地震波数值模拟方法研究综述
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摘要
地震波场数值模拟不仅是研究复杂地区地震资料采集、处理和解释的有效辅助手段,而且是研究地球深部精细构造的有效工具。地震波场数值模拟的主要方法包括3大类,即几何射线法、积分方程法和波动方程法。首先介绍了地震波数值模拟方法的理论基础和内容及特点,然后概括介绍了20世纪90年代以来几何射线法和各种波动方程数值模拟方法的新进展。因为波动方程数值模拟包含了丰富的波动信息,可为研究地震波的传播机理和复杂地层的解释提供更多的佐证,所以重点介绍波动方程数值模拟方法。最后,对各种数值模拟方法进行了评述,并给出了地震波传播理论和数值模拟方法发展的展望。
Seismic numerical modeling is an important tool not only to the sampling,processing and interpretation of seismic data in complex area,but also to the investigation of the accurate structure of the earth's interior.The seismic numerical modeling methods are mainly of three types,including ray tracing method,integral equation method and wave equation method.In this paper,firstly the basic principles are introduced,the theoretical basis and the contents as well as the characteristics of various seismic numerical modeling methods are then described. The developments of ray tracing method and various seismic numerical modeling methods since 1990s are also briefly reviewed.Since the wave equation includes abundant information and offers more evidences to the propagation mechanism of seismic waves and to the interpretation of complex stratum,emphasis is focused on the wave equation modeling methods.In the end of this paper,we give out our evaluation to various numerical modeling methods are evaluated and the prospect for the future development of various numerical modeling methods is provided.
Seismic numerical modeling is an important tool not only to the sampling,processing and interpretation of seismic data in complex area,but also to the investigation of the accurate structure of the earth's interior.The seismic numerical modeling methods are mainly of three types,including ray tracing method,integral equation method and wave equation method.In this paper,firstly the basic principles are introduced,the theoretical basis and the contents as well as the characteristics of various seismic numerical modeling methods are then described. The developments of ray tracing method and various seismic numerical modeling methods since 1990s are also briefly reviewed.Since the wave equation includes abundant information and offers more evidences to the propagation mechanism of seismic waves and to the interpretation of complex stratum,emphasis is focused on the wave equation modeling methods.In the end of this paper,we give out our evaluation to various numerical modeling methods are evaluated and the prospect for the future development of various numerical modeling methods is provided.
引文
[1]Alterman Z,Karal F C.Propagation of elastic wavesin layered media by finite-difference methods[J].Bull.Seism.Soc.Am.,1968,58(1):367-398
[2]Tal-EzarH,Carcione J.M,Kosloff D.An accurateand efficient scheme for wave propagation in linearviscoelastic media[J].Geophysics,1990,55(10):1366-1379
[3]Robertsson J O,Blanch J O,Symes W W.Viscoelastic finite-difference modeling[J].Geophysics,1994,59(9):1444-1456
[4]Carcione J M,Helle H B.Numerical solution of theporoviscoelastic wave equation on a staggered mesh[J].J.Comput.Phys.,1999,154(2):520-527
[5]Jastram C,Tessmer E.Elastic modeling on a gridwith vertically varying spacing[J].Geophs.Prosp.,1994,42(4):357-370
[6]Oprsal I,Zahradnik J.Elastic finite-differencemethod for irregular grids[J].Geophysics,1999,64(1):240-250
[7]Nordstorm J,Carpenter M H.High-order finitedifference methods,multidimensional linear problemsand curvilinear coordinates[J].J.Comput.Phys.,2001,173(1):149-174
[8]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 elastic waveequation[J].Chinese Journal of.Geophysics,2000,43(3):411-419
[9]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
[10]孙若昧,Vaccari F,Panza G F.局部地质条件对强地面运动影响的剪切波模拟[J].地球物理学报,2000,43(1):81-90Sun R M,F.Vaccari,G.F.panza.SH-wave modelingof influence of local geological condition on strongground motion[J].Chinese Journal of.Geophysics,2000,43(1):81-90
[11]Yang D H,Liu E,Zhang Z J,et al.Finite differencemodeling in two dimension anisotropic media using aflux-corrected transport technique[J].Geophys.J.Int.,2002,148(2):320-328
[12]殷文,印兴耀,吴国忱,等.高精度频率域弹性波方程有限差分方法及波场模拟[J].地球物理学报,2006,49(2):561-568Yin W,Yin X Y,Wu G C,et al.The method of finitedifference of high precision elastic wave equations inthe frequency domain and wavefield simulation[J].Chinese Journal of.Geophysics,2006,49(2):561-568
[13]王一博,杨慧珠.方位各向异性介质的多尺度有限差分法波场模拟[J].清华大学学报(自然科学版),2006,46(2):293-296Wang Y B,Yang HZ.Numerical simulation of elasticwave propagation in azimuthally anisotropic mediausing multi-level finite difference method[J].J.Tsinghua Univ ersity.(Sci&Tech),2006,46(2):293-296
[14]Lysmer J,Drake L A.A finite element method forseismology[M],In Alder B,Fernbach S,Bolt B A,Eds.,Methods in computational physics,Seismology.Academic Press,1972.181-216
[15]Seron F J,Sanz F J,Kindelan M,et al.Finite-element method for elastic wave propagation[J].Comm.Appl.Numerical Methods,1990,6(2):359-368
[16]Seron F J,Badal J,Sabadell.A numerical laboratoryfor simulation and visualization of seismic wavefields[J].Geophys.Prosp.,1996,44(4):603-642
[17]Padovani E,Priolo E,Seriani.Low and high-orderfinite element method:experience in seismic modeling[J].J.Comp.Acoust.,1994,2(1):371-422
[18]Sarma G S,Mallick K,Gadhinglajkar V R.Nonreflecting boundary condition in finite elementformulation for an elastic wave equation[J].Geophysics,1998,63(3):1006-1016
[19]张美根,王妙月,李小凡,等.各向异性弹性波场的有限元数值模拟[J].地球物理学进展,2002,17(3):384-389Zhang M G,Wang M Y,Li X F,et al.Finite elementforward modeling of anisotropic elastic waves[J].Progress in Geophysics,2002,17(3):384-389
[20]杨顶辉.双相各向异性介质中弹性波方程的有限元解法及波场模拟[J].地球物理学报,2002,45(4):575-583Yang D H.Finite element method of the elastic waveequation and wavefield simulation in two-phaseanisotropic media[J].Chinese Journal of.Geophysics,2002,45(4):575-583
[21]Kreiss H O,Oliger J.Comparison of accuratemethods for the integration of hyperbolic equations[J].Tellus,1972,24(3):199-215
[22]石玉梅.流体饱和多孔隙介质中弹性波运动方程的解——伪谱法[J].西南石油学院学报,1995,17(1):34-37Shi Y M.Solution of elastic wave equations on fluid-saturated porous media-the pseudospect al method[J].J.Southwestern Petroleum Institute,1995,17(1):34-37
[23]张文生,何樵登.二维横向各向同性介质的伪谱法正演模拟[J].石油地球物理勘探,1998,33(3):310-319Zhang W S,He Q D.Pseudo-spectral forwardmodeling in 2-D transversally isotropic media[J].OGP,1998,33(3):310-319
[24]Takashi Furunura,Takenaka H.A wraproundelimination technique for the pseudospectral wavesynthesis using an antiperiodic extension of thewavefield[J].Geophysics,1995,60(1):302-307
