Combination of GOCE Gravity Gradients in Regional Gravity Field Modelling Using Radial Basis Functions

The satellite gravity mission GOCE measured the second-order derivatives of the Earth's gravitational potential with high accuracy. The GOCE data enrich our gravity field knowledge especially at spatial resolutions from 750 km down to 80 km. In this paper we carry out regional gravity field analysis using radial localising basis functions that permit the combination of different data types tailored to their accuracy and spectral signal content. We formulate observation equations for each individual GOCE gravity gradient as they are distinctive reflections of the gravity field and contain directional information. To optimally use the original GOCE measurements, we derive the mathematical expressions in the gradiometer reference frame. The expressions and their implementation are validated for a test area in Scandinavia by comparison with the global gravity field model GOCO03s, which yields small differences of less than +/- 1mE. The relative weighting of the observations is determined by variance component estimation. Moreover manually fixing the weights leads to smaller residuals with respect to GOCO03s, which is probably caused by systematic errors in the gradients. We demonstrate the capabilities of our method through a combination of the gradient data with terrestrial free-air anomalies. At spatial resolutions down to 40 km the terrestrial data get much larger relative weights than the GOCE data, which indicates the proper performance of the combination method.