Comments on FFT Technique in Spectral Geoid Determination

The fast Fourier transform (FFT) technique is a very powerful tool for the efficient evaluation of gravity field convolution integrals. At present, there exist three types of convolution formulae in use, i.e. the planar 2D convolution, the spherical 2D convolution and the spherical 1D convolution. As we know, the largest drawback of both the planar and the spherical 2D FFT methods is that, due to the approximations in the kernel function, only non exact results can be achieved. Apparently, the reason is the meridian convergence at higher latitudes. As the meridians converge, the Δ φ , Δ λ blocks don't form a rectangular grid, as is assumpted in 2D FFT methods. It should be pointed out that the meridian convergence not only leads to an approximation error in the kernel function, but also causes a approximation error during the implementation of 2D FFT in computer. In order to reduce the impact of the second type of approximation error, a modified spherical 2D FFT formula for the computation of geoid undulations has been developed in this paper. A series of numerical tests have been carried out to illustrate the improvement made upon the old spherical 2D FFT. The second part of this paper is to discuss the influences of a spherical harmonic reference field, a limited cap size and a modified Stokes kernel on geoid computation. The geoid results over China by applying different modified Stokes kernel with different integration radii have been compared to GPS leveling and altimeter measured geoidal undulations to obtain a set of optimum geoid computation parameters.