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- Scale Continuous, Scale Discretized and Scale Discrete Harmonic Wavelets for the Outer and the Inner Space of a Sphere and Their Application to an Inverse Problem in Geomathematics (2000)
- In this paper we construct a multiscale solution method for the gravimetry problem, which is concerned with the determination of the earth's density distribution from gravitational measurements. For this purpose isotropic scale continuous wavelets for harmonic functions on a ball and on a bounded outer space of a ball, respectively, are constructed. The scales are discretized and the results of numerical calculations based on regularization wavelets are presented. The obtained solutions yield topographical structures of the earth's surface at different levels of localization ranging from continental boundaries to local structures such as Ayer's Rock and the Amazonas area.
- Local Multiscale Approximations of Geostrophic Flow: Theoretical Background and Aspects of Scientific Computing (2005)
- In modern geoscience, understanding the climate depends on the information about the oceans. Covering two thirds of the Earth, oceans play an important role. Oceanic phenomena are, for example, oceanic circulation, water exchanges between atmosphere, land and ocean or temporal changes of the total water volume. All these features require new methods in constructive approximation, since they are regionally bounded and not globally observable. This article deals with methods of handling data with locally supported basis functions, modeling them in a multiscale scheme involving a wavelet approximation and presenting the main results for the dynamic topography and the geostrophic flow, e.g., in the Northern Atlantic. Further, it is demonstrated that compressional rates of the occurring wavelet transforms can be achieved by use of locally supported wavelets.