Knowledge Bank

Mean gravity anomalies for a certain rectangular area (block) can be computed from observed point or profile gravity values using some interpolation method (e.g., representation or least squares interpolation). If the covariance function of the gravity anomalies is known and the interpolation method is specified, then we can compute the accuracy (standard error and error covariance) of the mean anomalies without any additional numerical data. The formulas for this purpose which were partly published earlier are evaluated numerically for different sizes of blocks and different interpolation methods using an estimate for the covariance function given by W. M. Kaula in 1959. The integrals involved are approximated by summations performed by a high-speed computer. The results show the accuracies obtainable with a given observational material, by different interpolation methods. They are useful for numerical studies on the error propagation in the computation of gravimetric quantities (e.g., geoid undulations).