A bilinear approximation of the surface relief in terrain correction computations |
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Authors: | D Tsoulis H Wziontek S Petrovi? |
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Institution: | (1) Institute of Geodesy and Geoinformatics, Berlin University of Technology, Sekretariat H12, 10623 Berlin, Germany |
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Abstract: | A new method is presented for the computation of the gravitational attraction of topographic masses when their height information is given on a regular grid. It is shown that the representation of the terrain relief by means of a bilinear surface not only offers a serious alternative to the polyhedra modeling, but also approaches even more smoothly the continuous reality. Inserting a bilinear approximation into the known scheme of deriving closed analytical expressions for the potential and its first-order derivatives for an arbitrarily shaped polyhedron leads to a one-dimensional integration with – apparently – no analytical solution. However, due to the high degree of smoothness of the integrand function, the numerical computation of this integral is very efficient. Numerical tests using synthetic data and a densely sampled digital terrain model in the Bavarian Alps prove that the new method is comparable to or even faster than a terrain modeling using polyhedra. |
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Keywords: | Terrain correction - Polyhedron - Bilinear surfaces |
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