On Helmert's 2nd condensation method

Zdenek Martinec , Ctirad Matyska , E.W. Grafarend & P. Vanicek


In the past, two different methods were proposed to consider the effect of the terrain in Helmert's 2nd condensation method. In Vanicek and Kleusberg (1987) approach the attraction of the topographical masses is evaluated at a point on the topographical surface. By analogy with the Molodensky's theory, Wang and Rapp (1990) claim that the free-air anomaly should be reduced by the terrain correction. They also state that the attraction of the topographical masses should be referred to a point on the geoid.

This paper shows that key to solve this discrepancy is hidden in the way how the downward continuation of the anomalous gravity is treated in the particular methods. In the Vanicek and Kleusberg approach (1987) the downward continuation of the anomalous gravity from the topographical surface to the geoid is completely neglected, whereas Wang and Rapp (1990) evaluate this term under implicit assumption that there is a linear relationship between free-air gravity anomaly and the elevation of topography. As Moritz (1966) showed such an assumption comes from a simplified view of the compensation of topographical masses; it has not been proved yet that this assumption is acceptable for a precise geoid determination. In other words it means that both methods, Vanicek and Kleusberg (1987) as well as Wang and Rapp (1990), are for different reasons only approximate. We will not be able to decide which method yields more accurate results until a correct procedure of computing downward continuation of anomalous gravity will be employed. Let us emphasize that this paper does not aspire to provide such an accurate procedure.

Manuscr. Geod., 18 (1993), 417-421.