The effect of the noise, spatial distribution, and interpolation of ground gravity data on uncertainties of estimated geoidal heights

Abstract

The uncertainties of the geoidal heights estimated from ground gravity data caused by their spatial distribution and noise are investigated in this study. To test these effects, the geoidal heights are estimated from synthetic ground gravity data using the Stokes- Helmert approach. Five different magnitudes of the random noise in ground gravity data and three types of their spatial distribution are considered in the study, namely grid, semigrid and random. The noise propagation is estimated for the two major computational steps of the Stokes-Helmert approach, i.e., the downward continuation of ground gravity and Stokes’s integration. Numerical results show that in order to achieve the 1-cm geoid, the ground gravity data should be distributed on the grid or semi-grid with the average angular distance less than 2′. If they are randomly distributed (scattered gravity points), the 1-cm geoid cannot be estimated if the average angular distance between scattered gravity points is larger than 1′. Besides, the noise of the gravity data for the tree types of their spatial distribution should be below 1 mGal to estimate the 1-cm geoid. The advantage of interpolating scattered gravity points onto the regular grid, rather than using them directly, is also investigated in this study. Numerical test shows that it is always worth interpolating the scattered points to the regular grid except if the scattered gravity points are sparser than 5′.