Time-domain, spectral finite-element approach to transient 2-D geomagnetic induction in a spherical heterogeneous Earth

Abstract

A time-domain, spectral finite-element approach is presented for computing the electromagnetic induction response of a 2-D heterogeneous conducting sphere to transient external current excitation. This method is appropriate for determining the induced spatiotemporal electromagnetic signature at satellite altitudes associated with the upper and mid-mantle conductivity heterogeneities. The new approach is based on an existing frequency-domain 2-D spectral finite-element technique modified by the implementation of a time-stepping algorithm. To validate the time-domain approach and the associated numerical code, transient responses of concentrically and eccentrically nested spheres to ring-current excitations are computed using the inverse Fourier transform of analytical and semi-analytical, frequency-domain solutions. We show that the time-domain approach is particularly appropriate when the external current excitation has a transient feature. Compared with the frequency-domain method, it may significantly reduce the computation time while maintaining the time resolution.