曲线坐标系程函方程的求解方法研究
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摘要
笛卡尔坐标系中经典的程函方程在静校正、叠前偏移、走时反演、地震定位、层析成像等许多地球物理工作都有应用,然而用其计算起伏地表的地震波走时时却比较困难.我们通过把曲线坐标系中的矩形网格映射到笛卡尔坐标系的贴体网格推导出了曲线坐标中的程函方程,此时,曲线坐标系的程函方程呈现为各向异性的程函方程(尽管在笛卡尔坐标系中介质是各向同同性的).然后尝试用求解各向同性程函方程的快速推进法和Lax-Friedrichs快速扫描算法来分别求解该方程.数值试验表明未加考虑各向异性程函方程与各向同性程函方程的差别而把求解各向同性程函方程的快速推进法直接拓展到曲线坐标中的程函方程的做法是错误的,而Lax-Friedrichs快速扫描算法总能稳定地求解曲线坐标系的程函方程,进而有效地处理了地表起伏的情况,得到稳定准确的计算结果.
The classical eikonal equation is commonly used in Cartesian coordinate system for problems that involve static correction,prestack migration,earthquake location and seismic tomography,but is less effective for calculating travel times in an earth model that has an irregular surface.We transform the eikonal equation to a curvilinear coordinate system that conforms with the boundaries of the domain.The eikonal equation in the curvilinear coordinate system displays the mathematical form of an anisotropic eikonal equations(even though the medium is isotropic in the Cartesian coordinate system).Then,we try to solve the anisotropic eikonal equations with two numerical methods,a simple modification of the fast marching method and Lax-Friedrichs fast sweeping method,respectively.Through a number of different numerical experiments we find: one may compute wrong solutions by extending fast marching methods designed for isotropic eikonal equations to anisotropic eikonal equations without taking into account the differences between them;the Lax-Friedrichs fast sweeping method is stable and valid for the eikonal equation in the curvilinear coordinate system,which has a significant meaning in the direction of solution of the eikonal equation in the curvilinear coordinate system.
The classical eikonal equation is commonly used in Cartesian coordinate system for problems that involve static correction,prestack migration,earthquake location and seismic tomography,but is less effective for calculating travel times in an earth model that has an irregular surface.We transform the eikonal equation to a curvilinear coordinate system that conforms with the boundaries of the domain.The eikonal equation in the curvilinear coordinate system displays the mathematical form of an anisotropic eikonal equations(even though the medium is isotropic in the Cartesian coordinate system).Then,we try to solve the anisotropic eikonal equations with two numerical methods,a simple modification of the fast marching method and Lax-Friedrichs fast sweeping method,respectively.Through a number of different numerical experiments we find: one may compute wrong solutions by extending fast marching methods designed for isotropic eikonal equations to anisotropic eikonal equations without taking into account the differences between them;the Lax-Friedrichs fast sweeping method is stable and valid for the eikonal equation in the curvilinear coordinate system,which has a significant meaning in the direction of solution of the eikonal equation in the curvilinear coordinate system.
引文
[1]Aki K,Richards P G.Quantitative seismology.2002:UnivScience Books.
[2]Hole J.Nonlinear high-resolution three-dimensional seismictravel time tomography.Journal of Geophysical Research,1992,97(B5):6553-6562.
[3]Chen Y,Badal J,Hu J.Love and Rayleigh wave tomographyof the Qinghai-Tibet Plateau and surrounding areas.Pureand Applied Geophysics,2010,167(10):1-33.
[4]Zelt C,Smith R.Seismic traveltime inversion for 2-D crustalvelocity structure.Geophysical Journal International,1992,108(1):16-34.
[5]Zhang Z J,Wang G J,Teng J W,et al.CDP mapping toobtain the fine structure of the crust and upper mantle fromseismic sounding data:an example for the southeasternChina.Physics of the Earth and Planetary Interiors,2000,122(1-2):133-146.
[6]张中杰,秦义龙,陈赟等.由宽角反射地震资料重建壳幔反射结构的相似性剖面.地球物理学报,2004,47(003):469-474.Zhang Z J,Qin Y L,Chen Y,et al.Reconstruction of thesemblance section for the crust and mantle reflection structureby wide-angle reflection seismic data.Chinese J.Geophys.(in Chinese),2004,47(3):469-474
[7]朱金明,王丽燕.地震波走时的有限差分法计算.地球物理学报,1992,35(1):86-92.Zhu J M,Wang L Y.Finite difference calculation of seismictravel times.Chinese J.Geophys.(in Chinese),1992,35(1):86-92.
[8]Cerveny V,Molotkov I A,and Psencik I.Ray methods inseismology.1977,Univ.of Karlova Press.
[9]Zhang Z,Badal J,Li Y,et al.Crust-upper mantle seismicvelocity structure across Southeastern China.Tectonophysics,2005,395(1-2):137-157.
[10]Zhang Z,Li Y,Lu D,et al.Velocity and anisotropystructure of the crust in the Dabieshan orogenic belt fromwide-angle seismic data.Physics of the Earth and PlanetaryInteriors,2000,122(1-2):115-131.
[11]Zhang Z,Wang Y,Chen Y,et al.Crustal structure acrossLongmenshan fault belt from passive source seismic profiling.Geophys.Res.Lett,2009,36.
[12]Xu T,Xu G,Gao E,et al.Block modeling and segmentallyiterative ray tracing in complex 3Dmedia.Geophysics,2006,71:T41-T51.
[13]Xu T,Zhang Z,Gao E,et al.Segmentally Iterative RayTracing in Complex 2Dand 3DHeterogeneous Block Models.Bulletin of the Seismological Society of America,100(2):841-850.
[14]Vidale J E.Finite-difference calculation of travel times.Bulletin of the Seismological Society of America,1988,78(6):2062-2076.
[15]Vidale J E.Finite-difference calculation of traveltimes inthree dimensions.Geophysics,1990,55(5):521-526.
[16]Qin F,Luo Y,Olsen K B,et al.Finite-difference solution ofthe eikonal equation along expanding wavefronts.Geophysics,1992,57:478-487.
[17]Van Trier J,Symes W W.Upwind finite-differencecalculation of traveltimes.Geophysics,1991,56(6):812-821.
[18]Sethian J.Evolution,implementation,and application oflevel set and fast marching methods for advancing fronts.Journal of Computational Physics,2001,169(2):503-555.
[19]Sethian J A.Fast marching methods.SIAM review,1999,41(2):199-235.
[20]Sethian J A,Popovici A M.Three dimensional traveltimescomputation using the Fast Marching Method.Geophysics,1999,64(2):516-523.
[21]Sethian J A.A fast marching level set method formonotonically advancing fronts.Proceedings of the NationalAcademy of Sciences of the United States of America,1996,93(4):1591-1595.
[22]Alkhalifah,T.&Fomel,S.,Implementing the fastmarching eikonal solver:spherical versus Cartesiancoordinates.Geophys.Prospect.,2001,49:165-178.
[23]Fomel S.A variational formulation of the fast marchingeikonal solver.SEP-95:Stanford Exploration Project,1997:127-147.
[24]Kim S.3-D eikonal solvers:First-arrival traveltimes.Geophysics,2002,67(4):1225-1231.
[25]Rawlinson N,Sambridge M.Wave front evolution instrongly heterogeneous layered media using the fast marchingmethod.Geophysical Journal International,2004,156(3):631-647.
[26]Rawlinson N,Sambridge M.Multiple reflection andtransmission phases in complex layered media using amultistage fast marching method.Geophysics,2004,69(5):1338.
[27]Rawlinson N,Sambridge M.The fast marching method:aneffective tool for tomographic imaging and tracking multiplephases in complex layered media.Exploration Geophysics,2005,36(4):341-350.
[28]孙章庆,孙建国,韩复兴.复杂地表条件下基于线性插值和窄带技术的地震波走时计算.地球物理学报,2009,52(11):2846-2853.Sun Z Q,Sun J G,Han F X.Travehimes computation usinglinear interpoiation and narrow band technique under complextopographical conditions.Chinese J.Geophys.(in Chinese),2009,52(11):2846-2853
[29]De Kool M,Rawlinson N,Sambridge M.A practical grid-based method for tracking multiple refraction and reflectionphases in three-dimensional heterogeneous media.Geophysical Journal International,2006,167(1):253-270.
[30]Zhao H.A fast sweeping method for eikonal equations.Mathematics of Computation,2005,74(250):603-628.
[31]Zhang Y T,Zhao H K,Qian J.High order fast sweepingmethods for static Hamilton-Jacobi equations.Journal ofScientific Computing,2006,29(1):25-56.
[32]兰海强,张智,徐涛等.地震波走时场模拟的快速推进法和快速扫描法比较研究.地球物理学进展,2012,已接受.Lan H Q,Zhang Z,Xu T,et.al.A comparative study onthe fast marching and fast sweeping methods in thecalculation of first-arrival traveltime field.Progress inGeophys.(in Chinese),2012,accepted.
[33]Zhang Z J,Yang L Q,Teng J W,Badal J.An overview ofthe earth crust under China.Earth-Science Reviews,104(1-3):143-166DOI:10.1016/j.earscirev.2010.10.003,2011.
[34]Lan H,Zhang Z.Three-dimensional wave-field simulation inheterogeneous transversely isotropic medium with irregularfree surface.Bulletin of the Seismological Society ofAmerica,2011 101(3):1354-1370.
[35]阎世信,刘怀山,姚雪根.山地地球物理勘探技术.北京:石油工业出版社,2000.Yan S X,Liu H S,Yao X G.Geophysical ExplorationTechnology in the Mountainous Area(in Chinese).Beijing:Petroleum Industry Press,2000
[36]Kao C Y,Osher S,Qian J.Legendre-transform-based fastsweeping methods for static Hamilton-Jacobi equations ontriangulated meshes.Journal of Computational Physics,2008,227(24):10209-10225.
[37]Kimmel R,Sethian J A.Computing geodesic paths onmanifolds.Proceedings of the National Academy ofSciences of the United States of America,1998,95(15):8431-7435.
[38]Lelièvre P G,Farquharson C G,Hurich C A.Computingfirst-arrival seismic traveltimes on unstructured 3-Dtetrahedral grids using the Fast Marching Method.Geophysical Journal International,184(2):885-896.
[39]Qian J,Zhang Y T,Zhao H K.A fast sweeping method forstatic convex Hamilton-Jacobi equations.Journal ofScientific Computing,2007,31(1):237-271.
[40]Qian J,Zhang Y T,Zhao H K.Fast sweeping methods forEikonal equations on triangular meshes.SIAM Journal onNumerical Analysis,2008,45(1):83-107.
[41]Sethian J A,Vladimirsky A.Fast methods for the Eikonaland related Hamilton-Jacobi equations on unstructuredmeshes.Proceedings of the National Academy of Sciencesof the United States of America,2000,97(11):5699.
[42]Appelo D,Petersson N.A stable finite difference method forthe elastic wave equation on complex geometries with freesurfaces.Communications in Computational Physics,2009,5(1):84-107.
[43]孙章庆,孙建国,张东良.二维起伏地表条件下坐标变换法直流电场数值模拟.吉林大学学报:地球科学版,2009,39(3):528-534.Sun Z Q,Sun J G,Zhang D L.2DDC electric field numericalmodeling including surface topography using coordinatetransformation method.Journal of Jilin University:EarthScience Edition,2009,39(3):528-534.
[44]Lan H,Zhang Z.2Dfinite-difference seismic modeling of anopen fluid-filled fracture with irregular free surface,in review
[45]Tessmer E,Kosloff D.3-D elastic modeling with surfacetopography by a Chebychev spectral method.Geophysics,1994,59:464.
[46]兰海强,刘佳,白志明.VTI介质起伏地表地震波场模拟.地球物理学报,2011,54(8):2072-2084.Lan H Q,Liu J,Bai Z M.Wave-field simulation in VTImedia with irregular free surface.Chinese J.Geophys.(inChinese),2011,54(8):2072-2084.
[47]孙建国.复杂地表条件下地球物理场数值模拟方法评述.世界地质,2007,26(003):345-362.Sun J G.Methods for numerical modeling of geophysicalfields under complex topographicaI conditions:a criticalreview.Global Geology(in Chinese),2007,26(003):345-362.
[48]Lan H,Zhang Z.Comparative study of the free-surfaceboundary condition in two-dimensional finite-difference elasticwave field simulation.Journal of Geophysics and Engineering,2011,8:275-286.
[49]Sun J,Sun Z,Han F.A finite difference scheme for solvingthe eikonal equation including surface topography.Geophysics,2011,76(4):T53-T63.
