feet and the absolute mean residual for streamflows improved by about 0.2 cubic feet per second. Advective-transport predictions in Camp Edwards generally were most sensitive to the parameters with the highest precision (lowest coefficients of variation), indicating that the numerical model is adequate for evaluating prediction uncertainties in and around Camp Edwards. The incorporation of an advective-transport observation, representing the leading edge of a contaminant plume that had been difficult to match by using trial-and-error calibration, improved the match between an

A Study of Terrain Reductions, Density Anomalies and Geophysical Inversion Methods in Gravity Field Modelling

DTIC Science & Technology

1984-04-01

5.15) where a is a positive constant and 11 IIH the Hilbert space norm associated with the chosen covariance function K. The constant a is arbitrary...Density Anomalies 14 5. Unknown Densities - Geophysical Inversion 16 6. Density Modelling Using Rectangular Prisms 24 6.1 Space Domain 24 6.2 Frequency...theory: to calculate the gravity potential and its derivatives in space due to 6 • given density distributions. When the prime interest is in "external

Modeling temperature inversion in southeastern Yellow Sea during winter 2016

NASA Astrophysics Data System (ADS)

Pang, Ig-Chan; Moon, Jae-Hong; Lee, Joon-Ho; Hong, Ji-Seok; Pang, Sung-Jun

2017-05-01

A significant temperature inversion with temperature differences larger than 3°C was observed in the southeastern Yellow Sea (YS) during February 2016. By analyzing in situ hydrographic profiles and results from a regional ocean model for the YS, this study examines the spatiotemporal evolution of the temperature inversion and its connection with wind-induced currents in winter. Observations reveal that in winter, when the northwesterly wind prevails over the YS, the temperature inversion occurs largely at the frontal zone southwest of Korea where warm/saline water of a Kuroshio origin meets cold/fresh coastal water. Our model successfully captures the temperature inversion observed in the winter of 2016 and suggests a close relation between northwesterly wind bursts and the occurrence of the large inversion. In this respect, the strong northwesterly wind drove cold coastal water southward in the upper layer via Ekman transport, which pushed the water mass southward and increased the sea level slope in the frontal zone in southeastern YS. The intensified sea level slope propagated northward away from the frontal zone as a shelf wave, causing a northward upwind flow response along the YS trough in the lower layer, thereby resulting in the large temperature inversion. Diagnostic analysis of the momentum balance shows that the westward pressure gradient, which developed with shelf wave propagation along the YS trough, was balanced with the Coriolis force in accordance with the northward upwind current in and around the inversion area.

Inversed estimation of critical factors for controlling over-prediction of summertime tropospheric O3 over East Asia based of the combination of DDM sensitivity analysis and modeled Green's function method

NASA Astrophysics Data System (ADS)

Itahashi, S.; Yumimoto, K.; Uno, I.; Kim, S.

2012-12-01

Air quality studies based on the chemical transport model have been provided many important results for promoting our knowledge of air pollution phenomena, however, discrepancies between modeling results and observation data are still important issue to overcome. One of the concerning issue would be an over-prediction of summertime tropospheric ozone in remote area of Japan. This problem has been pointed out in the model comparison study of both regional scale (e.g., MICS-Asia) and global scale model (e.g., TH-FTAP). Several reasons for this issue can be listed as, (i) the modeled reproducibility on the penetration of clean oceanic air mass, (ii) correct estimation of the anthropogenic NOx / VOC emissions over East Asia, (iii) the chemical reaction scheme used in model simulation. In this study, we attempt to inverse estimation of some important chemical reactions based on the combining system of DDM (decoupled direct method) sensitivity analysis and modeled Green's function approach. The decoupled direct method (DDM) is an efficient and accurate way of performing sensitivity analysis to model inputs, calculates sensitivity coefficients representing the responsiveness of atmospheric chemical concentrations to perturbations in a model input or parameter. The inverse solutions with the Green's functions are given by a linear, least-squares method but are still robust against nonlinearities, To construct the response matrix (i.e., Green's functions), we can directly use the results of DDM sensitivity analysis. The solution of chemical reaction constants which have relatively large uncertainties are determined with constraints of observed ozone concentration data over the remote area in Japan. Our inversed estimation demonstrated that the underestimation of reaction constant to produce HNO3 (NO2 + OH + M → HNO3 + M) in SAPRC99 chemical scheme, and the inversed results indicated the +29.0 % increment to this reaction. This estimation has good agreement when compared

Detailed Velocity and Density models of the Cascadia Subduction Zone from Prestack Full-Waveform Inversion

NASA Astrophysics Data System (ADS)

Fortin, W.; Holbrook, W. S.; Mallick, S.; Everson, E. D.; Tobin, H. J.; Keranen, K. M.

2014-12-01

Understanding the geologic composition of the Cascadia Subduction Zone (CSZ) is critically important in assessing seismic hazards in the Pacific Northwest. Despite being a potential earthquake and tsunami threat to millions of people, key details of the structure and fault mechanisms remain poorly understood in the CSZ. In particular, the position and character of the subduction interface remains elusive due to its relative aseismicity and low seismic reflectivity, making imaging difficult for both passive and active source methods. Modern active-source reflection seismic data acquired as part of the COAST project in 2012 provide an opportunity to study the transition from the Cascadia basin, across the deformation front, and into the accretionary prism. Coupled with advances in seismic inversion methods, this new data allow us to produce detailed velocity models of the CSZ and accurate pre-stack depth migrations for studying geologic structure. While still computationally expensive, current computing clusters can perform seismic inversions at resolutions that match that of the seismic image itself. Here we present pre-stack full waveform inversions of the central seismic line of the COAST survey offshore Washington state. The resultant velocity model is produced by inversion at every CMP location, 6.25 m laterally, with vertical resolution of 0.2 times the dominant seismic frequency. We report a good average correlation value above 0.8 across the entire seismic line, determined by comparing synthetic gathers to the real pre-stack gathers. These detailed velocity models, both Vp and Vs, along with the density model, are a necessary step toward a detailed porosity cross section to be used to determine the role of fluids in the CSZ. Additionally, the P-velocity model is used to produce a pre-stack depth migration image of the CSZ.

Wavelet-based 3-D inversion for frequency-domain airborne EM data

NASA Astrophysics Data System (ADS)

Liu, Yunhe; Farquharson, Colin G.; Yin, Changchun; Baranwal, Vikas C.

2018-04-01

In this paper, we propose a new wavelet-based 3-D inversion method for frequency-domain airborne electromagnetic (FDAEM) data. Instead of inverting the model in the space domain using a smoothing constraint, this new method recovers the model in the wavelet domain based on a sparsity constraint. In the wavelet domain, the model is represented by two types of coefficients, which contain both large- and fine-scale informations of the model, meaning the wavelet-domain inversion has inherent multiresolution. In order to accomplish a sparsity constraint, we minimize an L1-norm measure in the wavelet domain that mostly gives a sparse solution. The final inversion system is solved by an iteratively reweighted least-squares method. We investigate different orders of Daubechies wavelets to accomplish our inversion algorithm, and test them on synthetic frequency-domain AEM data set. The results show that higher order wavelets having larger vanishing moments and regularity can deliver a more stable inversion process and give better local resolution, while the lower order wavelets are simpler and less smooth, and thus capable of recovering sharp discontinuities if the model is simple. At last, we test this new inversion algorithm on a frequency-domain helicopter EM (HEM) field data set acquired in Byneset, Norway. Wavelet-based 3-D inversion of HEM data is compared to L2-norm-based 3-D inversion's result to further investigate the features of the new method.

Data-driven methods towards learning the highly nonlinear inverse kinematics of tendon-driven surgical manipulators.

PubMed

Xu, Wenjun; Chen, Jie; Lau, Henry Y K; Ren, Hongliang

2017-09-01

Accurate motion control of flexible surgical manipulators is crucial in tissue manipulation tasks. The tendon-driven serpentine manipulator (TSM) is one of the most widely adopted flexible mechanisms in minimally invasive surgery because of its enhanced maneuverability in torturous environments. TSM, however, exhibits high nonlinearities and conventional analytical kinematics model is insufficient to achieve high accuracy. To account for the system nonlinearities, we applied a data driven approach to encode the system inverse kinematics. Three regression methods: extreme learning machine (ELM), Gaussian mixture regression (GMR) and K-nearest neighbors regression (KNNR) were implemented to learn a nonlinear mapping from the robot 3D position states to the control inputs. The performance of the three algorithms was evaluated both in simulation and physical trajectory tracking experiments. KNNR performed the best in the tracking experiments, with the lowest RMSE of 2.1275 mm. The proposed inverse kinematics learning methods provide an alternative and efficient way to accurately model the tendon driven flexible manipulator. Copyright © 2016 John Wiley & Sons, Ltd.

