Improved Fourier terrain correction, Part Ⅱ

摘要

Fourier methods for potential fields have always been developed with the simplification that the calculation surface is a level plane. The Fourier approach can be extended to deal with an uneven observation surface. I consider the case of terrain correction for gravity surveys, in 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 convolutions. To avoid convergence problems, a cylindrical zone around the observer must be removed from the Fourier treatment and its contribution computed directly. The resultant algorithm is very fast: in an example based on a recent survey, the new method is shown to be more than 300 times faster than a calculation based on summing contributions from a column of material under each topographic grid point.