1887
Volume 37 Number 3
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

Bispherical coordinates are used to derive an exact mathematical solution for the potential field generated by direct current electric conduction in an earth model consisting of two spherical inclusions in a uniform whole‐space. The solution takes the form of a spherical harmonic expansion in bispherical coordinates; coefficients in the expansion are obtained by solving sets of linear equations. Rapid forward modelling of numerous interesting situations in d.c. resistivity prospecting is facilitated by the generality and computational efficiency inherent to this new solution. For example, the accuracy of image (or superposition) methods for calculating potential solutions can be quantified. Similarly, the ability of d.c. conduction methods to resolve two distinct bounded bodies in three‐dimensional space can be examined by repeatedly calculating the secondary potential or apparent resistivity response of an earth model as a selected parameter is varied. Synthetic mise à la masse, crosshole, or areal potential data sets can be generated for subsequent use in inversion studies. Improvements in solution technique derived here also apply to a simpler model consisting of a single sphere buried in a half‐space.

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2006-04-27
2024-03-28
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References

  1. ELKINS, T.A. and HAMMER, S.1938. The resolution of combined effects, with applications to gravitational and magnetic data. Geophysics3, 315–331.
    [Google Scholar]
  2. GRANT, F.S. and WEST, G.F.1965. Interpretation Theory in Applied Geophysics. McGraw‐Hill Book Co.
    [Google Scholar]
  3. KALLWEIT, R.S. and WOOD, L.C.1982. The limits of resolution of zero‐phase wavelets. Geophysics47, 1035–1046.
    [Google Scholar]
  4. LARGE, D.B.1971. Electric potential near a spherical body in a conducting half‐space. Geophysics36, 763–767.
    [Google Scholar]
  5. LIPSKAYA, N.V.1949. The field of a point electrode observed on the earth's surface near a buried conducting sphere. Doklady Akademii Nauk SSSR, Series Geografiya i Geofizika13, 409–427.
    [Google Scholar]
  6. MERKEL, R.H. and ALEXANDER, S.S.1971. Resistivity analysis for models of a sphere in a halfspace with buried current sources. Geophysical Prospecting19, 640–651.
    [Google Scholar]
  7. RICKER, N.H.1953. Wavelet contraction, wavelet expansion, and the control of seismic resolution. Geophysics18, 769–792.
    [Google Scholar]
  8. SNYDER, D.D. and MERKEL, R.H.1973. Analytic models for the interpretation of electrical surveys using buried current electrodes. Geophysics38, 513–529.
    [Google Scholar]
  9. TELFORD, W.M., GELDART, L.P., SHERIFF, R.E. and KEYS, D.A.1976. Applied Geophysics. Cambridge University Press.
    [Google Scholar]
  10. VAN NOSTRAND, R.G.1953. Limitations on resistivity methods as inferred from the buried sphere problem. Geophysics18, 423–433.
    [Google Scholar]
  11. WYLD, H.W.1976. Mathematical Methods for Physics. W. A. Benjamin Inc.
    [Google Scholar]
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  • Article Type: Research Article

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