QUASI‐ANALYTIC CONVOLUTION SOLUTION OF THE ELECTROMAGNETIC FIELD *

A bstract The objective of this study is to generate the separation‐distance‐domain ( r ‐domain) transformation of the theoretically calculated wave number domain ( m ‐domain) electromagnetic induction field component B z ( m , ω ) of a stratified medium and to search for interpretive information which has been absent in the previously achieved numerical solutions of the problem. The r ‐domain kernel R̃ ( r , ω ) function defining the induction field appears to adequately reflect the layering and electrical properties of the medium if it is expressed as a function of the frequency if the source‐receiver separation r is small with respect to the thickness of the first layer. However, exact values of the conductivity cannot be distinguished from those of the neighboring values unless a resistive basement layer is present. This feature is the result of the truncation in series representation of the kernel function R̃ ( m , ω ). However, this truncation is regarded as significant in the case of a conductive first layer. In m ‐domain static‐zone studies, a conductive first layer slightly influences its r ‐domain correspondent. Although the computational cost of obtaining the kernel B ( r , ω ) by evaluation of the convolution in a cylindrical coordinate system is high, this semi‐analytic solution is still superior to those based on the asymptotic assumptions.