一阶弹性波方程数值模拟中的混合吸收边界条件  

Numerical modeling of the first-order elastic equations with the hybrid absorbing boundary condition

作　　者：任志明[1,2] 刘洋[1,2] 

机构地区：[1]中国石油大学(北京)油气资源与探测国家重点实验室,北京102249 [2]中国石油大学(北京)CNPC物探重点实验室,北京102249

出　　处：《地球物理学报》2014年第2期595-606,共12页Chinese Journal of Geophysics

基　　金：国家"863"计划项目(2013AA064201)资助

摘　　要：Liu和Sen(2010和2012)在地震波场数值模拟中提出一种混合吸收边界条件.该方法具有计算量小、容易实现及吸收效果好等优点.但现有的混合吸收边界条件是针对二阶位移-应力方程设计的,存在稳定性问题.本文首先推导了两种速度-应力单程波方程:二阶Higdon单程波方程和一阶Higdon单程波方程.进而提出基于一阶弹性波方程的混合吸收边界条件方法.在内部区域和边界之间引入一个过渡区域,通过单程波与双程波方程平滑过渡来消除人工边界反射.为了改善混合吸收边界条件的吸收效果和稳定性,我们采用了能同时吸收纵、横波反射的一阶单程波方程和与变量位置有关的加权系数.为了验证混合吸收边界条件的有效性,将其与常规分裂完全匹配层(PML)方法进行了比较.数值模拟结果表明,与PML边界条件相比,混合吸收边界条件在耗用更小计算时间和存储量的前提下,可以获得更好的吸收效果.另外,本文提出的两种混合吸收边界条件中,混合一阶Higdon吸收边界条件具有更好的稳定性.Liu and Sen（2010and 2012）proposed a hybrid absorbing boundary condition（ABC）in numerical modeling of seismic wave propagation.The approach has the advantages of small computational amount,convenience to implement and nearly perfect absorption.However,their method is based on the second-order displacement-stress equations and has the stability problem.Here,we first derive two kinds of velocity-stress one way wave equations（OWWEs）：the 1stHigdon OWWEs and the 2nd-Higdon OWWEs.Then,we propose the hybrid ABC based on the first-order velocity-stress equations.A transition area between the inner area and boundary is used,and the smooth transition of OWWEs and two-way wave equations is adopted to eliminate the artificial boundary reflections.In order to improve the absorption effect and stability,a new firstorder OWWE,which can absorb both P-wave and S-wave reflections,and the weighting factor related toposition of variables are applied.To validate the effectiveness,we compare our hybrid ABCs with the conventional split PML（Perfectly Matched Layer）.The numerical experiments demonstrate that our method can obtain better absorption effect with smaller computational time and memory.Moreover,the hybrid 1st-Higdon ABC is more stable than the hybrid 2nd-Higdon ABC.

关 键 词：混合吸收边界条件 Higdon单程波方程 完全匹配层 数值模拟 一阶弹性波速度-应力方程 

分 类 号：P631[天文地球—地质矿产勘探]