高阶交错网格非稳态相移叠后深度偏移
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摘要
为更好地研究复杂构造和速度分布条件下地震资料的精确偏移.在波场模拟方面,本文采用了高阶交错网格有限差分[1]推导了二维各向同性介质声波方程的数值模拟公式.并给出了声波方程完全匹配层吸收边界[2-5](PML).在偏移方面,本文介绍了一种能适应介质速度横向变化的非稳态相移算子(NSPS)[6]及其叠后深度偏移方法.并对简单的四层模型和Marmousi模型进行试算.偏移结果表明,该方法可以有效地处理复杂条件下的各向同性介质声波偏移问题.
In order to the better study of complex structure and the accurate seismic data migration in condition of the velocity distribution,In the wave field simulation,deducing the two dimension isotropic medium of sound wave equation numerical simulation formulas using the high order staggered grid finite difference.The completely matched layer absorption boundary of the sound wave equation is given.In the migration,this paper introduces a non stationary phase shift operator(NSPS) which can to medium speed lateral changes and its post stack depth migration method.And the simple four layer model and Marmousi model is worked out.Migration results show that this method can effectively deal with the complex isotropic medium sound waves migration problem.
In order to the better study of complex structure and the accurate seismic data migration in condition of the velocity distribution,In the wave field simulation,deducing the two dimension isotropic medium of sound wave equation numerical simulation formulas using the high order staggered grid finite difference.The completely matched layer absorption boundary of the sound wave equation is given.In the migration,this paper introduces a non stationary phase shift operator(NSPS) which can to medium speed lateral changes and its post stack depth migration method.And the simple four layer model and Marmousi model is worked out.Migration results show that this method can effectively deal with the complex isotropic medium sound waves migration problem.
引文
[1]孙成禹.粗糙界面和复杂地表的地震发射特征研究与数值模拟.博士论文,2001:33-40.Sun chen yu.Rough interface and complicated surface seismicemission characteristics research and numerical simulation.Doctoral dissertation,2001:33-40.
[2]王守东.声波方程完全匹配吸收边界[J].石油地球物理勘探,2003,38(1):31-34.Wang shou dong.Acoustic equation fit absorbing boundary[J].Oil geophysical prospecting,2003,38(1):31-34.
[3]Frank D,Hastings et al.Application of the perfectly boundarycondition to elastic wave propagation matched layer(PML)absorbing[J].Acoustical Society of America,1996,100(5):3061-3069.
[4]Dimitri Komatitsch,Jeroen Tromp.A perfectly matched layerabsorbing boundary condition for the second-order seismicwave equation[J].Geophys.J.Int,2003,154:146-153.
[5]Francis Collino,Chrysoula Tsogka.Application of the perfectlymatched absorbing layer model to the linear elastodynamicproblem in anisotropic heterogeneous media[J].Geophysics,2001,66(1):294-307.
[6]Ferguson R J,Margrave G F.Prestack depth migration bysymmetric nonstationary phase shift method[J].Geophysics,2002,67(2):594-603.
[7]刘定进,印兴耀.傅里叶有限差分法保幅叠前深度偏移方法.地球物理学报,2007,50(1):168-276,doi:LIU Ding_Jin;YIN Xing_Yao.A method of Fourier finite_difference preserved_amplitude prestack depth migration.Chinese J.Geophys.(in Chinese),2007,50(1):168-276,doi:
[8]Alford R M,Kelly K R,Boore D M.Accuracy of finite-difference modeling of the acoustic wabe equation[J].Geophysics,1974,39:838-842.
[9]Dablain M A.The application of high-order differencing to scalarwave equation[J].Geophysics,1986,51(1):54-66.
[10]Mufti I R.Large-scale three-dimensional seismic models andtheir interpretive significance[J].Geophysics,1990,55:1166-1182.
[11]Graves R W.Simulating seismic wave propagation in 3delasticmedia using staggered-grid finite difference[J].Bull.Seism.Soc.Am,1996,86:1091-1106.
[12]Reynolds A C.Boundary conditions for the numerical solutionof wave propagation problems[J].Geophysics,1978,43(6):895-904.
[13]Clayton R,Engquist B.Absorbing boundary condition for acousticand elastic wave equations[J].Bull.Seis.Soc.Am.,1977,67(6):1529-540.
[14]Higdon R L.Absorbing boundary conditions for elastic waves[J].Geophysics,1991,56:231-241.
