近似解析离散化方法的粘弹声波方程数值模拟及波场特征分析
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摘要
地层的粘弹性对地震波产生的吸收和衰减规律非常复杂,所以研究地震波在粘弹性介质中的传播规律对地震勘探有着重要的意义。近似解析离散化方法是近年来出现的一种有限差分数值模拟方法,籍此探讨了几种近似解析离散化方法的原理和过程。通过与一维粘弹声波方程解析解的对比,认为改进的近似解析离散化方法(INAD)的精度、稳定性和计算效率更具优势,并将其首次应用于二维粘弹声波方程数值模拟。通过数值模拟,重点分析了声波振幅、频率、频带宽度随品质因子及传播距离的衰减规律,粘弹介质中的地震波不仅因波前扩散导致振幅衰减,还因吸收作用导致振幅和频率同时衰减,利用其衰减特征可以指导含油气储层的预测。
Viscoelasticity of the media has a very complicated relationship with the absorption and attenuation of seismic wave energy.Therefore,the research on the propagation law of seismic waves in the stratigraphic equivalent media carries great significance to the seismic exploration.Nearly-analytic discrete method is a finite-difference numerical simulation method developed in recent years.In this paper,the author firstly explored the principles and process of four different nearly-analytic discrete methods.In comparison with the one-dimensional analytical solutions,the improved nearly-analytic discrete method(INAD)was proved to excel in precision,stability and computational efficiency.Then INAD was applied to the numerical simulation of 2D viscoelastic acoustic wave equation for the first time.With the simulated viscoelastic wave field,the author focused on analyzing the propagation law of the amplitude,frequency and bandwidth of the acoustic wave with the change of Qvalues and propagation distance The amplitude of the seismic wave in the viscoelastic medium reduces not only due to the wavefront diffusion,but also the absorption which attenuates the frequency at the same time.These attenuation characteristics can guide the prediction of the oil and gas reservoir.The amplitude of the seismic wave in the viscoelastic medium reduces not only due to the wavefront diffusion,but also the absorption which attenuates the frequency at the same time.These attenuation characteristics can guide the prediction of the oil and gas reservoir.
Viscoelasticity of the media has a very complicated relationship with the absorption and attenuation of seismic wave energy.Therefore,the research on the propagation law of seismic waves in the stratigraphic equivalent media carries great significance to the seismic exploration.Nearly-analytic discrete method is a finite-difference numerical simulation method developed in recent years.In this paper,the author firstly explored the principles and process of four different nearly-analytic discrete methods.In comparison with the one-dimensional analytical solutions,the improved nearly-analytic discrete method(INAD)was proved to excel in precision,stability and computational efficiency.Then INAD was applied to the numerical simulation of 2D viscoelastic acoustic wave equation for the first time.With the simulated viscoelastic wave field,the author focused on analyzing the propagation law of the amplitude,frequency and bandwidth of the acoustic wave with the change of Qvalues and propagation distance The amplitude of the seismic wave in the viscoelastic medium reduces not only due to the wavefront diffusion,but also the absorption which attenuates the frequency at the same time.These attenuation characteristics can guide the prediction of the oil and gas reservoir.The amplitude of the seismic wave in the viscoelastic medium reduces not only due to the wavefront diffusion,but also the absorption which attenuates the frequency at the same time.These attenuation characteristics can guide the prediction of the oil and gas reservoir.
