叠后边界保持块约束共轭梯度波阻抗反演
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摘要
为提高地震波阻抗反演的分辨率及运算效率,提出一种边界保持块约束的叠后波阻抗反演方法。首先,根据反射系数的稀疏特性,并利用正则化技术,避免反演过程的平滑效应构造出波阻抗块约束反演的目标函数;其次,推导出用对数波阻抗差值代替反射系数的边界保持的块约束反演系统方程;再次,推导出对应反演系统方程的共轭梯度算法和关键的向量计算公式。结果表明:反演波阻抗呈明显分块特征,上下岩层界线明显,分辨率高,说明反演方法可靠,该方法具有边界保持、分辨率高、收敛速度快、精度高的特点,实现简单、高效。
To improve the resolution of seismic impedance inversion and computational efficiency,a post-stack seismic inversion method based edge preserving blocky constrain was developed.First,according to the sparse characteristic of reflection coefficient,and using regularization technique,the objective function of seismic inversion was constructed to avoid smoothing effect;Secondly,equations of inversion system were deduced based on edge preserving blocky constrain and using the difference of logarithmic impedance in stabilizing the reflection coefficient;Additionally,the conjugate gradient algorithm was deduced,and the key vectors formulas were also derived.The results show that inverted seismic impedance has significant block feature,and the rock bottom line is clear,which indicates that the inversion method is reliable.The features of inversion method are edge preserving,high resolution,fast convergence,and high accuracy,simplicity and efficiency.
To improve the resolution of seismic impedance inversion and computational efficiency,a post-stack seismic inversion method based edge preserving blocky constrain was developed.First,according to the sparse characteristic of reflection coefficient,and using regularization technique,the objective function of seismic inversion was constructed to avoid smoothing effect;Secondly,equations of inversion system were deduced based on edge preserving blocky constrain and using the difference of logarithmic impedance in stabilizing the reflection coefficient;Additionally,the conjugate gradient algorithm was deduced,and the key vectors formulas were also derived.The results show that inverted seismic impedance has significant block feature,and the rock bottom line is clear,which indicates that the inversion method is reliable.The features of inversion method are edge preserving,high resolution,fast convergence,and high accuracy,simplicity and efficiency.
引文
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[16]BARONE P.Fast deconvolution by a two-step method[J].SIAMJournal of Sci Comp,1999,21(3):883 899.
[17]张宏兵,杨长春.正则参数控制下的波阻抗约束反演[J].地球物理学报,2003,46(6):827 834.ZHANG Hong-bing,YANG Chang-chun.A constrainedimpedance inversion method controlled by regularizedparameters[J].Chinese Jouranal of Geophysics,2003,46(6):827 834.
[18]张宏兵,杨长春,尚作萍,杨青峰.基于软约束模式的波阻抗反演[J].地球物理学进展,2006,21(3):837 844.ZHANG Hong-bing,YANG Chang-chun,SHANG Zuo-ping,YANG Qing-feng.Impedance inversion with soft constrainedmode[J].Progress in Geophysics,2006,21(3):837 844.
[19]张宏兵,尚作萍,杨长春,段秋梁.波阻抗反演正则参数估计[J].地球物理学报,2005,48(1):181 188.ZHANG Hong-bing,SHANG Zuo-ping,YANG Chang-chun,DUAN Qiu-liang.Estimation of regular parameters for theimpedance inversion[J].Chinese Journal of Geophysics,2005,48(1):181 188.
[20]张罗磊,于鹏,王家林.光滑模型与尖锐边界结合的MT二维反演方法[J].地球物理学报,2009,52(6):1625 1632.ZHANG Luo-lei,YU Peng,WANG Jia-lin.Smoothest modeland sharp boundary based two-dimensional magnetotelluricinversion[J].Chinese Journal of Geophysics,2009,52(6):1625 1632.
