Geoid, topography, and the Bouguer plate or shell |
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Authors: | P Vaníc?ek P Novák Z Martinec |
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Affiliation: | (1) Department of Geodesy and Geomatics Engineering, University of New Brunswick, P.O. Box 4400, E3B 5A3 Fredericton, Canada e-mail: vanicek@unb.ca; Tel.: +1-506-4535144; Fax: +1-506-4534943, CA;(2) Department of Geophysics, Charles University, V Holes˘ovic˘kach 2, Pragues, Czech Republic, CZ |
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Abstract: | Topography plays an important role in solving many geodetic and geophysical problems. In the evaluation of a topographical
effect, a planar model, a spherical model or an even more sophisticated model can be used. In most applications, the planar
model is considered appropriate: recall the evaluation of gravity reductions of the free-air, Poincaré–Prey or Bouguer kind.
For some applications, such as the evaluation of topographical effects in gravimetric geoid computations, it is preferable
or even necessary to use at least the spherical model of topography. In modelling the topographical effect, the bulk of the
effect comes from the Bouguer plate, in the case of the planar model, or from the Bouguer shell, in the case of the spherical
model. The difference between the effects of the Bouguer plate and the Bouguer shell is studied, while the effect of the rest
of topography, the terrain, is discussed elsewhere. It is argued that the classical Bouguer plate gravity reduction should
be considered as a mathematical construction with unclear physical meaning. It is shown that if the reduction is understood
to be reducing observed gravity onto the geoid through the Bouguer plate/shell then both models give practically identical
answers, as associated with Poincaré's and Prey's work. It is shown why only the spherical model should be used in the evaluation
of topographical effects in the Stokes–Helmert solution of Stokes' boundary-value problem. The reason for this is that the
Bouguer plate model does not allow for a physically acceptable condensation scheme for the topography.
Received: 24 December 1999 / Accepted: 11 December 2000 |
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Keywords: | : Geoid Bouguer Reduction of Gravity Stokes Helmert's Problem |
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