引文
[1]CERVENY V.Seismic rays and ray intensities in inhomogeneous anisotropic media[J].Geophysical Journal International,1972,29(1):1-33
[2]KOSLOFF D D,BAYSAL E.Forward modeling by a Fourier method[J].Geophysics,1982,47(10):1402-1412
[3]RESHEF M,KOSLOFF D D,EDWARDS M,et al.Three dimensional elastic modeling by the Fourier method[J].Geophysics,1988,53(9):1184-1193
[4]DRAKE L A.Rayleigh waves at a continental boundary by the finite element method[J].Bulletin of the Seismological Society of America,1972,62(5):1259-1268
[5]BOUCHON M,COUTANT O.Calculation of synthetic seismograms in a laterally varying medium by the boundary element-discrete wavenumber method[J].Bulletin of the Seismological Society of America,1994,84(6):1869-1881
[6]KOMATISSCH D,BARNES C,TROMP J.Simulation of anisotropic wave propagation based upon a spectral element method[J].Geophysics,2000,65(4):1251-1260
[7]ALTERMAN Z,KARAL F C.Propagation of seismic wave in layered media by finite difference methods[J].Bulletin of the Seismological Society of America,1968,58(1):367-398
[8]KELLY K R,WARD R W,TREITEL S,et al.Synthetic seismograms:a finite-difference approach[J].Geophysics,1976,41(1):2-27
[9]VIRIEUX J.P-SV wave propagation in heterogeneous media:velocity-stress finite-difference method[J].Geophysics,1986,51(4):889-901
[10]GRAVES R W.Simulation seismic wave propagation in3Delastic media using staggered-grid finite differences[J].Bulletin of the Seismological Society of America,1996,86(4):1091-1106
[11]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):411-419DONG L G,MA Z T,CAO J Z,et al.The staggeredgrid high-order difference method of first-order elastic equation[J].Chinese Journal of Geophysics,2000,43(3):411-419
[12]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):856-864DONG L G,MA Z T,CAO J Z.The stability study of the staggered-grid high-order difference method of first-order elastic equation,[J].Chinese Journal of Geophysics,2000,43(6):856-864
[13]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):46-56DONG L G.Absorptive boundary condition in elasticwave numerical modeling[J].Oil Geophysical Prospecting,1999,34(1):46-56
[14]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):1128-1131WANG S Q,YANG D H,YANG K D.Compact finite difference scheme for elastic equations[J].Journal of Tsinghua University(Science and Technology),2002,42(8):1128-1131
[15]SAENGER E H,GOLD N,SHAPIRO S A.Modeling the propagation of elastic waves using a modified finitedifference grid[J].Wave Motion,2000,31(1):77-92
[16]SAENGER E H,BOHLEN T.Finite-difference modeling of viscoelastic and anisotropic wave propagation using the rotated staggered grid[J].Geophysics,2004,69(2):583-591
[17]KONDOH Y,HOSAKA Y,ISHII K.Kernel optimum nearly-analytical discrimination algorithm applied to parabolic and hyperbolic equations[J].Computers&Mathematics with Applications,1994,27(3):59-90
[18]杨顶辉,滕吉文,张中杰.三分量地震波场的近似解析离散模拟技术[J].地球物理学报,1996,39(增刊1):283-291YANG D H,TENG G W,ZHANG Z J.Nearly-analytical discretization modeling technique of 3-component seismic wave-fields[J].Chinese Journal of Geophysics,1996,39(S1):283-291
[19]YANG D H,TENG J W,ZHANG Z J,et al.A nearlyanalytic discrete method for acoustic and elastic wave equation[J].Bulletin of the Seismological Society of A-merica,2003,93(2):882-890
[20]YANG D H,LU M,WU R S,et al.An optimal nearlyanalytic discrete method for 2D acoustic and elastic wave equations[J].Bulletin of the Seismological Society of America,2004,94(5):1982-1991
[21]YANG D H,SONG G J,LU M.Optimally accurate nearly-analytic discrete scheme for wave-filed simulation in 3Danisotropic media[J].Bulletin of the Seismological Society of America,2007,97(5):1557-1569
[22]YANG D H,SONG G J,CHEN S,et al.An improved nearly analytical discrete method:an efficient tool to simulate the seismic response of 2-D porous structures[J].Journal of Geophysics&Engineering,2007,4(1):40-52
[23]卢明.改进的近似解析离散化方法及弹性波波场模拟[D].北京:清华大学,2004LU M.The optimum nearly analytic discrete method and elastic wave numerical simulations[D].Beijing:Tsinghua University,2004
