弹性介质的Lagrange动力学与地震波方程

方刚; 张斌

doi:10.7498/aps.62.154502

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.

关键词:

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.

Keywords:

作者及机构信息

方刚¹,
张斌²

1.
中国石油大学地球科学与技术学院, 青岛 266580;

2.
中国石油大学理学院, 青岛 266580

Authors and contacts

Fang Gang¹,
Zhang Bin²

1.
School of Geosciences in China University of Petroleum, Qingdao 266580, China;

2.
School of Science in China University of Petroleum, Qingdao 266580, China

参考文献

[1]	Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press) (in Chinese) [梅凤翔 2004 约束力学系统的对称性与守恒量 (北京: 北京理工大学出版社)]
[2]	Chen X W, Zhang R C, Mei F X 2000 Acta Mech. Sin. 16 282
[3]	Fu J L, Chen L Q 2004 Mech. Res. Commun. 31 9
[4]	Luo S K, Chen X W, Guo Y X 2007 Chin. Phys. 16 3176
[5]	Luo S K, Zhang Y F 2008 Advances in the Study of Dynamics of Constrained 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 B 2008 Phys. Lett. A 372 2141
[7]	Zhang Y 2009 Acta Phys. Sin. 58 7436 (in Chinese) [张毅 2009 物理学报 58 7436]
[8]	Dorodnitsyn V, Kozlov R 2010 J. Eng. Math. 66 253
[9]	Nucci M C 2011 Phys. Lett. A 375 1375
[10]	Jia L Q, Xie Y L, Luo S K 2011 Acta Phys. Sin. 60 040201 (in Chinese) [贾利群, 解银丽, 罗绍凯 2011 物理学报 60 040201]
[11]	Cai J L, Shi S S 2012 Acta Phys. Sin. 61 030201 (in Chinese) [蔡建乐, 史生水 2012 物理学报 61 030201]
[12]	Ge W K, Zhang Y, Lou Z M 2012 Acta Phys. Sin. 61 140204 (in Chinese) [葛伟宽, 张毅, 楼智美 2012 物理学报 61 140204]
[13]	Liu H, Luo M Q, Li Y M, Yang K Q 1999 Chin. J. Geophys. 42 685 (in Chinese) [刘洪, 罗明秋, 李幼铭, 杨孔庆 1999 地球物理学报 42 685]
[14]	Luo M Q, Liu H, Li Y M 2001 Chin. J. Geophys. 44 210 (in Chinese) [罗明秋, 刘洪, 李幼铭 2001 地球物理学报 44 210]
[15]	Sun C Y 2007 Theory 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 Y 1993 Advanced 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 B 2008 Elastic Mechanics (Hefei: University of Science and Technology 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)]

施引文献

[1]	Mei F X 2004 Symmetries and Conserved Quantities of Constrained Mechanical Systems (Beijing: Beijing Institute of Technology Press) (in Chinese) [梅凤翔 2004 约束力学系统的对称性与守恒量 (北京: 北京理工大学出版社)]
[2]	Chen X W, Zhang R C, Mei F X 2000 Acta Mech. Sin. 16 282
[3]	Fu J L, Chen L Q 2004 Mech. Res. Commun. 31 9
[4]	Luo S K, Chen X W, Guo Y X 2007 Chin. Phys. 16 3176
[5]	Luo S K, Zhang Y F 2008 Advances in the Study of Dynamics of Constrained 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 B 2008 Phys. Lett. A 372 2141
[7]	Zhang Y 2009 Acta Phys. Sin. 58 7436 (in Chinese) [张毅 2009 物理学报 58 7436]
[8]	Dorodnitsyn V, Kozlov R 2010 J. Eng. Math. 66 253
[9]	Nucci M C 2011 Phys. Lett. A 375 1375
[10]	Jia L Q, Xie Y L, Luo S K 2011 Acta Phys. Sin. 60 040201 (in Chinese) [贾利群, 解银丽, 罗绍凯 2011 物理学报 60 040201]
[11]	Cai J L, Shi S S 2012 Acta Phys. Sin. 61 030201 (in Chinese) [蔡建乐, 史生水 2012 物理学报 61 030201]
[12]	Ge W K, Zhang Y, Lou Z M 2012 Acta Phys. Sin. 61 140204 (in Chinese) [葛伟宽, 张毅, 楼智美 2012 物理学报 61 140204]
[13]	Liu H, Luo M Q, Li Y M, Yang K Q 1999 Chin. J. Geophys. 42 685 (in Chinese) [刘洪, 罗明秋, 李幼铭, 杨孔庆 1999 地球物理学报 42 685]
[14]	Luo M Q, Liu H, Li Y M 2001 Chin. J. Geophys. 44 210 (in Chinese) [罗明秋, 刘洪, 李幼铭 2001 地球物理学报 44 210]
[15]	Sun C Y 2007 Theory 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 Y 1993 Advanced 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 B 2008 Elastic Mechanics (Hefei: University of Science and Technology 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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