Accession Number:

ADA063194

Title:

A Comparison of Bjerhammar's Methods and Collocation in Physical Geodesy.

Descriptive Note:

Interim rept.,

Corporate Author:

OHIO STATE UNIV COLUMBUS DEPT OF GEODETIC SCIENCE

Personal Author(s):

Report Date:

1978-07-01

Pagination or Media Count:

89.0

Abstract:

In 1963 A. Bjerhammar solved the geodetic boundary value problem by applying Poissons integral equation for a finite set of observed free-air gravity anomalies. Due to the relation between the number of observations m and the number of chosen unknowns N different solutions are obtained non-singular m N, least squares m N and minimum norm solutions m N. In the special case N approaches infinity, it is shown that the Bjerhammar solution with Poissons kernel and a solution by collocation with the corresponding kernel are identical. Bjerhammars method is generalized by using other kernel functions, and each minimum norm solution is shown to correspond to one specific set of degree variances in collocation. The impulse approaches reflexive prediction, Dirac method of Bjerhammar are presented. In the theoretical case with a continuous coverage of observations at the surface of the earth, it is shown that both the Dirac method and collocation give a unique solution for any choice of positive degree variances of the kernel functions, whenever the solutions exist. However, the intermediate solutions for Delta g star and X at the Bjerhammar sphere do not exist in general. If collocation is applied by solving the Wiener-Hopf integral equation, a convergent solution is proved outside a sphere. However, inside the bounding sphere of the earth the convergence is still not proved.

Subject Categories:

  • Geodesy
  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE