Dictionary learning for downward continuation of gravity data

A multitude of basis functions is available for modelling the gravitational field based on satellite data. The Regularized Functional Matching Pursuit (RFMP) algorithm, which has been developed by the Geomathematics Group Siegen, proved to be able to combine different sets of such trial functions. For this purpose, a dictionary is built as a redundant union of different established basis systems (such as spherical harmonics, radial basis functions and Slepian functions). In an iterative scheme, a best basis is selected by minimizing a Tikhonov-Phillips functional. In a recent add-on (the LRFMP), the dictionary does not have to be discretely predefined but can be learned as part of the algorithm. This is implemented as a non-linear optimization problem. The LRFMP has several benefits, which will be demonstrated in the presentation, where we show numerical tests regarding the inversion of noisy gravity data on real satellite orbits.

References:

N. Schneider, V. Michel and N. Sneeuw, High-dimensional experiments for the downward continuation using the LRFMP algorithm, preprint available at http://arxiv.org/abs/2308.04167, 2023.

N. Schneider, V. Michel: A dictionary learning add-on for spherical downward continuation, Journal of Geodesy, 96 (2022), article 21 (22pp). 

Source Code:

N. Schneider, (L)IPMP source code for gravitational field modelling, v2-dc-2023. Zenodo. https://doi.org/10.5281/zenodo.8223771, 2023.