地震波有限差分模拟综述
|
摘要
本文从有限差分法数值模拟技术的各个方面对地震波有限差分模拟的发展和现状进行了论述.波场的数值模拟技术是认识地震波传播规律,检验各种处理方法正确性的重要工具,地震波的数值模拟是地震波传播规律研究的必要手段,贯穿于地震资料的采集、处理、解释的整个过程中.有限差分法数值模拟技术相对于射线方法具有更高的精度,同时比有限元方法计算量小,因此在实际应用中占很重要的地位.
The numerical seismic wave propagation modeling is a powerful tool in the oil exploration,such as the date collection,the processing and the interpretation and so on.It can not only find out the properties of the media,but also check the validity of processing methods,recognize the law of the wave propagation.In all the numerical methods,the finite-difference method is more useful with its advantages,such as high precision,flexibility,costless.In this paper,several parts of the finite-difference method are discussed,such as the finite-scheme,the source problem,the boundary condition and the numerical dispersion dumbness.
The numerical seismic wave propagation modeling is a powerful tool in the oil exploration,such as the date collection,the processing and the interpretation and so on.It can not only find out the properties of the media,but also check the validity of processing methods,recognize the law of the wave propagation.In all the numerical methods,the finite-difference method is more useful with its advantages,such as high precision,flexibility,costless.In this paper,several parts of the finite-difference method are discussed,such as the finite-scheme,the source problem,the boundary condition and the numerical dispersion dumbness.
引文
[1]王秀明,张海澜,王东.利用高阶交错网格有限差分法模拟地震波在非均匀孔隙介质中的传播[J].地球物理学报,2003,46(6):842~849.
[2]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.
[3]张剑锋.弹性波数值模拟的非规则网格差分法[J].地球物理学报,1998,41(增刊):357~365.
[4]张剑锋.各向异性介质中弹性波的数值模拟[J].固体力学学报,2000,21(3):234~242.
[5]张剑锋,刘铁林.三维非均匀介质中弹性波传播的数值模拟[J].固体力学学报,2001,22(4):356~360.
[6]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):283~291.
[7]杨顶辉.各向异性介质弹性波方程的正反演方法研究[D].北京:中国科学院地质与地球物理所,1996.
[8]任义庆,李勤学,马在田.地震波爆炸震源模拟[J].石油物探,1998,37(3):15~21.
[9]董清华.震源数值模拟[J].世界地质工程,2000,16(3):27~32.
[10]罗大清,宋炜,吴律.一种有效的处理模型角点反射的方法[J].石油物探,2000,39(4):26~31.
[11]田小波,吴庆举,曾融生.弹性波数值模拟的延迟边界方法[J].地球物理学报,2004,47(2):268~273.
[12]陈伟.起伏地表条件下二维地震波场的数值模拟[J].勘探地球物理进展,2005,28(1),25~31.
[13]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):856~864.
[14]谢里夫,吉尔达特著,初英,等译.勘探地震学(第二版)[M].北京:石油工业出版社,1999.
[15]蔡其新,何佩军,秦广胜,等.有限差分数值模拟的最小频散算法及其应用[J].石油地球物理勘探,2003,38(3).247~251.
[16]吴国忱,王华忠.波场模拟中的数值频散分析与校正策略.[J]地球物理学进展,2005,20(1):58~65.
[17]常旭,刘伊克.地震正反演与成像[M].北京:华文出版社,2001.
[18]牛滨华,孙春岩.地震波理论研究进展——介质模型与地震波传播[J].地球物理学进展,2004,19(2):255~163.
[19]王红落.地震波传播与成像若干问题的研究[D].北京:中国科学院地质与地球物理所,2004.
[20]孙若昧.地震波传播有限差分模拟的人工边界条件[J].地球物理学进展,1996,11(3):53~58.
[21]何兵寿,魏修成,刘洋.三维波动方程的数值频散关系及其叠前和叠后数值模拟[J].石油大学学报(自然科学版),2001,25(1):67~71.
[22]黄自萍,张铭,吴文清,等.弹性波传播数值模拟的区域分裂法[J].地球物理学报,2004,47(6):1094~1100..
[23]裴正林,牟永光.地震波传播数值模拟[J].地球物理学进展,2004,19(4):933~941.
[24]Alterman Z,Karal F C.Propagation of seismic wave in lay-ered media by finite difference methods[J].BSSA,1968,58(1):367~398.
