正交各向异性介质中qP波入射的二阶近似反射系数与透射系数
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摘要
地震波在各向异性介质中以一个准P波(qP)和两个准S波(qS1和qS2)的形式传播.研究三种波的相速度、群速度以及偏振方向等传播性质能够为各向异性介质中的正反演问题提供有效支撑.具有比横向各向同性(TI)介质更一般对称性的正交各向异性介质通常需要9个独立参数对其进行描述,这使得对传播特征的计算更为复杂.当两个准S波速度相近时具有耦合性,从而令慢度的计算产生奇异性.因此,奇异点(慢度面的鞍点和交叉点)附近的反射与透射(R/T)系数的求解不稳定,会导致波场振幅不准确.本文首次通过结合耦合S波射线理论和基于迭代的各向异性相速度与偏振矢量的高阶近似解,得到了适用于正交各向异性介质以qP波入射所产生的二阶R/T系数的计算方法.与基于一阶近似的结果相比,基于二阶近似的方法提高了qP波R/T系数的精度,能得到一阶耦合近似无法表达的准确的qP-qS转换波的R/T系数解,且方法适用于较强的各向异性介质.
Seismic wave propagation in the anisotropic media with one quasi-P wave(qP)and two quasi-S waves(qS1 and qS2).Studying of the propagation properties,such as phase velocity,group velocity and polarization,provides effective support for seismic forward modeling and inverse problems in anisotropic media.To describe the orthorhombic anisotropic media with more general symmetry than transverse isotropic(TI)media usually requires 9 independent parameters,which makes the calculation of propagation properties very complicated.The two quasi-S waves with similar velocities are coupled,causing the singularities in slowness calculation.As a result,thereflection and transmission(R/T)coefficients are unstable in the neighborhood of singularities(saddle points and cross points on slowness surface),which makes the wavefield amplitude calculation inaccurate.In this paper we propose a method to obtain the second-order R/T coefficients generated by incident qP wave in orthorhombic media by using coupled ray theory and high-order iterative solution of phase velocity and polarization vector in anisotropic media.Compared with the first-order results,the proposed method improves the accuracy of qP wave R/T coefficients,and obtains accurate qP-qS converted wave R/T coefficients which is not available in the first-order coupling approximation method.Furthermore,our method is applicable to strong anisotropic media.
Seismic wave propagation in the anisotropic media with one quasi-P wave(qP)and two quasi-S waves(qS1 and qS2).Studying of the propagation properties,such as phase velocity,group velocity and polarization,provides effective support for seismic forward modeling and inverse problems in anisotropic media.To describe the orthorhombic anisotropic media with more general symmetry than transverse isotropic(TI)media usually requires 9 independent parameters,which makes the calculation of propagation properties very complicated.The two quasi-S waves with similar velocities are coupled,causing the singularities in slowness calculation.As a result,thereflection and transmission(R/T)coefficients are unstable in the neighborhood of singularities(saddle points and cross points on slowness surface),which makes the wavefield amplitude calculation inaccurate.In this paper we propose a method to obtain the second-order R/T coefficients generated by incident qP wave in orthorhombic media by using coupled ray theory and high-order iterative solution of phase velocity and polarization vector in anisotropic media.Compared with the first-order results,the proposed method improves the accuracy of qP wave R/T coefficients,and obtains accurate qP-qS converted wave R/T coefficients which is not available in the first-order coupling approximation method.Furthermore,our method is applicable to strong anisotropic media.
引文
Cerven.2001.Seismic Ray Theory.Cambridge:Cambridge University Press.
Chapman C H.1994.Reflection/transmission coefficient reciprocities in anisotropic media.Geophysical Journal International,116(2):498-501,doi:10.1111/j.1365-246X.1994.tb01811.x.
Coates R T,Chapman C H.1990.Quasi-shear wave coupling in weakly anisotropic 3-D media.Geophysical Journal International,103(2):301-320,doi:10.1111/j.1365-246X.1990.tb01773.x.
Daley P F,Hron F.1977.Reflection and transmission coefficients for transversely isotropic media.Bulletin of the Seismological Society of America,67(8):661-675.
Farra V.2001.High-order perturbations of the phase velocity and polarization of qP and qS waves in anisotropic media.Geophysical Journal International,147(1):90-104,doi:10.1046/j.1365-246X.2001.00510.x.
Farra V,P2enˇcík I.2008.First-order ray computations of coupled Swaves in inhomogeneous weakly anisotropic media.Geophysical Journal International,173(3):979-989,doi:10.1111/j.1365-246X.2008.03778.x.
Farra V,P2enˇcík I.2010.First-order reflection/transmission coefficients for unconverted plane P waves in weakly anisotropic media.Geophysical Journal International,183(3):1443-1454,doi:10.1111/j.1365-246X.2010.04794.x.
Grechka V.2015.Shear-wave group-velocity surfaces in low-symmetry anisotropic media.Geophysics,80(1):C1-C7,doi:10.1190/GEO2014-0156.1.
