Skip to main content
SpringerLink
Log in

Three-Dimensional Electromagnetic Modelling and Inversion from Theory to Application

  • Published:
Surveys in Geophysics Aims and scope Submit manuscript

Abstract

The whole subject of three-dimensional (3-D) electromagnetic (EM) modelling and inversion has experienced a tremendous progress in the last decade. Accordingly there is an increased need for reviewing the recent, and not so recent, achievements in the field. In the first part of this review paper I consider the finite-difference, finite-element and integral equation approaches that are presently applied for the rigorous numerical solution of fully 3-D EM forward problems. I mention the merits and drawbacks of these approaches, and focus on the most essential aspects of numerical implementations, such as preconditioning and solving the resulting systems of linear equations. I refer to some of the most advanced, state-of-the-art, solvers that are today available for such important geophysical applications as induction logging, airborne and controlled-source EM, magnetotellurics, and global induction studies. Then, in the second part of the paper, I review some of the methods that are commonly used to solve 3-D EM inverse problems and analyse current implementations of the methods available. In particular, I also address the important aspects of nonlinear Newton-type optimisation techniques and computation of gradients and sensitivities associated with these problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

EM:

electromagnetic

3-D:

three-dimensional

FD:

finite-difference

FE:

finite-element

IE:

integral equation

NLCG:

nonlinear conjugate gradients

QN:

Quasi–Newton

References

  • A. Abubakar P. Berg Particlevan der (2000) ArticleTitle‘Non-Linear Three-Dimensional Inversion of Cross-Well Electrical Measurements’ Geophys. Prosp. 48 109–134

    Google Scholar 

  • A. Abubakar P. Berg Particlevan der (2001) ArticleTitle‘Nonlinear Inversion of the Electrode Logging Measurements in a Deviated Well’ Geophysics 66 110–124 Occurrence Handle10.1190/1.1444886

    Article  Google Scholar 

  • D. L. Alumbaugh G. A. Newman L. Prevost J. N. Shadid (1996) ArticleTitle‘Three-Dimensional Wide Band Electromagnetic Modeling on Massively Parallel Computers’ Radio Sci. 31 1–23 Occurrence Handle10.1029/95RS02815

    Article  Google Scholar 

  • D. A. Aruliah U. M. Ascher (2003) ArticleTitle‘Multigrid Preconditioning for Krylov Methods for Time-Harmonic Maxwell’s Equations in 3D’ SIAM J. Scient. Comput. 24 702–718

    Google Scholar 

  • D. B. Avdeev A. V. Kuvshinov O. V. Pankratov G.A. Newman (1997) ArticleTitle‘High-Performance Three-Dimensional Electromagnetic Modeling Using Modified Neumann Series. Wide-band Numerical Solution and Examples’ J. Geomagn. Geoelectr. 49 1519–1539

    Google Scholar 

  • D. B. Avdeev A. V. Kuvshinov O. V. Pankratov G. A. Newman (1998) ArticleTitle‘Three-Dimensional Frequency-Domain Modelling of Airborne Electromagnetic Responses’ Explor. Geophy. 29 111–119

    Google Scholar 

  • Avdeev, D. B., Kuvshinov, A. V., Pankratov, O. V., and Newman, G. A.: 2000, ‘3D EM Modelling Using Fast Integral Equation Approach with Krylov Subspace Accelerator, in Expanded abstracts of the 62nd EAGE Conference, Glasgow, Scotland, pp. 195–198

  • D. B. Avdeev A. V. Kuvshinov O. V. Pankratov G. A. Newman (2002a) ArticleTitle‘Three-Dimensional Induction Logging Problems. Part I. An Integral Equation Solution and Model Comparisons’ Geophysics 67 413–426 Occurrence Handle10.1190/1.1468601

    Article  Google Scholar 

  • D. B. Avdeev A. V. Kuvshinov X. A. Epova (2002b) ArticleTitle‘Three-Dimensional Modeling of Electromagnetic Logs From Inclined-Horizontal Wells, Izvestiya’ Phys. Solid Earth 38 975–980

    Google Scholar 

  • E. A. Badea M. E. Everett G. A. Newman O. Biro (2001) ArticleTitle‘Finite-Element Analysis of Controlled-Source Electromagnetic Induction Using Coulomb-Gauged Potentials’ Geophysics 66 786–799 Occurrence Handle10.1190/1.1444968

    Article  Google Scholar 

  • W. Boyce D. Lynch K. Paulsen G. Minerbot (1992) ArticleTitle‘Nodal Based Finite Element Modeling Maxwell’s Equations’ IEEE Trans. Antennas Propagat. 40 642–651

    Google Scholar 

  • C. G. Broyden (1969) ArticleTitle‘A New Double-Rank Minimization Algorithm’ Notices Am. Math. Soc. 16 670

    Google Scholar 

  • V. Cerv (1990) ArticleTitle‘Modelling and Analysis of Electromagnetic Fields in 3D Inhomogeneous Media’ Surv. Geophys. 11 205–230 Occurrence Handle10.1007/BF01901660

    Article  Google Scholar 

  • Champagne, N. J., Berryman, J. G., Buettner, H. M., Grant, J. B., and Sharpe, R. M.: 1999, ‘A Finite-Difference Frequency-Domain Code for Electromagnetic Induction Tomography’, in Proc. SAGEEP, Oakland, CA, pp. 931–940

  • W. C. Chew (1999) Waves and Fields in Inhomogeneous Media Wiley-IEEE Press Piscataway, NJ

    Google Scholar 

  • M. Commer G. Newman (2004) ArticleTitle‘A Parallel Finite-Difference Approach for 3D Transient Electromagnetic Modeling with Galvanic Sources’ Geophysics 69 1192–1202 Occurrence Handle10.1190/1.1801936

