Determination of the 3-D distribution of electrical conductivity in Earth's mantle from Swarm satellite data: Frequency domain approach based on inversion of induced coefficients

Mapping the three-dimensional (3-D) electrical conductivity of Earth's mantle has been identified as one of the primary scientific objectives for the Swarm satellite mission. We present a 3-D frequency domain inversion scheme to recover mantle conductivity from satellite magnetic data. The scheme is based on an inversion of time spectra of internal (induced) spherical harmonic coefficients of the magnetic potential due to magnetospheric sources. Time series of internal and external (inducing) coefficients, whose determination is a prerequisite for this formulation, will be available as a Swarm Level-2 data product. An iterative gradient-type (quasi-Newton) optimization method is chosen to solve our 3-D non-linear inverse problem. In order to make the inversion tractable, we elaborate an adjoint approach for a fast and robust calculation of the data misfit gradient. We verify our approach with synthetic, but realistic time spectra of internal coefficients, obtained by simulating induction due to a realistic magnetospheric source in a 3-D conductivity model of the Earth. In these model studies, both shape and conductivity of a large-scale conductivity anomaly in the mid-mantle are recovered very well. The inversion scheme also shows to be robust with respect to noise and is therefore ready to process Swarm data.