基于Biot理论的双相各向同性介质弹性波交错网格有限差分数值模拟
|
摘要
双相介质模型是一种相对单相介质来讲更加接近于实际地层情况的介质模型,因此,地震波在双相介质中的传播路径和衰减情况比单相介质更具有考察意义.交错网格有限差分法在不增加计算量和存储空间前提下,把速度对时间的奇数次高阶导数转化为应力对空间的导数,将高阶差分和交错网格有机地结合到一起,与一般差分法相比有频散小、精度高、效率高的特点,因此具有一定的优越性.本文首先研究了交错网格的稳定性条件和完全匹配层(Perfectly Matched Layer,简称PML)的边界条件;其次,对双相各向同向介质中弹性波波场进行数值模拟,分析了弹性波传播时受震源主频和耗散系数的影响;最后重点模拟了弹性波在黏滞性的双相介质分界面上的传播规律和衰减情况.研究结果表明:快慢纵波及横波在分界面处发生了反射和透射现象,且存在波型之间的相互转换,这与实际采集的地震资料中情况相符;且运用双相介质进行数值模拟对了解地震波在实际地下传播规律具有重要意义,并且上下层介质都为黏滞型的双层模型更为贴合实际地层情况.
The two-phase medium model is closer to the actual underground media than the single-phase medium. Therefore,the seismic wave propagation path and attenuation of the two-phase medium are more meaningful to be researched than the single-phase medium. The finite difference method of the staggered grid converts the odd-order derivative of velocity into the stress-to-space derivative without increasing the computational mass and the storage space,and the high order difference and the staggered grid are organically combined. Compared with general difference method, the finite difference method has superiority for its characteristics of small dispersion,high precision and high efficiency. In this paper,the stability condition of the staggered grid and the boundary conditions of the Perfectly Matched Layer( PML) are discussed in detail at first. Secondly,the elastic wave field in the two-phase isotropic medium is simulated numerically,and the influence of the main frequency and the dissipation coefficient of the elastic wave is analyzed. Last and most important, the propagation law and attenuation of elastic wave in viscous biphasic medium interface are simulated emphatically. The results show that fast P-wave,slow Pwave and S-wave reflect and transmit at the boundary of doublelayer two-phase porous media,there is mutual conversion between the wave modes,which is consistent with the actual acquisition of seismic data. And the numerical simulation of two-phase medium is of great significance to understand the propagation law of seismic wave in actual underground,and the double layered viscous medium model fits the actual formation situation better.
The two-phase medium model is closer to the actual underground media than the single-phase medium. Therefore,the seismic wave propagation path and attenuation of the two-phase medium are more meaningful to be researched than the single-phase medium. The finite difference method of the staggered grid converts the odd-order derivative of velocity into the stress-to-space derivative without increasing the computational mass and the storage space,and the high order difference and the staggered grid are organically combined. Compared with general difference method, the finite difference method has superiority for its characteristics of small dispersion,high precision and high efficiency. In this paper,the stability condition of the staggered grid and the boundary conditions of the Perfectly Matched Layer( PML) are discussed in detail at first. Secondly,the elastic wave field in the two-phase isotropic medium is simulated numerically,and the influence of the main frequency and the dissipation coefficient of the elastic wave is analyzed. Last and most important, the propagation law and attenuation of elastic wave in viscous biphasic medium interface are simulated emphatically. The results show that fast P-wave,slow Pwave and S-wave reflect and transmit at the boundary of doublelayer two-phase porous media,there is mutual conversion between the wave modes,which is consistent with the actual acquisition of seismic data. And the numerical simulation of two-phase medium is of great significance to understand the propagation law of seismic wave in actual underground,and the double layered viscous medium model fits the actual formation situation better.
引文
Chen K Y.2011.First-order Velocity-stress elastic wave field separation scheme for Biot Two-phase isotropic medium[J].Chinses Journal of Computational Physics(in Chinese),28(3):404-412.
Dong L G,Ma Z T,Cao J Z.2000a.A study on stability of the staggered-grid high-order difference method of first-order elastic wave equation[J].Chinese Journal of Geophysics(in Chinese),43(6):856-864,doi:10.3321/j.issn:0001-5733.2000.06.015.
Dong L G,Ma Z T,Cao J Z,et al.2000b.A staggered-grid high-order difference method of one-order elastic wave equation[J].Chinese Journal of Geophysics(in Chinese),43(3):411-419.
