多尺度全变分法及其在时移地震中的应用
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摘要
本文针对时间推移地震本身包含不同时期的两次或者两次以上的勘探反问题,构造了一种快速有效的反演方法——多尺度全变分法.通过引入全变分正则化来代替传统的Tikhonov正则化,针对待反演参数不连续的情况,提高了算法精度.为了提高计算效率,引入了多尺度方法,从而构造了多尺度全变分方法.在数值模拟中,针对一个时间推移地震反演问题对多尺度-Tikhonov正则化法、单一尺度全变分法、以及本文所构造的多尺度全变分法进行了比较.结果表明,本文所提出的多尺度全变分法是一种稳定、快速和精确的反演方法.
In this paper,a multiscale total variation method is applied to parameter identification problems for time-lapse seismic which consists of two or more seismic surveys shooting at different calendars.For the discontinuous parameters,a total variation regularization method is introduced instead of the traditional Tikhonov regularization.Combined with a multiscale method,a multiscale total variation regularization method is put forward to improve computational efficiency and accuracy.In numerical simulation,the multiscale total variation regularization method is compared with both the multiscale-Tikhonov regularization method and a single scale total variation regularization method for time-lapse seismic inversion.The numerical results show that the proposed multiscale total variation method is more stable,faster and more accurate than other methods.
In this paper,a multiscale total variation method is applied to parameter identification problems for time-lapse seismic which consists of two or more seismic surveys shooting at different calendars.For the discontinuous parameters,a total variation regularization method is introduced instead of the traditional Tikhonov regularization.Combined with a multiscale method,a multiscale total variation regularization method is put forward to improve computational efficiency and accuracy.In numerical simulation,the multiscale total variation regularization method is compared with both the multiscale-Tikhonov regularization method and a single scale total variation regularization method for time-lapse seismic inversion.The numerical results show that the proposed multiscale total variation method is more stable,faster and more accurate than other methods.
引文
[1] King G.4D seismic improves reservoir management decisions.Word Oil.1996,217(3) :75～77
[2] King G.4D seismic improves reservoir management decisions.Word Oil.1996,217(4) :79～86
[3] 刁顺,李景叶,唐鼎.基于黑油模型的时移地震正演模拟.勘探地球物理进展,2003,26(1) :19～23 Diao S,Li J Y,Tang D.Time-lapse seismic forward modeling based on black oil model.Progress in Exploration Geophysics(in Chinese),2003,26(1) :19～23
[4] Robertsson J O A,Chapman C H.An efficient method for calculating finite-difference seismograms after model alterations.Geophysics,2000,65:907～918
[5] Robertsson J O A,Ryan-Grigor S,Sayers C M.A finite-difference injection approach to modeling seismic fluid flow monitoring.Geophysics,2000,65:896～906
[6] Abubakar A,van den Berg P M,Fokkema J T.A feasibility study on nonlinear inversion of time-lapse seismic data.70~(th)Ann.Internats SEG.Expanded Abstracts,2001． 1664～1667
[7] Gluck S,Deschizeaux B,Mignot A,et al.Time-lapse impedance inversion of post-stack seismic data.70~(th)Ann.Internat Mtg.,Soc.Expi.Geophys.,Expanded Abstracts,2000． 509～512
[8] Herawati I.The use of time-lapse P-wave impedance inversion to monitor a CO_2 flood at Weyburn field,Saskatchewan[Master's thesis].Colorado:School of Mines,2002
