Mapping 3-D mantle electrical conductivity from space: a new 3-D inversion scheme based on analysis of matrix Q-responses

Abstract

We present a novel 3-D frequency-domain inversion scheme to recover 3-D mantle conductivity from satellite magnetic data, for example, provided by the Swarm mission. The scheme is based on the inversion of a new set of electromagnetic transfer functions, which form an array that we denote as matrix Q-response and which relate external (inducing) and internal (induced) coefficients of the spherical harmonic expansion of the time-varying magnetic field of magnetospheric origin. This concept overcomes the problems associated with source determination inherent to recent schemes based on direct inversion of internal coefficients. Matrix Q-responses are estimated from time-series of external and internal coefficients with a newly elaborated multivariate analysis scheme. An inversion algorithm that deals with matrix Q-responses has been developed. In order to make the inversion tractable, we elaborated an adjoint approach to compute the data misfit gradient and parallelized the numerical code with respect to frequencies and elementary sources, which describe the external part of the magnetic field of magnetospheric origin. Both parts of the scheme have been verified with realistic test data. Special attention is given to the issue of correlated noise due to undescribed sources.

Decadal period external magnetic field variations determined via eigenanalysis

“…Our findings confirm the prevailing view [cf. Püthe and Kuvshinov , ] that the symmetric ring current is the dominant inducing field. Furthermore, we show which additional inducing field harmonics are important to ground‐based data at all LTs and have provided information of the behavior of the baselines of these inducing fields over the course of a solar cycle.…”

“…Recent studies [e.g., Maus and Lühr , ; Lühr and Maus , ] have shown that the nonaxisymmetric magnetospheric source dominates the ring current at quiet times. More recently, Püthe and Kuvshinov [, ] used a fuller set of harmonics for the magnetospheric terms based on the study of Sabaka et al [] (though as discussed later, this is still possibly a simplification of the true case since it does not include the ionospheric contribution). Püthe et al [] have introduced a method allowing the resolution of the induced response from an inducing field of effectively unlimited complexity.…”

Ionospheric current source modeling and global geomagnetic induction using ground geomagnetic observatory data

“…As a step toward using more complex source models Püthe and Kuvshinov [2014] and Püthe et al [2015] developed transfer function methods for sources that could be modeled as a sum of a few low-degree spherical harmonics. In these studies it was assumed that the coefficients of the source expansion could be provided as input variables for transfer function estimation, either through analysis of satellite data [Sabaka et al, 2013] or by fitting fields observed in a sparse observatory array [Püthe et al, 2015].…”

A Comparison of Model‐Based Ionospheric and Ocean Tidal Magnetic Signals With Observatory Data

“…Oceanic tidal magnetic signals are of special interest because they are galvanically coupled with Earth's subsurface, making them ideal for probing shallow, resistive regions of the lithosphere and mantle—regions of great geodynamic interest because of their partial melts and volatiles, and role in plate tectonics. With the recent increase in high‐quality magnetic data from satellite missions (Øersted, CHAMP, SAC‐C and Swarm), there has been rising interest in probing Earth from space using signals of magnetospheric origin (Civet & Tarits, ; Civet et al, ; Kuvshinov et al, ; Püthe & Kuvshinov, , ; Püthe et al, ; Velímský, , ), as well as signals of tidal origin for these purposes (Schnepf et al, ). In fact, mapping the electrical conductivity of Earth's mantle is one of the primary scientific objectives of the Swarm mission (Olsen et al, ), and recently, there were breakthroughs in using oceanic magnetic tidal signals to probe the lithosphere and upper mantle (Grayver et al, , ).…”