1st Joint Commission 2 and IGFS Meeting
International Symposium on
Gravity, Geoid and Height Systems 2016

September 19-23, 2016
Thessaloniki, Greece

New modifications of stokes' integral to reduce the truncation error

21/09/2016 | 11:15 | Session 3: Recent Development in Theory and Modelling


Lars E. Sjöberg and Mehdi S. Shafiei Joud


In the numerical application of the Stokes’ integral the area of the integration is limited to a spherical cap around the point of the computation. Different geodesists developed some alternatives on the Molodenskii’s method of modifying the kernel function. A new stochastic modification of the Stokes integral is presented which reduces the truncation error when regional terrestrial gravity data are used in assimilation with a global geopotential model (GGM). We use a combination of two existing modifications from Meissl and Sjöberg. The latter applies a least squares to minimize the truncation error, while the former causes the truncation coefficients converge to zero more rapidly by using a continuous function. Our formulation provides two different derivations of the truncation errors using Green’s second identity and a smoothing operator for computing the mean gravity anomaly. The latter is suggested for further research as a regularization method of the first derivative of the truncation error kernel. Different modifications are tested including deterministic and stochastic modifications in an approach to a regional geoid determination.

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