黏弹双相介质中的松弛骨架模型
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摘要
本文基于Biot理论,考虑了多孔介质中固体骨架的松弛特征,引入了纵波品质因子、横波品质因子与耗散品质因子三参数来描述黏弹双相介质波动方程.采用虚谱法在地震频段进行了波场模拟,模拟结果表明:松弛骨架机制不仅适用于高频段,也可用于解释地震频段下的弹性波衰减现象,以描述固体微细颗粒的中观松弛特征.结合小生境遗传算法对三层模型24个介质参数进行了反演,反演结果表明:无噪波场的反演结果具有较高精度,对于含噪波场,取值在奇异点附近的介质参数反演精度降低.最后,对中国东部某地区的实际资料进行了浅层参数的反演,得到了该地区的表层固体体积模量、固体密度以及品质因子.
Based on the Biot theory,the relaxation effect of the solid skeleton is considered in porous media.We introduce the three parameters of P wave quality factor,S wave quality factor and diffusion quality factor to describe the poroviscoelastic wave equations.A pseudo-spectral method is used in wavefield forward modeling.Simulation results show that the skeleton-relaxed model not only works for the fluid saturated porous media in ultrasonic band.It can also be used for the explanation of elastic waves' high attenuation in seismic band,to approximate the solid particles' relaxation effect in a mesoscopic scale.Niche Genetic Algorithms are introduced in the inversion of 24 parameters for a three-layer model.Inversion results of the wavefield without noise hold high precision.But if white noise is added,the parameters whose true values are near singularity will get increased error.Finally,actual shot gather sections from some district in east China are processed.The solid bulk modulus,the solid density and the quality factors of the shallow layers are estimated.
Based on the Biot theory,the relaxation effect of the solid skeleton is considered in porous media.We introduce the three parameters of P wave quality factor,S wave quality factor and diffusion quality factor to describe the poroviscoelastic wave equations.A pseudo-spectral method is used in wavefield forward modeling.Simulation results show that the skeleton-relaxed model not only works for the fluid saturated porous media in ultrasonic band.It can also be used for the explanation of elastic waves' high attenuation in seismic band,to approximate the solid particles' relaxation effect in a mesoscopic scale.Niche Genetic Algorithms are introduced in the inversion of 24 parameters for a three-layer model.Inversion results of the wavefield without noise hold high precision.But if white noise is added,the parameters whose true values are near singularity will get increased error.Finally,actual shot gather sections from some district in east China are processed.The solid bulk modulus,the solid density and the quality factors of the shallow layers are estimated.
引文
[1]Liu Q R,Katsube N.The discovery of a second kind of rotational wave in a fluid-filled porous material.J.Acoust.Soc.Am.,1990,88(2):1045～1053
[2]刘洋,李承楚,牟永光.双相横向各向同性介质分界面上弹性波反射与透射问题研究.地球物理学报,2000,43(5):691～698Liu Y,Li C C,Mou Y G.Reflection and transmission of plane wave on an interface between dissimilar two-phase transversely isotropic media.Chinese.J.Geophys.(in Chinese),2000,43(5):691～698
[3]聂建新.含流体非饱和多孔隙介质的BISQ模型及储层参数反演[博士论文].北京:清华大学,2005Nie J X.The BISQ model in partially saturated porous mediumandinversion of reservoir parameters[Ph.D.thesis](in Chinese).Beijing:Tsinghua University,2005
[4]卢明辉.双相复杂介质中弹性波传播机理研究[博士论文].北京:清华大学,2006Lu M H.Mechanisms of elastic waves propagation in complex porous media[Ph.D.thesis](in Chinese).Beijing:Tsinghua University,2006
[5]裴正林.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.石油地球物理勘探,2006,41(2):137～143Pei Z L.Staggering grid high-order finite-difference modeling of elastic wave transmission in biphase anisotropic medium.Oil Geophysical Prospecting(in Chinese),2006,41(2):137～143
[6]Biot M A.Generalized theory of acoustic propagation in porous dissipative media.J.Acoust.Soc.Am.,1962,34(9):1254～1264
[7]Carcione J M,Helle H B.Numerical solution of the poroviscoelastic wave equation on a staggered mesh.Journal of Computational Physics,1999,154:520～527
[8]Carcione J M,Picotti S.P-wave seismic attenuation by slow-wave diffusion:Effects of inhomogeneous rock properties.Geophysics,2006,71(3):O1～O8
[9]Pride S R,Berryman J G,Harris J M.Seismic attenuation due to wave-inducedflow.Journal of Geophysical Research,2004,109,B01201doi:10.1029/2003JB002639
[10]Ba J,Nie J X,Cao H,Yang H Z.Mesoscopic fluid flow simulation in double-porosity rocks.Geophysical Research Letters,2008,35:L04303,doi:10.1029/2007GL032429
[11]White J E.Computed seismic speeds and attenuationin rocks with partial gas saturation.Geophysics,1975,40(2):224～232
[12]Carcione J M.Wave fieldsin real media:wave propagationin anisotropic,anelastic and porous media.Handbook of Geophysical Exploration,31.Oxford:Pergamon Press,2001.219～293
[13]Carcione J M,Arntsen B.Numerical simulation of the Biot slow wave in water-saturated viscoelastic sandstone.Geophysics,2001,66(3):890～896
[14]牟永光,裴正林.三维复杂介质地震数值模拟.北京:石油工业出版社,2005.62～71Mou Y G,Pei Z L.Seismic Numerical Modeling for3-D Complex Media(in Chinese).Beijing:Petroleum Industry Press,2005.62～71
[15]Carcione J M.Wave propagation in anisotropic linear viscoelastic media:theory and simulated wavefields.Geophys.J.Int.,1990,101:739～750
[16]杜启振,杨慧珠.裂缝性地层黏弹性地震多波波动方程.物理学报,2004,53(8):2801～2806Du Q Z,Yang H Z.Viscoelastic wave equations of seismic multi-wave in fractured media.Acta Physica Sinica(in Chinese),2004,53(8):2801～2806
[17]Carcione J M.Viscoacoustic wave propagation simulation in the earth.Geophysics,1988,53(4):769～777
[18]Dai N,Vafidis A,Kanasewich E R.Wave propagation in heterogeneous,porous media:A velocity-stress,finite-difference method.Geophysics,1995,60(2):327～339
[19]Carcione J M,Gerardo Quiroga-Goode.Some aspects of the physics and numerical modeling of Biot compressional waves.Journal of Computational Acoustics,1995,3(4):261～280
[20]Carcione J M,Gerardo Quiroga-Goode.Full frequency-range transient solutionfor compressional wavesin a fluid-saturated viscoacoustic porous medium.Geophysical Prospecting,1996,44(1):99～129
[21]何樵登,陶春辉.用遗传算法反演裂隙各向异性介质.石油物探,1995,34(3):46～50He Q D,Tao C H.Inversing fractured anisotropic media through a genetic algorithm.Geophysical Prospecting for Petroleum(in Chinese),1995,34(3):46～50
[22]Ba J,Yang H Z.Wave propagation simulation and parameters inversion in a viscoelastic porous media.Challenges in Seismic Rock Physics-Summer Workshop,China,Beijing,2007
[23]Hu B,Yang HZ.Niche Genetic Algorithmfor inversion on complex media.Challenges in Seismic Rock Physics-Summer Workshop,China,Beijing,2007
[24]张美根,王妙月,李小凡,杨晓春.时间域全波场各向异性弹性参数反演.地球物理学报,2003,46(1):96～100Zhang M G,Wamg M Y,Li X F,Yang X C.Full wavefield inversion of anisotropic elastic parametersinthe time domain.Chinese.J.Geophys.(in Chinese),2003,46(1):96～100
[2]刘洋,李承楚,牟永光.双相横向各向同性介质分界面上弹性波反射与透射问题研究.地球物理学报,2000,43(5):691～698Liu Y,Li C C,Mou Y G.Reflection and transmission of plane wave on an interface between dissimilar two-phase transversely isotropic media.Chinese.J.Geophys.(in Chinese),2000,43(5):691～698
[3]聂建新.含流体非饱和多孔隙介质的BISQ模型及储层参数反演[博士论文].北京:清华大学,2005Nie J X.The BISQ model in partially saturated porous mediumandinversion of reservoir parameters[Ph.D.thesis](in Chinese).Beijing:Tsinghua University,2005
[4]卢明辉.双相复杂介质中弹性波传播机理研究[博士论文].北京:清华大学,2006Lu M H.Mechanisms of elastic waves propagation in complex porous media[Ph.D.thesis](in Chinese).Beijing:Tsinghua University,2006
[5]裴正林.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.石油地球物理勘探,2006,41(2):137～143Pei Z L.Staggering grid high-order finite-difference modeling of elastic wave transmission in biphase anisotropic medium.Oil Geophysical Prospecting(in Chinese),2006,41(2):137～143
[6]Biot M A.Generalized theory of acoustic propagation in porous dissipative media.J.Acoust.Soc.Am.,1962,34(9):1254～1264
[7]Carcione J M,Helle H B.Numerical solution of the poroviscoelastic wave equation on a staggered mesh.Journal of Computational Physics,1999,154:520～527
[8]Carcione J M,Picotti S.P-wave seismic attenuation by slow-wave diffusion:Effects of inhomogeneous rock properties.Geophysics,2006,71(3):O1～O8
[9]Pride S R,Berryman J G,Harris J M.Seismic attenuation due to wave-inducedflow.Journal of Geophysical Research,2004,109,B01201doi:10.1029/2003JB002639
[10]Ba J,Nie J X,Cao H,Yang H Z.Mesoscopic fluid flow simulation in double-porosity rocks.Geophysical Research Letters,2008,35:L04303,doi:10.1029/2007GL032429
[11]White J E.Computed seismic speeds and attenuationin rocks with partial gas saturation.Geophysics,1975,40(2):224～232
[12]Carcione J M.Wave fieldsin real media:wave propagationin anisotropic,anelastic and porous media.Handbook of Geophysical Exploration,31.Oxford:Pergamon Press,2001.219～293
[13]Carcione J M,Arntsen B.Numerical simulation of the Biot slow wave in water-saturated viscoelastic sandstone.Geophysics,2001,66(3):890～896
[14]牟永光,裴正林.三维复杂介质地震数值模拟.北京:石油工业出版社,2005.62～71Mou Y G,Pei Z L.Seismic Numerical Modeling for3-D Complex Media(in Chinese).Beijing:Petroleum Industry Press,2005.62～71
[15]Carcione J M.Wave propagation in anisotropic linear viscoelastic media:theory and simulated wavefields.Geophys.J.Int.,1990,101:739～750
[16]杜启振,杨慧珠.裂缝性地层黏弹性地震多波波动方程.物理学报,2004,53(8):2801～2806Du Q Z,Yang H Z.Viscoelastic wave equations of seismic multi-wave in fractured media.Acta Physica Sinica(in Chinese),2004,53(8):2801～2806
[17]Carcione J M.Viscoacoustic wave propagation simulation in the earth.Geophysics,1988,53(4):769～777
[18]Dai N,Vafidis A,Kanasewich E R.Wave propagation in heterogeneous,porous media:A velocity-stress,finite-difference method.Geophysics,1995,60(2):327～339
[19]Carcione J M,Gerardo Quiroga-Goode.Some aspects of the physics and numerical modeling of Biot compressional waves.Journal of Computational Acoustics,1995,3(4):261～280
[20]Carcione J M,Gerardo Quiroga-Goode.Full frequency-range transient solutionfor compressional wavesin a fluid-saturated viscoacoustic porous medium.Geophysical Prospecting,1996,44(1):99～129
[21]何樵登,陶春辉.用遗传算法反演裂隙各向异性介质.石油物探,1995,34(3):46～50He Q D,Tao C H.Inversing fractured anisotropic media through a genetic algorithm.Geophysical Prospecting for Petroleum(in Chinese),1995,34(3):46～50
[22]Ba J,Yang H Z.Wave propagation simulation and parameters inversion in a viscoelastic porous media.Challenges in Seismic Rock Physics-Summer Workshop,China,Beijing,2007
[23]Hu B,Yang HZ.Niche Genetic Algorithmfor inversion on complex media.Challenges in Seismic Rock Physics-Summer Workshop,China,Beijing,2007
[24]张美根,王妙月,李小凡,杨晓春.时间域全波场各向异性弹性参数反演.地球物理学报,2003,46(1):96～100Zhang M G,Wamg M Y,Li X F,Yang X C.Full wavefield inversion of anisotropic elastic parametersinthe time domain.Chinese.J.Geophys.(in Chinese),2003,46(1):96～100
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