On the Regularization Problem in Gravity Field Determination from Satellite Gradiometric Data

Abstract

The determination of the Earth's exterior gravity field from noisy satellite gravity gradient (SGG) data lacks stability due to the polar gaps and the downward continuation process. After discretization, this property translates into an ill-conditioned system of normal equations, which has to be regularized in order to obtain a physically meaningful solution. Regularization requires the selection of (1) a regularization method and (2) a parameter choice rule. Important selection criteria are that the regularization strategy is applicable to the large-scale problem of COCE data analysis, characterized by millions of observations and ten thousands of unknowns, and that the parameter choice rule is independent of some prior information such as the total error power or the smoothness of the solution. We have investigated Tikhonov-type regularization with the Generalized Cross Validation (GCV) parameter choice method and an 'adjustable' regularization matrix, including Kaula stabilization as well as derivative-constraining regularization as special cases. The method has been modified allowing for coloured noise observations to be taken into account, and for fast computation of the trace-term in GCV by using a randomized trace-estimator. Results from a detailed numerical study following the baseline of the GOCE mission are presented. We can show that significant improvements with respect to the Kaula stabilization method are possible.