Considering data gaps in geoid modelling by modifying Stokes’ formula

Abstract

There are numerous methods to modify Stokes’ formula with the usually common feature of reducing the truncation error committed by the lack of gravity data in the far-zone, resulting in an integral formula over the near-zone combined with an Earth Gravity Model that mainly contributes with the long-wavelength information. Here we study the reverse problem, namely to estimate the geoid height with data missing in a cap around the computation point but available in the far-zone outside the cap. Secondly, we study also the problem with gravity data available only in a spherical ring around the computation point. In both cases the modified Stokes formulas are derived using Molodensky and least squares types of solutions. The numerical studies show that the Molodensky type of modification is useless, while the latter method efficiently depresses the various errors contributing to the geoid error. The least squares methods can be used for estimating geoid heights in regions with gravity data gaps, such as in Polar Regions, over great lakes and in some developing countries with lacking gravity data.