Mean Vertical Gradient of Gravity

Abstract

The Stokes-Helmert scheme for precise geoid determination requires that Helmert’s gravity anomalies are first evaluated on the earth surface. Subsequently, these anomalies must be continued downward onto the geoid, where they make the boundary values for solving the geodetic boundary value problem. The anomalies are continued downward using the Poisson integral; this can be done because the Helmert disturbing potential is harmonic everywhere above the geoid. Thus, the difference between Helmert’s gravity on the earth surface and on the geoid can be computed and the mean vertical gradient of gravity between the earth surface and the geoid can be obtained.

In this contribution we show a map of the mean gravity gradient for one particularly interesting area of the Rocky Mountains. We also point out that these values can be used to make orthometric heights more precise. The experiment presented here is just a first attempt, a pilot study to prove the validity of the physical concept.