A set of low degree geopotential coefficients can favourably be combined with Stokes’ and Vening Meinesz’ integrals for the determination of geoid undulations and deflections of the vertical. As the area of integration is normally limited to a spherical cap, the goal of the methods of combination (e.g. Molodenskii’s, Meissl’s, and Wong and Gore’s method) is to reduce the truncation error of the remote zone. For example, Molodenskii’s method implies minimizing the maximum remote zone error, while the potential coefficient errors are disregarded in the optimization.

Our new least squares method minimizes the mean square error of both truncation and potential coefficients. A numerical example indicates that a potential error reduction of roughly 10% for undulations and 8% for deflections can be achieved with this new method and a set of potential coefficients complete to degree and order 180. In particular the error in deflections stemming from erroneous potential coefficients can be reduced most significantly.