Geoid versus quasigeoid: a case of physics versus geometry

For decades now the geodetic community has been split down the middle over the question as to whether geoid or quasigeoid should be used as a reference surface for heights. The choice of the geoid implies that orthometric heights must be considered, the choice of the quasigeoid implies the use of the so-called normal heights. The problem with the geoid, a physically meaningful surface, is that it is sensitive to the density variations within the Earth. The problem with the quasigeoid, which is not a physically meaningful surface, is that it requires integration over the Earth's surface. Density variations that must be known for the geoid computation are those within topography and these are becoming known with an increasing accuracy. On the other hand, the surface of the Earth is not a surface over which we can integrate. Artificial "remedies" to this fatal problem exist but the effect of these remedies on the accuracy of quasigeoid are not known. We argue that using a specific technique, known as Stokes-Helmert's and using the increased knowledge of topographical density, the accuracy of the geoid can now be considered to be at least as good as the accuracy of the quasigeoid.