基于优化时空域频散关系的声波方程有限差分最小二乘逆时偏移
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摘要
相比常规逆时偏移,最小二乘逆时偏移(LSRTM)成像结果更趋真实,分辨率更高,其精确成像的关键之一是波动方程的精确、高效求解。为了提高LSRTM计算精度,本文通过优化时空域频散关系求取差分系数,进行有限差分正演模拟,频散分析和数值模拟结果表明采用该算法可提高数值模拟精度;利用混合吸收边界条件压制边界反射,可取得较好吸收效果;采用改进的共轭梯度法计算流程,能减少波动方程正演次数,提高计算效率。模型数据测试及分析表明,本文方法能有效提高LSRTM成像精度,精细刻画构造细节,提高迭代收敛速度。
Compared with conventional reverse time migration methods,least-square reverse time migration(LSRTM)has the advantage of high resolution imaging with more fidelity.One of the key factors in LSRTM is high-resolution scheme and highefficiency wave equation calculation.In order to improve the imaging accuracy in LSRTM,an optimal finite-difference scheme is used to obtain the differential coefficient with a time-space dispersion relation,and the coefficient is used to perform a finitedifference forward modeling.The results of frequency dispersion analysis and numerical simulation have demonstrated that higher accuracy can be obtained based on an optimal time-space-domain dispersion relation.Hybrid absorption boundary conditions are used to decrease edge reflections and achieve better absorption.An improved conjugate gradient algorithm is used to optimize the LSRTM workflow and can reduce the wave equation simulation time.Numerical simulation results verify that the proposed method can not only effectively improve the imaging accuracy and the imaging ability of fine structural details but also accelerate the iteration convergence.
Compared with conventional reverse time migration methods,least-square reverse time migration(LSRTM)has the advantage of high resolution imaging with more fidelity.One of the key factors in LSRTM is high-resolution scheme and highefficiency wave equation calculation.In order to improve the imaging accuracy in LSRTM,an optimal finite-difference scheme is used to obtain the differential coefficient with a time-space dispersion relation,and the coefficient is used to perform a finitedifference forward modeling.The results of frequency dispersion analysis and numerical simulation have demonstrated that higher accuracy can be obtained based on an optimal time-space-domain dispersion relation.Hybrid absorption boundary conditions are used to decrease edge reflections and achieve better absorption.An improved conjugate gradient algorithm is used to optimize the LSRTM workflow and can reduce the wave equation simulation time.Numerical simulation results verify that the proposed method can not only effectively improve the imaging accuracy and the imaging ability of fine structural details but also accelerate the iteration convergence.
引文
[1]Gray H,May P.Kirchhoff migration using eikonal equation traveltimes.Geophysics,1994,59(5):810-817.
[2]Hill R.Gaussian beam migration.Geophysics,1990,55(11):1416-1428.
[3]代福材,黄建平,李振春等.角度域黏声介质高斯束叠前深度偏移方法.石油地球物理勘探,2017,52(2):283-293.Dai Fucai,Huang Jianping,Li Zhenchun et al.Gaussian beam migration for visco-acoustic media.OGP,2017,52(2):283-293.
[4]Claerbout J.Toward a unified theory of reflector mapping.Geophysics,1971,36(3):467-481.
[5]Claerbout J,Doherty S.Downward continuation of moveout corrected seismograms.Geophysics,1972,37(5):741-768.
[6]Gazdag J.Wave equation migration with the phaseshift method.Geophysics,1978,43(7):1342-1351.
[7]Baysal E,Kosloff D,Sherwood J.Reverse time migration.Geophysics,1983,48(11):1514-1524.
[8]McMechan G.Migration by extrapolation of time-dependent boundary values.Geophysical Prospecting,1983,31(3):413-420.
