孙怀凤^1,3,,
张诺亚^1,3,
柳尚斌^1,3,
李敦仁^2,,,
陈成栋^1,3,
叶琼瑶²,
薛翊国¹,
杨洋^1,3
1. 山东大学 岩土与结构工程研究中心, 济南 250061
2. 广西交通设计集团有限公司, 南宁 530029
3. 山东大学 地球电磁探测研究所, 济南 250061

基金项目: 山东省重点研发计划（2018GSF117020），广西科技基地和人才专项（桂科AD17129047）资助


详细信息

作者简介: 孙怀凤, 男, 博士, 副教授, 博士生导师, 主要从事瞬变电磁正反演方面的教学与科研工作.E-mail:sunhuaifeng@gmail.com

通讯作者: 李敦仁, 男, 教授级高级工程师, 主要从事岩溶地质灾害探测与防治方面的科研与应用研究.E-mail:48388@qq.com

中图分类号: P631

收稿日期:2018-12-17
修回日期:2019-07-08
上线日期:2019-12-05

L1-norm based nonlinear inversion of transient electromagnetic data

SUN HuaiFeng^1,3,,
ZHANG NuoYa^1,3,
LIU ShangBin^1,3,
LI DunRen^2,,,
CHEN ChengDong^1,3,
YE QiongYao²,
XUE YiGuo¹,
YANG Yang^1,3
1. Geotechnical and Structural Engineering Researh Center, Shandong University, Jinan 250061, China
2. Guangxi Communications Design Group Co., Ltd., Nanning 530029, China
3. Laboratory of Earth Electromagnetic Exploration, Shandong University, Jinan 250061, China


More Information

Corresponding author: LI DunRen,E-mail:48388@qq.com

MSC: P631

--> Received Date: 17 December 2018
Revised Date: 08 July 2019
Available Online: 05 December 2019


摘要
摘要:瞬变电磁反演存在高度的非线性特征，常用的最小二乘等线性反演方法往往对初始模型高度依赖，并且极易陷入局部最优解.本文基于观测数据与模拟数据的L1范数建立目标函数，采用模拟退火非线性全局最优化方法实现瞬变电磁一维反演.初始模型完全随机产生，通过指数函数退温机制模拟系统能量最小实现迭代，通过接收概率函数评价当前模型，实现局部最优解的跳出，最终实现全局最优化求解.通过数值算例发现，无论给定的反演层数等于还是大于设计模型，都可以获得较好的反演效果，因而可以在反演初始就设计较多的层数，实现反演模型的自动拟合；同时，利用含噪声数据反演进一步验证算法的稳定性.最后，对实测数据进行了反演测试，结果与钻孔编录基本一致，表明提出的基于L1范数的模拟退火反演可用于实测数据处理.
关键词: 瞬变电磁/
模拟退火/
非线性/
反演/
L1范数

Abstract:Transient electromagnetic inversion is a highly nonlinear problem. The conventionally used linear inversion methods,such as Least Squares inversion,are often dependent on the initial model and will consequently be easy to obtain local minima. In this paper,we establish the objective function based on the L1-norm of the observed data and the simulated data,and propose a nonlinear simulated annealing inversion for Transient Electromagnetic (TEM) data. The initial model of our method can be completely random. We apply an exponential function to simulate the system energy minimum to realize the inversion iteration. The current step model can be evaluated by the receiving probability function. This is helpful to jump out of the local optimal solution. We obtain the global optimized solution at late interations. By numerical examples,we find very good inversion model no matter the start model layers is equal or bigger than the ture model. Thus,it's possible to design many layers models similar to Occam inversion to fit the ture model. We also test the algorithm with noise data and find good inversion results. Finally,we apply the algorithm to invert a field data. The inverted model are in good agreement with the borehole results.
Key words:TEM/
Simulated annealing/
Nonlinear/
Inversion/
L1-norm



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