OBTAINING EARTH SURFACE AND SPATIAL DEFLECTIONS OF THE VERTICAL FROM FREE-AIR GRAVITY-ANOMALY AND ELEVATION DATA WITHOUT DENSITY ASSUMPTIONS

The density-free scheme of Moritz (1980) is discussed. Two sites, having diverse topographies, were surveyed for 1 arc min by 1 arc min mean free-air anomaly and elevation values and for smaller sets of astronomically determined deflections to serve as control or "truth' values. In a topographically tranquil but gravimetrically turbulent Oklahoma site the overall RMS of the differences between true and predicted deflections was 0.3 arc secs and in a rugged New Mexico site it was 0.6 arc sec. Accurate first derivative terms (in both continuation steps) require a 1 arc min data set as interpolation-free as possible. A 1 arc min data grid is shown to be insufficient for meaningful computations of the higher order series terms. Potential pitfalls of the two-dimensional fast Fourier transform pair are discussed with an emphasis on unwanted circular convolution effects which, if unaccounted for, can increase the error in individual predicted deflections by as much as 100%. -from Author