一般TI介质中多震相旅行时层析成像——以井间成像为例
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摘要
传统的各向异性介质中的正、反演研究大多基于弱各向异性假设下的VTI介质,且主要是有关初至波的射线追踪和相应的旅行时反演。然而,随着勘探精度要求的不断提高,一般普适的(含强)TI介质中的多震相射线正、反演方法,则成为急需解决的问题。鉴于此,本文将基于各向同性介质多震相分区多步最短路径射线追踪算法推广到一般各向异性TI介质,结合相、群速度导数的一阶旅行时扰动方程,采用共轭梯度求解带约束的阻尼最小二乘问题,进而提出了一种利用多震相旅行时进行一般TI介质弹性参数反演的方法。井间地震数值实验结果表明,多震相旅行时联合反演可有效提高成像分辨率,验证了方法的有效性和正确性。
Conventional ray tracing and traveltime tomography are almost based on a weak anisotropic media assumption,and only direct arrivals and their corresponding inversion are considered in a simple VTI media.With increasing requirements for high accurate exploration,it is instructive to solve the general(including strong)anisotropic TI media for both multi-phase ray tracing and inversion.For this reason,we put forward in this paper an algorithm for multiple arrival tracking in the general anisotropic media,which is incorporated with the first-order traveltime perturbation equation for phase and group velocity derivatives and an inversion solver(damping minimum norm,and constrained least square problem with the conjugate gradient approach)to form a traveltime inversion method using multi-phase arrival times for the general anisotropic media.Finally we show an example for crosshole traveltime tomography to verify the efficiency and accuracy of the proposed inversion method.Tomographic results indicate that the proposed algorithm can improve the imaging resolution with later arrival time information included in the elastic parameter reconstruction.
Conventional ray tracing and traveltime tomography are almost based on a weak anisotropic media assumption,and only direct arrivals and their corresponding inversion are considered in a simple VTI media.With increasing requirements for high accurate exploration,it is instructive to solve the general(including strong)anisotropic TI media for both multi-phase ray tracing and inversion.For this reason,we put forward in this paper an algorithm for multiple arrival tracking in the general anisotropic media,which is incorporated with the first-order traveltime perturbation equation for phase and group velocity derivatives and an inversion solver(damping minimum norm,and constrained least square problem with the conjugate gradient approach)to form a traveltime inversion method using multi-phase arrival times for the general anisotropic media.Finally we show an example for crosshole traveltime tomography to verify the efficiency and accuracy of the proposed inversion method.Tomographic results indicate that the proposed algorithm can improve the imaging resolution with later arrival time information included in the elastic parameter reconstruction.
引文
[1]Crampin S.A review of wave motion in anisotropic and cracked elastic-media.Wave Motion,1981,3(81):343-391.
[2]Crampin S.Effective anisotropic elastic constants for wave-propagation through cracked solids.Geophysical Journal of the Royal Astronomical Society,1984,76(1):135-145.
[3]Helbig K.Systematic classifcation of layeredinduced transverse isotropy.Geophysical Prospecting,1981,29(4):550-577.
[4]Thomsen L.Weak elastic anisotropy.Geophysics,1986,51(10):1954-1966.
[5]CˇervenV.Seismic rays and ray intensities in inhomogeneous anisotropic media.Geophysical Journal of the Royal Astronomical Society,1972,29(1):1-13.
[6]Crampin S and Yedlin M.Shear-wave singularities of wave propagation in anisotropic media.Journal of Geophysics,1981,49(1):43-46.
[7]Helbig K.Foundations of Anisotropy for Exploration Seismics.Pergamon Press,Oxford,1994.
[8]CˇervenV.Seismic Ray Theory.Cambridge University Press,England,2001.
[9]CˇervenV and Jech J.Linearized solutions of kinematic problems of seismic body waves in inhomogeneous slightly anisotropic media.Journal of Geophysics Zeitschrift Fur Geophysik,1982,51(2):96-104.
[10]Hirahara K and Yuzo I.Travel-time inversion for three-dimensional P-wave velocity anisotropy.Journal of Physics of the Earth,1984,32(3):197-218.
[11]Jech J.Three-dimensional inverse problem for inhomogeneous transversely isotropic media.Studia Geophysica Et Geodaetica,1988,32(2):136-143.
[12]Jech J and Pencˇik I.First-order perturbation method for anisotropic media.Geophysical Journal International,1989,99(2):369-376.
[13]Chapman C H and Pratt R G.Traveltime tomography in anisotropic media,Ⅰ:Theory.Geophysical Journal International,1992,109(1):1-19.
