曲线坐标系下的完全匹配层吸收边界条件

doi:10.13278/j.cnki.jjuese.201706304

摘要/Abstract

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

刘志强, 孙建国, 孙辉, 刘明忱, 高正辉, 石秀林. 曲线坐标系下的完全匹配层吸收边界条件[J]. 吉林大学学报(地球科学版), 2017, 47(6): 1875-1884.

Liu Zhiqiang, Sun Jianguo, Sun Hui, Liu Mingchen, Gao Zhenghui, Shi Xiulin. A Perfectly Matched Layer Absorbing Boundary Condition Under the Curvilinear Coordinate System[J]. Journal of Jilin University(Earth Science Edition), 2017, 47(6): 1875-1884.

参考文献

[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.

相关文章 15

[1]	丁梦颜, 冯晅, 刘财. 裂缝对岩石非线性弹性特征的影响[J]. 吉林大学学报(地球科学版), 2026, 56(3): 1051-1061.
[2]	范佳奇, 吴秋莹, 王典, 李鹏. Radon变换的贪婪-快速迭代收缩阈值算法实现及多次波压制应用 [J]. 吉林大学学报(地球科学版), 2026, 56(2): 684-693.
[3]	赵天硕, 宋超, , 刘财, , , , 徐雨歆. 物理信息神经网络地震走时层析成像程函方程因式分解方法 [J]. 吉林大学学报(地球科学版), 2026, 56(2): 694-702.
[4]	谭晓淼, 周建波, 饶莹, 王海燕, 侯贺晟, 李明芮, 高锐. 中亚造山带中南部索伦缝合带岩石圈结构及其对古亚洲洋演化的制约[J]. 吉林大学学报(地球科学版), 2026, 56(1): 209-218.
[5]	毛子雄, 侯贺晟, 周建波, 符伟. 佳木斯地块—那丹哈达地体近地表速度结构[J]. 吉林大学学报(地球科学版), 2026, 56(1): 219-228.
[6]	韩复兴, 王源, 高正辉, 常志邈, 马飞, 秦昊, 尚浩. 基于NEWUOA的CRS叠加成像技术[J]. 吉林大学学报(地球科学版), 2026, 56(1): 386-396.
[7]	黄兴国, 翁央央, 韩丽. 基于广义递归卷积的孔隙黏弹地震波正演模拟[J]. 吉林大学学报(地球科学版), 2026, 56(1): 377-385.
[8]	韩复兴, 刘水源, 高正辉, 韩江涛, 张涛, 尚浩. 基于机器学习的微动HVSR数据干扰信号压制方法[J]. 吉林大学学报(地球科学版), 2025, 55(6): 2153-2163.
[9]	刘财, 张焱喆, 刘洋. 地震数据非平稳特征分析综述[J]. 吉林大学学报(地球科学版), 2025, 55(6): 2132-2152.
[10]	李丛, 张栋, 董果果, 袁青松, 许军, 朱德胜, 代磊, 李鹏飞, 焦通, 郑玉生, 魏俏巧, 刘家橘. 连续随机离散缝网表征技术在中牟凹陷裂缝发育区中的应用[J]. 吉林大学学报(地球科学版), 2025, 55(5): 1715-1727.
[11]	齐娇, 曹思远. 基于先验知识的深度学习表面相关多次波压制方法[J]. 吉林大学学报(地球科学版), 2025, 55(5): 1702-1714.
[12]	田广, 赵岩. 信噪比约束的可调节振幅补偿算子反Q滤波方法[J]. 吉林大学学报(地球科学版), 2025, 55(4): 1351-1360.
[13]	王志勇, 刘国昌, 王梓旭, 郭严粮, 秦晨. 基于振幅一致性残差卷积编码-解码器的不规则缺失数据重建 [J]. 吉林大学学报(地球科学版), 2025, 55(4): 1336-1350.
[14]	孙敬雯, 吕子强, 孔庆翰, 唐泽豪, 邱俊辉, 刘珈君. 基于背景噪声成像的沂沭断裂带及邻区波速变化[J]. 吉林大学学报(地球科学版), 2025, 55(4): 1361-1371.
[15]	丁乾龙, 沈金松, 陈双全, 冉尚, 龙刚. 频率域传播矩阵法地震AVA多参数反演[J]. 吉林大学学报(地球科学版), 2025, 55(3): 957-969.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed