Solutions to ellipsoidal boundary value problems for gravity field modelling
The determination of the figure of the Earth and its gravity field has long relied on methodologies that approximate the Earth by a sphere, but this level of accuracy is no longer adequate for many applications, due to the advent of new and advanced measurement techniques. New, practical and highly...
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| Format: | Thesis |
| Language: | English |
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Curtin University
2006
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| Online Access: | http://hdl.handle.net/20.500.11937/1637 |
| _version_ | 1848743724748636160 |
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| author | Claessens, Sten |
| author_facet | Claessens, Sten |
| author_sort | Claessens, Sten |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | The determination of the figure of the Earth and its gravity field has long relied on methodologies that approximate the Earth by a sphere, but this level of accuracy is no longer adequate for many applications, due to the advent of new and advanced measurement techniques. New, practical and highly accurate methodologies for gravity field modelling that describe the Earth as an oblate ellipsoid of revolution are therefore required. The foundation for these methodologies is formed by solutions to ellipsoidal geodetic boundary-value problems. In this thesis, new solutions to the ellipsoidal Dirichlet, Neumann and second-order boundary-value problems, as well as the fixed- and free-geodetic boundary-value problems, are derived. These solutions do not rely on any spherical approximation, but are nevertheless completely based on a simple spherical harmonic expansion of the function that is to be determined. They rely on new relations among spherical harmonic base functions. In the new solutions, solid spherical harmonic coefficients of the desired function are expressed as a weighted summation over surface spherical harmonic coefficients of the data on the ellipsoidal boundary, or alternatively as a weighted summation over coefficients that are computed under the approximation that the boundary is a sphere.Specific applications of the new solutions are the computation of geopotential coefficients from terrestrial gravimetric data and local or regional gravimetric geoid determination. Numerical closed-loop simulations have shown that the accuracy of geopotential coefficients obtained with the new methods is significantly higher than the accuracy of existing methods that use the spherical harmonic framework. The ellipsoidal corrections to a Stokesian geoid determination computed from the new solutions show strong agreement with existing solutions. In addition, the importance of the choice of the reference sphere radius in Stokes's formula and its effect on the magnitude and spectral sensitivity of the ellipsoidal corrections are pointed out. |
| first_indexed | 2025-11-14T05:50:07Z |
| format | Thesis |
| id | curtin-20.500.11937-1637 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T05:50:07Z |
| publishDate | 2006 |
| publisher | Curtin University |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-16372017-02-20T06:37:42Z Solutions to ellipsoidal boundary value problems for gravity field modelling Claessens, Sten gravity field gravity field modelling ellipsoidal geodetic boundary value problem solid spherical harmonic coefficients The determination of the figure of the Earth and its gravity field has long relied on methodologies that approximate the Earth by a sphere, but this level of accuracy is no longer adequate for many applications, due to the advent of new and advanced measurement techniques. New, practical and highly accurate methodologies for gravity field modelling that describe the Earth as an oblate ellipsoid of revolution are therefore required. The foundation for these methodologies is formed by solutions to ellipsoidal geodetic boundary-value problems. In this thesis, new solutions to the ellipsoidal Dirichlet, Neumann and second-order boundary-value problems, as well as the fixed- and free-geodetic boundary-value problems, are derived. These solutions do not rely on any spherical approximation, but are nevertheless completely based on a simple spherical harmonic expansion of the function that is to be determined. They rely on new relations among spherical harmonic base functions. In the new solutions, solid spherical harmonic coefficients of the desired function are expressed as a weighted summation over surface spherical harmonic coefficients of the data on the ellipsoidal boundary, or alternatively as a weighted summation over coefficients that are computed under the approximation that the boundary is a sphere.Specific applications of the new solutions are the computation of geopotential coefficients from terrestrial gravimetric data and local or regional gravimetric geoid determination. Numerical closed-loop simulations have shown that the accuracy of geopotential coefficients obtained with the new methods is significantly higher than the accuracy of existing methods that use the spherical harmonic framework. The ellipsoidal corrections to a Stokesian geoid determination computed from the new solutions show strong agreement with existing solutions. In addition, the importance of the choice of the reference sphere radius in Stokes's formula and its effect on the magnitude and spectral sensitivity of the ellipsoidal corrections are pointed out. 2006 Thesis http://hdl.handle.net/20.500.11937/1637 en Curtin University fulltext |
| spellingShingle | gravity field gravity field modelling ellipsoidal geodetic boundary value problem solid spherical harmonic coefficients Claessens, Sten Solutions to ellipsoidal boundary value problems for gravity field modelling |
| title | Solutions to ellipsoidal boundary value problems for gravity field modelling |
| title_full | Solutions to ellipsoidal boundary value problems for gravity field modelling |
| title_fullStr | Solutions to ellipsoidal boundary value problems for gravity field modelling |
| title_full_unstemmed | Solutions to ellipsoidal boundary value problems for gravity field modelling |
| title_short | Solutions to ellipsoidal boundary value problems for gravity field modelling |
| title_sort | solutions to ellipsoidal boundary value problems for gravity field modelling |
| topic | gravity field gravity field modelling ellipsoidal geodetic boundary value problem solid spherical harmonic coefficients |
| url | http://hdl.handle.net/20.500.11937/1637 |