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

Abstract

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.

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

“…the easy insertion of an alternative optimization scheme, such as non-linear conjugate gradients. This flexibility might allow the combination of the inversion scheme presented in this study with similar global inversion algorithms using observatory data Koch and Kuvshinov, 2013) and thus permit a more robust recovery of mantle conductivity, especially at shallow depths.…”

Do ocean tidal signals influence recovery of solar quiet variations?

“…To estimate the source coefficients ǫ m n , we used the S3D method presented in Koch and Kuvshinov (2013). It computes source coefficients while taking into account the 3-D ocean effect commonly observed at coastal and oceanic observatories (Kuvshinov and Olsen 2005).…”

“…Within the S3D method, we numerically solve the system of Eq. (1) for each j m,unit n (Koch and Kuvshinov 2013) by using a volume integral equation solver given by Kuvshinov (2008), hereinafter called X3DG. This solver computes an EM field induced by (arbitrary) sources for a specified 3-D conductivity model of the Earth.…”

“…By virtue of linearity of Maxwell's equations with respect to the source, magnetic fields at any location r j = (r j , ϑ j , ϕ j ) can be expressed by a sum of the unit magnetic fields scaled by the unknown source coefficients (Koch and Kuvshinov 2013) where ω p = 2π 24 p. We estimate ǫ m n by using a robust leastsquares fitting of the observed magnetic fields (corrected for core and crustal contributions with the CHAOS-6 model Finlay et al 2016) from a number of globally distributed magnetic observatories. Note that S3D allows us to estimate ǫ m n from any combination of magnetic field components.…”

Does the South Atlantic Anomaly influence the ionospheric Sq current system? Inferences from analysis of ground-based magnetic data

“…To determine the Sq source, we exploit the S3D method presented in (Koch and Kuvshinov 2013). It is an attractive alternative to the classic potential method of (Gauss 1838) as used for example by (Schmucker 1999).…”