Applications of downward-continuation in gravimetric geoid modeling: case studies in Western Canada

Abstract

The objective of this study is to evaluate two approaches, which use different representations of the Earth’s gravity field for downward continuation (DC), for determining Helmert gravity anomalies on the geoid. The accuracy of these anomalies is validated by 1) analyzing conformity of the two approaches; and 2) converting them to geoid heights and comparing the resulting values to GPS-leveling data. The first approach (A) consists of evaluating Helmert anomalies at the topography and downward-continuing them to the geoid. The second approach (B) downward-continues refined Bouguer anomalies to the geoid and transforms them to Helmert anomalies by adding the condensed topographical effect. Approach A is sensitive to the DC because of the roughness of the Helmert gravity field. The DC effect on the geoid can reach up to 2 m in Western Canada when the Stokes kernel is used to convert gravity anomalies to geoid heights. Furthermore, Poisson’s equation for DC provides better numerical results than Moritz’s equation when the resulting geoid models are validated against the GPS-leveling. On the contrary, approach B is significantly less sensitive to the DC because of the smoothness of the refined Bouguer gravity field. In this case, the DC (Poisson’s and Moritz’s) contributes only at the decimeter level to the geoid model in Western Canada. The maximum difference between the geoid models from approaches A and B is about 5 cm in the region of interest. The differences may result from errors in the DC such as numerical instability. The standard deviations of the h−H−N for both approaches are about 8 cm at the 664 GPS-leveling validation stations in Western Canada.