无单元法用于地震波波动方程模拟与成像
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摘要
波动方程方法是解决地震正反演问题的基本工具之一.无单元法作为一种新兴的偏微分方程数值计算方法,已经在材料力学、热传导等领域取得了显著的成功.由于抛弃了单元的概念及采用滑动最小二乘的拟合方法,使得无单元法具有前处理简单、精度高、独立变量解高次连续等优点.本文首先介绍无单元法求解波动方程的原理,指出影响其精度的主要因素.在算例的基础上详细讨论了无单元法用于实际波动问题的效果,并进一步尝试利用无单元法进行地震波数值模拟和反演成像的研究.模型计算的结果表明,无单元法能够较好的处理地震模拟和成像问题,精度和稳定性是令人满意的.
Wave equation method is one of the fundamental techniques for seismic modeling and imaging.In this paper we discuss a rather new numerical method-the Element-Free Method(EFM),which has demonstrated quite successful in elasticity,heat conduction and fatigue crack growth problems.The key point of this method is the absence of elements,which means potential cost savings.Besides,the Moving Least Squares(MLS) approximation in the EFM design leads to high accuracy and smooth derivatives.The basic principle and a simple example of vibrant film are discussed in details in this paper.Finally,some more examples will be given to show the good performance of EFM in seismic modeling and imaging problems.
Wave equation method is one of the fundamental techniques for seismic modeling and imaging.In this paper we discuss a rather new numerical method-the Element-Free Method(EFM),which has demonstrated quite successful in elasticity,heat conduction and fatigue crack growth problems.The key point of this method is the absence of elements,which means potential cost savings.Besides,the Moving Least Squares(MLS) approximation in the EFM design leads to high accuracy and smooth derivatives.The basic principle and a simple example of vibrant film are discussed in details in this paper.Finally,some more examples will be given to show the good performance of EFM in seismic modeling and imaging problems.
引文
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[2]Zhu T,Zhang J,Atluri S.A local boundary integral equation(LBIE)method in computational mechanics,and a meshlessdiscretization approach[J].Computational Mechanics,1998,21:223~235.
[3]Melenk J,Babuska I.The partition of unity method:basic the-ory and applications[J].Computer Methods in Applied Me-chanics and Engineering,1996,139:289~314.
[4]Lu Y Y,Belytschko T,Tabbara M.Element-free Garlerkinmethod for wave propagation and dynamic fracture[J].Com-puter Methods in Applied Mechanics and Engineering,1995,126:131~153.
[5]Zhu T,Atluri S N.A modified collocation method and a penaltyformulation for enforcing the essential boundary conditions inthe element-free galerkin method[J].Computational Mechan-ics,1998,21:211~222.
[6]周维垣,寇晓东.无单元法及其在岩土工程中的应用[J].岩土工程学报,1998,20(1):5~9.Zhou W Y,Kou X D.Element-free method and its applicationin geotechnique engineering[J].Chinese Journal of Geotechni-cal Engineering(in Chinese),1998,20(1):5~9.
[7]Dolbow J,Belytschko T.Numerical integration of the galerkinweak form in meshfree methods[J].Computational Mechan-ics,1999,23:219~230.
[8]贾晓峰,王润秋,胡天跃.求解波动方程的任意差分精细积分法[J].中国地震,2003,19(3):236~242.Jia X F,Wang R Q,Hu T Y.The arbitrary difference preciseintegration method for solving the seismic wave equation[J].Earthquake Research in China(in Chinese),2003,19(3):236~242.
[9]Clayton R,Engquist B.Absorbing boundary conditions for a-coustic and elastic wave equations[J].Bulletin of the Seismo-logical Society of America,1977,67:1529~1540.
[10]底青云,王妙月.弹性波有限元逆时偏移技术研究[J].地球物理学报,1997,40(4):570~579.
[11]Schneider W A,Ranzinger K A,Balch A H,Kruse C.A dy-namic programming approach to first arrival traveltime com-putation in media with arbitrarily distributed velocities[J].Geophysics,1992,57(1):39~50.
[12]Jia X F,Hu T Y,Wang R Q.Solving seismic wave equationby using element-free method[J].CPS/SEG 2004 Interna-tional Geophysical Conference,CPS/SEG.Expanded Ab-stracts,2004.235~237.
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