Boundary Conditions and Calculation of Surface Values for the General Two‐Dimensional Electromagnetic Induction Problem

Abstract

General boundary conditions for the problem of electromagnetic induction in a two‐dimensional model of a conductor with an arbitrary sub‐surface conductivity structure are considered. Program subroutines for both E‐polarization and H‐polarization cases are given. These boundary condition subroutines can be used to replace the previously presented subroutines and allow the solution of any conductivity configuration within the conducting region by use of the same numerical technique. An example of a particular model with a sub‐surface step structure is illustrated. Also, an improved method of calculating the surface values of the tangential component of the H‐field (E‐case) and the tangential component of the E‐field (H‐case) at the surface of the conducting region is given for the numerical solution. This new method uses a derivative approximated from the true functional form of the fields instead of a linear approximation and may be applied when a layered or subsurface anomaly is modelled. Some general discussion of the numerical method is given. Copyright © 1972, Wiley Blackwell. All rights reserved