Iterative updating of model error for Bayesian inversion

NASA Astrophysics Data System (ADS)

Calvetti, Daniela; Dunlop, Matthew; Somersalo, Erkki; Stuart, Andrew

2018-02-01

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when optimization algorithms are used to find a single estimate, or to speed up Markov chain Monte Carlo (MCMC) calculations in the Bayesian framework. The use of an approximate model introduces a discrepancy, or modeling error, that may have a detrimental effect on the solution of the ill-posed inverse problem, or it may severely distort the estimate of the posterior distribution. In the Bayesian paradigm, the modeling error can be considered as a random variable, and by using an estimate of the probability distribution of the unknown, one may estimate the probability distribution of the modeling error and incorporate it into the inversion. We introduce an algorithm which iterates this idea to update the distribution of the model error, leading to a sequence of posterior distributions that are demonstrated empirically to capture the underlying truth with increasing accuracy. Since the algorithm is not based on rejections, it requires only limited full model evaluations. We show analytically that, in the linear Gaussian case, the algorithm converges geometrically fast with respect to the number of iterations when the data is finite dimensional. For more general models, we introduce particle approximations of the iteratively generated sequence of distributions; we also prove that each element of the sequence converges in the large particle limit under a simplifying assumption. We show numerically that, as in the linear case, rapid convergence occurs with respect to the number of iterations. Additionally, we show through computed examples that point estimates obtained from this iterative algorithm are superior to those obtained by neglecting the model error.

A New Self-Constrained Inversion Method of Potential Fields Based on Probability Tomography

NASA Astrophysics Data System (ADS)

Sun, S.; Chen, C.; WANG, H.; Wang, Q.

2014-12-01

The self-constrained inversion method of potential fields uses a priori information self-extracted from potential field data. Differing from external a priori information, the self-extracted information are generally parameters derived exclusively from the analysis of the gravity and magnetic data (Paoletti et al., 2013). Here we develop a new self-constrained inversion method based on probability tomography. Probability tomography doesn't need any priori information, as well as large inversion matrix operations. Moreover, its result can describe the sources, especially the distribution of which is complex and irregular, entirely and clearly. Therefore, we attempt to use the a priori information extracted from the probability tomography results to constrain the inversion for physical properties. The magnetic anomaly data was taken as an example in this work. The probability tomography result of magnetic total field anomaly(ΔΤ) shows a smoother distribution than the anomalous source and cannot display the source edges exactly. However, the gradients of ΔΤ are with higher resolution than ΔΤ in their own direction, and this characteristic is also presented in their probability tomography results. So we use some rules to combine the probability tomography results of ∂ΔΤ⁄∂x, ∂ΔΤ⁄∂y and ∂ΔΤ⁄∂z into a new result which is used for extracting a priori information, and then incorporate the information into the model objective function as spatial weighting functions to invert the final magnetic susceptibility. Some magnetic synthetic examples incorporated with and without a priori information extracted from the probability tomography results were made to do comparison, results of which show that the former are more concentrated and with higher resolution of the source body edges. This method is finally applied in an iron mine in China with field measured ΔΤ data and performs well. ReferencesPaoletti, V., Ialongo, S., Florio, G., Fedi, M

Identification of moving sinusoidal wave loads for sensor structural configuration by finite element inverse method

NASA Astrophysics Data System (ADS)

Zhang, B.; Yu, S.

2018-03-01

In this paper, a beam structure of composite materials with elastic foundation supports is established as the sensor model, which propagates moving sinusoidal wave loads. The inverse Finite Element Method (iFEM) is applied for reconstructing moving wave loads which are compared with true wave loads. The conclusion shows that iFEM is accurate and robust in the determination of wave propagation. This helps to seek a suitable new wave sensor method.

An introduction of Markov chain Monte Carlo method to geochemical inverse problems: Reading melting parameters from REE abundances in abyssal peridotites

NASA Astrophysics Data System (ADS)

Liu, Boda; Liang, Yan

2017-04-01

Markov chain Monte Carlo (MCMC) simulation is a powerful statistical method in solving inverse problems that arise from a wide range of applications. In Earth sciences applications of MCMC simulations are primarily in the field of geophysics. The purpose of this study is to introduce MCMC methods to geochemical inverse problems related to trace element fractionation during mantle melting. MCMC methods have several advantages over least squares methods in deciphering melting processes from trace element abundances in basalts and mantle rocks. Here we use an MCMC method to invert for extent of melting, fraction of melt present during melting, and extent of chemical disequilibrium between the melt and residual solid from REE abundances in clinopyroxene in abyssal peridotites from Mid-Atlantic Ridge, Central Indian Ridge, Southwest Indian Ridge, Lena Trough, and American-Antarctic Ridge. We consider two melting models: one with exact analytical solution and the other without. We solve the latter numerically in a chain of melting models according to the Metropolis-Hastings algorithm. The probability distribution of inverted melting parameters depends on assumptions of the physical model, knowledge of mantle source composition, and constraints from the REE data. Results from MCMC inversion are consistent with and provide more reliable uncertainty estimates than results based on nonlinear least squares inversion. We show that chemical disequilibrium is likely to play an important role in fractionating LREE in residual peridotites during partial melting beneath mid-ocean ridge spreading centers. MCMC simulation is well suited for more complicated but physically more realistic melting problems that do not have analytical solutions.

Impact of transport and modelling errors on the estimation of methane sources and sinks by inverse modelling

NASA Astrophysics Data System (ADS)

Locatelli, Robin; Bousquet, Philippe; Chevallier, Frédéric

2013-04-01

Since the nineties, inverse modelling by assimilating atmospheric measurements into a chemical transport model (CTM) has been used to derive sources and sinks of atmospheric trace gases. More recently, the high global warming potential of methane (CH4) and unexplained variations of its atmospheric mixing ratio caught the attention of several research groups. Indeed, the diversity and the variability of methane sources induce high uncertainty on the present and the future evolution of CH4 budget. With the increase of available measurement data to constrain inversions (satellite data, high frequency surface and tall tower observations, FTIR spectrometry,...), the main limiting factor is about to become the representation of atmospheric transport in CTMs. Indeed, errors in transport modelling directly converts into flux changes when assuming perfect transport in atmospheric inversions. Hence, we propose an inter-model comparison in order to quantify the impact of transport and modelling errors on the CH4 fluxes estimated into a variational inversion framework. Several inversion experiments are conducted using the same set-up (prior emissions, measurement and prior errors, OH field, initial conditions) of the variational system PYVAR, developed at LSCE (Laboratoire des Sciences du Climat et de l'Environnement, France). Nine different models (ACTM, IFS, IMPACT, IMPACT1x1, MOZART, PCTM, TM5, TM51x1 and TOMCAT) used in TRANSCOM-CH4 experiment (Patra el al, 2011) provide synthetic measurements data at up to 280 surface sites to constrain the inversions performed using the PYVAR system. Only the CTM (and the meteorological drivers which drive them) used to create the pseudo-observations vary among inversions. Consequently, the comparisons of the nine inverted methane fluxes obtained for 2005 give a good order of magnitude of the impact of transport and modelling errors on the estimated fluxes with current and future networks. It is shown that transport and modelling errors

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.

Cerebellum as a forward but not inverse model in visuomotor adaptation task: a tDCS-based and modeling study.

PubMed

Yavari, Fatemeh; Mahdavi, Shirin; Towhidkhah, Farzad; Ahmadi-Pajouh, Mohammad-Ali; Ekhtiari, Hamed; Darainy, Mohammad

2016-04-01

Despite several pieces of evidence, which suggest that the human brain employs internal models for motor control and learning, the location of these models in the brain is not yet clear. In this study, we used transcranial direct current stimulation (tDCS) to manipulate right cerebellar function, while subjects adapt to a visuomotor task. We investigated the effect of this manipulation on the internal forward and inverse models by measuring two kinds of behavior: generalization of training in one direction to neighboring directions (as a proxy for inverse models) and localization of the hand position after movement without visual feedback (as a proxy for forward model). The experimental results showed no effect of cerebellar tDCS on generalization, but significant effect on localization. These observations support the idea that the cerebellum is a possible brain region for internal forward, but not inverse model formation. We also used a realistic human head model to calculate current density distribution in the brain. The result of this model confirmed the passage of current through the cerebellum. Moreover, to further explain some observed experimental results, we modeled the visuomotor adaptation process with the help of a biologically inspired method known as population coding. The effect of tDCS was also incorporated in the model. The results of this modeling study closely match our experimental data and provide further evidence in line with the idea that tDCS manipulates FM's function in the cerebellum.

A musculoskeletal shoulder model based on pseudo-inverse and null-space optimization.

