弹性介质的Lagrange动力学与地震波方程
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摘要
本文将地球介质看作是弹性介质,从弹性体的Navier方程出发,建立均匀弹性介质和非均匀弹性介质的分析动力学方程——Lagrange方程,利用弹性介质的Lagrange方程导出匀弹性介质和非均匀弹性介质的地震波方程,为用Lagrange分析动力学研究地球介质中地震波传播规律和解决地震勘探中的有关问题提供基础.
In seismic exploration, propagation of seismic wave in earth medium is very complex. Theory of analytical mechanics has advantages for solving complicated problems. In this paper, with the hypothesis of viewing geological medium as an elastic medium, the Lagrange equations of analytical dynamics are built for homogeneous and inhomogeneous earth media. Then the seismic wave equations of elastic medium are obtained from the Lagrange equations. The results provide the basis to study propagation of seismic wave in earth medium and discuss problems related to seismic exploration using Lagrange analytic dynamics.
In seismic exploration, propagation of seismic wave in earth medium is very complex. Theory of analytical mechanics has advantages for solving complicated problems. In this paper, with the hypothesis of viewing geological medium as an elastic medium, the Lagrange equations of analytical dynamics are built for homogeneous and inhomogeneous earth media. Then the seismic wave equations of elastic medium are obtained from the Lagrange equations. The results provide the basis to study propagation of seismic wave in earth medium and discuss problems related to seismic exploration using Lagrange analytic dynamics.
引文
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[6]Mei F X,Wu H B2008Phys.Lett.A3722141
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[8]Dorodnitsyn V,Kozlov R2010J.Eng.Math.66253
[9]Nucci M C2011Phys.Lett.A3751375
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[12]Ge W K,Zhang Y,Lou Z M2012Acta Phys.Sin.61140204(in Chinese)[葛伟宽,张毅,楼智美2012物理学报61140204]
[13]Liu H,Luo M Q,Li Y M,Yang K Q1999Chin.J.Geophys.42685(in Chinese)[刘洪,罗明秋,李幼铭,杨孔庆1999地球物理学报42685]
[14]Luo M Q,Liu H,Li Y M2001Chin.J.Geophys.44210(in Chinese)[罗明秋,刘洪,李幼铭2001地球物理学报44210]
[15]Sun C Y2007Theory and Methods of Seismic Waves(dongying:China University of Petroleum Press)(in Chinese)[孙成禹2007地震波理论与方法(东营:中国石油大学出版社)]
[16]Mei F X,Liu D,Luo Y1993Advanced Analytical Mechanics(Beijing:Beijing Institute of Technology Press)(in Chinese)[梅凤翔,刘端,罗勇1993高等分析力学(北京:北京理工大学出版社)]
[17]Zhu B2008Elastic Mechanics(Hefei:University of Science and Tech-nology of China Press)(in Chinese)[朱滨2008弹性力学(合肥:中国科学技术大学出版社)]
[2]Chen X W,Zhang R C,Mei F X2000Acta Mech.Sin.16282
[3]Fu J L,Chen L Q2004Mech.Res.Commun.319
[4]Luo S K,Chen X W,Guo Y X2007Chin.Phys.163176
[5]Luo S K,Zhang Y F2008Advances in the Study of Dynamics of Con-strained System(Beijing:Science Press)(in Chinese)[罗绍凯,张永发2008约束系统动力学研究进展(北京:科学出版社)]
[6]Mei F X,Wu H B2008Phys.Lett.A3722141
[7]Zhang Y2009Acta Phys.Sin.587436(in Chinese)[张毅2009物理学报587436]
[8]Dorodnitsyn V,Kozlov R2010J.Eng.Math.66253
[9]Nucci M C2011Phys.Lett.A3751375
[10]Jia L Q,Xie Y L,Luo S K2011Acta Phys.Sin.60040201(in Chi-nese)[贾利群,解银丽,罗绍凯2011物理学报60040201]
[11]Cai J L,Shi S S2012Acta Phys.Sin.61030201(in Chinese)[蔡建乐,史生水2012物理学报61030201]
[12]Ge W K,Zhang Y,Lou Z M2012Acta Phys.Sin.61140204(in Chinese)[葛伟宽,张毅,楼智美2012物理学报61140204]
[13]Liu H,Luo M Q,Li Y M,Yang K Q1999Chin.J.Geophys.42685(in Chinese)[刘洪,罗明秋,李幼铭,杨孔庆1999地球物理学报42685]
[14]Luo M Q,Liu H,Li Y M2001Chin.J.Geophys.44210(in Chinese)[罗明秋,刘洪,李幼铭2001地球物理学报44210]
[15]Sun C Y2007Theory and Methods of Seismic Waves(dongying:China University of Petroleum Press)(in Chinese)[孙成禹2007地震波理论与方法(东营:中国石油大学出版社)]
[16]Mei F X,Liu D,Luo Y1993Advanced Analytical Mechanics(Beijing:Beijing Institute of Technology Press)(in Chinese)[梅凤翔,刘端,罗勇1993高等分析力学(北京:北京理工大学出版社)]
[17]Zhu B2008Elastic Mechanics(Hefei:University of Science and Tech-nology of China Press)(in Chinese)[朱滨2008弹性力学(合肥:中国科学技术大学出版社)]
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