地球物理学进展 ›› 2013, Vol. 28 ›› Issue (6): 2984-2992.doi: 10.6038/pg20130620

• 应用地球物理 • 上一篇    下一篇

多轴完全匹配层的非分裂实现

李振春, 田坤, 黄建平, 曹晓莉, 李娜, 李庆洋   

  1. 中国石油大学(华东)地球科学与技术学院, 青岛 266580
  • 收稿日期:2012-11-22 修回日期:2013-03-01 出版日期:2013-12-20 发布日期:2013-12-20
  • 通讯作者: 田坤,男,1986年生,在读博士研究生.(E-mail:tiankunwudi@163.com) E-mail:tiankunwudi@163.com
  • 作者简介:李振春,男,1963年生,山东宁津人,教授,博士生导师,主要从事地震波正演及偏移成像工作.(E-mail:leonli_upc@163.com)
  • 基金资助:
    国家973计划(2011CB202402)、国家自然科学基金(41104069)、中国石化地球物理重点实验室开放研究基金(WTYJY-WX2013-04-11)和中国石油大学(华东)研究生创新工程资助项目(CX2013002)联合资助.

An unsplit implementation of the multiaxial perfectly matched layer

LI Zhen-chun, TIAN Kun, HUANG Jian-ping, CAO Xiao-li, LI Na, LI Qing-yang   

  1. School of Geoscience of China University of Petroleum(east China), Qingdao 266580, China
  • Received:2012-11-22 Revised:2013-03-01 Online:2013-12-20 Published:2013-12-20

摘要: 完全匹配层吸收边界(PML)已经被证明是非常有效的边界吸收技术,对体波和面波的吸收都具有非常好的效果,已经被广泛应用于弹性波的数值模拟中.但是在某些情况下传统的PML和C-PML(卷积完全匹配层)还是存在一定的问题,比如在一些介质中有固有的不稳定性等等.基于分裂的多轴完全匹配层(M-PML)通过引入多个衰减剖面可以有效地消除不稳定的现象.本文采用C-PML中不分裂的递推卷积方法,对M-PML进行了实现,这样在实现过程中不用分裂变量,与原来的分裂方法相比,直观易懂,方便简单,易于编程,而且可以减少计算量和存储量,节约计算成本.基于一阶速度-应力方程,采用交错网格高阶有限差分法对不同的介质模型进行了数值模拟,结果证明了本文的不分裂M-PML可以消除不稳定性,得到比较好的计算结果.

Abstract: The perfectly matched layer (PML) absorbing boundary condition has proven to be a very efficient method from a numerical point of view for the elastic wave equation to absorb both body waves with nongrazing incidence and surface waves. And the C-PML(convolution perfectly matched layer) which just modify the coordinate transformation of the classical PML can improve the absorption effect at grazing incidence for the differential seismic wave equation based on an unsplit convolution technique. But in some cases the classical PML and the C-PML suffers from some serious problems such as intrinsic instability in some media. That is to say, numerical errors can accumulate exponentially and terminate the simulation due to computational overflows. The multiaxial perfectly matched layer(M-PML) based on split-field attenuates the waves in PMLs using different damping profiles that are proportional to each other in orthogonal directions. The proportion coefficients of the damping profiles usually vary with the specific model settings. If they are set appropriately, the M-PML algorithm is stable for the media which are unstable for the PML and C-PML. This paper implement the M-PML adopting the unsplit recursive convolution method of the C-PML. In other words, coordinate transformation is carried out at all orthogonal directions and the computing method after coordinate transformation is recursive convolution method. So in the implementation procedure the variable need not split, and the unsplit recursive convolution method is straightforward, convenient, simple and easy to program comparing with the split method. In addition the calculated amount and the memory is less so the cost is saved. Numerical modeling for different media model is carried out employing the staggered-grid higher-order finite-difference method based on the first order velocity-stress equation. The results of unsplit C-PML and unsplit M-PML are compared. They prove that the unsplit M-PML of this paper can eliminate the instability and obtain good results.

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