Chapter 5 – 3-D EM Forward Modeling Using Balance Technique

Publisher Summary This chapter focuses on the balance technique for the forward modeling of electromagnetic fields in 3-D media. The chapter reviews numerical and analog approaches to the forward problem solution. Numerical methods, in turn, are subdivided into two large groups: Integral equation methods and differential equation methods. A comparative analysis of these two groups of methods and hybrid approaches based on their combination is also presented in the chapter. Parallel to the method of volume integral equations (VIE) that involves integration over the entire volume of the anomalous domain, a method of surface integral equations (SIE) implying integration only over the boundary of the domain, has been developed. Analysis and interpretation of electromagnetic field anomalies on the Earth, investigation of the resolution of soundings as well as a number of other methodological problems encountered today in electromagnetics require calculation of many different models. Advances in geoelectrics call forth computing 3-D electromagnetic fields in complicated situations when the inhomogeneity exhibits an arbitrary shape and dimension and the anomalous electric conductivity in the model varies arbitrarily—for example, in regional models.

[1]  J. T. Smith.  Conservative modeling of 3-D electromagnetic fields, Part I: Properties and error analysis , 1996 .

[2]  B. Sh. Singer,et al.  Method for solution of Maxwell's equations in non-uniform media , 1995 .

[3]  J. T. Weaver,et al.  Three-dimensional induction in a non-uniform thin sheet at the surface of a uniformly conducting earth , 1979 .

[4]  Eric H. Liu,et al.  5. Electromagnetic Modeling with Surface Integral Equations , 1999 .

[5]  G. Keller,et al.  Advanced theory of deep geomagnetic sounding , 1984 .

[6]  Douglas H. Norrie,et al.  An introduction to finite element analysis , 1978 .

[7]  Y. Sasaki.  Full 3-D inversion of electromagnetic data on PC , 2001 .

[8]  L. Knizhnerman,et al.  Spectral approach to solving three-dimensional Maxwell's diffusion equations in the time and frequency domains , 1994 .

[9]  M. Hvožďara,et al.  Electromagnetic induction of a three-dimensional conductivity inhomogeneity in a two-layer earth , 1981 .

[10]  H. W. Dosso.  A PLANE-WAVE ANALOGUE MODEL FOR STUDYING ELECTROMAGNETIC VARIATIONS , 1966 .

[11]  Viacheslav V. Spichak.  A method for constructing high-order differential boundary conditions for solving external boundary value problems in geoelectromagnetism , 2006 .

[12]  V. Červ,et al.  Modelling and analysis of electromagnetic fields in 3D inhomogeneous media , 1990 .

[13]  Gregory A. Newman,et al.  High-Performance Three-Dimensional Electromagnetic Modelling Using Modified Neumann Series. Wide-Band Numerical Solution and Examples , 1997 .

[14]  K. Mitzner,et al.  Digital computer solution of three-dimensional scattering problems , 1967 .

[15]  A. Raiche.  An Integral Equation Approach to Three-Dimensional Modelling , 1974 .

[16]  B.Sh. Singer,et al.  Fast and stable method for 3-D modelling of electromagnetic field , 1997 .

[17]  Vladimir Druskin,et al.  New spectral Lanczos decomposition method for induction modeling in arbitrary 3-D geometry , 1999 .

[18]  C. R. Brewitt-Taylor,et al.  On the finite difference solution of two-dimensional induction problems , 1976 .

[19]  F. W. Jones,et al.  The Perturbation of Alternating Geomagnetic Fields by Three-Dimensional Conductivity Inhomogeneities , 1972 .

[20]  Gerald W. Hohmann,et al.  Electromagnetic modeling of three-dimensional bodies in layered earths using integral equations , 1983 .

[21]  D. Rankin,et al.  Three-dimensional modelling in magnetotelluric and magnetic variational sounding , 1977 .

[22]  P. Wannamaker,et al.  Three-dimensional magnetotelluric modeling using difference equations­ Theory and comparisons to integral equation solutions , 1993 .

[23]  Michael S. Zhdanov,et al.  Quasi‐linear series in three‐dimensional electromagnetic modeling , 1997 .

[24]  Zonghou Xiong,et al.  Electromagnetic modeling of 3-D structures by the method of system iteration using integral equations , 1992 .

[25]  Gerald W. Hohmann,et al.  Magnetotelluric responses of three-dimensional bodies in layered earths , 1982 .

[26]  V. Dmitriev,et al.  Quasi-analytical approximations and series in electromagnetic modeling , 2000 .

[27]  Jian-Ming Jin,et al.  A spectral Lanczos decomposition method for solving 3-D low-frequency electromagnetic diffusion by the finite-element method , 1999 .

[29]  T. Habashy,et al.  Beyond the Born and Rytov approximations: A nonlinear approach to electromagnetic scattering , 1993 .

