极低频电磁法超高速振荡Bessel积分数值计算的解决方案——积分外推法

Solution for numerical calculation of ultra-high speed oscillation Bessel integral in Wire-less Electromagnetic Method(WEM):quadrature with extrapolation

极低频电磁法需要考虑电离层和位移电流的影响,Bessel积分核函数超高速振荡,超过了现有滤波系数的截止频率,收敛慢,甚至不收敛,导致数值计算极为困难,即使采用现有的、最高采样密度的Hankel滤波系数进行数值计算,高频时的计算误差大,不能满足需求.针对以上问题,本文将积分外推算法应用到极低频电磁法的数值计算中.首先通过计算CSAMT在均匀半空间的数值解与解析解验证算法的准确性;然后研究了极低频电磁法三层模型中给定收发距的波场频率响应曲线及给定频率的波场结构特征,积分外推法的低频结果与高采样密度Hankel滤波计算结果一致,高频结果优于Hankel滤波计算结果.本文研究表明,积分外推算法可有效解决超高速振荡Bessel积分数值计算难题.

To consider the influence of ionosphere and displacement current in Wire-less Electromagnetic Method(WEM),the Bessel integral kernel function is highly oscillated,exceeding the cutoff frequency of the existing filter coefficient,and the convergence is slow or even non-converge,which makes the numerical calculation extremely difficult.Even if the Hankel filter coefficient with the highest sampling density is adopted for numerical calculation,the calculation error at high-frequency is large and can not meet the requirements.In view of the above problems,this paper applies the quadrature with extrapolation to the numerical calculation of WEM.First,the accuracy of the algorithm is verified by numerical solution and analytical solution of CSAMT in uniform half space.Then,the wave field frequency response curves of a given transceiver distance and the wave field structure characteristics of a given frequency are studied in the three-layer model of WEM,the low-frequency result of the quadrature with extrapolation is consistent with the high sampling density Hankel filter,the high-frequency result is better than the Hankel filter calculation result.The research shows that quadrature with extrapolation can effectively solve the problem of ultra-high speed oscillations on Bessel integral numerical calculation.