PubMed

Terrier, Alexandre; Aeberhard, Martin; Michellod, Yvan; Mullhaupt, Philippe; Gillet, Denis; Farron, Alain; Pioletti, Dominique P

2010-11-01

The goal of the present work was assess the feasibility of using a pseudo-inverse and null-space optimization approach in the modeling of the shoulder biomechanics. The method was applied to a simplified musculoskeletal shoulder model. The mechanical system consisted in the arm, and the external forces were the arm weight, 6 scapulo-humeral muscles and the reaction at the glenohumeral joint, which was considered as a spherical joint. The muscle wrapping was considered around the humeral head assumed spherical. The dynamical equations were solved in a Lagrangian approach. The mathematical redundancy of the mechanical system was solved in two steps: a pseudo-inverse optimization to minimize the square of the muscle stress and a null-space optimization to restrict the muscle force to physiological limits. Several movements were simulated. The mathematical and numerical aspects of the constrained redundancy problem were efficiently solved by the proposed method. The prediction of muscle moment arms was consistent with cadaveric measurements and the joint reaction force was consistent with in vivo measurements. This preliminary work demonstrated that the developed algorithm has a great potential for more complex musculoskeletal modeling of the shoulder joint. In particular it could be further applied to a non-spherical joint model, allowing for the natural translation of the humeral head in the glenoid fossa. Copyright © 2010 IPEM. Published by Elsevier Ltd. All rights reserved.

Using the ARTMO toolbox for automated retrieval of biophysical parameters through radiative transfer model inversion: Optimizing LUT-based inversion

NASA Astrophysics Data System (ADS)

Verrelst, J.; Rivera, J. P.; Leonenko, G.; Alonso, L.; Moreno, J.

2012-04-01

Radiative transfer (RT) modeling plays a key role for earth observation (EO) because it is needed to design EO instruments and to develop and test inversion algorithms. The inversion of a RT model is considered as a successful approach for the retrieval of biophysical parameters because of being physically-based and generally applicable. However, to the broader community this approach is considered as laborious because of its many processing steps and expert knowledge is required to realize precise model parameterization. We have recently developed a radiative transfer toolbox ARTMO (Automated Radiative Transfer Models Operator) with the purpose of providing in a graphical user interface (GUI) essential models and tools required for terrestrial EO applications such as model inversion. In short, the toolbox allows the user: i) to choose between various plant leaf and canopy RT models (e.g. models from the PROSPECT and SAIL family, FLIGHT), ii) to choose between spectral band settings of various air- and space-borne sensors or defining own sensor settings, iii) to simulate a massive amount of spectra based on a look up table (LUT) approach and storing it in a relational database, iv) to plot spectra of multiple models and compare them with measured spectra, and finally, v) to run model inversion against optical imagery given several cost options and accuracy estimates. In this work ARTMO was used to tackle some well-known problems related to model inversion. According to Hadamard conditions, mathematical models of physical phenomena are mathematically invertible if the solution of the inverse problem to be solved exists, is unique and depends continuously on data. This assumption is not always met because of the large number of unknowns and different strategies have been proposed to overcome this problem. Several of these strategies have been implemented in ARTMO and were here analyzed to optimize the inversion performance. Data came from the SPARC-2003 dataset

Perturbational and nonperturbational inversion of Rayleigh-wave velocities

USGS Publications Warehouse

Haney, Matt; Tsai, Victor C.

2017-01-01

The inversion of Rayleigh-wave dispersion curves is a classic geophysical inverse problem. We have developed a set of MATLAB codes that performs forward modeling and inversion of Rayleigh-wave phase or group velocity measurements. We describe two different methods of inversion: a perturbational method based on finite elements and a nonperturbational method based on the recently developed Dix-type relation for Rayleigh waves. In practice, the nonperturbational method can be used to provide a good starting model that can be iteratively improved with the perturbational method. Although the perturbational method is well-known, we solve the forward problem using an eigenvalue/eigenvector solver instead of the conventional approach of root finding. Features of the codes include the ability to handle any mix of phase or group velocity measurements, combinations of modes of any order, the presence of a surface water layer, computation of partial derivatives due to changes in material properties and layer boundaries, and the implementation of an automatic grid of layers that is optimally suited for the depth sensitivity of Rayleigh waves.

Intrinsic nonlinearity and method of disturbed observations in inverse problems of celestial mechanics

NASA Astrophysics Data System (ADS)

Avdyushev, Victor A.

2017-12-01

Orbit determination from a small sample of observations over a very short observed orbital arc is a strongly nonlinear inverse problem. In such problems an evaluation of orbital uncertainty due to random observation errors is greatly complicated, since linear estimations conventionally used are no longer acceptable for describing the uncertainty even as a rough approximation. Nevertheless, if an inverse problem is weakly intrinsically nonlinear, then one can resort to the so-called method of disturbed observations (aka observational Monte Carlo). Previously, we showed that the weaker the intrinsic nonlinearity, the more efficient the method, i.e. the more accurate it enables one to simulate stochastically the orbital uncertainty, while it is strictly exact only when the problem is intrinsically linear. However, as we ascertained experimentally, its efficiency was found to be higher than that of other stochastic methods widely applied in practice. In the present paper we investigate the intrinsic nonlinearity in complicated inverse problems of Celestial Mechanics when orbits are determined from little informative samples of observations, which typically occurs for recently discovered asteroids. To inquire into the question, we introduce an index of intrinsic nonlinearity. In asteroid problems it evinces that the intrinsic nonlinearity can be strong enough to affect appreciably probabilistic estimates, especially at the very short observed orbital arcs that the asteroids travel on for about a hundredth of their orbital periods and less. As it is known from regression analysis, the source of intrinsic nonlinearity is the nonflatness of the estimation subspace specified by a dynamical model in the observation space. Our numerical results indicate that when determining asteroid orbits it is actually very slight. However, in the parametric space the effect of intrinsic nonlinearity is exaggerated mainly by the ill-conditioning of the inverse problem. Even so, as for the

Numerical convergence and validation of the DIMP inverse particle transport model

DOE PAGES

Nelson, Noel; Azmy, Yousry

2017-09-01

The data integration with modeled predictions (DIMP) model is a promising inverse radiation transport method for solving the special nuclear material (SNM) holdup problem. Unlike previous methods, DIMP is a completely passive nondestructive assay technique that requires no initial assumptions regarding the source distribution or active measurement time. DIMP predicts the most probable source location and distribution through Bayesian inference and quasi-Newtonian optimization of predicted detector re-sponses (using the adjoint transport solution) with measured responses. DIMP performs well with for-ward hemispherical collimation and unshielded measurements, but several considerations are required when using narrow-view collimated detectors. DIMP converged well to themore » correct source distribution as the number of synthetic responses increased. DIMP also performed well for the first experimental validation exercise after applying a collimation factor, and sufficiently reducing the source search vol-ume's extent to prevent the optimizer from getting stuck in local minima. DIMP's simple point detector response function (DRF) is being improved to address coplanar false positive/negative responses, and an angular DRF is being considered for integration with the next version of DIMP to account for highly collimated responses. Overall, DIMP shows promise for solving the SNM holdup inverse problem, especially once an improved optimization algorithm is implemented.« less

Optimal Inversion Parameters for Full Waveform Inversion using OBS Data Set

NASA Astrophysics Data System (ADS)

Kim, S.; Chung, W.; Shin, S.; Kim, D.; Lee, D.

2017-12-01

In recent years, full Waveform Inversion (FWI) has been the most researched technique in seismic data processing. It uses the residuals between observed and modeled data as an objective function; thereafter, the final subsurface velocity model is generated through a series of iterations meant to minimize the residuals.Research on FWI has expanded from acoustic media to elastic media. In acoustic media, the subsurface property is defined by P-velocity; however, in elastic media, properties are defined by multiple parameters, such as P-velocity, S-velocity, and density. Further, the elastic media can also be defined by Lamé constants, density or impedance PI, SI; consequently, research is being carried out to ascertain the optimal parameters.From results of advanced exploration equipment and Ocean Bottom Seismic (OBS) survey, it is now possible to obtain multi-component seismic data. However, to perform FWI on these data and generate an accurate subsurface model, it is important to determine optimal inversion parameters among (Vp, Vs, ρ), (λ, μ, ρ), and (PI, SI) in elastic media. In this study, staggered grid finite difference method was applied to simulate OBS survey. As in inversion, l2-norm was set as objective function. Further, the accurate computation of gradient direction was performed using the back-propagation technique and its scaling was done using the Pseudo-hessian matrix.In acoustic media, only Vp is used as the inversion parameter. In contrast, various sets of parameters, such as (Vp, Vs, ρ) and (λ, μ, ρ) can be used to define inversion in elastic media. Therefore, it is important to ascertain the parameter that gives the most accurate result for inversion with OBS data set.In this study, we generated Vp and Vs subsurface models by using (λ, μ, ρ) and (Vp, Vs, ρ) as inversion parameters in every iteration, and compared the final two FWI results.This research was supported by the Basic Research Project(17-3312) of the Korea Institute of

Statistic inversion of multi-zone transition probability models for aquifer characterization in alluvial fans

DOE PAGES

Zhu, Lin; Dai, Zhenxue; Gong, Huili; ...

