大地电磁二维DCG、NLCG和L-BFGS反演算法对比  

Comparison of Magnetotelluric Two-dimensional DCG、NLCG、L-BFGS Inversion Methods

作　　者：李磊 吴桂桔[1] 谈洪波[1] Li Lei;Wu Guiju;Tan Hongbo(Key Laboratory of Earthquake Geodesy, Institute of Seismology, CEA, Wuhan Hubei 430071, China)

机构地区：[1]中国地震局地震研究所地震大地测量重点实验室,湖北武汉430071

出　　处：《工程地球物理学报》2022年第1期106-116,共11页Chinese Journal of Engineering Geophysics

基　　金：国家自然科学基金项目(编号:42074172);地震星火计划项目(编号:XH21021)。

摘　　要：大地电磁(MT)法的二维反演算法种类较多,在实际应用中如何选取合适的二维反演方法仍是一个关键问题。通过对比典型理论地电模型与不同反演方法的应用效果,可为实际MT探测反演方法的选择提供参考。本文对数据空间共轭梯度法(DCG)、非线性共轭梯度法(NLCG)以及有限内存拟牛顿法(L-BFGS)三种常用的MT二维反演算法进行对比。首先描述了三种方法的基本原理,然后设计了两个典型的地电模型,对TE、TM、Tzy三种不同模式的数据组合进行了反演试算,分析了这三种模式下不同反演算法的效果。得出3点结论:①三种方法均能较好地反演地下异常体的位置和大小,其反演效果大体相当,但无论是低阻异常体还是高阻异常体都会向四周发散;②L-BFGS和NLCG反演结果更接近真实值,且L-BFGS更适用于复杂介质模型;③三种反演方法在计算迭代过程中,数据拟合差RMS值都呈下降状态,NLCG的拟合差RMS值最小、且收敛速度最快。There are many kinds of two-dimensional inversion algorithms of magnetotelluric(MT)method,and how to choose the appropriate two-dimensional inversion method in practical application remains a key problem.By comparing the application effects of typical theoretical geoelectric models with different inversion methods,it can provide reference for the selection of inversion methods in practical MT detection problems.In this paper,the data space conjugate gradient method(DCG),the nonlinear conjugate gradient method(NLCG)and the finite memory quasi-Newton method(L-BFGS)are compared.Firstly,the basic principles of the three methods are described,then two typical geoelectric models are designed,and the data combinations of TE,TM and Tzy are inversed and calculated.Finally,the effects of different inversion algorithms under these three modes are analyzed.The following conclusions are obtained:①All the three methods can well invert the position and size of underground anomalies,and their inversion results are roughly equal,but both low-resistance anomalies and high-resistance anomalies will diverge around;②The inversion results of L-BFGS and NLCG are closer to the real values,and L-BFGS is more suitable for complex media models;③In the iterative process of calculation,the RMS value of data fitting difference is declining,and the RMS value of NLCG is the smallest and the convergence speed is the fastest.

关 键 词：大地电磁法 二维反演 反演方法对比 

分 类 号：P631.3[天文地球—地质矿产勘探]