基于地震波正演模拟的边界算法研究

Research on boundary algorithm based on forward modeling of seismic wave

地震波正演模拟存在边界反射,构建人工边界吸收条件是消除边界反射的核心部分。针对传统边界吸收条件受入射角度影响,造成边界反射吸收不够彻底,对边界反射提出优化的PML吸收边界条件,能够克服入射角导致的吸收不完全的问题。首先,将模型区域划分为计算域和匹配层两部分;其次通过波动方程做坐标变化且加入衰减函数,经过傅里叶变化得到PML边界的声波方程;最后,当由计算域过渡至匹配层时,匹配层采用优化后衰减因子,从而达到消除边界反射的目的。通过对边界吸收算法研究表明,优化后PML(perfectlymatched layer,PML)吸收边界条件能够对边界反射获得更好的正演模拟结果,对不同入射角能做到完全吸收的效果。

Seismic wave forward modeling has boundary reflection,and the artificial boundary absorption condition is the core part of eliminating boundary reflection.Aiming at the traditional boundary absorption condition,which is affected by the incident angle,the boundary reflection absorption is not thorough enough.The PML absorption boundary condition optimized for boundary reflection can overcome the problem of incomplete absorption caused by the incident angle.Firstly,the model region is divided into two parts:the computational domain and the matching layer.Secondly,the wave equation is used to make coordinate changes and the attenuation function is added.After Fourier transform,the acoustic wave equation of the PML boundary is obtained.Finally,when transitioning from the computational domain to the matching layer The matching layer adopts an optimized attenuation factor to achieve the purpose of eliminating boundary reflection.The research on the boundary absorption algorithm shows that the optimized PML absorption boundary condition can obtain better forward simulation results for boundary reflection and achieve complete absorption for different incident angles.