含直立裂缝粘弹性介质地震波场正演模拟
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摘要
以Carcione各向异性粘弹性理论为基础,导出了适用于任意方位角的粘弹性方位各向异性(HTI)介质的波动方程,推导了该方程在交错网格空间中求解的高阶有限差分格式和对应的完全匹配层(PML)吸收边界条件,实现了该类介质的地震波场正演模拟。模拟结果表明,该方法能准确模拟地震波在含直立裂缝粘弹性介质中的传播过程,得到高精度的波场快照和合成记录。初步分析了介质的各向异性特征和衰减特征,研究了裂缝方位角和粘滞性参数对地震波场的影响机理。
On the basis of Carcione′s theories of viscoelasticity and anisotropy,this paper derived the wave equation of viscoelastic azimuth and anisotropic media suitable for all azimuths and deduced the high-order finite difference scheme for the equation solved in staggered-grid space and the absorbing boundary condition corresponding to the perfectly matched layer(PML),realizing the simulation of seismic wave field for that kind of media.The results show that the method can simulate the seismic propagation process accurately in the viscoslastic media with vertical fractures and can obtain the high precise snapshots of wave field and composite seismograms.Additionally,this work analyzed the anisotropic and viscoelastic characteristics of the media and investigated the effects of the azimuths of fractures and the viscosity parameters on wave field.
On the basis of Carcione′s theories of viscoelasticity and anisotropy,this paper derived the wave equation of viscoelastic azimuth and anisotropic media suitable for all azimuths and deduced the high-order finite difference scheme for the equation solved in staggered-grid space and the absorbing boundary condition corresponding to the perfectly matched layer(PML),realizing the simulation of seismic wave field for that kind of media.The results show that the method can simulate the seismic propagation process accurately in the viscoslastic media with vertical fractures and can obtain the high precise snapshots of wave field and composite seismograms.Additionally,this work analyzed the anisotropic and viscoelastic characteristics of the media and investigated the effects of the azimuths of fractures and the viscosity parameters on wave field.
引文
[1]CERVENY V,MOLOTKOVI,PSENCIKI.Ray method in seismology[M].Univerzita Karlova:Vlastislav erven,1977.
[2]ALTERMAN Z,KARAL JR F C.Propagation of elastic waves inlayered media by finite-difference Methods[J].Bulletin ofthe Seismological of America,1968,58:367-398.
[3]MARFURT KJ.Accuracy of finite-difference and finite-element modeling of the scalar and elastic wave equations[J].Geo-physics,1984,49(5):533-549.
[4]GAZDAGJ.Modeling of the acoustic wave equation with transform methods[J].Geophysics,1981,46(6):854-859.
[5]RICKER N H.粘弹性介质中的地震波[M].许云,译.北京:地质出版社,1981.
[6]范祯祥,邓玉琼.准各向异性粘弹介质地震波的数字仿真[J].地球物理学报,1988,31(2):184-210.FAN Zhen-xiang,DENG Yu-qiong.Digital si mulation of seismic wave in quasi-anisotopic and viscoelastic media[J].ChineseJournal of Geophysics,1988,31(2):184-210.
[7]傅旦丹,刘洋,陈遵德,等.粘弹介质中声波的伪谱法模拟[J].江汉石油学院报,1993,15(4):32-39.FU Dan-dan,LI U Yang,CHEN Zun-de,et al.Acoustic wave modeling in viscoelastic media by pseudospectral method[J].Journal of Jianghan PetroleumInstitute,1993,15(4):32-39.
[8]刘财,谢靖,韩道范,等.用Stokes方程的差分方法制作合成地震记录[J].石油地球物理勘探,2002,37(3):230-236.LIU Cai,XIE Jing,HAN Dao-fan,et al.Producing seismogram using difference method of Stocks equation[J].Oil GeophysicalProspecting,2002,37(3):230-236.
[9]高广宏,郭宝奇,范祯祥.标准线形体地震波有限元数值模拟[J].石油地球物理勘探,1991,26(8):547-556.GAO Guang-hong,GUOBao-qi,FANZhen-xiang.Seismic wavefieldforward modeling withfinite-element methodinstandardlinearsolid[J].Oil Geophysical Prospecting,1991,26(8):547-556.
