复杂各向异性介质中的地震波场有限差分模拟
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摘要
从具有倾斜对称轴的横向各向同性介质(TTI)中的弹性波动方程出发,在交错网格空间中采用高阶差分算子对弹性波方程进行差分离散,得到了TTI介质中地震波正演的高阶有限差分格式.研究了PML吸收边界条件,推导了该边界条件在交错网格中的高阶差分格式,在此基础上实现了二维TTI介质中弹性波方程正演的多波正演.数值算例表明:该方法能够精确模拟弹性波在复杂各向异性介质中的传播过程,得到高精度的正演记录.
From the elastic wave equations in transversely isotropic medium with a tilted symmetry,a high-order finite difference scheme was established using a high precision operator in staggered-grid.Proposed an perfectly matched absorbing layer(PML) boundary conditions and studied its computing methods.Based on above two techniques,the forward modeling of seismic wave fields in complex anisotropic media was implemented.The numerical tests show that the method can simulate the seismic propagation accurately and can obtain high precision multi-component seismograms.
From the elastic wave equations in transversely isotropic medium with a tilted symmetry,a high-order finite difference scheme was established using a high precision operator in staggered-grid.Proposed an perfectly matched absorbing layer(PML) boundary conditions and studied its computing methods.Based on above two techniques,the forward modeling of seismic wave fields in complex anisotropic media was implemented.The numerical tests show that the method can simulate the seismic propagation accurately and can obtain high precision multi-component seismograms.
引文
[1]周熙襄,刘学才,蒋先艺.二维高斯射线束地震模型[J].石油地球物理勘探,1991,26(4):452-464.Zhou Xixiang,Liu Xuecai,Jiang Xianyi.Seismic model made by two-dimensional Gaussian beam method[J].Oil Geophysi-cal Prospecting,1991,26(4):452-464.
[2]岳玉波,孙建国,杨昊,等.起伏地表下初值射线追踪的实现[J].勘探地球物理进展,2007,30(5):388-391,398.Yue Yubo,Sun Jianguo,Yang Hao,et al.Realization of initial value ray tracing for rugged topography[J].Progress in Ex-ploration Geophysics,2007,30(5):388-391,398.
[3]杨顶辉,腾吉文.各向异性介质中三分量地震记录的FCT有限差分模拟[J].石油地球物理勘探,1997,32(2):181-190.Yang Dinghui,Teng Jiwen.FCTfinite difference modeling of three-component seismic records in anisotropic medium[J].OilGeophysical Prospecting,1997,32(2):181-190.
[4]董良国,马在田,曹景忠,等.一阶弹性波方程交错网格高阶差分解法[J].地球物理学报,2000,43(3):411-419.Dong Liangguo,Ma Zaitian,Cao Jingzhong,et al.A staggered-grid high-order difference method of one-order elastic waveequation[J].Chinese Journal of Geophysics,2000,43(3):411-419.
[5]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.Mou Yongguang,Pei Zhenglin.Seismic numerical modeling for 3D complex media[M].Beijing:Petroleum Industry Press,2005.
[6]朱生旺,曲寿利,魏修成,等.变网格有限差分弹性波方程数值模拟方法[J].石油地球物理勘探,2007,42(6):634-639.Zhu Shengwang,Qu Shouli,Wei Xiucheng,et al.Numeric simulation by grid-various finite-difference elastic wave equation[J].Oil Geophysical Prospecting,2007,42(6):634-639.
[7]刘礼农,崔凤林,张剑锋.三维复杂构造中地震波模拟的单程波方法[J].地球物理学报,2004,47(3):514-520.Liu Linong,Cui Fenglin,Zhang Jianfeng.Seismic modeling with one-way wave equation in 3D complex structures[J].ChinaJournal of Geophysics,2004,47(3):514-520.
[8]张金海,王卫民,赵连锋,等.傅里叶有限差分法三维波动方程正演模拟[J].地球物理学报,2007,50(6):1 864-1 862.Zhang Jinhai,Wang Weimin,Zhao Lianfeng,et al.Modeling3D scalar waves using the Fourier finite-difference method[J].China Journal of Geophysics,2007,50(6):1 864-1 862.
[9]Crampin S.A review of wave motion in anisotropic and cracked elastic media[J].Wave Motion,1981,3:343-391.
[10]Collino F,Tsogka C.Application of the perfectly matched absorbing layer model to the linear elastodynamic problem in aniso-tropic heterogeneous media[J].Geophysics,2001,66(1):294-307.
[2]岳玉波,孙建国,杨昊,等.起伏地表下初值射线追踪的实现[J].勘探地球物理进展,2007,30(5):388-391,398.Yue Yubo,Sun Jianguo,Yang Hao,et al.Realization of initial value ray tracing for rugged topography[J].Progress in Ex-ploration Geophysics,2007,30(5):388-391,398.
[3]杨顶辉,腾吉文.各向异性介质中三分量地震记录的FCT有限差分模拟[J].石油地球物理勘探,1997,32(2):181-190.Yang Dinghui,Teng Jiwen.FCTfinite difference modeling of three-component seismic records in anisotropic medium[J].OilGeophysical Prospecting,1997,32(2):181-190.
[4]董良国,马在田,曹景忠,等.一阶弹性波方程交错网格高阶差分解法[J].地球物理学报,2000,43(3):411-419.Dong Liangguo,Ma Zaitian,Cao Jingzhong,et al.A staggered-grid high-order difference method of one-order elastic waveequation[J].Chinese Journal of Geophysics,2000,43(3):411-419.
[5]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.Mou Yongguang,Pei Zhenglin.Seismic numerical modeling for 3D complex media[M].Beijing:Petroleum Industry Press,2005.
[6]朱生旺,曲寿利,魏修成,等.变网格有限差分弹性波方程数值模拟方法[J].石油地球物理勘探,2007,42(6):634-639.Zhu Shengwang,Qu Shouli,Wei Xiucheng,et al.Numeric simulation by grid-various finite-difference elastic wave equation[J].Oil Geophysical Prospecting,2007,42(6):634-639.
[7]刘礼农,崔凤林,张剑锋.三维复杂构造中地震波模拟的单程波方法[J].地球物理学报,2004,47(3):514-520.Liu Linong,Cui Fenglin,Zhang Jianfeng.Seismic modeling with one-way wave equation in 3D complex structures[J].ChinaJournal of Geophysics,2004,47(3):514-520.
[8]张金海,王卫民,赵连锋,等.傅里叶有限差分法三维波动方程正演模拟[J].地球物理学报,2007,50(6):1 864-1 862.Zhang Jinhai,Wang Weimin,Zhao Lianfeng,et al.Modeling3D scalar waves using the Fourier finite-difference method[J].China Journal of Geophysics,2007,50(6):1 864-1 862.
[9]Crampin S.A review of wave motion in anisotropic and cracked elastic media[J].Wave Motion,1981,3:343-391.
[10]Collino F,Tsogka C.Application of the perfectly matched absorbing layer model to the linear elastodynamic problem in aniso-tropic heterogeneous media[J].Geophysics,2001,66(1):294-307.
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