TTI介质井间地震波场紧致交错网格高阶有限差分模拟及边界条件
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摘要
研究井间地震波场的形成过程以及波场的传播机理、规律,对于指导实际井间地震勘探有着重要的意义.从具有倾斜对称轴的横向各向同性介质(TTI)的二维三分量一阶速度-应力弹性波方程出发,采用高阶紧致交错网格差分算子对方程进行差分离散,得到了TTI介质中井间地震波场正演的高阶有限差分格式.并推导了TTI介质完全匹配层吸收边界条件公式和相应的紧致交错网格高阶差分格式,在此基础上实现了二维三分量TTI介质中井间地震波场模拟.数值算例表明:紧致交错网格高阶有限差分方法模拟的记录精度高,数值频散小,该方法能够精确的模拟复杂各向异性介质中的地震波传播过程,可以得到高精度的正演记录.完全匹配层吸收边界能有效地解决人工边界问题,是一种高效的边界吸收算法.
Study on the build-up process and the spreading mechanism of cross-hole seismic wave-field is important for guiding actual logging.Based on the two-dimensional three components first-order velocity-stress elastic wave equation in transversely isotropic media with a tilted symmetry axis(TTI),a high-order finite difference scheme was established using a high precision in compact staggered grid.The Perfectly Matched Layer(PML) absorbing boundary condition which fit the equation were thoroughly studied.Based on the studies above the forward modeling was realized for the first-order elastic wave equation in TTI medium. In summary,compact staggered-grid finite difference scheme could have a high degree of accuracy to simulate the spreading process of elastic wave in TTI medium.The perfectly matched layer(PML) is one of the best absorption boundary conditions which can effectively deal with the problem of article boundary.
Study on the build-up process and the spreading mechanism of cross-hole seismic wave-field is important for guiding actual logging.Based on the two-dimensional three components first-order velocity-stress elastic wave equation in transversely isotropic media with a tilted symmetry axis(TTI),a high-order finite difference scheme was established using a high precision in compact staggered grid.The Perfectly Matched Layer(PML) absorbing boundary condition which fit the equation were thoroughly studied.Based on the studies above the forward modeling was realized for the first-order elastic wave equation in TTI medium. In summary,compact staggered-grid finite difference scheme could have a high degree of accuracy to simulate the spreading process of elastic wave in TTI medium.The perfectly matched layer(PML) is one of the best absorption boundary conditions which can effectively deal with the problem of article boundary.
引文
[1]李建华,刘百红,张延庆,等.基于井间地震资料的储层精细描述方法[J].石油地球物理勘探,2008, 43(1):41-47.
[2]周建宇,何惺华,李安夏,等.罗家地区井间地震方法与效果[J].石油地球物理勘探,2001,36(6):745- 753.
[3]孔庆丰,王延光,左建军,等.井间地震有限角度叠加方法研究与应用[J].石油地球物理勘探,2007, 42(3):256-262.
[4]李万万,裴正林.井间地震弹性波传播特征数值模拟[J].物探与化探,2008,32(2):207-211.
[5]狄帮让,裴正林.盐丘模型弹性波方程正演模拟及波场特征分析[J].石油地球物理勘探,2010,45(6): 826-832.
[6]裴正林,何光明,谢芳.复杂地表复杂构造模型的弹性波方程正演模拟[J].石油地球物理勘探,2010, 45(6):807-818.
[7]祝贺君,张伟,陈晓非.二维各向异性介质中地震波场的高阶同位网格有限差分模拟[J].地球物理学报, 2009,52(6):1536-1546.
[8]汪利民,徐义贤,江贵.井中和井间地震波场正演模拟[J].石油物探,2009,48(2):146-152.
[9]Madariaga R.Dynamics of an expanding circular fault[J].BSSA,1976,66(3):639-666.
[10]Lele S K.Compact finite difference schemes with spectral-like resolution[J].J.Comput Phys,1992, 103:16-19.
[11]王书强,杨顶辉,杨宽德.弹性波方程的紧致差分方法[J].清华大学学报(自然科学版),2002,42(8): 1128-1131.
[12]马廷福,金涛,曹福军,等.三维双调和方程的高阶紧致差分格式及其多重网格方法[J].兰州理工大学学报,2010,36(3):142-147.
[13]葛永斌,刘国涛.三维Helmholtz方程的高阶隐式紧致差分方法[J].工程数学学报,2010,27(5):853- 858
[14]Nagarajan S.Lele S K,Ferziger J H.A robust high-order compact method for large eddy simulation [J].J.Comput.Phys,2003,191:392-419.
[15]Bendiks.A staggered compact finite difference formulation for the compressible Navier-Stokes equations[J].J.Comput.Phys,2005,208:675-690.
[16]牟永光,裴正林.三维复杂介质地震波数值模拟[M].北京:石油工业出版社,2005.
[17]Winterstein Z.Velocity anisotropy terminology for geophysicists[J].Geophysics,1990,55(8):1070- 1088.
[18]Zhu J L,Dorman J.Two-dimensional,three-component wave propagation in a transversely isotropic medium with arbitrary-orientation-finite-element modeling[J].Geophysics,2000,65(3):934-942.
[19]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.
[20]Du Q Z,Lin B,Hou B.Numerical modeling of seismic wavefields in transversely isotropic media with a compact staggered-grid finite difference scheme[J].Applied Geophysical,2009,6(1):42-49.
[21]赵海波,王秀明,王东,等.完全匹配层吸收边界在孔隙介质弹性波模拟中的应用[J].地球物理学报, 2007,50(2):581-591
[22]Collino F,Tsogka C.Application of the perfectly matched absorbing layer model to the linear elastodynamic problem in an isotropic heterogeneous media[J].Geophysics,2001,66(1):294-307.
[23]Zeng Y Q,He J Q,Liu Q H.The application of the perfectly matched layer in numerical modeling of wave propagation in poroelastic media[J].Geophysics,2001,66(4):1258-1266.
[2]周建宇,何惺华,李安夏,等.罗家地区井间地震方法与效果[J].石油地球物理勘探,2001,36(6):745- 753.
[3]孔庆丰,王延光,左建军,等.井间地震有限角度叠加方法研究与应用[J].石油地球物理勘探,2007, 42(3):256-262.
[4]李万万,裴正林.井间地震弹性波传播特征数值模拟[J].物探与化探,2008,32(2):207-211.
[5]狄帮让,裴正林.盐丘模型弹性波方程正演模拟及波场特征分析[J].石油地球物理勘探,2010,45(6): 826-832.
[6]裴正林,何光明,谢芳.复杂地表复杂构造模型的弹性波方程正演模拟[J].石油地球物理勘探,2010, 45(6):807-818.
[7]祝贺君,张伟,陈晓非.二维各向异性介质中地震波场的高阶同位网格有限差分模拟[J].地球物理学报, 2009,52(6):1536-1546.
[8]汪利民,徐义贤,江贵.井中和井间地震波场正演模拟[J].石油物探,2009,48(2):146-152.
[9]Madariaga R.Dynamics of an expanding circular fault[J].BSSA,1976,66(3):639-666.
[10]Lele S K.Compact finite difference schemes with spectral-like resolution[J].J.Comput Phys,1992, 103:16-19.
[11]王书强,杨顶辉,杨宽德.弹性波方程的紧致差分方法[J].清华大学学报(自然科学版),2002,42(8): 1128-1131.
[12]马廷福,金涛,曹福军,等.三维双调和方程的高阶紧致差分格式及其多重网格方法[J].兰州理工大学学报,2010,36(3):142-147.
[13]葛永斌,刘国涛.三维Helmholtz方程的高阶隐式紧致差分方法[J].工程数学学报,2010,27(5):853- 858
[14]Nagarajan S.Lele S K,Ferziger J H.A robust high-order compact method for large eddy simulation [J].J.Comput.Phys,2003,191:392-419.
[15]Bendiks.A staggered compact finite difference formulation for the compressible Navier-Stokes equations[J].J.Comput.Phys,2005,208:675-690.
[16]牟永光,裴正林.三维复杂介质地震波数值模拟[M].北京:石油工业出版社,2005.
[17]Winterstein Z.Velocity anisotropy terminology for geophysicists[J].Geophysics,1990,55(8):1070- 1088.
[18]Zhu J L,Dorman J.Two-dimensional,three-component wave propagation in a transversely isotropic medium with arbitrary-orientation-finite-element modeling[J].Geophysics,2000,65(3):934-942.
[19]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.
[20]Du Q Z,Lin B,Hou B.Numerical modeling of seismic wavefields in transversely isotropic media with a compact staggered-grid finite difference scheme[J].Applied Geophysical,2009,6(1):42-49.
[21]赵海波,王秀明,王东,等.完全匹配层吸收边界在孔隙介质弹性波模拟中的应用[J].地球物理学报, 2007,50(2):581-591
[22]Collino F,Tsogka C.Application of the perfectly matched absorbing layer model to the linear elastodynamic problem in an isotropic heterogeneous media[J].Geophysics,2001,66(1):294-307.
[23]Zeng Y Q,He J Q,Liu Q H.The application of the perfectly matched layer in numerical modeling of wave propagation in poroelastic media[J].Geophysics,2001,66(4):1258-1266.
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