HaoQ,Stovas A.2016.Analytic calculation of phase and group velocities of P-waves in orthorhombic media.Geophysics,81(3):C79-C97,doi:10.1190/geo2015-0156.1.
Huang J Q,Li Z C.2017.Modeling and reverse time migration of pure quasi-P-waves in complex TI media with a low-rank decomposition.Chinese Journal of Geophysics(in Chinese),60(2):704-721,doi:10.6038/cjg20170223.
Jílek P.2002.Converted PS-wave reflection coefficients in weakly anisotropic media.Pure and Applied Geophysics,159(7-8):1527-1562,doi:10.1007/s00024-002-8696-9.
Klime2L.2006.Common-ray tracing and dynamic ray tracing for Swaves in a smooth elastic anisotropic medium.Studia Geophysica et Geodaetica,50(3):449-461,doi:10.1007/s11200-006-0028-6.
Li Z C,Huang J Q,Huang J P,et al.2017.Fast least-squares reverse time migration based on plane-wave encoding for VTImedia.Chinese Journal of Geophysics(in Chinese),60(1):240-257,doi:10.6038/cjg20170120.
Liang K,Yin X Y,Wu G C.2011.Exact and approximate reflection and transmission coefficient for incident qP wave in TTI media.Chinese Journal of Geophysics(in Chinese),54(1):208-217,doi:10.3969/j.issn.0001-5733.2011.01.022.
Lu M H,Tang J H,Yang H Z,et al.2005.P-wave traveltime analysis and Thomsen parameters inversion in orthorhombic media.Chinese Journal of Geophysics(in Chinese),48(5):1167-1171,doi:10.3321/j.issn:0001-5733.2005.05.026.
Schoenberg M,Helbig K.1997.Orthorhombic media:Modeling elastic wave behavior in a vertically fractured earth.Geophysics,62(6):1954-1974,doi:10.1190/1.1444297.
Slawinski M A,Slawinski R A,Brown R J,et al.2000.Ageneralized form of Snell′s law in anisotropic media.Geophysics,65(2):632-637,doi:10.1190/1.1444759.
Sripanich Y,Fomel S.2015.On anelliptic approximations for qPvelocities in transversely isotropic and orthorhombic media.Geophysics,80(5):C89-C105,doi:10.1190/geo2014-0534.1.
Sripanich Y,Fomel S,Sun J Z,et al.2017.Elastic wave-vector decomposition in heterogeneous anisotropic media.Geophysical Prospecting,65(5):1231-1245,doi:10.1111/1365-2478.12482.
Thomsen L.1986.Weak elastic anisotropy.Geophysics,51(10):1954-1966,doi:10.1190/1.1442051.
Tsvankin I.1997.Anisotropic parameters and P-wave velocity for orthorhombic media.Geophysics,62(4):1292-1309,doi:10.1190/1.1444231.
Vavryˇcuk V.2003.Behavior of rays near singularities in anisotropic media.Physical Review B,67(5):054105,doi:10.1103/PhysRevB.67.054105.
Wu G C,Liang K,Yin X Y.2010.The analysis of phase velocity and polarization feature for elastic wave in TTI media.Chinese Journal of Geophysics(in Chinese),53(8):1914-1923,doi:10.3969/j.issn.0001-5733.2010.08.017.
Xu S B,Stovas A.2017.A new parameterization for acoustic orthorhombic media.Geophysics,82(6):C229-C240,doi:10.1190/GEO2017-0215.1.
黄金强,李振春.2017.基于Low-rank分解的复杂TI介质纯qP波正演模拟与逆时偏移.地球物理学报,60(2):704-721,doi:10.6038/cjg20170223.
李振春,黄金强,黄建平等.2017.基于平面波加速的VTI介质最小二乘逆时偏移.地球物理学报,60(1):240-257,doi:10.6038/cjg2017012.
梁锴,印兴耀,吴国忱.2011.TTI介质qP波入射精确和近似反射透射系数.地球物理学报,54(1):208-217,doi:10.3969/j.issn.0001-5733.2011.01.022.
卢明辉,唐建侯,杨慧珠等.2005.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,48(5):1167-1171,doi:10.3321/j.issn:0001-5733.2005.05.026.
吴国忱,梁锴,印兴耀.2010.TTI介质弹性波相速度与偏振特征分析.地球物理学报,53(8):1914-1923,doi:10.3969/j.issn.0001-5733.2010.08.017.
Chapman C H.1994.Reflection/transmission coefficient reciprocities in anisotropic media.Geophysical Journal International,116(2):498-501,doi:10.1111/j.1365-246X.1994.tb01811.x.
Coates R T,Chapman C H.1990.Quasi-shear wave coupling in weakly anisotropic 3-D media.Geophysical Journal International,103(2):301-320,doi:10.1111/j.1365-246X.1990.tb01773.x.
Daley P F,Hron F.1977.Reflection and transmission coefficients for transversely isotropic media.Bulletin of the Seismological Society of America,67(8):661-675.
Farra V.2001.High-order perturbations of the phase velocity and polarization of qP and qS waves in anisotropic media.Geophysical Journal International,147(1):90-104,doi:10.1046/j.1365-246X.2001.00510.x.
