3D finite-difference frequency-domain modeling of controlled-source electromagnetic data: Direct solution and optimization for high accuracy
TL;DR: In this article, a modeling tool for simulating 3D marine CSEM surveys, based on a finite-difference discretization of the Helmholtz equation for the electric fields, has been developed.
Abstract: Three-dimensional modeling of marine controlled-source electromagnetic (CSEM) data is vital to improve the understanding of electromagnetic (EM) responses collected in increasingly complex geologic settings. A modeling tool for simulating 3D marine CSEM surveys, based on a finite-difference discretization of the Helmholtz equation for the electric fields, has been developed. Optimizations for CSEM simulations include the use of a frequency-domain technique, a staggering scheme that reduces inaccuracies especially for horizontal electric-dipole sources located near the seafloor, and a new interpolation technique that provides highly accurate EM field values for receivers located in the immediate vicinity of the seafloor. Source singularities are eliminated through a secondary-field approach, in which the primary fields are computed analytically for a homogeneous or a 1D layered background; the secondary fields are computed using the finite-difference technique. Exploiting recent advances in computer technology and algorithmic developments, the system of finite-difference equations is solved using the MUMPS direct-matrix solver. In combination with the other optimizations, this allows accurate EM field computations for moderately sized models on small computer clusters. The explicit availability of matrix factorizations is advantageous for multisource modeling and makes the algorithm well suited for future use within an inversion scheme. Comparisons of simulated data for (1) 1D models to data generated using a 1D reflectivity technique and (2) 3D models to published 3D data demonstrate the accuracy and benefits of the approach.
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TL;DR: A goal-oriented adaptive finite element approach for plane wave 3D electromagnetic modeling is proposed in this paper, which is based on adaptive finite-element (AEFES) approach.
Abstract: A goal-oriented adaptive finite-element approach for plane wave 3-D electromagnetic modelling
159 citations
TL;DR: A new 3-D vector finite element code is presented and its strength is demonstrated by modelling a realistic marine CSEM scenario which shows that seafloor topography gives an important response which needs to be reproduced by numerical modelling to avoid the misinterpretation of measurements.
Abstract: SUMMARY
We present a new 3-D vector finite element code and demonstrate its strength by modelling a realistic marine CSEM scenario. Unstructured tetrahedral meshes easily allow for the inclusion of arbitrary seafloor bathymetry so that natural environments are mapped into the model in a close-to-reality way. A primary/secondary field approach, an adaptive mesh refinement strategy as well as a higher order polynomial finite element approximation improve the solution accuracy. A convergence study strongly indicates that the use of higher order finite elements is beneficial even if the solution is not globally smooth. The marine CSEM scenario also shows that seafloor topography gives an important response which needs to be reproduced by numerical modelling to avoid the misinterpretation of measurements.
155 citations
120 citations
TL;DR: The goal of this paper is to summarize all the important issues involving 3-D inversions, and to show how inversion works and how to use it properly.
Abstract: In the last few decades, the demand for three-dimensional (3-D) inversions for magnetotelluric data has significantly driven the progress of 3-D codes. There are currently a lot of new 3-D inversion and forward modeling codes. Some, such as the WSINV3DMT code of the author, are available to the academic community. The goal of this paper is to summarize all the important issues involving 3-D inversions. It aims to show how inversion works and how to use it properly. In this paper, I start by describing several good reasons for doing 3-D inversion instead of 2-D inversion. The main algorithms for 3-D inversion are reviewed along with some comparisons of their advantages and disadvantages. These algorithms are the classical Occam’s inversion, the data space Occam’s inversion, the Gauss–Newton method, the Gauss–Newton with the conjugate gradient method, the non-linear conjugate gradient method, and the quasi-Newton method. Other variants are based on these main algorithms. Forward modeling, sensitivity calculations, model covariance and its parallel implementation are all necessary components of inversions and are reviewed here. Rules of thumb for performing 3-D inversion are proposed for the benefit of the 3-D inversion novice. Problems regarding 3-D inversions are discussed along with suggested topics for future research for the developers of the next decades.
118 citations
Cites background from "3D finite-difference frequency-doma..."
...D problems, S is relative large, and almost impossible to solve with any direct methods (Streich 2009)....
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...For 3-D problems, S is relative large, and almost impossible to solve with any direct methods (Streich 2009)....
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TL;DR: Attempts at the very demanding task of using onshore controlled-source EM for reservoir monitoring are shown, and the possible future potential of EM monitoring is discussed.
