Representing Elongated Magnetic Sources by Prolate Spheroidal Harmonics Developed on an Optimized Coordinate System

A method is suggested for obtaining a compact and accurate representation of elongated magnetic sources by a series expansion of prolate spheroidal harmonics. While the general solution involves an infinite series of harmonics, practical measurement grids only support discrimination of a limited number of harmonics. In this paper, we present a method for minimizing the errors introduced when terminating the series expansion. In short, the coordinate system on which the harmonics are developed, is optimized for representing the main features of the source by the first few terms of the series expansion. This allows for an early termination of the series with minimal truncation errors. The improved source representation is demonstrated for both simulated and measured sources.