Some modifications of Stokes' formula that account for truncation and potential coefficient errors
2000 (English)In: Journal of Geodesy, ISSN 0949-7714, E-ISSN 1432-1394, Vol. 74, no 2, 232-238 p.Article in journal (Refereed) Published
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 rnodifications. 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.
Place, publisher, year, edition, pages
2000. Vol. 74, no 2, 232-238 p.
least squares, modified Stokes' kernel, truncated Stokes' formula
IdentifiersURN: urn:nbn:se:kth:diva-19710ISI: 000086651600002OAI: oai:DiVA.org:kth-19710DiVA: diva2:338402
QC 201005252010-08-102010-08-10Bibliographically approved