[10]LI U H P,ANDERSON D L,KANAMORI H.Velocity dispersion due to anelasticity:I mplications for seismology andmantle composition[J].Geophysical Journal of the Royal Astronomical Society,1976,47:41-58.
[11]DAY S M,MINISTERJ B.Numerical si mulation of attenuated wavefields using a Pade approxi mate method[J].Geophysi-cal Journal of the Royal Astronomical Society,1984,78:105-118.
[12]CARCIONE J M.Wave propagationin anisotropic linear viscoelastic media:Theory and si mulated wavefields[J].GeophysicalJournal International,1990,101:739-750.
[13]CARCIONE J M.Constitutive model and wave equations for linear,viscoelastic,anisotropic media[J].Geophysics,1995,60(2):537-548.
[14]CARCIONE J M.Staggered mesh for the anisotropic and viscoelastic wave equation[J].Geophysics,1999,64(6):1863-1866.
[15]CARCIONE J M.Wave fields in real media:Wave propagation in anisotropic,anelastic and porous media[M]//Handbookof Geophysical Exploration.New York:Pergamon Press Inc.,2001.
[16]张中杰,腾吉文,贺振华.EDA介质中地震波速度、衰减与品质因子方位异性研究[J].中国科学:E辑,1999,29(6):569-574.ZHANG Zhong-jie,TENGJi-wen,HE Zhen-hua.Azi muth anisotropy study on seismic velocity,attenuation and quality fac-tor in EDA media[J].Science in China:Series E,1999,29(6):569-574.
[17]杜启振,杨慧珠.方位各向异性粘弹性介质波场有限元模拟[J].物理学报,2003,52(8):2010-2014.DU Qi-zhen,YANG Hui-zhu.Finite-element methods for viscoelastic and azi muthally anisotropic media[J].Acta PhysicaSinica,2003,52(8):2010-2014.
[18]杜启振.各向异性黏弹性介质伪谱法波场模拟[J].物理学报,2004,53(12):4428-4434.DU Qi-zhen.Wavefield forward modeling withthe pseudo-spectral methodin viscoelastic and azi muthally anisotropic media[J].Acta Physica Sinica,2004,53(12):4428-4434.
[19]杜启振,杨慧珠.线性黏弹性各向异性介质速度频散和衰减特征研究[J].物理学报,2002,51(9):2101-2108.DU Qi-zhen,YANG Hui-zhu.Velocity dispersion and attenuation in anisotropic linear viscoelastic media[J].Acta PhysicaSinica,2002,51(9):2101-2108.
[20]董良国,马在田,曹景忠,等.一阶弹性波方程交错网格高阶差分解法[J].地球物理学报,2000,43(3):411-419.DONG Liang-guo,MA Zai-tian,CAOJing-zhong,et al.Astaggered-grid high-order difference method of one-order elasticwave equation[J].Chinese Journal of Geophysics,2000,43(3):411-419.
[21]COLLINO F,TSOGKA C.Application of the perfectly matched absorbing layer model to the linear elastodynamic problemin anisotropic heterogeneous media[J].Geophysics,2001,66(1):294-307.
[2]ALTERMAN Z,KARAL JR F C.Propagation of elastic waves inlayered media by finite-difference Methods[J].Bulletin ofthe Seismological of America,1968,58:367-398.
[3]MARFURT KJ.Accuracy of finite-difference and finite-element modeling of the scalar and elastic wave equations[J].Geo-physics,1984,49(5):533-549.
[4]GAZDAGJ.Modeling of the acoustic wave equation with transform methods[J].Geophysics,1981,46(6):854-859.
[5]RICKER N H.粘弹性介质中的地震波[M].许云,译.北京:地质出版社,1981.
[6]范祯祥,邓玉琼.准各向异性粘弹介质地震波的数字仿真[J].地球物理学报,1988,31(2):184-210.FAN Zhen-xiang,DENG Yu-qiong.Digital si mulation of seismic wave in quasi-anisotopic and viscoelastic media[J].ChineseJournal of Geophysics,1988,31(2):184-210.
