大地电磁与地震正则化同步联合反演
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摘要
文中在于鹏等提出的电阻率和速度随机分布的大地电磁与地震联合反演方法的基础上,将Tikhonov正则化思想引入到联合反演中,加入先验信息进行模型约束,以最小模型为稳定器,采用L曲线方法来确定近似最佳的正则化因子。考虑到线性寻优算法容易陷入局部极小,文中采用非线性的模拟退火方法来实现大地电磁与地震的同步联合反演。通过模型试验的对比分析,我们认为加入有效模型约束的正则化联合反演可以比单纯考虑数据拟合的联合反演和单独反演方法更有效地提高解的稳定性和计算效率,获得更接近实际而且稳定的解。
All the geophysical inversion problems are ill-posed.The application of regularization theory and joint inversion provide us ideas to solve the ill-posed inverse geophysical problems.Regularization theory has been widely used in single geophysical inversion problem which has achieved certain effects;however,what geophysicists concerned in the previous studies on joint inversion just was data misfit with little consideration about regularization theory.In this paper,based on the joint inversion method with random resistivity and velocity distributions proposed by YU Peng,the conception of regularization is introduced into synchronous joint inversion of magnetotelluric(MT) and seismic data.We use priori information to improve the stability of solution,and set stabilizer as the smallest model.How to meet the best trade-off between data misfit and model constraint,and what's intellectual choice for the regularization factor have always been the hotspots in the geophysical inversion problem.We use L-curve method to determine the quasi-optimal value of the regularization parameter,and apply it into joint inversion.To avoid immerging in local minimum of linear inversion method,nonlinear simulated annealing method is used to realize joint inversion.The forward modeling of MT data is obtained by using finite element method and the seismic travel-time computing is obtained by using improved ray-tracing method.Testing the regularized and conventional synchronous joint inversion on synthetic data sets shows that regularized joint inversion with effective model constraint has powerful availability to improve stability of solution and efficiency of computation,and to help us to obtain a stable solution which is close to the fact.
All the geophysical inversion problems are ill-posed.The application of regularization theory and joint inversion provide us ideas to solve the ill-posed inverse geophysical problems.Regularization theory has been widely used in single geophysical inversion problem which has achieved certain effects;however,what geophysicists concerned in the previous studies on joint inversion just was data misfit with little consideration about regularization theory.In this paper,based on the joint inversion method with random resistivity and velocity distributions proposed by YU Peng,the conception of regularization is introduced into synchronous joint inversion of magnetotelluric(MT) and seismic data.We use priori information to improve the stability of solution,and set stabilizer as the smallest model.How to meet the best trade-off between data misfit and model constraint,and what's intellectual choice for the regularization factor have always been the hotspots in the geophysical inversion problem.We use L-curve method to determine the quasi-optimal value of the regularization parameter,and apply it into joint inversion.To avoid immerging in local minimum of linear inversion method,nonlinear simulated annealing method is used to realize joint inversion.The forward modeling of MT data is obtained by using finite element method and the seismic travel-time computing is obtained by using improved ray-tracing method.Testing the regularized and conventional synchronous joint inversion on synthetic data sets shows that regularized joint inversion with effective model constraint has powerful availability to improve stability of solution and efficiency of computation,and to help us to obtain a stable solution which is close to the fact.
引文
陈洁,温宁,陈邦彦.2007.重磁电震联合反演研究进展与展望[J].地球物理学进展,22(5):1427—1438.CHEN Jie,WEN Ning,CHEN Bang-yan.2007.Joint inversion of gravity-magnetic-electrical-seismic combination sur-vey:Progress and prospect[J].Progress in Geophysics,22(5):1427—1438(in Chinese).
陈小斌,赵国泽.2009.自动构建大地电磁二维反演的测点中心网格[J].地球物理学报,52(6):1564—1572.CHEN Xiao-bin,ZHAO Guo-ze.2009.Automatic construction of a site-centered grid for2D magnetotelluric inversion[J].Chinese Journal of Geophysics,52(6):1564—1572(in Chinese).
陈小斌,赵国泽,汤吉,等.2005.大地电磁自适应正则化反演算法[J].地球物理学报,48(4):937—946.CHEN Xiao-bin,ZHAO Guo-ze,TANG Ji,et al.2005.An adaptive regularized inversion algorithm for magnetotelluric data[J].Chinese Journal of Geophysics,48(4):937—946(in Chinese).
过仲阳,王家林,吴健生.1999.应用遗传算法联合反演地震:大地电磁测深数据[J].石油物探,38(1):102—108.GUO Zhong-yang,WANG Jia-lin,WU Jian-sheng.1999.Joint inversion of seismic and magnetotelluric sounding data u-sing genetic algorithm[J].Geophysical Prospecting for Petroleum,38(1):102—108(in Chinese).
杨辉,戴世坤,宋海斌,等.2002a.综合地球物理联合反演综述[J].地球物理学进展,17(2):262—271.YANG Hui,DAI Shi-kun,SONG Hai-bin,et al.2002a.Overview of joint inversion of integrated geophysics[J].Pro-gress in Geophysics,17(2):262—271(in Chinese).
