Gravity Field Continuation of Irregularly Spaced Data Using Least Squares Collocation

Abstract

SUMMARY The calculation of Bouguer anomalies in high mountains requires a gravity field continuation from irregularly spaced gravity data on the topography to an equipotential surface. Least squares collocation (LSC) is successfully used for geodetic purposes and offers an elegant solution to this problem. A great advantage of this method is the possibility to give estimates of the accuracy of the approximated gravity field. Of central importance in LSC is the covariance function. The influence on the result of the model covariance function (MCF), which replaces in the calculation the empirical covariance function (ECF) of the data, is studied. The synthetic model used for these studies is as realistic as possible, including topography, data gaps and noise. The quality of the predicted error seems to be much more sensitive to the choice of the MCF than the quality of the approximation. The improvement of the field continuation to an equipotential surface compared to simple interpolation is remarkable. An example of such a field continuation is given. The Bouguer anomaly in the Andes of northern Chile is continued to the sea-level by the combined application of collocation and simple models, describing regional parts of the gravity field.