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On integral approach to regional gravity field modelling from satellite gradiometric data

Eshagh M.

Acta Geophysica

2011

Vol. 59, no. 1

29-54

Solution of the gradiometric boundary value problems leads to three integral formulas. If we are satisfied with obtaining a smooth solution for the Earth’s gravity field, we can use the formulas in regional gravity field modelling. In such a case, satellite gradiometric data are integrated on a sphere at satellite level and continued downward to the disturbing potential (geoid) at sea level simultaneously. This paper investigates the gravity field modelling from a full tensor of gravity at satellite level. It studies the truncation bias of the integrals as well as the filtering of noise of data. Numerical studies show that by integrating Tzz with 1 mE noise and in a cap size of 7°, the geoid can be recovered with an error of 12 cm after the filtering process. Similarly, the errors of the recovered geoids from Txz,yz and Txx-yy, 2xy are 13 and 21 cm, respectively.

Spatially restricted integrals in gradiometric boundary value problemsSpatially restricted integrals in gradiometric boundary value problems

Eshagh M.

Artificial Satellites : Journal of Planetary Geodesy

2009

Vol. 44, No. 4

131--148

The spherical Slepian functions can be used to localize the solutions of the gradiometric boundary value problems on a sphere. These functions involve spatially restricted integral products of scalar, vector and tensor spherical harmonics. This paper formulates these integrals in terms of combinations of the Gaunt coefficients and integrals of associated Legendre functions. The presented formulas for these integrals are useful in recovering the Earth’s gravity field locally from the satellite gravity gradiometry data.