[50]Zhang Z J,Teng J W,Wan Z C.Establishment of parametricequations of seismic-wavefronts in 2-D anisotropic media.Chinese Science Bulletin,1994,39(22):1890-1894.
[51]Hvid S L.Three dimensional algebraic grid generation[Ph.D.thesis],Technical University of Denmark,1994.
[52]Thompson J,Warsi Z,Mastin C.Numerical grid generation:foundations and applications.1985:North-holland Amsterdam.
[53]Hestholm S,Ruud B.3-D finite-difference elastic wavemodeling including surface topography.Geophysics,1998,63:613-622.
[54]Tessmer E,Kosloff D,Behle A.Elastic wave propagationsimulation in the presence of surface topography.Geophys.J.Int,1992,108(2):621-632.
[55]Tsai Y H R,Cheng L T,Osher S,et al.Fast sweepingalgorithms for a class of Hamilton-Jacobi equations.SIAMJournal on Numerical Analysis,2004:673-694.
[56]Kao C Y,Osher S,Qian J.Lax-Friedrichs sweeping schemefor static Hamilton-Jacobi equations.Journal of ComputationalPhysics,2004,196(1):367-391.
[57]兰海强,徐涛,白志明.贴体网格各向异性对坐标变换法求解起伏地表下地震初至波走时的影响研究.地球物理学报,已接受.Lan H Q,Xu T,Bai Z M.Study of the effects due to theanisotropic stretching of the surface-fitting grid on thetraveltime computation for irregular surface by the coordinatetransforming method.Chinese J.Geophys.(in Chinese),inpress.
[2]Hole J.Nonlinear high-resolution three-dimensional seismictravel time tomography.Journal of Geophysical Research,1992,97(B5):6553-6562.
[3]Chen Y,Badal J,Hu J.Love and Rayleigh wave tomographyof the Qinghai-Tibet Plateau and surrounding areas.Pureand Applied Geophysics,2010,167(10):1-33.
[4]Zelt C,Smith R.Seismic traveltime inversion for 2-D crustalvelocity structure.Geophysical Journal International,1992,108(1):16-34.
[5]Zhang Z J,Wang G J,Teng J W,et al.CDP mapping toobtain the fine structure of the crust and upper mantle fromseismic sounding data:an example for the southeasternChina.Physics of the Earth and Planetary Interiors,2000,122(1-2):133-146.
[6]张中杰,秦义龙,陈赟等.由宽角反射地震资料重建壳幔反射结构的相似性剖面.地球物理学报,2004,47(003):469-474.Zhang Z J,Qin Y L,Chen Y,et al.Reconstruction of thesemblance section for the crust and mantle reflection structureby wide-angle reflection seismic data.Chinese J.Geophys.(in Chinese),2004,47(3):469-474
[7]朱金明,王丽燕.地震波走时的有限差分法计算.地球物理学报,1992,35(1):86-92.Zhu J M,Wang L Y.Finite difference calculation of seismictravel times.Chinese J.Geophys.(in Chinese),1992,35(1):86-92.
[8]Cerveny V,Molotkov I A,and Psencik I.Ray methods inseismology.1977,Univ.of Karlova Press.
[9]Zhang Z,Badal J,Li Y,et al.Crust-upper mantle seismicvelocity structure across Southeastern China.Tectonophysics,2005,395(1-2):137-157.
[10]Zhang Z,Li Y,Lu D,et al.Velocity and anisotropystructure of the crust in the Dabieshan orogenic belt fromwide-angle seismic data.Physics of the Earth and PlanetaryInteriors,2000,122(1-2):115-131.
[11]Zhang Z,Wang Y,Chen Y,et al.Crustal structure acrossLongmenshan fault belt from passive source seismic profiling.Geophys.Res.Lett,2009,36.
[12]Xu T,Xu G,Gao E,et al.Block modeling and segmentallyiterative ray tracing in complex 3Dmedia.Geophysics,2006,71:T41-T51.
[13]Xu T,Zhang Z,Gao E,et al.Segmentally Iterative RayTracing in Complex 2Dand 3DHeterogeneous Block Models.Bulletin of the Seismological Society of America,100(2):841-850.
[14]Vidale J E.Finite-difference calculation of travel times.Bulletin of the Seismological Society of America,1988,78(6):2062-2076.
