DETERMINATION OF THE FIRST DERIVATIVES OF THE DISTURBING POTENTIAL BY GREEN'S FUNDAMENTAL FORMULA.

Abstract

Simplified evaluations of the first derivatives with respect to an arbitrary direction of the potential of a simple layer and a double layer are given. The obtained formulas are used to differentiate Green's fundamental formula, which follows from Green's identities. They are checked by another method of differentiation. An application of the derivative of Green's formula in geodesy leads to a linear integral equation for the derivative of the disturbing potential with respect to the earth's normal. Using a method due to Molodensky, the integral equation is transformed into an integral formula. This formula yields the first derivatives of the disturbing potential at the earth's surface with respect to an arbitrary direction, if the free-air anomalies and the disturbing potential are known at the earth's surface. (Author)

Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1967
Accession Number
AD0667540

Entities

People

  • Karl-rudolf Koch

Organizations

  • Ohio State University

Tags

DTIC Thesaurus Topics

  • Equations
  • Identities
  • Integral Equations
  • Integrals
  • Mathematics

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Space Exploration and Orbital Mechanics.
  • Theoretical Analysis.