黄谟涛, 翟国君, 管铮, 欧阳永忠. 利用FFT技术计算垂线偏差研究[J]. 武汉大学学报 ( 信息科学版), 2000, 25(5): 414-420.
引用本文: 黄谟涛, 翟国君, 管铮, 欧阳永忠. 利用FFT技术计算垂线偏差研究[J]. 武汉大学学报 ( 信息科学版), 2000, 25(5): 414-420.
HUANG Motao, ZHAI Guojun, GUAN Zheng, OUYANG Yongzhong. Determination of Vertical Deflections Using FFT Technique[J]. Geomatics and Information Science of Wuhan University, 2000, 25(5): 414-420.
Citation: HUANG Motao, ZHAI Guojun, GUAN Zheng, OUYANG Yongzhong. Determination of Vertical Deflections Using FFT Technique[J]. Geomatics and Information Science of Wuhan University, 2000, 25(5): 414-420.

利用FFT技术计算垂线偏差研究

Determination of Vertical Deflections Using FFT Technique

  • 摘要: 首先导出了更加严密的二维平面FFT垂线偏差计算公式,在深入分析和比较二维平面和二维球面FFT算法特点和差异的基础上,给出了二维球面FFT计算公式的改进形式,并通过大量的数值计算,详细讨论了参考场选取、积分球冠半径确定、边缘效应、积分元离散化误差以及计算点奇异积分处理对垂线偏差计算结果的作用和影响。最后,利用全国5'×5'实测重力异常对我国海陆垂线偏差进行了试算,并将计算结果同实际观测值作了比较。

     

    Abstract: 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.Up to now, many people are still used to applying the planar and spherical 2D FFT methods, due to the consideration of their gains in computer time, to perform the convolution evaluations in physical geodesy.It means that it is worthwhile discussing the question about making any possible improvement on the conventional 2D FFT approaches.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 Δφ, Δλ blocks do not form a rectangular grid, as is assumed 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 an approximation error during the implementation of 2D FFT in computer.In order to meet the increasing needs for precise determination of the vertical deflections, this paper derives a more precise planar 2D FFT formula for the computation of the vertical deflections.After having made a detailed comparison between the planar and the spherical 2D FFT formulae, we find out the main source of errors causing the loss in accuracy by applying the conventional spherical 2D FFT method.And then, a modified spherical 2D FFT formula for the computation of the vertical deflections is developed in this paper.A series of numerical tests have been carries out to illustrate the improvement made upon the old spherical 2D FFT.The second part of this paper is to discuss the influences of the spherical harmonic reference field, the limited capsize, the limited area extend, the discretization, the edge effects and the singular integral on the computation of the vertical deflections.The results of the vertical deflections over China by applying the spherical 1D FFT formula with different integration radii have been compared to the astro-observed vertical deflections in the South China Sea to obtain a set of optimum deflection computation parameters.

     

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