    Article  Google Scholar 

  • S. Davydycheva V. Druskin T. Habashy (2003) ArticleTitle‘An Efficient Finite Difference Scheme for Electromagnetic Logging in 3D Anisotropic Inhomogeneous Media’ Geophysics 68 1525–1536 Occurrence Handle10.1190/1.1620626

    Article  Google Scholar 

  • T. W. Dawson J. T. Weaver (1979) ArticleTitle‘Three-Dimensional Electromagnetic Induction in a Non-Uniform Thin Sheet at the Surface of Uniformly Conducting Earth’ Geophys. J. Roy. Astr. Soc. 59 445–462

    Google Scholar 

  • J. E. Dennis R. B. Schnabel (1996) Numerical Methods for Unconstrained Optimization and Nonlinear Equations SIAM Philadelphia

    Google Scholar 

  • A. Dey H. F. Morrison (1979) ArticleTitle‘Resistivity Modelling for Arbitrary Shaped Three-Dimensional Structures’ Geophysics 44 753–780 Occurrence Handle10.1190/1.1440975

    Article  Google Scholar 

  • V. I. Dmitriev (1969) Electromagnetic Fields in Inhomogeneous Media Moscow State University Moscow

    Google Scholar 

  • V. I. Dmitriev N. I. Nesmeyanova (1992) ArticleTitle‘Integral Equation Method in Three-Dimensional Problems of Low-Frequency Electrodynamics’ Comput. Math. Model. 3 313–317

    Google Scholar 

  • O. Dorn H. Bertete-Aguirre J. G. Berryman G. C. Papanicolaou (1999) ArticleTitle‘A Nonlinear Inversion Method for 3D Electromagnetic Imaging Using Adjoint Fields’ Inv. Prob. 15 1523–1558 Occurrence Handle10.1088/0266-5611/15/6/309

    Article  Google Scholar 

  • V. Druskin L. Knizhnerman (1994) ArticleTitle‘Spectral Approach to Solving Three-Dimensional Maxwell’s Equations in the Time and Frequency Domains’ Radio Sci. 29 937–953 Occurrence Handle10.1029/94RS00747

    Article  Google Scholar 

  • V. Druskin L. Knizhnerman P. Lee (1999) ArticleTitle‘A New Spectral Lanczos Decomposition Method for Induction Modeling in Arbitrary 3D Geometry’ Geophysics 64 701–706 Occurrence Handle10.1190/1.1444579

    Article  Google Scholar 

  • P. A. Eaton (1989) ArticleTitle‘3D Electromagnetic Inversion Using Integral Equations’ Geophys. Prosp. 37 407–426

    Google Scholar 

  • Ellis, R. G.: 1999, ‘Joint 3-D Electromagnetic Inversion’, in M. J. Oristaglio and B. R. Spies (eds.), Three Dimensional Electromagnetics, S.E.G. Geophysical Developments Series 7, pp. 179–192

  • Ellis, R. G.: 2002, Electromagnetic Inversion Using the QMR-FFT Fast Integral Equation Method, in 72st Ann. Internat. Mtg., Soc. Expl. Geophys., pp. 21–25

  • M. Everett A. Schultz (1996) ArticleTitle‘Geomagnetic Induction in a Heterogeneous Sphere, Azimuthally Symmetric Test Computations and the Response of an Undulating 660-km Discontinuity’ J. Geophys. Res. 101 2765–2783 Occurrence Handle10.1029/95JB03541

    Article  Google Scholar 

  • F. W. Jones L. J. Pascoe (1972) ArticleTitle‘The Perturbation of Alternating Geomagnetic Fields by Three-Dimensional Conductivity Inhomogeneities’ Geophys. J. Roy. Astr. Soc. 27 479–484

    Google Scholar 

  • M. N. Judin (1980) Magnetotelluric Field Calculation in Three-Dimensional Media Using a Grid Method, in Problems of the Sea Electromagnetic Investigations IZMIRAN Moscow 96–101

    Google Scholar 

  • V. Faber T. Manteuffel (1984) ArticleTitle‘Necessary and Sufficient Conditions for the Existence of a Conjugate Gradient Method’ SIAM J. Numer. Anal. 24 352–362

    Google Scholar 

  • C. G. Farquharson D. W. Oldenburg (1996) ArticleTitle‘Approximate Sensitivities for the Electromagnetic Inverse Problem’ Geophys. J. Int. 126 235–252

    Google Scholar 

  • C. G. Farquharson D. W. Oldenburg (1998) ArticleTitle‘Non-Linear Inversion Using General Measures of Data Misfit and Model Structure’ Geophys. J. Int. 134 213–233 Occurrence Handle10.1046/j.1365-246x.1998.00555.x

    Article  Google Scholar 

  • Farquharson, C. G., Oldenburg, D. W., Haber, E., and Shekhtman, R.: 2002, ‘An Algotithm for The Three-Dimensional Inversion of Magnetotelluric Data,’ in 72st Ann. Internat. Mtg., Soc. Expl. Geophys., pp.649–652

  • C. G. Farquharson D. W. Oldenburg (2004) ArticleTitle‘A Comparison of Automatic Techniques for Estimating the Regularization Parameter in Non-Linear Inverse Problems’ Geophys. J. Int. 156 411–425 Occurrence Handle10.1111/j.1365-246X.2004.02190.x

    Article  Google Scholar 

  • R. Fletcher C. M. Reeves (1964) ArticleTitle‘Function Minimization by Conjugate Gradients’ Comput. J. 7 149–154 Occurrence Handle10.1093/comjnl/7.2.149

    Article  Google Scholar 

  • E. Y. Fomenko T. Mogi (2002) ArticleTitle‘A New Computation Method for a Staggered Grid of 3D EM Field Conservative Modeling’ Earth Planets Space 54 499–509

