1887
ASEG2007 - 19th Geophysical Conference
  • ISSN: 2202-0586
  • E-ISSN:

Abstract

Summary

The objective of this paper is to seek a generalized understanding for the influence of incorporating the gradient of the model’s physical properties (e.g., conductivity, velocity) in the forward modelling numerical algorithm. In order to take a step towards that, we examine an example from Geophysics for solving 3-D Maxwell’s equations using finite difference (FD) methods. The 3-D FD methods to obtain discrete solutions of Maxwell’s equations include the staggeredgrid and balance methods. The balance method 3-D algorithm exploits the conductivity gradient in order to make the FD formulation a seven-point scheme and the resulting matrix a banded septa block diagonal but not symmetric. The staggered grid algorithm is free of conductivity gradient and results in a symmetric 13-diagonal banded matrix. The objective now is to examine and understand better the influence of the conductivity gradient incorporated in the FD equations on the accuracy of the electromagnetic (EM) modelling for two 3-D benchmark models. We use three various discretizations (fine, mildly coarse, and coarse) for each model. The modelling results of each discretization have been computed separately by the balance method and staggered grid method. We have found that the staggered grid method produces accurate results for all the three discretizations investigated. However, the balance method encountered some inaccuracies for the mildly coarse and coarse discretizations. This appears to be due to the presence of the conductivity gradient in the 3-D modelling algorithm. The model studies also suggest that the thicknesses of the horizontal and vertical discretizations at the conductivity boundaries should be about 1/25 and 1/100 skin depth to maintain accurate modelling results when the conductivity derivatives exist in the 3-D modelling algorithm.

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2007-12-01
2026-01-13

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References

  1. Avdeev, D. B., 2005, Three-dimensional electromagnetic modelling and inversion from theory to application: Surveys in Geophysics, 26, DOI 10.1007/s10712-005-1836-2.
  2. Balay, S., W. D. Gropp, L. C. McInnes, and B. F. Smith, 2000, PETSc 2.0 users manual (ANL-95/11-Revision 2.0.28), Argonne Natl. Lab, Chicago.
  3. Chen, P. F., and P.C.W. Fung, 1989, A mesh convergence test for the finite difference method in three-dimensional electromagnetic modelling: Chinese Journal of Geophysics, 32, 4, 569-573.
  4. Fomenko, E., and T. Mogi, 2002, A new computation method for a staggered grid of 3D EM field conservative modeling: Earth Planets Space, 54, 499-509.
  5. Haber, E., U. M. Ascher, D. A. Aruliah, and D. W. Oldenburg, 2000, Fast simulation of 3D electromagnetic problems using potentials: Journal of Computational Physics, 163, 150-171.
  6. Hohmann, G. W., 1983, Three-dimensional EM modelling: Geophysical Surveys, 6, 27-53.
  7. Hohmann, G. W., 1987, Numerical modeling for electromagnetic methods of geophysics, in\textit{Electromagnetic Methods in Applied Geophysics}, Volume 1: Theory, edited by M. N. Nabighian, pp. 314-363, Society of Exploration Geophysicists, Tulsa, Oklahoma.
  8. Mackie, R. L., T. R. Madden and P. E. Wannamaker, 1993, Three-dimensional magnetotelluric modeling using difference equations-Theory and comparisons to integral equation solutions: Geophysics, 58, 215-226.
  9. Mackie, R. L., J. T. Smith, T. R. Madden, 1994, Threedimensional electromagnetic modeling using finite difference equations: The magnetotelluric example: Radio Science, 29, 10.1029/94RS00326.
  10. Mehanee, S., 2003, Multidimensional finite difference electromagnetic modelling and inversion based on the balance method: PhD thesis, The University of Utah, USA.
  11. Mehanee, S., and M. Zhdanov, 2004, A quasi-analytical boundary condition for three-dimensional finite difference electromagnetic modeling: Radio Science, 39, RS6014, doi:10.1029/2004RS003029.
  12. Newman, G. A., and D. L. Alumbaugh, 1995, Frequencydomain modeling of airborne electromagnetic responses using staggered finite differences: Geophysical Prospecting, 43, 1021-1042.
  13. Lines, L. R., and F. W. Jones, 1973, The perturbation of alternating geomagnetic fields by three-dimensional island structures: Geophysical Journal of the Royal Astronomical Society, 32, 133-154.
  14. Jones, F. W., and K. Vozoff, 1978, The calculation of magnetotelluric quantities for three-dimensional conductivity inhomogeneities: Geophysics, 43, 1167-1175.
  15. Saad, Y., and M. N. Schultz, 1986, GMRES: A generalized minimal residual algorithm for solving a nonsymmetric linear system: SIAM Journal on Scientific Computing, 7, 856-869.
  16. Siripunvaraporn W., G. Egbert and Y. Lenbury, 2002, Numerical Accuracy of Magnetotelluric Modeling: A Comparison of Finite Difference Approximation: Earth Planets Space, 54, 721-725.
  17. Smith, J. T., 1996, Conservative modeling of 3-D electromagnetic fields, Part I: Properties and error analysis: Geophysics, 61, 1308-1318.
  18. Smith, J. T., 1996, Conservative modeling of 3-D electromagnetic fields, Part II: Biconjugate gradient solution and an accelerator: Geophysics, 61, 1319-1324.
  19. Wang, T. and G. W. Hohmann, 1993, A finite-difference timedomain solution for three-dimensional electromagnetic modelling: Geophysics, 58, 797-809.
  20. Yee, K. S., 1966, Numerical solution of initial boundary problems involving Maxwell’s equations in isotropic media, IEEE Transactions on Antennas and Propagation, 14, 302-309.
  21. Zhdanov, M. S., N. G. Golubev, V. V. Spichak, and I. M. Varentsov, 1982, The construction of effective methods for electromagnetic modelling: Geophysical Journal of the Royal Astronomical Society, 68, 623-638.
  22. Zhdanov, M. S., 1988, Integral transforms in geophysics: Springer-Verlag, New York.
  23. Zhdanov, M. S., and V. V. Spichak 1989, Mathematical modeling of three-dimensional quasi-stationary electromagnetic fields (in Russian): Dokl, Akad, Nauk. SSSR.
  24. Zhdanov, M. S., and V. V. Spichak 1992, Mathematical modeling of electromagnetic fields in three-dimensional inhomogeneous media (in Russian): Nauka Publishing House.
  25. Zhdanov, M. S., I. M. Varentsov, J. T. Weaver, N. G. Golubev, and V. A. Krylov, 1997, Methods for modeling electromagnetic fields. Results from COMMEMI-The international project on the comparison of modeling methods for electromagnetic induction: Journal of Applied Geophysics, 37, 1.
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  • Article Type: Research Article
Keyword(s): 3-D; conductivity; EM; FD; modelling

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