[25]Boore D M.Finite-difference methods for seismic wave prop-agation in heterogeneous materials in Methods in computa-tional physics[J].1972,11:B.A.Bolt,ed.,AcademicPress,inc.
[26]Kelly K R,Ward R W,Treitel S,Alford R M.Synthetic seis-mograms-a finite-difference approach[J].Geophysics,1976,41:2~27.
[27]Madariaga R.Dynamics of an expanding circular fault[J].Bull Seism Soc Am,1976,65:163~18.
[28]Virieux J.S H wave propagation in heterogeneous media:ve-locity-stress finite difference method[J].Geophysics,1984,49(11):1933~1957.
[29]Virieux J.P-SV wave propagation in heterogeneous media:velocity-stress finite difference method[J].Geophysics,1986,51(4):889~901.
[30]Igel H,Mora P,et al.Anisotropic wave propagation throughfinite-difference grids[J].Geophysics,1995,60(4):1203~1216.
[31]Igel H,weber M.P-SV wave propagation in the Earth’smantle using finite differences:application to heterogeneouslowermost mantle structure[J].Geophys,Res.Lett,1996,23:415~418.
[32]Jastram C,Behle A.Acoustic modeling on a grid of velocityvarying spacing[J].Geophysical prospecting,1992,40:157~169.
[33]Jastram C,Tessemer E.Elastic modeling on a grid with ver-tically varying spacing[J].Geophysical prospecting,1994,42:357~370.
[34]Falk J,Tessmer E,Gajewski D.Tube wave modeling by thefinite-difference method with varying grid spacing[J].Pa-geoph,1996,148:77~93.
[35]Falk J,Tessmer E,Gajewski D.Efficient finite-differencemodeling of seismic waves using locally adjustable time steps[J].Geophysical Prospecting,1998,46:603~616.
[36]Tessmer E.seismic finite difference modeling with spatiallyvarying time step[J].Geophysics,2000,65(4):1290~1293.
[37]Carcione J M.wave fields in real media:wave propagation inanisotropic an elastic and porous media[J].UK:Elsevier Sci-ence LTD,2001.
[38]Dablain M A.The application of high-order differencing tothe scalar wave equation[J].Geophysics,1986,51(1):54~66.
[39]Kneib G,Kerner C.Accurate and efficient seismic modelingin random media[J].Geophysics 1993,58(4):576~588.
[40]Levander A.R Fourth-order finite-difference P-SV seismo-grams[J].Geophysics,1988,53(11):1425~1436.
[41]Graves R W.Simulating seismic wave propagation in 3D elas-tic media using staggered-grid finite-difference[J].BSSA,1996,86:1091~1106.
[42]Hestholm S O,Ruud B O.3-D finite-difference elastic wavemodeling[J].Geophysics,1998,63:613~622.
[43]Oprsal I A,Zahradnik J.Elastic finite-difference method forirregular grids[J].Geophysics 1999,64:240~250.
[44]Komatitsch D,Barnes C,Tromp J.Simulation of the diffrac-tion by single cracks:An accuracy study.72nd Annual Inter-national meeting,SEG,Abstracts,2002,2007~2010.
[45]Carcione J M,et al.Seismic Modeling[J].Geophysics,2002,67(4):1304~1325.
[46]Saenger E H,Gold N,Shapiro S A.Modeling the propaga-tion of elastic waves using a modified finite-difference grid[J].Wave Motion,2000,31:77~92.
[47]Hicks G J.Arbitrary source and receiver positioning in finite-difference scheme using Kaiser windowed sinc functions[J].Geophysics,2002,67(1):156~166.
[48]Smith W D.A nonreflecting plane boundary for wave propa-gation problems[J].J Comp Phys,1974,15:492~503.
[49]Majda E B.A Absorbing boundary conditions for the numeri-cal simulation of wave[J].Math Comp,1977,629~651.
[50]Clayton R,Engquist B.Absorbing boundary conditions for a-coustic and elastic wave equation[J].BSSA,1977,67:1529~1540.
[51]Reynolds A C.Boundary conditions for the numerical solu-tion of wave propagation problem[J].Geophysics,1978,43:1099~1110.
[52]Keys R G.Absorbing boundary conditions for acoustic media[J].Geophysics,1985,50:892~902.
