Polyhedral approximations in physical geodesy

Summary A procedure is derived for the upward continuation of unevenly spaced gravity data. The topographic relief is approximated by a polyhedron with triangular faces and vertices placed at small distances around the surface of a sphere. The usual Fredholm integral equation of the second kind is modified considering the discontinuity of the normal vector. It is solved by successive approximations assuming the unknown function is linear inside each face at every step of the iteration process. An approximate formula to obtain the anomalous potential from the Bouguer anomaly is discussed. The potential of a homogeneous polyhedron is derived and used to compute relief corrections to the geoid undulations. Numerical applications are presented with respect to the Romanian territory.Partially presented at theJoint Symposium of IGC and IGC, Graz, Austria, 11–17 September 1994