2015-06-12

Understanding the heterogeneity arising from the complex architecture of sedimentary sequences in alluvial fans is challenging. This study develops a statistical inverse framework in a multi-zone transition probability approach for characterizing the heterogeneity in alluvial fans. An analytical solution of the transition probability matrix is used to define the statistical relationships among different hydrofacies and their mean lengths, integral scales, and volumetric proportions. A statistical inversion is conducted to identify the multi-zone transition probability models and estimate the optimal statistical parameters using the modified Gauss–Newton–Levenberg–Marquardt method. The Jacobian matrix is computed by the sensitivity equation method, which results in anmore » accurate inverse solution with quantification of parameter uncertainty. We use the Chaobai River alluvial fan in the Beijing Plain, China, as an example for elucidating the methodology of alluvial fan characterization. The alluvial fan is divided into three sediment zones. In each zone, the explicit mathematical formulations of the transition probability models are constructed with optimized different integral scales and volumetric proportions. The hydrofacies distributions in the three zones are simulated sequentially by the multi-zone transition probability-based indicator simulations. Finally, the result of this study provides the heterogeneous structure of the alluvial fan for further study of flow and transport simulations.« less

Probing numerical Laplace inversion methods for two and three-site molecular exchange between interconnected pore structures.

PubMed

Silletta, Emilia V; Franzoni, María B; Monti, Gustavo A; Acosta, Rodolfo H

2018-01-01

Two-dimension (2D) Nuclear Magnetic Resonance relaxometry experiments are a powerful tool extensively used to probe the interaction among different pore structures, mostly in inorganic systems. The analysis of the collected experimental data generally consists of a 2D numerical inversion of time-domain data where T 2 -T 2 maps are generated. Through the years, different algorithms for the numerical inversion have been proposed. In this paper, two different algorithms for numerical inversion are tested and compared under different conditions of exchange dynamics; the method based on Butler-Reeds-Dawson (BRD) algorithm and the fast-iterative shrinkage-thresholding algorithm (FISTA) method. By constructing a theoretical model, the algorithms were tested for a two- and three-site porous media, varying the exchange rates parameters, the pore sizes and the signal to noise ratio. In order to test the methods under realistic experimental conditions, a challenging organic system was chosen. The molecular exchange rates of water confined in hierarchical porous polymeric networks were obtained, for a two- and three-site porous media. Data processed with the BRD method was found to be accurate only under certain conditions of the exchange parameters, while data processed with the FISTA method is precise for all the studied parameters, except when SNR conditions are extreme. Copyright © 2017 Elsevier Inc. All rights reserved.

Inverse modeling with RZWQM2 to predict water quality

USDA-ARS?s Scientific Manuscript database

Agricultural systems models such as RZWQM2 are complex and have numerous parameters that are unknown and difficult to estimate. Inverse modeling provides an objective statistical basis for calibration that involves simultaneous adjustment of model parameters and yields parameter confidence intervals...

Neuronal couplings between retinal ganglion cells inferred by efficient inverse statistical physics methods

PubMed Central

Cocco, Simona; Leibler, Stanislas; Monasson, Rémi

2009-01-01

Complexity of neural systems often makes impracticable explicit measurements of all interactions between their constituents. Inverse statistical physics approaches, which infer effective couplings between neurons from their spiking activity, have been so far hindered by their computational complexity. Here, we present 2 complementary, computationally efficient inverse algorithms based on the Ising and “leaky integrate-and-fire” models. We apply those algorithms to reanalyze multielectrode recordings in the salamander retina in darkness and under random visual stimulus. We find strong positive couplings between nearby ganglion cells common to both stimuli, whereas long-range couplings appear under random stimulus only. The uncertainty on the inferred couplings due to limitations in the recordings (duration, small area covered on the retina) is discussed. Our methods will allow real-time evaluation of couplings for large assemblies of neurons. PMID:19666487

Adaptive multi-step Full Waveform Inversion based on Waveform Mode Decomposition

NASA Astrophysics Data System (ADS)

Hu, Yong; Han, Liguo; Xu, Zhuo; Zhang, Fengjiao; Zeng, Jingwen

2017-04-01

Full Waveform Inversion (FWI) can be used to build high resolution velocity models, but there are still many challenges in seismic field data processing. The most difficult problem is about how to recover long-wavelength components of subsurface velocity models when seismic data is lacking of low frequency information and without long-offsets. To solve this problem, we propose to use Waveform Mode Decomposition (WMD) method to reconstruct low frequency information for FWI to obtain a smooth model, so that the initial model dependence of FWI can be reduced. In this paper, we use adjoint-state method to calculate the gradient for Waveform Mode Decomposition Full Waveform Inversion (WMDFWI). Through the illustrative numerical examples, we proved that the low frequency which is reconstructed by WMD method is very reliable. WMDFWI in combination with the adaptive multi-step inversion strategy can obtain more faithful and accurate final inversion results. Numerical examples show that even if the initial velocity model is far from the true model and lacking of low frequency information, we still can obtain good inversion results with WMD method. From numerical examples of anti-noise test, we see that the adaptive multi-step inversion strategy for WMDFWI has strong ability to resist Gaussian noise. WMD method is promising to be able to implement for the land seismic FWI, because it can reconstruct the low frequency information, lower the dominant frequency in the adjoint source, and has a strong ability to resist noise.

Stochastic reduced order models for inverse problems under uncertainty

PubMed Central

Warner, James E.; Aquino, Wilkins; Grigoriu, Mircea D.

2014-01-01

This work presents a novel methodology for solving inverse problems under uncertainty using stochastic reduced order models (SROMs). Given statistical information about an observed state variable in a system, unknown parameters are estimated probabilistically through the solution of a model-constrained, stochastic optimization problem. The point of departure and crux of the proposed framework is the representation of a random quantity using a SROM - a low dimensional, discrete approximation to a continuous random element that permits e cient and non-intrusive stochastic computations. Characterizing the uncertainties with SROMs transforms the stochastic optimization problem into a deterministic one. The non-intrusive nature of SROMs facilitates e cient gradient computations for random vector unknowns and relies entirely on calls to existing deterministic solvers. Furthermore, the method is naturally extended to handle multiple sources of uncertainty in cases where state variable data, system parameters, and boundary conditions are all considered random. The new and widely-applicable SROM framework is formulated for a general stochastic optimization problem in terms of an abstract objective function and constraining model. For demonstration purposes, however, we study its performance in the specific case of inverse identification of random material parameters in elastodynamics. We demonstrate the ability to efficiently recover random shear moduli given material displacement statistics as input data. We also show that the approach remains effective for the case where the loading in the problem is random as well. PMID:25558115

The Focused Inverse Method for Linear Logic

DTIC Science & Technology

2006-12-04

design and engineering. Furthermore, it is a denouncement of the versatility of the inverse method if one were simply to abandon it for a radically...is technically unavoidable, but the impetus of design for such provers should be to reduce the size of the database. Our answer is to combine the...or “infinitely often P”. Systems such as Lamport’s TLA are not designed with automation as their primary aim; rather, they are intended to engage

Whole head quantitative susceptibility mapping using a least-norm direct dipole inversion method.

PubMed

Sun, Hongfu; Ma, Yuhan; MacDonald, M Ethan; Pike, G Bruce

2018-06-15

A new dipole field inversion method for whole head quantitative susceptibility mapping (QSM) is proposed. Instead of performing background field removal and local field inversion sequentially, the proposed method performs dipole field inversion directly on the total field map in a single step. To aid this under-determined and ill-posed inversion process and obtain robust QSM images, Tikhonov regularization is implemented to seek the local susceptibility solution with the least-norm (LN) using the L-curve criterion. The proposed LN-QSM does not require brain edge erosion, thereby preserving the cerebral cortex in the final images. This should improve its applicability for QSM-based cortical grey matter measurement, functional imaging and venography of full brain. Furthermore, LN-QSM also enables susceptibility mapping of the entire head without the need for brain extraction, which makes QSM reconstruction more automated and less dependent on intermediate pre-processing methods and their associated parameters. It is shown that the proposed LN-QSM method reduced errors in a numerical phantom simulation, improved accuracy in a gadolinium phantom experiment, and suppressed artefacts in nine subjects, as compared to two-step and other single-step QSM methods. Measurements of deep grey matter and skull susceptibilities from LN-QSM are consistent with established reconstruction methods. Copyright © 2018 Elsevier Inc. All rights reserved.

