An alternative algorithm to FFT for the numerical evaluation of Stokes's integral

Stokes's kernel used for the evaluation of a gravimetric geoid is a functio n of the spherical distance between the point of interest and the dummy poi nt in the integration. Its values thus are obtained from the positions of p airs of points on the geoid. For the integration over the near integration zone (near to the point of interest,) it is advantageous to pre-form an arr ay of kernel values where each entry corresponds to the appropriate locatio ns of the two points, or equivalently to the latitude and the longitude-dif ference between the point of interest and a dummy point. Thus, for points o f interest on the same latitude, the array of the Stokes kernel values rema ins the same and may only be evaluated once. Also, only one half of the arr ay need be evaluated interest. Numerical tests show that computation speed improves significantly after th is algorithm is implemented. For an area of 5 by 10 arc-degrees with the gr id of 5 by 5 arc-minutes, the computation time reduces from half an hour to about 1 minute. To compute the geoid for the whole of Canada (20 by 60 arc -degrees, with the grid of 5 by 5 arc-minutes), it takes only about 17 minu tes on a 400MHz PC computer. Compared with the Fast Fourier Transform algorithm, this algorithm is easie r to implement including the far zone contribution evaluation that can be d one precisely, using the (global) spectral description of the gravity field .