On the combination of high-resolution and satellite-only global gravity models

The issue of combining high-resolution gravity models, based on observations taken on the Earth surface, with those derived from satellite-only observations is of increasing importance, due to the new data provided by gravity satellite missions, CHAMP, GRACE and GOCE. The paper addresses this issue with a twofold purpose. On the one hand, it is an attempt to discuss and assess general concepts, well known in literature, such as achievable resolution, regularization in the least-squares sense or in an infinite dimensional setup, combination criteria, symmetry and block diagonal structures. In particular, as for the symmetry question, a well-defined result, generalizing known facts, is derived. On the other hand, the outcomes of the general discussion are specifically applied to the combination of a high-resolution model (e.g. EGM08) with a GOCE gravity model estimated by the so-called space-wise approach. Small numerical examples are developed to clarify the property of the proposed solution.