caa a22 4500 47573775X CHVBK 20180406123451.0 cr unu---uuuuu 170329e20000301xx s 000 0 eng 10.1007/s001900050284 doi (NATIONALLICENCE)springer-10.1007/s001900050284 Sjöberg L. E. Royal Institute of Technology, Department of Geodesy and Photogrammetry, S-100 44 Stockholm, Sweden e-mail: sjoberg@geomatics.kth.se; Tel.: +46 8 790 73 30; Fax: +46 8 790 73 43, SE aut Topographic effects by the Stokes-Helmert method of geoid and quasi-geoid determinations [Elektronische Daten] [L. E. Sjöberg] Abstract.: 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˜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). Springer-Verlag Berlin Heidelberg, 2000 Key words: Direct effect - Helmert reduction - Stokes' formula - Topographic effect nationallicence https://doi.org/10.1007/s001900050284 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s001900050284 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Sjöberg L. E. Royal Institute of Technology, Department of Geodesy and Photogrammetry, S-100 44 Stockholm, Sweden e-mail: sjoberg@geomatics.kth.se; Tel.: +46 8 790 73 30; Fax: +46 8 790 73 43, SE aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer