Modelling the electromagnetic response of a sphere located in a layered earth

Estimating the electromagnetic response of a conductive sphere in a layered earth is of great interest in terms of both modelling and interpretating data acquired via geophysical electromagnetic methods where the target is at some distance from the source and receiver. This is particularly the case when using Airborne Electromagnetic Method (AEM) where the source and receiver are located at some height above the subsurface. This problem can be solved by utilising field expansions representing derivatives of cylindrical functions, which describe the fields propagating in the layered earth, and spherical functions, which describe the fields reflected by the sphere. Furthermore, these representations allow the development of relationships between cylindrical and spherical functions. These functions and subsequent relationships have been used to develop an algorithm for estimating the electromagnetic response of a conductive sphere in an isotropic layered earth. Software based on this algorithm has been tested on both synthetic and field data. The field data presented were collected with the AEM AirTEM system over the Reid-Mahaffy test site, Ontario, Canada. Results from these tests prove the importance and utility of integrating the sphere in a layered earth model in the AEM interpretation toolbox.