Modeling tippers on a sphere

In the past three decades, a huge amount of long-period magnetic data (from weeks to years of measurements) has been collected around the world either inland or at sea bottom. It makes tempting to estimate from these data magnetotelluric (MT) vertical transfer functions - tippers – in as wide  period range as practicable and further probe with them the three-dimensional (3-D) distribution of electrical conductivity in the upper mantle on a global or semi-global/continental scale. Such problem setup requires modelling MT responses 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 cannot compute them on a sphere using this type of excitation, because the uniform external magnetic field of any polarization contains a non-zero vertical component. To overcome the problem, we elaborate a model of the source, which leads to valid MT tippers on a sphere or a part thereof. To compute tippers in spherical Earth models with 3-D conductivity distribution we use a novel accurate and computationally efficient solver called GEMMIE. The solver is based on nested integral equations, allowing researchers to calculate high-resolution MT tippers globally and regionally taking into account realistic oceans, sediments, and Earth’s conductivity.