Combining Airborne and Ground Gravity Using Collocation

Abstract

In the Greenland Aerogeophysical Project (GAP) airborne gravity data have been collected covering all of Greenland. In addition the coastal areas are covered by ground gravity data. Improved gravity field modeling results may be obtained by combining the two data sources. Least Squares Collocation (LSC) may be used with advantage for this purpose. The method furthermore allows for (a) the correct modeling of the (filtered) observation functional, (b) the use of an error correlation function, (c) the determination of biases in the airborne data and (d) the estimation of the errors of the quantities calculated for the obtained gravity field models. We describe here the results obtained using LSC in the two areas with good ground data coverage. The basis for using LSC is the estimation and subsequent analytic modeling of the empirical covariance function. However, this modeling was only successful when a model error correlation function was subtracted from the covariance function of the airborne data. The variances calculated from the ground data were used to control that the variances derived from the airborne covariance had correct values. This made it possible to correctly downward continue the GAP data using LSC. When comparing observed and ground data predicted from the GAP data, biases were found. This is probably due to systematic errors in the airborne data or systematic errors from terrain effects. The bias was removed by assigning a bias-parameter to each track and adding (a part of) the ground data as new observations. The remaining ground data were used to verify that the bias has been removed. The results, however, were in both areas only marginally better than those obtained when using one ground gravity sub-data set to predict the other. On the other hand they were much better than results obtained using LSC or frequency domain collocation for the prediction of ground gravity from the GAP data only.