Simultaneous inversion for source field and mantle electrical conductivity using the variable projection approach

Time-varying electromagnetic field observed on the ground or at a spacecraft consists of contributions from (i) electric source currents, such as those in the ionosphere and magnetosphere, and (ii) corresponding fields induced by source currents within the conductive Earth's interior by virtue of electromagnetic induction. Knowledge about the spatio-temporal structure of inducing currents is a key component in ionospheric and magnetospheric studies, and is also needed in space weather hazard evaluation, whereas the induced currents depend on the Earth's subsurface electrical conductivity distribution and allow us to probe this physical property. In this study, we present an approach that reconstructs the inducing source and subsurface conductivity structures simultaneously, preserving consistency between the two models by exploiting the inherent physical link. To achieve this, we formulate the underlying inverse problem as a separable nonlinear least-squares (SNLS) problem, where inducing current and subsurface conductivity parameters enter as linear and nonlinear model unknowns, respectively. We solve the SNLS problem using the variable projection method and compare it with other conventional approaches. We study the properties of the method and demonstrate its feasibility by simultaneously reconstructing the ionospheric and magnetospheric currents along with a 1-D average mantle conductivity distribution from the ground magnetic observatory data.

Automated summary

In this study, we propose an approach that simultaneously reconstructs the inducing source and subsurface conductivity structures by exploiting the inherent physical link between them. We formulate the underlying inverse problem as a separable nonlinear least-squares problem and solve it using the variable projection method. We compare our approach with other conventional methods and demonstrate its feasibility by simultaneously reconstructing the ionospheric and magnetospheric currents along with a 1-D average mantle conductivity distribution from the ground magnetic observatory data.