高阶旋转交错网格有限差分方法模拟TTI介质中横波分裂
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摘要
笔者给出了一种能够模拟弹性波在任意各向异性介质中传播的二维三分量高阶有限差分算法。相对于常规交错网格有限差分方法,旋转交错网格有限差分方法在介质具有强差异性时能更精确地模拟地震波的传播,避免常规交错网格中因对弹性系数进行插值而带来的误差。采用高阶旋转交错网格有限差分方法模拟并分析了零偏移距横波分裂现象随裂缝介质方位角和倾角变化的响应特征。结果表明:结合完全匹配层(PML)吸收边界条件的高阶旋转交错网格有限差分方法能获得高精度的地震波场模拟数据,并且在边界具有良好的吸收效果;横波分裂现象主要受裂缝走向与波的极化方向之间的夹角影响,受裂缝倾角影响较小,且快慢横波的能量也跟裂缝走向与波极化方向间的夹角有关。具有倾斜对称轴的横向各向同性(TTI)介质倾角的变化可能会导致记录中波到达时的变化,影响快慢横波的时差。利用横波分裂的能量分布和方位各向异性特征,可以帮助检测裂缝的方位角和倾角。横波在多层TTI介质中传播时会发生多次分裂的现象。
A high-order rotated staggered grid scheme(RSG) has been implemented to simulate the shear-wave splitting in tilted transversely isotropic(TTI) media.The high-order RSG can simulate wave propagation in media that contain high-contrast discontinuities like cracks more precisely than the standard staggered grid scheme(SSG) by avoiding the unstableness of the staggered grid scheme(SSG).The authors conducted a study of zero-offset S-wave splitting with the high-order RSG.The S-wave splitting study was mainly focused on fractured media which,on the scale of seismic wavelength,could be regarded as transversely isotropic(TI) media.The results of numerical modeling show that the high-order RSG scheme can be used to simulate waves' propagation in general anisotropic media.The perfect matched layer(PML) absorbing boundary condition combined with the high order RSG scheme can well attenuate reflections from the artificial boundary.The S-wave splitting is mainly affected by the angle between polarization direction of incoming wave and strike of the TTI media,and the energy of fast and slow shear waves is also associated with this angle.The dipping angle of TTI media may affect time lag between the fast and slow waves,which may result in variation of arrival time of waves from the same interface.Thus,the analysis of energy distribution of the fast and slow waves and the variation of arrival time may help detect the strike and dipping angle of the fracture.Besides,when propagating in the media that contain more than one layer of TTI media,the S-wave splitting will occur more than once.
A high-order rotated staggered grid scheme(RSG) has been implemented to simulate the shear-wave splitting in tilted transversely isotropic(TTI) media.The high-order RSG can simulate wave propagation in media that contain high-contrast discontinuities like cracks more precisely than the standard staggered grid scheme(SSG) by avoiding the unstableness of the staggered grid scheme(SSG).The authors conducted a study of zero-offset S-wave splitting with the high-order RSG.The S-wave splitting study was mainly focused on fractured media which,on the scale of seismic wavelength,could be regarded as transversely isotropic(TI) media.The results of numerical modeling show that the high-order RSG scheme can be used to simulate waves' propagation in general anisotropic media.The perfect matched layer(PML) absorbing boundary condition combined with the high order RSG scheme can well attenuate reflections from the artificial boundary.The S-wave splitting is mainly affected by the angle between polarization direction of incoming wave and strike of the TTI media,and the energy of fast and slow shear waves is also associated with this angle.The dipping angle of TTI media may affect time lag between the fast and slow waves,which may result in variation of arrival time of waves from the same interface.Thus,the analysis of energy distribution of the fast and slow waves and the variation of arrival time may help detect the strike and dipping angle of the fracture.Besides,when propagating in the media that contain more than one layer of TTI media,the S-wave splitting will occur more than once.
引文
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[11]张晶,何兵寿,张会星.含直立裂隙介质的弹性波动方程正演模拟[J].中国煤炭地质,2008,20(1):50-54.
[12]甘文权,董良国,马在田.含裂隙介质中横波分裂现象的数值模拟[J].同济大学学报,2000,28(5):547-551.
[13]刘洋,李承楚,牟永光.具有倾斜对称轴的横向各向同性介质中的弹性波[J].石油地球物理勘探,1998,33(2):161-169.
