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Numerical Aspects of a Spline-Based Multiresolution Recovery of the Harmonic Mass Density out of Gravity Functionals

  • We show the numerical applicability of a multiresolution method based on harmonic splines on the 3-dimensional ball which allows the regularized recovery of the harmonic part of the Earth's mass density distribution out of different types of gravity data, e.g. different radial derivatives of the potential, at various positions which need not be located on a common sphere. This approximated harmonic density can be combined with its orthogonal anharmonic complement, e.g. determined out of the splitting function of free oscillations, to an approximation of the whole mass density function. The applicability of the presented tool is demonstrated by several test calculations based on simulated gravity values derived from EGM96. The method yields a multiresolution in the sense that the localization of the constructed spline basis functions can be increased which yields in combination with more data a higher resolution of the resulting spline. Moreover, we show that a locally improved data situation allows a highly resolved recovery in this particular area in combination with a coarse approximation elsewhere which is an essential advantage of this method, e.g. compared to polynomial approximation.

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Author:Volker Michel, Kerstin Wolf
Serie (Series number):Schriften zur Funktionalanalysis und Geomathematik (28)
Document Type:Preprint
Language of publication:English
Year of Completion:2006
Year of Publication:2006
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2006/12/13
Tag:EGM96; GOCE <Satellitenmission>; GRACE <Satellitenmission>; Harmonische Dichte; Satellitendaten
GND-Keyword:Mehrskalenanalyse; Spline; Inverses Problem; Numerisches Verfahren; Gravimetrie; Lokalisation; CHAMP <Satellitenmission>
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):45-XX INTEGRAL EQUATIONS / 45Bxx Fredholm integral equations / 45B05 Fredholm integral equations
45-XX INTEGRAL EQUATIONS / 45Qxx Inverse problems / 45Q05 Inverse problems
65-XX NUMERICAL ANALYSIS / 65Dxx Numerical approximation and computational geometry (primarily algorithms) (For theory, see 41-XX and 68Uxx) / 65D07 Splines
65-XX NUMERICAL ANALYSIS / 65Rxx Integral equations, integral transforms / 65R30 Improperly posed problems
86-XX GEOPHYSICS [See also 76U05, 76V05] / 86Axx Geophysics [See also 76U05, 76V05] / 86A22 Inverse problems [See also 35R30]
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011