Computation of gravimetric terrain corrections using fast fourier transform techniques
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AbstractThe scope of this research is the development of a method for evaluating the terrain correction integral using Fast Fourier Transform (FFT) techniques. The FFT method presented herein is a very fast and rigorous method of computing the terrain corrections. The only data required are the elevations of the points on a plane grid with constant spacing along the x and the y direction. The terrain corrections are computed simultaneously for all grid points. This is a valuable feature of the method for use in the solution of bolll1dary value problems in physical geodesy. The method is insensitive to errors in the heights and gives results of about the same accuracy as those obtained by the conventional prism methods using the same gridded data. The main advantage of the FFT method is its computational efficiency. It requires, for the computation of the terrain corrections for all N points on a grid, a time roughly proportional to NlogN, while the prism methods require a time roughly proportional to N2. In addition to its speed, the FFT method provides the means for spectral and correlation analyses between heights and terrain corrections. The procedures for such analyses are given in this thesis together with a presentation of the main features of the two-dimensional discrete Fourier transform. A simple computer program, written in FORTRAN V, is given, which can be used as the basis for building up a complete and flexible software package on terrain correction computations.
Bibliography: p. 97-100.