含裂隙孔隙介质中纵波传播特征研究
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摘要
基于准静态孔隙弹性理论和White模型,给出了垂直于层面传播纵波的频散方程。在周期性层状孔隙介质中采用具有高孔隙度的柔性层表征裂隙从而构成裂隙孔隙介质,利用周期性层状孔隙介质的频散方程并综合线性滑动裂隙模型,推导出裂隙孔隙介质中垂直于裂隙传播纵波的等效介质模型。裂隙孔隙介质中介观尺度上的流体流动作用所引起的纵波速度频散与衰减值远高于Biot流作用,特征频率或衰减峰值通常可位于地震频段。介质中纵波速度频散及逆品质因子均会随裂隙弱度(密度)的增大而增大,背景孔隙介质的渗透率与粘度以及裂隙的间隔与弱度共同决定特征频率的大小。
The periodic layered porous media is used to present the fractured porous media with mesoscopic inhomogeneities.Based on quasi-static poroelastic theory and White model,the effective medium model of P-wave propagating normal to the layer is given.The thinner layer in the periodic layered porous media can be substituted by a very thin and highly compliant layer to model fractures in a porous background.Compared with linear-slip fracture model,a dispersion equation for a P-wave propagating normal to fracture is given.The magnitude of velocity dispersion and energy attenuation of Pwave caused by wave induced pore fluid flow between pores and fractures are apparently larger than that of Biot fluid,and their peak value often lies in the seismic frequency band.The magnitude of velocity dispersion and attenuation of P-wave will increase monotonically with the increase of fracture weakness(fracture density).The characteristic frequency of the attenuation and velocity dispersion of P-wave depends both on the permeability and fluid viscosity of background porous media and on the fracture weakness and spacing.
The periodic layered porous media is used to present the fractured porous media with mesoscopic inhomogeneities.Based on quasi-static poroelastic theory and White model,the effective medium model of P-wave propagating normal to the layer is given.The thinner layer in the periodic layered porous media can be substituted by a very thin and highly compliant layer to model fractures in a porous background.Compared with linear-slip fracture model,a dispersion equation for a P-wave propagating normal to fracture is given.The magnitude of velocity dispersion and energy attenuation of Pwave caused by wave induced pore fluid flow between pores and fractures are apparently larger than that of Biot fluid,and their peak value often lies in the seismic frequency band.The magnitude of velocity dispersion and attenuation of P-wave will increase monotonically with the increase of fracture weakness(fracture density).The characteristic frequency of the attenuation and velocity dispersion of P-wave depends both on the permeability and fluid viscosity of background porous media and on the fracture weakness and spacing.
引文
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[10]Biot M A.Theory of propagation of elastic waves influid saturated-porous solid,I:low frequency range,Ⅱ:high frequency range[J].Journal of the Acous-tical Society of America,1956,28(2):168-191
[11]He T,Zou C,Pei F,et al.Laboratory study on fluidviscosity induced ultrasonic velocity dispersion inreservoir sandstones[J].Applied Geophysics,2010,7(2):114-126
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[13]Müller T B,Rother E.Seismic attenuation due towave-induced flow:why Q in random structuresscales differently[J].Geophysical Research Letters,2006,33:L16305
[14]Backus G E.Long-wave elastic anisotropy producedby horizontal layering[J].Journal of GeophysicalResearch,1962,67(11):4427-4441
[15]Schoenberg M,Sayers C M.Seismic anisotropy offractured rock[J].Geophysics,1994,60(6):1777-1805
[16]Krief M,Garat J J,Stellingwerff J,et al.A petro-physical interpretation using the velocities of P and Swaves(full-waveform sonic)[J].Log Analyst,1990,31(1):355-369
[17]Mavko G,Mukerji T,Dvorkin J.The rock physicshandbook:tools for seismic analysis of porous media[M].New York:Cambridge University Press,2009:370-376
[18]Lambert G,Gurevich B,Brajanovski M.Attenuationand dispersion of P-waves in porous rocks with pla-nar fractures:comparison of theory and numericalsimulations[J].Geophysics,2006,71(1):N41-N45
[2]Schoenberg M,Douma J.Elastic wave propagation inmedia with parallel fractures and aligned cracks[J].Geophysical Prospecting,1988,36(2):571-590
[3]Bakulin A,Tsvankin I,Grechka V.Estimation offracture parameters from reflection seismic data-partI:HTI model due to a single fracture set[J].Geo-physics,2000,65(6):1788-1802
[4]Dutta N C,OdéH.Attenuation and dispersion ofcompressional waves in fluid-filled porous rockswith partial gas saturation(White model)-partⅠ:Biot theory,part II:results[J].Geophysics,1979,44(6):1777-1805
[5]Norris A N.Low-frequency dispersion and attenua-tion in partially saturated rocks[J].Journal of A-coustical Society of America,1993,94(2):359-369
[6]Brajanovski M,Gurevich B,Schoenberg M.A modelfor P-wave attenuation and dispersion in a porousmedium permeated by aligned fractures[J].Geo-physical Journal International,2005,163(2):372-384
[7]Ba J,Cao H,Yao P N,et al.Double-porosity rockmodel and squirt flow in the laboratory frequencyband[J].Applied Geophysics,2008,5(4):261-276
[8]Yang D H,Zhang Z J.Poroelastic wave equation in-cluding the Biot/squirt mechanism and the solid/flu-id coupling anisotropy[J].Wave Motion,2002,35(1):223-245
[9]邓继新,王尚旭,杜伟.介观尺度孔隙流体流动作用对纵波传播特征的影响研究——以周期性层状孔隙介质为例[J].地球物理学报,2012,55(8):2716-2727Deng J X,Wang S X,Du W.A study of the influenceof mesoscopic pore fluid flow on the propagationproperties of compressional wave—a case of periodiclayered porous media[J].Chinese Journal of Geo-physics(in Chinese),2012,55(8):2716-2727
[10]Biot M A.Theory of propagation of elastic waves influid saturated-porous solid,I:low frequency range,Ⅱ:high frequency range[J].Journal of the Acous-tical Society of America,1956,28(2):168-191
[11]He T,Zou C,Pei F,et al.Laboratory study on fluidviscosity induced ultrasonic velocity dispersion inreservoir sandstones[J].Applied Geophysics,2010,7(2):114-126
[12]Carcione J M.Wave fields in real media wave propa-gation in anisotropic,anelastic,porous and electro-magnetic media[M].Amsterdam:Elsevier Science,2007:1-538
[13]Müller T B,Rother E.Seismic attenuation due towave-induced flow:why Q in random structuresscales differently[J].Geophysical Research Letters,2006,33:L16305
[14]Backus G E.Long-wave elastic anisotropy producedby horizontal layering[J].Journal of GeophysicalResearch,1962,67(11):4427-4441
[15]Schoenberg M,Sayers C M.Seismic anisotropy offractured rock[J].Geophysics,1994,60(6):1777-1805
[16]Krief M,Garat J J,Stellingwerff J,et al.A petro-physical interpretation using the velocities of P and Swaves(full-waveform sonic)[J].Log Analyst,1990,31(1):355-369
[17]Mavko G,Mukerji T,Dvorkin J.The rock physicshandbook:tools for seismic analysis of porous media[M].New York:Cambridge University Press,2009:370-376
[18]Lambert G,Gurevich B,Brajanovski M.Attenuationand dispersion of P-waves in porous rocks with pla-nar fractures:comparison of theory and numericalsimulations[J].Geophysics,2006,71(1):N41-N45
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