裂缝、裂隙介质衰减频散研究
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摘要
为研究裂缝、裂隙介质中波致流引起的衰减,将裂缝看作背景孔隙岩石中非常薄且孔隙度非常高的层状介质,并等价成White周期层状模型.分别考虑不同类型的裂隙和孔隙之间的挤喷流影响,结合改进的Biot方程,推导得到裂缝裂隙介质的刚度与频率的关系.当缝隙中饱含流体时,介质的衰减和速度频散受裂缝、孔隙之间和裂隙、孔隙之间流体流动的显著影响.在低频极限下,裂缝裂隙介质的性质由各向异性Gassmann理论和挤喷流模型获得;而在非常高的频率时,由于缝隙中的压力来不及达到平衡,波致流的影响可忽略.分析表明,裂隙密度主要影响波的衰减,而裂隙纵横比主要控制优势衰减频率和速度显著变化的频率范围;由于不同裂隙的衰减机制不同,衰减和速度频散大小有所差异,但基本趋势相同.
This work studies the attenuation of seismic waves caused by wave-induced fluid flow in a cracked fractural medium.Fractures are regarded as very thin and porous layers in a porous background,and the fractured medium is equivalent to a periodically layered White model.Considering the influence of squirt-fluid between different types of cracks and pores,the relation between stiffness and frequency in the periodically layered medium is deduced by a modified version of Biot equation.When saturated with fluid,this model exhibits significant attenuation and velocity dispersion due to the wave-induced fluid flowing between fractures and pores or cracks and pores.Under the low frequency limit,the properties of the cracked fractural medium can be determined by the anisotropic Gassmann equation and squirt-fluid model.However at high frequencies,the effect of wave-induced flow can be ignored since the pressure in the cracks has not enough time to reach equilibrium.Analysis shows that wave attenuation is mainly affected by the density of cracks,while the frequency range of significant attenuation and velocity dispersion are mainly controlled by the crack aspect ratio.Owing to different crack attenuation mechanisms,the magnitudes of attenuation and velocity dispersion are different,while their general trends are the same.
This work studies the attenuation of seismic waves caused by wave-induced fluid flow in a cracked fractural medium.Fractures are regarded as very thin and porous layers in a porous background,and the fractured medium is equivalent to a periodically layered White model.Considering the influence of squirt-fluid between different types of cracks and pores,the relation between stiffness and frequency in the periodically layered medium is deduced by a modified version of Biot equation.When saturated with fluid,this model exhibits significant attenuation and velocity dispersion due to the wave-induced fluid flowing between fractures and pores or cracks and pores.Under the low frequency limit,the properties of the cracked fractural medium can be determined by the anisotropic Gassmann equation and squirt-fluid model.However at high frequencies,the effect of wave-induced flow can be ignored since the pressure in the cracks has not enough time to reach equilibrium.Analysis shows that wave attenuation is mainly affected by the density of cracks,while the frequency range of significant attenuation and velocity dispersion are mainly controlled by the crack aspect ratio.Owing to different crack attenuation mechanisms,the magnitudes of attenuation and velocity dispersion are different,while their general trends are the same.
引文
Bakulin A,Grechka V,Tsvankin I.2000.Estimation of fracture parameters from reflection seismic data-Part I:HTI model due to a single fracture set.Geophysics,65(6):1788-1802.
Berryman J G.1980.Confirmation of Biot′s theory.Applied Physics Letters,37(4):382-384.
Brajanovski M,Gurevich B,Schoenberg M.2005.A model for P-wave attenuation and dispersion in a porous medium permeated by aligned fractures.Geophysical Journal of the Royal Astronomical Society,163(1):372-384.
Brajanovski M,Müller T M,Gurevich B.2006.Characteristic frequencies of seismic attenuation due to wave-induced fluid flow in fractured porous media.Geophysical Journal of the Royal Astronomical Society,166(2):574-578.
Chapman M.2010.Frequency-dependent anisotropy due to mesoscale fractures in the presence of equant porosity.Geophysical Prospecting,51(5):369-379.
Chapman M,Liu E R,Li X Y.2010.The influence of fluid-sensitive dispersion and attenuation on AVO analysis.Geophysical Journal of the Royal Astronomical Society,167(1):89-105.
Gassmann F.1951.Uber die Elastizitt Por9ser Medien.Vierteljschr.Naturforsch.Ges.Zürich,96:1-23.
Guo J X,Rubino J G,Barbosa N D,et al.2017a.Seismic dispersion and attenuation in saturated porous rocks with aligned fractures of finite thickness:Theory and numerical simulationsPart 1:P-wave perpendicular to the fracture plane.Geophysics,83(1):WA 49-WA 62.