[21]张赛民.基于边界保持块约束叠后波阻抗及叠前AVA三参数同步反演研究[D].长沙:中南大学地球科学与信息物理学院,2011:71 72.ZHANG Sai-min.Research of post-stack impedance inversionand AVA three-term simultaneous inversion based on edgepreserving blocky constrain[D].Changsha:School ofGeosciences and Info-Physics,Central South University,2011:71 72.
[22]张赛民,周竹生,刘海飞.用改进的共轭梯度算法解波阻抗反演问题[J].物探化探计算技术,2009,31(4):338 343.ZHANG Sai-min,ZHOU Zhu-sheng,LIU Hai-fei.Acousticimpedance inversion using improved conjugate gradientalgorithm[J].Computing Technology for Geophysical andGeochemical Exploration,2009,31(4):338 343.
[2]单敬福,纪友亮,金利红,王峰,葛黛薇,陈欣欣.塔南—南贝尔凹陷沉南屯组沉积相特征[J].中南大学学报:自然科学版,2013,44(1):241 250.SHAN Jing-fu,JI You-liang,JIN Li-hong,WANG Feng,GEDai-wei,CHEN Xin-xin.Sedimentary facies characteristic ofNantun Formation in Tarnan—Southbell depression[J].Journalof Central South University:Science and Technology,2013,44(1):241 250.
[3]刘立峰,孙赞东,杨海军,韩剑发,敬兵,赵海涛.缝洞型碳酸盐岩储层地震综合预测——以塔里木盆地中古21井区为例[J].中南大学学报:自然科学版,2011,42(6):1731 1737.LIU Li-feng,SUN Zan-dong,YANG Hai-jun,HAN Jian-fa,JIANG Bing,ZHAO Hai-tao.Seismic integrative prediction offracture-cavity carbonate reservoir:Taking ZG21 well area inTarim Basin as an example[J].Journal of Central SouthUniversity:Science and Technology,2011,42(6):1731 1737.
[4]郑旭刚.波阻抗反演及相控砂体雕刻技术在滨5断块储层预测中的应用[J].石油天然气学报,2012,34(9):200 202.ZHENG Xu-gang.The application of wave impedance inversionand phase control sand body carving in reservoir forecasting offault bolck Bin 5[J].Journal of Oil and Gas Technology,2012,34(9):200 202.
[5]王家映.地球物理反演理论[M].北京:高等教育出版社,2002:1 2.WANG Jia-yin.Geophysical inversion theory[M].Beijing:Higher Education Press,2002:1 2.
[6]李宏兵.具有剔除噪音功能的多道广义线性反演[J].石油物探,1996,35(4):11 17.LI Hong-bing.Generalized multi-traces linear inversion with the removal of noise[J].Geophysical Prospecting for Petroleum,1996,35(4):11 17.
[7]周竹生,何继善,陆江南.地球物理反问题中的随机反演理论[J].物探化探计算技术,1997,19(4):289 297.ZHOU Zhu-sheng,HE Ji-shan,LU Jiang-nan.Stochasticinversion theory of geophysical inverse problems[J].ComputingTechnology for Geophysical and Geochemical Exploration,1997,19(4):289 297.
[8]卢占武,韩立国.波阻抗反演技术研究进展[J].世界地质,2002,21(4):372 377.LU Zhan-wu,HAN Li-guo.Aacoustic impedance inversionprogress[J].Global Geology,2002,21(4):372 377.
[9]邸海滨,郭玉倩,刘喜武.基于稀疏约束贝叶斯估计的相对波阻抗反演[J].石油物探,2011,50(2):124 128.DI Hai-bin,GUO Yu-qian,LIU Xi-wu.Relative acousticimpedance inversion based on Cauchy sparsenessconstraint Bayesian estimation[J].Geophysical Prospecting forPetroleum,2011,50(2):124 128.
