An Alternative Algorithm to FFT for the Numerical Evaluation of Stokes's Integral

ISSN： 0039-3169

Source： Studia Geophysica et Geodaetica, Vol.44, Iss.3, 2000-07, pp. : 374-380

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Abstract

Stokes's kernel used for the evaluation of a gravimetric geoid is a function of the spherical distance between the point of interest and the dummy point in the integration. Its values thus are obtained from the positions of pairs 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 array of kernel values where each entry corresponds to the appropriate locations of the two points, or equivalently, to the latitude and the longitude-difference between the point of interest and a dummy point. Thus, for points of interest on the same latitude, the array of the Stokes kernel values remains the same and may only be evaluated once. Also, only one half of the array need be evaluated because of its longitudinal symmetry: the near zone can be folded along the meridian of the point of interest.Numerical tests show that computation speed improves significantly after this algorithm is implemented. For an area of 5 by 10 arc-degrees with the grid 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 minutes on a 400MHz PC computer.Compared with the Fast Fourier Transform algorithm, this algorithm is easier to implement including the far zone contribution evaluation that can be done precisely, using the (global) spectral description of the gravity field.