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.
There is a good possibility tointerpolate a dense net of de ections of the vertical from Wgravity gradients measured by torsion balance and applying astronomical levelling to compute geoid heights. A new practical computation of astronomical levelling is suggested.
Sequence of neural networks has been applied to high accuracy regression in 3D as data representation in form z = f(x,y). The first term of this series of networks estimates the values of the dependent variable as it is usual, while the second term estimates the error of the first network, the third term estimates the error of the second network and so on. Assuming that the relative error of every network in this sequence is less than 100 %, the sum of the estimated values converges to the values to be estimated, therefore the estimation error can be reduced very significantly and effectively. To illustrate this method the geoid of Hungary was estimated via RBF type network. The computations were carried out with the symbolic - numeric integrated system Mathematica.
All the elements of the Eötvös tensor can be measured by torsion balance, except the vertical gradient. The knowledge of the real value of the vertical gradient is more and more important in gravimetry and geodesy.Determination of the 3D gravity potential W(x, y, z) can be produced by inversion reconstruction based on each of the gravity data Wz(= g) measured by gravimeters and gravity gradients Wzx, Wzy, WΔ, Wxy measured by torsion balance. Besides vertical gradients Wzz measured directly by gravimeters have to be used as reference values at some points. First derivatives of the potential Wx, Wy (can be derived from the components of deflection of the vertical) may be useful for the joint inversion, too. Determination of the potential function has a great importance, because all components of the gravity vector and the elements of the full Eötvös tensor can be derived from it as the first and the second derivatives of this function. The second derivatives of the potential function give the elements of the full Eötvöstensor including the vertical gradients, and all these elements can be determined not only in the torsion balance stations, but anywhere in the surroundings of these points.Test computations were performed at the characteristic region of a Hungarian plate area at the south part of the Csepel Island where torsion balance and vertical gradient measurements are available. There were about 30 torsion balance, 21 gravity and 27 vertical gradient measurements in our test area. Only a part of the 27 vertical gradient values was used as initial data for the inversion and the remaining part of these points were used for controlling the computation.
A method was developed, based on integration of horizontal gradients of gravity
to predict gravity at all points of a torsion balance network. Test computations were performed in a typically flat area where both torsion balance and gravimetric measurements are available. There were 248 torsion balance stations and 1197 gravity measurements on this area. 18 points from these 248 torsion balance stations were chosen as fixed points where gravity are known from measurements and the unknown gravity values were interpolated on the remaining 230 points.