[9] 李来林,牟永光,陈小宏.计算时移波阻抗的新方法.大庆石油地质与开发.2001,20(6) :54～55 Li L L,Mu Y G,Chen X H.A new method for calculating time shift wave impedance.Petroleum Geology & Oil Field Development in Daqing(in Chinese),2001,20(6) :54～55
[10] 李景叶,陈小宏,金龙.时移地震AVO反演在油藏定量解释中的应用.石油学报.2005,26(3) :68～73 Li J J,Chen X H,Jin L.Application of time-lapse seismic AVO inversion to quantitative interpretation of reservoir.Acta Petrolei Sinica(in Chinese),2005,26(3) :68～73
[11] 陈小宏,赵伟,马继涛等.时移地震非线性反演压力与饱和度变化研究.地球物理学进展,2006,21(3) :830～836 Chen X H,Zhao W,Ma J T,et al.Pressure and saturation change nonlinear inversion method using time-lapse seismic data.Progress in Exploration Geophysics(in Chinese),2006,21(3) :830～836
[12] 金龙,陈小宏,李景叶.基于误差准则和循环迭代的时移地震匹配滤波方法.地球物理学报,2005,48(3) :698～703 Jin L,Chen X H,Li J Y.A new method for time-lapse seismic matching filter based on error criteria and cyclic iteration.Chinese J.Geophys.(in Chinese),2005,48(3) :698～703
[13] 金龙,陈小宏,刘其成.基于奇异值分解的时移地震互均衡方法.地球物理学进展,2005,20(2) :294～297 Jin L,Chen X H,Liu Q C.New method for time-lapse seismic matching based on SVD.Progress in Geophysics(in Chinese),2005,20(2) :294～297
[14] Rudin L,Osher S,Fatemi E.Nonlinear total variation based noise removal algorithms.Physica D(in Chinese),1992,60:259～268
[15] Meyer Y.Oscillating patterns in image processing and nonlinear evolution equations.University Lecture Scries.Boston,USA:American Mathematical Society,2001． 11～34
[16] 傅红笋,韩波.二维波动方程速度的正则化-同伦-测井约束反演.地球物理学报,2005,48(6) :1441～1448 Fu H S,Han B.A regularization homotopy method for the inverse problem of 2-D wave equation and well log constraint inversion.Chinese J.Geophys.(in Chinese),2005,48(6) :1441～1448
[17] 任政勇,汤井田.基于局部加密非结构化网格的三维电阻率法有限元数值模拟.地球物理学报,2009,52(10) :2627～2634 Ren Z Y,Tang J T.Finite element modeling of 3D DC resistivity using locally refined unstructured meshes.Chinese.J.Geoghys.(in Chinese),2009,52(10) :2627～2634
[18] 黄超,董良国.可变网格与局部时间步长的交错网格高阶差分弹性波模拟.地球物理学报,2009,52(11) :2870～2878 Huang C,Dong L G.Staggered-grid high-order finite-difference method in elastic wave simulation with variable grids and local time-steps.Chinese J.Geophys.(in Chinese),2009,52(11) :2870～2878
[19] 田小波,吴庆举,曾融生.弹性波场数值模拟的隐式差分多重网格算法.地球物理学报,2004,47(1) :81～87 Tian X B,Wu Q J,Zeng R S.Multi-grid algorithm for numerical modeling of elastic wave field using finite-difference method.Chinese J.Geophys.(in Chinese),2004,47(1) :81～87
[20] Lu J J,Wu X P,Spitzer K.Algebraic multigride method for 3D DC resistvity modelling.Chinese J.Geophys.(in Chinese),2010,53(3) :700～707
[21] 陈勇,韩波.时间推移地震反演的连续模型与算法.地球物理学报,2006,49(4) :1164～1168 Chen Y,Han B.Continuous models and algorithms for timelapse seismic inversion.Chinese J.Geophys.(in Chinese),2006,49(4) :1164～1168
[2] King G.4D seismic improves reservoir management decisions.Word Oil.1996,217(4) :79～86
[3] 刁顺,李景叶,唐鼎.基于黑油模型的时移地震正演模拟.勘探地球物理进展,2003,26(1) :19～23 Diao S,Li J Y,Tang D.Time-lapse seismic forward modeling based on black oil model.Progress in Exploration Geophysics(in Chinese),2003,26(1) :19～23
[4] Robertsson J O A,Chapman C H.An efficient method for calculating finite-difference seismograms after model alterations.Geophysics,2000,65:907～918
[5] Robertsson J O A,Ryan-Grigor S,Sayers C M.A finite-difference injection approach to modeling seismic fluid flow monitoring.Geophysics,2000,65:896～906
