The Meissl scheme for the geodetic ellipsoid
We present a variant of the Meissl scheme to relate surface spherical harmonic coefficients of the disturbing potential of the Earth's gravity field on the surface of the geodetic ellipsoid to surface spherical harmonic coefficients of its first- and second-order normal derivatives on the same...
| Main Authors: | , |
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| Format: | Journal Article |
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Springer - Verlag
2008
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| Online Access: | http://hdl.handle.net/20.500.11937/17068 |
| _version_ | 1848749357456687104 |
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| author | Claessens, Sten Featherstone, Will |
| author_facet | Claessens, Sten Featherstone, Will |
| author_sort | Claessens, Sten |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | We present a variant of the Meissl scheme to relate surface spherical harmonic coefficients of the disturbing potential of the Earth's gravity field on the surface of the geodetic ellipsoid to surface spherical harmonic coefficients of its first- and second-order normal derivatives on the same or any other ellipsoid. It extends the original (spherical) Meissl scheme, which only holds for harmonic coefficients computed from geodetic data on a sphere. In our scheme, a vector of solid spherical harmonic coefficients of one quantity is transformed into spherical harmonic coefficients of another quantity by pre-multiplication with a transformation matrix. This matrix is diagonal for transformations between spheres, but block-diagonal for transformations involving the ellipsoid. The computation of the transformation matrix involves an inversion if the original coefficients are defined on the ellipsoid. This inversion can be performed accurately and efficiently (i.e., without regularisation) for transformation among different gravity field quantities on the same ellipsoid, due to diagonal dominance of the matrices. However, transformations from the ellipsoid to another surface can only be performed accurately and efficiently for coefficients up to degree and order 520 due to numerical instabilities in the inversion. |
| first_indexed | 2025-11-14T07:19:39Z |
| format | Journal Article |
| id | curtin-20.500.11937-17068 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:19:39Z |
| publishDate | 2008 |
| publisher | Springer - Verlag |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-170682019-02-19T05:34:59Z The Meissl scheme for the geodetic ellipsoid Claessens, Sten Featherstone, Will Geopotential models Spectral theory Spherical harmonics Gravity field functionals We present a variant of the Meissl scheme to relate surface spherical harmonic coefficients of the disturbing potential of the Earth's gravity field on the surface of the geodetic ellipsoid to surface spherical harmonic coefficients of its first- and second-order normal derivatives on the same or any other ellipsoid. It extends the original (spherical) Meissl scheme, which only holds for harmonic coefficients computed from geodetic data on a sphere. In our scheme, a vector of solid spherical harmonic coefficients of one quantity is transformed into spherical harmonic coefficients of another quantity by pre-multiplication with a transformation matrix. This matrix is diagonal for transformations between spheres, but block-diagonal for transformations involving the ellipsoid. The computation of the transformation matrix involves an inversion if the original coefficients are defined on the ellipsoid. This inversion can be performed accurately and efficiently (i.e., without regularisation) for transformation among different gravity field quantities on the same ellipsoid, due to diagonal dominance of the matrices. However, transformations from the ellipsoid to another surface can only be performed accurately and efficiently for coefficients up to degree and order 520 due to numerical instabilities in the inversion. 2008 Journal Article http://hdl.handle.net/20.500.11937/17068 10.1007/s00190-007-0200-y Springer - Verlag fulltext |
| spellingShingle | Geopotential models Spectral theory Spherical harmonics Gravity field functionals Claessens, Sten Featherstone, Will The Meissl scheme for the geodetic ellipsoid |
| title | The Meissl scheme for the geodetic ellipsoid |
| title_full | The Meissl scheme for the geodetic ellipsoid |
| title_fullStr | The Meissl scheme for the geodetic ellipsoid |
| title_full_unstemmed | The Meissl scheme for the geodetic ellipsoid |
| title_short | The Meissl scheme for the geodetic ellipsoid |
| title_sort | meissl scheme for the geodetic ellipsoid |
| topic | Geopotential models Spectral theory Spherical harmonics Gravity field functionals |
| url | http://hdl.handle.net/20.500.11937/17068 |