Comparison of interpolation and collocation techniques using torsion balance data

First the relewant theory of the interpolation and collocation methods, both used here for the recovery of deflections of the vertical and geoid heights from torsion balance data is discussed. We have selected a mostly flat area in Hungary where all kind of torsion balance measurements are available at 249 points. There were 3 astrogeodetic points providing initial data for the interpolation, and there were geoid heights at 10 checkpoints interpolated from an independent gravimetric geoid solution. The size of our test area is about 800 km sq.m. and the average site distance of torsion balance data is 1.5-2 km. The interpolation method provided a least squares solution for deflections of the vertical and geoid heights at all points of the test network. By collocation two independent solutions were computed from W(zx), W(zy) and W(yy)-W(xx), 2W(xy) gradients for all the above, using astrogeodetic data to achieve a complete agreement at these site with the interpolation method. These two solutions agreed at the cm level for geoid heights. The standard deviation of geoid height differences at checkpoints were about +-1-3 cm. The W(yy)-W(xx) , 2W(xy) combination (i.e. pure horizontal gradients) yielded better results since the maximum geoid height difference was only 3.6 cm. The differences in the deflection components were generally below 1", slightly better for the (pi) component. The above results confirm the fact that torsion balance measurements give good possibility to compute very precise local geoid heights at least for flat areas.