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Topographic effects by the Stokes-Helmert method of geoid and quasi-geoid determinations
KTH, Superseded Departments, Geodesy and Photogrammetry.
2000 (English)In: Journal of Geodesy, ISSN 0949-7714, E-ISSN 1432-1394, Vol. 74, no 2, 255-268 p.Article in journal (Refereed) Published
Abstract [en]

The topographic potential and the direct topographic effect on the geoid are presented as surface integrals, and the direct gravity effect is derived as a rigorous surface integral on the unit sphere. By Taylor-expanding the integrals at sea level with respect to topographic elevation (H) the power series of the effects is derived to arbitrary orders. This study is primarily limited to terms of order H-2. The limitations of the various effects in the frequently used planar approximations are demonstrated. In contrast, it is shown that the spherical approximation to power H-2 leads to a combined topographic effect on the geoid (direct plus indirect effect) proportional to (H) over tilde(2) (where terms of degrees 0 and 1 are missing) of the order of several metres, while the combined topographic effect on the height anomaly vanishes, implying that current frequent efforts to determine the direct effect to this order are not needed. The last result is in total agreement with Bjerhammar's method in physical geodesy. It is shown that the most frequently applied remove-restore technique of topographic masses in the application of Stokes' formula suffers from significant errors both in the terrain correction C (representing the sum of the direct topographic effect on gravity anomaly and the effect of continuing the anomaly to sea level) and in the term t (mainly representing the indirect effect on the geoidal or quasi-geoidal height).

Place, publisher, year, edition, pages
2000. Vol. 74, no 2, 255-268 p.
Keyword [en]
direct effect, Helmert reduction, Stokes' formula, topographic effect, analytical continuation, downward continuation, gravity
URN: urn:nbn:se:kth:diva-19711ISI: 000086651600005OAI: diva2:338403
QC 20100525Available from: 2010-08-10 Created: 2010-08-10Bibliographically approved

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Sjöberg, Lars Erik
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