A new method for computing the ellipsoidal correction for Stokes's formula

This paper generalizes the Stokes formula from the spherical boundary surfa ce to the ellipsoidal boundary surface. The resulting solution (ellipsoidal geoidal height), consisting of two parts, i.e. the spherical geoidal heigh t N-0 evaluated from Stokes's formula and the ellipsoidal correction N-1, m akes the relative geoidal height error decrease from O(e(2)) to O(e(4)), wh ich can be neglected for most practical purposes. The ellipsoidal correctio n N-1 is expressed as a sum of an integral about the spherical geoidal heig ht N-0 and a simple analytical function of N-0 and the first three geopoten tial coefficients. The kernel function in the integral has the same degree of singularity at the origin as the original Stokes function. A brief compa rison among this and other solutions shows that this solution is more effec tive than the solutions of Molodensky et al. and Moritz and, when the evalu ation of the ellipsoidal correction N-1 is done in an area where the spheri cal geoidal height N-0 has already been evaluated, it is also more effectiv e than the solution of Martinec and Grafarend.