NONLINEAR SOLUTIONS OF THE GEODETIC BOUNDARY-VALUE PROBLEM,

Abstract

A complete series solution of Molodensky's boundary value problem is derived using, instead of an integral equation, analytical continuation by means of power series. This solution is shown to be equivalent, term by term, to the Molodensky-Brovar series, but is simpler and practically more convenient. This equivalence gives a physical explanation of the divergence of the Molodensky series. The exclusion of topographic masses to improve convergence is discussed, and computational formulas for height anomalies and deflections of the vertical are given. In the Appendix, structural similarities between the series of celestial mechanics and of physical geodesy are used to get an insight into the convergence behavior of these series. Another argument for the divergence of series of Molodensky type is given. (Author)

Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1969
Accession Number
AD0702859

Entities

People

  • Helmut Moritz

Organizations

  • Ohio State University

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Celestial Mechanics
  • Convergence
  • Deflection
  • Equations
  • Integral Equations
  • Integrals
  • Mathematical Analysis
  • Mathematics
  • Mechanics
  • Power Series

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Geodesy