Visco-acoustic wave-equation traveltime inversion and its sensitivity to attenuation errors

NASA Astrophysics Data System (ADS)

Yu, Han; Chen, Yuqing; Hanafy, Sherif M.; Huang, Jiangping

2018-04-01

A visco-acoustic wave-equation traveltime inversion method is presented that inverts for the shallow subsurface velocity distribution. Similar to the classical wave equation traveltime inversion, this method finds the velocity model that minimizes the squared sum of the traveltime residuals. Even though, wave-equation traveltime inversion can partly avoid the cycle skipping problem, a good initial velocity model is required for the inversion to converge to a reasonable tomogram with different attenuation profiles. When Q model is far away from the real model, the final tomogram is very sensitive to the starting velocity model. Nevertheless, a minor or moderate perturbation of the Q model from the true one does not strongly affect the inversion if the low wavenumber information of the initial velocity model is mostly correct. These claims are validated with numerical tests on both the synthetic and field data sets.

Inversion group (IG) fitting: A new T1 mapping method for modified look-locker inversion recovery (MOLLI) that allows arbitrary inversion groupings and rest periods (including no rest period).

PubMed

Sussman, Marshall S; Yang, Issac Y; Fok, Kai-Ho; Wintersperger, Bernd J

2016-06-01

The Modified Look-Locker Inversion Recovery (MOLLI) technique is used for T1 mapping in the heart. However, a drawback of this technique is that it requires lengthy rest periods in between inversion groupings to allow for complete magnetization recovery. In this work, a new MOLLI fitting algorithm (inversion group [IG] fitting) is presented that allows for arbitrary combinations of inversion groupings and rest periods (including no rest period). Conventional MOLLI algorithms use a three parameter fitting model. In IG fitting, the number of parameters is two plus the number of inversion groupings. This increased number of parameters permits any inversion grouping/rest period combination. Validation was performed through simulation, phantom, and in vivo experiments. IG fitting provided T1 values with less than 1% discrepancy across a range of inversion grouping/rest period combinations. By comparison, conventional three parameter fits exhibited up to 30% discrepancy for some combinations. The one drawback with IG fitting was a loss of precision-approximately 30% worse than the three parameter fits. IG fitting permits arbitrary inversion grouping/rest period combinations (including no rest period). The cost of the algorithm is a loss of precision relative to conventional three parameter fits. Magn Reson Med 75:2332-2340, 2016. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.

Approximation Methods for Inverse Problems Governed by Nonlinear Parabolic Systems

DTIC Science & Technology

1999-12-17

We present a rigorous theoretical framework for approximation of nonlinear parabolic systems with delays in the context of inverse least squares...numerical results demonstrating the convergence are given for a model of dioxin uptake and elimination in a distributed liver model that is a special case of the general theoretical framework .

Local constitutive behavior of paper determined by an inverse method

Treesearch

John M. Considine; C. Tim Scott; Roland Gleisner; Junyong Zhu

2006-01-01

The macroscopic behavior of paper is governed by small-scale behavior. Intuitively, we know that a small-scale defect with a paper sheet effectively determines the global behavior of the sheet. In this work, we describe a method to evaluate the local constitutive behavior of paper by using an inverse method.

Stochastic inversion of ocean color data using the cross-entropy method.

PubMed

Salama, Mhd Suhyb; Shen, Fang

2010-01-18

Improving the inversion of ocean color data is an ever continuing effort to increase the accuracy of derived inherent optical properties. In this paper we present a stochastic inversion algorithm to derive inherent optical properties from ocean color, ship and space borne data. The inversion algorithm is based on the cross-entropy method where sets of inherent optical properties are generated and converged to the optimal set using iterative process. The algorithm is validated against four data sets: simulated, noisy simulated in-situ measured and satellite match-up data sets. Statistical analysis of validation results is based on model-II regression using five goodness-of-fit indicators; only R2 and root mean square of error (RMSE) are mentioned hereafter. Accurate values of total absorption coefficient are derived with R2 > 0.91 and RMSE, of log transformed data, less than 0.55. Reliable values of the total backscattering coefficient are also obtained with R2 > 0.7 (after removing outliers) and RMSE < 0.37. The developed algorithm has the ability to derive reliable results from noisy data with R2 above 0.96 for the total absorption and above 0.84 for the backscattering coefficients. The algorithm is self contained and easy to implement and modify to derive the variability of chlorophyll-a absorption that may correspond to different phytoplankton species. It gives consistently accurate results and is therefore worth considering for ocean color global products.

A Parameterized Inversion Model for Soil Moisture and Biomass from Polarimetric Backscattering Coefficients

NASA Technical Reports Server (NTRS)

Truong-Loi, My-Linh; Saatchi, Sassan; Jaruwatanadilok, Sermsak

2012-01-01

A semi-empirical algorithm for the retrieval of soil moisture, root mean square (RMS) height and biomass from polarimetric SAR data is explained and analyzed in this paper. The algorithm is a simplification of the distorted Born model. It takes into account the physical scattering phenomenon and has three major components: volume, double-bounce and surface. This simplified model uses the three backscattering coefficients ( sigma HH, sigma HV and sigma vv) at low-frequency (P-band). The inversion process uses the Levenberg-Marquardt non-linear least-squares method to estimate the structural parameters. The estimation process is entirely explained in this paper, from initialization of the unknowns to retrievals. A sensitivity analysis is also done where the initial values in the inversion process are varying randomly. The results show that the inversion process is not really sensitive to initial values and a major part of the retrievals has a root-mean-square error lower than 5% for soil moisture, 24 Mg/ha for biomass and 0.49 cm for roughness, considering a soil moisture of 40%, roughness equal to 3cm and biomass varying from 0 to 500 Mg/ha with a mean of 161 Mg/ha

A three-step Maximum-A-Posterior probability method for InSAR data inversion of coseismic rupture with application to four recent large earthquakes in Asia

NASA Astrophysics Data System (ADS)

Sun, J.; Shen, Z.; Burgmann, R.; Liang, F.

2012-12-01

We develop a three-step Maximum-A-Posterior probability (MAP) method for coseismic rupture inversion, which aims at maximizing the a posterior probability density function (PDF) of elastic solutions of earthquake rupture. The method originates from the Fully Bayesian Inversion (FBI) and the Mixed linear-nonlinear Bayesian inversion (MBI) methods , shares the same a posterior PDF with them and keeps most of their merits, while overcoming its convergence difficulty when large numbers of low quality data are used and improving the convergence rate greatly using optimization procedures. A highly efficient global optimization algorithm, Adaptive Simulated Annealing (ASA), is used to search for the maximum posterior probability in the first step. The non-slip parameters are determined by the global optimization method, and the slip parameters are inverted for using the least squares method without positivity constraint initially, and then damped to physically reasonable range. This step MAP inversion brings the inversion close to 'true' solution quickly and jumps over local maximum regions in high-dimensional parameter space. The second step inversion approaches the 'true' solution further with positivity constraints subsequently applied on slip parameters using the Monte Carlo Inversion (MCI) technique, with all parameters obtained from step one as the initial solution. Then the slip artifacts are eliminated from slip models in the third step MAP inversion with fault geometry parameters fixed. We first used a designed model with 45 degree dipping angle and oblique slip, and corresponding synthetic InSAR data sets to validate the efficiency and accuracy of method. We then applied the method on four recent large earthquakes in Asia, namely the 2010 Yushu, China earthquake, the 2011 Burma earthquake, the 2011 New Zealand earthquake and the 2008 Qinghai, China earthquake, and compared our results with those results from other groups. Our results show the effectiveness of

Exploring the Subtleties of Inverse Probability Weighting and Marginal Structural Models.

PubMed

Breskin, Alexander; Cole, Stephen R; Westreich, Daniel

2018-05-01

Since being introduced to epidemiology in 2000, marginal structural models have become a commonly used method for causal inference in a wide range of epidemiologic settings. In this brief report, we aim to explore three subtleties of marginal structural models. First, we distinguish marginal structural models from the inverse probability weighting estimator, and we emphasize that marginal structural models are not only for longitudinal exposures. Second, we explore the meaning of the word "marginal" in "marginal structural model." Finally, we show that the specification of a marginal structural model can have important implications for the interpretation of its parameters. Each of these concepts have important implications for the use and understanding of marginal structural models, and thus providing detailed explanations of them may lead to better practices for the field of epidemiology.

Forward modeling and inversion of tensor CSAMT in 3D anisotropic media

NASA Astrophysics Data System (ADS)

Wang, Tao; Wang, Kun-Peng; Tan, Han-Dong

2017-12-01

Tensor controlled-source audio-frequency magnetotellurics (CSAMT) can yield information about electric and magnetic fields owing to its multi-transmitter configuration compared with the common scalar CSAMT. The most current theories, numerical simulations, and inversion of tensor CSAMT are based on far-field measurements and the assumption that underground media have isotropic resistivity. We adopt a three-dimensional (3D) staggered-grid finite difference numerical simulation method to analyze the resistivity in axial anisotropic and isotropic media. We further adopt the limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) method to perform 3D tensor CSAMT axial anisotropic inversion. The inversion results suggest that when the underground structure is anisotropic, the isotropic inversion will introduce errors to the interpretation.

Bayesian Inference in Satellite Gravity Inversion

NASA Technical Reports Server (NTRS)

Kis, K. I.; Taylor, Patrick T.; Wittmann, G.; Kim, Hyung Rae; Torony, B.; Mayer-Guerr, T.

2005-01-01

To solve a geophysical inverse problem means applying measurements to determine the parameters of the selected model. The inverse problem is formulated as the Bayesian inference. The Gaussian probability density functions are applied in the Bayes's equation. The CHAMP satellite gravity data are determined at the altitude of 400 kilometer altitude over the South part of the Pannonian basin. The model of interpretation is the right vertical cylinder. The parameters of the model are obtained from the minimum problem solved by the Simplex method.

Model selection and Bayesian inference for high-resolution seabed reflection inversion.

PubMed

Dettmer, Jan; Dosso, Stan E; Holland, Charles W

2009-02-01

This paper applies Bayesian inference, including model selection and posterior parameter inference, to inversion of seabed reflection data to resolve sediment structure at a spatial scale below the pulse length of the acoustic source. A practical approach to model selection is used, employing the Bayesian information criterion to decide on the number of sediment layers needed to sufficiently fit the data while satisfying parsimony to avoid overparametrization. Posterior parameter inference is carried out using an efficient Metropolis-Hastings algorithm for high-dimensional models, and results are presented as marginal-probability depth distributions for sound velocity, density, and attenuation. The approach is applied to plane-wave reflection-coefficient inversion of single-bounce data collected on the Malta Plateau, Mediterranean Sea, which indicate complex fine structure close to the water-sediment interface. This fine structure is resolved in the geoacoustic inversion results in terms of four layers within the upper meter of sediments. The inversion results are in good agreement with parameter estimates from a gravity core taken at the experiment site.

Efficient calculation of full waveform time domain inversion for electromagnetic problem using fictitious wave domain method and cascade decimation decomposition

NASA Astrophysics Data System (ADS)

Imamura, N.; Schultz, A.

2016-12-01

Recently, a full waveform time domain inverse solution has been developed for the magnetotelluric (MT) and controlled-source electromagnetic (CSEM) methods. The ultimate goal of this approach is to obtain a computationally tractable direct waveform joint inversion to solve simultaneously for source fields and earth conductivity structure in three and four dimensions. This is desirable on several grounds, including the improved spatial resolving power expected from use of a multitude of source illuminations, the ability to operate in areas of high levels of source signal spatial complexity, and non-stationarity. This goal would not be obtainable if one were to adopt the pure time domain solution for the inverse problem. This is particularly true for the case of MT surveys, since an enormous number of degrees of freedom are required to represent the observed MT waveforms across a large frequency bandwidth. This means that for the forward simulation, the smallest time steps should be finer than that required to represent the highest frequency, while the number of time steps should also cover the lowest frequency. This leads to a sensitivity matrix that is computationally burdensome to solve a model update. We have implemented a code that addresses this situation through the use of cascade decimation decomposition to reduce the size of the sensitivity matrix substantially, through quasi-equivalent time domain decomposition. We also use a fictitious wave domain method to speed up computation time of the forward simulation in the time domain. By combining these refinements, we have developed a full waveform joint source field/earth conductivity inverse modeling method. We found that cascade decimation speeds computations of the sensitivity matrices dramatically, keeping the solution close to that of the undecimated case. For example, for a model discretized into 2.6x105 cells, we obtain model updates in less than 1 hour on a 4U rack-mounted workgroup Linux server, which

Application of Adjoint Method and Spectral-Element Method to Tomographic Inversion of Regional Seismological Structure Beneath Japanese Islands

NASA Astrophysics Data System (ADS)

Tsuboi, S.; Miyoshi, T.; Obayashi, M.; Tono, Y.; Ando, K.

2014-12-01

Recent progress in large scale computing by using waveform modeling technique and high performance computing facility has demonstrated possibilities to perform full-waveform inversion of three dimensional (3D) seismological structure inside the Earth. We apply the adjoint method (Liu and Tromp, 2006) to obtain 3D structure beneath Japanese Islands. First we implemented Spectral-Element Method to K-computer in Kobe, Japan. We have optimized SPECFEM3D_GLOBE (Komatitsch and Tromp, 2002) by using OpenMP so that the code fits hybrid architecture of K-computer. Now we could use 82,134 nodes of K-computer (657,072 cores) to compute synthetic waveform with about 1 sec accuracy for realistic 3D Earth model and its performance was 1.2 PFLOPS. We use this optimized SPECFEM3D_GLOBE code and take one chunk around Japanese Islands from global mesh and compute synthetic seismograms with accuracy of about 10 second. We use GAP-P2 mantle tomography model (Obayashi et al., 2009) as an initial 3D model and use as many broadband seismic stations available in this region as possible to perform inversion. We then use the time windows for body waves and surface waves to compute adjoint sources and calculate adjoint kernels for seismic structure. We have performed several iteration and obtained improved 3D structure beneath Japanese Islands. The result demonstrates that waveform misfits between observed and theoretical seismograms improves as the iteration proceeds. We now prepare to use much shorter period in our synthetic waveform computation and try to obtain seismic structure for basin scale model, such as Kanto basin, where there are dense seismic network and high seismic activity. Acknowledgements: This research was partly supported by MEXT Strategic Program for Innovative Research. We used F-net seismograms of the National Research Institute for Earth Science and Disaster Prevention.

Restoring Behavior via Inverse Neurocontroller in a Lesioned Cortical Spiking Model Driving a Virtual Arm

PubMed Central

Dura-Bernal, Salvador; Li, Kan; Neymotin, Samuel A.; Francis, Joseph T.; Principe, Jose C.; Lytton, William W.

2016-01-01

Neural stimulation can be used as a tool to elicit natural sensations or behaviors by modulating neural activity. This can be potentially used to mitigate the damage of brain lesions or neural disorders. However, in order to obtain the optimal stimulation sequences, it is necessary to develop neural control methods, for example by constructing an inverse model of the target system. For real brains, this can be very challenging, and often unfeasible, as it requires repeatedly stimulating the neural system to obtain enough probing data, and depends on an unwarranted assumption of stationarity. By contrast, detailed brain simulations may provide an alternative testbed for understanding the interactions between ongoing neural activity and external stimulation. Unlike real brains, the artificial system can be probed extensively and precisely, and detailed output information is readily available. Here we employed a spiking network model of sensorimotor cortex trained to drive a realistic virtual musculoskeletal arm to reach a target. The network was then perturbed, in order to simulate a lesion, by either silencing neurons or removing synaptic connections. All lesions led to significant behvaioral impairments during the reaching task. The remaining cells were then systematically probed with a set of single and multiple-cell stimulations, and results were used to build an inverse model of the neural system. The inverse model was constructed using a kernel adaptive filtering method, and was used to predict the neural stimulation pattern required to recover the pre-lesion neural activity. Applying the derived neurostimulation to the lesioned network improved the reaching behavior performance. This work proposes a novel neurocontrol method, and provides theoretical groundwork on the use biomimetic brain models to develop and evaluate neurocontrollers that restore the function of damaged brain regions and the corresponding motor behaviors. PMID:26903796

Bayesian inversion using a geologically realistic and discrete model space

NASA Astrophysics Data System (ADS)

Jaeggli, C.; Julien, S.; Renard, P.

2017-12-01

Since the early days of groundwater modeling, inverse methods play a crucial role. Many research and engineering groups aim to infer extensive knowledge of aquifer parameters from a sparse set of observations. Despite decades of dedicated research on this topic, there are still several major issues to be solved. In the hydrogeological framework, one is often confronted with underground structures that present very sharp contrasts of geophysical properties. In particular, subsoil structures such as karst conduits, channels, faults, or lenses, strongly influence groundwater flow and transport behavior of the underground. For this reason it can be essential to identify their location and shape very precisely. Unfortunately, when inverse methods are specially trained to consider such complex features, their computation effort often becomes unaffordably high. The following work is an attempt to solve this dilemma. We present a new method that is, in some sense, a compromise between the ergodicity of Markov chain Monte Carlo (McMC) methods and the efficient handling of data by the ensemble based Kalmann filters. The realistic and complex random fields are generated by a Multiple-Point Statistics (MPS) tool. Nonetheless, it is applicable with any conditional geostatistical simulation tool. Furthermore, the algorithm is independent of any parametrization what becomes most important when two parametric systems are equivalent (permeability and resistivity, speed and slowness, etc.). When compared to two existing McMC schemes, the computational effort was divided by a factor of 12.