[24]宋国杰.三维弹性波方程的改进近似解析离散化方法及波场模拟[D].北京:清华大学,2008SONG G J.The improved nearly analytic discrete method for 3Delastic equations and its numerical simulation[D].Beijing:Tsinghua University,2008
[25]宋国杰.基于WNAD方法的非一致网格算法及其弹性波场模拟[J].地球物理学报,2010,53(8):1985-1992SONG G J.Non-uniform grid algorithm based on the WNAD method and elastic wave-field simulations[J].Chinese Journal of Geophysics,2010,53(8):1985-1992
[26]TONG P,YANG D H,HUA B L.High accuracy wave simulation-Revised derivation,numerical analysis and testing of a nearly analytic integration discrete method for solving acoustic equation[J].International Journal of Solids&Structures,2011,48(1):56-70
[27]CARCIONE J M,KOSLOFF D,KOSLOFF R.Wave propagation simulation in a linear viscoacoustic medium[J].Geophysical Journal International,1988,93(2):393-401
[28]CARCIONE J M,KOSLOFF D,KOSLOFF R.Viscoacoustic wave propagation simulation in the Earth[J].Geophysics,1988,53(6):769-777
[29]ROBERTSSON J O A,BLANCH J O.Viscoelastic finite-difference modeling[J].Geophysics,1994,59(9):1444-1456
[30]杜启振.各向异性黏弹性介质伪谱法波场模拟[J].物理学报,2004,53(12):4428-4434 DU Q Z.Wavefield forward modeling with the pseudospectral method in viscoelastic and azimuthally anisotropic media[J].Acta Physica Sinica,2004,53(12):4428-4434
[31]奚先,姚姚.二维粘弹性随机介质中的波场特征分析[J].地球物理学进展,2004,19(3):608-615XI X,YAO Y.The analysis of the wave field characteristics in 2-D viscoelastic random medium[J].Progress in Geophysics,2004,19(3):608-615
[32]宋常瑜,裴正林.井间地震粘弹性波场特征的数值模拟研究[J].石油物探,2006,45(5):508-513SONG C Y,PEI Z L.Numerical simulation of viscoelastic wevefield exploration[J].Geophysical Prospecting for Petroleum,2006,45(5):508-513
[33]唐启军,韩立国,王恩利,等.基于随机各向异性背景的粘弹性单斜介质二维三分量正演模拟[J].西北地震学报,2009,30(1):35-39TANG Q J,HAN L G,WANG E L.2-D three-component seismic modeling for viscoelastic monoclinic media based on background of random isotropic media[J].Northwestern Seismological Journal,2009,30(1):35-39
[34]单启铜,乐友喜.PML边界条件下二维粘弹性介质波场模拟[J].石油物探,2007,46(2):126-130SHAN Q T,YUE Y X.Wavefield simulation of 2-Dviscoelastic medium in perfectly matched layer boundary[J].Geophysical Prospecting for Petroleum,2007,46(2):126-130
[2]KOSLOFF D D,BAYSAL E.Forward modeling by a Fourier method[J].Geophysics,1982,47(10):1402-1412
[3]RESHEF M,KOSLOFF D D,EDWARDS M,et al.Three dimensional elastic modeling by the Fourier method[J].Geophysics,1988,53(9):1184-1193
[4]DRAKE L A.Rayleigh waves at a continental boundary by the finite element method[J].Bulletin of the Seismological Society of America,1972,62(5):1259-1268
[5]BOUCHON M,COUTANT O.Calculation of synthetic seismograms in a laterally varying medium by the boundary element-discrete wavenumber method[J].Bulletin of the Seismological Society of America,1994,84(6):1869-1881
[6]KOMATISSCH D,BARNES C,TROMP J.Simulation of anisotropic wave propagation based upon a spectral element method[J].Geophysics,2000,65(4):1251-1260
[7]ALTERMAN Z,KARAL F C.Propagation of seismic wave in layered media by finite difference methods[J].Bulletin of the Seismological Society of America,1968,58(1):367-398
[8]KELLY K R,WARD R W,TREITEL S,et al.Synthetic seismograms:a finite-difference approach[J].Geophysics,1976,41(1):2-27
[9]VIRIEUX J.P-SV wave propagation in heterogeneous media:velocity-stress finite-difference method[J].Geophysics,1986,51(4):889-901
[10]GRAVES R W.Simulation seismic wave propagation in3Delastic media using staggered-grid finite differences[J].Bulletin of the Seismological Society of America,1996,86(4):1091-1106
[11]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):411-419DONG L G,MA Z T,CAO J Z,et al.The staggeredgrid high-order difference method of first-order elastic equation[J].Chinese Journal of Geophysics,2000,43(3):411-419
[12]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):856-864DONG L G,MA Z T,CAO J Z.The stability study of the staggered-grid high-order difference method of first-order elastic equation,[J].Chinese Journal of Geophysics,2000,43(6):856-864
[13]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):46-56DONG L G.Absorptive boundary condition in elasticwave numerical modeling[J].Oil Geophysical Prospecting,1999,34(1):46-56
