An inversion method of Gel'fand-Levitan type for the electromagnetic induction problem

Abstract

SUMMARY The inverse problem of electromagnetic induction for an assumed spherically symmetric conductivity distribution within the Earth is considered. In particular an adaptation (applicable in the case of external source fields) is made of the method proposed by Johnson & Smylie. This is based on the Gel'fand‐Levitan integral equation and is relevant to the determination of electrical conductivity in the lower mantle and internally generated source‐fields. A characteristic of this approach is that the predicted conductivity is a twice differentiable function with respect to the Earth's radius. It is shown here that the inversion procedure satisfactorily recovers the conductivity profile with data generated from a variety of synthetic conductivity structures. Typical response measurements covering a range of frequencies from 0.1 cycles per year to 11 cycles per day for the Earth allowed estimates of the conductivity profile for depths to about 2000 km.