Inverse Multiscale Geoid Computation

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Starting from geopotential values as data on the actual Earth's surface a multiscale method of determining the disturbing potential outside and on the telluroid is introduced. In contrast to the standard procedure an ellipsoid of revolution is proposed to act as reference surface instead of a sphere. Furthermore, the potential itself is intended to be approximated by ellipsoidal harmonic wavelets outside the telluroid from given potential values on the real Earth's surface. The solution process is performed by multiresolution analysis in terms of ellipsoidal harmonic regularization wavelets. The essential idea ist to approximate in suitable way the (regularization) wavelet transforms defined als integrals over the telluroid, i.e. the reference ellipsoid, by evaluation functionals, i.e. point values on the actual Earth's surface. The bandlimited (i.e. truncated singular value decomposition) case and the non-bandlimited (i.e. Tikhonov) case must be distinguished for regularization, and different types of pyramid schemata must be implemented for fast wavelets transform for the bandlimited and non-bandlimited appraoch, respectively. Finally, the disturbing potential is used for geoidal determination by using the well-known Bruns formula of physical geodesy. Both the theoretical and practical aspects can be formulated in such a way that high-precision geoidal modelling from global to local scale becomes efficiently and economically available by virtue of the zooming-in property of more and more space-localizing wavelets on the telluroid.