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Multiscale Modeling from EIGEN-1S, EIGEN-2, EIGEN-GRACE01S, GGM01, UCPH2002_0.5, EGM96

Martin Gutting(1), Martin J. Fengler(1) , and Willi Freeden(1)

(1) Geomathematics Group Kaiserslautern, K-Tech, P.O. Box 3049, 67653 Kaiserslautern, Germany

Abstract

Spherical wavelets have been developed by the Geomathematics Group Kaiserslautern for several years and have been successfully applied to georelevant problems. Wavelets can be considered as consecutive band-pass filters and allow local approximations due to their strong localizing properties. The wavelet transform can also be applied to spherical harmonic models of the Earth's gravitational field like the most up-to-date EIGEN-1S, EIGEN-2, EIGEN-GRACE01S, GGM01, UCPH2002_0.5, and the well-known EGM96. Thereby, wavelet coefficients arise and these have been made available to other interested groups. (They can be downloaded from our webpage: http://www.mathematik.uni-kl.de/~wwwgeo/waveletmodels.html) These wavelet coefficients allow the reconstruction of the wavelet approximations. The resulting models show the strong approximating capacity of wavelets as well as their applicability to local problems, e.g. modeling locally the geostrophic flow. Different types of wavelets are considered: bandlimited wavelets, i.e. Shannon and Cubic Polynomial (CuP) , as well as non-bandlimited ones, i.e. Abel-Poisson. For these types wavelet coefficients are computed and compared for the different spherical harmonic models. Moreover, wavelet variances are given in order to compare these quantities with the well-known degree variances. The presentation also includes the data format of the wavelet coefficients.

 

Workshop presentation

Full paper

Keywords: ESA European Space Agency - Agence spatiale europeenne, observation de la terre, earth observation, satellite remote sensing, teledetection, geophysique, altimetrie, radar, chimique atmospherique, geophysics, altimetry, radar, atmospheric chemistry

GOCE04