粘弹介质中可变网格地震波传播数值模拟
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摘要
从Kelvin介质的本构方程出发推导了粘弹介质中的弹性波方程和声波方程,建立了粘滞弹性波方程的交错网格高阶差分解和粘滞声波方程的高阶差分解,并应用可变空间网格与局部可变时间步长数值计算技术,形成了适用于粘弹介质中弹性(声)波传播的高效、高精度的数值模拟方法。数值实验结果表明,该方法可以有效模拟地震波在粘弹介质中的传播,并且可以比较准确地刻画精细介质结构,在保证模拟精度的同时极大地提高了计算效率。
Starting from the constitutive equation of the Kelvin media,the viscoelastic and visco-acoustic wave equation were derived,and Staggered-Grid High Order Finite Difference solutions for viscoe lastic wave equation were established.Meanwhile,by applying variable spatial grid and locally variable time step,a high-efficiency and high-precision numerical simulation method were achieved for the propagation of elastic(acoustic) wave in viscoelastic media.The numerical simulation results indicate that the methods can effectively simulate the propagation of seismic wave in the viscoelastic media.Furthermore,the methods can accurately characterize the fine structure of the media and greatly improve the computation efficiency while preserving simulation precision.
Starting from the constitutive equation of the Kelvin media,the viscoelastic and visco-acoustic wave equation were derived,and Staggered-Grid High Order Finite Difference solutions for viscoe lastic wave equation were established.Meanwhile,by applying variable spatial grid and locally variable time step,a high-efficiency and high-precision numerical simulation method were achieved for the propagation of elastic(acoustic) wave in viscoelastic media.The numerical simulation results indicate that the methods can effectively simulate the propagation of seismic wave in the viscoelastic media.Furthermore,the methods can accurately characterize the fine structure of the media and greatly improve the computation efficiency while preserving simulation precision.
引文
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[15]Arntsen B,Nebel A G,Amundsen L.Visco-acousticfinite-difference modeling in the frequency domain[J].Journal of seismic exploration,1998,7(1):45-64
[16]Dablain M A.The application of high-differencing toscalar wave equation[J].Geophysics,1986,51(1):54-66
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[18]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 viscoe-lastic wavefield for crosshole seismic exploration[J].Geophysical Prospecting for Petroleum,2006,45(5):508-513
[19]Moczo P.Finite-difference technique for SH wavesin 2-D media,using irregular grids:application to theseismic response problem[J].Geophysical JournalInternational,1989,99(2):321-329
[20]Falk J,Tessmer E,Gajewski D.Efficient finite-difference modeling of seismic waves using locallyadjustable time step sizes[J].Geophysical Prospec-ting,1998,46(6):603-616
[21]黄超,董良国.可变网格与局部时间步长的高阶差分地震波数值模拟[J].地球物理学报,2009,52(1):176-186Huang C,Dong L G.High-order finite-differencemethod in seismic wave simulation with variablegrids and local time-steps[J].Chinese Journal of Ge-ophysics,2009,52(1):176-186
[22]黄超,董良国.可变网格与局部时间步长的交错网格高阶差分弹性波模拟[J].地球物理学报,2009,52(11):2870-2878Huang C,Dong L G.Staggered-grid high-order fi-nite-difference method in elastic wave simulationwith variable grids and local time-steps[J].ChineseJournal of Geophysics,2009,52(11):2870-2878
[23]董良国,马在田,曹景忠,等.数值频散与人为边界反射的处理方法[C]//反射地震学论文集.上海:同济大学出版社,2000:161-169Dong L G,Ma Z T,Cao J Z,et al.Numerical disper-sion and artificial boundary reflection[C]//The pa-per collection of reflection seismology.Shanghai:Tongji University Press,2000:161-169
[24]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.A study on stability ofthe staggered-grid high-order difference method offirst-order elastic wave equation[J].Chinese Journalof Geophysics,2000,43(6):856-864
[2]Einar K.Constant Q-wave propagation and attenua-tion[J].Journal of Geophysical Research,1979,84(89):4737-4748
[3]Carcione J M,Dan K,Ronnie K.Viscoacoustic wavepropagation simulation in the earth[J].Geophysics,1988,53(6):769-777