[25]Hiroshi Takenaka,Yanbin Wang and TakashiFurumura.An efficient approach of thepseudospectral method for modeling of geometricallysymmetric seismic wavefield[J].Earth Planets Space,1999,51(2):73-79
[26]Yanbin Wang,Hiroshi Takenaka and Takashi Furumura.Effect of vertical velocity gradient on groundmotion in a sediment-filled basin due to incident SVwave[J].Earth Planets Space,2000,52(1):13-24
[27]Yanbin Wang,Hiroshi Takenaka.A multidomainapproach of the Fourier pseudospectral method usingdiscontinuous grid for elastic wave modeling[J].Earth Planets Space,2001,53(3):149-158
[28]Yanbin Wang,Hiroshi Takenaka and TakashiFurumura.Modeling seismic wave propagation in atwo-dimensional cylindrical whole-earth model usingthe pseudospectral method[J].Geophys.J.Int.,2001,145(3):689-708
[29]赵志新,徐纪人,堀内茂木.错格实数傅立叶变换微分算子及其在非均匀介质波动传播研究中的应用[J].地球物理学报,2003,46(2):234-240Zhao Z X,Xu J R,Shigeki Horiuchi.Staggered gridreal value FFT differentiation operator and itsapplication on wave propagation simulation in theheterogeneous medium[J].Chinese J.Geophys.(inChinese),2003,46(2):234-240
[30]赵景霞,张叔伦,孙沛勇.曲网络伪谱法二维声波模拟[J].石油物探,2003,42(1):1-5Zhao J X,Zhang S L,Sun P Y.Pseudospectralmethod on curved grid for 2D forward modeling[J].Geophysical prospecting for petroleum,2003,42(1):1-5
[31]张丽琴,於文辉,王家映.离散介质中地震波传播的数值模拟[J].西北地震学报,2004,26(1):89-92Zhang L Q,Yu W H,Wang J Y.Numericalsimulation of seismic waves propagation in discretemedia[J].Northwestern Seismological Journal,2004,26(1):89-92
[32]Patera A T.A spectral element method for fluiddynamics:laminar flow in a channel expansion[J].J.Comput.Phys.,1984,54(3):468-488
[33]Priolo E,Seriani G.A numerical investigation ofChebychev spectral element method for acoustic wavepropagation[A].In Proc.13thIMACS Conf.onComp.Appl.Math.[C].Ireland Dublin,1991.551-556
[34]Komatitsch D.Spectral and spectral-element methodsfor the 2D and 3D elastodynamics equations inheterogeneous media[D].Ph.D thesis,Institute dePhysique du Globe,Paris,France,1997
[35]Chaljub E.Numerical modeling of the propagation ofseismic waves in spherical geometry:application toglobal seismology[D].Ph.D.thesis,Universit'eParis VII Denis Diderot,Paris,France,2000
[36]Capdeville Y.M'ethode coupl'ee'el'ementsspectraux-solution modale pour la propagation d’ondes dans la Terre`a l’'echelle globale[D].Ph.D.thesis,Universit'e Paris 7,Paris,France,2000
[37]Capdeville Y,Chaljub E,Vilotte J P,et al.Couplingthe spectral element method with a modal solution forelastic wave propagation in global earth models[J].Geophys.J.Int.,2003,152(1):34-67
[38]Komatitsch D,Martin R,Tromp J,et al.Wavepropagation in 2-D elastic media using a spectralelement method with triangles and quadrangles[J].J.Comput.Acoust.,2001,9(2):703-718
[39]Komatitsch D,Tromp J.A Perfectly Matched Layerabsorbing boundary condition for the second-orderseismic wave equation[J].Geophys.J.Int.,2003,154(1):146-153
[40]Bakamjian B.Boundary integrals:An efficient methodfor modeling seismic wave propagation in 3-D[A].62th Ann.Internat.Mtg.Soc.Expl.Geophys.[C],Tulsa,Univ.of Tulsa,1992.1232-1235
[41]符力耘,牟永光.弹性波边界元法正演模拟[J].地球物理学报,1994,37(4):521-529Fu L Y,Mou Y G.Boundary element method forelastic wave forward modeling[J].Chinese Journal ofGeophysics,1994,37(4):521-529
[42]Fu L Y,Mou Y G,Yang H J.Forward problem ofnonlinear Fredholm integral equation in referencemedium via velocity-weighted wavefield function[J].Geophysics,1997,62(2):650-656
