On the boundary value problem of physical geodesy

A solution of the principal boundary value problem of physical geodesy is made using spherical harmonics for the global approach and gravity reduction by an integral equation for the local studies, all in a compatible system. This procedure should be unique. In the normal application gravity is reduced to the reference sphere (ellipsoid) which coincides with mean sea level.

For a computation of the vertical deflection a final gravity reduction is made to a reference surface through the actual point. An “isometric” gravity anomaly is introduced. The isostatic, Bouguer and Rudzky anomalies are interpreted in a new way.