Geoid versus quasigeoid: a case of physics versus geometry

Abstract

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.