任意裂隙方位双相HTI介质的地震波方程及正演模拟
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摘要
基于BISQ方程的高频极限,导出了适用于任意方位角的双相HTI介质波动方程,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双相HTI介质中的传播过程,得到高精度的波场快照和合成记录。分析得出:在双相各向异性介质中,弹性波的传播仍表现出各向异性特征;孔隙度、粘滞系数和固液耦合密度主要影响慢纵波的振幅和形态。
Based on the high-frequency limit of BISQ equation,this paper derived the dual-phase HTI media elastic wave equation that could be used in the arbitrary fracture azimuth angle and deduced the high-order finite difference scheme of the wave equation in the space of staggered-grid and the corresponding perfectly matched layer(PML) absorbing boundary conditions,realizing the simulation of seismic wave field for that kind of media.The simulation results showed that the method could accurately simulate the seismic wave propagation in the dual-phase HTI media and could get accurate snapshots and synthetic records.Additionally,the conclusion by analysis was that in the dual-phase anisotropic media,the propagation of elastic wave still showed the anisotropic feature and the porosity,the coefficient of viscosity and the density of solid-liquid coupling could mainly affect the amplitude and the morphology of slow longitudinal wave.
Based on the high-frequency limit of BISQ equation,this paper derived the dual-phase HTI media elastic wave equation that could be used in the arbitrary fracture azimuth angle and deduced the high-order finite difference scheme of the wave equation in the space of staggered-grid and the corresponding perfectly matched layer(PML) absorbing boundary conditions,realizing the simulation of seismic wave field for that kind of media.The simulation results showed that the method could accurately simulate the seismic wave propagation in the dual-phase HTI media and could get accurate snapshots and synthetic records.Additionally,the conclusion by analysis was that in the dual-phase anisotropic media,the propagation of elastic wave still showed the anisotropic feature and the porosity,the coefficient of viscosity and the density of solid-liquid coupling could mainly affect the amplitude and the morphology of slow longitudinal wave.
引文
[1]CRAMPINS.The dispersion of surface waves in multilayered anisotropic media[J].Geophysical Journal International,1970,21(3):387-402.
[2]GASSMANN F.Elastic waves through a packing of spheres[J].Geophysics,1951,16(4):673-685.
[3]BIOT M A.Theory of propagation of elastic waves in a fluid-saturated porous solid.I.low-frequency range[J].The Acous-tical Society of America,1956,28(2):168-178.
[4]BIOT M A.Theory of propagation of elastic waves in a fluid-saturated porous solid.Ⅱ.high-frequency range[J].The A-coustical Society of America,1956,28(2):179-191.
[5]BIOT M A.Mechanics of deformation and acoustic propagation in porous media[J].Journal of Applied Physics,1962,33(4):1482-1498.
[6]BIOT M A.Generalized theory of acoustic propagation in porous dissipative media[J].The Acoustical Society of America,1962,34(9A):1254-1264.
[7]DVORKINJ,NUR A.Dynamic poroelasticity:A unified model with the squirt and the Biot mechanisms[J].Geophysics,1993,58(4):524-533.
[8]YANG D H,ZHANG Z J.Poroelastic wave equation including the Biot/squirt mechanismand the solid/fluid coupling ani-sotropy[J].Wave Motion,2002,35:223-245.
[9]杨顶辉,张中杰.Biot和喷射流动耦合作用对各向异性弹性波的影响[J].科学通报,2000,12(45):1333-1340.YANG Dinghui,ZHANG Zhongjie.Biot and Squirt-flowcoupling influence on anisotropic elastic wave[J].Chinese ScienceBulletin,2000,45(23):1333-1340.
[10]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.YANG kuande,YANG Dinghui,WANG Shuqiang.Wave-field si mulation based on the Biot-Squirt equation[J].ChineseJournal of Geophysics,2002,56(6):853-861.
[11]杨宽德,杨顶辉,王书强.基于BISQ高频极限方程的交错网格法数值模拟[J].石油地球物理勘探,2002,37(5):463-468.YANG Kuande,YANG Dinghui,WANG Shuqiang.Numerical si mulation by staggered grid method for highfrequencyli m-ited BISQequation[J].Oil Geophysical Prospecting,2002,37(5):463-468.
[12]魏修成.双相各向异性介质中的地震波场研究[D].北京:中国石油大学,1995.
