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.

翻译：源自GRACE-FO等卫星任务的时间相关重力数据揭示了地球系统中不同时间尺度的质量重新分布：长期气候变化信号、厄尔尼诺等年际现象、季节性质量迁移以及地震等瞬态事件。针对这一当代问题，需要研究一个经典反问题：即根据空间测量数据在地球表面建立引力势模型，这被称为向下延拓问题。因此，进一步发展此类反问题的数学方法至关重要。为此，近十年来发展了（学习型）反问题匹配追踪（(L)IPMPs）算法。其独特之处在于将局部与全局试探函数相结合，用于引力势向下延拓等反问题的近似求解，从而融合了传统球谐函数展开法与径向基函数方法的思想。先前关于这些方法的研究已进行了概念验证。本文将其应用于高维实验场景：在真实卫星几何结构上，采用超过50万个网格点实现最佳20km分辨率。我们还阐述了为处理如此大规模数据而对方法进行的必要改进。相应代码（经更新适用于大数据场景）可在https://doi.org/10.5281/zenodo.8223771（CC BY-NC-SA 3.0 Germany许可协议）获取。