P波地震衰减的声子晶体效应
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摘要
研究储层中周期性复合介质的声带隙效应,给出一种地震波衰减机制.将周期分层孔隙介质模型看作一维声子晶体,采用改进的反射透射系数矩阵方法研究平面P波在其中传播时的声带隙现象.结果表明,当两种介质特征纵波速度不同时,在满足晶格厚度为平均纵波半波长整数倍的频率处,出现了一系列阻带,且低频阻带的宽度和衰减正比于该速度差异.不相溶流体的混合饱和与孔隙度的变化与颗粒和骨架参数的变化相比,其低频阻带具有更大的带宽和衰减.当晶格厚度为几米至几十米时,低频阻带处于地震频率范围内.
This paper deals with the acoustic band gaps in periodic composite materials,and gives out a new attenuation mechanism.Using the modified reflection and transmission matrices method,we considered the periodically stratified porous media as 1D phononic crystal,investigated the band gap properties of plane P-waves propagation.It is shown that there is a series of stop bands when the characteristic P-wave velocities of the two media are different and the stop band frequencies satisfy that lattice thickness is integer multiples of average P-wave half-wavelength.The bandwidth and attenuation of the low-frequency stop band correspond to the difference of velocity.And with the same velocity difference,they are much greater when the difference is caused by porosity variations and partial saturation,compared with grain-and frame-parameter variations.When the lattice thickness is in the magnitude of meters or decades meters,the low-frequency stop band is within the seismic band of frequencies.
This paper deals with the acoustic band gaps in periodic composite materials,and gives out a new attenuation mechanism.Using the modified reflection and transmission matrices method,we considered the periodically stratified porous media as 1D phononic crystal,investigated the band gap properties of plane P-waves propagation.It is shown that there is a series of stop bands when the characteristic P-wave velocities of the two media are different and the stop band frequencies satisfy that lattice thickness is integer multiples of average P-wave half-wavelength.The bandwidth and attenuation of the low-frequency stop band correspond to the difference of velocity.And with the same velocity difference,they are much greater when the difference is caused by porosity variations and partial saturation,compared with grain-and frame-parameter variations.When the lattice thickness is in the magnitude of meters or decades meters,the low-frequency stop band is within the seismic band of frequencies.
引文
[1]Biot M A.Mechanics of Deformation and Acoustic Propagation in Porous Media[J].J Appl Phys,1962,33:1482-1498.
[2]Mavko G M,Nur A.Wave Attenuation in Partially Saturated Rocks[J].Geophysics,1979,44(2):161-178.
[3]White J E.Computed Seismic Speeds and Attenuation in Rocks with Partial Gas Saturation[J].Geophysics,1975,40(2):224-232.
[4]Dutta N C,Od啨H.Attenuation and Dispersion of Compressional Waves in Fluid-filled Porous Rocks with Partial GasSaturation(White Model)——PartⅠ:Biot Theory[J].Geophysics,1979,44(11):1777-1788.
[5]Johnson D L.Theory of Frequency Dependent Acoustics in Patchy-saturated Porous Media[J].J Acoust Soc Am,2001,110(2):682-694.
[6]Pride S R,Berryman J G.Linear Dynamics of Double-porosity Dual-permeability Materials.Ⅰ.Governing Equationsand Acoustic Attenuation[J].Phys Rev E,2003,68:036603.
[7]Pride S R,Berryman J G,Harris J M.Seismic Attenuation Due to Wave-induced Flow[J].J Geophys Res,2004,109:B01201.
[8]Carcione J M,Picotti S.P-Wave Seismic Attenuation by Slow-wave Diffusion:Effects of Inhomogeneous Rock Properties[J].Geophysics,2006,71(3):O1-O8.
[9]White J E,Mikhaylova N G,Lyakhovitskiy F M.Low-frequency Seismic Waves in Fluid Saturated Layered Rocks[J].Physics of the Solid Earth,1975,11:654-659.
[10]Kushwaha M S,Halevi P,Dobrzynski L,et al.Acoustic Band Structure of Periodic Elastic Composites[J].Phys RevLett,1993,71:2022-2025.
[11]CHEN Xiao-fei,QUAN You-li,Harris J M.Seismogram Synthesis for Radially Layered Media Using the GeneralizedReflection/Transmission Coefficients Method:Theory and Applications to Acoustic Logging[J].Geophysics,1996,61(4):1150-1159.
[12]SONG Ruo-long,WANG Ke-xie,ZHANG Hong-bing,et al.A New Method for Calculation of Single Seismic Phase ofCylindrically Multilayered Media Including Liquid Interlayer[J].Chin Phys Lett,2007,24(5):1309-1312.
[2]Mavko G M,Nur A.Wave Attenuation in Partially Saturated Rocks[J].Geophysics,1979,44(2):161-178.
[3]White J E.Computed Seismic Speeds and Attenuation in Rocks with Partial Gas Saturation[J].Geophysics,1975,40(2):224-232.
[4]Dutta N C,Od啨H.Attenuation and Dispersion of Compressional Waves in Fluid-filled Porous Rocks with Partial GasSaturation(White Model)——PartⅠ:Biot Theory[J].Geophysics,1979,44(11):1777-1788.
[5]Johnson D L.Theory of Frequency Dependent Acoustics in Patchy-saturated Porous Media[J].J Acoust Soc Am,2001,110(2):682-694.
[6]Pride S R,Berryman J G.Linear Dynamics of Double-porosity Dual-permeability Materials.Ⅰ.Governing Equationsand Acoustic Attenuation[J].Phys Rev E,2003,68:036603.
[7]Pride S R,Berryman J G,Harris J M.Seismic Attenuation Due to Wave-induced Flow[J].J Geophys Res,2004,109:B01201.
[8]Carcione J M,Picotti S.P-Wave Seismic Attenuation by Slow-wave Diffusion:Effects of Inhomogeneous Rock Properties[J].Geophysics,2006,71(3):O1-O8.
[9]White J E,Mikhaylova N G,Lyakhovitskiy F M.Low-frequency Seismic Waves in Fluid Saturated Layered Rocks[J].Physics of the Solid Earth,1975,11:654-659.
[10]Kushwaha M S,Halevi P,Dobrzynski L,et al.Acoustic Band Structure of Periodic Elastic Composites[J].Phys RevLett,1993,71:2022-2025.
[11]CHEN Xiao-fei,QUAN You-li,Harris J M.Seismogram Synthesis for Radially Layered Media Using the GeneralizedReflection/Transmission Coefficients Method:Theory and Applications to Acoustic Logging[J].Geophysics,1996,61(4):1150-1159.
[12]SONG Ruo-long,WANG Ke-xie,ZHANG Hong-bing,et al.A New Method for Calculation of Single Seismic Phase ofCylindrically Multilayered Media Including Liquid Interlayer[J].Chin Phys Lett,2007,24(5):1309-1312.
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