VTI介质准P波频率空间域组合边界条件研究

Combined boundary conditions of quasi-P wave within frequency-space domain in VTI media

1. 同济大学教育部海洋地质重点实验室,上海 200092;2. 石油大学(华东)地球资源与信息学院,山东东营 257061

Laboratory of Marine Geology under Education Ministry, Tongji University, Shanghai 200092, China

讨论了VTI介质中准P波频率空间域的边界条件。首先给出了VTI介质准P波波动方程,阐述了特征分析方法的基本原理,讨论了边界上的反射系数与入射角和度量准纵、横波各向异性强度因子的关系;然后利用特征分析法结合Kelvin-Christoffel方程,构造了准P波波动方程在不同边界和角点的频率域吸收边界条件,利用最佳匹配层法构造了衰减边界条件;最后利用数值模拟对构造的边界条件进行了验证。为了得到好的吸收效果,将吸收边界条件和衰减边界条件有机地结合起来,即先用最佳匹配层法衰减传播到边界的入射波能量,然后再用吸收边界条件吸收边界反射,最终使边界反射降低到可以忽略不计。数值模拟的共炮点记录说明了组合边界条件的良好效果。

The absorbing boundary condition in VTI media at different boundary and corner point is constructed in frequency domain with eigenvalue analysis method and Kelvin-Christoffel equation, and the attenuation boundary is established simultaneously by using the perfectly matched layer (PML) method. The absorbing boundary condition and attenuation boundary condition are integrated into a combined boundary condition to get better rid of reflection of artificial boundary for utilizing their advantages. The energy of incident wave is attenuated in boundary by narrow PML, then the reflected wave is absorbed by the absorbing boundary condition, so the numerical quantity of computation increases a little and the reflection of artificial boundary is eliminated well. The efficiency of the method was presented by numerical experiments.