完全匹配层吸收边界条件研究

Study on perfectly matched layer absorbing boundary condition

为了提高人为截断边界的吸收效率,提出了一种完全匹配层边界吸收衰减因子——正、余弦型吸收衰减因子。采用声波波动方程,并应用统一格式的高阶交错网格有限差分法来构建正演递推算子实现声波全波场正演计算(边界处差分阶数依次递减)。以单层均匀介质模型为例,研究不同吸收层厚度与介质速度和声波模拟主频的关系。数值试算结果表明,不同吸收层厚度所消耗的时间按一定的函数关系变化,边界吸收层厚度与速度和最大频率之间无明确的对应关系,边界吸收层厚度所占节点数不小于6个时就可以得到较好的边界吸收效果。以Marmousi模型为例研究了完全匹配层边界吸收衰减因子在复杂地质模型中的边界吸收效果,与解析解的对比可知,该边界吸收衰减因子能在复杂地质模型中取得满意的边界吸收效果。

In order to improve the boundary absorbing efficient of manmade boundary,sine-cosine absorbing attenuation factor,an absorbing attenuation factor for perfectly matched layer,was proposed. High-order staggered-grid finite-difference was applied to construct forwarding recursion operator,and eventually realize full wavefield forward modeling with unified format(the difference order successively decreases at the boundary).Taking one-layer isotropic medium model as example,the relation between absorbing boundary thickness with velocity and frequency was studied.The result shows that the time consumption of different absorbing layer thickness increases according to a certain functional relation,and the absorbing layer thickness has no definite relation with velocity and frequency.When the number of nodes occupied by absorbing boundary thickness is no less than six,good boundary absorbing effect can be achieved.Based on the Marmousi model,the boundary absorbing effect of perfectly matched layer boundary absorbing attenuation factor in complex geologic model was studied.Comparison with the analytical solution shows that boundary absorbing attenuation factor can obtain satisfactory boundary absorbing effect in complex geologic model.