[43]Fu L Y.Numerical study of generalized Lipmann-Schwinger integral equation including surfacetopography[J].Geophysics,2003,68(2):665-671
[44]陈九辉,刘启元.合成三维横向非均匀介质远震体波接收函数的Maslov方法[J].地球物理学报,1999,42(1):84-93Chen J H,Liu Q Y.Lithospheric receiver function in3-D laterally inhomogeneous media using maslovasymptotic theory[J].Chinese Journal of.Geophysics,1999,42(1):84-93
[45]王辉,常旭.基于图形结构的三维射线追踪方法[J].地球物理学报,2000,43(4):534-541Wang H,Chang X.3D ray tracing method on graphicstructure[J].Chinese Journal of.Geophysics,2000,43(4):534-541
[46]赵爱华,张中杰,王光杰,等.非均匀介质中地震波走时与射线路径快速计算技术[J].地震学报,2000,22(2):151-157Zhao A H,Zhang Z J,Wang G J,et al.A fastcomputation technique of the seismic wave travaltimeand ray path in heterogeneous media[J].ActaSeismologica Sinica,2000,22(2):151-157
[47]高亮,李幼铭,陈旭荣,等.地震射线辛几何算法初探[J].地球物理学报,2000,43(3):402-410Gao L,Li Y M,Chen X R,et al.An attempt toseismic ray tracing with symplectic algorithm[J].Chinese Journal of.Geophysics,2000,43(3):402-410
[48]秦孟兆,陈景波.Maslov渐近理论与辛几何算法[J].地球物理学报,2000,43(4):522-533Qin M Z,Chen J B.Maslov asymptotic theory andsymplectic algorithm[J].Chinese J.Geophys.(inChinese),2000,43(4):522-533
[49]王真理,李幼铭.细胞自动机地震波模拟的并行化算法[J].地球物理学报,1999,42(3):410-415Wang Z L,Li Y M.Parallel algorithm for simulatingseismic wave propagation by cellular automata[J].Chinese Journal of.Geophysics,1999,42(3):410-415
[50]刘劲松,许云,乌达巴拉.用于地震波场模拟的变网格边长声格固体模型[J].地球物理学报,1999,42(4):536-542Liu J S,Xu Y,Uda Bala.Phononic lattice solid withvarious grid length for modeling seismic waves[J].Chinese Journal of.Geophysics,1999,42(4):536-542
[51]罗明秋,刘洪,李幼铭.基于螺旋线上谱因式分解的地震波场隐式辛算法[J].地球物理学报,2001,44(3):379-388Luo M Q,Liu H,Li Y M.Seismic wave modelingwith implicit symplectic method based on spectralfactorization on helix[J].Chinese Journal of.Geophysics,2001,44(3):379-388
[52]陈凌,吴如山,陈禺页,等.声子波及其在地震波资料分解中的应用[J].地球物理学报,2001,44(3):369-378Chen L,Wu R S,Chen Y,et al.Acoustic waveletand its applications to seismic data decomposition[J].Chinese J.Geophys.(in Chinese),2001,44(3):369-378
[53]刘礼农,崔凤林,张剑锋.三维复杂构造中地震波模拟的单程波方法[J].地球物理学报,2004,47(3):514-520Liu L N,Cui F L,Zhang J F.Seismic modeling withone-way wave equation in 3D complex structures[J].Chinese Journal of.Geophysics,2004,47(3):514-520
[54]谢桂生,刘洪,李幼铭,等.界面起伏条件下反射/透射算子+单程波方程的地震波模拟方法[J].地球物理学报,2005,48(5):1172-1178Xie G S,Liu H,Li Y M,et al.Seismic modeling byreflection/transmission operator and one-way waveequation under the condition of fluctuating reflectors.Chinese Journal of.Geophysics,2005,48(5):1172-1178
[55]孙建国,王雪秋.利用有限正弦和有限余弦变换模拟地震波场:声波方程[J].吉林大学学报(地球科学版),2006,36(1):108-112Sun J G,Wang X Q.Seismic Modeling by UsingFinite Sine and Cosine Transforms:AcousticEquations[J].J.Jilin Univ.(Earth Science Edition),2006,36(1):108-112
[56]贾晓峰,胡天跃,王润秋.无单元法用于地震波波动方程模拟与成像[J].地球物理学进展,2006,21(1):11-17Jia X F,Hu T Y,Wang R Q.Wave equationmodeling and imaging by using element-free method[J].Progress in Geophysics,2006,21(1):11-17
[2]Tal-EzarH,Carcione J.M,Kosloff D.An accurateand efficient scheme for wave propagation in linearviscoelastic media[J].Geophysics,1990,55(10):1366-1379
[3]Robertsson J O,Blanch J O,Symes W W.Viscoelastic finite-difference modeling[J].Geophysics,1994,59(9):1444-1456
