Abstrakt
Detailed mathematical derivations of the forward and adjoint sensitivity methods are presented for computing the electromagnetic induction response of a 3-D heterogeneous conducting sphere to a transient external electric current excitation. The forward method is appropriate for determining the induced spatiotemporal electromagnetic signature at satellite altitudes associated with the upper and mid-mantle conductivity heterogeneities, while the adjoint method provides an efficient tool for computing the sensitivity of satellite magnetic data to the conductivity structure of the Earth's interior.
The forward and adjoint initial boundary-value problems, both solved in the time domain, are identical, except for the specification of the prescribed boundary conditions.