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The EGM08 geopotential model complete to degree and order 2159 was used in a remove-compute-restore (RCR) method for the geoid computation in the State of Rio de Janeiro, Brazil. Terrain and indirect effect corrections were computed using a 6-arcsec resolution DTE, derived from the TOPODATA Project (Shuttle Radar Topography Mission data) raised by the National Institute for Space Research. INPE, Brazil. We applied Voronoi/Delaunay discretisations for discrete Stokes integration. In these schemes, target area is partitioned into polygons/triangles, respectively, and the computation is carried out by point-wise numerical integration and no gridding is mandatory. For both procedures, the cells were produced using either observed gravity data combined with gridded Bouguer derived information. Particularly in Delaunay scheme, as the gravity anomalies are interpolated into the triangular cells, and geoid undulations are computed for their vertices, Stokes function singularity was gone. Externally estimated errors resulting from a comparison with GPS/leveling data were presented for both the schemes and classical ones, as well as for the EGM08 undulations. They yielded RMS differences equal to 0.105 m, 0.110 m, 0.110 m, 0.115 m and 0.228 m, respectively, for Voronoi, Delaunay, computed between 32 GPS/leveling points. K e y w o r d s : Gravimetric geoid, Earth gravitational model, high resolution DTE, Voronoi and Delaunay tesselations

Gravity observations adjustment is studied having in view to take full advantage of the modern technology of gravity measurement. We present here results of a test performed with the mathematical model proposed by our group, on the adjustment of gravity observations carried out on network design. Additionally, considering the recent improvement on instrumental technology in gravimetry, that model was modified to take into account possible nonlinear local datum scale factors, in a 1900 mGal range network, and to check its significance for microgal precision measurements. The data set of the Brazilian Fundamental Gravity Network was used as case study. With about 1900 mGal gravity range and 11 control stations the Brazilian Fundamental Gravity Network (BFGN) was used as case study. It was established mainly with the use of LaCoste & Romberg, model G, gravimeters and new additional observations with Scintrex CG-5 gravimeters. The observables involved in the model are instrumental reading, calibration functions of the gravimeters used and the absolute gravity values at the control stations. Gravity values at the gravity stations and local datum scale factors for each gravimeter were determined by least square method. The results indicate good adaptation of the tested model to network adjustments. The gravity value in the IFE-172 control station, located in Santa Maria, had the largest estimated correction of ?10.4 μGal (1 μGal = 10 nm/s²), and the largest residual for an observed reading was estimated in 0.043 reading unit. The largest correction to the calibration functions was estimated in 6.9 × 10^-6mGal/reading unit.