一种高精度瞬变电磁响应正演的数值滤波算法

A high-accuracy numerical filtering algorithm for calculating transient electromagnetic responses

1.中国地质大学地球物理与空间信息学院,湖北武汉430074;2.油气资源与勘探技术教育部重点实验室（长江大学），湖北荆州434023

Xu Zhenping,Institute of Geophysics & Geomatics,China University of Geosciences,Wuhan 430074,China

在瞬变电磁测深正演中,时间域电磁场响应通常由频率域响应的逆Laplace变换得到,但常规的逆Laplace变换算法不能保证在大的计算时间范围内满足精度要求,有时甚至不能收敛。为此,对Laplace逆变换的求积公式进行了变换,得到与正弦有关的积分公式,然后对核函数进行离散,利用复数的围道积分方法推导得到快速正弦变换的算法及滤波系数,实现了逆Laplace变换的快速计算。通过具有解析解的算例,总结了多种逆Laplace变换算法的特点及适应性。将上述算法应用于瞬变电磁时间域响应的正演计算,得到了大时间范围的收敛解,解决了常规算法在大时间值时正演计算精度和收敛性差的问题。

Time domain response of transient electromagnetic sounding in forward modeling are often obtained from frequency responses by means of inverse Laplace transform.However,conventional inverse Laplace transform cannot ensure to satisfy the requirement of accuracy in a large range of computation time,sometimes it even cannot converge.Therefore,the inverse Laplace transform was alternated to obtain the integral formula related to sine.Then,the kernel function was discrete,and contour integral method of complex was used to reduce the algorithm of fast Sine transform and filtering coefficient and realize the fast computation of inverse Laplace transform.By the example with analytic solution,the characteristics and adaptability of several inverse Laplace transform methods were concluded.The algorithm was used for forward modeling of the response of transient electromagnetic time domain,and converging of large time range was obtained,which overcame the bad forward computation accuracy and convergence of conventional methods under large time value.