The use of height data in gravity field approximation by collocation

The accuracy of a gravity field model depends on the amount of available data and on the variation of the gravity field. When topographic height data are available, for example, in the form of a digital terrain model, it is possible to smooth the gravity field on a local scale by removing the gravitational effects calculated from models of the topographic masses. In this way, significant improvements of the prediction results are obtained in mountainous areas. In this paper we describe methods for the calculation of such gravitational terrain effects, applicable in collocation approximation of the gravity field. The terrain effects on gravity field quantities such as gravity anomalies, deflections of the vertical, and geoid undulations are calculated using a system of rectangular prisms, representing either a quasi-traditional model of the topography and the isostatic compensation or a residual terrain model, where only the deviation of the topography from a mean elevation surface is considered. To test the terrain reduction methods, numerical prediction experiments have been conducted in the mountainous White Sands area, New Mexico. From gravity anomalies spaced approximately 6 arc min apart, other known gravity anomalies and deflections of the vertical were predicted using collocation. When using terrain effects calculated on the basis of 0.5 × 0.5 arc min point heights, the rms errors decreased by a factor of nearly 3 to 1 arc sec for the deflections and 3–4 mGal for the gravity anomalies, quite insensitive to the actual type of terrain reduction used. The feasibility of using topographic reductions in collocation is thus effectively demonstrated.