The lecture is devoted to a new and promising way of recovering geopotentials (in gravitation, geomagnetics, etc) from spaceborne data using numerical progress obtainable by modern multivariate approximation. The presentation covers the following areas:
• the introduction of geoscientifically relevant wavelets and the explanation of their essential properties (i.e., basis property, decorrelation, and fast computation).
• the mathematical modelling of exponentially ill-posed (inverse) problems of satellite technology and their multiscale solution by multiresolution regularization.
The numerical properties of the resulting multiscale algorithms are illustrated for data of the German GFZ-satellite CHAMP (in gravitation and magnetics).
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