[6] Abubakar A,van den Berg P M,Fokkema J T.A feasibility study on nonlinear inversion of time-lapse seismic data.70~(th)Ann.Internats SEG.Expanded Abstracts,2001． 1664～1667
[7] Gluck S,Deschizeaux B,Mignot A,et al.Time-lapse impedance inversion of post-stack seismic data.70~(th)Ann.Internat Mtg.,Soc.Expi.Geophys.,Expanded Abstracts,2000． 509～512
[8] Herawati I.The use of time-lapse P-wave impedance inversion to monitor a CO_2 flood at Weyburn field,Saskatchewan[Master's thesis].Colorado:School of Mines,2002
[9] 李来林,牟永光,陈小宏.计算时移波阻抗的新方法.大庆石油地质与开发.2001,20(6) :54～55 Li L L,Mu Y G,Chen X H.A new method for calculating time shift wave impedance.Petroleum Geology & Oil Field Development in Daqing(in Chinese),2001,20(6) :54～55
[10] 李景叶,陈小宏,金龙.时移地震AVO反演在油藏定量解释中的应用.石油学报.2005,26(3) :68～73 Li J J,Chen X H,Jin L.Application of time-lapse seismic AVO inversion to quantitative interpretation of reservoir.Acta Petrolei Sinica(in Chinese),2005,26(3) :68～73
[11] 陈小宏,赵伟,马继涛等.时移地震非线性反演压力与饱和度变化研究.地球物理学进展,2006,21(3) :830～836 Chen X H,Zhao W,Ma J T,et al.Pressure and saturation change nonlinear inversion method using time-lapse seismic data.Progress in Exploration Geophysics(in Chinese),2006,21(3) :830～836
[12] 金龙,陈小宏,李景叶.基于误差准则和循环迭代的时移地震匹配滤波方法.地球物理学报,2005,48(3) :698～703 Jin L,Chen X H,Li J Y.A new method for time-lapse seismic matching filter based on error criteria and cyclic iteration.Chinese J.Geophys.(in Chinese),2005,48(3) :698～703
[13] 金龙,陈小宏,刘其成.基于奇异值分解的时移地震互均衡方法.地球物理学进展,2005,20(2) :294～297 Jin L,Chen X H,Liu Q C.New method for time-lapse seismic matching based on SVD.Progress in Geophysics(in Chinese),2005,20(2) :294～297
[14] Rudin L,Osher S,Fatemi E.Nonlinear total variation based noise removal algorithms.Physica D(in Chinese),1992,60:259～268
[15] Meyer Y.Oscillating patterns in image processing and nonlinear evolution equations.University Lecture Scries.Boston,USA:American Mathematical Society,2001． 11～34
[16] 傅红笋,韩波.二维波动方程速度的正则化-同伦-测井约束反演.地球物理学报,2005,48(6) :1441～1448 Fu H S,Han B.A regularization homotopy method for the inverse problem of 2-D wave equation and well log constraint inversion.Chinese J.Geophys.(in Chinese),2005,48(6) :1441～1448
[17] 任政勇,汤井田.基于局部加密非结构化网格的三维电阻率法有限元数值模拟.地球物理学报,2009,52(10) :2627～2634 Ren Z Y,Tang J T.Finite element modeling of 3D DC resistivity using locally refined unstructured meshes.Chinese.J.Geoghys.(in Chinese),2009,52(10) :2627～2634
[18] 黄超,董良国.可变网格与局部时间步长的交错网格高阶差分弹性波模拟.地球物理学报,2009,52(11) :2870～2878 Huang C,Dong L G.Staggered-grid high-order finite-difference method in elastic wave simulation with variable grids and local time-steps.Chinese J.Geophys.(in Chinese),2009,52(11) :2870～2878
[19] 田小波,吴庆举,曾融生.弹性波场数值模拟的隐式差分多重网格算法.地球物理学报,2004,47(1) :81～87 Tian X B,Wu Q J,Zeng R S.Multi-grid algorithm for numerical modeling of elastic wave field using finite-difference method.Chinese J.Geophys.(in Chinese),2004,47(1) :81～87
[20] Lu J J,Wu X P,Spitzer K.Algebraic multigride method for 3D DC resistvity modelling.Chinese J.Geophys.(in Chinese),2010,53(3) :700～707
[21] 陈勇,韩波.时间推移地震反演的连续模型与算法.地球物理学报,2006,49(4) :1164～1168 Chen Y,Han B.Continuous models and algorithms for timelapse seismic inversion.Chinese J.Geophys.(in Chinese),2006,49(4) :1164～1168
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