[53]Higdon R L.Numerical absorbing boundary conditions forthe wave equation[J].Math Comp,1987,49:65~90.
[54]Long L T,Liow J S.A transparent boundary for finite-difference wave simulation[J].Geophysics,1990,55:201~208.
[55]Hagstrom T.On high-order radiation boundary condition,inEngquist B,Kriegsmann G A Eds[J].Computational WavePropagation:Springer-Verlag New York,Inc,1997,86:1~21.
[56]Cerjan C,Kosloff D,Kosloff R,et al.A nonreflectingboundary condition for discrete acoustic and elastic wave e-quations[J].Geophysics,50:705~708.
[57]Kosloff R,Kosloff D.Absorbing boundary conditions forwave propagation problems[J].J Comp Phys,1986,63:363~376.
[58]Sochacki J,Kubichek R,et al.Absorbing boundary condi-tions and surface wave[J].Geophysics,1987,52:60~71.
[59]Berenger J.A perfectly matched layer for the absorption ofsorption of electromagnetic wave[J].J Comput Phys,1994,114:185~200.
[60]Peng C,Toksoz M N.Optimal absorbing boundary condi-tions for finite-difference modeling of acoustic and elasticwave propagation[J].J Acoust Soc Am,1994,95:733~745.
[61]Peng C,Toksoz M N.An optical absorbing boundary condi-tion for elastic wave modeling[J].Geophysics,1995,60:296~301.
[62]Hasting F,Schneider J B,et al.Application of the perfectlymatched layer(PML)absorbing boundary condition to elasticwave propagation[J].J Acoust Soc Am,1996,100:3061~3069.
[63]Jianlin Zhu.A transparent boundary technique for numericalmodeling of elastic waves[J].Geophysics,1999,64(3):963~966.
[64]Saenger E H,Shapiro S.A Effective velocities in fracturedmedia:A numerical study using the rotated staggered finite-difference grid[J].Geophysical Prospecting,2002,50:183~194.
[65]Saenger E H,Thomas Bohlen.Finite-difference modeling ofviscoelastic and anisotropic wave propagation using the rota-ted staggered grid[J].Geophysics,2004,69(2):583~591.
[66]Fornberg B.The pseudo-spectral method:comparisons wit-hfinite differences for the elastic wave equation[J].Geophys-ics,1987,52(4):483~501.
[67]Fei T,larner K.Elimination of numerical dispersion in finite-difference modeling and migration by flux-corrected transport[J].Geophysics,1995,60(6):1830~1842.
[68]Boris J,Book D.Flux-corrected transport.I.SHASTA,Afluid transport algorithm that works[J].J Comput.Phys,1973,11:38~69.
[69]Muller T M,Shapiro S A.Most probable seismic pulses insingle realizations of two-and three-dimensional random media[J].Geophysical Journal International,2001,144:83~95.
[70]Muller T M,Shapiro S A,Sick C M.A most probable ballis-tic waves in random media:A weak-fluctuation approximationand numerical results[J].Waves in Random media,2002,12:223~245.
[2]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.
[3]张剑锋.弹性波数值模拟的非规则网格差分法[J].地球物理学报,1998,41(增刊):357~365.
[4]张剑锋.各向异性介质中弹性波的数值模拟[J].固体力学学报,2000,21(3):234~242.
[5]张剑锋,刘铁林.三维非均匀介质中弹性波传播的数值模拟[J].固体力学学报,2001,22(4):356~360.
[6]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):283~291.
[7]杨顶辉.各向异性介质弹性波方程的正反演方法研究[D].北京:中国科学院地质与地球物理所,1996.
[8]任义庆,李勤学,马在田.地震波爆炸震源模拟[J].石油物探,1998,37(3):15~21.
[9]董清华.震源数值模拟[J].世界地质工程,2000,16(3):27~32.
[10]罗大清,宋炜,吴律.一种有效的处理模型角点反射的方法[J].石油物探,2000,39(4):26~31.
[11]田小波,吴庆举,曾融生.弹性波数值模拟的延迟边界方法[J].地球物理学报,2004,47(2):268~273.
[12]陈伟.起伏地表条件下二维地震波场的数值模拟[J].勘探地球物理进展,2005,28(1),25~31.
[13]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):856~864.
[14]谢里夫,吉尔达特著,初英,等译.勘探地震学(第二版)[M].北京:石油工业出版社,1999.
