Geoid, topography, and the Bouguer plate or shell

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, Poincare–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 Poincare'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.