Covariance models for geodetic applications of collocation

The recent gravity mission GOCE aims at measuring the global gravity field of the Earth with un-precedent accuracy. An improved description of gravity means improved knowledge in e.g. ocean circulation and climate and sea-level change with implications in areas such as geodesy and surveying. Through GOCE products, the low-medium frequency spectrum of the gravity field is properly estimated. This is enough to detect the main gravimetric structures but local applications are still questionable. GOCE data can be integrated with other kind of observations, having different features, frequency content, spatial coverage and resolution. Gravity anomalies (∆g) and geoid undulation (N) derived from radar-altimetry data (as well as GOCE T_rr) are all linear(ized) functional of the anomalous gravity potential (T). For local modeling of the gravity field, this useful connection can be used to integrate information of different observations, in order to obtain a better representation of high frequency, otherwise difficult to recover. The usual methodology is based on Collocation theory. The nodal problem of this approach is the correct modeling of the empirical covariance of the observations. Proper covariance models have been proposed by many authors. However, there are problems in fitting the empirical values when different functional of T are combined. The problem of modeling covariance functions has been dealt with an innovative methodology based on Linear Programming and the Simplex Algorithm. The results obtained during the test phase of this new methodology of modeling covariance function for local applications show improvements respect to the software packages available until now.