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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