[7]傅旦丹,刘洋,陈遵德,等.粘弹介质中声波的伪谱法模拟[J].江汉石油学院报,1993,15(4):32-39.FU Dan-dan,LI U Yang,CHEN Zun-de,et al.Acoustic wave modeling in viscoelastic media by pseudospectral method[J].Journal of Jianghan PetroleumInstitute,1993,15(4):32-39.
[8]刘财,谢靖,韩道范,等.用Stokes方程的差分方法制作合成地震记录[J].石油地球物理勘探,2002,37(3):230-236.LIU Cai,XIE Jing,HAN Dao-fan,et al.Producing seismogram using difference method of Stocks equation[J].Oil GeophysicalProspecting,2002,37(3):230-236.
[9]高广宏,郭宝奇,范祯祥.标准线形体地震波有限元数值模拟[J].石油地球物理勘探,1991,26(8):547-556.GAO Guang-hong,GUOBao-qi,FANZhen-xiang.Seismic wavefieldforward modeling withfinite-element methodinstandardlinearsolid[J].Oil Geophysical Prospecting,1991,26(8):547-556.
[10]LI U H P,ANDERSON D L,KANAMORI H.Velocity dispersion due to anelasticity:I mplications for seismology andmantle composition[J].Geophysical Journal of the Royal Astronomical Society,1976,47:41-58.
[11]DAY S M,MINISTERJ B.Numerical si mulation of attenuated wavefields using a Pade approxi mate method[J].Geophysi-cal Journal of the Royal Astronomical Society,1984,78:105-118.
[12]CARCIONE J M.Wave propagationin anisotropic linear viscoelastic media:Theory and si mulated wavefields[J].GeophysicalJournal International,1990,101:739-750.
[13]CARCIONE J M.Constitutive model and wave equations for linear,viscoelastic,anisotropic media[J].Geophysics,1995,60(2):537-548.
[14]CARCIONE J M.Staggered mesh for the anisotropic and viscoelastic wave equation[J].Geophysics,1999,64(6):1863-1866.
[15]CARCIONE J M.Wave fields in real media:Wave propagation in anisotropic,anelastic and porous media[M]//Handbookof Geophysical Exploration.New York:Pergamon Press Inc.,2001.
[16]张中杰,腾吉文,贺振华.EDA介质中地震波速度、衰减与品质因子方位异性研究[J].中国科学:E辑,1999,29(6):569-574.ZHANG Zhong-jie,TENGJi-wen,HE Zhen-hua.Azi muth anisotropy study on seismic velocity,attenuation and quality fac-tor in EDA media[J].Science in China:Series E,1999,29(6):569-574.
[17]杜启振,杨慧珠.方位各向异性粘弹性介质波场有限元模拟[J].物理学报,2003,52(8):2010-2014.DU Qi-zhen,YANG Hui-zhu.Finite-element methods for viscoelastic and azi muthally anisotropic media[J].Acta PhysicaSinica,2003,52(8):2010-2014.
[18]杜启振.各向异性黏弹性介质伪谱法波场模拟[J].物理学报,2004,53(12):4428-4434.DU Qi-zhen.Wavefield forward modeling withthe pseudo-spectral methodin viscoelastic and azi muthally anisotropic media[J].Acta Physica Sinica,2004,53(12):4428-4434.
[19]杜启振,杨慧珠.线性黏弹性各向异性介质速度频散和衰减特征研究[J].物理学报,2002,51(9):2101-2108.DU Qi-zhen,YANG Hui-zhu.Velocity dispersion and attenuation in anisotropic linear viscoelastic media[J].Acta PhysicaSinica,2002,51(9):2101-2108.
[20]董良国,马在田,曹景忠,等.一阶弹性波方程交错网格高阶差分解法[J].地球物理学报,2000,43(3):411-419.DONG Liang-guo,MA Zai-tian,CAOJing-zhong,et al.Astaggered-grid high-order difference method of one-order elasticwave equation[J].Chinese Journal of Geophysics,2000,43(3):411-419.
[21]COLLINO F,TSOGKA C.Application of the perfectly matched absorbing layer model to the linear elastodynamic problemin anisotropic heterogeneous media[J].Geophysics,2001,66(1):294-307.
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