The Calculation of Geophysical Induction Effects Using Surface Integrals

Abstract

Summary Two iterative methods, originally proposed by Price, for calculating electromagnetic induction effects in thin non-uniformly conducting sheets, are here extended to include mutual induction effects when a second conductor is present. The applicability of either method in a given problem depends on the resistivity of the conductors, and on the variation of the inducing field, and conditions for convergence are given. At each stage of the iteration, relations are required between the field components and streamline functions for the induced current systems. These relations have been expressed in surface integral form in a previous paper, in place of the usual spherical harmonic expansions, and it is shown that the integrals may be evaluated accurately. An indication of the accuracy of the iteration process is obtained by applying the method to a problem for which an analytic solution is known. As a preliminary to the study of induction in the oceans, the method is then applied to the problem of electromagnetic induction in a hemispherical shell, representing the Pacific Ocean, surrounding a concentric perfectly conducting sphere.