各向异性双相介质弹性波场褶积算法数值模拟
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摘要
从各向同性介质中波场数值模拟的褶积微分算子法出发,推导出了各向异性双相介质中波场传播数值计算的褶积新算法。将常见的二阶微分Biot波动方程用等效的一阶速度-应力双曲方程表示,其中未知的波场向量包括固相和流体的速度分量和应力分量,由此对方程的时间项使用交错网格差分方法计算,而对空间项则采用褶积微分算法进行求解。对各向异性双相介质在单层介质模型和双层介质模型中的波场特征进行了研究。研究的结果显示,在两层介质分界面上当地震波产生反射时能观测到两类纵波和横波,并且在衰减系数大的介质里慢纵波很难见到。
A new numerical simulation method with convolutional algorithm for elastic waves propagation in heterogeneous two-phase media is derived from the convolutional differential simulation for the propagation in homogeneous media,and the second-order Biot wave equation is expressed as first-order velocity-stress hyperbolic equations,in which the unknown wavefield vectors are velocity and stress components in both fluid and solid phases.The temporal term in the wave equation is computed by stager-grid finite difference method and the spatial term is computed by the new convolutional differentiator.The wavefield characters of heterogeneous two-phase media are studied in both single and two-layered models.The results show that on the subsurface in the two-layered model,two types of fast P-wave and one type of S-wave can be observed when seismic wave is reflected,meanwhile in the media with large attenuation coefficient the slow P-wave is hard to be observed.
A new numerical simulation method with convolutional algorithm for elastic waves propagation in heterogeneous two-phase media is derived from the convolutional differential simulation for the propagation in homogeneous media,and the second-order Biot wave equation is expressed as first-order velocity-stress hyperbolic equations,in which the unknown wavefield vectors are velocity and stress components in both fluid and solid phases.The temporal term in the wave equation is computed by stager-grid finite difference method and the spatial term is computed by the new convolutional differentiator.The wavefield characters of heterogeneous two-phase media are studied in both single and two-layered models.The results show that on the subsurface in the two-layered model,two types of fast P-wave and one type of S-wave can be observed when seismic wave is reflected,meanwhile in the media with large attenuation coefficient the slow P-wave is hard to be observed.
引文
[1]Gassmann F.Elastic waves through a packing of spheres[J].Geophysics,1951(16):673-685.
[2]Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid.Ⅰ.low-frequency range[J].J.Acoust.Soc.Am.,1956(28):168-178.
[3]Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid.Ⅱ.higher-frequency range[J].J.Acoust.Soc.Am.,1956(28):179-191.
[4]Zhu X,G A McMechan.Numerical simulation of seismic re-sponses of poroelastic reservoirs using Biot theory[J].Geo-physics,1991(56):328-339.
[5]Hassanzadeh S.Acoustic modeling in fluid-saturated porousmedia[J].Geophysics,1991(56):424-435.
[6]牛滨华,吴有校,孙春岩.裂隙含流体气体各向异性介质波场数值模拟[J].长春地质学院学报,1994,24(4):454-460.
[7]N Dai,Vafidis A,Kanasewieh E R.Wave propagation in heter-ogeneous,porous media:A velocity-stress,finite differencemethod[J].Geophysics,1995,60(2):327-34.
[8]牟永光.储层地球物理学[M].北京:石油工业出版社,1996:5.
[9]邵秀民,蓝志凌.流体饱和多孔介质波动方程的有限元解法[J].地球物理学报,2000,43(2):264-278.
[10]Arntsen B,Carcione J M.Numerical simulation of the Biotslow wave in water-saturated Nivelsteiner sandstone[J].Ge-ophysics,2001(66):890-896.
[11]杨宽德,杨顶辉,王书强.基于Biot-Squirt方程的波场模拟[J].地球物理学报,2002,45(6):853-861.
[12]杨顶辉.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,2002,45(4):575-583.
[13]刘洋,李承楚.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,2000,22(2):132-138.
[14]刘洋,魏修成.双相各向异性介质中弹性波传播有限元方程及数值模拟[J].地震学报,2003,25(2):154-162.
[15]孙卫涛,杨慧珠.双相各向异性介质弹性波场有限差分正演模拟[J].固体力学学报,2004,25(l):21-28.
[16]王东,张海澜,王秀明.部分饱和孔隙岩石中声波传播数值研究[J].地球物理学报,2006,49(2):524-532.
[17]裴正林.二维双相各向异性介质弹性波方程交错网格高阶有限差分法模拟[J].中国石油大学学报(自然科学版),2006,30(2):16-20.
[18]裴正林.三维各向同性介质弹性波方程交错网格高阶有限差分法模拟[J].石油物探,2006,41(2):308-315.
[19]李信富,李小凡.地震波传播的褶积微分算子法数值模拟[J].地球科学-中国地质大学学报,2008,33(6):861-866.
[2]Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid.Ⅰ.low-frequency range[J].J.Acoust.Soc.Am.,1956(28):168-178.
[3]Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid.Ⅱ.higher-frequency range[J].J.Acoust.Soc.Am.,1956(28):179-191.
[4]Zhu X,G A McMechan.Numerical simulation of seismic re-sponses of poroelastic reservoirs using Biot theory[J].Geo-physics,1991(56):328-339.
[5]Hassanzadeh S.Acoustic modeling in fluid-saturated porousmedia[J].Geophysics,1991(56):424-435.
[6]牛滨华,吴有校,孙春岩.裂隙含流体气体各向异性介质波场数值模拟[J].长春地质学院学报,1994,24(4):454-460.
[7]N Dai,Vafidis A,Kanasewieh E R.Wave propagation in heter-ogeneous,porous media:A velocity-stress,finite differencemethod[J].Geophysics,1995,60(2):327-34.
[8]牟永光.储层地球物理学[M].北京:石油工业出版社,1996:5.
[9]邵秀民,蓝志凌.流体饱和多孔介质波动方程的有限元解法[J].地球物理学报,2000,43(2):264-278.
[10]Arntsen B,Carcione J M.Numerical simulation of the Biotslow wave in water-saturated Nivelsteiner sandstone[J].Ge-ophysics,2001(66):890-896.
[11]杨宽德,杨顶辉,王书强.基于Biot-Squirt方程的波场模拟[J].地球物理学报,2002,45(6):853-861.
[12]杨顶辉.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,2002,45(4):575-583.
[13]刘洋,李承楚.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,2000,22(2):132-138.
[14]刘洋,魏修成.双相各向异性介质中弹性波传播有限元方程及数值模拟[J].地震学报,2003,25(2):154-162.
[15]孙卫涛,杨慧珠.双相各向异性介质弹性波场有限差分正演模拟[J].固体力学学报,2004,25(l):21-28.
[16]王东,张海澜,王秀明.部分饱和孔隙岩石中声波传播数值研究[J].地球物理学报,2006,49(2):524-532.
[17]裴正林.二维双相各向异性介质弹性波方程交错网格高阶有限差分法模拟[J].中国石油大学学报(自然科学版),2006,30(2):16-20.
[18]裴正林.三维各向同性介质弹性波方程交错网格高阶有限差分法模拟[J].石油物探,2006,41(2):308-315.
[19]李信富,李小凡.地震波传播的褶积微分算子法数值模拟[J].地球科学-中国地质大学学报,2008,33(6):861-866.
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