The optimum expression for the gravitational potential of polyhedral bodies having a linearly varying density distribution

Hamayun, I. Prutkin, Robert Tenzer

Research output: Journal article publicationJournal articleAcademic researchpeer-review

38 Citations (Scopus)


When topography is represented by a simple regular grid digital elevation model, the analytical rectangular prism approach is often used for a precise gravity field modelling at the vicinity of the computation point. However, when the topographical surface is represented more realistically, for instance by a triangular irregular network (TIN) model, the analytical integration using arbitrary polyhedral bodies (the analytical line integral approach) can be implemented directly without additional data pre-processing (gridding or interpolation). The analytical line integral approach can also facilitate 3-D density models created for complex geometrical bodies. For the forward modelling of the gravitational field generated by the geological structures with variable densities, the analytical integration can be carried out using polyhedral bodies with a varying density. The optimal expression for the gravitational attraction vector generated by an arbitrary polyhedral body having a linearly varying density is known. In this article, the corresponding optimal expression for the gravitational potential is derived by means of line integrals after applying the Gauss divergence theorem.
Original languageEnglish
Pages (from-to)1163-1170
Number of pages8
JournalJournal of Geodesy
Issue number12
Publication statusPublished - 1 Dec 2009
Externally publishedYes


  • Gravitational potential
  • Line integral
  • Linear density
  • Polyhedron

ASJC Scopus subject areas

  • Geophysics
  • Geochemistry and Petrology
  • Computers in Earth Sciences

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