瞬变电磁频-时转换混合优化算法研究  

Hybrid optimization algorithm of transient electromagnetic time-frequency conversion

作　　者：甘露[1] 唐荣江[1] 王绪本[2] GAN Lu;TANG Rong-jiang;WANG Xu-ben(School of Geophysics, Chengdu University of Technology, Chengdu 610059, China;Key Laboratory of Earth Exploration and Information Techniques of the Ministry of Education, Chengdu University of Technology, Chengdu 610059, China)

机构地区：[1]成都理工大学地球物理学院,成都610059 [2]成都理工大学,地球勘探与信息技术教育部重点实验室,成都610059

出　　处：《地球物理学进展》2018年第2期596-602,共7页Progress in Geophysics

基　　金：国土资源部公益性行业科研专项“基于无人机的半航空瞬变电磁勘察技术研究”(201311037)资助

摘　　要：瞬变电磁正演的常规算法是把频率域响应转化到时间域,通常有三种方法:Guptasma算法、余弦变换折线逼近算法和Gaver-Stehfest逆拉普拉斯变换算法.在计算精度上,余弦变换折线逼近算法难以求出符合精度的感应电动势,误差集中在晚期,但是当频率范围取值合理时,可以得到精度较高的磁感应强度.Guptasma算法和Gaver-Stehfest逆拉普拉斯变换算法在晚期通常有较大误差,而早期的感应电动势和磁感应强度精度都较高.在计算速度上,Guptasma算法最快,折线逼近算法由于需要计算大量频点导致速度很慢.因此,为了能够既快速又有效的完成频率域到时间域的转换,为反演奠定基础,本文以电性源为例,设计出一种新的混合算法,该算法在早期采用Guptasma算法,在误差较大的晚期采用余弦变换多项式近似算法,首先求出磁感应强度,然后采用数值差分的方法求得感应电动势.通过对Guptasma算法、余弦变换折线逼近算法以及混合优化算法的最终结果的误差和运算时间进行比较,说明混合优化算法充分发挥了Guptasma算法和余弦变换折线逼近算法的各自的优势,计算速度较快且精度较高,能够取得较好的效果.The conventional algorithm for transient electromagnetic forward modeling is to transform the frequency domain response to the time domain. Usually there are three methods： Guptasma algorithm,Cosine transform line approximation algorithm and GaverStehfest inverse Laplasse transform algorithm. In the calculation accuracy,Cosine transform polygonal approximation algorithm is difficult to obtain the induced electromotive force that meet the accuracy requirement,and the error usually in late stage,but when the frequency range is reasonable, it can get higher precision magnetic induction intensity. The Guptasma algorithm and the Gaver-Stehfest inverse Laplasse transform algorithm usually have large errors in the later stage,while induction electromotive force and magnetic induction intensity are higher in the early stage. In the computation speed,the Guptasma algorithm is the fastest,and the line approximation algorithm is the lowest due to the needs of calculating a large number of frequency points. Therefore,in order to quickly and effectively complete the conversion from frequency domain to time domain, and lays the better foundation for the inversion,a new hybrid optimization algorithm is designed based on the electrical source in this paper. In this hybrid optimization algorithm,the Guptasma algorithm is adopted in the early stage,and the cosine transform line approximation algorithm is used in the later stage with large error. First,the magnetic induction intensity is obtained,and then the induction electromotive force is obtained by numerical difference method. By comparing the error of the final results and computation time between the Guptasma algorithm,cosine transform line approximation algorithm and the hybrid optimization algorithm,it is concluded that the advantages of the cosine transform line approximation algorithm and Guptasma algorithm are fully utilized in the hybrid optimization algorithm,so that the hybrid optimization algorithm can achieve a better effect—the calculation speed is fast and th

关 键 词：电偶源瞬变电磁 频时转换 一维正演 

分 类 号：P631[天文地球—地质矿产勘探]