吉林大学学报(地球科学版) ›› 2017, Vol. 47 ›› Issue (6): 1875-1884.doi: 10.13278/j.cnki.jjuese.201706304

• 地球探测与信息技术 • 上一篇    下一篇

曲线坐标系下的完全匹配层吸收边界条件

刘志强, 孙建国, 孙辉, 刘明忱, 高正辉, 石秀林   

  1. 吉林大学地球探测科学与技术学院, 长春 130026
  • 收稿日期:2017-03-02 出版日期:2017-11-26 发布日期:2017-11-26
  • 通讯作者: 孙建国(1956)男,教授,博士,博士生导师,主要从事波动理论与成像技术、地震资料处理方法与解释技术等方面的教学和研究工作,E-mail:sun_jg@jlu.edu.cn E-mail:sun_jg@jlu.edu.cn
  • 作者简介:刘志强(1987)男,博士研究生,主要从事地震波数值模拟研究,E-mail:490681597@qq.com
  • 基金资助:
    国家自然科学基金项目（41274120，41404085，41504084）

A Perfectly Matched Layer Absorbing Boundary Condition Under the Curvilinear Coordinate System

Liu Zhiqiang, Sun Jianguo, Sun Hui, Liu Mingchen, Gao Zhenghui, Shi Xiulin   

  1. GeoExploration of Science and Technology, Jilin University, Changchun 130026, China
  • Received:2017-03-02 Online:2017-11-26 Published:2017-11-26
  • Supported by:
    Supported by National Natural Science Foundation of China (41274120, 41404085, 41504084)

PDF (PC)

356

摘要： 在地震波数值模拟中，需要采用吸收边界条件以吸收人为边界反射。本文针对曲线坐标系下的二阶弹性波方程提出了一种完全匹配层（PML）吸收边界条件。与直角坐标系下的PML吸收边界条件类似，曲线坐标系下的PML吸收边界条件是一种在频率域中给出的人工边界条件，由相应的复坐标变换得到。在变换到时间域后，完全匹配层中将出现复杂的卷积运算。为了避免这些卷积运算，引入了4个中间变量。为了简化自由边界条件，采用正交贴体网格对起伏地表模型进行网格剖分。数值算例表明，该方法可以有效消除人为边界反射。

关键词: 人为边界反射, 完全匹配层吸收边界, 正交贴体网格

Abstract: An absorbing boundary condition is needed to absorb the artificial boundary reflections in a numerical simulation of seismic wave. We presented a perfectly matched layer (PML) absorbing boundary condition for a second-order elastic wave equation in a curvilinear coordinate system. Similar to the PML in a Cartesian coordinate system, the PML absorbing boundary condition in a curvilinear coordinate system was formulated in frequency domain, which was obtained by the corresponding complex coordinate transformation. To transform the condition into time domain will result in complex convolutions in the perfectly matched layer. To avoid these convolutions, we introduced 4 intermediate variables. Furthermore, to simplify the free boundary condition, we adopted the orthogonal body-fitted grid for mesh generation of a rugged topography model. The numerical results show that the proposed method can absorb artificial boundary reflections effectively.

Key words: artificial boundary reflection, PML absorbing boundary, orthogonal body fitted grid

中图分类号: 

