A NEW TIME-DOMAIN APPROACH FOR THE ELECTROMAGNETIC INDUCTION PROBLEM IN A THREE-DIMENSIONAL HETEROGENEOUS EARTH

Abstract

We present a new time-domain approach to the forward modelling of 3-D electromagnetic induction in a heterogeneous conducting sphere excited by external and internal sources. This method utilizes the standard decomposition of the magnetic field into toroidal and poloidal parts, and spherical harmonic expansions of both the magnetic fields and the conductivity heterogeneity. Resulting induction equations for the spherical harmonics are solved simultaneously in the time domain. Coupling terms between the electromagnetic fields and the conductivity structure are re-expanded in spherical harmonics, so that the terms can be calculated by matrix multiplications at each time step of the computation. A finite difference approximation was used to solve the set of diffusion equations for the spherical harmonics up to degree 20. This method can be efficiently used to analyse transient geomagnetic variations to estimate the 3-D conductivity structure of the Earth.