TY  - INPR
A1  - Bayer, Michael
A1  - Beth, Stefan
A1  - Freeden, Willi
T1  - Geophysical Field Modelling by Multiresolution Analysis
N2  - Wavelet transform originated in 1980's for the analysis of seismic signals has seen an explosion of applications in geophysics. However, almost all of the material is based on wavelets over Euclidean spaces. This paper deals with the generalization of the theory and algorithmic aspects of wavelets to a spherical earth's model and geophysically relevant vector fields such as the gravitational, magnetic, elastic field of the earth.A scale discrete wavelet approach is considered on the sphere thereby avoiding any type of tensor-valued 'basis (kernel) function'. The generators of the vector wavelets used for the fast evaluation are assumed to have compact supports. Thus the scale and detail spaces are finite-dimensional. As an important consequence, detail information of the vector field under consideration can be obtained only by a finite number of wavelet coefficients for each scale. Using integration formulas that are exact up to a prescribed polynomial degree, wavelet decomposition and reconstruction are investigated for bandlimited vector fields. A pyramid scheme for the recursive computation of the wavelet coefficients from level to level is described in detail. Finally, data compression is discussed for the EGM96 model of the earth's gravitational field.
T3  - Berichte der Arbeitsgruppe Technomathematik (AGTM Report) - 191 
KW  - vectorial multiresolution analysis
KW  - scale discrete spherical vector wavelets
KW  - exact fully discrete vectorial wavelet transform
KW  - pyramid scheme
KW  - da
Y1  - 1998
UR  - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/628
UR  - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-5972
N1  - Altdaten, kein Volltext verfügbar ; Printversion in Bereichsbibliothek Mathematik vorhanden: MAT 144/620-191
ER  -