On the solution of the Molodenskii boundary value problem using successive approximations

Gravimetric methods of determining the figure of the Earth can be divided into two groups. The first employs an auxiliary surface—the geoid. The second employs the so-called quasigeoid as an auxiliary surface. Its main advantage is in that it only uses surface measurements and that it does not require knowledge of the structure of the Earth's crust. This method was treated in 1]. The results display an accuracy of the order of the Earth's flattening. The purpose of this paper is to show that this method can be applied theoretically to reach an arbitrary accuracy.