Ellipsoidal corrections for geoid undulation computations

The computation of accurate geoid undulations is usually done combining potential coefficient information and terrestrial gravity data in a cap surrounding the computation point. In doing this a spherical approximation is made that can cause the errors that were investigated. The equations dealing with ellipsoidal corrections developed by Lelgemann and by Moritz were used to develop a computational procedure considering the ellipsoid as a reference surface. Terms in the resulting expression for the geoid undulation are identified as ellipsoidal correction terms. These equations were developed for the case where the Stokes function is used, and for the case where the modified Stokes function is used. For a cap of 20 deg the correction can reach -33 cm.