A surface spherical harmonic expansion of gravity anomalies on the ellipsoid
A surface spherical harmonic expansion of gravity anomalies with respect to a geodetic reference ellipsoid can be used to model the global gravity field and reveal its spectral properties. In this paper, a direct and rigorous transformation between solid spherical harmonic coefficients of the Earth’...
| Main Authors: | , |
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| Format: | Journal Article |
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Springer Verlag
2015
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| Online Access: | http://hdl.handle.net/20.500.11937/40788 |
| _version_ | 1848755965080371200 |
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| author | Claessens, Sten Hirt, C. |
| author_facet | Claessens, Sten Hirt, C. |
| author_sort | Claessens, Sten |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | A surface spherical harmonic expansion of gravity anomalies with respect to a geodetic reference ellipsoid can be used to model the global gravity field and reveal its spectral properties. In this paper, a direct and rigorous transformation between solid spherical harmonic coefficients of the Earth’s disturbing potential and surface spherical harmonic coefficients of gravity anomalies in ellipsoidal approximation with respect to a reference ellipsoid is derived. This transformation cannot rigorously be achieved by the Hotine–Jekeli transformation between spherical and ellipsoidal harmonic coefficients. The method derived here is used to create a surface spherical harmonic model of gravity anomalies with respect to the GRS80 ellipsoid from the EGM2008 global gravity model. Internal validation of the model shows a global RMS precision of <1 nGal. This is significantly more precise than previous solutions based on spherical approximation or approximations to order e2 or e3, which are shown to be insufficient for the generation of surface spherical harmonic coefficients with respect to a geodetic reference ellipsoid. Numerical results of two applications of the new method (the computation of ellipsoidal corrections to gravimetric geoid computation, and area means of gravity anomalies in ellipsoidal approximation) are provided. |
| first_indexed | 2025-11-14T09:04:41Z |
| format | Journal Article |
| id | curtin-20.500.11937-40788 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:04:41Z |
| publishDate | 2015 |
| publisher | Springer Verlag |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-407882019-02-19T05:35:06Z A surface spherical harmonic expansion of gravity anomalies on the ellipsoid Claessens, Sten Hirt, C. A surface spherical harmonic expansion of gravity anomalies with respect to a geodetic reference ellipsoid can be used to model the global gravity field and reveal its spectral properties. In this paper, a direct and rigorous transformation between solid spherical harmonic coefficients of the Earth’s disturbing potential and surface spherical harmonic coefficients of gravity anomalies in ellipsoidal approximation with respect to a reference ellipsoid is derived. This transformation cannot rigorously be achieved by the Hotine–Jekeli transformation between spherical and ellipsoidal harmonic coefficients. The method derived here is used to create a surface spherical harmonic model of gravity anomalies with respect to the GRS80 ellipsoid from the EGM2008 global gravity model. Internal validation of the model shows a global RMS precision of <1 nGal. This is significantly more precise than previous solutions based on spherical approximation or approximations to order e2 or e3, which are shown to be insufficient for the generation of surface spherical harmonic coefficients with respect to a geodetic reference ellipsoid. Numerical results of two applications of the new method (the computation of ellipsoidal corrections to gravimetric geoid computation, and area means of gravity anomalies in ellipsoidal approximation) are provided. 2015 Journal Article http://hdl.handle.net/20.500.11937/40788 10.1007/s00190-015-0832-2 Springer Verlag fulltext |
| spellingShingle | Claessens, Sten Hirt, C. A surface spherical harmonic expansion of gravity anomalies on the ellipsoid |
| title | A surface spherical harmonic expansion of gravity anomalies on the ellipsoid |
| title_full | A surface spherical harmonic expansion of gravity anomalies on the ellipsoid |
| title_fullStr | A surface spherical harmonic expansion of gravity anomalies on the ellipsoid |
| title_full_unstemmed | A surface spherical harmonic expansion of gravity anomalies on the ellipsoid |
| title_short | A surface spherical harmonic expansion of gravity anomalies on the ellipsoid |
| title_sort | surface spherical harmonic expansion of gravity anomalies on the ellipsoid |
| url | http://hdl.handle.net/20.500.11937/40788 |