Global 3-D EM inversion of Sq variations based on simultaneous source and conductivity determination: concept validation and resolution studies

We present a novel global 3-D electromagnetic (EM) inverse solution that allows to work in a unified and consistent manner with frequency-domain data that originate from ionospheric and magnetospheric sources irrespective of their spatial complexity. The main idea behind the approach is simultaneous determination of the source and conductivity distribution in the Earth. Such a determination is implemented in our solution as a looped sequential procedure that involves two steps: (1) determination of the source using a fixed 3-D conductivity model and (2) recovery of a 3-D conductivity model using a fixed source. We focus in this paper on analysis of Sq data and numerically verify each step separately and combined using data synthesized from 3-D models of the Earth induced by a realistic Sq source. To determine the source we implement an approach that makes use of a known conductivity structure of the Earth with non-uniform oceans. Based on model studies we show that this approach outperforms the conventional potential method. As for recovery of 3-D conductivity in the mantle, our inverse scheme relies on a regularized least-square formulation, exploits a limited-memory quasi-Newton optimization method and makes use of the adjoint source approach to calculate efficiently the misfit gradient. We perform resolution studies with checkerboard conductivity structures at depths between 10 and 1600 km for different inverse setups and conclude from these studies that: (1) inverting Z component gives much better results than inverting all (X, Y and Z) components; (2) data from the Sq source allows for resolving 3-D structures in depth range between 100 and 520 km; (3) the best resolution is achieved in the depth range of 100-250 km.