caa a22 4500 475737776 CHVBK 20180406123451.0 cr unu---uuuuu 170329e20000301xx s 000 0 eng 10.1007/s001900050281 doi (NATIONALLICENCE)springer-10.1007/s001900050281 Some modifications of Stokes' formula that account for truncation and potential coefficient errors [Elektronische Daten] [L. E. Sjöberg, A. Hunegnaw] Abstract.:  Stokes' formula from 1849 is still the basis for the gravimetric determination of the geoid. The modification of the formula, originating with Molodensky, aims at reducing the truncation error outside a spherical cap of integration. This goal is still prevalent among various modifications. In contrast to these approaches, some least-squares types of modification that aim at reducing the truncation error, as well as the error stemming from the potential coefficients, are demonstrated. The least-squares estimators are provided in the two cases that (1) Stokes' kernel is a priori modified (e.g. according to Molodensky's approach) and (2) Stokes' kernel is optimally modified to minimize the global mean square error. Meissl-type modifications are also studied. In addition, the use of a higher than second-degree reference field versus the original (Pizzetti-type) reference field is discussed, and it is concluded that the former choice of reference field implies increased computer labour to achieve the same result as with the original reference field. Springer-Verlag Berlin Heidelberg, 2000 Key words: Least squares - Modified Stokes' kernel - Truncated Stokes' formula nationallicence Sjöberg L. E. Department of Geodesy and Photogrammetry, Royal Institute of Technology, S-10044 Stockholm, Sweden e-mail: sjoberg@geomatics.kth.se; Tel.: +46 08 790 7330; Fax: +46 08 790 7343, SE aut Hunegnaw A. Department of Geodesy and Photogrammetry, Royal Institute of Technology, S-10044 Stockholm, Sweden e-mail: sjoberg@geomatics.kth.se; Tel.: +46 08 790 7330; Fax: +46 08 790 7343, SE aut https://doi.org/10.1007/s001900050281 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s001900050281 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Sjöberg L. E. Department of Geodesy and Photogrammetry, Royal Institute of Technology, S-10044 Stockholm, Sweden e-mail: sjoberg@geomatics.kth.se; Tel.: +46 08 790 7330; Fax: +46 08 790 7343, SE aut NATIONALLICENCE 700 1- Hunegnaw A. Department of Geodesy and Photogrammetry, Royal Institute of Technology, S-10044 Stockholm, Sweden e-mail: sjoberg@geomatics.kth.se; Tel.: +46 08 790 7330; Fax: +46 08 790 7343, SE aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer