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Comments on FFT Technique in Spectral Geoid Determination

HUANG Mo tao, ZHAI Guo jun, GUAN Zheng, LING Yong, OUYANG Yong zhong(Tianjin Institute of Hydrographic Surveying and Charting, Tianjin 300061,China)  
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.
【CateGory Index】: P223
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Chinese Journal Full-text Database 2 Hits
1 HUANG Mo-tao~1, ZHAI Guo-jun~1, OUYANG Yong-zhong~1, SUN Ji-zhang~2, LU Xiu-ping~1, XU Guang-xiu~1, REN Lai-ping~1, WANG Ke-ping~1, LIU Chuan-yong~1, HOU Shi-xi~1 (1.(Naval) Institute of Hydrographic Surveying and Charting, Tianjin, 300061; 2.(61365) Troops, Tianjin, 300140);Review and Prospect of Application Study in Altimetry[J];Hydrographic Surveying and Charting;2004-04
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1 HUANG Zhi-zhou~①,ZHONG Jin-ning~①,ZHOU Wei~②,CUI Li-xin~③(①Nanjin Academy of Reconnaissancing and Surveying,Nanjing 210005;②Nanjing University,Nanjing 210093;③Yancheng Academy of Reconnaissancing and Surveying,Yancheng 224002,China);Calclation of local geoid[J];Science of Surveying and Mapping;2004-02
2 ZHANG Chao~①,ZHENG Yong~①,LI Chang-hui~②(①Institute of Surveying and Mapping,Information Engineering University,Zhengzhou Henan 450052;②First surveying team of PLA);Research on astronomy orientation by using the random star[J];Science of Surveying and Mapping;2005-04
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【Secondary References】
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1 Duan Hurong,Jiao Shengjun(Road and Bridge Department,Shanxi Vocational College of Railway Engineering Technology,Weinan Shanxi 714000,China);A Study of Geoid Deformation of Hexi by the Repetition Gravity[J];Chinese Journal of Engineering Geophysics;2007-02
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3 PEI Wen-bin,NIU Gui-zhi(Tianjin Research Institute for Water Transport Engineering,Tianjin 300456,China);Present situation and future tendency of port and waterway engineering survey[J];Journal of Waterway and Harbor;2007-04
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