Understanding the Yellowstone magmatic system using 3D geodynamic inverse models

NASA Astrophysics Data System (ADS)

Kaus, B. J. P.; Reuber, G. S.; Popov, A.; Baumann, T.

2017-12-01

The Yellowstone magmatic system is one of the largest magmatic systems on Earth. Recent seismic tomography suggest that two distinct magma chambers exist: a shallow, presumably felsic chamber and a deeper much larger, partially molten, chamber above the Moho. Why melt stalls at different depth levels above the Yellowstone plume, whereas dikes cross-cut the whole lithosphere in the nearby Snake River Plane is unclear. Partly this is caused by our incomplete understanding of lithospheric scale melt ascent processes from the upper mantle to the shallow crust, which requires better constraints on the mechanics and material properties of the lithosphere.Here, we employ lithospheric-scale 2D and 3D geodynamic models adapted to Yellowstone to better understand magmatic processes in active arcs. The models have a number of (uncertain) input parameters such as the temperature and viscosity structure of the lithosphere, geometry and melt fraction of the magmatic system, while the melt content and rock densities are obtained by consistent thermodynamic modelling of whole rock data of the Yellowstone stratigraphy. As all of these parameters affect the dynamics of the lithosphere, we use the simulations to derive testable model predictions such as gravity anomalies, surface deformation rates and lithospheric stresses and compare them with observations. We incorporated it within an inversion method and perform 3D geodynamic inverse models of the Yellowstone magmatic system. An adjoint based method is used to derive the key model parameters and the factors that affect the stress field around the Yellowstone plume, locations of enhanced diking and melt accumulations. Results suggest that the plume and the magma chambers are connected with each other and that magma chamber overpressure is required to explain the surface displacement in phases of high activity above the Yellowstone magmatic system.

Parameter optimisation for a better representation of drought by LSMs: inverse modelling vs. sequential data assimilation

NASA Astrophysics Data System (ADS)

Dewaele, Hélène; Munier, Simon; Albergel, Clément; Planque, Carole; Laanaia, Nabil; Carrer, Dominique; Calvet, Jean-Christophe

2017-09-01

Soil maximum available water content (MaxAWC) is a key parameter in land surface models (LSMs). However, being difficult to measure, this parameter is usually uncertain. This study assesses the feasibility of using a 15-year (1999-2013) time series of satellite-derived low-resolution observations of leaf area index (LAI) to estimate MaxAWC for rainfed croplands over France. LAI interannual variability is simulated using the CO2-responsive version of the Interactions between Soil, Biosphere and Atmosphere (ISBA) LSM for various values of MaxAWC. Optimal value is then selected by using (1) a simple inverse modelling technique, comparing simulated and observed LAI and (2) a more complex method consisting in integrating observed LAI in ISBA through a land data assimilation system (LDAS) and minimising LAI analysis increments. The evaluation of the MaxAWC estimates from both methods is done using simulated annual maximum above-ground biomass (Bag) and straw cereal grain yield (GY) values from the Agreste French agricultural statistics portal, for 45 administrative units presenting a high proportion of straw cereals. Significant correlations (p value < 0.01) between Bag and GY are found for up to 36 and 53 % of the administrative units for the inverse modelling and LDAS tuning methods, respectively. It is found that the LDAS tuning experiment gives more realistic values of MaxAWC and maximum Bag than the inverse modelling experiment. Using undisaggregated LAI observations leads to an underestimation of MaxAWC and maximum Bag in both experiments. Median annual maximum values of disaggregated LAI observations are found to correlate very well with MaxAWC.

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.

A unified inversion scheme to process multifrequency measurements of various dispersive electromagnetic properties

NASA Astrophysics Data System (ADS)

Han, Y.; Misra, S.

2018-04-01

Multi-frequency measurement of a dispersive electromagnetic (EM) property, such as electrical conductivity, dielectric permittivity, or magnetic permeability, is commonly analyzed for purposes of material characterization. Such an analysis requires inversion of the multi-frequency measurement based on a specific relaxation model, such as Cole-Cole model or Pelton's model. We develop a unified inversion scheme that can be coupled to various type of relaxation models to independently process multi-frequency measurement of varied EM properties for purposes of improved EM-based geomaterial characterization. The proposed inversion scheme is firstly tested in few synthetic cases in which different relaxation models are coupled into the inversion scheme and then applied to multi-frequency complex conductivity, complex resistivity, complex permittivity, and complex impedance measurements. The method estimates up to seven relaxation-model parameters exhibiting convergence and accuracy for random initializations of the relaxation-model parameters within up to 3-orders of magnitude variation around the true parameter values. The proposed inversion method implements a bounded Levenberg algorithm with tuning initial values of damping parameter and its iterative adjustment factor, which are fixed in all the cases shown in this paper and irrespective of the type of measured EM property and the type of relaxation model. Notably, jump-out step and jump-back-in step are implemented as automated methods in the inversion scheme to prevent the inversion from getting trapped around local minima and to honor physical bounds of model parameters. The proposed inversion scheme can be easily used to process various types of EM measurements without major changes to the inversion scheme.

Emulation: A fast stochastic Bayesian method to eliminate model space

NASA Astrophysics Data System (ADS)

Roberts, Alan; Hobbs, Richard; Goldstein, Michael

2010-05-01

Joint inversion of large 3D datasets has been the goal of geophysicists ever since the datasets first started to be produced. There are two broad approaches to this kind of problem, traditional deterministic inversion schemes and more recently developed Bayesian search methods, such as MCMC (Markov Chain Monte Carlo). However, using both these kinds of schemes has proved prohibitively expensive, both in computing power and time cost, due to the normally very large model space which needs to be searched using forward model simulators which take considerable time to run. At the heart of strategies aimed at accomplishing this kind of inversion is the question of how to reliably and practicably reduce the size of the model space in which the inversion is to be carried out. Here we present a practical Bayesian method, known as emulation, which can address this issue. Emulation is a Bayesian technique used with considerable success in a number of technical fields, such as in astronomy, where the evolution of the universe has been modelled using this technique, and in the petroleum industry where history matching is carried out of hydrocarbon reservoirs. The method of emulation involves building a fast-to-compute uncertainty-calibrated approximation to a forward model simulator. We do this by modelling the output data from a number of forward simulator runs by a computationally cheap function, and then fitting the coefficients defining this function to the model parameters. By calibrating the error of the emulator output with respect to the full simulator output, we can use this to screen out large areas of model space which contain only implausible models. For example, starting with what may be considered a geologically reasonable prior model space of 10000 models, using the emulator we can quickly show that only models which lie within 10% of that model space actually produce output data which is plausibly similar in character to an observed dataset. We can thus much

Indium oxide inverse opal films synthesized by structure replication method

NASA Astrophysics Data System (ADS)

Amrehn, Sabrina; Berghoff, Daniel; Nikitin, Andreas; Reichelt, Matthias; Wu, Xia; Meier, Torsten; Wagner, Thorsten

2016-04-01

We present the synthesis of indium oxide (In2O3) inverse opal films with photonic stop bands in the visible range by a structure replication method. Artificial opal films made of poly(methyl methacrylate) (PMMA) spheres are utilized as template. The opal films are deposited via sedimentation facilitated by ultrasonication, and then impregnated by indium nitrate solution, which is thermally converted to In2O3 after drying. The quality of the resulting inverse opal film depends on many parameters; in this study the water content of the indium nitrate/PMMA composite after drying is investigated. Comparison of the reflectance spectra recorded by vis-spectroscopy with simulated data shows a good agreement between the peak position and calculated stop band positions for the inverse opals. This synthesis is less complex and highly efficient compared to most other techniques and is suitable for use in many applications.

Inverse geothermal modelling applied to Danish sedimentary basins

NASA Astrophysics Data System (ADS)

Poulsen, Søren E.; Balling, Niels; Bording, Thue S.; Mathiesen, Anders; Nielsen, Søren B.