[14]Pratt R G and Chapman C H.Traveltime tomography in anisotropic media,Ⅱ:Applications.Geophysical Journal International,1992,109(1):20-37.
[15]Grechka V,Pech A and Tsvankin I.P-wave stackingvelocity tomography for VTI media.Geophysical Prospecting,2002,50(2):151-168.
[16]Grechka V,Pech A and Tsvankin I.Multicomponent stacking-velocity tomography for transversely isotro-pic media.Geophysics,2002,67(5):1564-1574.
[17]Grechka V,Pech A and Tsvankin I.Quartic reflection moveout in a weakly anisotropic dipping layer.Geophysics,2006,71(1):D1-D13.
[18]Pech A,Tsvankin I and Grechka V.Quartic moveout coeffcient:3Ddescription and application to tilted TI media.Geophysics,2003,68(5):1600-1610.
[19]Behera H and Tsvankin I.Migration velocity analysis and imaging for tilted TI medium.SEG Technical Program Expanded Abstracts,2007,26:129-133.
[20]何樵登,陶春辉.用遗传算法反演裂隙各向异性介质.石油物探,1995,34(3):46-50.He Qiaodeng,Tao Chunhui.Inversing fractured anisotropic media through a genetic algorithm.GPP,1995,34(3):46-50.
[21]张文生,何樵登.利用VSP和跨孔走时反演横向各向同性介质中的弹性常数.石油地球物理勘探,1997,32(3):345-356.Zhang Wensheng,He Qiaodeng.Deriving the elastic constants of tranversal isotropic medium from VSP and crosshole travel times.OGP,1997,32(3):345-356.
[22]杨顶辉,滕吉文,张中杰.各向异性动力学方程反演新算法.地震学报,1997,19(4):376-382.Yang Dinghui,Teng Jiwen and Zhang Zhongjie.A new inversion algorithm based on the dynamic equations in anisotropic medium.Acta Seismologica Sinica,1997,19(4):376-382.
[23]张秉铭,张中杰.一种新的地层弹性参数直接反演方法.地震学报,2000,22(6):654-660.Zhang Bingming,Zhang Zhongjie.A new way of directly elastic parameters inversion.Acta Seismologica Sinica,2000,22(6):654-660.
[24]傅旦丹,何樵登,刘一峰等.一种新的全局最优化反演计算方法.石油地球物理勘探,2000,35(4):536-542.Fu Dandan,He Qiaodeng,Liu Yifeng et al.A novel global-optimized inversion method.OGP,2000,35(4):536-542.
[25]阮爱国,王椿镛.上地幔各向异性的反演方法.西北地震学报,2002,24(2):104-112.Ruan Aiguo,Wang Chunyong.The inversion methods of the upper mantle anisotropy.Northwestern Seismological Journal,2002,24(2):104-112.
[26]卢明辉,唐建侯,杨慧珠等.正交各向异性介质P波走时分析及Thomsen参数反演.地球物理学报,2005,48(5):1167-1171.Lu Minghui,Tang Jianhou,Yang Huizhu et al.Pwave traveltime analysis and Thomsen parameters inversion in orthorhombic media.Chinese Journal of Geophysics,2005,48(5):1167-1171.
[27]郭飚.非均匀各向异性介质的地震P波旅行时层析成像研究[学位论文].北京:中国地震局地震研究所,2010.Guo Biao.Seismic P-wave Travel-time Tomography in Heterogeneous and Anisotropic Media[D].Institute of Seismology,China Earthquake Administration,Beijing,2010.
[28]Zhou B and Greenhalgh S A.On the computation of elastic wave group velocity for a general anisotropic medium.Journal of Geophysics and Engineering,2004,1(3):205-215.
[29]Zhou B and Greenhalgh S A.Raypath and traveltime computations for 2Dtransversely isotropic media with dipping symmetry axes.Exploration Geophysics,2006,37(2):150-159.
[30]Zhou B and Greenhalgh S A.Nonlinear traveltime inversion for 3Dseismic tomography in strongly anisotropic media.Geophysical Journal International,2008,172(1):383-394.
[31]Bai C Y.Three-dimensional Seismic Kinematic Inversion with Application to Reconstruction of the Velocity Structure of Rabaul Volcano[D].University of Adelaide,Australia,2004.
[32]Bai C Y,Tang X P and Zhao R.2-D/3-D multiply transmitted,converted and reflected arrivals in complex layered media with the modified shortest path method.Geophysical Journal International,2009,179(1):201-214.
