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Published in:
2018 | OriginalPaper | Chapter
Sampling of Potential and Stream Functions
Authors : Willi Freeden, M. Zuhair Nashed, Michael Schreiner
Published in: Spherical Sampling
Publisher: Springer International Publishing
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Usually, spacelimited wavelets do not reflect appropriately physical constraints. They mainly are of importance from numerical point of view because of their economy. In this chapter, however, we construct spacelimited wavelets which are close to the physical reality. The essential idea is to find multiscale regularizations of Green’s functions to spherical operators so that spacelimitation is a result of forming two certain differences of mollifications (regularizations). The concept was first realized in local geoid determination from deflections of the vertical (cf. [149]). It can be applied to potential methods of exploration (cf. e.g., [30]) and in seismic reflection as well (see, e.g., [110]). Our aim here is to explain exemplarily multiscale regularizations to potential and stream functions on the sphere (in canonical extension to [149]).