[15]蔡其新,何佩军,秦广胜,等.有限差分数值模拟的最小频散算法及其应用[J].石油地球物理勘探,2003,38(3).247~251.
[16]吴国忱,王华忠.波场模拟中的数值频散分析与校正策略.[J]地球物理学进展,2005,20(1):58~65.
[17]常旭,刘伊克.地震正反演与成像[M].北京:华文出版社,2001.
[18]牛滨华,孙春岩.地震波理论研究进展——介质模型与地震波传播[J].地球物理学进展,2004,19(2):255~163.
[19]王红落.地震波传播与成像若干问题的研究[D].北京:中国科学院地质与地球物理所,2004.
[20]孙若昧.地震波传播有限差分模拟的人工边界条件[J].地球物理学进展,1996,11(3):53~58.
[21]何兵寿,魏修成,刘洋.三维波动方程的数值频散关系及其叠前和叠后数值模拟[J].石油大学学报(自然科学版),2001,25(1):67~71.
[22]黄自萍,张铭,吴文清,等.弹性波传播数值模拟的区域分裂法[J].地球物理学报,2004,47(6):1094~1100..
[23]裴正林,牟永光.地震波传播数值模拟[J].地球物理学进展,2004,19(4):933~941.
[24]Alterman Z,Karal F C.Propagation of seismic wave in lay-ered media by finite difference methods[J].BSSA,1968,58(1):367~398.
[25]Boore D M.Finite-difference methods for seismic wave prop-agation in heterogeneous materials in Methods in computa-tional physics[J].1972,11:B.A.Bolt,ed.,AcademicPress,inc.
[26]Kelly K R,Ward R W,Treitel S,Alford R M.Synthetic seis-mograms-a finite-difference approach[J].Geophysics,1976,41:2~27.
[27]Madariaga R.Dynamics of an expanding circular fault[J].Bull Seism Soc Am,1976,65:163~18.
[28]Virieux J.S H wave propagation in heterogeneous media:ve-locity-stress finite difference method[J].Geophysics,1984,49(11):1933~1957.
[29]Virieux J.P-SV wave propagation in heterogeneous media:velocity-stress finite difference method[J].Geophysics,1986,51(4):889~901.
[30]Igel H,Mora P,et al.Anisotropic wave propagation throughfinite-difference grids[J].Geophysics,1995,60(4):1203~1216.
[31]Igel H,weber M.P-SV wave propagation in the Earth’smantle using finite differences:application to heterogeneouslowermost mantle structure[J].Geophys,Res.Lett,1996,23:415~418.
[32]Jastram C,Behle A.Acoustic modeling on a grid of velocityvarying spacing[J].Geophysical prospecting,1992,40:157~169.
[33]Jastram C,Tessemer E.Elastic modeling on a grid with ver-tically varying spacing[J].Geophysical prospecting,1994,42:357~370.
[34]Falk J,Tessmer E,Gajewski D.Tube wave modeling by thefinite-difference method with varying grid spacing[J].Pa-geoph,1996,148:77~93.
[35]Falk J,Tessmer E,Gajewski D.Efficient finite-differencemodeling of seismic waves using locally adjustable time steps[J].Geophysical Prospecting,1998,46:603~616.
[36]Tessmer E.seismic finite difference modeling with spatiallyvarying time step[J].Geophysics,2000,65(4):1290~1293.
[37]Carcione J M.wave fields in real media:wave propagation inanisotropic an elastic and porous media[J].UK:Elsevier Sci-ence LTD,2001.
[38]Dablain M A.The application of high-order differencing tothe scalar wave equation[J].Geophysics,1986,51(1):54~66.
[39]Kneib G,Kerner C.Accurate and efficient seismic modelingin random media[J].Geophysics 1993,58(4):576~588.
[40]Levander A.R Fourth-order finite-difference P-SV seismo-grams[J].Geophysics,1988,53(11):1425~1436.
[41]Graves R W.Simulating seismic wave propagation in 3D elas-tic media using staggered-grid finite-difference[J].BSSA,1996,86:1091~1106.
[42]Hestholm S O,Ruud B O.3-D finite-difference elastic wavemodeling[J].Geophysics,1998,63:613~622.
[43]Oprsal I A,Zahradnik J.Elastic finite-difference method forirregular grids[J].Geophysics 1999,64:240~250.