    Google Scholar 

  • G. H. Golub C. F. Loan ParticleVan (1996) Matrix Computations EditionNumberThird The Johns Hopkins University Press Baltimore and London

    Google Scholar 

  • N. Grammatica P. Tarits (2002) ArticleTitle‘Contribution at Satellite Altitude of Electromagnetically Induced Anomalies Arising from a Three-Dimensional Heterogeneously Conducting Earth, using Sq as an Inducing Source Field’ Geophys. J. Int. 151 913–923 Occurrence Handle10.1046/j.1365-246X.2002.01817.x

    Article  Google Scholar 

  • A. Greenbaum (1997) Iterative Methods for Solving Linear Systems SIAM Philadelphia

    Google Scholar 

  • T. M. Habashy R. W. Groom B. R. Spies (1993) ArticleTitle‘Beyond the Born and Rytov Approximations: A Nonlinear Approach to Electromagnetic Scattering’ J. Geophys. Res. 98 1759–1775

    Google Scholar 

  • Haber, E.: 1999, ‘Modeling 3D EM Using Potentials and Mixed Finite Elements,’ in M. J. Oristaglio and B. R. Spies (eds.), Three Dimensional Electromagnetics, S.E.G. Geophysical Developments Series 7, pp. 12–15

  • E. Haber U. M. Ascher D. A. Aruliah D. W. Oldenburg (2000a) ArticleTitle‘Fast Simulation of 3D Electromagnetic Problems Using Potentials’ J. Comp. Phys. 163 150–171

    Google Scholar 

  • E. Haber U. M. Ascher D. A. Aruliah D. W. Oldenburg (2000b) ArticleTitle‘On Optimisation Techniques for Solving Nonlinear Inverse Problems’ Inv. Prob. 16 1263–1280 Occurrence Handle10.1088/0266-5611/16/5/309

    Article  Google Scholar 

  • Haber, E., Ascher, U. M., Oldenburg, D. W., Shekhtman R. and Chen J.: 2002a, ‘3-D Frequency Domain CSEM Inversion Using Unconstrained Optimization,’ in 72st Ann. Internat. Mtg., Soc. Expl. Geophys., pp.653–656

  • E. Haber U. M. Ascher D. W. Oldenburg (2004) ArticleTitle‘Inversion of 3D Electromagnetic Data in Frequency and Time Domain Using an Inexact All-at-Once Approach’ Geophysics 69 1216–1228 Occurrence Handle10.1190/1.1801938

    Article  Google Scholar 

  • E. Haber (2005) ArticleTitle‘Quasi–Newton Methods for Large-Scale Electromagnetic Inverse Problems’ Inv. Prob. 21 305–323 Occurrence Handle10.1088/0266-5611/21/1/019

    Article  Google Scholar 

  • Y. Hamano (2002) ArticleTitle‘A New Time-Domain Approach for the Electromagnetic Induction Problem in a Three-Dimensional Heterogeneous Earth’ Geophys. J. Int. 150 753–169 Occurrence Handle10.1046/j.1365-246X.2002.01746.x

    Article  Google Scholar 

  • M. R. Hestenes E. Stiefel (1952) ArticleTitle‘Methods of Conjugate Gradients for Solving Linear Systems’ J. Res. Nat. Bur. Stand. 49 409–436

    Google Scholar 

  • G. W. Hohmann (1975) ArticleTitle‘Three-Dimensional Induced-Polarization and Electromagnetic Modeling’ Geophysics 40 309–324 Occurrence Handle10.1190/1.1440527

    Article  Google Scholar 

  • Hohmann G. W.: 1988, ‘Numerical Modelling of Electromagnetic Methods of Geophysics’, in M. N. Nabighian (ed.), Electromagnetic methods in applied geophysics, Vol. 1, S.E.G. Investigations in geophysics 3, pp. 314–364

  • G. Hursan M. S. Zhdanov (2002) ArticleTitle‘Contraction Integral Equation Method in Three-Dimensional Modeling’ Radio Sci. 37 1089

    Google Scholar 

  • A. A. Kaufman P. A. Eaton (2001) The Theory of Inductive Prospectings, Methods in Geochemistry and Geophysics 35 Elsevier Amsterdam–NewYork–Tokyo

    Google Scholar 

  • C. T. Kelly (1999) Iterative Methods for Optimization SIAM Philadelphia

    Google Scholar 

  • T. Koyama H. Shimizu H. Utada (2002) ArticleTitle‘Possible Effects of Lateral Heterogeneity in the D’ Layer on Electromagnetic Variations of Core Origin’ Phys. Earth Planet. Interiors 129 99–116 Occurrence Handle10.1016/S0031-9201(01)00263-1

    Article  Google Scholar 

  • Kuvshinov, A. V., Avdeev, D. B., Pankratov, O. V., Golyshev, S. A., and Olsen, N.: 2002, ‘Modelling Electromagnetic Fields in 3-D Spherical Earth Using Fast Integral Equation Approach’, in M. S. Zhdanov and P. E. Wannamaker (eds.), Three Dimensional Electromagnetics, Methods in Geochemistry and Geophysics 35: Elsevier, pp. 43–54

  • A. V. Kuvshinov H. Utada D. B. Avdeev T. Koyama (2005) ArticleTitle‘3-D Modelling and Analysis of Dst C-Responses in the North Pacific Ocean Region, Revisited’ Geophys. J. Int. 160 505–526 Occurrence Handle10.1111/j.1365-246X.2005.02477.x

