8. 3-D Conductivity Models: Implications of Electrical Anisotropy

Weidelt, Peter

doi:10.1190/1.9781560802154.ch8

Cited by 71 publications

(53 citation statements)

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“…implications of electrical anisotropy in applications see also Weidelt [Wei95]. It can be observed in our numerical experiments (not shown here, but see [DBBP2]) that the shapes of the x, y and z-component sensitivity functions typically differ from each other, and certain source-receiver constellations are very sensitive to some of these components and much less sensitive to others.…”

Section: A Short Discussion Of Sensitivity Functionsmentioning

confidence: 75%

Adjoint Fields and Sensitivities for 3D Electromagnetic Imaging in Isotropic and Anisotropic Media

Dorn

Bertete‐Aguirre

Papanicolaou

2008

Inverse Problems and Imaging

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Summary. In this paper we give an overview of a recently developed method for solving an inverse Maxwell problem in environmental and geophysical imaging. Our main focus is on low-frequency cross-borehole electromagnetic induction tomography (EMIT), although related problems arise also in other applications in nondestructive testing and medical imaging. In typical applications (e.g. in environmental remediation), the isotropic or anisotropic conductivity distribution in the earth needs to be reconstructed from surface-to-borehole electromagnetic data. Our method uses a backpropagation strategy (based on adjoint fields) for solving this inverse problem. The method works iteratively, and can be considered as a nonlinear generalization of the Algebraic Reconstruction Technique (ART) in x-ray tomography, or as a nonlinear Kaczmarz-type approach. We will also propose a new regularization scheme for this method which is based on a proper choice of the function spaces for the inversion. A detailed sensitivity analysis for this problem is given, and a set of numerically calculated sensitiviy functions for homogeneous isotropic media is presented.

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Section: A Short Discussion Of Sensitivity Functionsmentioning

confidence: 75%

Adjoint Fields and Sensitivities for 3D Electromagnetic Imaging in Isotropic and Anisotropic Media

Dorn

Bertete‐Aguirre

Papanicolaou

2008

Inverse Problems and Imaging

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“…This work differs from a previously developed FD solution (Weidelt, 1999), also designed to simulate induction in anisotropic media. Both methods incorporate the staggered grid approach: This study, an edgebased discretization; Weidelt (1999), a face-centered discretization.…”

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confidence: 80%

“…We note that the choice of an "edg+centered" staggered grid instead of a "face-centered" one (Weidelt, 1999) results in comparatively simple expressions for the spatiaIly-averaged conductivity values (equations 10b-c). In the above expression, the conductivity values are averaged arithmetically since the Jz component is continuous at the point (i + 1/2, j, k).…”

Section: Methodsmentioning

confidence: 99%

“…Both methods incorporate the staggered grid approach: This study, an edgebased discretization; Weidelt (1999), a face-centered discretization. For the face-based discretization, the governing PDE (derived from Maxwell's equations in the quasi-static limit) is discretized using components of the electric field vector which are normal to and located at the centers of FD cell faces.…”

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confidence: 99%

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Electromagnetic induction in a fully 3‐D anisotropic earth

2002

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The bulk electrical anisotropy of sedimentary formations is a macroscopic phenomenon which can result from the presence of sand/shale laminae and varations in grain size and pore space. Accounting for its effects on induction log response is an ongoing research problem for the well-logging community since these types of sedimentary stuctures have long been correlated with productive hydrocarbon reservoirs. Presented here is a staggered grid finite difference method for simulating EM induction in a fully 3D anisotropic medium.Here, the electrical conductivity of the formation is represented as a full 3 x 3 tensor whose elements can vary arbitrarily with position throughout the formation. To demonstrate the validity of this approach, finite difference results are compared against analytic and quasianalytic solutions for tractable ID and 2D model geometries. As an final example, we simulate 2C-40 induction tool responses in a crossbedded eolian sandstone to illustrate the magnitude of the challenge faced by interpreters when electrical anisotropy is neglected.

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“…For a solution mesh including the air region, the resulting matrix can be very ill-conditioned. Iterative solutions of such a matrix system are indeed very slow and correction schemes such as divergence corrections (Smith, 1996a;Mackie et al, 1994;Weidelt, 1998) are necessary to speed up convergence.…”

Section: Introductionmentioning

confidence: 99%

Domain decomposition for 3D electromagnetic modeling

Xiong

2014

Earth Planet Sp

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Using the staggered grid full domain 3D modeling schemes of various accuracies have been developed. This study focuses on the second order finite difference method with the 13-point rule for meshes extending into the air. Tests with Krylov space iterative solvers indicate that the restarted Bi-CG Stablised method offers the best convergence for our problems. Because the air and the conductive earth have distinctive physical properties which greatly broaden the spectra of the whole matrix system, the whole mesh with both domains in one system either converges very slowly or fails to converge completely. However, the matrix systems for each domain have much smaller condition numbers. To overcome instability caused by the inclusion of the air in the mesh a domain decomposition method are experimented. Tests show that the adaptive iteration amongst the subdomains converges exponentially, which implies that large models can be solved by using the domain decomposition method.

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8. 3-D Conductivity Models: Implications of Electrical Anisotropy

Cited by 71 publications

References 0 publications

Adjoint Fields and Sensitivities for 3D Electromagnetic Imaging in Isotropic and Anisotropic Media

Adjoint Fields and Sensitivities for 3D Electromagnetic Imaging in Isotropic and Anisotropic Media

Electromagnetic induction in a fully 3‐D anisotropic earth

Domain decomposition for 3D electromagnetic modeling

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