Du Q Z,Kong L Y,Han S C.2009.Wavefield propagation characteristics in the fracture-induced anisotropic double-porosity medium[J].Chinese Journal of Geophysics(in Chinese),52(4):1049-1058,doi:10.3969/j.issn.0001-5733.2009.04.022.
Du Y K.2012.Research on seismic wave attenuation and its application in two-phase media(in Chinese)[Master’s thesis].Qingdao:Ocean University of China.
Guo J.1992.Finite difference modeling of P-wave field in two-phase medium[J].Oil Geophysical Prospecting(in Chinese),27(2):182-199.
Han C.2007.Numerical simulation of seismic wave and analysis of wave field’s character(in Chinese)[Master’s thesis].Chengdu:Chengdu University of Technology.
Hassanzadeh S.1991.Acoustic modeling in fluid-saturated porous media[J].Geophysics,56(4):424-435.
Kong L Y,Wang Y B,Yang H Z.2012.Fracture parameters analyses in fracture-induced HTI double-porosity medium[J].Chinese Journal of Geophysics(in Chinese),55(1):189-196,doi:10.6038/j.issn.0001-5733.2012.01.018.
Li Y J.2014.Elastic wave two-phase medium finite difference numerical simulation(in Chinese)[Master’s thesis].Chengdu:Southwest Petroleum University.
Liu C,Guo Z Q,Lan H T,et al.2014a.Numerical Modeling for Deismie Wave Propagation in Complex Media(in Chinese)[M].Beijing:Geological Press,68-69.
Liu C,Yang Q J,Lu Q,et al.2014b.Simulation of wave propagation in two-phase porous media using a frequency-space domain method[J].Chinese Journal of Geophysics(in Chinese),57(9):2885-2899,doi:10.6038/cg20140914.
Liu Y,Li C C.2000.Study of elastic wave propagation in two-phase anisotropic media by numerical modeling of pseudospectral method[J].Acta Seismologica Sinica(in Chinese),22(2):132-138.
Masson Y J,Pride S R,Nihei K T.2006.Finite difference modeling of Biot’s poroelastic equations at seismic frequencies[J].Journal of Geophysical Research,111(B10):B10305.
Pei Z L.2006.Staggering grid high-order finite-difference modeling of elastic wave transmission in biphase anisotropic medium[J].Oil Geophysical Prospecting(in Chinese),41(2):137-143.
Yang D H.2002.Finite element method of the elastic wave equation and wavefield simulation in two-phase anisotropic media[J].Chinese Journal of Geophysics(in Chinese),45(4):575-583,doi:10.3321/j.issn:0001-5733.2002.04.015.
Yang Q J.2015.Wavefield simulation of Two-phase porous medium and propagation characteristics analysis(in Chinese)[Ph.D.thesis].Changchun:Jilin University.
Yang Q J,Liu C,Geng M X,et al.2014.Staggered grid finite difference scheme and coefficients deduction of any number of derivatives[J].Journal of Jilin University(Earth Science Edition)(in Chinese),44(1):375-385.
Zhang J D,Le Y X,Wang Y X.2008.Numerical simulation of seismic wave field by pseudo-spectrum method in isotropic two-phase media[J].Geophysical Prospecting for Petroleum(in Chinese),47(4):338-345.
Zhang W Z.2007.Numerical modeling in Biot’s porous media by staggered-grid difference scheme(in Chinese)[Master’s thesis].Beijing:China University of Geosciences(Beijing).
Zhu X,Mc Mechan G A.1991.Numerical simulation of seismic responses of poroelastic reservoirs using Biot theory[J].Geophysics,56(3):328-339.
陈可洋.2011.一阶速度-应力Biot双相各向同性介质弹性波波场分离数值模拟[J].计算物理,28(3):404-412.
董良国,马在田,曹景中.2000a.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,43(6):856-864,doi:10.3321/j.issn:0001-5733.2000.06.015.
董良国,马在田,曹景中,等.2000b.一阶弹性波方程交错网格高阶差分解法[J].地球物理学报,43(3):411-419.
杜启振,孔丽云,韩世春.2009.裂缝诱导各向异性双孔隙介质波场传播特征[J].地球物理学报,52(4):1049-1058,doi:10.3969/j.issn.0001-5733.2009.04.022.
杜艺可.2012.双相介质中地震波衰减特性研究及应用[硕士论文].青岛:中国海洋大学.
