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《地球科学与环境学报》[ISSN:1672-6561/CN:61-1423/P]

卷:

第26卷

期数:

2004年第01期

页码:

61-64

栏目:

出版日期:

2004-03-20

文章信息/Info

Title:

Hybrid method combining finite difference and pseudospectral method for solving the elastic wave equation

作者:

马德堂¹; 朱光明²

1.长安大学理学院,陕西西安710064;2.长安大学地质工程与测绘工程学院,陕西西安710054

Author(s):

MA De-tang¹; ZHU Guang-ming²

1 .School of Science , Chang'an University , Xi'an 710064, China ;2.School of Geological Engineering and Surveying Engineering , Chang'an University , Xi'an 710054 , China

关键词:

弹性波场数值模拟; 有限元法; 伪谱法; 混合模拟方法

Keywords:

elastic wave field numerical modeling ; finite difference method; pseudospectral method ; hybrid method

分类号:

P315.3+1

DOI:

-

文献标志码:

A

摘要:

在地震波场数值模拟中,有限差分法、有限元法和伪谱法都是常用的基本方法,但它们各有不 同的适应性和优缺点,如有限差分法、有限元法都存在减弱网格频散和提高计算效率的矛盾,而伪谱法 的网格频散小且计算效率高。有限差分法和伪谱法在处理地表结构复杂或地表剧烈起伏以及地下结构 复杂的情况时存在较大的难度,而有限元法可较为理想地拟合起伏地表和任意弯曲界面,且可方便地处 理自由边界条件和界面边界条件。尝试将有限元法和伪谱法相结合,形成地震波场数值模拟的一种混 合方法,利用二者的优点,克服二者的缺点,达到既减弱网格频散又提高计算精度和效率的目的。并采 用所谓的`过度区域'技术解决两种不同算法的衔接问题。模拟实例表明,给出的混合模拟方法不失为 弹性波场数值模拟的一种有效方法。

Abstract:

Many different methods proposed for modeling waves have their own range of validity and limitation.For example .Finite different FD)techniques have been widely used in wave modeling .One advantage of FD techniques is their ability to model wave propagation in media with fairly general spatial variation of elastic properties.However , particularly for models with sharp discontinuities, FD schemes are by no means free from accuracy problem.Finite elementFE)method has been shown to be an efficient alternative tool for modeling wave propagation in complex structures.Pseudo-spectral methodPS)has advantages of higher accuracy and lower dispersion than FD method and FE method, but , there exists difficulties in dealing with free surface boundary condition as FD method. Here we develop a hybid method which couples the FE method with PS method to model near boundary wave field and inner wave field respectively , to use the advantages of the two methods and to increase the numerical accuracy and computation efficiency .The problems concerning connection of the two methods are solved by introducing the transition region between near boundary and inner region .Numerical examples have demonstrated the validity and the advantages of the hybid method given here .

参考文献/References:

[1] Benxi Ke , Bo Zhao ,Jiaming Cai et al.2-D finite element acoustic wave modeling including rugged topography[A] .Soc .Expl.Geophys .71th Ann .Internat .Mtg[C] .Tulsa , USA, 2001 .
[2] Bengt Fornberg .The pseudospectral method :comparisons wi th finite dif ferences for the elasti c wave equation .Geophysics[J] , 1987 , 52 4):483 ～ 501 .
[3] Takashi Furumura and Hiroshi Takenaka, .A wraparound elimination technique for the pseudospectral wave synthesis using an antiperiodi c extension of the wavefield[J] .Geophysics , 1995 , 602):302 ～ 307 .
[4] Rushan Wu , Li Yun Fu .A hybrid method for wave propagation simulation in near-surface regions[A] .Soc.Expl.Geophys .68th Ann . Internat .Mtg[C] .Tulsa, San Antonio, USA ,1998 .

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备注/Memo

备注/Memo:

[收稿日期]2003-05-20
[基金项目]国家863项目2171;2755)
[作者简介]马德堂1965-),男,陕西旬阳人,讲师,博士研究生,现从事数学教学和波动方程数值解法的研究工作。

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更新日期/Last Update: 2004-03-20