An algorithm for computation of resistivity soundings over inhomogeneous layers

Abstract

Calculation of dc resistivity sounding curves for a multilayer earth with transition layers has been treated by several authors since Mallick and Roy (1968). However, derivation of the kernel function for such problems has remained difficult for more than three‐layer models for want of a proper algorithm. The problem was first solved by Pekeris (1942) in the case of uniformly resistive layers. Other forms of recurrence relations for the kernel function of a half‐space containing such homogeneous layers were forwarded by Flathe (1955), Kunetz (1966), and Koefoed (1968). Patella (1977) considered the kernel function for a half‐space which contained a series of alternate layers, one having a linearly varying conductivity with depth while the other was homogeneously conductive. Koefoed (1979a) considered the case of a half‐space containing a transition layer situated anywhere among a series of homogeneous layers and possessing a resistivity that changed linearly with depth. In this article a very general form of algorithm is developed for generating the kernel function for a layered half‐space containing any number of transition layers having an arbitrary resistivity distribution [Formula: see text] in such ith layer. This new general form is very similar to the homogeneous form derived by Pekeris (1942).