    Article  Google Scholar 

  • A. V. Kuvshinov N. Olsen (2004) ‘Modelling the Coast Effect of Geomagnetic Storms at Ground and Satellite Altitude’ C. Reigber H. Luhr P. Schwintzer J. Wickert (Eds) Earth Observation with CHAMP. Results from Three Years in Orbit Springer-Verlag Berlin 353–359

    Google Scholar 

  • LaBrecque, D.: 1999, ‘Finite Difference Modeling of 3-D EM Fields with Scalar and Vector Potentials’, in M. J. Oristaglio and B. R. Spies (eds.), Three Dimensional Electromagnetics, S.E.G. Geophysical Developments Series 7, pp. 148–160

  • I. E. Lager G. Mur (1998) ArticleTitle‘Generalized Cartesian finite elements’ IEEE Trans. Magn. 34 2220–2227

    Google Scholar 

  • C. Lanczos (1952) ArticleTitle‘Solution of Systems of Linear Equations by Minimized Iterations’ J. Res. Nat. Bur. Stand. 49 33–53

    Google Scholar 

  • Lesselier, D. and Habashy, T. (eds.) 2000, ‘Special Section on Electromagnetic Imaging and Inversion of the Earth’s subsurface’, Inv. Prob. 16(5) 1083–1376

    Google Scholar 

  • Lesselier, D. and Chew, W. C. (eds.): 2004, ‘Special Section on Electromagnetic Characterization of Buried Obstacles’, Inv. Prob. 20(6), S1–S256

    Google Scholar 

  • Y. Li D. W. Oldenburg (2000) ArticleTitle‘3-D Inversion of Induced Polarization Data’ Geophysics 65 1931–1945

    Google Scholar 

  • Y. Li K. Spitzer (2002) ArticleTitle‘Three-Dimensional DC Resistivity Forward Modeling Using Finite Elements in Comparison With Finite-Difference Solutions’ Geophys. J. Int. 151 924–934 Occurrence Handle10.1046/j.1365-246X.2002.01819.x

    Article  Google Scholar 

  • D. Livelybrooks (1993) ArticleTitle‘Program 3Dfeem, A Multidimensional Electromagnetic Finite Element Model’ Geophys. J. Int. 114 443–458

    Google Scholar 

  • R. L. Mackie T. R. Madden (1993) ArticleTitle‘Three-Dimensional Magnetotelluric Inversion Using Conjugate Gradients’ Geophys. J. Int. 115 215–229

    Google Scholar 

  • R. L. Mackie T. R. Madden P. Wannamaker (1993) ArticleTitle‘3-D Magnetotelluric Modeling Using Difference Equations – Theory and Comparisons to Integral Equation Solutions’ Geophysics 58 215–226

    Google Scholar 

  • R. L. Mackie T. J. Smith T. R. Madden (1994) ArticleTitle‘3-D Electromagnetic Modeling Using Difference Equations, The Magnetotelluric Example’ Radio Sci. 29 923–935 Occurrence Handle10.1029/94RS00326

    Article  Google Scholar 

  • Mackie, R.L., Rodi, W., and Watts, M.D.: 2001, ‘3-D Magnetotelluric Inversion for Resource Exploration, in 71st Ann. Internat. Mtg., Soc. Expl. Geophys., pp. 1501–1504

  • Mackie, R.L.: 2004, Private communication

  • Macnae, J. and Liu, G. (eds.): 2003, Three Dimensional Electromagnetics III, Austr. Soc. Expl. Geophys

  • T. R. Madden R. L. Mackie (1989) ArticleTitle‘Three-Dimensional Magnetotelluric Modeling and Inversion’ Proc. IEEE 77 318–333 Occurrence Handle10.1109/5.18628

    Article  Google Scholar 

  • Z. Martinec (1999) ArticleTitle‘Spectral-Finite Element Approach to Three-Dimensional Electromagnetic Induction in a Spherical Earth’ Geophys. J. Int. 136 229–250 Occurrence Handle10.1046/j.1365-246X.1999.00713.x

    Article  Google Scholar 

  • P. R. McGillivray D. W. Oldenburg (1990) ArticleTitle‘Methods for Calculating Frechet Derivatives and Sensitivities for the Non-Linear Inverse Problems’ Geophysics 60 899–911

    Google Scholar 

  • D. McKirdy J. T. Weaver T. W. Dawson (1985) ArticleTitle‘Induction in a Thin Sheet of Variable Conductance at the Surface of a Stratified Earth- II. Three-dimensional theory’ Geophys. Roy. Astr. Soc. 80 177–194

    Google Scholar 

  • Y. Mitsuhata T. Uchida H. Amano (2002) ArticleTitle‘2.5-D Inversion of Frequency-Domain Electromagnetic Data Generated by a Grounded-Wire Source’ Geophysics 67 1753–1768 Occurrence Handle10.1190/1.1527076

    Article  Google Scholar 

  • Y. Mitsuhata T. Uchida (2004) ArticleTitle‘3D Magnetotelluric Modeling Using the T-Ω Document Finite-Element Method’ Geophysics 69 108–119 Occurrence Handle10.1190/1.1649380

    Article  Google Scholar 

  • G. A. Newman G. W. Hohmann (1988) ArticleTitle‘Transient Electromagnetic Response of High-Contrast Prisms in a Layered Earth’ Geophysics 53 691–706 Occurrence Handle10.1190/1.1442503

    Article  Google Scholar 

  • G. A. Newman D. L. Alumbaugh (1995) ArticleTitle‘Frequency-Domain Modeling of Airborne Electromagnetic Responses Using Staggered Finite Differences’ Geophys. Prosp. 43 1021–1042

    Google Scholar 

  • G. A. Newman D. L. Alumbaugh (1997) ArticleTitle‘Three-Dimensional Massively Parallel Electromagnetic Inversion- I.’ Theory, Geophys. J. Int. 128 345–354

