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Alternative expressions for gravity gradients in local north-oriented frame and tensor spherical harmonics

100%

Eshagh M.

Acta Geophysica

2010

tom Vol. 58, no. 2

215-243

The traditional expressions for gravity gradients in local northoriented frame and tensor spherical harmonics have complicated forms involved with first- and second-order derivatives of spherical harmonics and also singular terms. In this paper we present alternative expressions for these quantities, which are simpler and contain no singular terms. The presented formulas are useful for those disciplines of geosciences which are involved with potential theory, tensor spherical harmonics and second- order derivatives of spherical harmonic series in the local northoriented frame. A simple numerical test on the solution of the gradiometric boundary value problems presents the correctness of these new expressions and ability of the solutions to continue the gravity gradients from satellite level down to sea level using spherical harmonics.

Smoothing impact of isostatic crustal thickness models on local integral inversion of satellite gravity gradiometry data

70%

Eshagh M. , Bagherbandi M.

tom Vol. 59, no. 5

891-906

The effects of topographic masses on satellite gradiometric data are large and in order to reduce the magnitude of these effects some compensation mechanisms should be considered. Here we use the isostatic hypotheses of Airy-Heiskanen and the recent Vening Meinesz-Moritz for compensating these effects and to smooth the data prior to their downward continuation to gravity anomaly. The second-order partial derivatives of extended Stokes' formula are used for the continuations over a topographically rough territory like Persia. The inversions are performed and compared based on two schemes of the remove-compute-restore technique and direct downward continuation. Numerical results show that the topographic-isostatic effect based on Vening Meinesz-Mortiz's hypothesis smoothes the data better than that based on Airy-Heiskanen's hypothesis. Also the quality of inversions of the smoothed data by this mechanism is twice better than that of the nonsmoothed ones.

Spherical harmonics expansion of the atmospheric gravitational potential based on exponential and power models of atmosphere

60%

Eshagh M.

tom Vol. 43, No. 1

25--43

Spherical harmonic formulation of gravitational potential of the atmosphere depends on the analytical model of the atmospheric density which is used. Exponential and power models are two well-known mathematical tools which are used in atmospheric applications. This paper presents simple formulas for the harmonic coefficients of internal and external types of the atmospheric potential based on these models which can be used in most of the gravimetric aspects. It considers the atmospheric effect on the satellite gravity gradiometry data as an example for numerical investigations. The numerical studies on these data show that the maximum atmospheric effect is about 2 mE over Fennoscandia based on both models, and their differences are less than 0.1 mE. The difference between indirect atmospheric effects reaches 2 cm and 0.02 mGal on the geoid and gravity anomaly, respectively in this region.