On Satellite Gravity Gradiometry

by Eshagh, Mehdi

Satellite gravity gradiometry measures the second-order partial derivatives of the Earth’s gravitational potential based on differential accelerometry. Measuring the gravitational gradients at satellite level opens a new way to compute a precise and high resolution geopotential model from space. The upcoming satellite mission gravity field and steady-state ocean circulation (GOCE) is dedicated to provide precise gradiometric data in this respect. It is claimed to achieve geoid and gravity anomaly with 1 cm and 1 mGal accuracies, respectively with 1 ? ×1 ? resolution using the delivered Earth gravitational model from GOCE data. In this thesis new expressions for the gravitational gradients are developed. A new expression for tensor spherical harmonics are presented and used to solve the gradiometric boundary value problems and to compute a geopotential model. It is found that the vertical-horizontal gradients are more suited than the other gradients in geopotential modeling. Topographic and atmospheric effects on the satellite gravity gradiometry data are formulated in spherical harmonics, and numerically investigations in Fennoscandia and Iran show that the topographic effect is in the 1 and 2 E level in these areas. A new atmospheric density model is proposed, and the atmospheric effect based on this model is within 5 mE. Second-order partial derivatives of the extended Stokes’ formula are modified in a least-squares sense to validate the satellite gravity gradiometry data. Downward continuation of each element of the gravitational tensor is studied using the Tikhonov regularization. The gravitational gradients T zz , T xx ,T yy , T xz , T yz and T xy are suited for determining gravity anomaly at sea level. Combination of the satellite data to recover the global and local gravity field is investigated. It is shown that the combination of integral solutions of the gradiometric boundary value problems using variance component estimation, is beneficial in geopotential modeling. In local gravity field determination, it is concluded that a grid of 1 ? ×1 ? gravity anomalies with 1 mGal accuracy is achievable from directly combined continuation of the satellite gradiometric data. The polar gaps due to an inclined orbit are studied, and it is shown that T xy and T yz are better than the other gradients for estimating the gravity anomaly in the polar gaps. The combined inversion of the satellite gradiometric data (after biased-correction step) can determine 1 ? ×1 ? gravity anomalies with 1 and 3 mGal accuracy in the north and south polar gaps, respectively.