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《Chinese Journal of Geophysics》 1998-S1
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WALSH-FOURIER SERIES EXPANSION AND TRANSFORM FOR THE GRAVITATIONNAL POTENTIAL

MENG JIA-CHUN; CAI XI-MEI(Institute of Geodesy and Geophysics,Chinese Academy of Sciences,Wuhan 430077, China)MENG WEI(Wuhan Documentation and Information Center, Chinese Academy of Sciences, Wuhan 430071, China)  
In this paper the fast Fourier transform of spherical harmonics for the gravitational POtential is carried out by means of the Walsh transform. The Walsh-Fourier transform of spherical harmonics and the fast Walsh-Hadamard transform algorithm of transition matrix and itS data compaction method are derived, the characteristics of Walsh-Fourier transform and its applications in spherical harmonic analysis are discussed as well. The researches show that the results of Walsh-Fourier transform coincide fully with Foaurer transform when the sequency is equated to the frequency, the figures of curve for the tWo transformations are the same; According to the operation of double precision type, the computational accuracy of two different methods can come to±(10 - 15-10 -14);The Walsh-Fourier transform can replace the complex transformation of Fourier transform by the real transformation; The range of speeding up the fast Walsh-Hadamaxd transform will be increased with the increase of order;The Walsh-Fourier transform can be used for the case where the sequency and the frequency are equalled or unequalled. The Walsh-Fourier transform is better than the Fourier transform in the computational accuracy, data compaction and representation of potential field spectrum.
【Fund】: 国家自然科学基金!49384003;;中国科学院院长基金!930156
【CateGory Index】: P631.1
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