The optimum expression for the gravitational potential of polyhedral bodies having a linearly varying density distribution |
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Authors: | Hamayun I Prutkin R Tenzer |
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Institution: | (1) Delft Institute of Earth Observation and Space Systems (DEOS), Delft University of Technology, Delft, 2629 HS, The Netherlands;(2) Delft Institute of Earth Observation and Space Systems (DEOS), Delft University of Technology, Delft, 2629, The Netherlands |
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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. |
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Keywords: | |
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