Modelling tippers on a sphere

Abstract

SUMMARY In the past three decades, an immense amount of magnetic field data (with periods of measurements from months to years) has been collected worldwide, either inland or at the sea bottom. This makes it tempting to estimate from these data magnetotelluric (MT) vertical transfer functions—tippers—and further probe with them the 3-D distribution of electrical conductivity on a continental or even global scale. Such a problem setup requires modelling tippers in spherical geometry. It is known that MT impedances in spherical coordinates can be modelled using different polarizations of a uniform external magnetic field. As for tippers, one needs another type of excitation because the uniform external magnetic field of any polarization contains a non-zero radial component. In the paper, we elaborate a source model, which leads to valid tippers on a whole sphere. We also present a novel, accurate and computationally efficient solver to calculate the electromagnetic field in a spherical shell or a part thereof. To illustrate the workability of both the introduced source model and the developed new solver, we present the results of modelling the ocean induction effect in tippers on a global scale. We performed computations in the models with and without oceanic sediments and show that the sediments substantially influence the results in the coastal regions where the thickness of sediments is comparable with or even exceeds the ocean’s bathymetry.