郭建.1992.双相介质中P波波场的有限差分模拟[J].石油地球物理勘探,27(2):182-199.
韩翀.2007.地震波数值模拟及波场特征分析[硕士论文].成都:成都理工大学.
孔丽云,王一博,杨慧珠.2012.裂缝诱导HTI双孔隙介质中的裂缝参数分析[J].地球物理学报,55(1):189-196,doi:10.6038/j.issn.0001-5733.2012.01.018.
李勇军.2014.弹性波双相介质有限差分数值模拟[硕士论文].成都:西南石油大学.
刘财,郭志奇,兰慧田,等.2014a.复杂介质地震波场数值模拟[M].北京:地质出版社,68-69.
刘财,杨庆节,鹿琪,等.2014b.双相介质中地震波的频率-空间域数值模拟[J].地球物理学报,57(9):2885-2899,doi:10.6038/cg20140914.
刘洋,李承楚.2000.双相各向异性介质中弹性波传播伪谱法数值模拟研究[J].地震学报,22(2):132-138.
裴正林.2006.双相各向异性介质弹性波传播交错网格高阶有限差分法模拟[J].石油地球物理勘探,41(2):137-143.
杨顶辉.2002.双相各向异性介质中弹性波方程的有限元解法及波场模拟[J].地球物理学报,45(4):575-583,doi:10.3321/j.issn:0001-5733.2002.04.015.
杨庆节.2015.双相孔隙介质地震波场模拟及传播特性分析[博士论文].长春:吉林大学.
杨庆节,刘财,耿美霞,等.2014.交错网格任意阶导数有限差分格式及差分系数推导[J].吉林大学学报(地球科学版),44(1):375-385.
张军舵,乐友喜,王艳香.2008.双相各向同性介质伪谱法地震波场数值模拟[J].石油物探,47(4):338-345.
张文忠.2007.Biot介质的交错网格差分法波场模拟研究[硕士论文].北京:中国地质大学(北京).
Dong L G,Ma Z T,Cao J Z.2000a.A study on stability of the staggered-grid high-order difference method of first-order elastic wave equation[J].Chinese Journal of Geophysics(in Chinese),43(6):856-864,doi:10.3321/j.issn:0001-5733.2000.06.015.
Dong L G,Ma Z T,Cao J Z,et al.2000b.A staggered-grid high-order difference method of one-order elastic wave equation[J].Chinese Journal of Geophysics(in Chinese),43(3):411-419.
Du Q Z,Kong L Y,Han S C.2009.Wavefield propagation characteristics in the fracture-induced anisotropic double-porosity medium[J].Chinese Journal of Geophysics(in Chinese),52(4):1049-1058,doi:10.3969/j.issn.0001-5733.2009.04.022.
Du Y K.2012.Research on seismic wave attenuation and its application in two-phase media(in Chinese)[Master’s thesis].Qingdao:Ocean University of China.
Guo J.1992.Finite difference modeling of P-wave field in two-phase medium[J].Oil Geophysical Prospecting(in Chinese),27(2):182-199.
Han C.2007.Numerical simulation of seismic wave and analysis of wave field’s character(in Chinese)[Master’s thesis].Chengdu:Chengdu University of Technology.
Hassanzadeh S.1991.Acoustic modeling in fluid-saturated porous media[J].Geophysics,56(4):424-435.
Kong L Y,Wang Y B,Yang H Z.2012.Fracture parameters analyses in fracture-induced HTI double-porosity medium[J].Chinese Journal of Geophysics(in Chinese),55(1):189-196,doi:10.6038/j.issn.0001-5733.2012.01.018.
Li Y J.2014.Elastic wave two-phase medium finite difference numerical simulation(in Chinese)[Master’s thesis].Chengdu:Southwest Petroleum University.
Liu C,Guo Z Q,Lan H T,et al.2014a.Numerical Modeling for Deismie Wave Propagation in Complex Media(in Chinese)[M].Beijing:Geological Press,68-69.
Liu C,Yang Q J,Lu Q,et al.2014b.Simulation of wave propagation in two-phase porous media using a frequency-space domain method[J].Chinese Journal of Geophysics(in Chinese),57(9):2885-2899,doi:10.6038/cg20140914.
Liu Y,Li C C.2000.Study of elastic wave propagation in two-phase anisotropic media by numerical modeling of pseudospectral method[J].Acta Seismologica Sinica(in Chinese),22(2):132-138.