[44]Komatitsch D,Barnes C,Tromp J.Simulation of the diffrac-tion by single cracks:An accuracy study.72nd Annual Inter-national meeting,SEG,Abstracts,2002,2007~2010.
[45]Carcione J M,et al.Seismic Modeling[J].Geophysics,2002,67(4):1304~1325.
[46]Saenger E H,Gold N,Shapiro S A.Modeling the propaga-tion of elastic waves using a modified finite-difference grid[J].Wave Motion,2000,31:77~92.
[47]Hicks G J.Arbitrary source and receiver positioning in finite-difference scheme using Kaiser windowed sinc functions[J].Geophysics,2002,67(1):156~166.
[48]Smith W D.A nonreflecting plane boundary for wave propa-gation problems[J].J Comp Phys,1974,15:492~503.
[49]Majda E B.A Absorbing boundary conditions for the numeri-cal simulation of wave[J].Math Comp,1977,629~651.
[50]Clayton R,Engquist B.Absorbing boundary conditions for a-coustic and elastic wave equation[J].BSSA,1977,67:1529~1540.
[51]Reynolds A C.Boundary conditions for the numerical solu-tion of wave propagation problem[J].Geophysics,1978,43:1099~1110.
[52]Keys R G.Absorbing boundary conditions for acoustic media[J].Geophysics,1985,50:892~902.
[53]Higdon R L.Numerical absorbing boundary conditions forthe wave equation[J].Math Comp,1987,49:65~90.
[54]Long L T,Liow J S.A transparent boundary for finite-difference wave simulation[J].Geophysics,1990,55:201~208.
[55]Hagstrom T.On high-order radiation boundary condition,inEngquist B,Kriegsmann G A Eds[J].Computational WavePropagation:Springer-Verlag New York,Inc,1997,86:1~21.
[56]Cerjan C,Kosloff D,Kosloff R,et al.A nonreflectingboundary condition for discrete acoustic and elastic wave e-quations[J].Geophysics,50:705~708.
[57]Kosloff R,Kosloff D.Absorbing boundary conditions forwave propagation problems[J].J Comp Phys,1986,63:363~376.
[58]Sochacki J,Kubichek R,et al.Absorbing boundary condi-tions and surface wave[J].Geophysics,1987,52:60~71.
[59]Berenger J.A perfectly matched layer for the absorption ofsorption of electromagnetic wave[J].J Comput Phys,1994,114:185~200.
[60]Peng C,Toksoz M N.Optimal absorbing boundary condi-tions for finite-difference modeling of acoustic and elasticwave propagation[J].J Acoust Soc Am,1994,95:733~745.
[61]Peng C,Toksoz M N.An optical absorbing boundary condi-tion for elastic wave modeling[J].Geophysics,1995,60:296~301.
[62]Hasting F,Schneider J B,et al.Application of the perfectlymatched layer(PML)absorbing boundary condition to elasticwave propagation[J].J Acoust Soc Am,1996,100:3061~3069.
[63]Jianlin Zhu.A transparent boundary technique for numericalmodeling of elastic waves[J].Geophysics,1999,64(3):963~966.
[64]Saenger E H,Shapiro S.A Effective velocities in fracturedmedia:A numerical study using the rotated staggered finite-difference grid[J].Geophysical Prospecting,2002,50:183~194.
[65]Saenger E H,Thomas Bohlen.Finite-difference modeling ofviscoelastic and anisotropic wave propagation using the rota-ted staggered grid[J].Geophysics,2004,69(2):583~591.
[66]Fornberg B.The pseudo-spectral method:comparisons wit-hfinite differences for the elastic wave equation[J].Geophys-ics,1987,52(4):483~501.
[67]Fei T,larner K.Elimination of numerical dispersion in finite-difference modeling and migration by flux-corrected transport[J].Geophysics,1995,60(6):1830~1842.
[68]Boris J,Book D.Flux-corrected transport.I.SHASTA,Afluid transport algorithm that works[J].J Comput.Phys,1973,11:38~69.
[69]Muller T M,Shapiro S A.Most probable seismic pulses insingle realizations of two-and three-dimensional random media[J].Geophysical Journal International,2001,144:83~95.
[70]Muller T M,Shapiro S A,Sick C M.A most probable ballis-tic waves in random media:A weak-fluctuation approximationand numerical results[J].Waves in Random media,2002,12:223~245.
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心