New modifications of stokes' integral to reduce the truncation error
21/09/2016 | 11:15 | Session 3: Recent Development in Theory and Modelling
Author(s): Lars E. Sjöberg and Mehdi S. Shafiei Joud
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.