Abstract
In the context of inverse problems of mathematical geodesy, the calculation of the gravitational potential at the Earth’s surface from its Hesse tensor at satellite’s height turns out to be exponentially ill-posed. In fact, it requires specific tensorial procedures for its solution. This paper proposes a wavelet-based regularization method to overcome the calamities of the ill-posedness, thereby providing a “zooming-in” technique of modeling the gravitational potential from global to local scale. As a particularly remarkable ingredient the paper offers a new procedure of multiscale regularization by use of locally adapted regularization parameters.
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Freeden, W., Nutz, H. Satellite gravity gradiometry as tensorial inverse problem. Int J Geomath 2, 177–218 (2011). https://doi.org/10.1007/s13137-011-0026-x
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DOI: https://doi.org/10.1007/s13137-011-0026-x