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Journal of Geodesy

, 83:1163 | Cite as

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

  • Hamayun
  • I. Prutkin
  • R. Tenzer
Open Access
Original Article

Abstract

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.

Keywords

Gravitational potential Line integral Linear density Polyhedron 

Notes

Acknowledgments

We thank V. Pohánka (Geophysical Institute of the Slovak Academy of Sciences) and two anonymous reviewers for their constructive comments.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Copyright information

© The Author(s) 2009

Authors and Affiliations

  1. 1.Delft Institute of Earth Observation and Space Systems (DEOS), TU DelftDelftThe Netherlands
  2. 2.Faculty of Sciences, School of SurveyingUniversity of OtagoDunedinNew Zealand

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