The electrical conductivity is an important geophysical parameter connected to the thermal, chemical, and mineralogical state of the Earth’s mantle. In this paper, we apply the previously developed ...methodology of forward and inverse EM induction modeling to the latest version of satellite-derived spherical harmonic coefficients of external and internal magnetic field, and obtain the first 3-D mantle conductivity models with contributions from Swarm and CryoSat-2 satellite data. We recover degree 3 conductivity structures which partially overlap with the shape of the large low-shear velocity provinces in the lower mantle.
This study deals with the analysis of Swarm vector magnetic data in order to create a circuit model of electric currents flowing in the Earth’s polar ionosphere and the inner magnetosphere. The model ...is composed of a system of two-dimensional electric currents representing the magnetic fields of three-dimensional ionospheric polar electrojets (PEJs), the field-aligned currents (FACs), magnetospheric ring currents (MRCs) and magnetospherically induced electric currents inside the Earth (MICs) for each Swarm track. The aim of this paper is to model PEJ and FAC magnetic fields in terms of electric currents on a track-by-track base, subtract those magnetic fields from along-track Swarm magnetic data and estimate the magnetospheric magnetic field (MMF) in discrete time bins. The proposed method is primarily intended to apply to Swarm signals recorded during magnetic storms. The electric circuit model is set up in three steps. After subtracting the main, lithospheric, Sq ionospheric and oceanic tidal magnetic fields from along-track Swarm magnetic signals, the residuals are grouped in 1-h time bins and adjusted by the magnetic field of a two-circular loop model of MRCs and MICs represented by
3
×
2
parameters of the electric circular loops in the magnetosphere and the Earth. The adjustment is carried out for the
X
and
Z
magnetic field components only because the
Y
component contains a large signal due to FACs. In the second step, the modelled MRC–MIC magnetic field is removed from the original residuals and the reduced residuals are adjusted by the magnetic field of a system of two-dimensional electric circuits in the polar ionosphere and FACs. The circuit model is set up according to known geometry of PEJs and FACs. In the final step, the modelled magnetic fields of PEJs and FACs are subtracted from the original residuals and all three magnetic field components are adjusted by the MRC–MIC model, named MMC, in a similar way as in the first step. Reliability of the approach is demonstrated by the scatter plots of model MMC showing a significantly better agreement with Swarm magnetic field residuals than the existing MMFs.
Graphical Abstract
The magnetic field induced in the Earth's ocean by the large-scale global circulation consists of the toroidal and poloidal modes. Lateral variations of the ocean electrical conductivity allow for ...the energy exchange between both regimes. In this paper, we predict that the eastward component of the toroidal magnetic field in the area of the Antarctic Circumpolar Current can reach amplitudes of 15 nT at the depth of about 1800 m. Moreover, even though the toroidal field is invisible on the ocean surface, it can significantly influence the observable poloidal field, both in terms of its amplitude, and seasonal variations.
•The ocean-induced magnetic field has a large toroidal component.•Its magnitude can be an order of magnitude larger than the poloidal field.•It is driven by the vertical stratification of horizontal ocean flows.•The toroidal field influences the observable poloidal field on the surface.
The magnetic signatures of ocean
M
2
tides have been successfully detected by the low-orbit satellite missions CHAMP and Swarm. They have been also used to constrain the electrical conductivity in ...the uppermost regions of the Earth’s mantle. Here, we concentrate on the problem of accurate numerical modelling of tidally induced magnetic field, using two different three-dimensional approaches: the contraction integral equation method and the spherical harmonic-finite element method. In particular, we discuss the effects of numerical resolution, self-induction, the galvanic and inductive coupling between the oceans and the underlying mantle. We also study the applicability of a simplified two-dimensional approximation, where the ocean is approximated by a single layer with vertically averaged conductivity and tidal forcing. We demonstrate that the two-dimensional approach is sufficient to predict the large-scale tidal signals observable on the satellite altitude. However, for accurate predictions of
M
2
tidal signals in the areas with significant variations of bathymetry, and close to the coastlines, full three-dimensional calculations are required. The ocean–mantle electromagnetic coupling has to be treated in the full complexity, including the toroidal magnetic field generated by the vertical currents flowing from and into the mantle.
SUMMARY
A new global model of the present-day thermochemical state of the lithosphere and upper mantle based on global waveform inversion, satellite gravity and gradiometry measurements, surface ...elevation and heat flow data has been recently presented: WINTERC-G (Fullea et al. 2021). WINTERC-G is built within an integrated geophysical-petrological framework where the mantle seismic velocity and density fields are computed in a thermodynamically self-consistent framework, allowing for a direct parametrization in terms of the temperature, pressure and composition of the subsurface rocks. In this paper, we combine WINTERC-G thermal and compositional fields along with laboratory experiments constraining the electrical conductivity of mantle minerals, melt and water, and derive a set of new global three dimensional electrical conductivity models of the upper mantle. The new conductivity models, WINTERC-e, consist of two end-members corresponding to minimum and maximum conductivity of the in situ rock aggregate accounting for mantle melting, mineral water content and the individual conductivities of the main stable mantle mineral phases. The end-member models are validated over oceans by simulating the magnetic field induced by the ocean M2 tidal currents and comparing the predicted fields with the M2 tidal magnetic field estimated from 6-yr Swarm satellite observations. Our new conductivity model, derived independently from any surface or satellite magnetic data sets, is however able to predict tidal magnetic fields that are in good agreement with the Swarm M2 tidal magnetic field models estimated by Sabaka et al. and Grayver & Olsen. Our predicted M2 tidal magnetic fields differ in amplitudes by about 5–20 per cent from the Swarm M2 tidal magnetic field, with the high conductivity WINTERC-e end-member model accounting for mantle melt and water content capturing the structure of Swarm data better than the low conductivity end-member model. Spherically symmetric conductivity models derived by averaging new WINTERC-e conductivities over oceanic areas are slightly more conductive than the recent global conductivity models AA17 by Grayver et al. derived from Swarm and CHAMP satellite data in the 60–140 km depth range, while they are less conductive deeper in the mantle. The conductivities in WINTERC-e are about three to four times smaller than the AA17 conductivities at a depth of 400 km. Despite the differences in electrical conductivity, our spherically symmetric high conductivity end-member model WINTERC-e captures the structure of Swarm M2 tidal magnetic field almost the same as a state of the art 1-D conductivity models derived entirely from magnetic data (AA17, Grayver et al.). Moreover, we show that realistic lateral electrical conductivity inhomogeneities of the oceanic upper mantle derived from the temperature, melt and water distributions in WINTERC-e contribute to the M2 tidal magnetic field up to ±0.3 nT at 430 km altitude.
One of the primary goals of the
Swarm
multisatellite mission is to determine the 3-D distribution of electrical conductivity in the Earth’s mantle. This paper presents an inversion method based on ...direct integration of magnetic fields in the time domain, and using the adjoint solution for fast evaluation of data sensitivities to model perturbations. Two tests of the method are presented. The first one is using a 3-D checkerboard conductivity model and noise-free synthetic data. The second test is based on the closed-loop simulation of
Swarm
mission, including recovery of external and induced fields from simulated data along satellite tracks, and realistic noise estimates.
Time-domain EM induction is used to obtain 1-D conductivity structure in the Earth using seven years of vector magnetometer measurements by the CHAMP satellite. An optimal model is obtained by means ...of quasi-Newton minimization with regularization. Sensitivity of data to deep Earth conductivity is checked by limited grid search of the model space in the vicinity of the optimal model. While regularization plays a considerable role in constraining the conductivity model, data misfit poses upper limits on the lower mantle and
D
″
conductivity at 2
S/m, and 10
S/m, respectively.
The magnetic signatures of ocean
tides have been successfully detected by the low-orbit satellite missions CHAMP and Swarm. They have been also used to constrain the electrical conductivity in the ...uppermost regions of the Earth's mantle. Here, we concentrate on the problem of accurate numerical modelling of tidally induced magnetic field, using two different three-dimensional approaches: the contraction integral equation method and the spherical harmonic-finite element method. In particular, we discuss the effects of numerical resolution, self-induction, the galvanic and inductive coupling between the oceans and the underlying mantle. We also study the applicability of a simplified two-dimensional approximation, where the ocean is approximated by a single layer with vertically averaged conductivity and tidal forcing. We demonstrate that the two-dimensional approach is sufficient to predict the large-scale tidal signals observable on the satellite altitude. However, for accurate predictions of
tidal signals in the areas with significant variations of bathymetry, and close to the coastlines, full three-dimensional calculations are required. The ocean-mantle electromagnetic coupling has to be treated in the full complexity, including the toroidal magnetic field generated by the vertical currents flowing from and into the mantle.
The interactions of flowing electrically conductive seawater with Earth’s magnetic field generate electric currents within the oceans, as well as secondary electric currents induced in the resistive ...solid Earth. The ocean-induced magnetic field (OIMF) is an observable signature of these currents. Ignoring tidally forced ocean flows, the global ocean circulation system is driven by wind forcing on the ocean surface and by the temperature- and salinity-dependent buoyancy force. Ocean circulation’s magnetic signals contribute to the total magnetic field observed at the Earth’s surface or by low-orbit satellite missions. In this paper, we concentrate on accurate numerical modelling of the OIMF employing various approaches. Using a series of numerical test cases in different scenarios of increasing complexity, we evaluate the applicability of the unimodal thin-sheet approximation, the importance of galvanic coupling between the oceans and the underlying mantle (i.e. the bimodal solution), the effects of vertical stratification of ocean flow as well as the effects of vertical stratification of both oceanic and underlying electrical conductivity, and the influence of electromagnetic self-induction. We find that the inclusion of galvanic ocean-mantle coupling has the largest effect on the predicted OIMF. Self-induction is important only on the largest spatial scales, influencing the lowest spherical harmonic coefficients of the OIMF spectrum. We find this conclusion important in light of the recent Swarm satellite mission which has the potential to observe the large-scale OIMF and its seasonal variations. The implementation of fully three-dimensional ocean flow and conductivity heterogeneity due to bathymetry, which substantially increases the computational demands of the calculations, can play some role for regional studies, or when a more accurate OIMF prediction is needed within the oceans, e.g. for comparison with seafloor observations. However, the large-scale signals at the sea surface or at satellite altitude are less affected.
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