[4]Carcione J M,Helle H B.Numerical solution of theporoviscoelastic wave equation on a staggered mesh[J].J.Comput.Phys.,1999,154(2):520-527
[5]Jastram C,Tessmer E.Elastic modeling on a gridwith vertically varying spacing[J].Geophs.Prosp.,1994,42(4):357-370
[6]Oprsal I,Zahradnik J.Elastic finite-differencemethod for irregular grids[J].Geophysics,1999,64(1):240-250
[7]Nordstorm J,Carpenter M H.High-order finitedifference methods,multidimensional linear problemsand curvilinear coordinates[J].J.Comput.Phys.,2001,173(1):149-174
[8]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 elastic waveequation[J].Chinese Journal of.Geophysics,2000,43(3):411-419
[9]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
[10]孙若昧,Vaccari F,Panza G F.局部地质条件对强地面运动影响的剪切波模拟[J].地球物理学报,2000,43(1):81-90Sun R M,F.Vaccari,G.F.panza.SH-wave modelingof influence of local geological condition on strongground motion[J].Chinese Journal of.Geophysics,2000,43(1):81-90
[11]Yang D H,Liu E,Zhang Z J,et al.Finite differencemodeling in two dimension anisotropic media using aflux-corrected transport technique[J].Geophys.J.Int.,2002,148(2):320-328
[12]殷文,印兴耀,吴国忱,等.高精度频率域弹性波方程有限差分方法及波场模拟[J].地球物理学报,2006,49(2):561-568Yin W,Yin X Y,Wu G C,et al.The method of finitedifference of high precision elastic wave equations inthe frequency domain and wavefield simulation[J].Chinese Journal of.Geophysics,2006,49(2):561-568
[13]王一博,杨慧珠.方位各向异性介质的多尺度有限差分法波场模拟[J].清华大学学报(自然科学版),2006,46(2):293-296Wang Y B,Yang HZ.Numerical simulation of elasticwave propagation in azimuthally anisotropic mediausing multi-level finite difference method[J].J.Tsinghua Univ ersity.(Sci&Tech),2006,46(2):293-296
[14]Lysmer J,Drake L A.A finite element method forseismology[M],In Alder B,Fernbach S,Bolt B A,Eds.,Methods in computational physics,Seismology.Academic Press,1972.181-216
[15]Seron F J,Sanz F J,Kindelan M,et al.Finite-element method for elastic wave propagation[J].Comm.Appl.Numerical Methods,1990,6(2):359-368
[16]Seron F J,Badal J,Sabadell.A numerical laboratoryfor simulation and visualization of seismic wavefields[J].Geophys.Prosp.,1996,44(4):603-642
[17]Padovani E,Priolo E,Seriani.Low and high-orderfinite element method:experience in seismic modeling[J].J.Comp.Acoust.,1994,2(1):371-422
[18]Sarma G S,Mallick K,Gadhinglajkar V R.Nonreflecting boundary condition in finite elementformulation for an elastic wave equation[J].Geophysics,1998,63(3):1006-1016
[19]张美根,王妙月,李小凡,等.各向异性弹性波场的有限元数值模拟[J].地球物理学进展,2002,17(3):384-389Zhang M G,Wang M Y,Li X F,et al.Finite elementforward modeling of anisotropic elastic waves[J].Progress in Geophysics,2002,17(3):384-389
[20]杨顶辉.双相各向异性介质中弹性波方程的有限元解法及波场模拟[J].地球物理学报,2002,45(4):575-583Yang D H.Finite element method of the elastic waveequation and wavefield simulation in two-phaseanisotropic media[J].Chinese Journal of.Geophysics,2002,45(4):575-583
[21]Kreiss H O,Oliger J.Comparison of accuratemethods for the integration of hyperbolic equations[J].Tellus,1972,24(3):199-215
[22]石玉梅.流体饱和多孔隙介质中弹性波运动方程的解——伪谱法[J].西南石油学院学报,1995,17(1):34-37Shi Y M.Solution of elastic wave equations on fluid-saturated porous media-the pseudospect al method[J].J.Southwestern Petroleum Institute,1995,17(1):34-37
[23]张文生,何樵登.二维横向各向同性介质的伪谱法正演模拟[J].石油地球物理勘探,1998,33(3):310-319Zhang W S,He Q D.Pseudo-spectral forwardmodeling in 2-D transversally isotropic media[J].OGP,1998,33(3):310-319
