A numerical test of the topographic bias
In 1962 A. Bjerhammar introduced the method of analytical continuation in physical geodesy, implying that surface gravity anomalies are downward continued into the topographic masses down to an internal sphere (the Bjerhammar sphere). The method also includes analytical upward continuation of the po...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2018-02-01
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| Series: | Journal of Geodetic Science |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/jogs-2018-0002 |
| _version_ | 1817991147421696000 |
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| author | Sjöberg L.E. Joud M.S.S. |
| author_facet | Sjöberg L.E. Joud M.S.S. |
| author_sort | Sjöberg L.E. |
| collection | DOAJ |
| description | In 1962 A. Bjerhammar introduced the method of analytical continuation in physical geodesy, implying that surface gravity anomalies are downward continued into the topographic masses down to an internal sphere (the Bjerhammar sphere). The method also includes analytical upward continuation of the potential to the surface of the Earth to obtain the quasigeoid. One can show that also the common remove-compute-restore technique for geoid determination includes an analytical continuation as long as the complete density distribution of the topography is not known. The analytical continuation implies that the downward continued gravity anomaly and/or potential are/is in error by the so-called topographic bias, which was postulated by a simple formula of L E Sjöberg in 2007. Here we will numerically test the postulated formula by comparing it with the bias obtained by analytical downward continuation of the external potential of a homogeneous ellipsoid to an inner sphere. The result shows that the postulated formula holds: At the equator of the ellipsoid, where the external potential is downward continued 21 km, the computed and postulated topographic biases agree to less than a millimetre (when the potential is scaled to the unit of metre). |
| first_indexed | 2024-04-14T01:09:29Z |
| format | Article |
| id | doaj.art-8d595299767e4dbca23d62f79dffd290 |
| institution | Directory Open Access Journal |
| issn | 2081-9943 |
| language | English |
| last_indexed | 2024-04-14T01:09:29Z |
| publishDate | 2018-02-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Journal of Geodetic Science |
| spelling | doaj.art-8d595299767e4dbca23d62f79dffd2902022-12-22T02:21:09ZengDe GruyterJournal of Geodetic Science2081-99432018-02-0181141710.1515/jogs-2018-0002jogs-2018-0002A numerical test of the topographic biasSjöberg L.E.0Joud M.S.S.1Royal Institute of Technology (KTH) Stockholm, Stockholm, SwedenDivision of Geodesy and Satellite Positioning, Stockholm, SwedenIn 1962 A. Bjerhammar introduced the method of analytical continuation in physical geodesy, implying that surface gravity anomalies are downward continued into the topographic masses down to an internal sphere (the Bjerhammar sphere). The method also includes analytical upward continuation of the potential to the surface of the Earth to obtain the quasigeoid. One can show that also the common remove-compute-restore technique for geoid determination includes an analytical continuation as long as the complete density distribution of the topography is not known. The analytical continuation implies that the downward continued gravity anomaly and/or potential are/is in error by the so-called topographic bias, which was postulated by a simple formula of L E Sjöberg in 2007. Here we will numerically test the postulated formula by comparing it with the bias obtained by analytical downward continuation of the external potential of a homogeneous ellipsoid to an inner sphere. The result shows that the postulated formula holds: At the equator of the ellipsoid, where the external potential is downward continued 21 km, the computed and postulated topographic biases agree to less than a millimetre (when the potential is scaled to the unit of metre).https://doi.org/10.1515/jogs-2018-0002analytical continuationhomogeneous ellipsoidtopographic bias |
| spellingShingle | Sjöberg L.E. Joud M.S.S. A numerical test of the topographic bias Journal of Geodetic Science analytical continuation homogeneous ellipsoid topographic bias |
| title | A numerical test of the topographic bias |
| title_full | A numerical test of the topographic bias |
| title_fullStr | A numerical test of the topographic bias |
| title_full_unstemmed | A numerical test of the topographic bias |
| title_short | A numerical test of the topographic bias |
| title_sort | numerical test of the topographic bias |
| topic | analytical continuation homogeneous ellipsoid topographic bias |
| url | https://doi.org/10.1515/jogs-2018-0002 |
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