1887
Volume 27 Number 1
  • E-ISSN: 1365-2478

Abstract

A

A numerical technique is developed to solve the three‐dimensional potential distribution about a point source of current located in or on the surface of a half‐space containing arbitrary two‐dimensional conductivity distribution. Finite difference equations are obtained for Poisson's equations by using point‐ as well as area‐discretization of the subsurface. Potential distributions at all points in the set defining the half‐space are simultaneously obtained for multiple point sources of current injection. The solution is obtained with direct explicit matrix inversion techniques. An empirical mixed boundary condition is used at the “infinitely distant” edges of the lower half‐space. Accurate solutions using area‐discretization method are obtained with significantly less attendant computational costs than with the relaxation, finite‐element, or network solution techniques for models of comparable dimensions.

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2006-04-27
2024-04-19
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References

  1. Aiken, C. L., Hastings, D. A., and Sturgul, J. R., 1973, Physical and computer modeling of induced polarization, Geophysical Prospecting21, 763.
    [Google Scholar]
  2. Apparao, A., Roy, A., and Mallick, K., 1969, Resistivity model experiments, Geoexploration7, 45.
    [Google Scholar]
  3. Coggon, J. H., 1971, Electromagnetic and electrical modeling by the finite element method, Geophysics36, 132.
    [Google Scholar]
  4. Concus, P., and Colub, G. H., 1973, Use of fast direct methods for the efficient numerical solution of non‐separable eliptic equations, SIAM J. Numer. Anal.10, 1103.
    [Google Scholar]
  5. Dey, A., 1967, Model studies on electrical profiling over thick conducting veins, M.Sc. Thesis, Indian Institute of Technology, Kharagpur .
  6. Douglas, J.Jr., and Rachford, H. H., Jr., 1956, On the numerical solution of heat conduction problems in two or three space variables, Trans. Amer. Math. Soc.82, 421.
    [Google Scholar]
  7. Forsythe, G. E., and Wasow, W. R., 1960, Finite difference methods for partial differential equations, John Wiley and Sons, Inc., New York .
    [Google Scholar]
  8. Gunn, J. E., 1964, The numerical solution of ∇·au=f by a semi‐explicit alternating direction iterative method, Numer. Math.6, 181.
    [Google Scholar]
  9. Jepsen, A. F., 1969, Numerical modeling in resistivity prospecting, Ph.D. Thesis, University of California, Berkeley .
  10. McPharGeophysics, 1967, Catalogue of resistivity and IP model data, McPhar Geophysics Ltd., Ontario , Canada .
    [Google Scholar]
  11. Madden, T. R., 1967, Calculations of induced polarization anomalies for arbitrary two‐dimensional resistivity structure, Paper presented at Symposium on IP, University of California, Berkeley .
    [Google Scholar]
  12. Madden, T. R., 1971, The resolving power of geoelectric measurements for delineating resistive zones within the crust, Geophys. Monogr. 14, AGU, p. 95.
    [Google Scholar]
  13. Martin, R. S., and Wilkinson, J. H., 1965, Symmetric decomposition of positive definite band matrices, Numer. Math.7, 355.
    [Google Scholar]
  14. Mitchell, A. R., 1969, Computational methods in partial differential equations, John Wiley and Sons, Inc., New York .
    [Google Scholar]
  15. Peacemann, D. W., and Rachford, H. H., Jr., 1955, The numerical solution of parabolic and elliptic differential equations, Jour. of Soc. Indus. Appl. Math.3, 28.
    [Google Scholar]
  16. Southwell, R. V., 1946, Relaxation methods in theoretical physics, vol. 1, Clarendon Press, Oxford .
    [Google Scholar]
  17. Van Nostrand, R. G., and Cook, K. L., 1966, Interpretation of resistivity data, U.S.G.S. Prof. paper 499.
  18. Varga, R. S., 1962, Matrix iterative analysis, Prentice‐Hall, Englewood Cliffs , New Jersey .
    [Google Scholar]
  19. Young, D., 1954, Iterative methods for solving partial difference equations of elliptic type, Trans. Amer. Math. Soc.76, 92.
    [Google Scholar]
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  • Article Type: Research Article

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