[14]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):1128-1131WANG S Q,YANG D H,YANG K D.Compact finite difference scheme for elastic equations[J].Journal of Tsinghua University(Science and Technology),2002,42(8):1128-1131
[15]SAENGER E H,GOLD N,SHAPIRO S A.Modeling the propagation of elastic waves using a modified finitedifference grid[J].Wave Motion,2000,31(1):77-92
[16]SAENGER E H,BOHLEN T.Finite-difference modeling of viscoelastic and anisotropic wave propagation using the rotated staggered grid[J].Geophysics,2004,69(2):583-591
[17]KONDOH Y,HOSAKA Y,ISHII K.Kernel optimum nearly-analytical discrimination algorithm applied to parabolic and hyperbolic equations[J].Computers&Mathematics with Applications,1994,27(3):59-90
[18]杨顶辉,滕吉文,张中杰.三分量地震波场的近似解析离散模拟技术[J].地球物理学报,1996,39(增刊1):283-291YANG D H,TENG G W,ZHANG Z J.Nearly-analytical discretization modeling technique of 3-component seismic wave-fields[J].Chinese Journal of Geophysics,1996,39(S1):283-291
[19]YANG D H,TENG J W,ZHANG Z J,et al.A nearlyanalytic discrete method for acoustic and elastic wave equation[J].Bulletin of the Seismological Society of A-merica,2003,93(2):882-890
[20]YANG D H,LU M,WU R S,et al.An optimal nearlyanalytic discrete method for 2D acoustic and elastic wave equations[J].Bulletin of the Seismological Society of America,2004,94(5):1982-1991
[21]YANG D H,SONG G J,LU M.Optimally accurate nearly-analytic discrete scheme for wave-filed simulation in 3Danisotropic media[J].Bulletin of the Seismological Society of America,2007,97(5):1557-1569
[22]YANG D H,SONG G J,CHEN S,et al.An improved nearly analytical discrete method:an efficient tool to simulate the seismic response of 2-D porous structures[J].Journal of Geophysics&Engineering,2007,4(1):40-52
[23]卢明.改进的近似解析离散化方法及弹性波波场模拟[D].北京:清华大学,2004LU M.The optimum nearly analytic discrete method and elastic wave numerical simulations[D].Beijing:Tsinghua University,2004
[24]宋国杰.三维弹性波方程的改进近似解析离散化方法及波场模拟[D].北京:清华大学,2008SONG G J.The improved nearly analytic discrete method for 3Delastic equations and its numerical simulation[D].Beijing:Tsinghua University,2008
[25]宋国杰.基于WNAD方法的非一致网格算法及其弹性波场模拟[J].地球物理学报,2010,53(8):1985-1992SONG G J.Non-uniform grid algorithm based on the WNAD method and elastic wave-field simulations[J].Chinese Journal of Geophysics,2010,53(8):1985-1992
[26]TONG P,YANG D H,HUA B L.High accuracy wave simulation-Revised derivation,numerical analysis and testing of a nearly analytic integration discrete method for solving acoustic equation[J].International Journal of Solids&Structures,2011,48(1):56-70
[27]CARCIONE J M,KOSLOFF D,KOSLOFF R.Wave propagation simulation in a linear viscoacoustic medium[J].Geophysical Journal International,1988,93(2):393-401
[28]CARCIONE J M,KOSLOFF D,KOSLOFF R.Viscoacoustic wave propagation simulation in the Earth[J].Geophysics,1988,53(6):769-777
[29]ROBERTSSON J O A,BLANCH J O.Viscoelastic finite-difference modeling[J].Geophysics,1994,59(9):1444-1456
[30]杜启振.各向异性黏弹性介质伪谱法波场模拟[J].物理学报,2004,53(12):4428-4434 DU Q Z.Wavefield forward modeling with the pseudospectral method in viscoelastic and azimuthally anisotropic media[J].Acta Physica Sinica,2004,53(12):4428-4434
[31]奚先,姚姚.二维粘弹性随机介质中的波场特征分析[J].地球物理学进展,2004,19(3):608-615XI X,YAO Y.The analysis of the wave field characteristics in 2-D viscoelastic random medium[J].Progress in Geophysics,2004,19(3):608-615
[32]宋常瑜,裴正林.井间地震粘弹性波场特征的数值模拟研究[J].石油物探,2006,45(5):508-513SONG C Y,PEI Z L.Numerical simulation of viscoelastic wevefield exploration[J].Geophysical Prospecting for Petroleum,2006,45(5):508-513
[33]唐启军,韩立国,王恩利,等.基于随机各向异性背景的粘弹性单斜介质二维三分量正演模拟[J].西北地震学报,2009,30(1):35-39TANG Q J,HAN L G,WANG E L.2-D three-component seismic modeling for viscoelastic monoclinic media based on background of random isotropic media[J].Northwestern Seismological Journal,2009,30(1):35-39
[34]单启铜,乐友喜.PML边界条件下二维粘弹性介质波场模拟[J].石油物探,2007,46(2):126-130SHAN Q T,YUE Y X.Wavefield simulation of 2-Dviscoelastic medium in perfectly matched layer boundary[J].Geophysical Prospecting for Petroleum,2007,46(2):126-130