Investigations on the accuracy concerning the derivation of absolute gravimetric height anomalies and deflections of the vertical based on the theory of Molodensky

Abstract

The investigations refer to the compartment method by using mean terrestrial free air anomalies only.

Three main error influences of remote areas (distance from the fixed point >9°) on height anomalies and deflections of the vertical are being regarded:

• a) The prediction errors of mean terrestrial free air anomalies have the greatest influence and amount to about ±0″.2 in each component for deflections of the vertical and to ±3 m for height anomalies;

• b) The error of the compartment method, which originates from converting the integral formulas of Stokes and Vening-Meinesz into summation formulas, can be neglected if the anomalies for points and gravity profiles are compiled to 5°×5° mean values.

• c) The influences of the mean gravimetric correction terms of Arnold—estimated for important mountains of the Earth by means of an approximate formula—on height anomalies may amount to 1–2 m and on deflections of the vertical to 0″0.5–0″.1, and, therefore, they have to be taken into account for exact calculations.

The computations of errors are carried out using a global covariance function of point free air anomalies.