[30]  Art Raiche,et al.  Hybrid calculations of the three-dimensional electromagnetic response of buried conductors , 1987 .

[31]  G. Newman,et al.  Three-dimensional magnetotelluric inversion using non-linear conjugate gradients , 2000 .

[32]  M. Zhdanov,et al.  Quasi‐linear approximation in 3-D electromagnetic modeling , 1996 .

[33]  Carlos Torres-Verdín,et al.  Implications of the Born approximation for the magnetotelluric problem in three-dimensional environments , 1992 .

[34]  G. W. Hohmann,et al.  Integral equation modeling of three-dimensional magnetotelluric response , 1981 .

[35]  Tohru Mogi.  Three-dimensional modeling of magnetotelluric data using finite element method , 1996 .

[36]  P. B. Johns,et al.  On the construction and numerical solution of transmission‐line and lumped network models of Maxwell's equations , 1980 .

[37]  K. Yee.  Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media , 1966 .

[38]  Ki Ha Lee,et al.  A hybrid three-dimensional electromagnetic modeling scheme , 1981 .

[39]  Gerard L. G. Sleijpen,et al.  BiCGstab(l) and other hybrid Bi-CG methods , 1994, Numerical Algorithms.

[40]  Numerical modeling of the electromagnetic response of three-dimensional conductors in a layered earth , 1985 .

[41]  E. B. Fainberg,et al.  Generalization of the iterative dissipative method for modeling electromagnetic fields in nonuniform media with displacement currents , 1995 .

[42]  Gerald W. Hohmann.  Three-dimensional em modeling , 1983 .

[43]  Randall L. Mackie,et al.  Conjugate direction relaxation solutions for 3-d magnetotelluric modeling , 1993 .

[44]  S. K. Verma,et al.  Numerical considerations on computing the EM response of three‐dimensional inhomogeneities in a layered earth , 1981 .

[45]  R. D. Hibbs,et al.  Electromagnetic induction in three dimensional structures for various source fields. , 1978 .

[46]  Philip E. Wannamaker,et al.  Advances in three-dimensional magnetotelluric modeling using integral equations , 1991 .

[47]  F. W. Jones,et al.  The Perturbation of Alternating Geomagnetic Fields by Three‐dimensional Island Structures , 1973 .

[48]  T. Habashy,et al.  Rapid 2.5‐dimensional forward modeling and inversion via a new nonlinear scattering approximation , 1994 .

[49]  Keith D. Paulsen,et al.  Nodal-based finite-element modeling of Maxwell's equations , 1992 .

[50]  Gregory A. Newman,et al.  Three-dimensional induction logging problems, Part 2: A finite-difference solution , 2002 .

[51]  J. T. Smith,et al.  Three-dimensional electromagnetic modeling using finite difference equations: The magnetotelluric example , 1994 .

[53]  I. M. Varentsov,et al.  Modern trends in the solution of forward and inverse 3D electromagnetic induction problems , 1983 .

[54]  Toru Mogi,et al.  A new computation method for a staggered grid of 3D EM field conservative modeling , 2002 .

[55]  J. T. Smith.  Conservative modeling of 3-D electromagnetic fields, Part II: Biconjugate gradient solution and an accelerator , 1996 .

[56]  M. Zhdanov.  Integral Transforms in Geophysics , 1988 .

[57]  Gregory A. Newman,et al.  Electromagnetic induction in a fully 3‐D anisotropic earth , 2000 .

[58]  J. T. Weaver,et al.  Induction in a thin sheet of variable conductance at the surface of a stratified earth — I. Two-dimensional theory , 1984 .

[59]  D. Livelybrooks,et al.  Program 3Dfeem: a multidimensional electromagnetic finite element model , 1993 .

[60]  G. W. Hohmann,et al.  An investigation of finite-element modeling for electrical and electromagnetic data in three dimensions , 1981 .

[61]  Tsili Wang,et al.  3‐D electromagnetic anisotropy modeling using finite differences , 2001 .

[62]  The construction of effective methods for electromagnetic modelling , 1982 .

[63]  Michael S. Zhdanov,et al.  Methods for modelling electromagnetic fields Results from COMMEMI—the international project on the comparison of modelling methods for electromagnetic induction , 1997 .

[64]  G. W. Hohmann.  Three-Dimensional Induced Polarization and Electromagnetic Modeling , 1975 .

[65]  J. E. Lokken,et al.  Irregular coastline and channeling effects in three-dimensional geomagnetic perturbation models , 1975 .

[66]  Gregory A. Newman,et al.  Chapter 8 Three-dimensional magnetotelluric modeling and inversion: Application to sub-salt imaging , 2002 .

[67]  The perturbation of geomagnetic fields by two-dimensional and three-dimensional conductivity inhomogeneities , 1974 .

[68]  Brian R. Spies,et al.  Three-Dimensional Electromagnetics , 1999 .