[10]马劲风,王学军.测井资料约束的波阻抗反演中的多解性问题[J].石油与天然气地质,1999,20(1):7 10.MA Jin-feng,WANG Xue-jun.Multiple roots in well-restrictedimpedance inversion[J].Oil&Gas Geology,1999,20(1):7 10.
[11]马劲风,王学军,赵圣亮,赵建勋.波阻抗初值选择与地震道反演的多解性[J].石油地球物理勘探,1999,34(3):332 340.MA Jin-feng,WANG Xue-jun,ZHAO Sheng-liang,ZHAOJian-xun.Choice of initial wave impedance value and themultisolution of seismic trace inversion[J].Oil GeophysicalProspecting,1999,34(3):332 340.
[12]CHARBONNIER P,FRAUD L B,AUBERT G,BARLAUD M.Deterministic edge-preserving regularization in computedimaging[J].IEEE Transactions on Image Processing,1997,6(2):298 311.
[13]THéVENAZ P,SAGE D,UNSER M.Bi-exponentialedge-preserving smoother[J].IEEE Trans Image Process,2012,21(9):3924 3936.
[14]MOLINA R,NUNEZ J,CORTIJO F J,MATEOS J.Imagerestoration in astronomy:A Bayesian perspective[J].IEEESignal Proc Mag,2001,18(2):11 29.
[15]YANG Jun-feng,YIN Wo-tao,ZHANG Yin.A fast algorithm foredge-preserving variational multichannel image restoration[J].Siam J Imaging Sciences,2009,2(2):569 592.
[16]BARONE P.Fast deconvolution by a two-step method[J].SIAMJournal of Sci Comp,1999,21(3):883 899.
[17]张宏兵,杨长春.正则参数控制下的波阻抗约束反演[J].地球物理学报,2003,46(6):827 834.ZHANG Hong-bing,YANG Chang-chun.A constrainedimpedance inversion method controlled by regularizedparameters[J].Chinese Jouranal of Geophysics,2003,46(6):827 834.
[18]张宏兵,杨长春,尚作萍,杨青峰.基于软约束模式的波阻抗反演[J].地球物理学进展,2006,21(3):837 844.ZHANG Hong-bing,YANG Chang-chun,SHANG Zuo-ping,YANG Qing-feng.Impedance inversion with soft constrainedmode[J].Progress in Geophysics,2006,21(3):837 844.
[19]张宏兵,尚作萍,杨长春,段秋梁.波阻抗反演正则参数估计[J].地球物理学报,2005,48(1):181 188.ZHANG Hong-bing,SHANG Zuo-ping,YANG Chang-chun,DUAN Qiu-liang.Estimation of regular parameters for theimpedance inversion[J].Chinese Journal of Geophysics,2005,48(1):181 188.
[20]张罗磊,于鹏,王家林.光滑模型与尖锐边界结合的MT二维反演方法[J].地球物理学报,2009,52(6):1625 1632.ZHANG Luo-lei,YU Peng,WANG Jia-lin.Smoothest modeland sharp boundary based two-dimensional magnetotelluricinversion[J].Chinese Journal of Geophysics,2009,52(6):1625 1632.
[21]张赛民.基于边界保持块约束叠后波阻抗及叠前AVA三参数同步反演研究[D].长沙:中南大学地球科学与信息物理学院,2011:71 72.ZHANG Sai-min.Research of post-stack impedance inversionand AVA three-term simultaneous inversion based on edgepreserving blocky constrain[D].Changsha:School ofGeosciences and Info-Physics,Central South University,2011:71 72.
[22]张赛民,周竹生,刘海飞.用改进的共轭梯度算法解波阻抗反演问题[J].物探化探计算技术,2009,31(4):338 343.ZHANG Sai-min,ZHOU Zhu-sheng,LIU Hai-fei.Acousticimpedance inversion using improved conjugate gradientalgorithm[J].Computing Technology for Geophysical andGeochemical Exploration,2009,31(4):338 343.
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