双相介质中储层波场特征数值模拟研究
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摘要
根据双相介质弹性波方程,并对弹性波方程进行分离得到了膨胀波方程。利用高阶差分对膨胀波方程进行数值模拟,边界处理采用完全匹配层的吸收边界条件,算法实现了任意高阶差分和自动加载边界条件的纵波方程正演模拟。计算结果表明,在双相各向同性介质中存在快纵波、慢纵波,两种纵波有明显的区别,快纵波的速度远大于慢纵波的速度。在分界面上,快纵波要产生透射快纵波、透射转换慢纵波,反射快纵波、反射转换慢纵波。慢纵波具有很强的衰减性,耗散系数越小,慢纵波越明显,反之亦然。该算法的高阶差分形式可以显著地降低数值频散,有效提高地震波正演计算的精度,适应性好,操作简便灵活。
Based on the equation of elastic wave propagation in two-phase media and by separating the equation of elastic wave,the dilatational wave equation in two-phase in media is derived.The higher finite-difference (FD) and the perfectly matched layer boundary conditions are used to numerical simulation.The numerical simulation of the any higher-order difference and automatic loading boundary conditions is realized.The results of the calculation show that in the two-phase media,there are the fast dilatational wave and slow dilatational wave and they are different obviously.The velocity of the fast P wave is higher.On the interface,incident fast P-wave will generate two kinds of transmission and two kinds of reflection waves.The slow P-wave has intensive attenuation.The dissipation modulus is smaller,then the slow P-wave is more obvious,vice versa.The high-order FD pattern of this method can reduce the numerical dispersion markedly,and improve the accuracy of numerical simulation effectively and with good adaptability.The operation is convenient and flexible.
Based on the equation of elastic wave propagation in two-phase media and by separating the equation of elastic wave,the dilatational wave equation in two-phase in media is derived.The higher finite-difference (FD) and the perfectly matched layer boundary conditions are used to numerical simulation.The numerical simulation of the any higher-order difference and automatic loading boundary conditions is realized.The results of the calculation show that in the two-phase media,there are the fast dilatational wave and slow dilatational wave and they are different obviously.The velocity of the fast P wave is higher.On the interface,incident fast P-wave will generate two kinds of transmission and two kinds of reflection waves.The slow P-wave has intensive attenuation.The dissipation modulus is smaller,then the slow P-wave is more obvious,vice versa.The high-order FD pattern of this method can reduce the numerical dispersion markedly,and improve the accuracy of numerical simulation effectively and with good adaptability.The operation is convenient and flexible.
引文
[1]Amos Nur.双相介质中波的传播[M].许云,译.北京:石油工业出版社,1986.
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[12]迟新刚,贺振华,黄德济.基于商算子的地震裂缝检测方法[J].矿物岩石,2003,23(2):117-119.
[2]董良国,郭晓玲,吴晓丰,等.起伏地表弹性波传播有限差分法数值模拟[J].天然气工业,2007,27(10):38-41.
[3]王晓欢.声学各向异性介质中的S波[J].西南石油大学学报(自然科学版),2008,30(3):4-7.
[4]WANG Run-qiu,JIA Xiao-feng,HU Tian-yue.The precise finite difference method for seismic Modeling[J].Applied Geophysics,2004,1(2):69-74.
[5]Kelly K R.Synthetic seismograms-a finite difference ap-proach[J].Geophysics,1976,41(1):2-27.
[6]Clayton R,Engquist B.Absorbing boundary conditions for wave-equation migration[J].Geophysics,1980,45(5):895.
[7]Collino F,Tsogka C.Application of the perfectly matched absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media[J].Geophysics,2001,66(1):294-307.
[8]牟永光.储层地球物理学[M].北京:石油工业出版社,1996.
[9]熊煜,李录明,罗省贤.各向异性介质弹性波场正演及偏移[J].成都理工大学学报(自然科学版),2006,33(3):310-316.
[10]贺振华,熊晓军.等时叠加波动方程叠加正演[J].物探化探计算技术,2005,27(3):194-198.
[11]牟永光,裴正林.三维复杂介质地震数值模拟[M].北京:石油工业出版社,2005.
[12]迟新刚,贺振华,黄德济.基于商算子的地震裂缝检测方法[J].矿物岩石,2003,23(2):117-119.
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