Preparations for the Numerical Evaluation of Second Order Molodensky Type Formulas

摘要

A set of formulas proposed by Moritz and constituting a second order solution of Molodensky's problem has been transformed in a way that the resulting formulas are numerically tractable. The difficulty in the original formulas was the occurrence of singular integrals. Their regularization introduces derivatives of gravity anomalies and terrain heights and necessitates a numerical differentiation procedure. Spline function interpolation has been chosen to deal with this. The existing truncation theory has been extended to cover more sophisticated truncation procedures as well as a sucdession of heavier and heavier smoothed versions of the integrand. (Author)