    Google Scholar 

  • G. A. Newman D. L. Alumbaugh (2000) ArticleTitle‘Three-Dimensional Magnetotelluric Inversion Using Non-Linear Conjugate Gradients’ Geophys. J. Int. 140 410–424 Occurrence Handle10.1046/j.1365-246x.2000.00007.x

    Article  Google Scholar 

  • G. A. Newman G. M. Hoversten (2000) ArticleTitle‘Solution Strategies for 2D and 3D EM Inverse Problem’ Inv. Prob. 16 1357–1375 Occurrence Handle10.1088/0266-5611/16/5/314

    Article  Google Scholar 

  • Newman, G. A., Hoversten, G. M., and Alumbaugh, D. L.: 2002, ‘3D Magnetotelluric Modeling and Inversion, Applications to Sub-Salt Imaging’, in M.S. Zhdanov and P.E. Wannamaker (eds.), Three Dimensional Electromagnetics, Methods in Geochemistry and Geophysics 35, Elsevier, pp. 127–152

  • G. A. Newman D. L. Alumbaugh (2002) ArticleTitle‘Three-Dimensional Induction Logging Problems. Part I. An Integral Equation Solution and Model Comparisons’ Geophysics 67 484–491 Occurrence Handle10.1190/1.1468608

    Article  Google Scholar 

  • G. A. Newman S. Recher B. Tezkan F. M. Neubauer (2003) ArticleTitle‘3D Inversion of a Scalar Radio Magnetotelluric Field Data Set’ Geophysics 68 791–802 Occurrence Handle10.1190/1.1581032

    Article  Google Scholar 

  • G. A. Newman P. T. Boggs (2004) ArticleTitle‘Solution Accelerators for Large-Scale Three-Dimensional Electromagnetic Inverse Problem’ Inv. Prob. 20 s151–s170 Occurrence Handle10.1088/0266-5611/20/6/S10

    Article  Google Scholar 

  • G. A. Newman M. Commer (2005) ArticleTitle‘New Advances in Three-Dimensional Transient Electromagnetic Inversion’ Geophys. J. Int. 160 5–32 Occurrence Handle10.1111/j.1365-246X.2004.02468.x

    Article  Google Scholar 

  • J. Nocedal S. Wright (1999) Numerical Optimization Springer-Verlag New York

    Google Scholar 

  • O’Leary, D. P.: 1996, ‘Conjugate Gradients and Related KMP Algorithms, the Beginnings’, in L. Adams and J.L. Nazareth (eds.), Linear and Nonlinear Conjugate Gradient-Related Methods, SIAM, pp. 1–9

  • Oristaglio, M. J. and Spies, B.R.: 1999, ‘Three Dimensional Electromagnetics’, in M. J. Oristaglio and B. R. Spies (eds.), Three Dimensional Electromagnetics, S.E.G. Geophysical Developments Series 7

  • C. C. Paige M. A. Sounders (1974) ArticleTitle‘Solution of Sparse Indefinite Systems of Linear Equations’ SIAM J. Numer. Anal. 11 197–209 Occurrence Handle10.1137/0711019

    Article  Google Scholar 

  • O. V. Pankratov D. B. Avdeev A. V. Kuvshinov (1995) ArticleTitle‘Electromagnetic Field Scattering in a Heterogeneous Earth, A Solution to the Forward Problem’ Phys. Solid Earth 31 201–209

    Google Scholar 

  • O. V. Pankratov A. V. Kuvshinov D. B. Avdeev (1997) ArticleTitle‘High-Performance Three-Dimensional Electromagnetic Modeling Using Modified Neumann series. Anisotropic case’ J. Geomagn. Geoelectr. 49 1541–1547

    Google Scholar 

  • K. D. Paulsen D. R. Linch J. W. Strohbehn (1988) ArticleTitle‘Three-dimensional finite, boundary, and hybrid element solutions of the Maxwell equations for lossy dielectric media’ IEEE Trans. Microwave Theory Tech. 36 682–693

    Google Scholar 

  • E. Polak G. Ribiere (1969) ArticleTitle‘Note sur la convergence de methode de directions conjuguees’ Revue Francaise d’Informatique et de Recherche Operationnelle 16 35–43

    Google Scholar 

  • O. Portniaguine M. S. Zhdanov (1999) ArticleTitle‘Focusing Geophysical Inversion Images’ Geophysics 64 874–887 Occurrence Handle10.1190/1.1444596

    Article  Google Scholar 

  • D. F. Pridmore G. W. Hohmann S. H. Ward W. R. Still (1981) ArticleTitle‘An Investigation of Finite-Element Modeling For Electrical and Electromagnetic Data in Three Dimensions’ Geophysics 46 1009–1024 Occurrence Handle10.1190/1.1441239

    Article  Google Scholar 

  • A. Raiche (1974) ArticleTitle‘An Integral Equation Approach to Three-Dimensional Modeling’ Geophys. J. 36 363–376

    Google Scholar 

  • Ratz, S.: 1999, ‘A 3D Finite Element Code for Modeling of Electromagnetic Responses, in Expanded abstracts of the 2nd International Symposium on 3D Electromagnetics, Salt Lake City, Utah, pp.33–36

  • I. K. Reddy D. Rankin R. J. Phillips (1977) ArticleTitle‘Three-dimensional modelling in magnetotelluric and magnetic variational sounding’ Geophys. J. Roy. Astr. Soc. 51 313–325

    Google Scholar 

  • W. Rodi R. L. Mackie (2000) ArticleTitle‘Nonlinear conjugate gradients algorithm for 2-D magnetotelluric inversion’ Geophysics 66 174–187

    Google Scholar 

  • V. G Romanov S. I. Kabanikhin (1994) Inverse Problems for Maxwell’s Equations VSP Utrecht

