2.5维非均匀介质中的地震波数值模拟
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摘要
目前,完全的3D弹性波数值模拟计算仍然需要庞大的计算资源,而2D弹性波数值模拟,又不能准确地近似3D数值模拟.因此,本文在较高数值精度的一阶应力-速度弹性波动方程的基础上,采用时间错格差分拟谱方法在2D模型介质中计算3D弹性波场,即2.5D数值模拟.并将3D计算结果与2.5D和2D结果进行比较,发现2.5D模拟结果在波场形态和振幅方面比2D模拟结果更接近3D模拟结果,从而证实了2.5D数值模拟比2D数值模拟可以更好地近似3D波场数值模拟,同时证实了时间错格差分拟谱方法是一种高精度、高效率的正演模拟方法.
At present,pure 3D elastic wave numerical simulations still require huge computation resources and 2D elastic wave numerical simulations can not accurately represent 3D situation.Thus this paper puts forwards a kind of 2.5D numerical simulation method which computes 3D elastic wave fields in 2D media by using the time-staggered difference pseudospectral method based on high accurate one-order elastic wave equations expressed with velocity and stress.Compared with 2D and 3D simulation results,the 2.5D results are closer to 3D results than 2D results in waveformes and amplitudes.And it confirms that the 2.5D method proposed in this paper,in 3D waveform simulation,is better than 2D method to approximate the 3D wave field and the time-staggered difference pseudospectral method is efficient and accurate in forward modeling.
At present,pure 3D elastic wave numerical simulations still require huge computation resources and 2D elastic wave numerical simulations can not accurately represent 3D situation.Thus this paper puts forwards a kind of 2.5D numerical simulation method which computes 3D elastic wave fields in 2D media by using the time-staggered difference pseudospectral method based on high accurate one-order elastic wave equations expressed with velocity and stress.Compared with 2D and 3D simulation results,the 2.5D results are closer to 3D results than 2D results in waveformes and amplitudes.And it confirms that the 2.5D method proposed in this paper,in 3D waveform simulation,is better than 2D method to approximate the 3D wave field and the time-staggered difference pseudospectral method is efficient and accurate in forward modeling.
引文
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[16]李景叶,陈小宏.横向各向同性介质地震波场数值模拟研究[J].地球物理学进展,2006,21(3):700~705.Li J Y,Chen X H.Study on seismic wave field numericalsimulation in transverse isotropic medium[J].Progress inGeophysics(in Chinese),2006,21(3):700~705.
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[18]Lysmer.Shear waves in plane infinite structures[J].Journalof the Engineering Mechanics Division,1972,98,(1):85~105.
[19]陈少林,廖振鹏,陈进.两相介质近场波动模拟的一种解耦有限元方法[J].地球物理学报,2005,48(4):909~917.Chen S L,Liao Z P,Chen J.A decoupling FEM for simula-ting near-field wave motions in two-phase media[J].ChineseJ.Geophys.(in Chinese),2005,48(4):909~917.
[20]张新明,刘克安,刘家琦.流体饱和多孔隙介质二维弹性波方程正演模拟的小波有限元法[J].地球物理学报,2005,48(5):1156~1166.Zhang X M,Liu K A,Liu J Q.A wavelet finite elementmethod for the 2D wave equation in fluid-saturated porousmedia[J].Chinese J.Geophys.(in Chinese),2005,48(5):1156~1166.
[21]Virieux J.SH-wave propagation in heterogeneous media:ve-locity-stress finite-difference method[J].Geophysics,1984,49(11):1933~1957.
[22]冷建华.傅里叶变换[M].北京:清华大学出版社,2004.Leng J H.The Fourer Transform[M].Beijing:Qing Hua U-niversity,2004.
[23]Kosloff D,et al.Forward modeling by a fourier method[J].Geophysics,1982,47(10):1402~1412.
[2]Kang I B,McMechan G A.Two-dimensional elasticpseudospectral modeling of wide-aperture seismic array datawith application to the Wichita Uplift-Anadarako Basin regionof southwestern Oklahoma[J].Bull.Seis.Soc.Am,1990,80:1677~1695.
[3]Chen H E.McMechan G A.3D physical modeling andpseudospectral simulation of seismic common-source data vol-umes[J].Geophysics,1993,58:121~133.
[4]Takashi F,Hiroshi T,2.5D modelling of elastic waves usingthe pseudospectral method[J].Geophys,J.Int,1996,124:820~832.
[5]Eskola L,Hongisto H.The solution of the stationary electricfield strength and potential of a point current source in a 2.5Dimensional environment[J].Geophys.Prospect.,1981,29:260~273.
[6]Bleistein N.Two-and-one-half dimensional in-plane wavepropagation[J],Prospect.,1986,34,686~703.