杨辉,王家林,吴健生,等.2002b.大地电磁与地震资料仿真退火约束联合反演[J].地球物理学报,45(5):723—734.YANG Hui,WANG Jia-lin,WU Jian-sheng,et al.2002b.Constrained joint inversion of magnetotelluric and seismic data using simulated annealing algorithm[J].Chinese Journal of Geophysics,45(5):723—734(in Chinese).
杨振武,王家映,张胜业,等.1998.一维大地电磁和地震数据联合反演方法研究[J].石油地球物理勘探,33(1):78—88.YANG Zhen-wu,WANG Jia-ying,ZHANG Sheng-ye,et al.1998.Research on joint inversion of1-D magnetotelluric and seismic data[J].Oil Geophysical Prospecting,33(1):78—88(in Chinese).
于鹏,戴明刚,王家林,等.2008.密度和速度随机分布共网格模型的重力与地震联合反演[J].地球物理学报,51(3):845—852.YU Peng,DAI Ming-gang,WANG Jia-lin,et al.2008.Joint inversion of gravity and seismic data based on common grid-ded model with random density and velocity distributions[J].Chinese Journal of Geophysics,51(3):845—852(in Chinese).
于鹏,戴明刚,王家林,等.2009.电阻率和速度随机分布的MT与地震联合反演[J].地球物理学报,52(4):1089—1097.YU Peng,DAI Ming-gang,WANG Jia-lin,et al.2009.Joint inversion of magnetotelluric and seismic data based on ran-dom resistivity and velocity distributions[J].Chinese Journal of Geophysics,52(4):1089—1097(in Chinese).
于鹏,王家林,吴健生,等.2006.地球物理联合反演的研究现状和分析[J].勘探地球物理进展,29(2):87—93.YU Peng,WANG Jia-lin,WU Jian-sheng,et al.2006.Review and discussions on geophysical joint inversion[J].Pro-gress in Exploration Geophysics,29(2):87—93(in Chinese).
周辉,刘财,渠广学.1995.地震-大地电磁数据非线性联合反演方法研究[J].长春地质学院学报,25(2):205—211.ZHOU Hui,LIU Cai,QU Guang-xue.1995.The study of nonlinear joint inversion method for seismic and magnetotelluric sounding data[J].Journal of Changchun University of Science and Technology,25(2):205—211(in Chinese).
周辉,杨宝俊,刘财.1994.地震-大地电磁测深资料综合反演[J].地球物理学报,37(增刊):477—485.ZHOU Hui,YANG Bao-jun,LIU Cai.1994.Combined inversion of seismic and magnetotelluric sounding data[J].Chi-nese Journal of Geophysics,37(Suppl):477—485(in Chinese).
Colombo D,Stefano M D.2007.Geophysical modeling via simultaneous joint inversion of seismic,gravity,and electro-magnetic data:Application to prestack depth imaging[J].The Leading Edge,26(3):326—331.
Haber E,Oldenburg D.2000.A GCV based method for nonlinear ill-posed problems[J].Computational Geosciences,4(1):41—63.
Hansen P C,Leary D P.1993.The use of the L-curve in the regularization of discrete ill-posed problems[J].Society for Induction and Applied Mathematics,14(6):1487—1503.
Hansen P C.1994.Regularization tools:A Matlab package for analysis and solution of discrete ill-posed problems[J].Numerical Algorithm,14(6):1—35.
Heincke B,Hobbs R.2006.Joint inversion of MT,gravity and seismic data applied to sub-basalt imaging[A].In:SEG2006Expanded Abstract.SEG.784—787.
Kumar A,Wan L,Zhdanov M S.2007.Regularization analysis of three-dimensional magnetotelluric inversion[A].In:SEG2007Annual Meeting.San Antonio.482—486.
Stando D K,Rudnicki M.2007.Regularization parameter selection in discrete ill-posed problems:The use of the U-curve[J].International Journal of Applied Mathematics and Computer Science,17(2):157—164.
Wahba G.1997.Practical approximate solutions to linear operator equations when the data are noisy[J].SIAM Journal on Numerical Analysis,14(4):651—667.
Zhdanov M S.2002.Geophysical Inverse Theory and Regularization Problems[M].Netherlands.Elsevier Science.
陈小斌,赵国泽.2009.自动构建大地电磁二维反演的测点中心网格[J].地球物理学报,52(6):1564—1572.CHEN Xiao-bin,ZHAO Guo-ze.2009.Automatic construction of a site-centered grid for2D magnetotelluric inversion[J].Chinese Journal of Geophysics,52(6):1564—1572(in Chinese).
陈小斌,赵国泽,汤吉,等.2005.大地电磁自适应正则化反演算法[J].地球物理学报,48(4):937—946.CHEN Xiao-bin,ZHAO Guo-ze,TANG Ji,et al.2005.An adaptive regularized inversion algorithm for magnetotelluric data[J].Chinese Journal of Geophysics,48(4):937—946(in Chinese).
