On the error of analytical downward continuation of the earth's external gravitational potential on and inside the earth's surface

The error of the analytical downward continuation was studied under planar approximation in a previous paper by the author (1994). This error is studied further by taking the earth's curvature into account in this paper. It is shown that if a smoothing procedure is applied, the analytical downward continuation can be used to determine the earth's gravitational potential on and above the earth's surface to any required accuracy. For the potential inside the earth's topographic mass the error can also be controlled and corrected. Received 1 August 1995; Accepted 13 September 1996