Accounting for topography in the calculation of quasigeoidal heights and plumb-line deflections from gravity anomalies

Abstract

A calculation of quasigeoidal heights and plumb-line deflections according to Molodensky formulae was carried out under elimination of the effect of topography from gravity anomalies. After the masses of topography had been removed a smoothed-out surface passing through astronomical and gravity stations was considered as representing the physical surface of the Earth. Thus it has been practically rendered possible to use the first-approximation formulae of Molodensky, and, in many cases, also the “zero-approximation” formulae analogous to the formulae of Stokes and Vening-Meinesz. The effect of the restored masses of topography was then added to the quantities found; the said effect was expressed as the effect of topography condensed on the normal equipotential surface passing through the point under investigation, plus a correction for condensation. Following some transformations, the resulting formulae (13) and (18) were obtained which formulae differ in their “zero-approximation” (15) and (20) from traditional formulas in that they contain terrait reductions added to free-air anomalies. Moreover, in the calculation of plumb-line deflections directly in mountain regions a correction for differing effects of topography before and after its condensation is to be introduced.