2017-10-01

This paper presents a numerical procedure for predicting subsurface temperatures and heat-flow distribution in 3-D using inverse calibration methodology. The procedure is based on a modified version of the groundwater code MODFLOW by taking advantage of the mathematical similarity between confined groundwater flow (Darcy's law) and heat conduction (Fourier's law). Thermal conductivity, heat production and exponential porosity-depth relations are specified separately for the individual geological units of the model domain. The steady-state temperature model includes a model-based transient correction for the long-term palaeoclimatic thermal disturbance of the subsurface temperature regime. Variable model parameters are estimated by inversion of measured borehole temperatures with uncertainties reflecting their quality. The procedure facilitates uncertainty estimation for temperature predictions. The modelling procedure is applied to Danish onshore areas containing deep sedimentary basins. A 3-D voxel-based model, with 14 lithological units from surface to 5000 m depth, was built from digital geological maps derived from combined analyses of reflection seismic lines and borehole information. Matrix thermal conductivity of model lithologies was estimated by inversion of all available deep borehole temperature data and applied together with prescribed background heat flow to derive the 3-D subsurface temperature distribution. Modelled temperatures are found to agree very well with observations. The numerical model was utilized for predicting and contouring temperatures at 2000 and 3000 m depths and for two main geothermal reservoir units, the Gassum (Lower Jurassic-Upper Triassic) and Bunter/Skagerrak (Triassic) reservoirs, both currently utilized for geothermal energy production. Temperature gradients to depths of 2000-3000 m are generally around 25-30 °C km-1, locally up to about 35 °C km-1. Large regions have geothermal reservoirs with characteristic temperatures

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).

Applications of He's semi-inverse method, ITEM and GGM to the Davey-Stewartson equation

NASA Astrophysics Data System (ADS)

Zinati, Reza Farshbaf; Manafian, Jalil

2017-04-01

We investigate the Davey-Stewartson (DS) equation. Travelling wave solutions were found. In this paper, we demonstrate the effectiveness of the analytical methods, namely, He's semi-inverse variational principle method (SIVPM), the improved tan(φ/2)-expansion method (ITEM) and generalized G'/G-expansion method (GGM) for seeking more exact solutions via the DS equation. These methods are direct, concise and simple to implement compared to other existing methods. The exact solutions containing four types solutions have been achieved. The results demonstrate that the aforementioned methods are more efficient than the Ansatz method applied by Mirzazadeh (2015). Abundant exact travelling wave solutions including solitons, kink, periodic and rational solutions have been found by the improved tan(φ/2)-expansion and generalized G'/G-expansion methods. By He's semi-inverse variational principle we have obtained dark and bright soliton wave solutions. Also, the obtained semi-inverse variational principle has profound implications in physical understandings. These solutions might play important role in engineering and physics fields. Moreover, by using Matlab, some graphical simulations were done to see the behavior of these solutions.

Performance of some numerical Laplace inversion methods on American put option formula

NASA Astrophysics Data System (ADS)

Octaviano, I.; Yuniar, A. R.; Anisa, L.; Surjanto, S. D.; Putri, E. R. M.

2018-03-01

Numerical inversion approaches of Laplace transform is used to obtain a semianalytic solution. Some of the mathematical inversion methods such as Durbin-Crump, Widder, and Papoulis can be used to calculate American put options through the optimal exercise price in the Laplace space. The comparison of methods on some simple functions is aimed to know the accuracy and parameters which used in the calculation of American put options. The result obtained is the performance of each method regarding accuracy and computational speed. The Durbin-Crump method has an average error relative of 2.006e-004 with computational speed of 0.04871 seconds, the Widder method has an average error relative of 0.0048 with computational speed of 3.100181 seconds, and the Papoulis method has an average error relative of 9.8558e-004 with computational speed of 0.020793 seconds.

Inverse gravity modeling for depth varying density structures through genetic algorithm, triangulated facet representation, and switching routines

NASA Astrophysics Data System (ADS)

King, Thomas Steven

A hybrid gravity modeling method is developed to investigate the structure of sedimentary mass bodies. The method incorporates as constraints surficial basement/sediment contacts and topography of a mass target with a quadratically varying density distribution. The inverse modeling utilizes a genetic algorithm (GA) to scan a wide range of the solution space to determine initial models and the Marquardt-Levenberg (ML) nonlinear inversion to determine final models that meet pre-assigned misfit criteria, thus providing an estimate of model variability and uncertainty. The surface modeling technique modifies Delaunay triangulation by allowing individual facets to be manually constructed and non-convex boundaries to be incorporated into the triangulation scheme. The sedimentary body is represented by a set of uneven prisms and edge elements, comprised of tetrahedrons, capped by polyhedrons. Each underlying prism and edge element's top surface is located by determining its point of tangency with the overlying terrain. The remaining overlying mass is gravitationally evaluated and subtracted from the observation points. Inversion then proceeds in the usual sense, but on an irregular tiered surface with each element's density defined relative to their top surface. Efficiency is particularly important due to the large number of facets evaluated for surface representations and the many repeated element evaluations of the stochastic GA. The gravitation of prisms, triangular faceted polygons, and tetrahedrons can be formulated in different ways, either mathematically or by physical approximations, each having distinct characteristics, such as evaluation time, accuracy over various spatial ranges, and computational singularities. A decision tree or switching routine is constructed for each element by combining these characteristics into a single cohesive package that optimizes the computation for accuracy and speed while avoiding singularities. The GA incorporates a subspace

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.

Spectral reflectance inversion with high accuracy on green target

NASA Astrophysics Data System (ADS)

Jiang, Le; Yuan, Jinping; Li, Yong; Bai, Tingzhu; Liu, Shuoqiong; Jin, Jianzhou; Shen, Jiyun

2016-09-01

Using Landsat-7 ETM remote sensing data, the inversion of spectral reflectance of green wheat in visible and near infrared waveband in Yingke, China is studied. In order to solve the problem of lower inversion accuracy, custom atmospheric conditions method based on moderate resolution transmission model (MODTRAN) is put forward. Real atmospheric parameters are considered when adopting this method. The atmospheric radiative transfer theory to calculate atmospheric parameters is introduced first and then the inversion process of spectral reflectance is illustrated in detail. At last the inversion result is compared with simulated atmospheric conditions method which was a widely used method by previous researchers. The comparison shows that the inversion accuracy of this paper's method is higher in all inversion bands; the inversed spectral reflectance curve by this paper's method is more similar to the measured reflectance curve of wheat and better reflects the spectral reflectance characteristics of green plant which is very different from green artificial target. Thus, whether a green target is a plant or artificial target can be judged by reflectance inversion based on remote sensing image. This paper's research is helpful for the judgment of green artificial target hidden in the greenery, which has a great significance on the precise strike of green camouflaged weapons in military field.

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.

A PC-based inverse design method for radial and mixed flow turbomachinery

NASA Technical Reports Server (NTRS)

Skoe, Ivar Helge

1991-01-01

An Inverse Design Method suitable for radial and mixed flow turbomachinery is presented. The codes are based on the streamline curvature concept; therefore, it is applicable for current personal computers from the 286/287 range. In addition to the imposed aerodynamic constraints, mechanical constraints are imposed during the design process to ensure that the resulting geometry satisfies production consideration and that structural considerations are taken into account. By the use of Bezier Curves in the geometric modeling, the same subroutine is used to prepare input for both aero and structural files since it is important to ensure that the geometric data is identical to both structural analysis and production. To illustrate the method, a mixed flow turbine design is shown.

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

Recovering Long-wavelength Velocity Models using Spectrogram Inversion with Single- and Multi-frequency Components

NASA Astrophysics Data System (ADS)

Ha, J.; Chung, W.; Shin, S.

2015-12-01

Many waveform inversion algorithms have been proposed in order to construct subsurface velocity structures from seismic data sets. These algorithms have suffered from computational burden, local minima problems, and the lack of low-frequency components. Computational efficiency can be improved by the application of back-propagation techniques and advances in computing hardware. In addition, waveform inversion algorithms, for obtaining long-wavelength velocity models, could avoid both the local minima problem and the effect of the lack of low-frequency components in seismic data. In this study, we proposed spectrogram inversion as a technique for recovering long-wavelength velocity models. In spectrogram inversion, decomposed frequency components from spectrograms of traces, in the observed and calculated data, are utilized to generate traces with reproduced low-frequency components. Moreover, since each decomposed component can reveal the different characteristics of a subsurface structure, several frequency components were utilized to analyze the velocity features in the subsurface. We performed the spectrogram inversion using a modified SEG/SEGE salt A-A' line. Numerical results demonstrate that spectrogram inversion could also recover the long-wavelength velocity features. However, inversion results varied according to the frequency components utilized. Based on the results of inversion using a decomposed single-frequency component, we noticed that robust inversion results are obtained when a dominant frequency component of the spectrogram was utilized. In addition, detailed information on recovered long-wavelength velocity models was obtained using a multi-frequency component combined with single-frequency components. Numerical examples indicate that various detailed analyses of long-wavelength velocity models can be carried out utilizing several frequency components.

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