物探化探计算技术Issue(1)：1-9,9.DOI:10.3969/j.issn.1001-1749.2015.01.01
联用高斯求积与连分式求和计算Hankel变换及在地球物理上的应用
Using united Gaussian quadrature and continued fraction summation to evaluate Hankel transforms and its’application in geophysics
摘要
Abstract
It is necessary to evaluate Hankel transforms in optics,electromagnetics and seismology.The numerical integra-tion method is generally used to compute approximately most Hankel transforms,except few kernel functions'Hankel trans-forms having analytic expression.Although the digital filtering method is the conventional numerical aspects,the results from the method are not completely concordant because of inconsistent filtering coefficients,and in some instances the calculations are even wrong.To solve the problem,the direct numerical integration is adopted to compute Hankel transforms.Specific process is as the following:to begin with,the method is to break the Hankel transforms into integral parts'summations.These integral parts are made up of integrals which range of integration are from zero to the first zero value and subsequent adjacent zero value of Bessel function,then using Gaussian quadrature method evaluates each integral parts.The continued fraction method is applied to sum the sequence of partial integration terms,which is better than the direct summation method both the computational result precision and convergent speed.The paper first elaborates the basic principle and the correlation algo-rithms of computation Hankel transforms used the method of united Gaussian quadrature and continued fraction summation, then contrasts calculation results between the direct summation method and the continued fraction method using Matlab pro-gramming,finally the method has been applied to evaluate the electromagnetic field of two instances stimulated by electric di-pole in homogeneous half space.The application shows that it is effective way to evaluate Hankel transforms using the method of united Gaussian quadrature and continued fraction summation,which is widely used by applications of geophysics.关键词
Hankel变换/高斯求积/连分式求和/均匀半空间/场计算Key words
Hankel transforms/Gauss quadrature/continued fraction/homogeneous earth/field calculation分类
数理科学引用本文复制引用
胡瑞华,林君,孙彩堂,刘长胜,周逢道..联用高斯求积与连分式求和计算Hankel变换及在地球物理上的应用[J].物探化探计算技术,2015,(1):1-9,9.基金项目
国家级基金(OSR-02-01) （OSR-02-01）
吉林大学学部基金(4305050102RV) （4305050102RV）
