IMPROVED FOURIER TERRAIN CORRECTION .2.

Fourier methods for potential fields have always been developed with t he simplification that the calculation surface is a level plane. The F ourier approach can be extended to deal with an uneven observation sur face. I consider the case of terrain correction for gravity surveys, i n which the attraction of a variable-thickness layer is calculated at points on its upper surface. The main idea is to use a power series in topographic height that is then converted into a series of convolutio ns. To avoid convergence problems, a cylindrical zone around the obser ver must be removed from the Fourier treatment and its contribution co mputed directly. The resultant algorithm is very fast: in an example b ased on a recent survey, the new method is shown to be more than 300 t imes faster than a calculation based on summing contributions from a c olumn of material under each topographic grid point.