[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.LI U Yang,LI Chengshu.Research on elastic wave propagationin dual-phase anisotropic media with pseudo-spectral methodnumerical si mulation[J].Acta Seismologica Sinica,2000,22(2):132-138.
[14]轩义华,何樵登,林炎,等.双相各向异性介质正演研究[J].石油天然气学报,2006,28(6):69-72.XUAN Yihua,HE Qiaodeng,LIN Yan,et al.Research on forward modeling in dual-phase anisotropic media[J].Journal ofOil and Gas Technology,2006,28(6):69-72.
[15]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 Liangguo,MA Zaitian,CAO Jingzhong,et al.A staggered-grid high-order difference method of one-order elasticwave equation[J].Chinese Journal of Geophysics,2000,43(3):411-419.
[16]牟永光,裴正林.三维复杂介质地震数值模拟[M].北京:石油工业出版社,2005.
[17]COLLINO F,TSOGKA C.Application of the PML absorbing layer model to the linear elastodynamic problemin anisot-ropic heterogeneous media[J].Geophysics,2001,9(1):294-307.
[2]GASSMANN F.Elastic waves through a packing of spheres[J].Geophysics,1951,16(4):673-685.
[3]BIOT M A.Theory of propagation of elastic waves in a fluid-saturated porous solid.I.low-frequency range[J].The Acous-tical Society of America,1956,28(2):168-178.
[4]BIOT M A.Theory of propagation of elastic waves in a fluid-saturated porous solid.Ⅱ.high-frequency range[J].The A-coustical Society of America,1956,28(2):179-191.
[5]BIOT M A.Mechanics of deformation and acoustic propagation in porous media[J].Journal of Applied Physics,1962,33(4):1482-1498.
[6]BIOT M A.Generalized theory of acoustic propagation in porous dissipative media[J].The Acoustical Society of America,1962,34(9A):1254-1264.
[7]DVORKINJ,NUR A.Dynamic poroelasticity:A unified model with the squirt and the Biot mechanisms[J].Geophysics,1993,58(4):524-533.
[8]YANG D H,ZHANG Z J.Poroelastic wave equation including the Biot/squirt mechanismand the solid/fluid coupling ani-sotropy[J].Wave Motion,2002,35:223-245.
[9]杨顶辉,张中杰.Biot和喷射流动耦合作用对各向异性弹性波的影响[J].科学通报,2000,12(45):1333-1340.YANG Dinghui,ZHANG Zhongjie.Biot and Squirt-flowcoupling influence on anisotropic elastic wave[J].Chinese ScienceBulletin,2000,45(23):1333-1340.
[10]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.YANG kuande,YANG Dinghui,WANG Shuqiang.Wave-field si mulation based on the Biot-Squirt equation[J].ChineseJournal of Geophysics,2002,56(6):853-861.
[11]杨宽德,杨顶辉,王书强.基于BISQ高频极限方程的交错网格法数值模拟[J].石油地球物理勘探,2002,37(5):463-468.YANG Kuande,YANG Dinghui,WANG Shuqiang.Numerical si mulation by staggered grid method for highfrequencyli m-ited BISQequation[J].Oil Geophysical Prospecting,2002,37(5):463-468.
[12]魏修成.双相各向异性介质中的地震波场研究[D].北京:中国石油大学,1995.
[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.LI U Yang,LI Chengshu.Research on elastic wave propagationin dual-phase anisotropic media with pseudo-spectral methodnumerical si mulation[J].Acta Seismologica Sinica,2000,22(2):132-138.
[14]轩义华,何樵登,林炎,等.双相各向异性介质正演研究[J].石油天然气学报,2006,28(6):69-72.XUAN Yihua,HE Qiaodeng,LIN Yan,et al.Research on forward modeling in dual-phase anisotropic media[J].Journal ofOil and Gas Technology,2006,28(6):69-72.
[15]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 Liangguo,MA Zaitian,CAO Jingzhong,et al.A staggered-grid high-order difference method of one-order elasticwave equation[J].Chinese Journal of Geophysics,2000,43(3):411-419.
[16]牟永光,裴正林.三维复杂介质地震数值模拟[M].北京:石油工业出版社,2005.
[17]COLLINO F,TSOGKA C.Application of the PML absorbing layer model to the linear elastodynamic problemin anisot-ropic heterogeneous media[J].Geophysics,2001,9(1):294-307.
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