基于临界孔隙度模型的地震波传播
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摘要
基于岩石物里学中临界孔隙度模型,建立一种简洁的均匀弹性流体饱和孔隙介质模型,进行地震波传播研究.首先定义了构建目标模型的基本力学模型:介绍了全孔隙度区间内基本力学模型和目标孔隙介质的含义,其中基本力学模型除了完全弹性固体模型S和完全弹性流体模型F还包括临界孔隙模型C.然后通过等效力学模型推出了目标力学模型介质本构关系的组分表达形式.文中分别通过直接求取弹性参数的表达形式和运用应力应变关系两种方法得到介质模型的本构关系,进而得到该模型波动方程的组分表达形式.最后对这种介质模型进行了地震波传播的数值模拟,结合模拟结果分析孔隙对地震波传播的影响.
A novel fluid saturated heterogeneous elastic porous media model was proposed based on the critical porosity model.It was used to study the seismic wave propagation in saturated porous media.Firstly,the target mechanical model and basic elements to construct it were introduced.The basic element contained critical porosity element C,beside elastic solid element S and elastic fluid model F.Then,the component form of constitutive relation of target porous media was derived.The constitutive relation′s component forms were derived in two ways: from the component form of elastic parameters in stiffness tensor and from the stress-strain relation in the porous media.With this constitutive relation,wave equation in this porous media was obtained.Finally,wave propagation in this model was simulated with FDTD method,and the effect of porosity was discussed.
A novel fluid saturated heterogeneous elastic porous media model was proposed based on the critical porosity model.It was used to study the seismic wave propagation in saturated porous media.Firstly,the target mechanical model and basic elements to construct it were introduced.The basic element contained critical porosity element C,beside elastic solid element S and elastic fluid model F.Then,the component form of constitutive relation of target porous media was derived.The constitutive relation′s component forms were derived in two ways: from the component form of elastic parameters in stiffness tensor and from the stress-strain relation in the porous media.With this constitutive relation,wave equation in this porous media was obtained.Finally,wave propagation in this model was simulated with FDTD method,and the effect of porosity was discussed.
引文
[1]Terzaghi K.Auftrieb und Kapillardruck an betoniertenTalsperren.Die Wasserwirtschaft,1933,(26):397-399.
[2]Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid:I.Low-frequency range.Acoust.Soc.Am.,1956,28(2):168-178.
[3]Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid:II.higher frequency range.Acoust.Soc.Am.,1956,28(2):179-191.
[4]Hajra S,Mukhopadhyay A.Reflection and refraction ofseismic waves incident obliquely at the boundary of a Liquid-saturated porous solid.Bulletin of the Seismological Societyof America,1982,72(5):1509-1533.
[5]Deresiewicz H.The effect of boundaries on wave propagationin a Liquid-filled porous solid:IV.surface waves in a half-space.Bull.Seism.Soc.Am,1962,52(3):627-638.
[6]Zhu X,McMechan G A.Numerical simulation of seismicresponses of poroelastic reservoirs using biot theory.Geophysics,1991,56(3):328-339.
[7]Berryman J G,Wang H F.The elastic coefficients of double-porosity models for fluid transport in jointed rock.Journalof Geophysical Research-Solid Earth,1995,100(B12):24611-24627.
[8]Berryman J G,Wang H F.Elastic wave propagation andattenuation in a double-porosity dual-permeability medium.International Journal of Rock Mechanics and MiningSciences,2000,37(1-2):63-78.
[9]Pride S R,Berryman J G,Harris J M.Seismic attenuationdue to wave-induced flow.Journal of Geophysical Research-Solid Earth,2004,109:B01201,doi:10.1029/2003JB002639.
[10]李伟华,赵成刚.饱和土沉积谷场地对平面SV波的散射问题的解析解.地球物理学报,2004,47(5):911-919.Li W H,Zhao C G.Scattering of plane SV waves by circulararc alluvial valleys with saturated soil deposits.Chinese J.Geophys.,2004,47(5):911-919.
[11]Chand S,Minshull T A,Gei D,et al.Elastic velocity modelsfor gas-hydrate-bearing sediments—a comparison.GeophysicalJournal International,2004,159(2):573-590.
