Accession Number : AD0671127

Title :   MODEL COMPUTATIONS FOR DIFFERENT SOLUTIONS OF THE GEODETIC BOUNDARY-VALUE PROBLEM,

Corporate Author : OHIO STATE UNIV COLUMBUS DEPT OF GEODETIC SCIENCE

Personal Author(s) : Koch,Karl-Rudolf

Report Date : FEB 1968

Pagination or Media Count : 43

Abstract : To solve the boundary-value problem of physical geodesy, the perturbing potential is usually expressed by the potential of a simple layer. By introducing this expression into the boundary condition, Molodensky's basic integral equation is obtained; the solution of which enables us to compute the perturbing potential and its first derivative. To check the results of this method, Green's formula can be used. After transforming this formula and its derivative by a method, due to Molodensky, a linear integral equation for the disturbing potential is obtained. With the solutions of this integral equation, the first derivative of the disturbing potential can be computed from the transformed derivative of Green's formula. For a model consisting of a cone on a plane the basic integral equation and the integral equation of Green's formula are solved by successive approximation with a computer. The solution of the basic integral equation is also obtained by Molodensky's method. These three solutions are compared for different inclination angles of the surface of the cone. The results agree very well for small inclination angles, but the approximations don't converge for greater inclination angles. The reason has to be sought in the errors of numerical integration, by which the integration over the surface of the model is solved. (Author)

Descriptors :   (*GEODESICS, *BOUNDARY VALUE PROBLEMS), PERTURBATION THEORY, APPROXIMATION(MATHEMATICS), INTEGRAL EQUATIONS, MATHEMATICAL MODELS, CONVERGENCE

Subject Categories : Geodesy
      Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE