Direct analysis of resistivity kernel function over a two layer Earth with a transitional boundary

Abstract

The problem of resistivity stratification for a layered Earth model with transitional boundary is discussed theoretically in the present work. It makes use of Kernel function in the integral expression (Stefanesco and Schlumberger 1930) for potential for a stratified earth. The Kernel functions are evaluated for two types of conductivity inhomogeneity in the transition layer, using a new matrix method (Upadhyay and Sri Niwas 1971). The analysis of Kernel function is performed by Pekeris (1940) method. The relevant results are : (i) The kernel functions for a sharp and a transition boundary possess similar pattern of variation; (ii) The analysis of the kernel curve for a sharp boundary gives a closely true picture of resistivity stratification. In the case of transitional boundary, the analysis does not reveal the actual presence of continuous conductivity variation. On the other hand, one is led to interpret the transition boundary as made up of two homogeneous layers. The analysis presented herein is restricted to the theoretical study of kernel function for transitional boundary and the determination of resistivity stratification, starting from the integral expression for the potential.