[14]裴正林,王尚旭.任意倾斜各向异性介质中弹性波波场交错网格高阶有限差分法模拟[J].地震学报,2005,27(4).
[15]刘洋,董敏煜.各向异性介质中的方位AVO[J].石油地球物理勘探,1999,34(3):260-268.
[16]Thomsen L.Weak elastic anisotropy[J].Geophysics,1986,51(10):1954-966.
[17]Berenger J P.A perfectly matched layer for the absorption of elec-tromagnetic waves[J].Journal of Computational Physics,1994,114:185-200.
[18]陈浩,王秀明,赵海波.旋转交错网格有限差分及其完全匹配层吸收边界条件[J].科学通报,2006,51(17):1985-1994.
[19]Collino F,Tsogka C.Application of the perfectly matched absorb-ing layer model to the linear elastodynamic problem in anisotropicheterogeneous media[J].Geophysics,2001,66(1):294-307.
[20]董良国,马在田,曹景忠.一阶弹性波方程交错网格高阶差分解法稳定性研究[J].地球物理学报,2000,43(6):856-864.
[21]Liu Y,Sen M K.An implicit staggered-grid finite-difference meth-od for seismic modelling[J].Geophysical Journal International,2009,179:459-474.
[2]Virieux J.P-SV Wave propagation in heterogeneous media:Veloci-ty-stress finite-difference method[J].Geophysics,1986,51(4):889-901.
[3]Levander A R.Four-order finite-difference P-SV seismograms[J].Geophysics,1988,53(11):1425-1436.
[4]侯安宁,何樵登.各向异性介质中弹性波动高阶差分法及其稳定性的研究[J].地球物理学报,1995,38(2):243-251.
[5]Gold N,Shapiro S A,Burr E,et al.Modelling of high contrasts inelastic media using a modified finite difference scheme[J].SEGExpanded Abstracts,1997,16:1850-1853.
[6]Saenger E H,Gold N,Shapiro S A.Modeling the propagation of e-lastic waves using a modified finite-difference grid[J].Wave Mo-tion,2000,31:77-92.
[7]Saenger E H,Bohlen T.Finite-difference modeling of viscoelasticand anisotropic wave propagation using the rotated staggered grid[J].Geophysics,2004,69:583-591.
[8]Crampin S.A review of wave motion in anisotropic and cracked e-lastic media[J].Wave Motion,1981,3(4):343-391.
[9]Martinez J R,Ortega A A,McMechan G A.3-D seismic modelingfor cracked media:Shear-wave splitting at zero-offset[J].Geo-physics,2000,65(1):211-221.
[10]Bansal R,Sen M K.Finite-difference modelling of S-wave splittingin anisotropic media[J].Geophysical Prospecting,2008,56:293-312.
[11]张晶,何兵寿,张会星.含直立裂隙介质的弹性波动方程正演模拟[J].中国煤炭地质,2008,20(1):50-54.
[12]甘文权,董良国,马在田.含裂隙介质中横波分裂现象的数值模拟[J].同济大学学报,2000,28(5):547-551.
[13]刘洋,李承楚,牟永光.具有倾斜对称轴的横向各向同性介质中的弹性波[J].石油地球物理勘探,1998,33(2):161-169.
[14]裴正林,王尚旭.任意倾斜各向异性介质中弹性波波场交错网格高阶有限差分法模拟[J].地震学报,2005,27(4).
[15]刘洋,董敏煜.各向异性介质中的方位AVO[J].石油地球物理勘探,1999,34(3):260-268.
[16]Thomsen L.Weak elastic anisotropy[J].Geophysics,1986,51(10):1954-966.
[17]Berenger J P.A perfectly matched layer for the absorption of elec-tromagnetic waves[J].Journal of Computational Physics,1994,114:185-200.
[18]陈浩,王秀明,赵海波.旋转交错网格有限差分及其完全匹配层吸收边界条件[J].科学通报,2006,51(17):1985-1994.
[19]Collino F,Tsogka C.Application of the perfectly matched absorb-ing layer model to the linear elastodynamic problem in anisotropicheterogeneous media[J].Geophysics,2001,66(1):294-307.
[20]董良国,马在田,曹景忠.一阶弹性波方程交错网格高阶差分解法稳定性研究[J].地球物理学报,2000,43(6):856-864.
[21]Liu Y,Sen M K.An implicit staggered-grid finite-difference meth-od for seismic modelling[J].Geophysical Journal International,2009,179:459-474.
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