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.
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.
The differences between local and reference geopotential values are the fundamental quantities of interest in the geodetic boundary value problem approach for connecting independent height reference ...frames. The local gravity potential values are usually derived from gravimetric and geometric geoid undulations. In determining the short-wavelength components of the gravimetric geoid, a harmonic or analytical downward continuation of the external harmonic functions of gravity to the geoid is necessary. This study analyses the stability of the Poisson downward continuation technique with respect to varying the spatial resolution of surface gravity data in Ireland in order to estimate an effective grid resolution on this reduction. Results of the study show that the minimum range of 500-m resolution provides an unconditionally stable solution to downward continuation without the need for regularisation of the computation algorithm. In this case, downward continued data contribute from −13 to 12 mm to geoid heights and from −0.128 to 0.118 m
2
s
−2
to local gravity potential value at Malin-Head tide gauge station in Ireland.
There is a growing interest in tidal effects on the global wind-driven oceanic circulation. Tidal models used in such investigations have been verified by comparison with satellite and tide gauge ...data, but synthetic tests have not been published. In this paper we present three numerical tests in spherical geometry, which are suitable for testing the tidal component of global ocean models. The first test is a tsunami-like propagation of an initial Gaussian depression with no external forcing. The other two tests examine the tidal response of an ocean with an undulating bottom with four Gaussian ridges and an ocean with a flat bottom with a realistic land mask. We provide the results from six model configurations, which differ in the time-stepping scheme and computational grid used. Most of them are implemented in present-day global ocean models. Although the proposed numerical tests are simple compared to realistic simulations, their analytic solutions are not available. We thus check the conservation of time invariants to ensure that the solutions are physically meaningful. We also compare the time evolution of certain physical quantities and the differences in sea surface heights at particular time instants with respect to a reference solution. All tested time stepping schemes are suitable for tidal studies except for the Euler implicit time stepping scheme. Model configurations based on the Arakawa grids B/E use smoothing to suppress the grid-scale noise which results in an energy leakage of around 5%. The B/E-grid energy leakage is probably acceptable if we consider that tuned diffusive terms are used in real-world configurations. The C-grid and B/E-grid solutions differ in the vicinity of solid boundaries as a consequence of different boundary conditions. The B-grid and E-grid solutions are similar, unless the shape of the solid boundaries is complex due to the different shapes of the respective grid cells.
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 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.
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.
The first-order Born approximation is a weak scattering perturbation method which is a powerful tool. The combination of the Born approximation and the ray theory enables to extend the applicability ...of the ray theory in terms of the required smoothness of the model and ensures faster computations than with, e.g., the finite difference method. We are motivated to describe and explain the effects of the numerical discretization of the Born integral on the resulting seismograms.
We focus on forward modelling and study the cases in which perturbation from the background model contains the interface. We restrict ourselves to isotropic models that contain two homogeneous layers. We compare the 2D and 3D ray-based Bornapproximation seismograms with the ray-theory seismograms.
The Born seismograms are computed using a grid of finite extent. We anticipate that the computational grid should contain an appropriate number of gridpoints, otherwise the seismogram would be inaccurate. We also anticipate that the limited size of the computational grid can cause problems.
We demonstrate numerically that an incorrect grid can produce significant errors in the amplitude of the wave, or it can shift the seismogram in time. Moreover, the grid boundaries work as interfaces, where spurious waves can be generated. We also attempt to explain these phenomena theoretically. We give and test the options of removing the spurious waves. We show that it is possible to compute the Born approximation in a sparser grid, if we use elastic parameters averaged from some dense grid.
The magnetic signatures of ocean Formula omitted 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 Formula omitted 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.
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