Analytical computation of EM field components in a uniform half-space

Abstract

Analytical expressions for the electromagnetic field components at an arbitrary location in a half-space are presented for a vertical magnetic dipole source on the surface of the Earth. The Hankel transforms required in the computation are enumerated using expressions based on the modified Bessel functions of the first and second kind. For surface electromagnetic fields, the Bessel function expressions are shown to consistently produce results that are up to four orders of magnitude more accurate than the results commonly obtained using digital filters. In addition, initial speed tests reveal that considerable computational time is saved compared with the use of numerical routines based on digital filters. It is expected that the increased speed and accuracy of the analytical solution will find application in forward modelling and inversion routines where a half-space is considered to be a suitable model and Hankel transforms need to evaluated many times.