Analysis of equivalence for the Schlumberger resistivity methods using the RHO-R and RHO-C curves in the resistivity transform domain

Abstract

The problem of equivalence in the resistivity methods is studied in the resistivity transform domain. The RHO-R and RHO-C curves, which are, respectively, determined by the transverse resistance and longitudinal conductance, are shown to define the asymptotes of the resistivity transform curve. Models which give almost identical asymptotes also give almost identical resistivity transform curves. Thus, equivalent models can be found by obtaining models which do not change the shape of these asymptotes. For a given layered model, a plot of the RHO-R, RHO-C, and resistivity transform curves graphically shows the range of equivalence of the model. Equivalent models can be obtained by changing either resistivity, thickness, or depth of the given model through a simple graphical procedure.