    Google Scholar 

  • Y. Saad M. H. Schultz (1986) ArticleTitle‘GMRES, A Generalized Minimal Residual Algorithm for Nonsymmetric Linear Systems’ SIAM J. Sci. Stat. Comput. 7 856–869 Occurrence Handle10.1137/0907058

    Article  Google Scholar 

  • Y. Sasaki (2001) ArticleTitle‘Full 3-D Inversion of Electromagnetic Data on PC’ J. Appl. Geophys. 46 45–54 Occurrence Handle10.1016/S0926-9851(00)00038-0

    Article  Google Scholar 

  • Y. Sasaki (2004) ArticleTitle‘Three-Dimensional Inversion of Static-Shifted Magnetotelluric Data’ Earth Planets Space 56 239–248

    Google Scholar 

  • Schultz, A. and Pritchard, G.: 1999, Three-Dimensional Inversion for Large-Scale Structure in a Spherical Domain’, in M. J. Oristaglio and B. R. Spies (eds.), Three Dimensional Electromagnetics, S.E.G. Geophysical Developments Series 7, pp. 451–476

  • B. Sh. Singer E. B. Fainberg (1985) Electromagnetic Induction in Non-uniform Thin Layers IZMIRAN Moscow (in Russian)

    Google Scholar 

  • B. Sh. Singer (1995) ArticleTitle‘Method for Solution of Maxwell’s Equations in Non-Uniform Media’ Geophys. J. Int. 120 590–598

    Google Scholar 

  • B. Sh. Singer E. B. Fainberg (1995) ArticleTitle‘Generalization of the Iterative-Dissipative Method for Modeling Electromagnetic Fields in Nonuniform Media with Displacement Currents’ J. Appl. Geophys. 34 41–46 Occurrence Handle10.1016/0926-9851(95)00002-J

    Article  Google Scholar 

  • Sh. B. Singer E. B. Fainberg (1997) ArticleTitle‘Fast and Stable Method for 3-D Modelling of Electromagnetic Field’ Explor. Geophys. 28 130–135

    Google Scholar 

  • Singer, B. Sh., Mezzatesta, A., and Wang, T.: 2003, Integral equation approach based on contraction operators and Krylov subspace optimisation, in J. Macnae and G. Liu (eds.), Three Dimensional Electromagnetics III, Austr. Soc. Expl. Geophys

  • W. Siripunvaraporn M. Uyeshima G. Egbert (2004a) ArticleTitle‘Three-Dimensional Inversion for Network-Magnetotelluric Data’ Earth Planets Space 56 893–902

    Google Scholar 

  • W. Siripunvaraporn G. Egbert Y. Lenbury M. Uyeshima (2004b) ArticleTitle‘Three-Dimensional Magnetotelluric Inversion: Data Space Method’ Phys. Earth Planet. Inter. 150 3–14

    Google Scholar 

  • J. T. Smith J. R. Booker (1991) ArticleTitle‘Rapid Inversion of Two- and Three-Dimensional Magnetotelluric Data’ J. Geophys. Res. 96 IssueIDB3 3905–3922 Occurrence Handle10.1029/90JB02416

    Article  Google Scholar 

  • J. T. Smith (1996a) ArticleTitle‘Conservative Modeling of 3-D Electromagnetic Fields, Part I, Properties and Error Analysis’ Geophysics 61 1308–1318

    Google Scholar 

  • J. T. Smith (1996b) ArticleTitle‘Conservative Modeling of 3-D Electromagnetic Fields, Part II, Biconjugate Gradient Solution and an Accelertor’ Geophysics 61 1319–1324

    Google Scholar 

  • L.-P. Song Q. H. Liu (2004) ArticleTitle‘Fast Three-Dimensional Electromagnetic Nonlinear Inversion in Layered Media with a Novel Scattering Approximation’ Inv. Prob. 20 S171–S194 Occurrence Handle10.1088/0266-5611/20/6/S11

    Article  Google Scholar 

  • Spichak, V. V.: 1983, Numerically modeling the electromagnetic fields in three-dimensional media, Ph. D. thesis, Moscow, 215 p. (in Russian)

  • V. Spichak I. Popova (2000) ArticleTitle‘Artificial Neural Network Inversion of Magnetotelluric Data in Terms of Three-Dimensional Earth Macroparameters’ Geophys. J. Int. 142 15–26 Occurrence Handle10.1046/j.1365-246x.2000.00065.x

    Article  Google Scholar 

  • Sugeng, F., Raiche, A. and Xiong, Z.: 1999, ‘An Edge-Element Approach to Model the 3D EM Response of Complex Structures with High Contrasts’, in Expanded abstracts of the 2nd International Symposium on 3D Electromagnetics, Salt Lake City, Utah, pp. 25–28

  • L. A. Tabarovsky (1975) Application of Integral Equation Method to Geoelectrical Problems Novosibirsk Nauka (in Russian)

    Google Scholar 

  • Tamarchenko, T., Frenkel, M., and Mezzatesta, A.: 1999, Three-dimensional modeling of microresistivity devices, in M. J. Oristaglio and B. R. Spies (eds.), Three Dimensional Electromagnetics, S.E.G. Geophysical Developments Series 7, pp. 77–83

  • A. Tarantola (1987) Inverse Problem Theory Elsevier Amsterdam–Oxford–New York–Tokyo

    Google Scholar 

  • P. Tarits (1994) ArticleTitle‘Electromagnetic Studies of Global Geodynamic Processes’ Surv. Geophys. 15 209–238 Occurrence Handle10.1007/BF00689860

    Article  Google Scholar 

  • A. N. Tikhonov V. Y. Arsenin (1977) Solutions of Ill-posed Problems Wiley New York

