Inversion of the geomagnetic induction problem

Abstract

Abstract An algorithm has been found for inverting the problem of geomagnetic induction in a con­centrically stratified Earth. It determines the (radial) conductivity distribution from the frequency spectrum of the ratio of internal to external magnetic potentials of any surface harmonic mode. The derivation combines the magnetic induction equation with the principle of causality in the form of an integral constraint on the frequency spectrum. This algorithm generates a single solution for the conductivity. This solution is here proved unique if the conductivity is a bounded, real analytic function with no zeros. Suggestions are made regarding the numerical application of the algorithm to real data.