The effect of remote zones on the accuracy of evaluating the Molodensky

An analytical method is presented for determining the error in computing the gravity anomaly from the Molodensky integral if geoidal undulation data in remote zones are neglected. The error is given in terms of the usual degree variance and a set of parameters which are functions only of the size of the area in which undulation data are taken. A numerical calculation using Kaula's degree variances indicates that it is necessary to integrate the Molodensky integral over approximately a hemisphere in order to reduce the effect of neglected data to the order of 1 milligal in the computation of gravity anomaly.