Spherical Cap regularization of GOCE normal equation systems

Since the determination of a high-resolution gravity field model from GOCE measurements is an ill-posed problem, the application of regularization techniques is neccessary. Applying Tikhonov Regularization leads to stable, but biased solutions. The so-called regularization error is introduced globally, and cannot be computed strictly without the knowledge of the true gravity field. As exemplarily demonstrated in this paper, its estimation on the basis of regularized solutions may be problematic. Due to the introduction of an a-priori gravity field model, the magnitude of the regularization error can be reduced significantly. However, for the mission verification and validation internally consistent and independent solutions are required. In this context, the incorporation of external gravity field information on a global scale should be avoided. A way out is the application of spatially restricted regularization techniques. In Spherical Cap Regularization the a-priori gravity field model is introduced explicitly at the polar regions, where no GOCE measurements are available. Consequently, major parts of the earth remain almost unaffected of the prior information and the regularization error. Second-order Spherical Cap Regularization enables the computation of stable solutions without the introduction of any external gravity field information at all. The performance of Tikhonov Regularization and Spherical Cap Regularization is assessed on the basis of a numerical case study.