The Inverse Problem in Geoelectrical Prospecting Assuming a Horizontally Layered Half-Space

  • E. Mundry
Part of the Progress in Scientific Computing book series (PSC, volume 2)


The Marquardt method is used for the inversion of geoelectrical measurements for a stratified half-space (determination of layer thicknesses and resistivities). Equivalent models are obtained from eigenvalue analysis of the Gaussian matrix.


Inverse Problem Apparent Resistivity Equivalent Model Ridge Regression Gaussian Matrix 


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  1. [1]
    W. Bosum: Ein automatisches Verfahren zur Interpretation magnetischer Anomalien nach der Methode der kleinsten Quadrate. Geophys. Prospecting 16, 107–126 (1968).CrossRefGoogle Scholar
  2. [2]
    S. Coen, M.W.H. Yu: The inverse problem of the direct current conductivity profile of a layered earth. Geophysics 46, 1702–1713 (1981).CrossRefGoogle Scholar
  3. [3]
    D.P. Ghosh: Inverse filter coefficients for the computation of apparent resistivity standard curves for a horizontally stratified earth. Geophys. Prospecting 19, 769–775 (1971).CrossRefGoogle Scholar
  4. [4]
    S.-E. Hjelt: Performance comparison of non-linear optimization methods applied to interpretation in magnetic prospecting. Geophysica 13, 143–166 (1975).Google Scholar
  5. [5]
    J.R. Inman: Resistivity inversion with ridge regression. Geophysics 40, 798–817 (1975).CrossRefGoogle Scholar
  6. [6]
    D.D. Jackson: Interpretation of inaccurate, insufficient and inconsistent data. Geophys. J.R. astr. Soc. 28, 970–109 (1972).Google Scholar
  7. [7]
    H.K. Johansen: A man/computer interpretation system for resistivity soundings over a horizontally stratified earth. Geophys. Prospecting 25, 667–691 (1972).CrossRefGoogle Scholar
  8. [8]
    D.L.B. Jupp, K. Vozoff: Stable iterative methods for the inversion of geophysical data. Geophys. J.R. astr. Soc. 42, 957–976 (1975).CrossRefGoogle Scholar
  9. [9]
    O. Koefoed: Geosounding Principles, 1 — Resistivity Sounding Measurements. Elsevier, Amsterdam (1979).Google Scholar
  10. [10]
    D.W. Marquardt: An algorithm for least-squares estimation of nonlinear parameters. J. Soc. indust. Appl. Math. 11, 431–441 (1963).MathSciNetMATHCrossRefGoogle Scholar
  11. [11]
    W. Müller: Inversion by simultaneous fitting of apparent resistivity and phase angle. Acta Geodaet., Geophys. et Montanist. Acad. Sci. Hung. 12, 215–222 (1977).Google Scholar
  12. [12]
    E. Mundry, U. Dennert: Das Umkehrproblem in der Geoelektrik. Geol. Jb. E 19, 19–38 (1980).Google Scholar
  13. [13]
    D.W. Oldenburg: The interpretation of direct current resistivity measurements. Geophysics 43, 610–625 (1978).CrossRefGoogle Scholar
  14. [14]
    L.B. Pedersen: Interpretation of potential field data, a generalized inverse approach. Geophys. Prospecting 25, 199–230 (1977).CrossRefGoogle Scholar
  15. [15]
    C.L. Pekeris: Direct method of interpretation in resistivity prospecting. Geophysics 5, 31–46 (1940).CrossRefGoogle Scholar
  16. [16]
    F.T. Wu: The inverse problem of magnetotelluric sounding. Geophysics 33, 972–979 (1968).CrossRefGoogle Scholar

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© Birkhäuser Boston 1983

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  • E. Mundry

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