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.
Original language | English |
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Pages (from-to) | 1163-1170 |
Number of pages | 8 |
Journal | Journal of Geodesy |
Volume | 83 |
Issue number | 12 |
DOIs | |
Publication status | Published - 1 Dec 2009 |
Externally published | Yes |
Keywords
- Gravitational potential
- Line integral
- Linear density
- Polyhedron
ASJC Scopus subject areas
- Geophysics
- Geochemistry and Petrology
- Computers in Earth Sciences