    Google Scholar 

  • S. C. Ting G. W. Hohmann (1981) ArticleTitle‘Integral Equation Modeling of Three-Dimensional Magnetotelluric Response’ Geophysics 46 182–197 Occurrence Handle10.1190/1.1441188

    Article  Google Scholar 

  • C. Torres-Verdin T. M. Habashy (1994) ArticleTitle‘Rapid 2.5-D Forward Modeling and Inversion Via a New Nonlinear Scattering Approximation’ Radio Sci. 29 1051–1079

    Google Scholar 

  • C. Torres-Verdin T. M. Habashy (2002) ArticleTitle‘Rapid Numerical Simulations of Axisymmetric Single-well Induction Data Using the Extended Born Approximation’ Radio Sci. 36 1287–1306

    Google Scholar 

  • H. -W. Tseng K. H. Lee A. Becker (2003) ArticleTitle‘3-D Interpretation of Electromagnetic Data Using a Modified Extended Born Approximation’ Geophysics 68 127–137 Occurrence Handle10.1190/1.1543200

    Article  Google Scholar 

  • M. Uyeshima A. Schultz (2000) ArticleTitle‘Geoelectromagnetic Induction in a Heterogeneous Sphere, A New 3-D Forward Solver Using a Staggered-Grid Integral Formulation’ Geophys. J. Int. 140 636–650 Occurrence Handle10.1046/j.1365-246X.2000.00051.x

    Article  Google Scholar 

  • Uchida, T. and Sasaki, Y.: 2003, Stable 3-D Inversion of MT Data and Its Application for Geothermal Exploration, in J. Macnae and G. Liu (eds.), Three Dimensional Electromagnetics III, Austr. Soc. Expl. Geophys

  • Varentsov, Iv. M.: 1999, ‘The Selection of Effective Finite Difference Solvers in 3D Electromagnetic Modeling’, in Expanded Abstracts of 2nd International Symposium on 3D Electromagnetics, Salt Lake City, Utah

  • Varentsov, Iv. M.: 2002, ‘A General Approach to the Magnetotelluric Data Inversion in a Piece-Continuous Medium’ Fizika Zemli 11 (in Russian)

  • G. Vasseur P. Weidelt (1977) ArticleTitle‘Bimodal Electromagnetic Induction in Non-Uniform Thin Sheets with Application to the Northern Pyrenean Induction Anomaly’ Geophys. J. R. Astr. Soc. 51 669–690

    Google Scholar 

  • Velimsky, J., Everett, M. E., and Martinec, Z.: 2003, ‘The Transient Dst Electromagnetic Induction Signal at Satellite Altitudes for a Realistic 3-D Electrical Conductivity in the Crust and Mantle, Geophys. Res. Letts. 30(7), doi,10.1029/2002GL016671

  • T. Wang G. W. Hohmann (1993) ArticleTitle‘A Finite-Difference Time-Domain Solution for Three-Dimensional Electromagnetic Modeling’ Geophysics 58 797–809 Occurrence Handle10.1190/1.1443465

    Article  Google Scholar 

  • T. Wang M. Oristaglio A. Tripp G. W. Hohmann (1994) ArticleTitle‘Inversion of Diffusive Transient Electromagnetic Data by a Conjugate Gradient Method’ Radio Sci. 29 1143–1156

    Google Scholar 

  • T. Wang A. Tripp (1996) ArticleTitle‘FDTD Simulation of EM Wave Propagation in 3-D Media’ Geophysics 61 110–120

    Google Scholar 

  • T. Wang S. Fang (2001) ArticleTitle‘3D Electromagnetic Anisotropy Modeling Using Finite Differences’ Geophysics 66 1386–1398

    Google Scholar 

  • P. E. Wannamaker G. W. Hohmann W. A. San Filipo (1984) ArticleTitle‘Electromagnetic Modeling of Three-Dimensional Bodies in Layered Earth Using Integral Equations’ Geophysics 49 60–74

    Google Scholar 

  • P. E. Wannamaker (1991) ArticleTitle‘Advances in Three-Dimensional Magnetotelluric Modeling Using Integral Equations’ Geophysics 56 1716–1728

    Google Scholar 

  • J. T. Weaver (1994) Mathematical Methods for Geo-electromagnetic Induction John Wiley and Sons Taunton, UK

    Google Scholar 

  • Weaver, J. T., Agarwal, A. K. and Pu, X. H.: 1999, ‘Three-Dimensional Finite-Difference Modeling of the Magnetic Field in Geo-Electromagnetic Induction’, in M. J. Oristaglio and B. R. Spies (eds.), Three Dimensional Electromagnetics, S.E.G. Geophysical Developments Series 7, pp. 426–443

  • P. Weidelt (1975) ArticleTitle‘Electromagnetic Induction in 3D Structures’ J. Geophys. 41 85–109

    Google Scholar 

  • Weidelt, P.: 1999, 3D conductivity models, Implications of electrical anisotropy, in M. J. Oristaglio and B. R. Spies (eds.), Three Dimensional Electromagnetics, S.E.G. Geophysical Developments Series 7, pp. 119–137

  • Ch. J. Weiss M. E. Everett (1998) ArticleTitle‘Geomagnetic Induction in a Heterogeneous Sphere, Fully Three-Dimensional Test Computation and the Response of a Realistic Distribution of Oceans and Continents’ Geophys. J. Int. 135 650–662 Occurrence Handle10.1046/j.1365-246X.1998.00670.x

    Article  Google Scholar 

  • Ch. J. Weiss G. A. Newman (2002) ArticleTitle‘Electromagnetic Induction in a Fully 3-D Anisotropic Earth’ Geophysics 67 1104–1114 Occurrence Handle10.1190/1.1500371

