Diffusion of electromagnetic fields into the earth from a line source of current

Abstract

The popularity of time‐domain electromagnetic (EM) systems in geophysical exploration has stimulated much interest in transient solutions of Maxwell’s equations. Although the fields at the surface of the earth are of the most practical value, the patterns of current flow in the ground can also be very enlightening, as demonstrated by Nabighian (1979) who showed the development and diffusion of the now famous “smoke ring” of current in the earth after shut‐off of a steady current in a loop at the surface. Nabighian’s result, which is based on Weaver’s (1970) general theory of EM induction in a half‐space, is an approximate image solution involving a single current filament; however, calculation of the full solution by numerical integration of the appropriate Hankel transforms showed that the real currents in the earth follow a similar smoke‐ring pattern (Nabighian, 1979; Lewis and Lee, 1978). Since the two‐dimensional (2-D) approximation is often used in solving EM scattering problems, it is interesting to consider the currents generated by a line source at the surface of a half‐space.