Splines and local approximation of the earth's gravity field

 

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dc.contributor.advisor Merry, Charles en_ZA
dc.contributor.author Van Gysen, Hermanus Gerhardus en_ZA
dc.date.accessioned 2015-12-20T15:27:23Z
dc.date.available 2015-12-20T15:27:23Z
dc.date.issued 1988 en_ZA
dc.identifier.citation Van Gysen, H. 1988. Splines and local approximation of the earth's gravity field. University of Cape Town. en_ZA
dc.identifier.uri http://hdl.handle.net/11427/15821
dc.description Bibliography: pages 214-220. en_ZA
dc.description.abstract The Hilbert space spline theory of Delvos and Schempp, and the reproducing kernel theory of L. Schwartz, provide the conceptual foundation and the construction procedure for rotation-invariant splines on Euclidean spaces, splines on the circle, and splines on the sphere and harmonic outside the sphere. Spherical splines and surface splines such as multi-conic functions, Hardy's multiquadric functions, pseudo-cubic splines, and thin-plate splines, are shown to be largely as effective as least squares collocation in representing geoid heights or gravity anomalies. A pseudo-cubic spline geoid for southern Africa is given, interpolating Doppler-derived geoid heights and astro-geodetic deflections of the vertical. Quadrature rules are derived for the thin-plate spline approximation (over a circular disk, and to a planar approximation) of Stokes's formula, the formulae of Vening Meinesz, and the L₁ vertical gradient operator in the analytical continuation series solution of Molodensky's problem. en_ZA
dc.language.iso eng en_ZA
dc.subject.other Gravity en_ZA
dc.subject.other Gravity anomalies en_ZA
dc.subject.other Spline theory en_ZA
dc.title Splines and local approximation of the earth's gravity field en_ZA
dc.type Doctoral Thesis
uct.type.publication Research en_ZA
uct.type.resource Thesis en_ZA
dc.publisher.institution University of Cape Town
dc.publisher.faculty Faculty of Engineering and the Built Environment
dc.publisher.department Division of Geomatics en_ZA
dc.type.qualificationlevel Doctoral
dc.type.qualificationname PhD en_ZA
uct.type.filetype Text
uct.type.filetype Image
dc.identifier.apacitation Van Gysen, H. G. (1988). <i>Splines and local approximation of the earth's gravity field</i>. (Thesis). University of Cape Town ,Faculty of Engineering & the Built Environment ,Division of Geomatics. Retrieved from http://hdl.handle.net/11427/15821 en_ZA
dc.identifier.chicagocitation Van Gysen, Hermanus Gerhardus. <i>"Splines and local approximation of the earth's gravity field."</i> Thesis., University of Cape Town ,Faculty of Engineering & the Built Environment ,Division of Geomatics, 1988. http://hdl.handle.net/11427/15821 en_ZA
dc.identifier.vancouvercitation Van Gysen HG. Splines and local approximation of the earth's gravity field. [Thesis]. University of Cape Town ,Faculty of Engineering & the Built Environment ,Division of Geomatics, 1988 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/15821 en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Van Gysen, Hermanus Gerhardus AB - The Hilbert space spline theory of Delvos and Schempp, and the reproducing kernel theory of L. Schwartz, provide the conceptual foundation and the construction procedure for rotation-invariant splines on Euclidean spaces, splines on the circle, and splines on the sphere and harmonic outside the sphere. Spherical splines and surface splines such as multi-conic functions, Hardy's multiquadric functions, pseudo-cubic splines, and thin-plate splines, are shown to be largely as effective as least squares collocation in representing geoid heights or gravity anomalies. A pseudo-cubic spline geoid for southern Africa is given, interpolating Doppler-derived geoid heights and astro-geodetic deflections of the vertical. Quadrature rules are derived for the thin-plate spline approximation (over a circular disk, and to a planar approximation) of Stokes's formula, the formulae of Vening Meinesz, and the L₁ vertical gradient operator in the analytical continuation series solution of Molodensky's problem. DA - 1988 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1988 T1 - Splines and local approximation of the earth's gravity field TI - Splines and local approximation of the earth's gravity field UR - http://hdl.handle.net/11427/15821 ER - en_ZA


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