Spherical harmonic analysis of a harmonic function given on a spheroid
A new analytical method for the computation of a truncated series of solid spherical harmonic coefficients (HCs) from data on a spheroid (i.e. an oblate ellipsoid of revolution) is derived, using a transformation between surface and solid spherical HCs. A two-step procedure is derived to extend this...
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| Format: | Journal Article |
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Blackwell Publishing Ltd
2016
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| Online Access: | http://hdl.handle.net/20.500.11937/30661 |
| _version_ | 1848753151483576320 |
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| author | Claessens, Sten |
| author_facet | Claessens, Sten |
| author_sort | Claessens, Sten |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | A new analytical method for the computation of a truncated series of solid spherical harmonic coefficients (HCs) from data on a spheroid (i.e. an oblate ellipsoid of revolution) is derived, using a transformation between surface and solid spherical HCs. A two-step procedure is derived to extend this transformation beyond degree and order (d/o) 520. The method is compared to the Hotine-Jekeli transformation in a numerical study based on the EGM2008 global gravity model. Both methods are shown to achieve submicrometre precision in terms of height anomalies for a model to d/o 2239. However, both methods result in spherical harmonic models that are different by up to 7.6 mm in height anomalies and 2.5 mGal in gravity disturbances due to the different coordinate system used. While the Hotine-Jekeli transformation requires the use of an ellipsoidal coordinate system, the new method uses only spherical polar coordinates. The Hotine-Jekeli transformation is numerically more efficient, but the new method can more easily be extended to cases where (a linear combination of) normal derivatives of the function under consideration are given on the surface of the spheroid. It therefore provides a solution to many types of ellipsoidal boundary-value problems in the spectral domain. |
| first_indexed | 2025-11-14T08:19:57Z |
| format | Journal Article |
| id | curtin-20.500.11937-30661 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:19:57Z |
| publishDate | 2016 |
| publisher | Blackwell Publishing Ltd |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-306612017-09-13T15:08:55Z Spherical harmonic analysis of a harmonic function given on a spheroid Claessens, Sten A new analytical method for the computation of a truncated series of solid spherical harmonic coefficients (HCs) from data on a spheroid (i.e. an oblate ellipsoid of revolution) is derived, using a transformation between surface and solid spherical HCs. A two-step procedure is derived to extend this transformation beyond degree and order (d/o) 520. The method is compared to the Hotine-Jekeli transformation in a numerical study based on the EGM2008 global gravity model. Both methods are shown to achieve submicrometre precision in terms of height anomalies for a model to d/o 2239. However, both methods result in spherical harmonic models that are different by up to 7.6 mm in height anomalies and 2.5 mGal in gravity disturbances due to the different coordinate system used. While the Hotine-Jekeli transformation requires the use of an ellipsoidal coordinate system, the new method uses only spherical polar coordinates. The Hotine-Jekeli transformation is numerically more efficient, but the new method can more easily be extended to cases where (a linear combination of) normal derivatives of the function under consideration are given on the surface of the spheroid. It therefore provides a solution to many types of ellipsoidal boundary-value problems in the spectral domain. 2016 Journal Article http://hdl.handle.net/20.500.11937/30661 10.1093/gji/ggw126 Blackwell Publishing Ltd fulltext |
| spellingShingle | Claessens, Sten Spherical harmonic analysis of a harmonic function given on a spheroid |
| title | Spherical harmonic analysis of a harmonic function given on a spheroid |
| title_full | Spherical harmonic analysis of a harmonic function given on a spheroid |
| title_fullStr | Spherical harmonic analysis of a harmonic function given on a spheroid |
| title_full_unstemmed | Spherical harmonic analysis of a harmonic function given on a spheroid |
| title_short | Spherical harmonic analysis of a harmonic function given on a spheroid |
| title_sort | spherical harmonic analysis of a harmonic function given on a spheroid |
| url | http://hdl.handle.net/20.500.11937/30661 |