On the topographic bias by harmonic continuation of the geopotential for a spherical sea-level approximation
Topography is a problem in geoid determination by the Stokes formula, a high degree Earth Gravitational Model (EGM), or for a combination thereof. Herein, we consider this problem in analytical/harmonic downward continuation of the external potential at point P to a geocentric spherical sea level ap...
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| Language: | English |
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De Gruyter
2024-11-01
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| Series: | Journal of Geodetic Science |
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| Online Access: | https://doi.org/10.1515/jogs-2022-0180 |
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| author | Sjöberg Lars E. |
| author_facet | Sjöberg Lars E. |
| author_sort | Sjöberg Lars E. |
| collection | DOAJ |
| description | Topography is a problem in geoid determination by the Stokes formula, a high degree Earth Gravitational Model (EGM), or for a combination thereof. Herein, we consider this problem in analytical/harmonic downward continuation of the external potential at point P to a geocentric spherical sea level approximation in geoid determination as well as to a sphere through the footpoint at the topography of the normal through P. Decomposing the topographic bias into a Bouguer shell component and a terrain component, we derive these components. It is shown that there is no terrain bias outside a spherical dome of base radius equal to the height H
P of P above the sphere, and the height of the dome is about 0.4 × H
P. In the case of dealing with an EGM, utilizing Molodensky truncation coefficients is one way to cope with the bias. |
| format | Article |
| id | doaj-art-3fc070c8fbb348b68033f4b024794f30 |
| institution | OA Journals |
| issn | 2081-9943 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Journal of Geodetic Science |
| spelling | doaj-art-3fc070c8fbb348b68033f4b024794f302025-08-20T02:23:36ZengDe GruyterJournal of Geodetic Science2081-99432024-11-011411124410.1515/jogs-2022-0180On the topographic bias by harmonic continuation of the geopotential for a spherical sea-level approximationSjöberg Lars E.0Geodesy and Geoinformatics, Royal Institute of Technology: Kungliga Tekniska Hogskolan, Stockholm, SwedenTopography is a problem in geoid determination by the Stokes formula, a high degree Earth Gravitational Model (EGM), or for a combination thereof. Herein, we consider this problem in analytical/harmonic downward continuation of the external potential at point P to a geocentric spherical sea level approximation in geoid determination as well as to a sphere through the footpoint at the topography of the normal through P. Decomposing the topographic bias into a Bouguer shell component and a terrain component, we derive these components. It is shown that there is no terrain bias outside a spherical dome of base radius equal to the height H P of P above the sphere, and the height of the dome is about 0.4 × H P. In the case of dealing with an EGM, utilizing Molodensky truncation coefficients is one way to cope with the bias.https://doi.org/10.1515/jogs-2022-0180analytical continuationdownward continuationharmonic continuation(quasi)geoid determinationtopographic bias |
| spellingShingle | Sjöberg Lars E. On the topographic bias by harmonic continuation of the geopotential for a spherical sea-level approximation Journal of Geodetic Science analytical continuation downward continuation harmonic continuation (quasi)geoid determination topographic bias |
| title | On the topographic bias by harmonic continuation of the geopotential for a spherical sea-level approximation |
| title_full | On the topographic bias by harmonic continuation of the geopotential for a spherical sea-level approximation |
| title_fullStr | On the topographic bias by harmonic continuation of the geopotential for a spherical sea-level approximation |
| title_full_unstemmed | On the topographic bias by harmonic continuation of the geopotential for a spherical sea-level approximation |
| title_short | On the topographic bias by harmonic continuation of the geopotential for a spherical sea-level approximation |
| title_sort | on the topographic bias by harmonic continuation of the geopotential for a spherical sea level approximation |
| topic | analytical continuation downward continuation harmonic continuation (quasi)geoid determination topographic bias |
| url | https://doi.org/10.1515/jogs-2022-0180 |
| work_keys_str_mv | AT sjoberglarse onthetopographicbiasbyharmoniccontinuationofthegeopotentialforasphericalsealevelapproximation |