[15]董良国.弹性波数值模拟中的吸收边界条件[J].石油地球物理勘探,1999,34(1):45-56.Dong guo liang.Elastic wave numerical modeling of theabsorbing boundary conditions[J].Oil geophysicalprospecting,1999,34(1):45-56.
[16]Cerjan C,Kosloff D,Kosloff R.A nonreflecting Boundarycondition for discrete acoustic and elastic wave equations[J].Geophysics,1985,50(4):705-708.
[17]Kosloff R,Kosloff D.Absorbing boundaries for wave propagationproblems[J].J.Comput.Phys.,1986,63:363-376.
[18]Berenger J P.A perfectly matched layer for the absorption ofelectromagnetics waves[J].J Comput.Phys,1994,114:185-200.
[19]刘礼农,陈小宏,张剑锋,刘洪.轴对称各向异性介质波动方程深度偏移的对称非平稳相移方法.地球物理学报,2007,50(1):277-284.LIU Li_Nong,GHEN Xiao_Hong,ZHANG Jian_Feng,LIUHong.Wave equation depth migration with symmetric non_stationary phase shift method in axi_symmetrical anisotropicmedia.Chinese J.Geophys.(in Chinese),2007,50(1):277-284.
[20]张扑,李幼铭,刘洪.几类叠前深度偏移方法的研究现状[J].地球物理学进展,2000,15(2):30-39.Zhang pu,Li you-min,Liu hong.A few kind of prestackdepth migration method research present situation[J].Geophysics progress,2000,15(2):30-39.
[21]Stoffa P L,Fokkema J T,de Luna Freire R M,Kessinger WP.Split-step Fouriermigration[J].Geophysics,1990,55:410-421.
[22]Gazdag J,Sguazerro P.Migration of seismic data by phaseshift plus interpolation[J].Geophysics,1984,49:124-131.
[23]Margrave G F.Theory of nonstationary linear filtering in theFourier domain with application to time-variant filtering[J].Geophysics,1998,63:244-259.
[24]张剑锋,卢宝坤,刘礼农.波动方程深度偏移的频率相关变步长延拓方法[J].地球物理学报,2008,51(1):221-227.ZHANG Jian-Feng,LU Bao-Kun,LIU Li-Nong.Frequency-dependent varying-step depth extrapolation scheme for waveequation based migration.Chinese J.Geophys.(in Chinese),2008,51(1):221-227.
[25]王昌龙,张叔伦,赵景霞,杨其强.基于控制照明的合成震源记录交互剩余偏移速度分析[J].地球物理学报,2007,50(3):860-867.WANG Chang_Long,ZHANG Shu_Lun,ZHAO Jing_Xia,YANG Qi_Qiang.Synthetic source record interactive residualmigration velocity analysis based on controlled illumination.Chinese J.Geophys.(in Chinese),2007,50(3):860-867.
[26]陈生昌,马在田,Wu Ru_Shan.波动方程偏移成像阴影的照明补偿[J].地球物理学报,2007,50(3):844-850.CHEN Sheng_Chang,MA Zai_Tian,WU Ru_Shan.Illumination compensation for wave equation migrationshadow.Chinese J.Geophys.(in Chinese),2007,50(3):844-850.
[2]王守东.声波方程完全匹配吸收边界[J].石油地球物理勘探,2003,38(1):31-34.Wang shou dong.Acoustic equation fit absorbing boundary[J].Oil geophysical prospecting,2003,38(1):31-34.
[3]Frank D,Hastings et al.Application of the perfectly boundarycondition to elastic wave propagation matched layer(PML)absorbing[J].Acoustical Society of America,1996,100(5):3061-3069.
[4]Dimitri Komatitsch,Jeroen Tromp.A perfectly matched layerabsorbing boundary condition for the second-order seismicwave equation[J].Geophys.J.Int,2003,154:146-153.
[5]Francis Collino,Chrysoula Tsogka.Application of the perfectlymatched absorbing layer model to the linear elastodynamicproblem in anisotropic heterogeneous media[J].Geophysics,2001,66(1):294-307.
[6]Ferguson R J,Margrave G F.Prestack depth migration bysymmetric nonstationary phase shift method[J].Geophysics,2002,67(2):594-603.
