Deflections of the vertical and geoid heights from gravity gradients

In the 20th century more than 60000 torsion balance measurements were made in Hungary. At present efforts are made to rescue the historical torsion balance data; today 24544 torsion balance measurements are available for further processing in computer database. Previously only the horizontal gradients of gravity were used by geophysicists, but there is a good possibility in geodesy to interpolate deflections of the vertical, and to compute geoid heights from curvature gradients of gravity. First the theory of the interpolation method is discussed, than results of test computations are presented. We have selected a test area where all kinds of torsion balance measurements are available at 249 points. There were 3 astrogeodetic points providing initial data for the interpolation, and 10 checkpoints for controlling the results. The size of our test area is about 750 km2 and the average site distance of torsion balance data is 1.5-2 km. The standard deviations of geoid height and deflection of the vertical differences at checkpoints were about ±1-3 cm, and ± 0.6'' respectively; which confirm that torsion balance measurements give possibility to compute very precise deflections of the vertical and local geoid heights at least for flat areas