Masson Y J,Pride S R,Nihei K T.2006.Finite difference modeling of Biot’s poroelastic equations at seismic frequencies[J].Journal of Geophysical Research,111(B10):B10305.
Pei Z L.2006.Staggering grid high-order finite-difference modeling of elastic wave transmission in biphase anisotropic medium[J].Oil Geophysical Prospecting(in Chinese),41(2):137-143.
Yang D H.2002.Finite element method of the elastic wave equation and wavefield simulation in two-phase anisotropic media[J].Chinese Journal of Geophysics(in Chinese),45(4):575-583,doi:10.3321/j.issn:0001-5733.2002.04.015.
Yang Q J.2015.Wavefield simulation of Two-phase porous medium and propagation characteristics analysis(in Chinese)[Ph.D.thesis].Changchun:Jilin University.
Yang Q J,Liu C,Geng M X,et al.2014.Staggered grid finite difference scheme and coefficients deduction of any number of derivatives[J].Journal of Jilin University(Earth Science Edition)(in Chinese),44(1):375-385.
Zhang J D,Le Y X,Wang Y X.2008.Numerical simulation of seismic wave field by pseudo-spectrum method in isotropic two-phase media[J].Geophysical Prospecting for Petroleum(in Chinese),47(4):338-345.
Zhang W Z.2007.Numerical modeling in Biot’s porous media by staggered-grid difference scheme(in Chinese)[Master’s thesis].Beijing:China University of Geosciences(Beijing).
Zhu X,Mc Mechan G A.1991.Numerical simulation of seismic responses of poroelastic reservoirs using Biot theory[J].Geophysics,56(3):328-339.
陈可洋.2011.一阶速度-应力Biot双相各向同性介质弹性波波场分离数值模拟[J].计算物理,28(3):404-412.
董良国,马在田,曹景中.2000a.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,43(6):856-864,doi:10.3321/j.issn:0001-5733.2000.06.015.
董良国,马在田,曹景中,等.2000b.一阶弹性波方程交错网格高阶差分解法[J].地球物理学报,43(3):411-419.
杜启振,孔丽云,韩世春.2009.裂缝诱导各向异性双孔隙介质波场传播特征[J].地球物理学报,52(4):1049-1058,doi:10.3969/j.issn.0001-5733.2009.04.022.
杜艺可.2012.双相介质中地震波衰减特性研究及应用[硕士论文].青岛:中国海洋大学.
郭建.1992.双相介质中P波波场的有限差分模拟[J].石油地球物理勘探,27(2):182-199.
韩翀.2007.地震波数值模拟及波场特征分析[硕士论文].成都:成都理工大学.
孔丽云,王一博,杨慧珠.2012.裂缝诱导HTI双孔隙介质中的裂缝参数分析[J].地球物理学报,55(1):189-196,doi:10.6038/j.issn.0001-5733.2012.01.018.
李勇军.2014.弹性波双相介质有限差分数值模拟[硕士论文].成都:西南石油大学.
刘财,郭志奇,兰慧田,等.2014a.复杂介质地震波场数值模拟[M].北京:地质出版社,68-69.
刘财,杨庆节,鹿琪,等.2014b.双相介质中地震波的频率-空间域数值模拟[J].地球物理学报,57(9):2885-2899,doi:10.6038/cg20140914.
刘洋,李承楚.2000.双相各向异性介质中弹性波传播伪谱法数值模拟研究[J].地震学报,22(2):132-138.
裴正林.2006.双相各向异性介质弹性波传播交错网格高阶有限差分法模拟[J].石油地球物理勘探,41(2):137-143.
杨顶辉.2002.双相各向异性介质中弹性波方程的有限元解法及波场模拟[J].地球物理学报,45(4):575-583,doi:10.3321/j.issn:0001-5733.2002.04.015.
杨庆节.2015.双相孔隙介质地震波场模拟及传播特性分析[博士论文].长春:吉林大学.
杨庆节,刘财,耿美霞,等.2014.交错网格任意阶导数有限差分格式及差分系数推导[J].吉林大学学报(地球科学版),44(1):375-385.
张军舵,乐友喜,王艳香.2008.双相各向同性介质伪谱法地震波场数值模拟[J].石油物探,47(4):338-345.
张文忠.2007.Biot介质的交错网格差分法波场模拟研究[硕士论文].北京:中国地质大学(北京).