Title

Application of perfectly matched layer in time-domain finite-element elastic wave modeling

单位

1.长江大学地球物理与石油资源学院,湖北武汉430100;2.长江大学管理学院,湖北荆州434023;3.中国石油天然气股份有限公司新疆油田分公司采油一厂,新疆克拉玛依834000;4.中国石油天然气股份有限公司辽河油田分公司勘探开发研究院,辽宁盘锦124010

Organization

1.Geophysics and Oil Resource Institute,Yangtze University,Wuhan 430100,China;2.School of Management,Yangtze University,Jingzhou 434023,China;3.No.1 Production Plant,Xinjiang Oilfield Company,PetroChina,Karamay 834000,China;4.Research Institute of Petroleum Exploration and Development,Liaohe Oilfield Company,CNPC,Panjin 124010,China

摘要

完全匹配层(perfectly matched layer,PML)边界条件是消除人工边界虚假反射的经典方法之一,但不易在时域有限元方法中实现,尤其是求解二阶弹性波方程。为此,详细推导了PML在时域有限元法求解二阶位移弹性波方程中的加载过程,得到了含PML的有限元控制方程;通过数值算例,讨论了PML衰减参数中理论反射系数对PML吸收效果的影响以及在PML吸收层最外层加载狄利克雷边界条件对PML数值稳定性的影响。数值模拟结果表明:当PML吸收层厚度一定时,理论反射系数越小,PML吸收效果越好;当PML吸收层厚度为半个最大主波长时,理论反射系数小于(等于)10-5,PML吸收效果最优;虽然在PML吸收层的最外层加载狄利克雷边界条件可增强PML的数值稳定性,但对处于自由表面上的PML吸收层最外层部分,不可加载狄利克雷边界条件,否则会产生严重的虚假反射。

Abstract

The perfectly matched layer (PML) is traditionally used to suppress artificial boundary reflections.It is difficult to apply the PML using a time-domain finite-element method,especially when solving second-order elastic wave equations.We proposed a detailed derivation that can be used to embed the PML into time-domain finite-element formulas and solve second-order displacement elastic wave equations;the final objective would be to obtain finite-element governing equations that include the PML.We also discussed the influence of a theoretical reflection coefficient on the PML,and the effects of Dirichlet boundary conditions (which were imposed on the outermost PML) on the PML numerical stability.The results showed that when the thickness of the absorption layer was constant,the theoretical reflection coefficient was small and the absorption effect of the PML was improved.On the other hand,when the thickness of the absorption layer was equal to half of the maximum dominant wavelength,the PML presented optimal absorbing properties only if the theoretical reflection coefficient was less than or equal to 10-5.The numerical stability of the PML could be enhanced imposing Dirichlet boundary conditions on its outermost layer;however,these conditions could not be imposed on the free surface of the outermost part of the PML without running the risk of serious false reflection.

关键词：

完全匹配层; 弹性波; 数值模拟; 边界条件; 狄利克雷条件;

Keywords:

perfectly matched layer (PML),; elastic waves,; numerical modeling,; boundary condition,; Dirichlet condition;

基金项目

湖北省教育厅科技研究计划青年人才项目(Q20161304)及油气资源与勘探技术教育部重点实验室(长江大学)开放基金(Q20161304)共同资助。

DOI

10.3969/j.issn.1000-1441.2019.04.003

完全匹配层在时域有限元弹性波数值模拟中的应用