[7]刘定进,印兴耀.傅里叶有限差分法保幅叠前深度偏移方法.地球物理学报,2007,50(1):168-276,doi:LIU Ding_Jin;YIN Xing_Yao.A method of Fourier finite_difference preserved_amplitude prestack depth migration.Chinese J.Geophys.(in Chinese),2007,50(1):168-276,doi:
[8]Alford R M,Kelly K R,Boore D M.Accuracy of finite-difference modeling of the acoustic wabe equation[J].Geophysics,1974,39:838-842.
[9]Dablain M A.The application of high-order differencing to scalarwave equation[J].Geophysics,1986,51(1):54-66.
[10]Mufti I R.Large-scale three-dimensional seismic models andtheir interpretive significance[J].Geophysics,1990,55:1166-1182.
[11]Graves R W.Simulating seismic wave propagation in 3delasticmedia using staggered-grid finite difference[J].Bull.Seism.Soc.Am,1996,86:1091-1106.
[12]Reynolds A C.Boundary conditions for the numerical solutionof wave propagation problems[J].Geophysics,1978,43(6):895-904.
[13]Clayton R,Engquist B.Absorbing boundary condition for acousticand elastic wave equations[J].Bull.Seis.Soc.Am.,1977,67(6):1529-540.
[14]Higdon R L.Absorbing boundary conditions for elastic waves[J].Geophysics,1991,56:231-241.
[15]董良国.弹性波数值模拟中的吸收边界条件[J].石油地球物理勘探,1999,34(1):45-56.Dong guo liang.Elastic wave numerical modeling of theabsorbing boundary conditions[J].Oil geophysicalprospecting,1999,34(1):45-56.
[16]Cerjan C,Kosloff D,Kosloff R.A nonreflecting Boundarycondition for discrete acoustic and elastic wave equations[J].Geophysics,1985,50(4):705-708.
[17]Kosloff R,Kosloff D.Absorbing boundaries for wave propagationproblems[J].J.Comput.Phys.,1986,63:363-376.
[18]Berenger J P.A perfectly matched layer for the absorption ofelectromagnetics waves[J].J Comput.Phys,1994,114:185-200.
[19]刘礼农,陈小宏,张剑锋,刘洪.轴对称各向异性介质波动方程深度偏移的对称非平稳相移方法.地球物理学报,2007,50(1):277-284.LIU Li_Nong,GHEN Xiao_Hong,ZHANG Jian_Feng,LIUHong.Wave equation depth migration with symmetric non_stationary phase shift method in axi_symmetrical anisotropicmedia.Chinese J.Geophys.(in Chinese),2007,50(1):277-284.
[20]张扑,李幼铭,刘洪.几类叠前深度偏移方法的研究现状[J].地球物理学进展,2000,15(2):30-39.Zhang pu,Li you-min,Liu hong.A few kind of prestackdepth migration method research present situation[J].Geophysics progress,2000,15(2):30-39.
[21]Stoffa P L,Fokkema J T,de Luna Freire R M,Kessinger WP.Split-step Fouriermigration[J].Geophysics,1990,55:410-421.
[22]Gazdag J,Sguazerro P.Migration of seismic data by phaseshift plus interpolation[J].Geophysics,1984,49:124-131.
[23]Margrave G F.Theory of nonstationary linear filtering in theFourier domain with application to time-variant filtering[J].Geophysics,1998,63:244-259.
[24]张剑锋,卢宝坤,刘礼农.波动方程深度偏移的频率相关变步长延拓方法[J].地球物理学报,2008,51(1):221-227.ZHANG Jian-Feng,LU Bao-Kun,LIU Li-Nong.Frequency-dependent varying-step depth extrapolation scheme for waveequation based migration.Chinese J.Geophys.(in Chinese),2008,51(1):221-227.
[25]王昌龙,张叔伦,赵景霞,杨其强.基于控制照明的合成震源记录交互剩余偏移速度分析[J].地球物理学报,2007,50(3):860-867.WANG Chang_Long,ZHANG Shu_Lun,ZHAO Jing_Xia,YANG Qi_Qiang.Synthetic source record interactive residualmigration velocity analysis based on controlled illumination.Chinese J.Geophys.(in Chinese),2007,50(3):860-867.
[26]陈生昌,马在田,Wu Ru_Shan.波动方程偏移成像阴影的照明补偿[J].地球物理学报,2007,50(3):844-850.CHEN Sheng_Chang,MA Zai_Tian,WU Ru_Shan.Illumination compensation for wave equation migrationshadow.Chinese J.Geophys.(in Chinese),2007,50(3):844-850.
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