A statistical analysis of errors in gravimetrically computed vertical deflections

In general, vertical deflections are obtained either by astrogeodetic methods or by gravimetric methods. In the latter approach, gravity anomaly measurements are processed by using the so-called Vening Meinesz equations to yield the vertical deflections. These calculated values of vertical deflections differ from the true values for two reasons: the measurements of the gravity anomalies are subject to error, and a numerical algorithm must be used to approximate the Vening Meinesz equations. In this paper, the autocorrelation functions of the deflection errors arising from these two sources are determined under the assumption that the anomalies and the error in measuring the anomalies are random processes.