Effect of topographical density on geoid in the Canadian Rocky Mountains

Abstract.

 Gravity reduction from the Earth's surface to the geoid requires knowledge of topographical mass density. However, in practice the constant density (2.67 g/cm³) is mostly used to approximate the actual density because of the difficulty and complexity of obtaining the actual density. This approximation introduces errors in the reduced gravity, and consequently, in the geoid. Recently, the geographical information system (GIS) was introduced as an efficient tool to geo-reference actual bedrock densities to digital geological maps.

As a part of the effort towards the construction of the `one-centimetre geoid' for Canada, the effects of the lateral variation of topographical density on gravity and geoid were investigated in the Canadian Rocky Mountains. Density values were estimated from the geological maps of Canada and the US and bedrock density tables compiled for use in the ArcView GIS. The 5^′×5^′ mean and point topographical effects were computed from height and density data available on a 30^″×60^″ grid. The mean direct (topographical) density effect (DDE) on gravity ranges between −4.5 and 2.3 mGal (mean of 0.008 mGal) at the Earth's surface, and from −12.7 to 9.8 mGal (mean of 0.007 mGal) at the geoid. The secondary indirect (topographical) density effect (SIDE) on gravity varies between −8 and 5 μGal. The primary indirect (topographical) density effect (PIDE) on the geoid changes from −2.5 to 1.7 cm (mean of 0.2 cm). The total topographical density effect on the geoid ranges between −7.0 and 2.8 cm (mean of −0.8 cm). Our results suggest that the effect of topographical density lateral variations is significant enough and ought to be taken into account for the determination of the one-centimetre geoid.