VTI介质准P波旋转交错有限差分数值模拟
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摘要
本文采用旋转交错网格差分格式对VTI(垂直对称轴的横向各向同性)介质准P波一阶应力-速度方程进行数值模拟。并在PML边界条件和稳定性条件下得出Marmousi等复杂模型的高精度波场快照和地震记录,分析了各向异性对地震波的影响。数值结果表明:旋转交错网格有限差分能获得高精度的地震模拟数据,PML边界有较好的吸收效果。
Using the rotated staggered-grid of finite difference form, the numerical modeling of the first-order stress-velocity equation of quasi-P wave in VTI(vertical axis of symmetry of the transversely isotropic) medium is achieved. Under the PML boundary conditions and the stability condition, high precision wave field snapshots and synthetic record of complex models such as Marmousi are obtained. Besides, we analyze the effect of the anisotropy on seismic wave. The results show that the rotated staggered-grid of finite difference can get high precision seismic simulation data, and the PML boundary has better absorption effect.
Using the rotated staggered-grid of finite difference form, the numerical modeling of the first-order stress-velocity equation of quasi-P wave in VTI(vertical axis of symmetry of the transversely isotropic) medium is achieved. Under the PML boundary conditions and the stability condition, high precision wave field snapshots and synthetic record of complex models such as Marmousi are obtained. Besides, we analyze the effect of the anisotropy on seismic wave. The results show that the rotated staggered-grid of finite difference can get high precision seismic simulation data, and the PML boundary has better absorption effect.
引文
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[19]陈浩,王秀明,赵海波.旋转交错网格有限差分及其完全匹配层吸收边界条件[J].科学通报,2006,51(17):1985-1994.Chen H,Wang XM,Zhao HB.A rotated staggered grid finite-difference with the absorbing boundary condition of a perfectly matched layer[J].Chinese Science Bulletin,2006,51(17):1985-1994.
[20]Alkhalifah T.An anisotropic Marmousi model[J].SEP Report,1997,95:265-283.
[2]Virieux J.P-SV wave propagation in heterogeneous media:Velocity-stress finite-difference method[J].Geophysics,1986,51(4):889-901.
[3]Saenger E,Bohlen T.Finite-difference modeling of viscoelastic and anisotropic wave propagation using the rotated staggered grid[J].Geophysics,2004,69(2):583-591.
[4]Saenger EH,Gold N,Shapiro SA.Modeling the propagation of elastic waves using a modified finite-difference grid[J].Wave Motion,2000,31(1):77-92.
[5]陈双全,王尚旭,李向阳,等.P-SV与P-P波的时间匹配[J].石油地球物理勘探,2010,45(4):497-501.Chen SQ,Wang SX,Li XY,et al.Time matching between P-SV wave and P-P wave[J].Oil Geophysical Prospecting,2010,45(4):497-501.
[6]梁锴,吴国忱,印兴耀,等.三维TTI介质波动方程分解[J].石油地球物理勘探,2009,44(1):19-27.Liang K,Wu GC,Yin XY,et al.Wave equation decomposition in 3-D TTI medium[J].Oil Geophysical Prospecting,2009,44(1):19-27.
[7]裴正林,王尚旭.任意倾斜各向异性介质中弹性波波场交错网格高阶有限差分法模拟[J].地震学报,2005,27(4):441-451.Pei ZL,Wang SX.A staggered-grid high-order finite-difference modeling for elastic wave field in arbitrary tilt anisotropic media[J].Acta Seismologica Sinica,2005,27(4):441-451.
[8]Alkhalifah T.An acoustic wave equation for anisotropic media[J].Geophysics,2000,65(4):1239-1250.
[9]Alkhalifah T.Acoustic approximations for processing in transversely isotropic media[J].Geophysics,1998,63(2):623-631.
[10]Hestholm S.Acoustic VTI modeling using high-order finite differences[J].Geophysics,2009,74(5):T67-T73.
[11]韩令贺,何兵寿.VTI介质一阶准P波方程正演模拟及边界条件[J].石油地球物理勘探,2010,45(6):819-825.Han LH,He BS.First-order Quasi-P wave equation forward modeling and boundary conditions in VTI medium[J].Oil Geophysical Prospecting,2010,45(6):819-825.
[12]吴国忱,梁锴,王华忠.VTI介质q P波广义高阶屏单程传播算子[J].石油地球物理勘探,2007,42(6):640-650.Wu GC,Liang K,Wang HZ.High-order one-way generalized-screen propagation operator of q P-wave in VTI medium[J].Oil Geophysical Prospecting,2007,42(6):640-650.
[13]吴国忱,梁锴.VTI介质q P波方程高精度有限差分算子[J].地球物理学进展,2007,22(3):896-904.Wu GC,Liang K.High precision finite difference operators for q P wave equation in VTI media[J].Progress in Geophysics,2007,22(3):896-904.
[14]严红勇,刘洋.黏弹TTI介质中旋转交错网格高阶有限差分数值模拟[J].地球物理学报,2012,55(4):1354-1365.Yan HY,Liu Y.Rotated staggered grid high-order finite-difference numerical modeling for wave propagation in viscoelastic TTI media[J].Chinese Journal of Geophysics,2012,55(4):1354-1365.
[15]吴国忱.各向异性介质地震波传播与成像[M].北京:中国石油大学出版社,2006.Wu GC.Seismic wave propagation and imaging in anisotropic medium[M].Beijing:China University of Petroleum Press,2006.
[16]董良国,马在田,曹景忠.一阶弹性波方程交错网格高阶差分解法稳定性研究[J].地球物理学报,2000,43(6):856-864.Dong LG,Ma ZT,Cao JZ.A study on stability of the staggered-grid high-ordered difference method of first-order elastic wave equation[J].Chinese Journal of Geophysics,2000,43(6):856-864.
[17]Berenger J.A perfectly matched layer for the absorption of electromagnetic waves[J].Journal of Computational Physics,1994,114(2):185-200.
[18]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.
[19]陈浩,王秀明,赵海波.旋转交错网格有限差分及其完全匹配层吸收边界条件[J].科学通报,2006,51(17):1985-1994.Chen H,Wang XM,Zhao HB.A rotated staggered grid finite-difference with the absorbing boundary condition of a perfectly matched layer[J].Chinese Science Bulletin,2006,51(17):1985-1994.
[20]Alkhalifah T.An anisotropic Marmousi model[J].SEP Report,1997,95:265-283.
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