| 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.
A tentative expansion of terrain reduction in terms of spherical harmonics up to the third order is given; it can be seen
therefrom that the Stokes series in its usual form is subject to a mean arror about 15–20%. It is also shown that the expansion
of free-air anomalies in terms of spherical functions contains a first-order harmonic with a mean values about ±0.3 mgl. The
said harmonic practically disappears in the expansion of the sum of free-air anomalies and terrain reductions. |
