共反射点轨迹的Hamilton方法
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摘要
本文采用Ｈａｍｉｌｔｏｎ理论方法，研究反射地震记录域中地下同一反射点对应的反射走时随炮检距变化的特性，这在叠前地震资料处理中具有重要意义．由于走时函数可以表示成炮点位置、检波点位置、地震波射线出射角和接收角的函数，通过对共反射点走时与炮点位置变化关系的分析，提出了复杂介质中共反射点轨迹可用Ｈａｍｉｌｔｏｎ正则方程描述．在线性变速介质中，走时函数可以解析给出，由此可导出该介质中共反射点轨迹的Ｈａｍｉｌｔｏｎ正则方程．文中结合常速度、横向变速和线性变速介质模型，计算了地下不同反射面上各点相应的共反射点轨迹，阐明Ｈａｍｉｌｔｏｎ方法的一些特点，并首次引入Ｈａｍｉｌｔｏｎ理论方法描述共反射点走时随炮检距的变化特性，开创了该领域研究的一条新途径．
In this paper, Hamilton method is introduced to study the characters of howseismic reflective traveltime of the same reflective point varies with the off offset, whichis important in prestack seismic processing. Since the traveltime is a function ofscarce location, receiver location, setoff angle and receiver angle of the seismic ray,the Hamilton canonical equation that describes the CRP trajectory in complex mediacan be proposed after analyzing the differential characters that common reflectiontravel bine varies with the source location. As an example, the Hamilton canonicalequation has been analytically derived for the traveltime function in the linearly variedvelocity media is analytical. The trajectories of the pointS on several typical reflectivesurfaces are calculated in three different earth model, which has consent velocity,transverse varied velocity or linearly varied velocity. Some characters of Hamiltonmethod can be deduced from the trajectories. It is the first bine for Hamilton methodis introduced tO describe the CRP trajectory, which gives a new way in this field.
In this paper, Hamilton method is introduced to study the characters of howseismic reflective traveltime of the same reflective point varies with the off offset, whichis important in prestack seismic processing. Since the traveltime is a function ofscarce location, receiver location, setoff angle and receiver angle of the seismic ray,the Hamilton canonical equation that describes the CRP trajectory in complex mediacan be proposed after analyzing the differential characters that common reflectiontravel bine varies with the source location. As an example, the Hamilton canonicalequation has been analytically derived for the traveltime function in the linearly variedvelocity media is analytical. The trajectories of the pointS on several typical reflectivesurfaces are calculated in three different earth model, which has consent velocity,transverse varied velocity or linearly varied velocity. Some characters of Hamiltonmethod can be deduced from the trajectories. It is the first bine for Hamilton methodis introduced tO describe the CRP trajectory, which gives a new way in this field.
引文
1 Fomel S. Amplitude Preserving offset Continuation in Theory. SEP-84, Cambridge: Stanford Univ., 1994
2 Un Hong, Yin Xing-Yao, Li You--Ming. The offset continuation in complex media. Soc. Expl. Geophys.67th ann. Internat. Mtg. Abstract 1997. 1901-1904
3 Perroud R Hubral P. Common reflection point stacking in laterally inhomogeneous media. ExpandedAbstract 66th SEG Annual Meeting, 1996. 496-498
4 Miller T. Tager R, Hocht G. Common reflection surfaces sacking method imaging with an unknownvelocity model. Soc. Expl. Geophys. 68th ann. Internat. Mtg. Abstract 1998. 1764-1766
5 Gajewski T. Determining the my propagation from traveltimes. Soc. Expl. Geophs. 68th axm. Internat. Mtg.Abstract, 1998, 1900~1903
6 Arnold V I. Mathematical Method of Classical Mechanics. New York: Springer-Verlag, 1978. 162-266
7罗明秋.反射地震运动学中的Hamilton方法[硕士论文].兰州:兰州大学物理系,1998 LUO Ming-Qiu Hamilton method in kinematics reflective seismology [Ph. M. thesis] (in Chinese). Lanzhou:Lanzhou Univ., 1998
8杨孔庆,罗明秋,李幼铭.地震波传播的微分几何描述.地球物理学进展,1998,13(3):32—37YANG Kong-Qing, LOU Ming-Qiu, LI You-Ming.Differential geometric describing on seismic wavepropapation. Progress in Geophysics (in Chinese), 1998, 13(3):32-37(2): 110~120
9冯康,秦孟兆Hamilton动力体系的Hamilton算法.自然科学进展——国家重点实验室通讯,1990,试刊(2):110—120 FENG Kang, QIN Meng-Zhao. Hamilton algorithm in Hamilton dynamic system. Progress in science(Communication of state Key labr.)(in Chinese), 1990, (2): 110-120
10 QIN Meng-Zhao. An implicit scheme for nonlinear evolution equations. Journal of Computational Physics,1982, 48: 57-71
2 Un Hong, Yin Xing-Yao, Li You--Ming. The offset continuation in complex media. Soc. Expl. Geophys.67th ann. Internat. Mtg. Abstract 1997. 1901-1904
3 Perroud R Hubral P. Common reflection point stacking in laterally inhomogeneous media. ExpandedAbstract 66th SEG Annual Meeting, 1996. 496-498
4 Miller T. Tager R, Hocht G. Common reflection surfaces sacking method imaging with an unknownvelocity model. Soc. Expl. Geophys. 68th ann. Internat. Mtg. Abstract 1998. 1764-1766
5 Gajewski T. Determining the my propagation from traveltimes. Soc. Expl. Geophs. 68th axm. Internat. Mtg.Abstract, 1998, 1900~1903
6 Arnold V I. Mathematical Method of Classical Mechanics. New York: Springer-Verlag, 1978. 162-266
7罗明秋.反射地震运动学中的Hamilton方法[硕士论文].兰州:兰州大学物理系,1998 LUO Ming-Qiu Hamilton method in kinematics reflective seismology [Ph. M. thesis] (in Chinese). Lanzhou:Lanzhou Univ., 1998
8杨孔庆,罗明秋,李幼铭.地震波传播的微分几何描述.地球物理学进展,1998,13(3):32—37YANG Kong-Qing, LOU Ming-Qiu, LI You-Ming.Differential geometric describing on seismic wavepropapation. Progress in Geophysics (in Chinese), 1998, 13(3):32-37(2): 110~120
9冯康,秦孟兆Hamilton动力体系的Hamilton算法.自然科学进展——国家重点实验室通讯,1990,试刊(2):110—120 FENG Kang, QIN Meng-Zhao. Hamilton algorithm in Hamilton dynamic system. Progress in science(Communication of state Key labr.)(in Chinese), 1990, (2): 110-120
10 QIN Meng-Zhao. An implicit scheme for nonlinear evolution equations. Journal of Computational Physics,1982, 48: 57-71
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