The realization of precise height systems demands to assess the effect and necessity of approximations made to the pure theory. In this context, the formulas for the geoid–quasigeoid separation as presented by Flury and Rummel (J Geod 83:829–847, 2009) and further discussed by Sjöberg (J Geod 84:699–702, 2010) are reinterpreted. Starting from the fully topographically reduced gravity disturbance, a modification of the strict formulation of the downward continuation and the indirect effect according to Sjöberg (2010) is given. In practice any implementation of the formula requires approximations in order to realize the downward continuation of gravity along the plumbline with the help of density assumptions and a topography model. The significance of the individual contributors to a refined approximation, taking into account the indirect effect and the first-order gravity gradient, is elaborated in a numerical simulation for the example of the Himalaya region. Special focus is given on the sensitivity and convergency of the topography-induced terms with respect to the integration radius.
|Number of pages
|Acta geodaetica et geophysica : a quarterly of the Hungarian Academy of Sciences
|Published - 1 Sept 2016