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.

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Author:Willi Freeden, Volker Michel
URN (permanent link):urn:nbn:de:hbz:386-kluedo-13697
Serie (Series number):Schriften zur Funktionalanalysis und Geomathematik (9)
Document Type:Preprint
Language of publication:English
Year of Completion:2004
Year of Publication:2004
Publishing Institute:Technische Universität Kaiserslautern
Cauchy-Navier equation
GND-Keyword:Dirichlet-Problem ; Elastische Deformation ; Kugel ; Mehrskalenanalyse; Neumann-Problem ; Skalierungsfunktion ; Wavelet-Analyse
Source:zur Veröffentlichung angenommen durch "International Journal on Wavelets, Multiresolution and Information Processing"
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:510 Mathematik
MSC-Classification (mathematics):33F05 Numerical approximation and evaluation [See also 65D20]
42C40 Wavelets and other special systems
74B05 Classical linear elasticity
86A20 Potentials, prospecting

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