[15]Vidale J E.Finite-difference calculation of traveltimes inthree dimensions.Geophysics,1990,55(5):521-526.
[16]Qin F,Luo Y,Olsen K B,et al.Finite-difference solution ofthe eikonal equation along expanding wavefronts.Geophysics,1992,57:478-487.
[17]Van Trier J,Symes W W.Upwind finite-differencecalculation of traveltimes.Geophysics,1991,56(6):812-821.
[18]Sethian J.Evolution,implementation,and application oflevel set and fast marching methods for advancing fronts.Journal of Computational Physics,2001,169(2):503-555.
[19]Sethian J A.Fast marching methods.SIAM review,1999,41(2):199-235.
[20]Sethian J A,Popovici A M.Three dimensional traveltimescomputation using the Fast Marching Method.Geophysics,1999,64(2):516-523.
[21]Sethian J A.A fast marching level set method formonotonically advancing fronts.Proceedings of the NationalAcademy of Sciences of the United States of America,1996,93(4):1591-1595.
[22]Alkhalifah,T.&Fomel,S.,Implementing the fastmarching eikonal solver:spherical versus Cartesiancoordinates.Geophys.Prospect.,2001,49:165-178.
[23]Fomel S.A variational formulation of the fast marchingeikonal solver.SEP-95:Stanford Exploration Project,1997:127-147.
[24]Kim S.3-D eikonal solvers:First-arrival traveltimes.Geophysics,2002,67(4):1225-1231.
[25]Rawlinson N,Sambridge M.Wave front evolution instrongly heterogeneous layered media using the fast marchingmethod.Geophysical Journal International,2004,156(3):631-647.
[26]Rawlinson N,Sambridge M.Multiple reflection andtransmission phases in complex layered media using amultistage fast marching method.Geophysics,2004,69(5):1338.
[27]Rawlinson N,Sambridge M.The fast marching method:aneffective tool for tomographic imaging and tracking multiplephases in complex layered media.Exploration Geophysics,2005,36(4):341-350.
[28]孙章庆,孙建国,韩复兴.复杂地表条件下基于线性插值和窄带技术的地震波走时计算.地球物理学报,2009,52(11):2846-2853.Sun Z Q,Sun J G,Han F X.Travehimes computation usinglinear interpoiation and narrow band technique under complextopographical conditions.Chinese J.Geophys.(in Chinese),2009,52(11):2846-2853
[29]De Kool M,Rawlinson N,Sambridge M.A practical grid-based method for tracking multiple refraction and reflectionphases in three-dimensional heterogeneous media.Geophysical Journal International,2006,167(1):253-270.
[30]Zhao H.A fast sweeping method for eikonal equations.Mathematics of Computation,2005,74(250):603-628.
[31]Zhang Y T,Zhao H K,Qian J.High order fast sweepingmethods for static Hamilton-Jacobi equations.Journal ofScientific Computing,2006,29(1):25-56.
[32]兰海强,张智,徐涛等.地震波走时场模拟的快速推进法和快速扫描法比较研究.地球物理学进展,2012,已接受.Lan H Q,Zhang Z,Xu T,et.al.A comparative study onthe fast marching and fast sweeping methods in thecalculation of first-arrival traveltime field.Progress inGeophys.(in Chinese),2012,accepted.
[33]Zhang Z J,Yang L Q,Teng J W,Badal J.An overview ofthe earth crust under China.Earth-Science Reviews,104(1-3):143-166DOI:10.1016/j.earscirev.2010.10.003,2011.
[34]Lan H,Zhang Z.Three-dimensional wave-field simulation inheterogeneous transversely isotropic medium with irregularfree surface.Bulletin of the Seismological Society ofAmerica,2011 101(3):1354-1370.
[35]阎世信,刘怀山,姚雪根.山地地球物理勘探技术.北京:石油工业出版社,2000.Yan S X,Liu H S,Yao X G.Geophysical ExplorationTechnology in the Mountainous Area(in Chinese).Beijing:Petroleum Industry Press,2000
[36]Kao C Y,Osher S,Qian J.Legendre-transform-based fastsweeping methods for static Hamilton-Jacobi equations ontriangulated meshes.Journal of Computational Physics,2008,227(24):10209-10225.
[37]Kimmel R,Sethian J A.Computing geodesic paths onmanifolds.Proceedings of the National Academy ofSciences of the United States of America,1998,95(15):8431-7435.