[33]Bai C Y,Huang G J and Zhao R.2-D/3-D irregular shortest-path raytracing for multiple arrivals and its applications.Geophysical Journal International,2010,183(3):1596-1612.
[34]黄国娇,白超英.二维复杂层状介质中地震多波旅行时联合反演成像.地球物理学报,2010,53(12):2972-2981.Huang Guojiao,Bai Chaoying.Simultaneous inversion with multiple traveltimes within 2-D complex layered media.Chinese Journal of Geophysics,2010,53(12):2972-2981.
[35]白超英,黄国娇,李忠生.三维复杂层状介质中多震相旅行时联合反演成像.地球物理学报,2011,54(1):182-192.Bai Chaoying,Huang Guojiao,Li Zhongsheng.Simultaneous inversion combining multiple-phase travel times within 3D complex layered media.Chinese Journal of Geophysics,2011,54(1):182-192.
[36]Zhou B and Greenhalgh S A.Analytic expressions for the velocity sensitivity to the elastic moduli for the most general anisotropic media.Geophysical Prospecting,2005,53(4):619-641.
[37]Daley P F and Hron F.Reflection and transmission coefficients for transversely isotropic media.Bulletin of Seismological Society of America,1977,67(8):661-675.
[38]Bai C Y and Greenhalgh S.3-D non-linear travel time tomography:Imaging high contrast velocity anomalies.Pure and Applied Geophysics,2005,162(11):2029-2049.
[2]Crampin S.Effective anisotropic elastic constants for wave-propagation through cracked solids.Geophysical Journal of the Royal Astronomical Society,1984,76(1):135-145.
[3]Helbig K.Systematic classifcation of layeredinduced transverse isotropy.Geophysical Prospecting,1981,29(4):550-577.
[4]Thomsen L.Weak elastic anisotropy.Geophysics,1986,51(10):1954-1966.
[5]CˇervenV.Seismic rays and ray intensities in inhomogeneous anisotropic media.Geophysical Journal of the Royal Astronomical Society,1972,29(1):1-13.
[6]Crampin S and Yedlin M.Shear-wave singularities of wave propagation in anisotropic media.Journal of Geophysics,1981,49(1):43-46.
[7]Helbig K.Foundations of Anisotropy for Exploration Seismics.Pergamon Press,Oxford,1994.
[8]CˇervenV.Seismic Ray Theory.Cambridge University Press,England,2001.
[9]CˇervenV and Jech J.Linearized solutions of kinematic problems of seismic body waves in inhomogeneous slightly anisotropic media.Journal of Geophysics Zeitschrift Fur Geophysik,1982,51(2):96-104.
[10]Hirahara K and Yuzo I.Travel-time inversion for three-dimensional P-wave velocity anisotropy.Journal of Physics of the Earth,1984,32(3):197-218.
[11]Jech J.Three-dimensional inverse problem for inhomogeneous transversely isotropic media.Studia Geophysica Et Geodaetica,1988,32(2):136-143.
[12]Jech J and Pencˇik I.First-order perturbation method for anisotropic media.Geophysical Journal International,1989,99(2):369-376.
[13]Chapman C H and Pratt R G.Traveltime tomography in anisotropic media,Ⅰ:Theory.Geophysical Journal International,1992,109(1):1-19.
[14]Pratt R G and Chapman C H.Traveltime tomography in anisotropic media,Ⅱ:Applications.Geophysical Journal International,1992,109(1):20-37.
[15]Grechka V,Pech A and Tsvankin I.P-wave stackingvelocity tomography for VTI media.Geophysical Prospecting,2002,50(2):151-168.
[16]Grechka V,Pech A and Tsvankin I.Multicomponent stacking-velocity tomography for transversely isotro-pic media.Geophysics,2002,67(5):1564-1574.
[17]Grechka V,Pech A and Tsvankin I.Quartic reflection moveout in a weakly anisotropic dipping layer.Geophysics,2006,71(1):D1-D13.
[18]Pech A,Tsvankin I and Grechka V.Quartic moveout coeffcient:3Ddescription and application to tilted TI media.Geophysics,2003,68(5):1600-1610.
[19]Behera H and Tsvankin I.Migration velocity analysis and imaging for tilted TI medium.SEG Technical Program Expanded Abstracts,2007,26:129-133.
[20]何樵登,陶春辉.用遗传算法反演裂隙各向异性介质.石油物探,1995,34(3):46-50.He Qiaodeng,Tao Chunhui.Inversing fractured anisotropic media through a genetic algorithm.GPP,1995,34(3):46-50.