    Article  Google Scholar 

  • Ch. J. Weiss G. A. Newman (2003) ArticleTitle‘Electromagnetic Induction in a Fully 3-D Anisotropic Earth, Part 2, The LIN Preconditioner’ Geophysics 68 922–930 Occurrence Handle10.1190/1.1581044

    Article  Google Scholar 

  • Z. Xiong (1992) ArticleTitle‘EM Modeling Three-Dimensional Structures by the Method of System Iteration Using Integral Equations’ Geophysics 57 1556–1561

    Google Scholar 

  • Z. Xiong A. C. Tripp (1995) ArticleTitle‘Electromagnetic Scattering of Large Structures in Layered Earth Using Integral Equations’ Radio Sci. 30 921–929 Occurrence Handle10.1029/95RS00833

    Article  Google Scholar 

  • Z. Xiong A. Raiche F. Sugeng (2000) ArticleTitle‘Efficient Solution of Full Domain 3D Electromagnetic Modeling Problems’ Explor. Geophys. 31 158–161

    Google Scholar 

  • K. Yamane H. J. Kim Y. Ashida (2000) ArticleTitle‘Three-Dimensional Magnetotelluric Inversion Using a Generalized RRI Method and Its Applications’ Butsuri-Tansa (Geophys. Explor.) 53 1501–1513

    Google Scholar 

  • K. S. Yee (1966) ArticleTitle‘Numerical Solution of Initial Boundary Value Problems Involving Maxwell’s Equations in Isotropic Media’ IEEE Trans. Ant. Prop. AP-14 302–307

    Google Scholar 

  • Yoshimura, R. and Oshiman, N.: 2002, Edge-based Finite Element Approach to the Simulation of Geoelectromagnetic Induction in a 3-D sphere, Geophys. Res. Letts. 29(3), doi,10.1029/2001GL014121

  • Z. Zhang (2003) ArticleTitle‘3D Resistivity Mapping of Airborne EM Data’ Geophysics 68 1896–1905

    Google Scholar 

  • M. S. Zhdanov S. Fang (1996) ArticleTitle‘Quasi-Linear Approximation in 3-D EM Modeling’ Geophysics 61 646–665

    Google Scholar 

  • M. S. Zhdanov S. Fang (1997) ArticleTitle‘Quasi-Linear Series in Three-Dimensional Electromagnetic Modeling’ Radio Sci. 32 2167–2188 Occurrence Handle10.1029/97RS02284

    Article  Google Scholar 

  • M. S. Zhdanov O. Portniaguine (1997) ArticleTitle‘Time-Domain Electromagnetic Migration in the Solution of Inverse Problems’ Geophys. J. Int. 131 293–309

    Google Scholar 

  • Zhdanov, M. S., Varentsov, I. M., Weaver, J. T., Golubev, N. G., and Krylov, V. A.: 1997, ‘Methods for Modelling Electromagnetic Fields; Results from COMMEMI – the International Project On the Comparison of Modelling Methods for Electromagnetic Induction’, in J. T. Weaver (ed.), J. Appl. Geophys. 37, 133–271

  • M. S. Zhdanov S. Fang G. Hursan (2000) ArticleTitle‘Electromagnetic Inversion using Quasi-Linear Approximation’ Geophysics 65 1501–1513

    Google Scholar 

  • M. S. Zhdanov (2002) Geophysical Inverse Theory and Regularization problems Elsevier Amsterdam-New York-Tokyo

    Google Scholar 

  • Zhdanov, M. S. and Wannamaker, P. E.: 2002, ‘Three Dimensional Electromagnetics’, in M. S. Zhdanov and P. E. Wannamaker (eds.), Three Dimensional Electromagnetics, Methods in Geochemistry and Geophysics 35, Elsevier

  • Zhdanov, M. S. and Golubev, N. G.: 2003, ‘Three-Dimensional Inversion of Magnetotelluric Data in Complex Geological Structures’, in J. Macnae and G. Liu (eds.), Three Dimensional Electromagnetics III, Austr. Soc. Expl. Geophys

  • M. S. Zhdanov E. Tolstaya (2004) ArticleTitle‘Minimum Support Nonlinear Parametrization in the Solution of a 3D Magnetotelluric Inverse Problem’ Inv. Prob. 20 937–952 Occurrence Handle10.1088/0266-5611/20/3/017

    Article  Google Scholar 

  • M. R. Zunoubi J. -M. Jin K. C. Donepudi W. C. Chew (1999) ArticleTitle‘A Spectral Lanczos Decomposition Method for Solving 3-D Low-Frequency Electromagnetic Diffusion by the Finite-Element Method’ IEEE Trans. Antennas Propogat. 47 242–248

    Google Scholar 

  • F. I. Zyserman J. E. Santos (2000) ArticleTitle‘Parallel Finite Element Algorithm with Domain Decomposition for Three-Dimensional Magnetotelluric Modeling’ J. Appl. Geophys. 44 337–351 Occurrence Handle10.1016/S0926-9851(00)00012-4

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Russian Academy of Sciences, Institute of Terrestrial Magnetism, Ionosphere and Radiowave Propagation, 142190, Troitsk, Moscow region, Russia

    Dmitry B. Avdeev

  2. Dublin Institute for Advanced Studies, School of Cosmic Physics, 5 Merrion Square, Dublin 2, Ireland

    Dmitry B. Avdeev

Authors
  1. Dmitry B. Avdeev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dmitry B. Avdeev.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Avdeev, D.B. Three-Dimensional Electromagnetic Modelling and Inversion from Theory to Application. Surv Geophys 26, 767–799 (2005). https://doi.org/10.1007/s10712-005-1836-x

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10712-005-1836-x

Keywords

Search

Navigation