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Volume 25 Number 4
  • E-ISSN: 1365-2478

Abstract

A

The proposed system works as follows:

  • 1  By a trial‐and‐error procedure using a graphic display terminal a geologically relevant layer sequence with parameters (ρ, ) is adjusted to yield roughly the measured curve.
  • 2  The resulting layer sequence is used as starting model for an iterative least squares procedure with singular value decomposition. Minimization of the sum of the squares of the logarithmic differences between measured and calculated values with respect to the of the resistivities and thicknesses as parameters linearizes the problem to a great extent, with two important implications:

  • a)   a considerable increase in speed (the number of iterations goes down), thus making it cheap to achieve the optimum solution;
  • b)   the confidence surfaces in parameter space are well approximated by the hyper‐ellipsoids defined by the eigenvalues and eigenvectors of the normal equations.

Since these are known from the singular value decomposition we do in fact know all possible solutions compatible with the measured curve and the geological concept.

  • 3  It is possible to “freeze” any combination of parameters at predetermined values. Thus extra knowledge and/or hypotheses are easily incorporated and can be tested by rerunning step (2). The overall computing time for a practical case is of the order of 10 sec on a CDC 6400.

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2006-04-27
2024-04-19

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