[38]Lelièvre P G,Farquharson C G,Hurich C A.Computingfirst-arrival seismic traveltimes on unstructured 3-Dtetrahedral grids using the Fast Marching Method.Geophysical Journal International,184(2):885-896.
[39]Qian J,Zhang Y T,Zhao H K.A fast sweeping method forstatic convex Hamilton-Jacobi equations.Journal ofScientific Computing,2007,31(1):237-271.
[40]Qian J,Zhang Y T,Zhao H K.Fast sweeping methods forEikonal equations on triangular meshes.SIAM Journal onNumerical Analysis,2008,45(1):83-107.
[41]Sethian J A,Vladimirsky A.Fast methods for the Eikonaland related Hamilton-Jacobi equations on unstructuredmeshes.Proceedings of the National Academy of Sciencesof the United States of America,2000,97(11):5699.
[42]Appelo D,Petersson N.A stable finite difference method forthe elastic wave equation on complex geometries with freesurfaces.Communications in Computational Physics,2009,5(1):84-107.
[43]孙章庆,孙建国,张东良.二维起伏地表条件下坐标变换法直流电场数值模拟.吉林大学学报:地球科学版,2009,39(3):528-534.Sun Z Q,Sun J G,Zhang D L.2DDC electric field numericalmodeling including surface topography using coordinatetransformation method.Journal of Jilin University:EarthScience Edition,2009,39(3):528-534.
[44]Lan H,Zhang Z.2Dfinite-difference seismic modeling of anopen fluid-filled fracture with irregular free surface,in review
[45]Tessmer E,Kosloff D.3-D elastic modeling with surfacetopography by a Chebychev spectral method.Geophysics,1994,59:464.
[46]兰海强,刘佳,白志明.VTI介质起伏地表地震波场模拟.地球物理学报,2011,54(8):2072-2084.Lan H Q,Liu J,Bai Z M.Wave-field simulation in VTImedia with irregular free surface.Chinese J.Geophys.(inChinese),2011,54(8):2072-2084.
[47]孙建国.复杂地表条件下地球物理场数值模拟方法评述.世界地质,2007,26(003):345-362.Sun J G.Methods for numerical modeling of geophysicalfields under complex topographicaI conditions:a criticalreview.Global Geology(in Chinese),2007,26(003):345-362.
[48]Lan H,Zhang Z.Comparative study of the free-surfaceboundary condition in two-dimensional finite-difference elasticwave field simulation.Journal of Geophysics and Engineering,2011,8:275-286.
[49]Sun J,Sun Z,Han F.A finite difference scheme for solvingthe eikonal equation including surface topography.Geophysics,2011,76(4):T53-T63.
[50]Zhang Z J,Teng J W,Wan Z C.Establishment of parametricequations of seismic-wavefronts in 2-D anisotropic media.Chinese Science Bulletin,1994,39(22):1890-1894.
[51]Hvid S L.Three dimensional algebraic grid generation[Ph.D.thesis],Technical University of Denmark,1994.
[52]Thompson J,Warsi Z,Mastin C.Numerical grid generation:foundations and applications.1985:North-holland Amsterdam.
[53]Hestholm S,Ruud B.3-D finite-difference elastic wavemodeling including surface topography.Geophysics,1998,63:613-622.
[54]Tessmer E,Kosloff D,Behle A.Elastic wave propagationsimulation in the presence of surface topography.Geophys.J.Int,1992,108(2):621-632.
[55]Tsai Y H R,Cheng L T,Osher S,et al.Fast sweepingalgorithms for a class of Hamilton-Jacobi equations.SIAMJournal on Numerical Analysis,2004:673-694.
[56]Kao C Y,Osher S,Qian J.Lax-Friedrichs sweeping schemefor static Hamilton-Jacobi equations.Journal of ComputationalPhysics,2004,196(1):367-391.
[57]兰海强,徐涛,白志明.贴体网格各向异性对坐标变换法求解起伏地表下地震初至波走时的影响研究.地球物理学报,已接受.Lan H Q,Xu T,Bai Z M.Study of the effects due to theanisotropic stretching of the surface-fitting grid on thetraveltime computation for irregular surface by the coordinatetransforming method.Chinese J.Geophys.(in Chinese),inpress.
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