Inversion of the satellite observations of the tidally induced magnetic field in terms of 3-D upper-mantle electrical conductivity: method and synthetic tests

Abstract

SUMMARY The interaction of the oceanic tidal flow with the Earth’s main magnetic field provides a powerful natural source of electromagnetic (EM) energy suitable for suboceanic upper-mantle electrical conductivity sounding. In this paper, we have developed and tested a new frequency-domain, spherical harmonic-finite element approach to the inverse problem of global EM induction. It is set up for an effective inversion of satellite-observed tidally induced magnetic field in terms of 3-D structure of the electrical conductivity in the suboceanic upper mantle. Before proceeding to the inversion of Swarm-derived models of tidal magnetic signatures, we have performed a series of parametric studies, using the 3-D conductivity model WINTERC-e as a testbed. The WINTERC-e model has been derived using state-of-the-art laboratory conductivity measurements of mantle minerals, and thermal and compositional model of the lithosphere and upper mantle WINTERC-G. The latter model is based on the inversion of global surface waveforms, satellite gravity and gradiometry measurements, surface elevation and heat flow data in a thermodynamically self-consistent framework. Therefore, the WINTERC-e model, independent of any EM data, represents an ideal target for synthetic tests of the 3-D EM inversion. We tested the impact of the truncation degree of the spherical-harmonic expansion of the M2 tidal signal, the effect of random noise in synthetic data and inclusion of the N2 and O1 tidal constituents on the ability to recover the suboceanic upper-mantle conductivity structure. We demonstrate that with suitable regularization we can successfully reconstruct the 3-D upper-mantle conductivity beneath world oceans. In the ideal noise-free case, the correlation coefficient between the target and recovered conductivity is greater than 0.8 in the 150–270 km depth range.