Geophysical Field Modelling by Multiresolution Analysis

  • 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.

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Author:Michael Bayer, Stefan Beth, Willi Freeden
URN (permanent link):urn:nbn:de:hbz:386-kluedo-5972
Serie (Series number):Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (191)
Document Type:Preprint
Language of publication:English
Year of Completion:1998
Year of Publication:1998
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2000/04/03
Tag:da; exact fully discrete vectorial wavelet transform ; pyramid scheme ; scale discrete spherical vector wavelets ; vectorial multiresolution analysis
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC-Classification (mathematics):41-XX APPROXIMATIONS AND EXPANSIONS (For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx) / 41Axx Approximations and expansions / 41A58 Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)
42-XX FOURIER ANALYSIS / 42Cxx Nontrigonometric harmonic analysis / 42C15 General harmonic expansions, frames
44-XX INTEGRAL TRANSFORMS, OPERATIONAL CALCULUS (For fractional derivatives and integrals, see 26A33. For Fourier transforms, see 42A38, 42B10. For integral transforms in distribution spaces, see 46F12. For numerical methods, see 65R10) / 44Axx Integral transforms, operational calculus / 44A35 Convolution
65-XX NUMERICAL ANALYSIS / 65Dxx Numerical approximation and computational geometry (primarily algorithms) (For theory, see 41-XX and 68Uxx) / 65D15 Algorithms for functional approximation
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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