  • P631.4
[1] Clayton R,Engquist B. Absorbing Boundary Conditi-ons for Acoustic and Elastic Wave Equations[J]. Bulletin of the Seismological Society of America, 1977, 67(6):1529-1540.
[2] Cerjan C, Kosloff D, Kosloff R, et al.A Nonreflecting Boundary Condition for Discrete Acoustic and Elastic Wave Equations[J]. Geophysics, 1985, 50(4):705-708.
[3] Berenger J P.A Perfectly Matched Layer for the Ab-sorption of Electromagnetic Waves[J]. Journal of Computational Physics, 1994, 114(2):185-200.
[4] Hastings F D, Schneider J B,Broschat S L. Appli-cation of the Perfectly Matched Layer (PML) Absorbing Boundary Condition to Elastic Wave Propagation[J]. The Journal of the Acoustical Society of America, 1996, 100(5):3061-3069.
[5] Collino F, Tsogka C. Application of the Perfectly Ma-tched Absorbing Layer Model to the Linear Elastodynamic Problem in Anisotropic Heterogeneous Media[J]. Geophysics, 2001, 66(1):294-307.
[6] Zeng Y Q, He J Q, Liu Q H.The Application of the Perfectly Matched Layer in Numerical Modeling of Wave Propagation in Poroelastic Media[J]. Geophysics, 2001, 66(4):1258-1266.
[7] Jih R S, McLaughlin K L, Der Z A. Free-Boundary Conditions of Arbitrary Polygonal Topography in a Two-Dimensional Explicit Elastic Finite-Difference Scheme[J]. Geophysics, 1988, 53(8):1045-1055.
[8] Ilan A. Finite-Difference Modeling for P-Pulse Propa-gation in Elastic Media With Arbitrary Polygonal Surface[J]. Journal of Geophysics, 1977, 43(1/2):41-58.
[9] Opršal I, Zahradnik J. Elastic Finite-Difference Me-thod for Irregular Grids[J]. Geophysics, 1999, 64(1):240-250.
[10] Frankel A, Leith W. Evaluationof Topographic Eff-ects on P and S-Waves of Explosions at the Northern Novaya Zemlya Test Site Using 3-D Numerical Simulations[J]. Geophysical Research Letters, 1992, 19(18):1887-1890.
[11] Hestholm S, Ruud B. 2D Finite-Difference Elastic Wave Modelling Including Surface Topography[J]. Geophysical Prospecting, 1994, 42(5):371-390.
[12] Hestholm S, Ruud B. 3-D Finite-Difference Elastic Wave Modeling Including Surface Topography[J]. Geophysics, 1998, 63(2):613-622.
[13] Tessmer E, Kosloff D, Behle A. Elastic Wave Propa-gation Simulation in the Presence of Surface Topography[J]. Geophysical Journal International, 1992, 108(2):621-632.
[14] 李庆洋,李振春,黄建平,等. 基于贴体全交错网格的起伏地表正演模拟影响因素[J]. 吉林大学学报(地球科学版),2016,46(3):920-929. Li Qingyang, Li Zhenchun, Huang Jianping, et al. Factor Analysis of Seismic Modeling with Topography Based on a Fully Staggered Body-Fitted Grids[J]. Journal of Jilin University (Earth Science Edition), 2016, 46(3):920-929.
[15] Appelö D, Petersson N A. A Stable Finite Difference Method for the Elastic Wave Equation on Complex Geometries with Free Surfaces[J]. Communications in Computational Physics, 2009, 5(1):84-107.
[16] Lan H, Zhang Z. Three-Dimensional Wave-Field Si-mulation in Heterogeneous Transversely Isotropic Medium with Irregular Free Surface[J]. Bulletin of the Seismological Society of America, 2011, 101(3):1354-1370.
[17] Festa G, Vilotte J P. The Newmark Scheme as Ve-locity-Stress Time-Staggering:An Efficient PML Implementation for Spectral Element Simulations of Elastodynamics[J]. Geophysical Journal International, 2005, 161(3):789-812.