[24]Takashi Furunura,Takenaka H.A wraproundelimination technique for the pseudospectral wavesynthesis using an antiperiodic extension of thewavefield[J].Geophysics,1995,60(1):302-307
[25]Hiroshi Takenaka,Yanbin Wang and TakashiFurumura.An efficient approach of thepseudospectral method for modeling of geometricallysymmetric seismic wavefield[J].Earth Planets Space,1999,51(2):73-79
[26]Yanbin Wang,Hiroshi Takenaka and Takashi Furumura.Effect of vertical velocity gradient on groundmotion in a sediment-filled basin due to incident SVwave[J].Earth Planets Space,2000,52(1):13-24
[27]Yanbin Wang,Hiroshi Takenaka.A multidomainapproach of the Fourier pseudospectral method usingdiscontinuous grid for elastic wave modeling[J].Earth Planets Space,2001,53(3):149-158
[28]Yanbin Wang,Hiroshi Takenaka and TakashiFurumura.Modeling seismic wave propagation in atwo-dimensional cylindrical whole-earth model usingthe pseudospectral method[J].Geophys.J.Int.,2001,145(3):689-708
[29]赵志新,徐纪人,堀内茂木.错格实数傅立叶变换微分算子及其在非均匀介质波动传播研究中的应用[J].地球物理学报,2003,46(2):234-240Zhao Z X,Xu J R,Shigeki Horiuchi.Staggered gridreal value FFT differentiation operator and itsapplication on wave propagation simulation in theheterogeneous medium[J].Chinese J.Geophys.(inChinese),2003,46(2):234-240
[30]赵景霞,张叔伦,孙沛勇.曲网络伪谱法二维声波模拟[J].石油物探,2003,42(1):1-5Zhao J X,Zhang S L,Sun P Y.Pseudospectralmethod on curved grid for 2D forward modeling[J].Geophysical prospecting for petroleum,2003,42(1):1-5
[31]张丽琴,於文辉,王家映.离散介质中地震波传播的数值模拟[J].西北地震学报,2004,26(1):89-92Zhang L Q,Yu W H,Wang J Y.Numericalsimulation of seismic waves propagation in discretemedia[J].Northwestern Seismological Journal,2004,26(1):89-92
[32]Patera A T.A spectral element method for fluiddynamics:laminar flow in a channel expansion[J].J.Comput.Phys.,1984,54(3):468-488
[33]Priolo E,Seriani G.A numerical investigation ofChebychev spectral element method for acoustic wavepropagation[A].In Proc.13thIMACS Conf.onComp.Appl.Math.[C].Ireland Dublin,1991.551-556
[34]Komatitsch D.Spectral and spectral-element methodsfor the 2D and 3D elastodynamics equations inheterogeneous media[D].Ph.D thesis,Institute dePhysique du Globe,Paris,France,1997
[35]Chaljub E.Numerical modeling of the propagation ofseismic waves in spherical geometry:application toglobal seismology[D].Ph.D.thesis,Universit'eParis VII Denis Diderot,Paris,France,2000
[36]Capdeville Y.M'ethode coupl'ee'el'ementsspectraux-solution modale pour la propagation d’ondes dans la Terre`a l’'echelle globale[D].Ph.D.thesis,Universit'e Paris 7,Paris,France,2000
[37]Capdeville Y,Chaljub E,Vilotte J P,et al.Couplingthe spectral element method with a modal solution forelastic wave propagation in global earth models[J].Geophys.J.Int.,2003,152(1):34-67
[38]Komatitsch D,Martin R,Tromp J,et al.Wavepropagation in 2-D elastic media using a spectralelement method with triangles and quadrangles[J].J.Comput.Acoust.,2001,9(2):703-718
[39]Komatitsch D,Tromp J.A Perfectly Matched Layerabsorbing boundary condition for the second-orderseismic wave equation[J].Geophys.J.Int.,2003,154(1):146-153
[40]Bakamjian B.Boundary integrals:An efficient methodfor modeling seismic wave propagation in 3-D[A].62th Ann.Internat.Mtg.Soc.Expl.Geophys.[C],Tulsa,Univ.of Tulsa,1992.1232-1235
