双相各向异性介质弹性波传播交错网格高阶有限差分法模拟
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摘要
含流体孔隙各向异性介质中的弹性波传播问题是目前石油勘探和地震学研究的难点之一。基于Biot理论,本文提出了二维双相任意倾斜各向异性介质三分量弹性波方程交错网格任意偶阶精度有限差分解法,并对均匀及两层双相VTI介质和TTI介质中的弹性波场进行了模拟。波场快照和合成记录表明:当横波源的偏振方向与TI介质的对称轴存在一定夹角、且耗散系数较小时,在固相与流相中存在快横波、慢横波、快纵波和慢纵波;双相TI介质中横波分裂现象及波前面尖角和三分叉现象与TI介质中的基本相同,只是黏滞相界中弹性波速度有所减小,且具有频散和衰减特性;从直达波转换为反射波后,该波型具有反射波的性质。
The issue of elastic wave transmission in ani-sotropic fluid-filled pore medium is one of difficulties in current petroleum exploration and study of seismology. Based on Biot theory, the paper presented staggering grid finite-difference algorithm with any even-order precision of 3-C elastic wave e-quation in 2-D biphase dip anisotropic medium,and conducted simulation of elastic wavefield in homogeneous and two-layered biphase VTI and TTI media. The snapshots of wavefields and synthetic seismograms showed that under the conditions of the certain angle between the polarization direction of S-wave source and the symmetric axis of TI medium with smaller scattering coefficient, there exist fast S-wave, slow S-wave, fast P-wave and slow P-wave in solid and fluid phases; the phenomenon of S-wave splitting and acute angle and triple-branch of wave front in biphase TI medium are basically similar to that in TI medium. The only difference is that the velocity of elastic wave become slower with the characters of dispersion and attenuation in viscid phase; the wave pattern is character of reflection when the reflecting wave is transformed from the direct wave.
The issue of elastic wave transmission in ani-sotropic fluid-filled pore medium is one of difficulties in current petroleum exploration and study of seismology. Based on Biot theory, the paper presented staggering grid finite-difference algorithm with any even-order precision of 3-C elastic wave e-quation in 2-D biphase dip anisotropic medium,and conducted simulation of elastic wavefield in homogeneous and two-layered biphase VTI and TTI media. The snapshots of wavefields and synthetic seismograms showed that under the conditions of the certain angle between the polarization direction of S-wave source and the symmetric axis of TI medium with smaller scattering coefficient, there exist fast S-wave, slow S-wave, fast P-wave and slow P-wave in solid and fluid phases; the phenomenon of S-wave splitting and acute angle and triple-branch of wave front in biphase TI medium are basically similar to that in TI medium. The only difference is that the velocity of elastic wave become slower with the characters of dispersion and attenuation in viscid phase; the wave pattern is character of reflection when the reflecting wave is transformed from the direct wave.
引文
[1] Biot M A. Theory of propagation of elastic waves in a fluid-saturated solid, I. Low-frequency range, II. high-frequency range. JAcoust Soc Amer ,1956, 28(2): 168 -191
[2]王尚旭．双相介质中弹性波问题有限元数值解和AVO 问题[博士学位论文]．石油大学(北京),1990
[3]刘洋等．双相各向异性介质中地震波场数值模拟． CPS／SEG／EAGE北京98国际地球物理研讨会论文 详细摘要集,1998,646～649
[4]杨顶辉．双相各向异性介质中弹性波方程的有限元解 法及波场模拟．地球物理学报。2002,45(4):575～583
[5] Zhu X and McMechan G A. Numerical simulation of seismic responses of poroelastic reservoirs using Biot theory. Geophysics, 1991,56(3) :328~339
[6] Dai N et al. Wave propagation in heterogeneous, porous media: A velocity-stress, finite-difference method. Geophysics, 1995, 60(2) :327-340
[7]王秀明等．利用高阶交错网格有限差分法模拟地震波 在非均匀孔隙介质中的传播．地球物理学报,2003,46 (6):842～849
[8]魏修成．双相各向异性介质中的地震波场研究[博士 学位论文]．石油大学(北京),1995
[9] Okaya D A et al. Elastic wave propagation in anisotrop-ic crustal material possessing arbitrary internal tilt. Geophys J Int, 2003,153:344 - 358
[10]裴正林．层状各向异性介质中横波分裂和再分裂数值 模拟．石油地球物理勘探,2006,41(1):17～25
[11] Zeng Y Q et al. The application of the perfectly matched layer in numerical modeling of wave propagation in poroelastic media. Geophysics, 2001,66(4): 1258 - 1266
[2]王尚旭．双相介质中弹性波问题有限元数值解和AVO 问题[博士学位论文]．石油大学(北京),1990
[3]刘洋等．双相各向异性介质中地震波场数值模拟． CPS／SEG／EAGE北京98国际地球物理研讨会论文 详细摘要集,1998,646～649
[4]杨顶辉．双相各向异性介质中弹性波方程的有限元解 法及波场模拟．地球物理学报。2002,45(4):575～583
[5] Zhu X and McMechan G A. Numerical simulation of seismic responses of poroelastic reservoirs using Biot theory. Geophysics, 1991,56(3) :328~339
[6] Dai N et al. Wave propagation in heterogeneous, porous media: A velocity-stress, finite-difference method. Geophysics, 1995, 60(2) :327-340
[7]王秀明等．利用高阶交错网格有限差分法模拟地震波 在非均匀孔隙介质中的传播．地球物理学报,2003,46 (6):842～849
[8]魏修成．双相各向异性介质中的地震波场研究[博士 学位论文]．石油大学(北京),1995
[9] Okaya D A et al. Elastic wave propagation in anisotrop-ic crustal material possessing arbitrary internal tilt. Geophys J Int, 2003,153:344 - 358
[10]裴正林．层状各向异性介质中横波分裂和再分裂数值 模拟．石油地球物理勘探,2006,41(1):17～25
[11] Zeng Y Q et al. The application of the perfectly matched layer in numerical modeling of wave propagation in poroelastic media. Geophysics, 2001,66(4): 1258 - 1266
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