[18] Gao H, Zhang J. Implementationof Perfectly Matched Layers in an Arbitrary Geometrical Boundary for Elastic Wave Modelling[J]. Geophysical Journal International, 2008, 174(3):1029-1036.
[19] 孙建国,蒋丽丽. 用于起伏地表条件下地球物理场数值模拟的正交曲网格生成技术[J]. 石油地球物理勘探, 2009,44(4):494-500. Sun Jianguo,Jiang Lili. Orthogonal Curvilinear Grid Generation Technique Used for Numeric Simulation of Geophysical Fields in Undulating Surface Condition[J]. Oil Geophysical Prospecting, 2009, 44(4):494-500.
[20] Hvid S L. Three Dimensional Algebraic Grid Gene-ration[M]. Kongens Lyngby:Technical University of Denmark, 1995.
[21] Fornberg B. Generation of Finite Difference Formulas on Arbitrarily Spaced Grids[J]. Mathematics of Computation, 1988, 51(184):699-706.
[22] Lan H Q, Zhang Z J. Seismic Wavefield Modeling in Media with Fluid-Filled Fractures and Surface Topography[J]. Applied Geophysics, 2012, 9(3):301-312.
[23] Collino F, Tsogka C. Application of the Perfectly Matched Absorbing Layer Model to the Linear Elastodynamic Problem in Anisotropic Heterogeneous Media[J]. Geophysics, 2001, 66(1):294-307.
[24] Collino F, Monk P. The Perfectly Matched Layer in Curvilinear Coordinates[J]. SIAM Journal on Scientific Computing, 1998, 19(6):2061-2090.
[25] 丘磊,田钢,石战结, 等. 起伏地表条件下有限差分地震波数值模拟:基于广义正交曲线坐标系[J]. 浙江大学学报(工学版), 2012,46(10):1923-1931. Qiu Lei,Tian Gang,Shi Zhanjie, et al. Finite-Difference Method for Seismic Wave Numerical Simulation in Presence of Topography[J]. Journal of Zhejiang University (Engineering Scinice), 2012,46(10):1923-1931.
[1] 叶云飞, 孙建国, 张益明, 熊凯. 基于立体层析反演的低频模型构建在深水区储层反演中的应用:以南海深水W构造为例[J]. 吉林大学学报(地球科学版), 2018, 48(4): 1253-1259.
[2] 刘一, 刘财, 刘洋, 勾福岩, 李炳秀. 复杂地震波场的自适应流预测插值方法[J]. 吉林大学学报(地球科学版), 2018, 48(4): 1260-1267.
[3] 邓馨卉, 刘财, 郭智奇, 刘喜武, 刘宇巍. 济阳坳陷罗家地区各向异性页岩储层全波场地震响应模拟及分析[J]. 吉林大学学报(地球科学版), 2018, 48(4): 1231-1243.
[4] 张冰, 郭智奇, 徐聪, 刘财, 刘喜武, 刘宇巍. 基于岩石物理模型的页岩储层裂缝属性及各向异性参数反演[J]. 吉林大学学报(地球科学版), 2018, 48(4): 1244-1252.
[5] 刘明忱, 孙建国, 韩复兴, 孙章庆, 孙辉, 刘志强. 基于自适应加权广义逆矢量方向滤波估计地震同相轴倾角[J]. 吉林大学学报(地球科学版), 2018, 48(3): 881-889.
[6] 胡宁, 刘财. 分数阶时间导数计算方法在含黏滞流体黏弹双相VTI介质波场模拟中的应用[J]. 吉林大学学报(地球科学版), 2018, 48(3): 900-908.
[7] 周进举, 王德利, 李博文, 李强, 王睿. 基于解耦传播的波场分解方法在VTI介质弹性波逆时偏移中的应用[J]. 吉林大学学报(地球科学版), 2018, 48(3): 909-921.
[8] 孙建国, 苗贺. 基于Chebyshev走时逼近的三维多次反射射线计算[J]. 吉林大学学报(地球科学版), 2018, 48(3): 890-899.
[9] 郑确, 刘财, 田有. 辽宁海城及其邻区地震b值空间分布特征[J]. 吉林大学学报(地球科学版), 2018, 48(3): 922-933.
[10] 刘四新, 朱怡诺, 王旭东, 宋二乔, 贺文博. 工程地震折射波解释方法研究进展[J]. 吉林大学学报(地球科学版), 2018, 48(2): 350-363.
[11] 单刚义, 韩立国, 张丽华. 基于模型约束的Kirchhoff积分法叠前深度成像[J]. 吉林大学学报(地球科学版), 2018, 48(2): 379-383.
[12] 孙建国, 李懿龙, 孙章庆, 苗贺. 基于模型参数化的地震波走时与射线路径计算[J]. 吉林大学学报(地球科学版), 2018, 48(2): 343-349.
[13] 宁亚灵, 许家姝, 解滔, 张国苓, 卢军. 大柏舍深井地电阻率观测布极方式分析[J]. 吉林大学学报(地球科学版), 2018, 48(2): 525-533.
[14] 徐泰然, 卢占武, 王海燕, 李洪强, 李文辉. 深地震反射剖面揭示的西藏娘热矿集区上地壳结构[J]. 吉林大学学报(地球科学版), 2018, 48(2): 556-565.
[15] 王通, 王德利, 冯飞, 程浩, 魏敬轩, 田密. 三维稀疏反演多次波预测及曲波域匹配相减技术[J]. 吉林大学学报(地球科学版), 2017, 47(6): 1865-1874.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 《吉林大学学报(地球科学版)》编辑部
地址：长春市西民主大街938号(130026)　电话：+86-431-88502374；13756165364　E-mail: xuebao1956@jlu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发