Time-Domain Approach to Geomagnetic Induction Based on Joint Use of Surface and Satellite Data

Availability of high precision data from satellite-borne magnetometers has recently motivated rapid development of effective methods to address the forward geomagnetic induction problem in heterogeneous Earth. We present a modification of the time-domain, spherical harmonic-finite element approach (Velímský and Martinec, 2005) that is based on joint use of vector magnetic field measurements from satellites and surface observatories. We use a physical model that consists of a spherical Earth with heterogeneous conductivity distribution surrounded sequentially by 1) an insulating atmosphere; 2) ionosphere approximated by an infinitesimally thin spherical sheet of horizontal currents; 3) another insulating layer where satellite data are acquired; and 4) a distant current system in the magnetosphere. Gaussian spherical harmonic analysis performed in both insulating layers and continuity of the vertical magnetic field across the ionosphere allow us to parametrize the magnetic field outside the Earth by three sets of spherical harmonic coefficients. These correspond respectively to current systems in the magnetosphere, in the ionosphere and in the solid Earth. Two of these sets (or any two independent linear combinations of them) can be imposed in the forward formulation as the boundary condition leaving the third set (or the remaining independent linear combination) for misfit evaluation of the conductivity model. Such a general forward approach allows to formulate the inverse problem using various combinations of a-priori models of magnetospheric and ionospheric currents and measurements of vertical and horizontal magnetic field components on the surface and in the space.