Global High-Resolution Magnetic Field Inversion Using Spherical Harmonic Representation of Tesseroids as Individual Sources

In this study, we present a novel approach combining the advantages of tesseroids in representing geophysical structures though their voxel-like discretization features with a spherical harmonic representation of the magnetic field. Modelling of the Earth lithospheric magnetic field is challenging since part of the spectra is hidden by the core field and the forward modeled field of a lithospheric magnetization is always biased by the spectral range used. In our approach, a spherical harmonic representation of the magnetic field of spherical prisms (tesseroids) is used for high-resolution magnetic inversion of lithospheric field models. The use of filtered spherical harmonic models of the magnetic field of each tesseroid ensures that the resulting field matches the spectral range of the input data. For the inversion, we use the projected gradient method. The projected gradient method easily allows us to assign an initial guess (i.e., a-priori assumption) for the inversion and avoids negative values of susceptibilities. The latter is providing more plausible models since induced magnetization is assumed to be dominant over the continents and, for the oceans, a remanence model can be subtracted. We show an application of the technique to a synthetic dataset and a satellite-derived lithospheric field model where the model geometry is based on seismic information. We also demonstrate a proof-of-concept for high-resolution tile-wise inversion for the Bangui anomaly in Africa.