Effects of Hypothetical Complex Mass-Density Distributions on Geoidal Height

Abstract

Geoid computation according to the Stokes-Helmert scheme requires accurate modelling of the variations of mass-density within topography. Current topographical models used in this scheme consider only horizontal variations, although in reality density varies three-dimensionally. Insufficient knowledge of regional three-dimensional density distributions prevents evaluation from real data. In light of this deficiency, we attempt to estimate the order of magnitude of the error in geoidal heights caused by neglecting the depth variations by calculating, for artificial but realistic mass-density distributions, the difference between results from 2D and 3D models.

Our previous work has shown that for simulations involving simple mass-density distributions in the form of planes, discs or wedges, the effect of mass-density variation unaccounted for in 2D models can reach centimeter-level magnitude in areas of high elevation, or where large mass-density contrasts exist. However, real mass-density distributions are more complicated than those we have modeled so far, and involve multiple structures whose effects might mitigate each other. We form a more complex structure by creating an array of discs that individually we expect to have a very significant effect, and show that while the contribution of such an array to the direct topographical effect on geoidal height is sub centimeter (0.85 cm for our simulation), the resulting primary indirect topographical effect may reach several centimeters or more (5 cm for our simulation).