1. Engineering Research Center of Nuclear Technology Application(East China University of Technology) Mi-nistry of Education, Nanchang, Jiangxi 330013, China; 2. School of Geophysics and Measurement-control Technology, East China University of Technology, Nanchang, Jiangxi 330013, China
Abstract：How to reasonably choose a regularization factor has always been a hotspot and difficulty in geophysical inversion.Choosing the regularization factor from the perspective of improving the stability of inversion is a new idea. In addition,the randomness of nonlinear optimization algorithm is not considered enough in previous studies on regularized inversion. Based on the adaptive algorithm proposed by Zhdanov,we propose a self-adaptive regularized algorithm,also called "Staged Adaptive Algorithm",which adjusts the regularization factor stage by stage. We use the algorithm for magnetotelluric (MT) conjugate gradient inversion and differential evolution inversion. Model tests show that the new adaptive algorithm can improve the stability of inversion,reduce the influence of the attenuation factor to some extent,and it is applicable for linear and nonlinear optimization algorithms.
Tikhonov A N.Regularization of Incorrectly Posed Problem[M].Soviet Math,Dokl,1963.
[2]
Wahba G.Spline Models for Observational Data[M].SIAM,Philadelphia,1990.
[3]
Wahba G.Practical approximate solutions to linear operator equations when the data are noisy[J].SIAM Journal on Numerical Analysis,1977,14(4):651-667.
[4]
Golub G H,Heath M,Wahba G.Generalized cross-validation as a method for choosing a good ridge parameter[J].Technometrics,1979,21(2):215-223.
[5]
Hansen P C,O'Leary D P.The use of the L-curve in the regularization of discrete ill-posed problems[J].SIAM Journal on Scientific Computing,1993,14(6):1487-1503.
[6]
Hansen P C.Regularization tools:a Matlab package for analysis and solution of discrete ill-posed problems[J].Numerical algorithms,1994,6(1):1-35.
[7]
Lima W A,Silva J B C,Santos D F,et al.A robust interactive estimation of the regularization parameter[J].Geophysics,2019,84(3):IM19-IM33.
[8]
Zhdanov M S.Geophysical Inverse Theory and Regularization Problems[M].Elsevier Science,Netherlands,2002.
[9]
陈小斌,赵国泽,汤吉,等.大地电磁自适应正则化反演算法[J].地球物理学报,2005,48(4):937-946.CHEN Xiaobin,ZHAO Guoze,TANG Ji,et al.An adaptive inversion algorithm for magnetotelluric data[J].Chinese Journal of Geophysics,2005,48(4):937-946.
[10]
向阳,于鹏,陈晓,等.大地电磁反演中改进的自适应正则化因子选取[J].同济大学学报(自然科学版),2013,41(9):1429-1434.XIANG Yang,YU Peng,CHEN Xiao,et al.An improve adaptive regularized parameter selection in magnetotelluric inversion[J].Journal of Tongji University(Natural Science Edition),2013,41(9):1429-1434.
[11]
黄贤阳,邓居智,陈晓,等.基于不同稳定泛函约束的大地电磁极值边界反演研究及其在内蒙古塔木素测区的应用[J].应用地球物理学报,2019,16(3),367-377.HUANG Xianyang,DENG Juzhi,CHEN Xiao,et al.Magnetotelluric extremum boundary inversion based on different stabilizers and its application in Inner Mongolia Tamusu area[J].Journal of Applied Geophysics,2019,16(3):367-377.
[12]
陈晓,于鹏,张罗磊,等.地震与大地电磁测深数据的自适应正则化同步联合反演[J].地球物理学报,2011,54(10):2673-2681.CHEN Xiao,YU Peng,ZHANG Luolei,et al.Adaptive regularized synchronous joint inversion of MT and seismic data[J].Chinese Journal of Geophysics,2011,54(10):2673-2681.
[13]
陈晓,于鹏, 邓居智,等.基于宽范围岩石物性约束的大地电磁和地震联合反演[J].地球物理学报,2016,59(12):4690-4700.CHEN Xiao,YU Peng,DENG Juzhi,et al.Joint inversion of MT and seismic data based on wide-range petrophysical constraints[J].Chinese Journal of Geophysics,2016,59(12):4690-4700.
[14]
徐姣.基于快速遗传算法的速度反演研究及应用[D].四川成都:成都理工大学,2009.XU Jiao.The Research and Application in Velocity Inversion Based on Rapid Genetic Algorithm[D].Chengdu University of Technology,Chengdu,Sichuan,2009.
[15]
Zeng Z W,Chen X,Liu X,et al.Joint inversion of MT and gravity based on differential evolution algorithm[C].China International Geo-electromagnetism Workshop,2019,105-108.
[16]
赵德杨.地震波阻抗粒子群优化反演方法的研究[D].四川成都:成都理工大学,2014.ZHAO Deyang.Acoustic Impendence Inversion Based on Particle Swarm Optimization Algorithm[D].Chengdu University of Technology,Chengdu,Sichuan,2014.
[17]
Kumar A,Wan L,Zhdanov M S.Regularization analysis of three-dimensional magnetotelluric inversion[C].SEG Technical Program Expanded Abstracts,2007,26:482-486.
[18]
Gribenko A,Zhdanov M.Rigorous 3D inversion of marine CSEM data based on the integral equation method[J].Geophysics,2007,72(2):WA73-WA84.
[19]
Storn R,Price K.Differential Evolution:A simple and efficient heuristic for global optimization over conti-nuous spaces[J].Journal of Global Optimization,1997,11(4):341-359.
[20]
王天意,杨进,颜廷杰,等.地球物理反演中的差分进化算法[J].地质与勘探,2014,50(5):971-975.WANG Tianyi,YANG Jin,YAN Tingjie,et al.The differential evolution algorithm in geophysical inversion[J].Geology and Exploration,2014,50(5):971-975.
[21]
余胜威.MATLAB优化算法案例分析与应用(进阶篇)[M].北京:清华大学出版社,2015.
[22]
张罗磊.OCCAM与SBI结合的MT二维反演方法[D].上海:同济大学,2008.ZHANG Luolei.OCCAM and SBI Based Two-Dimensional Magnetotelluric Inversion[D].Tongji University,Shanghai,2008.
[23]
王家林,钟慧智,于鹏,等.苏北中古生界MT精细处理及综合解释[R].上海:同济大学,2012.
[24]
王建.江苏盐阜地区中生界综合地球物理研究[D].上海:同济大学,2005.WANG Jian.Integrated Geophysical Research about Mesozoic in Yanfu,Jiangsu[D].Tongji University,Shanghai,2005.
[25]
陈晓.大地电磁与地震正则化联合反演研究[D].上海:同济大学,2013.CHEN Xiao.Regularized Joint Inversion of MT and Seismic Data[D].Tongji University,Shanghai,2013.
