The main theme of this paper is to study two important aspects of precise geoid determination using Helrnerts second method of condensation. This work illustrates via numerical investigations the importance of using actual density information of topographical bulk and the effects that different gravimetric reductions have on gravity interpolation in Helmert geoid computational process, in addition to the commonly used Bouguer scheme. A rugged area in the Canadian Rockies bounded by latitude between 49°N and 54°N and longitude between 236°E and 246°E is selected to carry out numerical investigations. The lateral density information is used in all steps of the Helmert geoid computational process. The Bouguer and residual terrain modelling (RTM) topographic reductions, the Rudzki inversion scheme, and the topographic-isostatic reductions of Pratt-Hayford (PH) and Airy-Heiskanen (AH) are used for gravity interpolation. Results show that the density information should be applied in all steps of the Helmert geoid computational process and that the topographic-isostatic gravimetric reduction schemes like the PH or AH models or the RTM reduction, should be applied for smooth gravity interpolation instead of the commonly used Bouguer reduction scheme for precise Helmert geoid determination.

This paper investigates the terrain-aliasing effects on geoid determination using different gravimetric reduction schemes. The high resolution of digital terrain model (DTM), if available, should be used for every gravimetric reduction scheme since it can precisely map the details of the terrain. The reduction methods used in this study are the Rudzki inversion method, Helmert's second method of condensation, the residual terrain model (RTM) method, and the Pratt-Hayford (PH) topographic-isostatic reduction technique. The effect of using different DTM grid resolutions of 6", 15", 30", 45", I' and 2' on gravity anomalies and absolute geoid undulations is studied for each of these reduction schemes. A rugged area in the Canadian Rockies bounded by latitude between 49°N and 54°N and longitude between 236°E and 246°E is selected to conduct numerical tests. Our results suggest that a DTM grid resolution of 6" or higher is required for precise geoid determination with an accuracy of a decimetre or higher for any gravimetric reduction method chosen to treat the topographical masses above the geoid in rugged areas. The most precise geoid models obtained in this test are the ones obtained using Rudzki, Helmert, and RTM methods with 6" DTM resolution.