[21]张文生,何樵登.利用VSP和跨孔走时反演横向各向同性介质中的弹性常数.石油地球物理勘探,1997,32(3):345-356.Zhang Wensheng,He Qiaodeng.Deriving the elastic constants of tranversal isotropic medium from VSP and crosshole travel times.OGP,1997,32(3):345-356.
[22]杨顶辉,滕吉文,张中杰.各向异性动力学方程反演新算法.地震学报,1997,19(4):376-382.Yang Dinghui,Teng Jiwen and Zhang Zhongjie.A new inversion algorithm based on the dynamic equations in anisotropic medium.Acta Seismologica Sinica,1997,19(4):376-382.
[23]张秉铭,张中杰.一种新的地层弹性参数直接反演方法.地震学报,2000,22(6):654-660.Zhang Bingming,Zhang Zhongjie.A new way of directly elastic parameters inversion.Acta Seismologica Sinica,2000,22(6):654-660.
[24]傅旦丹,何樵登,刘一峰等.一种新的全局最优化反演计算方法.石油地球物理勘探,2000,35(4):536-542.Fu Dandan,He Qiaodeng,Liu Yifeng et al.A novel global-optimized inversion method.OGP,2000,35(4):536-542.
[25]阮爱国,王椿镛.上地幔各向异性的反演方法.西北地震学报,2002,24(2):104-112.Ruan Aiguo,Wang Chunyong.The inversion methods of the upper mantle anisotropy.Northwestern Seismological Journal,2002,24(2):104-112.
[26]卢明辉,唐建侯,杨慧珠等.正交各向异性介质P波走时分析及Thomsen参数反演.地球物理学报,2005,48(5):1167-1171.Lu Minghui,Tang Jianhou,Yang Huizhu et al.Pwave traveltime analysis and Thomsen parameters inversion in orthorhombic media.Chinese Journal of Geophysics,2005,48(5):1167-1171.
[27]郭飚.非均匀各向异性介质的地震P波旅行时层析成像研究[学位论文].北京:中国地震局地震研究所,2010.Guo Biao.Seismic P-wave Travel-time Tomography in Heterogeneous and Anisotropic Media[D].Institute of Seismology,China Earthquake Administration,Beijing,2010.
[28]Zhou B and Greenhalgh S A.On the computation of elastic wave group velocity for a general anisotropic medium.Journal of Geophysics and Engineering,2004,1(3):205-215.
[29]Zhou B and Greenhalgh S A.Raypath and traveltime computations for 2Dtransversely isotropic media with dipping symmetry axes.Exploration Geophysics,2006,37(2):150-159.
[30]Zhou B and Greenhalgh S A.Nonlinear traveltime inversion for 3Dseismic tomography in strongly anisotropic media.Geophysical Journal International,2008,172(1):383-394.
[31]Bai C Y.Three-dimensional Seismic Kinematic Inversion with Application to Reconstruction of the Velocity Structure of Rabaul Volcano[D].University of Adelaide,Australia,2004.
[32]Bai C Y,Tang X P and Zhao R.2-D/3-D multiply transmitted,converted and reflected arrivals in complex layered media with the modified shortest path method.Geophysical Journal International,2009,179(1):201-214.
[33]Bai C Y,Huang G J and Zhao R.2-D/3-D irregular shortest-path raytracing for multiple arrivals and its applications.Geophysical Journal International,2010,183(3):1596-1612.
[34]黄国娇,白超英.二维复杂层状介质中地震多波旅行时联合反演成像.地球物理学报,2010,53(12):2972-2981.Huang Guojiao,Bai Chaoying.Simultaneous inversion with multiple traveltimes within 2-D complex layered media.Chinese Journal of Geophysics,2010,53(12):2972-2981.
[35]白超英,黄国娇,李忠生.三维复杂层状介质中多震相旅行时联合反演成像.地球物理学报,2011,54(1):182-192.Bai Chaoying,Huang Guojiao,Li Zhongsheng.Simultaneous inversion combining multiple-phase travel times within 3D complex layered media.Chinese Journal of Geophysics,2011,54(1):182-192.
[36]Zhou B and Greenhalgh S A.Analytic expressions for the velocity sensitivity to the elastic moduli for the most general anisotropic media.Geophysical Prospecting,2005,53(4):619-641.
[37]Daley P F and Hron F.Reflection and transmission coefficients for transversely isotropic media.Bulletin of Seismological Society of America,1977,67(8):661-675.
[38]Bai C Y and Greenhalgh S.3-D non-linear travel time tomography:Imaging high contrast velocity anomalies.Pure and Applied Geophysics,2005,162(11):2029-2049.