[4]Carcione J M.Seismic modeling in viscoelastic media[J].Geophysics,1993,58(1):110-120
[5]Chen H W.Staggered-grid pseudospectral viscoacousticwave field simulation in two-dimensional media[J].A-coustical Society of America,1996,100(1):120-131
[6]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):4428-4434Du Q Z.Wavefield forward modeling with the pseu-do-spectral method in viscoelastic and azimuthallyanisotropic media[J].Acta Physica Sinica,2004,53(12):4428-4434
[7]张智,刘财,邵志刚,等.伪谱法在常Q粘弹介质地震波场模拟中的应用效果[J].地球物理学进展,2005,20(4):945-949Zhang Z,Liu C,Shao Z G,et al.The application ofpseudo-spectral forward modeling of seismic wavefield in constant Q viscoelastic medium[J].Progressin Geophysics,2005,20(4):945-949
[8]Mcdonal F J,Angona F A,Mills R L,et al.Attenua-tion of shear and compressional waves in PierreShale[J].Geophysics,1958,23(3):421-439
[9]Blanch J O,Robertsson J O A,Symes W W.Model-ing of a constant Q:methodology and algorithm foran efficient and optimally inexpensive viscoelastictechnique[J].Geophysics,1995,60(1):176-184
[10]孙成禹,印兴耀.三参数常Q粘弹性模型构造方法研究[J].地震学报,2007,29(4):348-357Sun C Y,Yin X Y.Construction of constant-Q vis-coelastic model with three parameters[J].Acta Seis-mologica Sinica,2007,29(4):348-357
[11]孙成禹,肖云飞,印兴耀,等.黏弹介质波动方程有限差分解的稳定性研究[J].地震学报,2010,32(2):147-156Sun C Y,Xiao Y F,Yin X Y,et al.Study on the sta-bility of finite difference solution of visco-elasticwave equations[J].Acta Seismologica Sinica,2010,32(2):147-156
[12]苑春方,彭苏萍,张中杰,等.Kelvin-Voigt均匀黏弹性介质中传播的地震波[J].中国科学D辑,2005,35(10):957-962Yuan C F,Peng S P,Zhang Z J,et al.Seismic wavepropagating in Kelvin-Voigt homogeneous visco-e-lastic media[J].Science in China Ser.D Earth Sci-ences,2005,35(10):957-962
[13]Madariaga R.Dynamics of an expanding circularfault[J].Bulletin of the Seismological Society of A-merica,1976,66(3):639-666
[14]Robertsson J O A,Blanch J O,Symes W W.Viscoe-lastic finite-differnce modeling[J].Geophysics,1994,59(9):1444-1456
[15]Arntsen B,Nebel A G,Amundsen L.Visco-acousticfinite-difference modeling in the frequency domain[J].Journal of seismic exploration,1998,7(1):45-64
[16]Dablain M A.The application of high-differencing toscalar wave equation[J].Geophysics,1986,51(1):54-66
[17]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.A staggered-gridhigh-order difference method of one-order elasticwave equation[J].Chinese Journal of Geophysics,2000,43(3):411-419
[18]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 viscoe-lastic wavefield for crosshole seismic exploration[J].Geophysical Prospecting for Petroleum,2006,45(5):508-513
[19]Moczo P.Finite-difference technique for SH wavesin 2-D media,using irregular grids:application to theseismic response problem[J].Geophysical JournalInternational,1989,99(2):321-329
[20]Falk J,Tessmer E,Gajewski D.Efficient finite-difference modeling of seismic waves using locallyadjustable time step sizes[J].Geophysical Prospec-ting,1998,46(6):603-616
[21]黄超,董良国.可变网格与局部时间步长的高阶差分地震波数值模拟[J].地球物理学报,2009,52(1):176-186Huang C,Dong L G.High-order finite-differencemethod in seismic wave simulation with variablegrids and local time-steps[J].Chinese Journal of Ge-ophysics,2009,52(1):176-186
[22]黄超,董良国.可变网格与局部时间步长的交错网格高阶差分弹性波模拟[J].地球物理学报,2009,52(11):2870-2878Huang C,Dong L G.Staggered-grid high-order fi-nite-difference method in elastic wave simulationwith variable grids and local time-steps[J].ChineseJournal of Geophysics,2009,52(11):2870-2878
[23]董良国,马在田,曹景忠,等.数值频散与人为边界反射的处理方法[C]//反射地震学论文集.上海:同济大学出版社,2000:161-169Dong L G,Ma Z T,Cao J Z,et al.Numerical disper-sion and artificial boundary reflection[C]//The pa-per collection of reflection seismology.Shanghai:Tongji University Press,2000:161-169
[24]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.A study on stability ofthe staggered-grid high-order difference method offirst-order elastic wave equation[J].Chinese Journalof Geophysics,2000,43(6):856-864
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