过仲阳,王家林,吴健生.1999.应用遗传算法联合反演地震:大地电磁测深数据[J].石油物探,38(1):102—108.GUO Zhong-yang,WANG Jia-lin,WU Jian-sheng.1999.Joint inversion of seismic and magnetotelluric sounding data u-sing genetic algorithm[J].Geophysical Prospecting for Petroleum,38(1):102—108(in Chinese).
杨辉,戴世坤,宋海斌,等.2002a.综合地球物理联合反演综述[J].地球物理学进展,17(2):262—271.YANG Hui,DAI Shi-kun,SONG Hai-bin,et al.2002a.Overview of joint inversion of integrated geophysics[J].Pro-gress in Geophysics,17(2):262—271(in Chinese).
杨辉,王家林,吴健生,等.2002b.大地电磁与地震资料仿真退火约束联合反演[J].地球物理学报,45(5):723—734.YANG Hui,WANG Jia-lin,WU Jian-sheng,et al.2002b.Constrained joint inversion of magnetotelluric and seismic data using simulated annealing algorithm[J].Chinese Journal of Geophysics,45(5):723—734(in Chinese).
杨振武,王家映,张胜业,等.1998.一维大地电磁和地震数据联合反演方法研究[J].石油地球物理勘探,33(1):78—88.YANG Zhen-wu,WANG Jia-ying,ZHANG Sheng-ye,et al.1998.Research on joint inversion of1-D magnetotelluric and seismic data[J].Oil Geophysical Prospecting,33(1):78—88(in Chinese).
于鹏,戴明刚,王家林,等.2008.密度和速度随机分布共网格模型的重力与地震联合反演[J].地球物理学报,51(3):845—852.YU Peng,DAI Ming-gang,WANG Jia-lin,et al.2008.Joint inversion of gravity and seismic data based on common grid-ded model with random density and velocity distributions[J].Chinese Journal of Geophysics,51(3):845—852(in Chinese).
于鹏,戴明刚,王家林,等.2009.电阻率和速度随机分布的MT与地震联合反演[J].地球物理学报,52(4):1089—1097.YU Peng,DAI Ming-gang,WANG Jia-lin,et al.2009.Joint inversion of magnetotelluric and seismic data based on ran-dom resistivity and velocity distributions[J].Chinese Journal of Geophysics,52(4):1089—1097(in Chinese).
于鹏,王家林,吴健生,等.2006.地球物理联合反演的研究现状和分析[J].勘探地球物理进展,29(2):87—93.YU Peng,WANG Jia-lin,WU Jian-sheng,et al.2006.Review and discussions on geophysical joint inversion[J].Pro-gress in Exploration Geophysics,29(2):87—93(in Chinese).
周辉,刘财,渠广学.1995.地震-大地电磁数据非线性联合反演方法研究[J].长春地质学院学报,25(2):205—211.ZHOU Hui,LIU Cai,QU Guang-xue.1995.The study of nonlinear joint inversion method for seismic and magnetotelluric sounding data[J].Journal of Changchun University of Science and Technology,25(2):205—211(in Chinese).
周辉,杨宝俊,刘财.1994.地震-大地电磁测深资料综合反演[J].地球物理学报,37(增刊):477—485.ZHOU Hui,YANG Bao-jun,LIU Cai.1994.Combined inversion of seismic and magnetotelluric sounding data[J].Chi-nese Journal of Geophysics,37(Suppl):477—485(in Chinese).
Colombo D,Stefano M D.2007.Geophysical modeling via simultaneous joint inversion of seismic,gravity,and electro-magnetic data:Application to prestack depth imaging[J].The Leading Edge,26(3):326—331.
Haber E,Oldenburg D.2000.A GCV based method for nonlinear ill-posed problems[J].Computational Geosciences,4(1):41—63.
Hansen P C,Leary D P.1993.The use of the L-curve in the regularization of discrete ill-posed problems[J].Society for Induction and Applied Mathematics,14(6):1487—1503.
Hansen P C.1994.Regularization tools:A Matlab package for analysis and solution of discrete ill-posed problems[J].Numerical Algorithm,14(6):1—35.
Heincke B,Hobbs R.2006.Joint inversion of MT,gravity and seismic data applied to sub-basalt imaging[A].In:SEG2006Expanded Abstract.SEG.784—787.
Kumar A,Wan L,Zhdanov M S.2007.Regularization analysis of three-dimensional magnetotelluric inversion[A].In:SEG2007Annual Meeting.San Antonio.482—486.
Stando D K,Rudnicki M.2007.Regularization parameter selection in discrete ill-posed problems:The use of the U-curve[J].International Journal of Applied Mathematics and Computer Science,17(2):157—164.
Wahba G.1997.Practical approximate solutions to linear operator equations when the data are noisy[J].SIAM Journal on Numerical Analysis,14(4):651—667.
Zhdanov M S.2002.Geophysical Inverse Theory and Regularization Problems[M].Netherlands.Elsevier Science.
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