大地电磁一维正则化反演算法研究  

Research on regularized inversion algorithms of one-dimensional magnetotelluric data

作　　者：周君君 胡祥云[1] 肖调杰 白宁波 ZHOU Junjun;HU Xiangyun;XIAO Tiaojie;BAI Ningbo(Institute of Geophysics and Geomatics,China University of Geosciences,Wuhan 430074,China;Science and Technology on Parallel and Distributed Processing Laboratory,National University of Defense Technology,Changsha 410073,China;School of Physics and Electronic Information Engineering,Henan Polytechnic University,Jiaozuo 454000,China)

机构地区：[1]中国地质大学(武汉)地球物理与空间信息学院,湖北武汉430074 [2]国防科技大学并行与分布处理实验室,湖南长沙410073 [3]河南理工大学物理与电子信息学院,河南焦作454000

出　　处：《煤炭科学技术》2021年第8期174-180,共7页Coal Science and Technology

基　　金：国家自然科学基金资助项目(41630317),国家重点研究开发资助项目(2017YFC0602405)。

摘　　要：为了解决大地电磁反演的不适定问题,正则化方法处理是用于解决该问题的主要方法。正则化方法是在数据目标泛函中增加一项稳定泛函,从而获得病态问题的稳定解。为了有效地改善大地电磁反演过程中解的不唯一性和不稳定性等问题,最小二乘光滑约束反演算法和同伦正则反演算法被提出解决该类问题。其中,同伦正则反演算法具有解非线性问题收敛性好的优点,该算法将同伦思想与Tikhonov正则化思想结合构造反演目标泛函。在大地电磁一维正则化反演算法正则因子的选取上与现有成果不同,这2种正则化算法均采用Morozov偏差原理决定正则因子。为了验证2种算法的稳健性,对理论数据添加随机高斯噪声后进行反演,基本上也能反演出模型参数,结果表明了2种算法都有较好的鲁棒性。考虑到同伦正则算法首次应用到大地电磁一维反演中,因此进一步将其对实测数据进行反演。反演数据来自吉林桦皮厂地热田的一个实测点,并将反演结果与Bostick反演和Occam反演结果进行了对比分析,同伦正则算法反演结果与实际勘探结果更加吻合,表明了同伦正则算法在大地电磁实测数据的处理中,有更高的精确度。算例结果证明了2种算法是有效的,能够改善大地电磁反演问题的不适定性。In order to solve the ill-posed problem of magnetotelluric inversion,regularization is the main application method at present.Regularization is to add a stable functional to the objective functional of data,so as to obtain the stable solution of ill-conditioned problem.In order to effectively improve the non-uniqueness and instability of solutions in magnetotelluric inversion,the least square smoothing constraint inversion algorithm and homotopy regular inversion algorithm are proposed to solve these problems.Among them,homotopy regular inversion algorithm has the advantage of good convergence in solving nonlinear problems.This algorithm combines homotopy idea with Tikhonov regularization idea to construct inversion objective functional.Different from the existing achievements in the selection of regularization factors in magnetotelluric one-dimensional regularization inversion algorithm,both regularization algorithms use Morozov deviation principle to determine the regularization factors.In order to verify the robustness of the two algorithms,the theoretical data can be inverted after adding random Gaussian noise,and the model parameters can also be inverted basically.The results show that the two algorithms have good robustness.Considering that homotopy regularization algorithm is applied to magnetotelluric one-dimensional inversion for the first time,it further inverts the measured data.Inversion data comes from a measured point in Huapichang geothermal field,Jilin Province,and the inversion results are compared with Bostick inversion and Occam inversion results.The inversion results of homotopy regularization algorithm are more consistent with the actual exploration results,which shows that homotopy regularization algorithm has higher accuracy in the processing of magnetotelluric measured data.The results of an example show that the two algorithms are effective and can improve the ill-posed problem of magnetotelluric inversion.

关 键 词：大地电磁反演 不适定问题 最小二乘光滑约束反演 同伦正则反演 

分 类 号：P631[天文地球—地质矿产勘探]