On the Use and Abuse of Helmert’s Second Method of Condensation

Helmert’s methods of condensation are generalized, considering a variable depth of the condensation layer below the geoid. Expressing the respective formulae for the combined topographic-condensation reduction both in space and frequency domain for a spherical approximation of the Earth, some drawbacks of Helmert’s second method of condensation become visible. It is shown by theoretical arguments that the residual gravity field is very rough after applying Helmert’s second model of reduction; this property, well-known from practical calculations, makes this procedure unsuitable for downward continuation. It is concluded that for precise geoid and quasigeoid determination Helmert’s second condensation method should be replaced by the generalized model in order to provide reasonable results in rugged terrain.