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.