FIRST RESULTS ON THE COMPUTATION OF TERRAIN CORRECTIONS BY THE 3D FFTMETHOD

The computation of gravity terrain corrections is implemented in this paper by the three-dimensional fast Fourier transform (3D FFT) method. By using density values on a 3D grid, a 3D grid of terrain correction s is produced from which the terrain corrections of the points on the Earth's surface are evaluated by interpolation. The technique gives di rectly the results at the geoid level, i.e., the indirect effect of th e topographic reduction, and at a flight level, which will find a very important application in the upcoming measurement systems of airborne gravimetry and gradiometry. Numerical results by the 3D FFT are compa red with those by the linear 2D FFT and numerical integration methods (NIM), in terms of computational accuracy and required time, with diff erent interpolating methods. It is indicated by comparisons that more accurate numerical results can be achieved by the 3D FFT than by the l inear 2D FFT when the grid spacing in the z-direction is small. Althou gh it is possible to get comparable results with the 2D FFT method by evaluating more terms in the Taylor series expansion, there are two si tuations in which the 2D FFT method cannot be applied. These are (a) w hen the density varies in the z-direction and (b) when there are large terrain inclinations. In these cases, the 3D FFT method is the only e fficient alternative to numerical integration. Besides the feasibility and the accuracy of the 3D FFT method, the paper also discusses some strategies for minimizing its required computer memory and CPU time.