Geoid, topography, and the Bouguer plate or shell

Topography plays an important role in solving many geodetic and geophysical problems. In the evaluation of a topographical effect, a planar model, a s pherical model or an even more sophisticated model can be used. In most app lications, the planar model is considered appropriate: recall the evaluatio n of gravity reductions of the free-air, Poincare-Prey or Bouguer kind. For some applications, such as the evaluation of topographical effects in grav imetric geoid computations, it is preferable or even necessary to use at le ast the spherical model of topography. In modelling the topographical effec t, 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 s hell is studied, while the effect of the rest of topography, the terrain, i s discussed elsewhere. It is argued that the classical Bouguer plate gravit y reduction should be considered as a mathematical construction with unclea r physical meaning. It is shown that if the reduction is understood to be r educing observed gravity onto the geoid through the Bouguer plate/shell the n both models give practically identical answers, as associated with Poinca re's and Prey's work. It is shown why only the spherical model should be us ed in the evaluation of topographical effects in the Stokes-Helmert solutio n of Stokes' boundary-value problem. The reason for this is that the Bougue r plate model does not allow for a physically acceptable condensation schem e for the topography.