饱和度变化对弹性波在非饱和砂岩表面反射和透射的影响
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摘要
通过将等效流体模型和非饱和土Darcy定理引入Biot-Geertsma-Gassmann方程,研究弹性波由饱和孔隙介质向非饱和孔隙介质传播时,饱和度变化对弹性波反射系数、透射系数,以及弹性波携带的能量分配的影响。分别推导了振幅反射系数、透射系数以及能流密度的反射系数、透射系数的理论表达式,并在此基础上给出数值算例。计算结果表明,饱和度的轻微变动不仅对波的反射系数、透射系数产生巨大的影响,还将极大地影响到入射波的能量分配。得出的结论一方面在理论上揭示了土动力学研究中应更加重视饱和度变化的影响,另一方面对工程地震勘探中常用的地震反射波法、地震折射波法以及声波测井数据处理有实际工程意义。
After effective fluid model and Darcy′s law in partially saturated porous media are introduced to Biot-Geertsma-Gassmann(BGG) equation,the elastic wave propagating from a saturated porous medium to a Biot-type porous medium saturated by a liquid-gas mixture is investigated.Theoretical formulation is developed for the computation of amplitude reflection and transmission coefficients,and energy density flux reflection and transmission coefficients at the interface,which are considered as the functions of saturation degree and incidence angle.All the coefficients are studied in a wide range of frequencies and angles of incidence.Numerical results are given to illustrate the influence of saturation degree on amplitude reflection and transmission coefficients and energy splitting at plane interfaces.It′s found that even a slight decrease of complete saturation may lead to a substantial change of the reflection and transmission coefficients.The reflected and transmission type II waves of Biot at the contact interface of two media carry little energies at low frequencies,but they carry much more energies when frequency arises.The energy carried by reflected or transmission shear wave is affected slightly by frequency.The results imply that more attention should be paid to saturation degree effects in the interpretation of field observations.
After effective fluid model and Darcy′s law in partially saturated porous media are introduced to Biot-Geertsma-Gassmann(BGG) equation,the elastic wave propagating from a saturated porous medium to a Biot-type porous medium saturated by a liquid-gas mixture is investigated.Theoretical formulation is developed for the computation of amplitude reflection and transmission coefficients,and energy density flux reflection and transmission coefficients at the interface,which are considered as the functions of saturation degree and incidence angle.All the coefficients are studied in a wide range of frequencies and angles of incidence.Numerical results are given to illustrate the influence of saturation degree on amplitude reflection and transmission coefficients and energy splitting at plane interfaces.It′s found that even a slight decrease of complete saturation may lead to a substantial change of the reflection and transmission coefficients.The reflected and transmission type II waves of Biot at the contact interface of two media carry little energies at low frequencies,but they carry much more energies when frequency arises.The energy carried by reflected or transmission shear wave is affected slightly by frequency.The results imply that more attention should be paid to saturation degree effects in the interpretation of field observations.
引文
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[22]Campbell I J,Pitcher A S.Supplement to the proceedings of joint admiralty US navy meeting on hydro-ballistics[R].US:Navy,1955.8-28.
[23]Childs E C.An Introduction to the Physical Basis of Soil Water Phenomena[M].London:Wiley-Interscience,1969.493.
[24]Childs E C,Collis-George N.The permeability of porous materials[J].Proc.Royal Soc.(series A),1950,201:392-405.
[25]Carcione J M,Cavallini F,Santos J E,et al.Wave propagation in partially saturated porous media:simulation of a second slow wave[J].Wave Motion,2004,39:227-240.
[26]Stoll R D,Kan T K.Reflection of acoustic waves at a water-sediment interface[J].J.Acoust.Soc.Am.,1981,69(1):149-156.
[27]Deresiewicz H,Skalak R.On uniqueness in dynamic poroelasticity[J].Bulletin of the Seismological Society of America,1963,53(4):783-788.
[28]Dutta N C,Ode H.Seismic reflections from a gas-water contact[J].Geophysics,1983,48(2):148-162.
[29]Santos J E,Corbero J M,Ravazzoli C L,et al.Reflection and transmission coefficients in fluid-saturated porous media[J].J.Acoust.Soc.Am.,1992,92(4):1 911-1 923.
[2]邓涛,韩文峰,保翰璋.饱水大理岩的波速变化特性研究[J].岩石力学与工程学报,2000,19(6):762-765.(Deng Tao,Han Wenfeng,Bao Hanzhang.On the characteristics of wave velocity variations for marbles saturated in water[J].Chinese Journal of Rock Mechanics and Engineering,2000,19(6):762-765.(in Chinese))
[3]Gardner T N,Sills G C.An examination of parameters that govern the acoustic behavior of sea bed sediments containing gas bubbles[J].J.Acoust.Soc.Am.,2001,110(4):1 878-1 889.
