Three-dimensional magnetotellurics modeling using edgebased finite-element unstructured meshes

Liu, Chiangsheng; Ren, Zhengyong; Tang, Jingtian; Yan, Yan

doi:10.1007/s11770-008-0024-4

Cited by 33 publications

(4 citation statements)

References 17 publications

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“…Recently, finite-element methods have received increased attention (Börner et al, 2008;Liu et al, 2008;Mukherjee and Everett, 2011;Nam et al, 2007;Um et al, 2010). They are attractive because they are better suited to unstructured meshes than finite-difference methods, and such meshes enable more faithful representation of topography and realistic subsurface interfaces than rectilinear grids.…”

Section: Introductionmentioning

confidence: 99%

“…Edge elements were first applied to geophysical electromagnetic methods by Sugeng (1998), using a rectilinear mesh. Edge elements are used by Nam et al (2007) for a structured mesh of hexahedral (i.e., distorted brick) elements, and by Börner et al (2008) and Liu et al (2008) for unstructured meshes of tetrahedral elements. Zyserman and Santos (2000) use higher-order vector elements on a rectilinear mesh.…”

Section: Introductionmentioning

confidence: 99%

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Three-dimensional finite-element modelling of magnetotelluric data with a divergence correction

Farquharson

Miensopust

2011

Journal of Applied Geophysics

122

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Three-dimensional finite-element modelling of magnetotelluric data with a divergence correction

Farquharson

Miensopust

2011

Journal of Applied Geophysics

122

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“…When using the FE method for the EM‐fields equations, nodal basis functions are not appropriate because the continuity of the nodal basis function would lead to the violation of the rule that the normal component of the E‐field should be allowed to be discontinuous across interfaces between distinct conductivities. However, vector basis functions can be used to satisfy the discontinuity of the normal component of the E‐field across the inner‐element boundaries while guaranteeing the continuity of its tangential component (Sugeng,1998; Biro, 1999; Liu et al ., 2008; Farquharson & Miensopust, 2011). For the potential equations, the unknowns are the magnetic vector potential A and electric scalar potential φ , which are both continuous across the conductivity contrasts.…”

Section: Introductionmentioning

confidence: 99%

Comparison of nodal and edge basis functions for the forward modelling of three‐dimensional frequency‐domain wire source electromagnetic data using a potentials formulation

Zhang

Farquharson

Lin

2022

Geophysical Prospecting

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An investigation of forward modelling 3‐D wire source electromagnetic data in the frequency domain using nodal and edge finite‐element basis functions is presented. The equations solved are those for the coupled secondary vector–scalar potentials (i.e. magnetic vector potential A and electric scalar potential φ), which give rise to a less ill‐conditioned system of equations to be solved. The effectiveness of these two methods is validated with two 3‐D examples, i.e. multi‐blocks models and topography models, which considered the computation of the A–φ potentials and the electromagnetic fields due to a grounded electric line source by inter‐comparing the numerical solutions computed from each method and by comparing them against the equivalent solutions for the same model computed using other methods. Based on the multiple‐blocks models, we compare the relative contributions of the inductive and galvanic parts to the E‐field for different frequencies. Results show that for the type of source considered in this paper, the galvanic parts dominate for a relatively low frequency (10 Hz), but that for a relatively high frequency (10 kHz), the inductive parts also contribute. The extent to which the Coulomb gauge condition is satisfied when using nodal basis functions for A is also investigated, with results showing that the divergence of the numerically calculated A is almost zero as desired. Based on the topography models, we analyse the electromagnetic response characteristics at different survey planes, with results of this investigation indicating that the electromagnetic responses measured over a plane close to the target will carry more accurate geometry information (such as position, shape and size) of the target, which is expected, and less distortion due to topography compared to those measured at the earth's surface. This suggests that when conducting electromagnetic prospecting in an area with complex topography, it is possible to obtain better anomaly detection affected less by topography if the electromagnetic measurement is carried out underground (such as in a borehole).

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“…The FE approach has been developed and implemented by many developers (see, e.g., [69,65,68,66,52,8,80,138,73]).…”

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confidence: 99%

An approximate hybrid method for modeling of electromagnetic scattering from an underground target

Bakr¹

2011

GEOPHYSICS

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The main focus of this thesis is to develop and analyze a fast and accurate hybrid method, simplified integral equation (SIE) modeling, for modeling of electromagnetic scattering from an underground target. The method consists of solving a finite volume problem in a localized region containing the target, and using the integral equation (IE) method to obtain the field outside that region. The hybrid method thus replaces the dense-matrix part of the rigorous IE method by sparsematrix calculations based on an approximation of Maxwell's Equations. The thesis is divided into two parts. Part I, is devoted to overview and background theory and is structured as follows: Chapter 1 provides a general introduction and presents a general framework of forward and inverse modeling. An introductory discussion of model parameters, such as porosity, saturation and electrical conductivity, is presented in Chapter 2. Emphasis has been placed on the relationship between conductivity and saturation through Archie's law. Exploration and monitoring of a petroleum reservoir are important applications of the marine controlled source electromagnetic (CSEM). These applications are presented in Chapter 3. Chapter 4 provides a review of different electromagnetic modeling approaches. In addition, detailed derivation of integral formulation of Maxwell's Equations is presented. Different solutions and approaches in the frequency domain are discussed in Chapter 5. Emphasis has been placed on IE and SIE methods. All the praises and thanks be to ALLAH for giving me the life, strength, and spirit, to complete my research in a manner that advances both my purpose in the life and the science of mathematics. Also, my beloved Prophet, Mohamed (peace be upon him), ALLAH protect you and your family. There are many people whom I would like to thank. First of all, I would like to thank my principle supervisor Trond Mannseth for his guidance, helpful discussions and continuous encouragement during the development of this work. I am also grateful for the help and support from my advisors Martha Lien and the late Magne Espedal. I would like to thank VISTA for the funding of this project. I would also like to thank friends and colleagues at CIPR for a good research environment and company for lunch. Special thanks to Mona Wolff (human resources manager) for her smile and ability to handle any social problem. I am very grateful to my beloved parents who taught me the value of education, specially for my dear father who passed away last year before seeing my success. Also, special thanks are due my wife and my three children, Radwa, Sohila and Mohamed, whose endless support and understanding have been profound throughout the difficult times of this PhD study. Without your love and support I am sure that I would not have been able to achieve so much.

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Three-dimensional magnetotellurics modeling using edgebased finite-element unstructured meshes

Cited by 33 publications

References 17 publications

Three-dimensional finite-element modelling of magnetotelluric data with a divergence correction

Three-dimensional finite-element modelling of magnetotelluric data with a divergence correction

Comparison of nodal and edge basis functions for the forward modelling of three‐dimensional frequency‐domain wire source electromagnetic data using a potentials formulation

An approximate hybrid method for modeling of electromagnetic scattering from an underground target

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