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

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