Guo J X,Rubino J G,Barbosa N D,et al.2018.Seismic dispersion and attenuation in saturated porous rocks with aligned fractures of finite thickness:Theory and numerical simulations-Part 2:Frequency-dependent anisotropy.Geophysics,83(1):WA63-WA71.
Guo J X,Rubino J G,Glubokovskikh S,et al.2017b.Effects of fracture intersections on seismic dispersion:theoretical predictions versus numerical simulations.GeophysicalProspecting,65(5):1264-1276.
Gurevich B,Brajanovski M,Galvin R J,et al.2010.P-wave dispersion and attenuation in fractured and porous reservoirsporoelasticity approach.Geophysical Prospecting,57(2):225-237.
Hsu C J,Schoenberg M.1993.Elastic waves through a simulated fractured medium.Geophysics,58(7):964-977.
Hudson J A.1980.Overall properties of a cracked solid.Mathematical Proceedings of the Cambridge Philosophical Society,88(2):371-384.
Jakobsen M.2004.The interacting inclusion model of wave-induced fluid flow.Geophysical Journal of the Royal Astronomical Society,158(3):1168-1176.
Lambert G,Gurevich B,Brajanovski M.2006.Attenuation and dispersion of P-waves in porous rocks with planar fractures:Comparison of theory and numerical simulations.Geophysics,71(3):N41-N45.
Li L,Yan S H,Liu Q M,et al.2018b.Micro-and macroscopic study of crack propagation in coal:theoretical and experimental results and engineering practice.Journal of Geophysics and Engineering,15(4):1706-1718.
Li S G,Du X H,Zhao P X,et al.2018a.Experimental study on crack evolution characteristics of rock-like materials under different strain rates.Journal of Geophysics and Engineering,15(5):2071-2078.
Mavko G,Mukerji T,Dvorkin J.2009.The Rock Physics Handbook:Tools for Seismic Analysis of Porous Media.Cambridge:Cambridge University Press.
Müller T M,Rothert E.2006.Seismic attenuation due to waveinduced flow:Why Qin random structures scales differently.Geophysical Research Letters,33(16):L16305,doi:10.1029/2006GL026789.
Schoenberg M.1998.Elastic wave behavior across linear slip interfaces.The Journal of the Acoustical Society of America,68(5):1516-1521.
Tang X M,Chen X L,Xu X K.2012.A cracked porous medium elastic wave theory and its application to interpreting acoustic data from tight formations.Geophysics,77(6):245-D252.
Wang X Q,Ge H K,Han P.2018.A new model for fracability evaluation with consideration of natural cracks.Journal of Geophysics and Engineering,15(4):1492-1505.
White J E.1975.Computed seismic speeds and attenuation in rocks with partial gas saturation.Geophysics,40(2):224-232.
White J E,Mihailova N,Lyakhovitsky F.2005.Low-frequency seismic waves in fluid-saturated layered rocks.The Journal of the Acoustical Society of America,57(S1):S30-S30.
Wu G C,Wu J L,Zong Z Y.2014.The attenuation of P wave in a periodic layered porous media containing cracks.Chinese Journal of Geophysics(in Chinese),57(8):2666-2677,doi:10.6038/cjg20140825.
Wu J L,Wu G C,Zong Z Y.2015.Attenuation of P waves in a porous medium containing various cracks.Chinese Journal of Geophysics(in Chinese),58(4):1378-1389,doi:10.6038/cjg20150424.
宋永佳,胡恒山.2013.裂隙挤喷流对孔隙介质排水体积模量的影响.力学学报,45(3):395-405,doi:10.6052/0459-1879-12-230.
唐晓明.2011.含孔隙、裂隙介质弹性波动的统一理论---Biot理论的推广.中国科学:地球科学,41(6):784-795.
吴国忱,吴建鲁,宗兆云.2014.周期性层状含孔隙、裂隙介质模型纵波衰减特征.地球物理学报,57(8):2666-2677,doi:10.6038/cjg20140825.
吴建鲁,吴国忱,宗兆云.2015.含混合裂隙、孔隙介质的纵波衰减规律研究.地球物理学报,58(4):1378-1389,doi:10.6038/cjg20150424.
Berryman J G.1980.Confirmation of Biot′s theory.Applied Physics Letters,37(4):382-384.
Brajanovski M,Gurevich B,Schoenberg M.2005.A model for P-wave attenuation and dispersion in a porous medium permeated by aligned fractures.Geophysical Journal of the Royal Astronomical Society,163(1):372-384.
Brajanovski M,Müller T M,Gurevich B.2006.Characteristic frequencies of seismic attenuation due to wave-induced fluid flow in fractured porous media.Geophysical Journal of the Royal Astronomical Society,166(2):574-578.
Chapman M.2010.Frequency-dependent anisotropy due to mesoscale fractures in the presence of equant porosity.Geophysical Prospecting,51(5):369-379.
Chapman M,Liu E R,Li X Y.2010.The influence of fluid-sensitive dispersion and attenuation on AVO analysis.Geophysical Journal of the Royal Astronomical Society,167(1):89-105.
Gassmann F.1951.Uber die Elastizitt Por9ser Medien.Vierteljschr.Naturforsch.Ges.Zürich,96:1-23.
Guo J X,Rubino J G,Barbosa N D,et al.2017a.Seismic dispersion and attenuation in saturated porous rocks with aligned fractures of finite thickness:Theory and numerical simulationsPart 1:P-wave perpendicular to the fracture plane.Geophysics,83(1):WA 49-WA 62.
Guo J X,Rubino J G,Barbosa N D,et al.2018.Seismic dispersion and attenuation in saturated porous rocks with aligned fractures of finite thickness:Theory and numerical simulations-Part 2:Frequency-dependent anisotropy.Geophysics,83(1):WA63-WA71.
Guo J X,Rubino J G,Glubokovskikh S,et al.2017b.Effects of fracture intersections on seismic dispersion:theoretical predictions versus numerical simulations.GeophysicalProspecting,65(5):1264-1276.
Gurevich B,Brajanovski M,Galvin R J,et al.2010.P-wave dispersion and attenuation in fractured and porous reservoirsporoelasticity approach.Geophysical Prospecting,57(2):225-237.
Hsu C J,Schoenberg M.1993.Elastic waves through a simulated fractured medium.Geophysics,58(7):964-977.
Hudson J A.1980.Overall properties of a cracked solid.Mathematical Proceedings of the Cambridge Philosophical Society,88(2):371-384.
Jakobsen M.2004.The interacting inclusion model of wave-induced fluid flow.Geophysical Journal of the Royal Astronomical Society,158(3):1168-1176.
Lambert G,Gurevich B,Brajanovski M.2006.Attenuation and dispersion of P-waves in porous rocks with planar fractures:Comparison of theory and numerical simulations.Geophysics,71(3):N41-N45.
Li L,Yan S H,Liu Q M,et al.2018b.Micro-and macroscopic study of crack propagation in coal:theoretical and experimental results and engineering practice.Journal of Geophysics and Engineering,15(4):1706-1718.
Li S G,Du X H,Zhao P X,et al.2018a.Experimental study on crack evolution characteristics of rock-like materials under different strain rates.Journal of Geophysics and Engineering,15(5):2071-2078.
Mavko G,Mukerji T,Dvorkin J.2009.The Rock Physics Handbook:Tools for Seismic Analysis of Porous Media.Cambridge:Cambridge University Press.
Müller T M,Rothert E.2006.Seismic attenuation due to waveinduced flow:Why Qin random structures scales differently.Geophysical Research Letters,33(16):L16305,doi:10.1029/2006GL026789.
Schoenberg M.1998.Elastic wave behavior across linear slip interfaces.The Journal of the Acoustical Society of America,68(5):1516-1521.
Tang X M,Chen X L,Xu X K.2012.A cracked porous medium elastic wave theory and its application to interpreting acoustic data from tight formations.Geophysics,77(6):245-D252.
Wang X Q,Ge H K,Han P.2018.A new model for fracability evaluation with consideration of natural cracks.Journal of Geophysics and Engineering,15(4):1492-1505.
White J E.1975.Computed seismic speeds and attenuation in rocks with partial gas saturation.Geophysics,40(2):224-232.
White J E,Mihailova N,Lyakhovitsky F.2005.Low-frequency seismic waves in fluid-saturated layered rocks.The Journal of the Acoustical Society of America,57(S1):S30-S30.
Wu G C,Wu J L,Zong Z Y.2014.The attenuation of P wave in a periodic layered porous media containing cracks.Chinese Journal of Geophysics(in Chinese),57(8):2666-2677,doi:10.6038/cjg20140825.
Wu J L,Wu G C,Zong Z Y.2015.Attenuation of P waves in a porous medium containing various cracks.Chinese Journal of Geophysics(in Chinese),58(4):1378-1389,doi:10.6038/cjg20150424.
宋永佳,胡恒山.2013.裂隙挤喷流对孔隙介质排水体积模量的影响.力学学报,45(3):395-405,doi:10.6052/0459-1879-12-230.
唐晓明.2011.含孔隙、裂隙介质弹性波动的统一理论---Biot理论的推广.中国科学:地球科学,41(6):784-795.
吴国忱,吴建鲁,宗兆云.2014.周期性层状含孔隙、裂隙介质模型纵波衰减特征.地球物理学报,57(8):2666-2677,doi:10.6038/cjg20140825.
吴建鲁,吴国忱,宗兆云.2015.含混合裂隙、孔隙介质的纵波衰减规律研究.地球物理学报,58(4):1378-1389,doi:10.6038/cjg20150424.