不同滤波系数在电磁法数值计算中的应用研究

Application of Several Sets of Filter Coefficients in Numerical Computation of Electromagnetic Fields

摘要:

电磁法存在大量的汉克尔积分，由于积分核函数的复杂性，该类积分不存在解析解，采用数值方法求解汉克尔积分是电磁法正演研究中的关键问题。数值滤波法运算速度快、执行效率高，克服了被积函数的奇异性和高振荡性问题，是数值求解汉克尔积分的重要方法。采用存在解析解的汉克尔积分，对比研究了5套高精度汉克尔滤波系数，总结了不同数值滤波算法的计算精度和误差分布特点。结果表明，5套数字滤波的快速汉克尔变换算法在逼近相应的理论解析解时，不存在振荡现象，且计算精度高；汉克尔积分计算精度均随着发收距的增大而降低；计算精度并不一定随着数值滤波系数个数的增多而提高。分别采用5种滤波系数对水平电偶极子和垂直磁偶极子的电磁场进行计算，得到的电场和磁场的形态基本一致。

Abstract:

Many kinds of Hankel integral appear in electromagnetic methods. Due to the complexity of the kernel function, there are no analytic solution for these Hankel integral. Thus numerical methods for the computation of Hankel integral play an important part in electromagnetic forward modeling. Numerical filtering methods is high efficient, overcome the singularity and high oscillation of the kernel functions, and become the most important methods for numerical computation of Hankel integral. In this work, by using Hankel integral which has analytic solution and comparing five numerical filtering coefficients, the computation accuracy and error distribution have been summarized. It is showed that in approximating the analytic solution, all five numerical filtering methods have no oscillation and have high accuracy. Computation accuracy for Hankel integral decreases with increasing of transmit-receive distance, and is not improved by increasing the number of filtering coefficients. Electromagnetic fields produced by horizontal electric dipole and vertical magnetic dipole are computed by the five numerical filtering methods, and the contour of the resultant fields are substantially consistent.