1887
Volume 28, Issue 1-2
  • ISSN: 0812-3985
  • E-ISSN: 1834-7533

Abstract

The paper discusses constrains imposed by the energy conservation law on a set of possible solutions to Maxwell’s equations. An integral equation having a contraction kernel is derived for the electromagnetic field induced by an external source in a dissipative medium. The equation can always be solved using simple iterations. The Iterative-Dissipative Method (IDM) based on this integral equation has been successfully applied to a wide range of practical 3-D problems encountered in surface and borehole electromagnetic exploration.

The approach imposes no restrictions on the frequency of the field variations, gradients of the electric conductivity or dielectric permittivity. It can also be applied to an anisotropic medium. The IDM integral equation keeps its contraction properties on a numerical grid. This makes the convergence of the iterative process practically independent of the grid parameters.

The paper presents a brief theory of the method and an example of the electromagnetic field calculation for a geoelectric model of the Australian continent and the surrounding oceanic area.

© 1997 ASEG
Loading

Article metrics loading...

/content/journals/10.1071/EG997130
1997-03-01
2026-01-19

  • From This Site

    /content/journals/10.1071/EG997130
    dcterms_title,dcterms_subject,pub_keyword
    -contentType:Journal -contentType:Contributor -contentType:Concept -contentType:Institution
    10
    5
Loading full text...

Full text loading...

References

  1. Dawson, T. W. and Weaver, J. T., 1979, Three-dimensional electromagnetic induction in a non-uniform thin sheet at the surface of a uniformly conducting Earth: Geophysical Journal of the Royal astronomical Society 59, 445-462.
  2. Druskin, V. L. and Knizhnerman, L. A., 1988, A spectral semi-discrete method for the numerical solution of 3-D nonstationary problems in electrical prospecting: Physics of the Solid Earth 24, 63-74.
  3. Fainberg, E. B. Pankratov, O. V. and Singer, B. Sh., 1993, Thin sheet modeling of subsurface and deep inhomogeneities: Geophysical Journal International 113, 144-154.
  4. Fainberg, E. B. and Singer, B. Sh., 1980, Electromagnetic induction in a nonuniform spherical model of the Earth: Annales de Geophysique 36, 127-134.
  5. Fainberg, E. B. and Singer, B. Sh., 1981, Electromagnetic induction in a spherical model of the Earth with a real distribution of near surface conductivity: Physics of the Earth and Planetary Interiors 25, 56-65.
  6. Hohmann, G. W. 1975, Three-dimensional induced polarization and electromagnetic modeling: Geophysics 40, 309-324.
  7. Kantorovich, L. V. and Akilov, G. P., 1964, Functional analysis in normed spaces: Pergamon Press.
  8. Landau, L. D. and Lifshitz, E. M, 1963, Electrodynamics of continuous media: Pergamon Press.
  9. Lee, K. H. and Morrison, H. F 1989, A new approach to modeling the electromagnetic response of conductive media: Geophysics 54, 1180-1192.
  10. Raiche, A. P., 1974, An integral equation approach to three-dimensional modelling: Geophysical Journal of the Royal astronomical Society 36, 363-376.
  11. Richtmyer, R. D 1978, Principles of advanced mathematical physics: SpringerVerlag, v. 1.
  12. Sidorov, B. A. and Fainberg, E. B., ed., 1978, Integrated longitudinal conductance of the Earth water and sedimentary cover: Nauka, 12 pp. (in Russian).
  13. Singer, B. Sh., 1995, Method for solution of Maxwell’s equations in non-uniform media: Geophysical Journal International 20, 590-598.
  14. Vasseur, G. and Weidelt, P., 1977, Bimodal electromagnetic induction in non-uniform thin sheets with application to the northern Pyrenean induction anomaly: Geophysical Journal of the Royal astronomical Society 51, 669-690.
  15. Weidelt. P., 1975, Electromagnetic induction in three-dimensional structures: Journal of Geophysics 41, 85-109.
  16. Weidelt, P., 1995, Three-dimensional conductivity models; implications of electrical anisotropy, Proceedings of the International Symposium on Three-Dimensional Electromagnetics, Schlumberger-Doll Research, Ridgefield, Connecticut, USA, 1-11.
  17. Xiong, Z., 1992, Electromagnetic modeling of 3-D structures by the method of system iterations using integral equations: Geophysics 57, 1556-1561.
  18. Zinger, B. Sh., Strack, K.-M. and Tabarovsky, L. A., 1994, Modeling of electrical effects of borehole casing inhomogeneities: Expanded Abstracts, Society of Exploration Geophysicists 64th Annual Meeting, 399-402.
/content/journals/10.1071/EG997130
Loading
  • Article Type: Research Article
Keyword(s): 3-D modelling; Australia; electromagnetic field; Iterative-Dissipative Method; ocean

Most Cited This Month Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error