[7]Song Z M,Williamson P R.Frequency-domain acoustic-wavemodeling and inversion of crosshole data;Part I—2.5D model-ing method[J].Geophysics,1995,60:556~562.
[8]滕吉文,张中杰,杨顶辉,等.各向异性介质中褶积微分算子法三分量地震资料的数字仿真[J].石油物探,1995,34(3):14~22.Teng J W,Zhang Z J,Yang D H,et al.Digital emulation oftricomponent seismic data in anisotropic media through convo-lution differential operator[J].GPP,1995,34(3):14~22.
[9]王德利,何樵登,韩立国.裂隙型单斜介质中多方位地面三分量记录模拟[J].地球物理学报,2005,48(2):386~393.Wang D L,He Q D,Han L G.Multi-azimuth three-compo-nent surface seismic modeling for cracked monoclinic media[J].Chinese J.Geophys.(in Chinese),2005,48(2):386~393.
[10]郑海山,张中杰.横向各向同性(VTI)介质中非线性地震波场模拟[J].地球物理学报,2005,48(3):660~67.Zheng H S,Zhang Z J.Synthetic seismograms of nonlinearseismic waves in anisotropic(VTI)media[J].Chinese J.Geophys.(in Chinese),2005,48(3):660~671.
[11]周辉,刘斌,等.二维各向异性介质中三分量波动方程有限元法模拟[J],青岛海洋大学学报,2000,30(4),125~129.Zhou H,Liu B,et al.The modeling of three componentwave equation for anisotropic medium using the finite elementmethod[J].Journal of Ocean University of Qingdao,2000,30(4),125~129.
[12]张新明,刘克安,刘家琦.流体饱和多孔隙介质二维弹性波方程正演模拟的小波有限元法[J].地球物理学报,2005,48(5):1156~1166.Zhang X M,Liu K A,Liu J Q.A wavelet finite elementmethod for the 2D wave equation in fluid-saturated porousmedia[J].Chinese J.Geophys.(in Chinese),2005,48(5):1156~1166.
[13]刘财,张智,邵志刚,等.线性粘弹体中地震波场伪谱法模拟技术[J].地球物理学进展,2005,20(3):640~652.Liu C,Zhang Z,Shao Z G,et al.Pseudospectral forwardmodeling of seismic wave in linear viscoelasic solid[J].Pro-gress in Geophysics(in Chinese),2005,20(3):640~652..
[14]郑洪伟,李廷栋,高锐,等.数值模拟在地球动力学中的研究进展[J].地球物理学进展,2006,21(2):360~369.Zheng H W,Li T D,Gao R,et al.The advance of numericalsimulation in geodynamics[J].Progress in Geophysics(inChinese),2006,21(2):360~369.
[15]杜启振,王延光,付水华.方位各向异性粘弹性介质波场数值模拟[J].地球物理学进展,2006,21(2):502~504.Du Q Z,Wang Y G,Fu S H.Wavefield forward modelingwith the pseudo-spectral method in viscoelastic and azimuth-ally anisotropic media[J].Progress in Geophysics(in Chi-nese),2006,21(2):502~504.
[16]李景叶,陈小宏.横向各向同性介质地震波场数值模拟研究[J].地球物理学进展,2006,21(3):700~705.Li J Y,Chen X H.Study on seismic wave field numericalsimulation in transverse isotropic medium[J].Progress inGeophysics(in Chinese),2006,21(3):700~705.
[17]Marfurt K J.Accuracy of finite difference and finite elementmodeling of the scalar and elastic wave equations[J].Geo-physics,1984,49(5):533~549.
[18]Lysmer.Shear waves in plane infinite structures[J].Journalof the Engineering Mechanics Division,1972,98,(1):85~105.
[19]陈少林,廖振鹏,陈进.两相介质近场波动模拟的一种解耦有限元方法[J].地球物理学报,2005,48(4):909~917.Chen S L,Liao Z P,Chen J.A decoupling FEM for simula-ting near-field wave motions in two-phase media[J].ChineseJ.Geophys.(in Chinese),2005,48(4):909~917.
[20]张新明,刘克安,刘家琦.流体饱和多孔隙介质二维弹性波方程正演模拟的小波有限元法[J].地球物理学报,2005,48(5):1156~1166.Zhang X M,Liu K A,Liu J Q.A wavelet finite elementmethod for the 2D wave equation in fluid-saturated porousmedia[J].Chinese J.Geophys.(in Chinese),2005,48(5):1156~1166.
[21]Virieux J.SH-wave propagation in heterogeneous media:ve-locity-stress finite-difference method[J].Geophysics,1984,49(11):1933~1957.
[22]冷建华.傅里叶变换[M].北京:清华大学出版社,2004.Leng J H.The Fourer Transform[M].Beijing:Qing Hua U-niversity,2004.
[23]Kosloff D,et al.Forward modeling by a fourier method[J].Geophysics,1982,47(10):1402~1412.
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