Application of Voronoi and Delaunay Diagrams in Gravimetric Geoid Determination

Two approaches based on Voronoi and Delaunay structures are investigated to compute the Stokes integral for geoid determination. In the Voronoi approach, polygonal areas contain the observed gravity anomalies instead of the interpolated ones, and original data is used. In Delaunay approach, gravity anomalies are interpolated into triangular cells whose vertices hold the stations. The geoidal undulations are computed at the barycenters. Both schemes were applied to the geoid determination in Rio de Janeiro and Resende sites. Stokes component was also computed by numerical integration and ID FFT, and RMS differences did not exceed 0.047 m and 0.053 m, respectively, in Rio de Janeiro and Resende. Relative comparisons with GPS-levelling gave RMS differences smaller than 0.071 m, showing the schemes are adequate to compute high-precision geoid. Since both techniques avoid gridding step, pre-processing and labour are reduced, and the schemes proved to be as efficient as ID FFT method.