地球物理学进展 ›› 2016, Vol. 31 ›› Issue (6): 2762-2766.doi: 10.6038/pg20160655

• 应用地球物理学Ⅱ • 上一篇    下一篇

三维弹性波数值模拟中改进的NPML研究

谢波1,2, 熊章强1,3, 张大洲1,3   

  1. 1. 中南大学地球科学与信息物理学院, 长沙 410083;
    2. 四川大学锦城学院, 成都 611731;
    3. 中南大学有色金属成矿预测与地质环境监测教育部重点实验室, 长沙 410083
  • 收稿日期:2016-02-12 修回日期:2016-06-13 出版日期:2016-12-20 发布日期:2016-12-20
  • 作者简介:谢波,男,1979年生,博士研究生,主要从事地震学及数值模拟相关工作.(E-mail:40252126@qq.com)
  • 基金资助:

    国家自然科学基金项目(41274123)资助.

Reformulated NPML in 3D elastic-wave numerical simulation

XIE Bo1,2, XIONG Zhang-qiang1,3, ZHANG Da-zhou1,3   

  1. 1. School of Geosciences and Info-Physics, Central South University, Changsha 410083, China;
    2. JinCheng College of SiChuan University, ChengDu 611731, China;
    3. Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring, Ministry of Education, Changsha 410083, China
  • Received:2016-02-12 Revised:2016-06-13 Online:2016-12-20 Published:2016-12-20

摘要:

在地震波传播数值模拟的过程中,需要使用吸收边界条件达到衰减人为边界反射的目的,其中完全匹配层(PML)吸收边界条件被认为是目前最理想的吸收边界条件.但在三维地震波传播数值模拟中直接应用常规的PML吸收边界条件存在编程实现复杂、计算资源需求高等不足之处.本文基于传统的NPML吸收边界条件,提出了一种改进的方法.该方法通过引入伸展函数和辅助变量,把PML介质中的三维弹性波动方程分解成正常计算项和衰减项,其中衰减项的计算只在PML区域内部进行,其值只与坐标轴的方向相关,可通过离散数值迭代求解.分析和试验结果表明,该方法避免了卷积运算,减少了辅助变量的个数,具有理论方程简洁、编程实现简单、计算资源需求少等优点,能更有效地解决三维地震波传播数值模拟中的吸收边界问题.

Abstract:

The absorbing boundary conditions to avoid the artificial boundary reflections must be required in the numerical simulation of seismic wave propagation. The perfectly matched layer has been generally proved to be the best available absorbing boundary condition. However, the classical PML absorbing boundary condition in 3D Elastic-Wave numerical simulation has some disadvantages:it is difficult to implement and needs more computing resources. In this paper, we present a reformulated method based on the traditional NPML absorbing boundary condition. we divided the 3D elastic-wave equation in PML media into the normal calculation and decay by introducing the extension function and auxiliary variables. The decay needs to be calculated only when the calculation area is located in the PML area. It's value relates to the axis direction, and it can be calculated through discrete numerical iteration computing. Analysis and experimental results show that the reformulated NPML given in this paper, since it avoids the convolution and decreases the auxiliary variables, has some advantages:the theoretical equation is more simple, easier to implement and needs less computing resources, so it is more effective than the traditional PML to resolve the absorbing boundary condition in 3D elastic-wave numerical simulation.

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