Fundamental Mode Approach to Forward Problem Solutions in EMI Scattering ---- Inferring fundamental solutions from training data

Electromagnetic induction (EMI: 10's of Hz to 100's of kHz) is the leading technology for discrimination of subsurface metallic targets such as unexploded ordnance (UXO). The cleanup problem requires solution of remote sensing inverse problem inevitably based on some very fast forward algorithms for calculating EMI. The forward model must determine responses of arbitrarily complicated metallic objects. Here a very fast and complete forward solution system is presented, based on fundamental mode excitations. For a given target (or a set of targets), the EMI responses to fundamental modes are obtained from training data and saved. Any realistic excitation field is then decomposed into a limited number of constituent fundamental modes and the scatterer's EMI response is obtained by superposition of the fundamental mode solutions. In this paper we define the fundamental excitations explicitly and consider their rationale; show how to construct any particular solutions from solutions to the fundamental excitations; and focus particularly on how to obtain, retain, express responses to the fundamental solutions in the face of inherent ill-conditioning.