The Rudzki inversion gravimetric reduction scheme in geoid determination

Abstract

Gravimetric reduction schemes play an important role in precise geoid determination, especially in rugged areas. The Rudzki inversion is the only gravimetric reduction scheme that does not change the equipotential surface. The topographical masses above the geoid are inverted into its interior in this scheme. Although the potential of the topography is equal to that of the inverted masses, and thus there is no indirect effect on the geoid using this mass reduction scheme, the attractions of the topography and the inverted topography are not equal. The formulas to compute the attraction due to topographical masses above the geoid and due to inverted masses are studied in planar approximation. One of the most rugged areas in the Canadian Rocky Mountains, which lies between 49°N and 54°N latitude and between 236°E and 246°E longitude, is selected to compute the gravimetric geoid solution using the Rudzki method. It is compared with geoid models based on Helmert’s second method of condensation and the residual terrain model (RTM), which are most commonly used in practice, and also with those based on the topographic–isostatic reduction methods of Airy–Heiskanen and Pratt–Hayford. Results show that the Rudzki geoid solution performs as well as the Helmert and RTM geoid solutions (in terms of standard deviation and range of maximum and minimum values) when compared to GPS-leveling data in this test area.