二维随机孔隙岩石模型及其波场分析
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摘要
建立非均匀介质中随机孔隙岩石模型,引入局部半径(r)和局部孔隙密度(p)两个模型参数。用局部半径(r)表示每一个孔隙分布区的半径,用局部孔隙密度(p)表示孔隙介质在各个孔隙分布区中所占空间的百分比。这个模型可以模拟孔隙尺度具有空间统计分布的随机孔隙岩石介质,并将随机介质模型参数(r,p)与孔隙介质的宏观特性(弹性波速度)直接联系起来。结果表明,选择合适的模型参数能够描述实际复杂的孔隙岩石介质。不同形式的随机孔隙岩石模型中纵波速度和横波速度的变化程度各不相同。弹性波速度相对于大孔隙的响应更容易分辨,在一定的局部孔隙密度和局部半径下,孔隙分布的相对位置变化对波速几乎没有影响。横波对随机孔隙岩石的分辨率比纵波高,横波对随机介质各向异性,特别是对微裂隙相当敏感。
A new heterogeneous constitutive model of random porous rock is established by introducing two model parameters:the local radius(r) and the local porous density(p). In this model,the local radius(r) and the local porous density(p) are used to describe the length of the porous medium and the local porous space density in each distributed porous zone respectively. The elastic properties of rocks containing a random spatial distribution of porous size can be simulated by this model with the connection of the macro-mechanical properties(the elastic wave speeds) of the porous rocks and the model parameters(r and p). Numerical example indicates that the real heterogeneous medium can be modeled effectively as long as appropriate model parameters are given. Different heterogeneous random porous rocks have different scattering effects on wave speeds. The elastic wave speeds caused by larger pore are more distinguishable. The relative random distribution characteristics of pores hardly affect wave speeds under the same random distribution of the local porous density and local radius. The resolving power of S-wave on random porous rock is stronger than that of P-wave,and S-wave is more sensitive to anisotropy caused by micro-cracks.
A new heterogeneous constitutive model of random porous rock is established by introducing two model parameters:the local radius(r) and the local porous density(p). In this model,the local radius(r) and the local porous density(p) are used to describe the length of the porous medium and the local porous space density in each distributed porous zone respectively. The elastic properties of rocks containing a random spatial distribution of porous size can be simulated by this model with the connection of the macro-mechanical properties(the elastic wave speeds) of the porous rocks and the model parameters(r and p). Numerical example indicates that the real heterogeneous medium can be modeled effectively as long as appropriate model parameters are given. Different heterogeneous random porous rocks have different scattering effects on wave speeds. The elastic wave speeds caused by larger pore are more distinguishable. The relative random distribution characteristics of pores hardly affect wave speeds under the same random distribution of the local porous density and local radius. The resolving power of S-wave on random porous rock is stronger than that of P-wave,and S-wave is more sensitive to anisotropy caused by micro-cracks.
引文
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[15]奚先,姚姚.二维弹性随机介质中的波场特征[J].地球物理学进展,2005,20(1):147–154.(XI Xian,YAO Yao.The wave field characteristics in2D elastic random media[J].Progress in Geophysics,2005,20(1):147–154.(in Chinese))
[2]HUDSON J A.A higher order approximation to the wave propagation constants for cracked solid[J].Geophysical Journal of the Royal Astronomical Society,1986,87(2):265–274.
[3]ENRU L,HUDSON J A,TIM P.Equivalent medium representation of fractured rock[J].Journal of Geophysical Research,2000,105(B2):2981–3000.
[4]KORN M.Seismic wave in random media[J].Journal of Applied Geophysics,1993,29(3):247–269.
[5]TAE-KYUNG H.Scattering attenuation ratios of P and S waves in elastic media[J].Geophysical Journal international,2004,158(1):211–244.
[6]TAE-KYUNG H,KENNETT B L N.Scattering of elastic waves in media with a random distribution of fluid-filled cavities:theory and numerical modelling[J].Geophysical Journal International,2004,159(3):961–977.
[7]LUDEK K.Correlation functions of random media[J].Pure and Applied Geophysics,2002,159(8):1811–1831.
[8]YOMOGIDA K,BENITES R.Scattering of seismic waves by cracks with the boundary integral method[J].Pure and Applied Geophysics,2002,159(8):1771–1789.
[9]CHERNOV L A.Wave propagation in random medium[M].New York:McGraw-Hill,1960.
[10]韩开锋,曾新吾.边界元法模拟含随机分布裂纹介质中波的传播[J].岩土工程学报,2006,28(7):922–925.(HAN Kaifeng,ZENG Xinwu.Boundary element modeling of elastic waves propagating in the media with randomly distributed cracks[J].Chinese Journal of Geotechnical Engineering,2006,28(7):922–925.(in Chinese))
[11]董敏煜.多波多分量地震勘探[M].北京:石油工业出版社,2002.(DONG Minyu.Multiwave and multicomponent seismology exploration[M].Beijing:Petroleum Industy Press,2002.(in Chinese))
[12]IKELLE L,YUNG S,DAUBE F.2D random media with ellipsoidal autocorrelation function[J].Geophysics,1993,58(9):1359–1372.
[13]KARAL F C,KELLER J B.Elastic,electromagnetic,and other waves in a random medium[J].Journal of Mathematical Physics,1964,5(4):537–547.
[14]LERCHE I,PETROY D.Multiple scattering of seismic waves in fractured media:velocity and effective attenuation of the coherent components of P waves and S wave[J].Pure and Applied Geophysics,1986,124(6):975–1019.
[15]奚先,姚姚.二维弹性随机介质中的波场特征[J].地球物理学进展,2005,20(1):147–154.(XI Xian,YAO Yao.The wave field characteristics in2D elastic random media[J].Progress in Geophysics,2005,20(1):147–154.(in Chinese))
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