结合向量化和FFT技术的模型扰动引力快速计算  

On fast computation of model disturbing gravity vectors by vectorization technique and FFT technique

作　　者：邢志斌[1] 李姗姗[1] 范雕 张驰[1] 马越原 XING Zhibin;LI Shanshan;FAN Diao;ZHANG Chi;MA Yueyuan(Information Engineering University School of Surveying and Mapping, Zhengzhou 450001, China)

机构地区：[1]信息工程大学地理空间信息学院

出　　处：《中国惯性技术学报》2019年第3期321-326,共6页Journal of Chinese Inertial Technology

基　　金：国家自然科学基金(41274029,41774018,41504018,41404020);校内自立课题(2017503902,2018222)

摘　　要：用地球重力场模型计算扰动引力矢量时,随着模型阶次的提高,计算效率会迅速降低。针对此问题,研究了扰动引力矢量计算的矩阵表示形式、计算过程的向量化技术以及顾及起始计算点坐标的快速傅里叶变换(FFT)计算表达式。利用EGM2008地球重力场模型进行数值实验,结果表明:结合向量化和FFT技术可实现快速计算区域和全球格网模型扰动引力矢量,计算全球扰动引力矢量时,当重力场模型展开至2160阶次对应5′×5′的分辨率,计算效率可提高5倍,展开至360 阶次对应30′×30′的分辨率,计算效率可提高近10倍。所提出的方法对于快速计算模型重力场元具有一定的参考作用。In using the earth’s gravity field model to calculate the disturbing gravity vectors, the computational efficiency will decrease rapidly with the increasing of the model degrees. To solve this problem, the matrix form of disturbing gravity vectors, the vectorization technique in calculation process, and the fast Fourier transform (FFT) calculation expressions taking into account the coordinates of first grid midpoint are studied. Numerical experiments using EGM2008 gravity field model show that, the area and global grid model disturbing gravity vectors can be rapidly calculated by combining vectorization technique and FFT technique. In the calculation of global grid disturbing gravity vectors, when the earth’s gravity field model extends to 2160 degrees corresponding a resolution of 5′ 5′, the computational efficiency can be increased by 5 times. While, when extending to 360 degrees corresponding a resolution of 30′ 30′, the computational efficiency can be increased by nearly 10 times. The proposed method could be used to provide references for quickly calculating the model gravity field elements.

关 键 词：扰动引力矢量 矩阵运算 向量化技术 快速傅里叶变换 

分 类 号：P223[天文地球—大地测量学与测量工程]