[9]王鹏飞,何兵寿.基于行波分离的三维弹性波矢量场点积互相关成像条件.石油地球物理勘探,2017,52(3):477-483.Wang Pengfei,He Bingshou.Vector field dot product cross-correlation imaging based on 3D elastic wave separation.OGP,2017,52(3):477-483.
[10]Schuster G T.Least-squares crosswell migration.SEGTechnical Program Expanded Abstracts,1993,12:110-113.
[11]Tarantola A.Inversion of seismic reflection data in the acoustic approximation.Geophysics,1984,49(8):1259-1266.
[12]Nemeth T,Wu C,Schuster G T.Least-squares migration of incomplete reflection data.Geophysics,1999,64(1):208-221.
[13]Wang J,Kuehl H,Sacchi M D.High-resolution waveequation AVA imaging:Algorithm and tests with a data set from the Western Canadian Sedimentary Basin.Geophysics,2005,70(5):S91-S99.
[14]Dai W,Wang X,Schuster G T.Least-squares migration of multisource data with a deblurring filter.Geophysics,2011,76(5):R135-R146.
[15]Tang Y,Biondi B.Least-squares migration/inversion of blended data.SEG Technical Program Expanded Abstracts,2009,28:2859-2863.
[16]Yao G,Jakubowicz H.Least-squares reverse-time migration.SEG Technical Program Expanded Abstracts,2012,31:1-5.
[17]Zhang Y,Duan L,Xie Y.A stable and practical implementation of least-squares reverse time migration.SEG Technical Program Expanded Abstracts,2013,32:3716-3720.
[18]Zhang Y,Duan L,Xie Y.A stable and practical implementation of least-squares reverse time migration.Geophysics,2015,80(1):V23-V31.
[19]郭振波,李振春.最小平方逆时偏移真振幅成像.石油地球物理勘探,2014,49(1):113-120.Guo Zhenbo,Li Zhenchun.True-amplitude imaging based on least-squares reverse time migration.OGP,2014,49(1):113-120.
[20]李庆洋,黄建平,李振春等.去均值归一化互相关最小二乘逆时偏移及其应用.地球物理学报,2016,59(8):3006-3015.Li Qingyang,Huang Jianping,Li Zhenchun et al.Mean-residual normalized cross-correlation leastsquares reverse time migration and its application.Chinese Journal of Geophysics,2016,59(8):3006-3015.
[21]郭书娟,马方正,段心标等.最小二乘逆时偏移成像方法的实现与应用研究.石油物探,2015,54(3):301-308.Guo Shujuan,Ma Fangzheng,Duan Xinbiao et al.Research of least-square reverse-time migration imaging method and its application.GPP,2015,54(3):301-308.
[22]刘洋.波动方程时空域有限差分数值解及吸收边界条件研究进展.石油地球物理勘探,2014,49(1):35-46.Liu Yang.Research progress on time-space domain finite-difference numerical solution and absorption boundary conditions of wave equation.OGP,2014,49(1):35-46.
[23]Dablain M A.The application of high-order differencing to the scalar wave equation.Geophysics,1986,51(1):54-66.
[24]Liu Y,Sen M K.A new time-space domain high-order finite-different method for the acoustic wave equation.Journal of Computational Physics,2009,228(23):8779-8806.
[25]Liu Y,Sen M K.Acoustic VTI modeling with a timespace domain dispersion-relation-based finite-difference scheme.Geophysics,2010,75(3):A11-A17.
[26]Robertsson J O A,Blanch J O,Symes W W et al.Galerkin-wavelet modeling of wave propagation:Optimal finite difference stencil design.Mathematical and Computer Modelling,1994,19(1):31-38.
[27]Shan G J.Optimized implicit finite-difference and Fourier finite-difference migration for VTI media.Geophysics,2009,74(6):WCA189-WCA197.
[28]Kosloff D,Pestana R C,Tal-Ezer H.Acoustic and elastic numerical wave simulations by recursive spatial derivative operators.Geophysics,2010,75(6):T167-T174.
