The effect of downward continuation of gravity anomaly to sea level in Stokes' formula

Stokes' well-known formula integrates gravity anomalies on a sphere to geoi dal undulations. Traditionally the effect of continuing the observed gravit y anomaly from the Earth's surface to sea level is estimated in a rather ro ugh manner, which significantly degrades the resulting geoidal undulations. In addition, the derived fictitious gravity anomalies at sea level are num erically unstable. This problem is solved by directly deriving a surface in tegral for the effects on the geoidal undulation and height anomaly. In add ition, the solution is stabilized by optimized spectral smoothing by minimi zing the mean square error. The final formula is a function of the gravity anomaly, height anomaly and topographic height.