[12]董俊,赵成刚.三维半球形凹陷饱和土场地对平面P波散射.地球物理学报,2005,48(3):680-688.Dong J,Zhao C G.An analytic solution for the diffraction ofplane P-wave by three-dimensional hemispherical canyons in afluid-saturated porous media half space.Chinese J.Geophys.(in Chinese),2005,48(3):680-688.
[13]魏修成,卢明辉,巴晶等.含黏滞流体各向异性孔隙介质中弹性波的频散和衰减.地球物理学报,2008,51(1):213-220.Wei X C,Lu M H,Ba J,et al.Dispersion and attenuation ofelastic waves in a viscous fluid-saturated anisotropic poroussolid.Chinese J.Geophys.(in Chinese),2008,51(1):213-220.
[14]陈颙,黄庭芳,刘恩儒.岩石物理学.安徽:中国科学技术大学出版社,2009.Chen Y,Huang T F,Liu E R.Rock Physics(in Chinese).Anhui:Press of University of Science and Technology ofChina,2009.
[15]Maxwell J C.On the dynamical theory of gases.Phil.Trans.Roy.Soc.London,1867,157:49-88.
[16]Kelvin L.Vortex statics.Collected works,1875,IV:115-128.
[17]Voigt W.Uber innere reibung fester korper,insbesondereder metalle.Annalen der Physik,1892,283(12):671-693.
[18]Nur A.Critical porosity and the seismic velocities in rocks.EOS.Trans.Am.Geophys Union,1992,73:43-66.
[19]Nur A,Marion D,Yin H.Wave velocites in sediments.//Hovem J M,Richardson M D,Stoll R D,eds.Shear Wave inMarine Sediments.Dordrecht:Kluwer Academic Publisher,1991:131-140.
[20]Mavko G,Mukerji T,Dvorkin J.The Rock PhysicsHandbook.New York:Cambridge University Press,1998.
[21]Dvorkin J,Prasad M,Sakai A,et al.Elasticity of marinesediments:Rock physics modeling.Geophysical ResearchLetters,1999,26(12):1781-1784.
[22]Mukerji T,Berryman J,Mavko G,et al.Differentialeffective medium modeling of rock elastic moduli with criticalporosity constraints.Geophysical Research Letters,1995,22(5):555-558.
[23]Chen Q,Nur A.Critical concentration models for porousmaterials.//Corapcioglu M Y,ed.Advance in PorousMedia.New York:Elsevier.1994:169-308.
[24]牛滨华,孙春岩,闫国英等.含气介质临界点,流体和骨架弹性参数的数值计算方法.地球物理学报,2010,53(6):1495-1501.Niu B H,Sun C Y,Yan G Y,et al.Numerical calculationmethod for getting critical point,pore fluid and frameworkparameters of gas-bearing media.Chinese J.Geophys.(inChinese),2010,53(6):1495-1501.
[25]牛滨华,郭继亮,孙春岩.CLYJ饱水石灰岩骨架和流体弹性参数估算.地球物理学报.2011,54(10):2652-2664.Niu B H,Guo J L,Sun C Y,et al.Estimating elasticparameters of framework and pore fluid from CLYJ saturatedlimestone samples.Chinese J.Geophys.,2011,54(10):2652-2664.
[26]Niu B,Sun C Y,Yan G Y,et al.Linear numericalcalculation method for obtaining critical point,pore fluid,andframework parameters of gas-bearing media.AppliedGeophysics,2009,6(4):319-326.
[27]贾冀辉,牛滨华,孙春岩等.水合物密度的数值计算及储层识别.现代地质,2011,25(6):1180-1186.Jia J H,Niu B H,Sun C Y,et al.Density calculation andreservoir identification of gas hydrates.Geoscience(inChinese),2011,25(6):1180-1186.
[28]牛滨华,孙春岩,李明.半空间介质与地震波传播.北京:石油工业出版社,2002.Niu B H,Sun C Y,Li M.Seismic Wave Propagation in HalfSpace Media(in Chinese).Beijing:Petroleum IndustryPress,2002.
[29]牛滨华,孙春岩.固体弹性介质与地震波传播:半空间均匀各向同性单相.北京:地质出版社,2005.Niu B H,Sun C Y.Seismic Wave Propagation in SinglePhase Homogeneous Isotropic Half Space Media(inChinese).Beijing:Geological Puldishing House,2005.
[30]牛滨华,孙晟,孙春岩等.Biot介质密度参数的容差密度表达.现代地质,2007,21(3):551-556.Niu B H,Sun S,Sun C Y,et al.Expressions of densityParameters of Biot medium with differential density.Geoscience(in Chinese),2007,21(3):551-556.
[31]邹荃,牛滨华,孙春岩等.饱水石灰岩骨架和流体弹性参数的估算.石油地球物理勘探,2011,46(5):763-768.Zou Q,Niu B H,Sun C Y,et al.Estimation of componentelastic parameters from saturated limestone samples.OilGeophysical Prospecting(in Chinese),2011,46(5):763-768.
[32]张艳,牛滨华,孙春岩等.基于典型饱水砂岩样品的多维空间多元统计密度反演方法.现代地质,2011,25(6):1174-1179.Zhang Y,Niu B H,Sun C Y,et al.Density inversion oftypical water-saturated sandstones with multivariatestatistical analysis in multidimensional space.Geoscience(inChinese),2011,25(6):1174-1179.
[33]Berge P A,Bonner B P,Berryman J G.Ultrasonic velocity-porosity relationships for sandstone analogs made from fusedglass beads.Geophysics,1995,60(1):108-119.
[2]Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid:I.Low-frequency range.Acoust.Soc.Am.,1956,28(2):168-178.
[3]Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid:II.higher frequency range.Acoust.Soc.Am.,1956,28(2):179-191.
[4]Hajra S,Mukhopadhyay A.Reflection and refraction ofseismic waves incident obliquely at the boundary of a Liquid-saturated porous solid.Bulletin of the Seismological Societyof America,1982,72(5):1509-1533.
[5]Deresiewicz H.The effect of boundaries on wave propagationin a Liquid-filled porous solid:IV.surface waves in a half-space.Bull.Seism.Soc.Am,1962,52(3):627-638.
[6]Zhu X,McMechan G A.Numerical simulation of seismicresponses of poroelastic reservoirs using biot theory.Geophysics,1991,56(3):328-339.
[7]Berryman J G,Wang H F.The elastic coefficients of double-porosity models for fluid transport in jointed rock.Journalof Geophysical Research-Solid Earth,1995,100(B12):24611-24627.
[8]Berryman J G,Wang H F.Elastic wave propagation andattenuation in a double-porosity dual-permeability medium.International Journal of Rock Mechanics and MiningSciences,2000,37(1-2):63-78.
[9]Pride S R,Berryman J G,Harris J M.Seismic attenuationdue to wave-induced flow.Journal of Geophysical Research-Solid Earth,2004,109:B01201,doi:10.1029/2003JB002639.
[10]李伟华,赵成刚.饱和土沉积谷场地对平面SV波的散射问题的解析解.地球物理学报,2004,47(5):911-919.Li W H,Zhao C G.Scattering of plane SV waves by circulararc alluvial valleys with saturated soil deposits.Chinese J.Geophys.,2004,47(5):911-919.
[11]Chand S,Minshull T A,Gei D,et al.Elastic velocity modelsfor gas-hydrate-bearing sediments—a comparison.GeophysicalJournal International,2004,159(2):573-590.
[12]董俊,赵成刚.三维半球形凹陷饱和土场地对平面P波散射.地球物理学报,2005,48(3):680-688.Dong J,Zhao C G.An analytic solution for the diffraction ofplane P-wave by three-dimensional hemispherical canyons in afluid-saturated porous media half space.Chinese J.Geophys.(in Chinese),2005,48(3):680-688.
[13]魏修成,卢明辉,巴晶等.含黏滞流体各向异性孔隙介质中弹性波的频散和衰减.地球物理学报,2008,51(1):213-220.Wei X C,Lu M H,Ba J,et al.Dispersion and attenuation ofelastic waves in a viscous fluid-saturated anisotropic poroussolid.Chinese J.Geophys.(in Chinese),2008,51(1):213-220.
[14]陈颙,黄庭芳,刘恩儒.岩石物理学.安徽:中国科学技术大学出版社,2009.Chen Y,Huang T F,Liu E R.Rock Physics(in Chinese).Anhui:Press of University of Science and Technology ofChina,2009.
[15]Maxwell J C.On the dynamical theory of gases.Phil.Trans.Roy.Soc.London,1867,157:49-88.
[16]Kelvin L.Vortex statics.Collected works,1875,IV:115-128.
[17]Voigt W.Uber innere reibung fester korper,insbesondereder metalle.Annalen der Physik,1892,283(12):671-693.
[18]Nur A.Critical porosity and the seismic velocities in rocks.EOS.Trans.Am.Geophys Union,1992,73:43-66.
[19]Nur A,Marion D,Yin H.Wave velocites in sediments.//Hovem J M,Richardson M D,Stoll R D,eds.Shear Wave inMarine Sediments.Dordrecht:Kluwer Academic Publisher,1991:131-140.
[20]Mavko G,Mukerji T,Dvorkin J.The Rock PhysicsHandbook.New York:Cambridge University Press,1998.
[21]Dvorkin J,Prasad M,Sakai A,et al.Elasticity of marinesediments:Rock physics modeling.Geophysical ResearchLetters,1999,26(12):1781-1784.
[22]Mukerji T,Berryman J,Mavko G,et al.Differentialeffective medium modeling of rock elastic moduli with criticalporosity constraints.Geophysical Research Letters,1995,22(5):555-558.
[23]Chen Q,Nur A.Critical concentration models for porousmaterials.//Corapcioglu M Y,ed.Advance in PorousMedia.New York:Elsevier.1994:169-308.
[24]牛滨华,孙春岩,闫国英等.含气介质临界点,流体和骨架弹性参数的数值计算方法.地球物理学报,2010,53(6):1495-1501.Niu B H,Sun C Y,Yan G Y,et al.Numerical calculationmethod for getting critical point,pore fluid and frameworkparameters of gas-bearing media.Chinese J.Geophys.(inChinese),2010,53(6):1495-1501.
[25]牛滨华,郭继亮,孙春岩.CLYJ饱水石灰岩骨架和流体弹性参数估算.地球物理学报.2011,54(10):2652-2664.Niu B H,Guo J L,Sun C Y,et al.Estimating elasticparameters of framework and pore fluid from CLYJ saturatedlimestone samples.Chinese J.Geophys.,2011,54(10):2652-2664.
[26]Niu B,Sun C Y,Yan G Y,et al.Linear numericalcalculation method for obtaining critical point,pore fluid,andframework parameters of gas-bearing media.AppliedGeophysics,2009,6(4):319-326.
[27]贾冀辉,牛滨华,孙春岩等.水合物密度的数值计算及储层识别.现代地质,2011,25(6):1180-1186.Jia J H,Niu B H,Sun C Y,et al.Density calculation andreservoir identification of gas hydrates.Geoscience(inChinese),2011,25(6):1180-1186.
[28]牛滨华,孙春岩,李明.半空间介质与地震波传播.北京:石油工业出版社,2002.Niu B H,Sun C Y,Li M.Seismic Wave Propagation in HalfSpace Media(in Chinese).Beijing:Petroleum IndustryPress,2002.
[29]牛滨华,孙春岩.固体弹性介质与地震波传播:半空间均匀各向同性单相.北京:地质出版社,2005.Niu B H,Sun C Y.Seismic Wave Propagation in SinglePhase Homogeneous Isotropic Half Space Media(inChinese).Beijing:Geological Puldishing House,2005.
[30]牛滨华,孙晟,孙春岩等.Biot介质密度参数的容差密度表达.现代地质,2007,21(3):551-556.Niu B H,Sun S,Sun C Y,et al.Expressions of densityParameters of Biot medium with differential density.Geoscience(in Chinese),2007,21(3):551-556.
[31]邹荃,牛滨华,孙春岩等.饱水石灰岩骨架和流体弹性参数的估算.石油地球物理勘探,2011,46(5):763-768.Zou Q,Niu B H,Sun C Y,et al.Estimation of componentelastic parameters from saturated limestone samples.OilGeophysical Prospecting(in Chinese),2011,46(5):763-768.
[32]张艳,牛滨华,孙春岩等.基于典型饱水砂岩样品的多维空间多元统计密度反演方法.现代地质,2011,25(6):1174-1179.Zhang Y,Niu B H,Sun C Y,et al.Density inversion oftypical water-saturated sandstones with multivariatestatistical analysis in multidimensional space.Geoscience(inChinese),2011,25(6):1174-1179.
[33]Berge P A,Bonner B P,Berryman J G.Ultrasonic velocity-porosity relationships for sandstone analogs made from fusedglass beads.Geophysics,1995,60(1):108-119.
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