地震射线辛几何算法初探
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摘要
走时计算已广泛用于地震建模、成像及速度分析等诸方面．基于地震波场的Ｈａｍｉｌｔｏｎ力学性质，本文探索应用适于Ｈａｍｉｌｔｏｎ力学的计算方法──辛几何算法对地震射线 进行走时及路径的计算．利用辛几何算法和属于耗散算法的四阶 Ｒｕｎｇｅ－Ｋｕｔｔａ算法进行射线 路径和走时的计算对比，结果表明这两类算法数值精度相当，但辛几何算法的速度却快了３ 倍．本文还利用二阶Ｅｕｌｅｒ型辛差分格式对Ｍａｒｍｏｕｓｉ模型进行了射线追踪计算，结果显示所 得射线具有良好的光滑性和较强的阴影区穿透能力．
Traveltime-computation is widely used in seismic modeling, imaging and velocity analysis, etc. The technology of ray tracing is one of the common methods to acquire traveltime. With the development of the research in complex geology and considering Hamilton mechanics quality of seismic wave field, the symplectic algorithm which is based on Hamilton mechanics is used to obtain traveltime and path of Seismic ray in this paper. The traveltime and path obtained by both Symplectic algorithm and Runge-Kutta algorithm belonging to dissipative algorithm are compared. The result indicates the precision of both is very adjacent however the Symplectic algorithm is far more faster. In addition, the ray tracing have been carried on complex Marmousi Model. The result has proved that Symplectic algorithm is a preferable robust and has a better ability to penetrate shadow zones.
Traveltime-computation is widely used in seismic modeling, imaging and velocity analysis, etc. The technology of ray tracing is one of the common methods to acquire traveltime. With the development of the research in complex geology and considering Hamilton mechanics quality of seismic wave field, the symplectic algorithm which is based on Hamilton mechanics is used to obtain traveltime and path of Seismic ray in this paper. The traveltime and path obtained by both Symplectic algorithm and Runge-Kutta algorithm belonging to dissipative algorithm are compared. The result indicates the precision of both is very adjacent however the Symplectic algorithm is far more faster. In addition, the ray tracing have been carried on complex Marmousi Model. The result has proved that Symplectic algorithm is a preferable robust and has a better ability to penetrate shadow zones.
引文
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[2] Vidale J. Finite difference calculation of traveltime. Bull. Seis. Soc. Am., 1988, 78:2062--2076.
[3] Vidale J. Finite difference calculation of traveltime in three Dimensions. Geophysics, 1990, 55:521--526.
[4]黄联捷,李幼铭,吴如山.用于图像重建的波前法射线追踪.地球物理学报,1992,35(2):223—233.HLJANG Lian-Jie, LI You-Ming, WU Ru-Shan. The wave--front ray tracing method for image reconstruction.Chinese J. Geophys. (in Chinese), 1992, 35(2):223--233.
[ 5 ] Satio H Traveltime and rqyypaths of first arrival seismic waves, computation method based upon Huygens's principle. Expanded Abstacts Society of Exploration Geophysicisrt(SEG) 59th Annual International Meeting,1989, 244-247.
[6 ] Moser T., Shortest path calculation of seismic rays. Geophysics, 1991, 56:59--67.
[7]刘洪,孟繁林,李幼铭.计算最小走时和射线路径的界面网全局方法.地球物理学报,1995,38(1):823- 831.LIU Hong, MENG Fan-Lin, LI You-Ming. The interface grid method for seeking global minumuntravel-time and the correspondent raypath. Chinese J Geophys. (in Chinese), 1995, 38(l):23--831.
[8 ] Langan R T, Lerehe i, Cutier R T. Tracing of rays though heterogenous media: an accurate and efficient procedure. Geophysics 50: 1456-1465.
[9] G Nolet. Seismic Tomography with applications in Global Seismology and Exploration Geophysics. D.Reidel, Publishing Company, 1987, 77-78.
[10]冯康.冯康文集(Ⅱ).北京,国防工业出版社,1995.FENG Kang, Collected works of Feng Kang (II) (in Chinese). Beijing: National Defence Industry Press, 1995, 269.
[11]冯康,秦孟兆.Hamilton动力体系的Hamiltion算法.自然科学进展一国家重点实验室通讯,1991,2:104-112.FENG Kang, QIN Meng-Zhao, The Hamiltonian method for Hamiltonian dynamic systems. Progress ofNatural Science--Letters of National Laboratory (in Chinese), 1991, 2: 104--112.
[12] FENG Kang. Differential schemes for hamiltonian formalism and symplectic geometry. J Compu. Math,1986, 4(3): 279--289.
[13] V. I. Arnold. Mathematical methods of classical mechanics. Springer--Veried, 1978, 201--229.
[14]尹峰,李幼铭.反演二维非均匀介质背景中速度扰动的波动方程层析成像方法.见:杨文采等主编.应用 地震层析成像.北京:地质出版社,1993,124—131.YING Feng, LI You-Ming. Wave equation tomography with the 2-D inversion of velocity perturbation incomplex media. In: YANG Wei-Cai et al. ed. Applied Seismic Tomography (in Chinese). Beijing:Geological Publishing House, 1993, 124--131.