[29]Chen J B.An average-derivative optimal scheme for frequency-domain scalar wave equation.Geophysics,2012,77(6):T201-T210.
[30]Zhang J H,Yao Z X.Globally optimized finite-difference extrapolator for strongly VTI media.Geophysics,2012,77(4):T125-T135.
[31]Liu Y.Globally optimal finite-difference schemes based on least squares.Geophysics,2013,78(4):T113-T132.
[32]Claerbout J.Earth Soundings Analysis:Processing Versus Inversion.Blackwell Scientific Publications,Boston,2004,404-411.
[33]Liu Y,Sen M K.A hybrid scheme for absorbing edge reflections in numerical modeling of wave propagation.Geophysics,2010,75(2):A1-A6.
[34]王维红,柯璇,裴江云.完全匹配层吸收边界条件应用研究.地球物理学进展,2013,28(5):2508-2514.Wang Weihong,Ke Xuan,Pei Jiangyun.Application investigation of perfectly matched layer absorbing boundary condition.Progress in Geophysics,2013,28(5):2508-2514.
[35]杨宗青.基于优化时空域有限差分方法的声波最小二乘逆时偏移[学位论文].中国石油大学(北京),2015.Yang Zongqing.Acoustic least-square reverse time migration based on optimal time-space domain finite difference method[D].China University of Petroleum(Beijing),2015.
[2]Hill R.Gaussian beam migration.Geophysics,1990,55(11):1416-1428.
[3]代福材,黄建平,李振春等.角度域黏声介质高斯束叠前深度偏移方法.石油地球物理勘探,2017,52(2):283-293.Dai Fucai,Huang Jianping,Li Zhenchun et al.Gaussian beam migration for visco-acoustic media.OGP,2017,52(2):283-293.
[4]Claerbout J.Toward a unified theory of reflector mapping.Geophysics,1971,36(3):467-481.
[5]Claerbout J,Doherty S.Downward continuation of moveout corrected seismograms.Geophysics,1972,37(5):741-768.
[6]Gazdag J.Wave equation migration with the phaseshift method.Geophysics,1978,43(7):1342-1351.
[7]Baysal E,Kosloff D,Sherwood J.Reverse time migration.Geophysics,1983,48(11):1514-1524.
[8]McMechan G.Migration by extrapolation of time-dependent boundary values.Geophysical Prospecting,1983,31(3):413-420.
[9]王鹏飞,何兵寿.基于行波分离的三维弹性波矢量场点积互相关成像条件.石油地球物理勘探,2017,52(3):477-483.Wang Pengfei,He Bingshou.Vector field dot product cross-correlation imaging based on 3D elastic wave separation.OGP,2017,52(3):477-483.
[10]Schuster G T.Least-squares crosswell migration.SEGTechnical Program Expanded Abstracts,1993,12:110-113.
[11]Tarantola A.Inversion of seismic reflection data in the acoustic approximation.Geophysics,1984,49(8):1259-1266.
[12]Nemeth T,Wu C,Schuster G T.Least-squares migration of incomplete reflection data.Geophysics,1999,64(1):208-221.
[13]Wang J,Kuehl H,Sacchi M D.High-resolution waveequation AVA imaging:Algorithm and tests with a data set from the Western Canadian Sedimentary Basin.Geophysics,2005,70(5):S91-S99.
[14]Dai W,Wang X,Schuster G T.Least-squares migration of multisource data with a deblurring filter.Geophysics,2011,76(5):R135-R146.
[15]Tang Y,Biondi B.Least-squares migration/inversion of blended data.SEG Technical Program Expanded Abstracts,2009,28:2859-2863.
[16]Yao G,Jakubowicz H.Least-squares reverse-time migration.SEG Technical Program Expanded Abstracts,2012,31:1-5.
[17]Zhang Y,Duan L,Xie Y.A stable and practical implementation of least-squares reverse time migration.SEG Technical Program Expanded Abstracts,2013,32:3716-3720.