[41]符力耘,牟永光.弹性波边界元法正演模拟[J].地球物理学报,1994,37(4):521-529Fu L Y,Mou Y G.Boundary element method forelastic wave forward modeling[J].Chinese Journal ofGeophysics,1994,37(4):521-529
[42]Fu L Y,Mou Y G,Yang H J.Forward problem ofnonlinear Fredholm integral equation in referencemedium via velocity-weighted wavefield function[J].Geophysics,1997,62(2):650-656
[43]Fu L Y.Numerical study of generalized Lipmann-Schwinger integral equation including surfacetopography[J].Geophysics,2003,68(2):665-671
[44]陈九辉,刘启元.合成三维横向非均匀介质远震体波接收函数的Maslov方法[J].地球物理学报,1999,42(1):84-93Chen J H,Liu Q Y.Lithospheric receiver function in3-D laterally inhomogeneous media using maslovasymptotic theory[J].Chinese Journal of.Geophysics,1999,42(1):84-93
[45]王辉,常旭.基于图形结构的三维射线追踪方法[J].地球物理学报,2000,43(4):534-541Wang H,Chang X.3D ray tracing method on graphicstructure[J].Chinese Journal of.Geophysics,2000,43(4):534-541
[46]赵爱华,张中杰,王光杰,等.非均匀介质中地震波走时与射线路径快速计算技术[J].地震学报,2000,22(2):151-157Zhao A H,Zhang Z J,Wang G J,et al.A fastcomputation technique of the seismic wave travaltimeand ray path in heterogeneous media[J].ActaSeismologica Sinica,2000,22(2):151-157
[47]高亮,李幼铭,陈旭荣,等.地震射线辛几何算法初探[J].地球物理学报,2000,43(3):402-410Gao L,Li Y M,Chen X R,et al.An attempt toseismic ray tracing with symplectic algorithm[J].Chinese Journal of.Geophysics,2000,43(3):402-410
[48]秦孟兆,陈景波.Maslov渐近理论与辛几何算法[J].地球物理学报,2000,43(4):522-533Qin M Z,Chen J B.Maslov asymptotic theory andsymplectic algorithm[J].Chinese J.Geophys.(inChinese),2000,43(4):522-533
[49]王真理,李幼铭.细胞自动机地震波模拟的并行化算法[J].地球物理学报,1999,42(3):410-415Wang Z L,Li Y M.Parallel algorithm for simulatingseismic wave propagation by cellular automata[J].Chinese Journal of.Geophysics,1999,42(3):410-415
[50]刘劲松,许云,乌达巴拉.用于地震波场模拟的变网格边长声格固体模型[J].地球物理学报,1999,42(4):536-542Liu J S,Xu Y,Uda Bala.Phononic lattice solid withvarious grid length for modeling seismic waves[J].Chinese Journal of.Geophysics,1999,42(4):536-542
[51]罗明秋,刘洪,李幼铭.基于螺旋线上谱因式分解的地震波场隐式辛算法[J].地球物理学报,2001,44(3):379-388Luo M Q,Liu H,Li Y M.Seismic wave modelingwith implicit symplectic method based on spectralfactorization on helix[J].Chinese Journal of.Geophysics,2001,44(3):379-388
[52]陈凌,吴如山,陈禺页,等.声子波及其在地震波资料分解中的应用[J].地球物理学报,2001,44(3):369-378Chen L,Wu R S,Chen Y,et al.Acoustic waveletand its applications to seismic data decomposition[J].Chinese J.Geophys.(in Chinese),2001,44(3):369-378
[53]刘礼农,崔凤林,张剑锋.三维复杂构造中地震波模拟的单程波方法[J].地球物理学报,2004,47(3):514-520Liu L N,Cui F L,Zhang J F.Seismic modeling withone-way wave equation in 3D complex structures[J].Chinese Journal of.Geophysics,2004,47(3):514-520
[54]谢桂生,刘洪,李幼铭,等.界面起伏条件下反射/透射算子+单程波方程的地震波模拟方法[J].地球物理学报,2005,48(5):1172-1178Xie G S,Liu H,Li Y M,et al.Seismic modeling byreflection/transmission operator and one-way waveequation under the condition of fluctuating reflectors.Chinese Journal of.Geophysics,2005,48(5):1172-1178
[55]孙建国,王雪秋.利用有限正弦和有限余弦变换模拟地震波场:声波方程[J].吉林大学学报(地球科学版),2006,36(1):108-112Sun J G,Wang X Q.Seismic Modeling by UsingFinite Sine and Cosine Transforms:AcousticEquations[J].J.Jilin Univ.(Earth Science Edition),2006,36(1):108-112
[56]贾晓峰,胡天跃,王润秋.无单元法用于地震波波动方程模拟与成像[J].地球物理学进展,2006,21(1):11-17Jia X F,Hu T Y,Wang R Q.Wave equationmodeling and imaging by using element-free method[J].Progress in Geophysics,2006,21(1):11-17
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