[15] George A, Mcmenchan, walter D Mooney Asyrnptotic my theroy and synthetic seismograms for laterallyvarying structures: theory and application to the imperial valley. California. Bull. Seism. Soc. Am. 70:2021-2035.
[16] Chapman C. H K Drummond Body-Wave seismograms in inhomogenous media using Maslov asympotictheory. Bull. Seism. Soc. am. 1982, 72(6):277--317.
[17] Chapman C.H. Ray theory and its extensions: WKBJ and Maslovseismograms. J Geophs, 1985, 58:27--43.
[18] Chapman C.H. The computation of body wave synthetic seismograms in laterally homogeneous media. Rev.Geophys. Res., 1985, 92:2697--2712.
[19] Richard P Feynman. The Feynman lectures on physics. Addison-wesley publishing company, 1975, 26.
[20] Versteeg R. Grau G Practical aspects of seismic data inversion. The Marmousi experience EAEG Workshop,52 nd EAEG Meeting. Eur. Assoc. Expl. Geophys., Proceedings of 1990 EAEG WorkshopP, 1990, 52 nd EAEG Meehng, 1-194.
[2] Vidale J. Finite difference calculation of traveltime. Bull. Seis. Soc. Am., 1988, 78:2062--2076.
[3] Vidale J. Finite difference calculation of traveltime in three Dimensions. Geophysics, 1990, 55:521--526.
[4]黄联捷,李幼铭,吴如山.用于图像重建的波前法射线追踪.地球物理学报,1992,35(2):223—233.HLJANG Lian-Jie, LI You-Ming, WU Ru-Shan. The wave--front ray tracing method for image reconstruction.Chinese J. Geophys. (in Chinese), 1992, 35(2):223--233.
[ 5 ] Satio H Traveltime and rqyypaths of first arrival seismic waves, computation method based upon Huygens's principle. Expanded Abstacts Society of Exploration Geophysicisrt(SEG) 59th Annual International Meeting,1989, 244-247.
[6 ] Moser T., Shortest path calculation of seismic rays. Geophysics, 1991, 56:59--67.
[7]刘洪,孟繁林,李幼铭.计算最小走时和射线路径的界面网全局方法.地球物理学报,1995,38(1):823- 831.LIU Hong, MENG Fan-Lin, LI You-Ming. The interface grid method for seeking global minumuntravel-time and the correspondent raypath. Chinese J Geophys. (in Chinese), 1995, 38(l):23--831.
[8 ] Langan R T, Lerehe i, Cutier R T. Tracing of rays though heterogenous media: an accurate and efficient procedure. Geophysics 50: 1456-1465.
[9] G Nolet. Seismic Tomography with applications in Global Seismology and Exploration Geophysics. D.Reidel, Publishing Company, 1987, 77-78.
[10]冯康.冯康文集(Ⅱ).北京,国防工业出版社,1995.FENG Kang, Collected works of Feng Kang (II) (in Chinese). Beijing: National Defence Industry Press, 1995, 269.
[11]冯康,秦孟兆.Hamilton动力体系的Hamiltion算法.自然科学进展一国家重点实验室通讯,1991,2:104-112.FENG Kang, QIN Meng-Zhao, The Hamiltonian method for Hamiltonian dynamic systems. Progress ofNatural Science--Letters of National Laboratory (in Chinese), 1991, 2: 104--112.
[12] FENG Kang. Differential schemes for hamiltonian formalism and symplectic geometry. J Compu. Math,1986, 4(3): 279--289.
[13] V. I. Arnold. Mathematical methods of classical mechanics. Springer--Veried, 1978, 201--229.
[14]尹峰,李幼铭.反演二维非均匀介质背景中速度扰动的波动方程层析成像方法.见:杨文采等主编.应用 地震层析成像.北京:地质出版社,1993,124—131.YING Feng, LI You-Ming. Wave equation tomography with the 2-D inversion of velocity perturbation incomplex media. In: YANG Wei-Cai et al. ed. Applied Seismic Tomography (in Chinese). Beijing:Geological Publishing House, 1993, 124--131.
[15] George A, Mcmenchan, walter D Mooney Asyrnptotic my theroy and synthetic seismograms for laterallyvarying structures: theory and application to the imperial valley. California. Bull. Seism. Soc. Am. 70:2021-2035.
[16] Chapman C. H K Drummond Body-Wave seismograms in inhomogenous media using Maslov asympotictheory. Bull. Seism. Soc. am. 1982, 72(6):277--317.
[17] Chapman C.H. Ray theory and its extensions: WKBJ and Maslovseismograms. J Geophs, 1985, 58:27--43.
[18] Chapman C.H. The computation of body wave synthetic seismograms in laterally homogeneous media. Rev.Geophys. Res., 1985, 92:2697--2712.
[19] Richard P Feynman. The Feynman lectures on physics. Addison-wesley publishing company, 1975, 26.
[20] Versteeg R. Grau G Practical aspects of seismic data inversion. The Marmousi experience EAEG Workshop,52 nd EAEG Meeting. Eur. Assoc. Expl. Geophys., Proceedings of 1990 EAEG WorkshopP, 1990, 52 nd EAEG Meehng, 1-194.
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