Stokes和Hotine积分离散求和的快速算法  

Fast Algorithm for the Discrete Summation of Stokes’ and Hotine’s Integral

作　　者：蒋涛[1,2] 王正涛[3,2] 李大炜[3] 丰海[3] 

机构地区：[1]中国测绘科学研究院 [2]武汉大学地球空间环境与大地测量教育部重点实验室,武汉市珞喻路129号430079 [3]武汉大学测绘学院,武汉市珞喻路129号430079

出　　处：《武汉大学学报（信息科学版）》2012年第5期606-609,共4页Geomatics and Information Science of Wuhan University

基　　金：国家自然科学基金资助项目(41074014;40804003;40904003;41004007;41104006);武汉大学地球空间环境与大地测量教育部重点实验室开放研究基金资助项目(10-02-14)

摘　　要：提出了一种用于Stokes积分和Hotine积分直接离散求和的快速算法。该算法将积分核表达为计算点纬度、流动点纬度和两点间经度差的函数,充分利用核函数的对称性,相同纬度的所有计算点只需计算一组核函数,计算次数远少于普通离散求和。基于EGM2008地球重力位模型的模拟实验表明,快速算法的计算效率远高于普通算法,有效解决了离散求和计算速度太慢的数值问题,且保留了球面积分的特性,可取代一维FFT用于计算Stokes积分和Hotine积分。A fast algorithm is proposed for the direct discrete summation of Stokes ’ and Hotine ’ s integral,the integral kernels are expressed as the functions of the latitudes of computation point and running point and the longitude-difference between them,the symmetries of the kernels are exploited so that they may only be evaluated once for all the computation points on the same latitude,the computation times of fast algorithm are far less than that of ordinary algorithm.The numerical simulation based on EGM2008 Earth gravitational model shows that the fast algorithm is far more efficient than the oridinary algorithm that the problem of numerical inefficiency can be effectively solved.Besides,the new algorithm retains the attributes of surface integral and can be used to replace 1DFFT for evaluating Stokes ’ or Hotine ’ s integral.

关 键 词：Stokes积分 Hotine积分 离散求和 

分 类 号：P223.0[天文地球—大地测量学与测量工程]