Abstract: Electromagnetic methods that utilize controlled sources have been applied for natural resource exploration for more than a century Nevertheless, concomitant with the recent adoption of marine controlled-source electromagnetics (CSEM) by the hydrocarbon industry, the overall usefulness of CSEM methods on land has been questioned within the industry Truly, there are few published examples of land CSEM surveys carried out completely analogously to the current marine CSEM standard approach of towing a bipole source across an array of stationary receivers, continuously transmitting a low-frequency signal and interpreting the data in the frequency domain Rather, different sensitivity properties of different exploration targets in diverse geological settings, gradual advances in theoretical understanding, acquisition and computer technology, and different schools in different parts of the world have resulted in a sometimes confusing multitude of land-based controlled-source EM surveying approaches Here, I aim to review previous and present-day approaches, and provide reasoning for their diversity I focus on surface-based techniques while excluding airborne EM and well logging and on applications for hydrocarbon exploration Attempts at the very demanding task of using onshore controlled-source EM for reservoir monitoring are shown, and the possible future potential of EM monitoring is discussed
113 citations
Additional excerpts
...Recently developed three-dimensional EM modeling codes (e.g., Weiss and Constable 2006; Streich 2009; Schwarzbach et al. 2011; Puzyrev et al. 2013; Um et al. 2013) and imaging solutions (e.g., Haber et al. 2007; Gribenko and Zhdanov 2007; Commer and Newman 2008; Plessix and Mulder 2008; Commer and…...
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References
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TL;DR: The main features and the tuning of the algorithms for the direct solution of sparse linear systems on distributed memory computers developed in the context of a long term European research project are analyzed and discussed.
Abstract: In this paper, we analyze the main features and discuss the tuning of the algorithms for the direct solution of sparse linear systems on distributed memory computers developed in the context of a long term European research project. The algorithms use a multifrontal approach and are especially designed to cover a large class of problems. The problems can be symmetric positive definite, general symmetric, or unsymmetric matrices, both possibly rank deficient, and they can be provided by the user in several formats. The algorithms achieve high performance by exploiting parallelism coming from the sparsity in the problem and that available for dense matrices. The algorithms use a dynamic distributed task scheduling technique to accommodate numerical pivoting and to allow the migration of computational tasks to lightly loaded processors. Large computational tasks are divided into subtasks to enhance parallelism. Asynchronous communication is used throughout the solution process to efficiently overlap communication with computation.
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TL;DR: Experiments demonstrate that a wide set of unsymmetric linear systems can be solved and high performance is consistently achieved for large sparse unsympetric matrices from real world applications.
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TL;DR: This work considers the problem of designing a dynamic scheduling strategy that takes into account both workload and memory information in the context of the parallel multifrontal factorization and shows that a new scheduling algorithm significantly improves both the memory behaviour and the factorization time.
Abstract: We consider the problem of designing a dynamic scheduling strategy that takes into account both workload and memory information in the context of the parallel multifrontal factorization. The originality of our approach is that we base our estimations (work and memory) on a static optimistic scenario during the analysis phase. This scenario is then used during the factorization phase to constrain the dynamic decisions that compute fully irregular partitions in order to better balance the workload. We show that our new scheduling algorithm significantly improves both the memory behaviour and the factorization time. We give experimental results for large challenging real-life 3D problems on 64 and 128 processors.
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TL;DR: Three new variations of a direct factorization scheme to tackle the is- sue of indeniteness in sparse symmetric linear systems, including a reordering that is based on a symmetric weighted matching of the matrix, which is effective for highly indenite symmetric systems.
Abstract: This paper discusses new pivoting factorization methods for solving sparse symmetric indenite sys- tems. As opposed to many existing pivoting methods, our SupernodenBunchnKaufman (SBK) pivoting method dy- namically selects and pivots and may be supplemented by pivot perturbation techniques. We demonstrate the effectiveness and the numerical accuracy of this algorithm and also show that a high performance implementa- tion is feasible. We will also show that symmetric maximum-weighted matching strategies add an additional level of reliability to SBK. These techniques can be seen as a complement to the alternative idea of using more complete pivoting techniques during the numerical factorization. Numerical experiments validate these conclusions. where is a diagonal matrix with and pivot blocks, is a sparse lower triangu- lar matrix, and is a symmetric indenite diagonal matrix that reects small half-machine precision perturbations, which might be necessary to tackle the problem of tiny pivots. is a reordering that is based on a symmetric weighted matching of the matrix , and tries to move the largest off-diagonal elements directly alongside the diagonal in order to form good initial or diagonal block pivots. is a ll reducing reordering which honors the structure of . We will present three new variations of a direct factorization scheme to tackle the is- sue of indeniteness in sparse symmetric linear systems. These methods restrict the pivoting search, to stay as long as possible within predened data structures for efcient Level-3 BLAS factorization and parallelization. On the other hand, the imposed pivoting restrictions can be reduced in several steps by taking the matching permutation into account. The rst al- gorithm uses SupernodenBunchnKaufman (SBK) pivoting and dynamically selects and pivots. It is supplemented by pivot perturbation techniques. It uses no more storage than a sparse Cholesky factorization of a positive denite matrix with the same sparsity structure due to restricting the pivoting to interchanges within the diagonal block associated to a single supernode. The coefcient matrix is perturbed whenever numerically acceptable and pivots cannot be found within the diagonal block. One or two steps of iterative re- nement may be required to correct the effect of the perturbations. We will demonstrate that this restricting notion of pivoting with iterative renement is effective for highly indenite symmetric systems. Furthermore the accuracy of this method is for a large set of matrices from different applications areas as accurate as a direct factorization method that uses com- plete sparse pivoting techniques. In addition, we will discuss two preprocessing algorithms to identify large entries in the coefcient matrix that, if permuted close to the diagonal, permit
474 citations