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Time-dependent gravity data from satellite missions like GRACE-FO reveal massredistribution in the system Earth at various time scales: long-term climatechange signals, inter-annual phenomena like El Nino, seasonal mass transportsand transients, e. g. due to earthquakes. For this contemporary issue, aclassical inverse problem has to be considered: the gravitational potential hasto be modelled on the Earth's surface from measurements in space. This is alsoknown as the downward continuation problem. Thus, it is important to furtherdevelop current mathematical methods for such inverse problems. For this, the(Learning) Inverse Problem Matching Pursuits ((L)IPMPs) have been developedwithin the last decade. Their unique feature is the combination of local aswell as global trial functions in the approximative solution of an inverseproblem such as the downward continuation of the gravitational potential. Inthis way, they harmonize the ideas of a traditional spherical harmonic ansatzand the radial basis function approach. Previous publications on these methodsshowed proofs of concept. Here, we consider the methods for high-dimensionalexperiments settings with more than 500 000 grid points which yields aresolution of 20 km at best on a realistic satellite geometry. We also explainthe changes in the methods that had to be done to work with such a large amountof data. The corresponding code (updated for big data use) is available athttps://doi.org/10.5281/zenodo.8223771 under the licence CC BY-NC-SA 3.0Germany.

High-dimensional experiments for the downward continuation using the LRFMP algorithm