A study of the upward continuation of gravity data from a plane surface

Summary

A summation method of upward continuation of gravity data has been considered under the assumption that observations are available at regular intervals. The upward continued value has been obtained as the sum of products of individual gravity values and corresponding theoretical coefficients. Besides the usual parameter involving horizontal and vertical distances, the theoretical coefficients have been generalized to be dependent also on i) the order of a low order polynomial assumed to represent the gravity variation around a grid point and ii) the weights assigned to the gravity values at the nearest four grid points used for least-squares determination of the polynomial. Since the observations in practical cases are available over a finite area only, the effect of truncation of the area of the integration has also been discussed separately. The method has been programmed and tested on a three-dimensional model, whose true gravity effects were computed at various levels over a finite area. Upward continued values have been computed under various assumptions about the gravity field in the “outside” region. Comparisons of these results with the true values indicate that the truncation effect becomes increasingly important for larger values of the ratio of elevation to grid separation and/or when the gravity field is not a local one. It has also been found that the greater is the above ratio, the less important is the effect of weights on the theoretical coefficients and practically vanishes(<10⁻⁴) when the ratio is greater than5.0.