Efficient Computation of Sommerfeld Integral by Cubic Spline Interpolation to Determine Spatial Domain Dyadic Greens Function in Horizontally Layered TI Medium
It is very important to fast compute the spatial domain dyadic Greens function in horizontal layered TI formations for use of integral equation to solve 3D EM field.The Greens function is usually expressed by the Sommerfeld integral with complex kernel functions.Their integrands always contain singular points so their numerical integrations often show rapid oscillations and slow convergent characteristics and their computations are very time-consuming.Based on the complexity of the kernel function in horizontal layered TI formations in magnetotelluric exploration,we advance a simple and novel approach called as cubic spline interpolation method(CSIM)to quickly solve the Sommerfeld integral.First,we divide the integral range into a series of small segments with gradual increase of the lengths and compute the values of the kernel functions at all nodes.Then we use cubic spline functions to interpolate the kernel function and obtain the semianalytic expression of the function.We can further transform the integral into a series of simple Bessel integral with kernel of polynomial functions at each segment.Furthermore,using Bessel function recursion formula and the asymptotic expansion of Lommel formula to analytically solve all the integrals and sum them,we can efficiently obtain numerical results of spatial domain dyadic Greens function.The numerical results show that the new algorithm largely increases efficiency of computation of the Greens function and faster than other digital filter techniques.
Jianmei Zhou Hongnian Wang
School of Physics,Jinlin University,Changchun 130012,China
国际会议
Progress in Electromagnetics Research Symposium 2011(2011年电磁学研究新进展学术研讨会)
苏州
英文
1139-1142
2011-09-01（万方平台首次上网日期，不代表论文的发表时间）