Modeling topographical density for geoid determinationThis article is one of a series of papers published in this Special Issue on the theme GEODESY.

Abstract

In geoid computation, effects of real three-dimensional topographic masses on the Earth’s gravity field must be accurately quantified and, in the Stokes–Helmert scheme, replaced with effects of those masses condensed on the geoid. The most comprehensive modern schemes for evaluation of topographical effects account for terrain effects, use a spherical model of topography, and incorporate two-dimensionally varying models of topographical mass density. In this contribution, we employ a three-dimensionally varying model of topographical density. We use Newton’s integration to determine the direct topographical effect (DTE) on gravity and primary indirect topographical effect (PITE) on gravity potential. Lastly, we apply Stokes’ integration to calculate the DTE, PITE, and secondary indirect topographical effect (SITE) on geoidal height. We focus here on validation of our results and demonstration of our software’s capabilities. We present results for the simple geometrical shape of a disc under various rotations and for the anomalous density of lake waters. Effects on geoidal height for these simulations reach centimetre level, up to 2.2 cm in magnitude. For a simulation of the effects of neglected mass anomalies of the lakes, we find results reaching 0.8 cm in magnitude. We examine the behavior of our results as calculated using various step sizes for numerical integration and by comparing numerical results with analytical results for the specific case of a disc. These results suggest that the maximum percent error of our results is about 23.5% for the DTE on gravity and 7.6% for the PITE on gravity potential.