Non-linear conjugate gradient inversion for global EM induction: resolution studies

We develop a non-linear conjugate gradient inversion for global long period electromagnetic induction studies. The scheme requires computation of derivatives of the regularized penalty functional. We derive analytical and numerical expressions for these derivatives, and the associated Jacobian, and show how these can be efficiently implemented by generalizing and extending an existing finite difference forward solver. Using layered spherical harmonics to parametrize the model space, we invert a range of synthetic data sets to test the inversion, and to study vertical and horizontal resolution of currently available data sets. We conclude that the currently available long-period global geomagnetic observatory data in the period range 5-107 d can resolve large scale (300-500 km vertically, thousands of km horizontally) heterogeneities in mantle electrical conductivity reliably at depths similar to 670-1600 km. By extending induction response to 0.2-5 d (including daily variation periods), upper-mantle structure could also be resolved.