[18]Zhang Y,Duan L,Xie Y.A stable and practical implementation of least-squares reverse time migration.Geophysics,2015,80(1):V23-V31.
[19]郭振波,李振春.最小平方逆时偏移真振幅成像.石油地球物理勘探,2014,49(1):113-120.Guo Zhenbo,Li Zhenchun.True-amplitude imaging based on least-squares reverse time migration.OGP,2014,49(1):113-120.
[20]李庆洋,黄建平,李振春等.去均值归一化互相关最小二乘逆时偏移及其应用.地球物理学报,2016,59(8):3006-3015.Li Qingyang,Huang Jianping,Li Zhenchun et al.Mean-residual normalized cross-correlation leastsquares reverse time migration and its application.Chinese Journal of Geophysics,2016,59(8):3006-3015.
[21]郭书娟,马方正,段心标等.最小二乘逆时偏移成像方法的实现与应用研究.石油物探,2015,54(3):301-308.Guo Shujuan,Ma Fangzheng,Duan Xinbiao et al.Research of least-square reverse-time migration imaging method and its application.GPP,2015,54(3):301-308.
[22]刘洋.波动方程时空域有限差分数值解及吸收边界条件研究进展.石油地球物理勘探,2014,49(1):35-46.Liu Yang.Research progress on time-space domain finite-difference numerical solution and absorption boundary conditions of wave equation.OGP,2014,49(1):35-46.
[23]Dablain M A.The application of high-order differencing to the scalar wave equation.Geophysics,1986,51(1):54-66.
[24]Liu Y,Sen M K.A new time-space domain high-order finite-different method for the acoustic wave equation.Journal of Computational Physics,2009,228(23):8779-8806.
[25]Liu Y,Sen M K.Acoustic VTI modeling with a timespace domain dispersion-relation-based finite-difference scheme.Geophysics,2010,75(3):A11-A17.
[26]Robertsson J O A,Blanch J O,Symes W W et al.Galerkin-wavelet modeling of wave propagation:Optimal finite difference stencil design.Mathematical and Computer Modelling,1994,19(1):31-38.
[27]Shan G J.Optimized implicit finite-difference and Fourier finite-difference migration for VTI media.Geophysics,2009,74(6):WCA189-WCA197.
[28]Kosloff D,Pestana R C,Tal-Ezer H.Acoustic and elastic numerical wave simulations by recursive spatial derivative operators.Geophysics,2010,75(6):T167-T174.
[29]Chen J B.An average-derivative optimal scheme for frequency-domain scalar wave equation.Geophysics,2012,77(6):T201-T210.
[30]Zhang J H,Yao Z X.Globally optimized finite-difference extrapolator for strongly VTI media.Geophysics,2012,77(4):T125-T135.
[31]Liu Y.Globally optimal finite-difference schemes based on least squares.Geophysics,2013,78(4):T113-T132.
[32]Claerbout J.Earth Soundings Analysis:Processing Versus Inversion.Blackwell Scientific Publications,Boston,2004,404-411.
[33]Liu Y,Sen M K.A hybrid scheme for absorbing edge reflections in numerical modeling of wave propagation.Geophysics,2010,75(2):A1-A6.
[34]王维红,柯璇,裴江云.完全匹配层吸收边界条件应用研究.地球物理学进展,2013,28(5):2508-2514.Wang Weihong,Ke Xuan,Pei Jiangyun.Application investigation of perfectly matched layer absorbing boundary condition.Progress in Geophysics,2013,28(5):2508-2514.
[35]杨宗青.基于优化时空域有限差分方法的声波最小二乘逆时偏移[学位论文].中国石油大学(北京),2015.Yang Zongqing.Acoustic least-square reverse time migration based on optimal time-space domain finite difference method[D].China University of Petroleum(Beijing),2015.