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.
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Received: 14 December 1998 / Accepted: 4 October 1999
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Sjöberg, L., Hunegnaw, A. Some modifications of Stokes' formula that account for truncation and potential coefficient errors. Journal of Geodesy 74, 232–238 (2000). https://doi.org/10.1007/s001900050281
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DOI: https://doi.org/10.1007/s001900050281