[4]Ravazzoli C L,Santos J E,Carcione J M.Acoustic and mechanical response of reservoir rocks under variable saturation and effective pressure[J].J.Acoust.Soc.Am.,2003,113(4):1 801-1 811.
[5]Biot M A.Theory of propagation of elastic waves in a fluid-saturated porous solid[J].J.Acoust.Soc.Am.,1956,28(2):168-191.
[6]Gassmann F.Uber die elastizit at poroser medien[J].Vier Teljahrss-chrift der Naturforschenden Gesellschaft in Zurich,1951,96:1-23.(in German)
[7]Geertsma J.Velocity-log interpretation:the effect of rock bulk compressibility[J].Soc.Petr.Eng.J.,1961,1:235-248.
[8]Domenico S N.Effect of water saturation on seismic reflectivity of sand reservoirs encased in shale[J].Geophysics,1974,39(6):759-769.
[9]Mavko G,Mukerji T.Bounds on low-frequency seismic velocities in partially saturated rocks[J].Geophysics,1998,63(3):918-924.
[10]Murphy W F.Acoustic measures of partial gas saturation in tight sandstones[J].Journal of Geophysical Research,1984,89(B13):11 549-11 560.
[11]Cadoret T,Marion D,Zinszner B.Influence of frequency and fluid distribution on elastic wave velocities in partially saturated limestones[J].Journal of Geophysical Research,1995,100(B6):9 789-9 804.
[12]Yang J,Sato T.Influence of water saturation on horizontal and vertical motion at a porous soil interface induced by incident P wave[J].Soil Dynamics and Earthquake Engineering,2000,19(5):339-346.
[13]Yang J.Saturation effects on horizontal and vertical motions in a layered soil-bedrock system due to inclined SV waves[J].Soil Dynamics and Earthquake Engineering,2001,21(6):527-536.
[14]Ravazzoli C L.Analysis of the reflection and transmission coefficients in three-phase sandstone reservoirs[J].Journal of Computational Acoustics,2001,9(4):1 437-1 454.
[15]D.G.弗雷德隆德,H.拉哈尔佐.非饱和土力学[M].陈仲颐译.北京:中国建筑工业出版社,1997.(Fredlund D G,Rahardjo H.Soil Mechanics for Unsaturated Soils[M].Translated by Chen Zhongyi.Beijing:China Architecture and Building Press,1997.(in Chinese))
[16]Brooks R H,Corey A T.Hydraulic properties of porous media[R].Colorada:Colorada State University,1964.
[17]Klimentos T,McCann C.Relationships among compressional wave attenuation,porosity,clay content,and permeability in sandstones[J].Geophysics,1990,55(8):998-1 014.
[18]Klimentos T.The effects of porosity-permeability-clay content on the velocity of compressional waves[J].Geophysics,1991,56(12):1 930-1 939.
[19]Koning H L.Some observations on the modulus of compressibility of water[A].In:Proceedings of the Conference on the Settlement and Compressibility of Soils[C].Weisbaden,Germany:[s.n.],1963.33-36.
[20]Verruijt A.Elastic storage of aquifers[A].In:de Wiest R J M ed.Flow Through Porous Media[C].New York:Academic Press,1969.
[21]Silberman E.Sound velocity and attenuation in bubbly mixtures measured in standing waves tubes[J].J.Acoust.Soc.Am.,1957,29(8):925-933.
[22]Campbell I J,Pitcher A S.Supplement to the proceedings of joint admiralty US navy meeting on hydro-ballistics[R].US:Navy,1955.8-28.
[23]Childs E C.An Introduction to the Physical Basis of Soil Water Phenomena[M].London:Wiley-Interscience,1969.493.
[24]Childs E C,Collis-George N.The permeability of porous materials[J].Proc.Royal Soc.(series A),1950,201:392-405.
[25]Carcione J M,Cavallini F,Santos J E,et al.Wave propagation in partially saturated porous media:simulation of a second slow wave[J].Wave Motion,2004,39:227-240.
[26]Stoll R D,Kan T K.Reflection of acoustic waves at a water-sediment interface[J].J.Acoust.Soc.Am.,1981,69(1):149-156.
[27]Deresiewicz H,Skalak R.On uniqueness in dynamic poroelasticity[J].Bulletin of the Seismological Society of America,1963,53(4):783-788.
[28]Dutta N C,Ode H.Seismic reflections from a gas-water contact[J].Geophysics,1983,48(2):148-162.
[29]Santos J E,Corbero J M,Ravazzoli C L,et al.Reflection and transmission coefficients in fluid-saturated porous media[J].J.Acoust.Soc.Am.,1992,92(4):1 911-1 923.
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