ELECTROMAGNETIC SCATTERING FROM CYLINDERS OF ARBITRARY CROSS‐SECTION IN A CONDUCTIVE HALF‐SPACE

Abstract

A general numerical technique is presented for solving the problem of electromagnetic scattering by conducting cylinders of arbitrary cross‐section located in a conductive half‐space. Solutions to the electromagnetic wave equation are required for the free space above the half‐space, for the half‐space surrounding the cylinder, and for the cylinder. The problem is formulated by choosing an integral representation for the electromagnetic fields in each of the three homogeneous regions. By enforcing the boundary conditions on tangential E and H, we obtain a set of coupled integral equations which can be solved numerically for the unknown equivalent surface current densities on the interface bounding each homogeneous region. Once these current densities have been estimated, the fields can be calculated at any point from the general integral representations. The following conclusions are among those of importance to AFMAG and VLF surveys: 1) the ratio of Re (H) to Im (H) is a function of traverse position and of ground conductivity, as well as of cylinder conductivity and of survey frequency; 2) in no case was a zero phase observed, even for perfectly conducting cylinders; and 3) reverse crossovers in Im (H) can occur in the field scattered by a single conductor whenever the radius of curvature on the upper portion of a “poor” conductor is small.