Three-dimensional modelling of controlled source electro-magnetic surveys using non-conforming finite element methods

Elías, Matías W; Zyserman, Fabio; Rosas‐Carbajal, Marina; Manassero, María Constanza

doi:10.1093/gji/ggab524

Cited by 5 publications

(1 citation statement)

References 72 publications

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“…Nevertheless, owing to successive advances in direct solution algorithms [5,78], as well as the increasing availability and power of highperformance computing facilities [60], direct solvers are often used when solving the EM forward problem see (e.g. [29,32,35,68,71,72,81,85], for details).…”

Section: Introductionmentioning

confidence: 99%

Iterative solution methods for 3D controlled-source electromagnetic forward modelling of geophysical exploration scenarios

2022

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We develop an efficient and robust iterative framework suitable for solving the linear system of equations resulting from the spectral element discretisation of the curl-curl equation of the total electric field encountered in geophysical controlled-source electromagnetic applications. We use the real-valued equivalent form of the original complex-valued system and solve this arising real-valued two-by-two block system (outer system) using the generalised conjugate residual method preconditioned with a highly efficient block-based PREconditioner for Square Blocks (PRESB). Applying this preconditioner equates to solving two smaller inner symmetric systems which are either solved using a direct solver or iterative methods, namely the generalised conjugate residual or the flexible generalised minimal residual methods preconditioned with the multigrid-based auxiliary-space preconditioner AMS. Our numerical experiments demonstrate the robustness of the outer solver with respect to spatially variable material parameters, for a wide frequency range of five orders of magnitude (0.1-10’000 Hz), with respect to the number of degrees of freedom, and for stretched structured and unstructured as well as locally refined meshes. For all the models considered, the outer solver reaches convergence in a small (typically < 20) number of iterations. Further, our numerical tests clearly show that solving the two inner systems iteratively using the indicated preconditioned iterative methods is computationally beneficial in terms of memory requirement and time spent as compared to a direct solver. On top of that, our iterative framework works for large-scale problems where direct solvers applied to the original complex-valued systems succumb due to their excessive memory consumption, thus making the iterative framework better suited for large-scale 3D problems. Comparison to a similar iterative framework based on a block-diagonal and the auxiliary-space preconditioners reveals that the PRESB preconditioner requires slightly fewer iterations to converge yielding a certain gain in time spent to obtain the solution of the two-by-two block system.

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Section: Introductionmentioning

confidence: 99%

Iterative solution methods for 3D controlled-source electromagnetic forward modelling of geophysical exploration scenarios

2022

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Electromagnetic Subsurface Imaging in the Presence of Metallic Structures: A Review of Numerical Strategies

Castillo-Reyes,

Queralt,

Piñas-Varas

et al. 2024

Surv Geophys

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Electromagnetic (EM) imaging aims to produce large-scale, high-resolution soil conductivity maps that provide essential information for Earth subsurface exploration. To rigorously generate EM subsurface models, one must address both the forward problem and the inverse problem. From these subsurface resistivity maps, also referred to as volumes of resistivity distribution, it is possible to extract useful information (lithology, temperature, porosity, permeability, among others) to improve our knowledge about geo-resources on which modern society depends (e.g., energy, groundwater, and raw materials, among others). However, this ability to detect electrical resistivity contrasts also makes EM imaging techniques sensitive to metallic structures whose EM footprint often exceeds their diminutive stature compared to surrounding materials. Depending on target applications, this behavior can be advantageous or disadvantageous. In this work, we review EM modeling and inverse solutions in the presence of metallic structures, emphasizing how these structures affect EM data acquisition and interpretation. By addressing the challenges posed by metallic structures, our aim is to enhance the accuracy and reliability of subsurface EM characterization, ultimately leading to improved management of geo-resources and environmental monitoring. Here, we consider the latter through the lens of a triple helix approach: physics behind metallic structures in EM modeling and imaging, development of computational tools (conventional strategies and artificial intelligence schemes), and configurations and applications. The literature review shows that, despite recent scientific advancements, EM imaging techniques are still being developed, as are software-based data processing and interpretation tools. Such progress must address geological complexities and metallic casing measurements integrity in increasing detail setups. We hope this review will provide inspiration for researchers to study the fascinating EM problem, as well as establishing a robust technological ecosystem to those interested in studying EM fields affected by metallic artifacts.

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A parallel adaptive finite-element approach for 3-D realistic controlled-source electromagnetic problems using hierarchical tetrahedral grids

Liu

Ren

Hongbo

et al. 2022

Geophysical Journal International

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Summary To effectively and efficiently interpret or invert controlled-source electromagnetic (CSEM) data which are recorded in areas with the kind of complex geological environments and arbitrary topography that are typical, three-dimensional (3D) CSEM forward modeling software that can quickly solve large-scale problems, provide accurate electromagnetic responses for complex geo-electrical models, and can be easily incorporated into inversion algorithms are required. We have developed a parallel goal-oriented adaptive mesh refinement (AMR) finite-element approach for frequency-domain 3D CSEM forward modeling with hierarchical tetrahedral grids that can offer accurate electromagnetic responses for large-scale complex models and that can efficiently serve for inversion. The approach uses the goal-oriented adaptive vector finite element method to solve the total electric field vector equation. The geo-electrical model is discretized by unstructured tetrahedral grids which can deal with complex underground geological models with arbitrary surface topography. Different from previous adaptive finite element software working on unstructured tetrahedral grids, we have utilized a novel mesh refinement technique named the longest edge bisection method to generate hierarchically refined grids. As the refined grids are nested into the coarse grids, the refinement technique can precisely map the electrical parameters of inversion grids onto the forward modeling grids so that the extra numerical errors generated by the inconsistency of electrical parameters between inversion grids and forward modeling grids are eliminated. In addition, we employ the parallel domain-decomposition technique to further accelerate the computations, and the flexible generalized minimum residual solver (FGMRES) with an auxiliary Maxwell solver preconditioner to solve the final large-scale system of linear equations. In the end, we validate the performance of the proposed scheme using two synthetic models and one realistic model. We demonstrate that accurate electromagnetic fields can be obtained by comparison with the analytic solutions and that the code is highly scalable for large-scale problems with millions or even hundreds of millions of unknowns. For the synthetic 3D model and the realistic model with complex geometry, our solutions match well with the results calculated by an exsiting 3D CSEM forward modelling code. Both synthetic and realistic examples demonstrate that our newly developed code is an effective, efficient forward modeling engine for interpreting CSEM field data acquired in areas of complex geology and topography.

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Three-dimensional modelling of controlled source electro-magnetic surveys using non-conforming finite element methods

Cited by 5 publications

References 72 publications

Iterative solution methods for 3D controlled-source electromagnetic forward modelling of geophysical exploration scenarios

Iterative solution methods for 3D controlled-source electromagnetic forward modelling of geophysical exploration scenarios

Electromagnetic Subsurface Imaging in the Presence of Metallic Structures: A Review of Numerical Strategies

A parallel adaptive finite-element approach for 3-D realistic controlled-source electromagnetic problems using hierarchical tetrahedral grids

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