DIRECT METHODS OF INTERPRETING RESISTIVITY OBSERVATIONS*

Publisher Website
Google Scholar
Abstract
In this paper direct interpretation methods of resistivity observations are discussed, which use the kernel function in the integral expression for the potential as an intermediary step. This kernel function can be expressed in the form of an integral expression, involving in the integrand a Bessel function and the apparent resistivity. This expression is the basis for the determination of the kernel function from the apparent resistivity curve. The integral can be determined directly; this method of computation, however, although practically feasible, is rather time consuming. Another method of computation is to approximate to the resistivity curve by a sum of a small number of two‐layer curves which are asymptotic to the observed resistivity curve. This method, which was described in a previous paper by the present author, is briefly restated. A more general method is to approximate to the observed resistivity curve by a sum of functions of other types; the choice of such functions is only restricted by the requirement that the contribution to the kernel function corresponding to them should be easily computable. Two different types of functions, that satisfy this condition, are discussed. The standard curves required for the application of the method are presented. An example of application of the method is given.The problem of determining the resistivity stratification from the kernel function has been solved by Pekeris in 1940. The method of Pekeris is briefly restated.