Full Text Available
Note: Clicking the button above will open the full text document at the original institutional repository in a new window.
Splines and local approximation of the earth's gravity field
Bibliography: pages 214-220.
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Language: | English |
| Published: |
Division of Geomatics
2015
|
| Subjects: | |
| Tags: |
No Tags, Be the first to tag this record!
|
| _version_ | 1867613230545764352 |
|---|---|
| access_status_str | Open Access |
| author | Van Gysen, Hermanus Gerhardus |
| author2 | Merry, Charles |
| author_browse | Merry, Charles Van Gysen, Hermanus Gerhardus |
| author_facet | Merry, Charles Van Gysen, Hermanus Gerhardus |
| author_sort | Van Gysen, Hermanus Gerhardus |
| collection | Thesis |
| description | Bibliography: pages 214-220. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/15821 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:32:50.328Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2015 |
| publishDateRange | 2015 |
| publishDateSort | 2015 |
| publisher | Division of Geomatics |
| publisherStr | Division of Geomatics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/15821 Splines and local approximation of the earth's gravity field Van Gysen, Hermanus Gerhardus Merry, Charles Gravity Gravity anomalies Spline theory Bibliography: pages 214-220. 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. 2015-12-20T15:27:23Z 2015-12-20T15:27:23Z 1988 Doctoral Thesis Doctoral PhD http://hdl.handle.net/11427/15821 eng application/pdf Division of Geomatics Faculty of Engineering and the Built Environment University of Cape Town |
| spellingShingle | Gravity Gravity anomalies Spline theory Van Gysen, Hermanus Gerhardus Splines and local approximation of the earth's gravity field |
| thesis_degree_str | Doctoral |
| title | Splines and local approximation of the earth's gravity field |
| title_full | Splines and local approximation of the earth's gravity field |
| title_fullStr | Splines and local approximation of the earth's gravity field |
| title_full_unstemmed | Splines and local approximation of the earth's gravity field |
| title_short | Splines and local approximation of the earth's gravity field |
| title_sort | splines and local approximation of the earth s gravity field |
| topic | Gravity Gravity anomalies Spline theory |
| url | http://hdl.handle.net/11427/15821 |
| work_keys_str_mv | AT vangysenhermanusgerhardus splinesandlocalapproximationoftheearthsgravityfield |