Farra V,P2enˇcík I.2008.First-order ray computations of coupled Swaves in inhomogeneous weakly anisotropic media.Geophysical Journal International,173(3):979-989,doi:10.1111/j.1365-246X.2008.03778.x.
Farra V,P2enˇcík I.2010.First-order reflection/transmission coefficients for unconverted plane P waves in weakly anisotropic media.Geophysical Journal International,183(3):1443-1454,doi:10.1111/j.1365-246X.2010.04794.x.
Grechka V.2015.Shear-wave group-velocity surfaces in low-symmetry anisotropic media.Geophysics,80(1):C1-C7,doi:10.1190/GEO2014-0156.1.
HaoQ,Stovas A.2016.Analytic calculation of phase and group velocities of P-waves in orthorhombic media.Geophysics,81(3):C79-C97,doi:10.1190/geo2015-0156.1.
Huang J Q,Li Z C.2017.Modeling and reverse time migration of pure quasi-P-waves in complex TI media with a low-rank decomposition.Chinese Journal of Geophysics(in Chinese),60(2):704-721,doi:10.6038/cjg20170223.
Jílek P.2002.Converted PS-wave reflection coefficients in weakly anisotropic media.Pure and Applied Geophysics,159(7-8):1527-1562,doi:10.1007/s00024-002-8696-9.
Klime2L.2006.Common-ray tracing and dynamic ray tracing for Swaves in a smooth elastic anisotropic medium.Studia Geophysica et Geodaetica,50(3):449-461,doi:10.1007/s11200-006-0028-6.
Li Z C,Huang J Q,Huang J P,et al.2017.Fast least-squares reverse time migration based on plane-wave encoding for VTImedia.Chinese Journal of Geophysics(in Chinese),60(1):240-257,doi:10.6038/cjg20170120.
Liang K,Yin X Y,Wu G C.2011.Exact and approximate reflection and transmission coefficient for incident qP wave in TTI media.Chinese Journal of Geophysics(in Chinese),54(1):208-217,doi:10.3969/j.issn.0001-5733.2011.01.022.
Lu M H,Tang J H,Yang H Z,et al.2005.P-wave traveltime analysis and Thomsen parameters inversion in orthorhombic media.Chinese Journal of Geophysics(in Chinese),48(5):1167-1171,doi:10.3321/j.issn:0001-5733.2005.05.026.
Schoenberg M,Helbig K.1997.Orthorhombic media:Modeling elastic wave behavior in a vertically fractured earth.Geophysics,62(6):1954-1974,doi:10.1190/1.1444297.
Slawinski M A,Slawinski R A,Brown R J,et al.2000.Ageneralized form of Snell′s law in anisotropic media.Geophysics,65(2):632-637,doi:10.1190/1.1444759.
Sripanich Y,Fomel S.2015.On anelliptic approximations for qPvelocities in transversely isotropic and orthorhombic media.Geophysics,80(5):C89-C105,doi:10.1190/geo2014-0534.1.
Sripanich Y,Fomel S,Sun J Z,et al.2017.Elastic wave-vector decomposition in heterogeneous anisotropic media.Geophysical Prospecting,65(5):1231-1245,doi:10.1111/1365-2478.12482.
Thomsen L.1986.Weak elastic anisotropy.Geophysics,51(10):1954-1966,doi:10.1190/1.1442051.
Tsvankin I.1997.Anisotropic parameters and P-wave velocity for orthorhombic media.Geophysics,62(4):1292-1309,doi:10.1190/1.1444231.
Vavryˇcuk V.2003.Behavior of rays near singularities in anisotropic media.Physical Review B,67(5):054105,doi:10.1103/PhysRevB.67.054105.
Wu G C,Liang K,Yin X Y.2010.The analysis of phase velocity and polarization feature for elastic wave in TTI media.Chinese Journal of Geophysics(in Chinese),53(8):1914-1923,doi:10.3969/j.issn.0001-5733.2010.08.017.
Xu S B,Stovas A.2017.A new parameterization for acoustic orthorhombic media.Geophysics,82(6):C229-C240,doi:10.1190/GEO2017-0215.1.
黄金强,李振春.2017.基于Low-rank分解的复杂TI介质纯qP波正演模拟与逆时偏移.地球物理学报,60(2):704-721,doi:10.6038/cjg20170223.
李振春,黄金强,黄建平等.2017.基于平面波加速的VTI介质最小二乘逆时偏移.地球物理学报,60(1):240-257,doi:10.6038/cjg2017012.
梁锴,印兴耀,吴国忱.2011.TTI介质qP波入射精确和近似反射透射系数.地球物理学报,54(1):208-217,doi:10.3969/j.issn.0001-5733.2011.01.022.
卢明辉,唐建侯,杨慧珠等.2005.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,48(5):1167-1171,doi:10.3321/j.issn:0001-5733.2005.05.026.
吴国忱,梁锴,印兴耀.2010.TTI介质弹性波相速度与偏振特征分析.地球物理学报,53(8):1914-1923,doi:10.3969/j.issn.0001-5733.2010.08.017.