Comparisons of spectral techniques for geoid computations over large regions

The Stokes formula is efficiently evaluated by the one- and two- dimensional (1D, 2D) fast Fourier transform (FFT) technique in the plane and on the sphere in order to obtain precise geoid determinatiover a large area such as Europe. Using a high-pass filtered spherical harmonic reference model (OSU91A truncated to different degrees), gridded gravity anomalies and geoid heights were produced and the anomalies were used as input in the FFT software. Various tests were performed with respect to the different kernel functions used, to the spherical computations in bands, as well as to windowing, edge effects and extent of the area. It is thus demonstrated that, in geoid computations over large regions, the 1D spherical FFT and the 2D multiband spherical FFT in combination with discrete spectra for the kernel functions and 100% zero-padding give better results than those obtained by the other transform techniques. Additionally, numerical tests were carried out at the same test area using the planar fast Hartley transform (FHT) instead of the FFT and the results obtained by the two attractive alternatives were compared regarding the requirements in both computer time and computer memory needed in geoid height computations.