## Wavelet Deformation Analysis for Spherical Bodies

• In this paper we introduce a multiscale technique for the analysis of deformation phenomena of the Earth. Classically, the basis functions under use are globally defined and show polynomial character. In consequence, only a global analysis of deformations is possible such that, for example, the water load of an artificial reservoir is hardly to model in that way. Up till now, the alternative to realize a local analysis can only be established by assuming the investigated region to be flat. In what follows we propose a local analysis based on tools (Navier scaling functions and wavelets) taking the (spherical) surface of the Earth into account. Our approach, in particular, enables us to perform a zooming-in procedure. In fact, the concept of Navier wavelets is formulated in such a way that subregions with larger or smaller data density can accordingly be modelled with a higher or lower resolution of the model, respectively.

Author: Willi Freeden, Volker Michel urn:nbn:de:hbz:386-kluedo-13697 Schriften zur Funktionalanalysis und Geomathematik (9) Preprint English 2004 2004 Technische Universität Kaiserslautern 2005/02/17 Cauchy-Navier-GleichungCauchy-Navier equation Dirichlet-Problem ; Elastische Deformation ; Kugel ; Mehrskalenanalyse; Neumann-Problem ; Skalierungsfunktion ; Wavelet-Analyse zur Veröffentlichung angenommen durch "International Journal on Wavelets, Multiresolution and Information Processing" Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik 33-XX SPECIAL FUNCTIONS (33-XX DEALS WITH THE PROPERTIES OF FUNCTIONS AS FUNCTIONS) (For orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; for representation theory see 22Exx) / 33Fxx Computational aspects / 33F05 Numerical approximation and evaluation [See also 65D20] 42-XX FOURIER ANALYSIS / 42Cxx Nontrigonometric harmonic analysis / 42C40 Wavelets and other special systems 74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Bxx Elastic materials / 74B05 Classical linear elasticity 86-XX GEOPHYSICS [See also 76U05, 76V05] / 86Axx Geophysics [See also 76U05, 76V05] / 86A20 Potentials, prospecting Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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