A SEMI‐DIRECT METHOD OF INTERPRETING RESISTIVITY OBSERVATIONS*

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Abstract
In this paper a method of interpreting resistivity observations is proposed which consists of two steps. The first of these steps is to approximate the observed resistivity curve by a sum of two‐layer resistivity curves—which are asymptotic to the observed curve—decreased by a constant value. Experience shows that this approximation usually can be made to be reasonably close. In cases where the residue is too large to be neglected, this residue can be accounted for by the addition of the effect of a pair of fictitious current poles of equal and opposite strength.The approximation by asymptotic two‐layer curves could then be translated either into a distribution of fictitious current poles on the vertical through the current electrode, or into the kernel function in the integral expression for the apparent resistivity. Experience shows, however, that the distribution of fictitious poles derived from the approximation by asymptotic two‐layer curves, may deviate very strongly from the actual distribution of image poles. The error in the kernel function, on the other hand, is shown to be of the same order of magnitude as the relative error in the apparent resistivity. The kernel function is therefore used in the proposed method as an intermediary for determining the resistivity stratification.From the approximated kernel function some information can be obtained directly on the resistivity stratification in the subsurface. This information, however, is sometimes incomplete and often not very accurate. The step from the approximated kernel function to the resistivity stratification is therefore essentially indirect, i.e. the approximated kernel function is compared with kernel functions computed for different resistivity stratifications. The advantage of this method over comparison of the observed resistivity curve itself with theoretical resistivity curves is that the computation of the kernel function, starting from the resistivity stratification, can be done far more quickly than that of the resistivity curve. The kernel function for any number of resistivity layers is a quotient, of which both thé numerator and the denominator contain only terms which, when plotted on monologarithmic graph paper, are straight lines. This property of the kernel function makes it possible to compute e.g. the kernel function for a three‐layer case in about a quarter of an hour.