近似完全匹配层边界条件吸收效果分析及衰减函数的改进

完全匹配层边界条件存在两个问题，一是如何减少实际应用带来的额外存储量以及提升计算速度，另一个是如何提升匹配层的吸收效果。对于第一个问题发展了多种非分裂形式，本文采用一种直接对波场进行变换的新型非分裂方法，相比卷积完全匹配层具有不改变方程的形式以及易于实现等优势。对于如何进一步提升完全匹配层吸收效果，没有太大的进展。这是因为离散差异使匹配层的吸收问题更为复杂，一般采取增加匹配层层数的措施缩小离散差，但是又会导致计算量和存储量的增加。本文以在不增加匹配层层数以及不减小理论误差的情况下减小离散差异所带来的虚假反射为目的，分析传统的衰减因子，研究匹配层的吸收机理，设计新的衰减因子，以提高完全匹配层的吸收性能。新衰减因子能够进一步削弱虚假反射振幅，在匹配层层数为5~20层时，对应的边界反射振幅只有改进前的40%~80%。

Absorption effects in nearly perfectly matched layers and damping factor improvement

There are two kinds of problems in perfectly matched layers (PML) introduced in the seismic wave field simulation:one is how to reduce the extra storage capacity in the practical boundary application and enhance the calculation speed; the other is how to absorb incident wave more quickly and make the absorption better.The first problem is well solved with a few advanced non-split perfectly matched layer approaches.For this issue,we adopt a newly-developed non-split perfectly matched layer approach,which transforms directly the wavefield,and will not change wavefield form and use convolution.For the second issue,there is not much progress in boundary absorption enhancement due to the discrepancy complexity caused by discretization.Currently,we decrease the discretization discrepancy by adding the number of layers.In this paper,we analyze the property of damping term and design a new attenuation function which can improve the absorption effect.The function could weaken the reflection amplitude value by 20%~60% when the number of layers is 5~10 compared with conventional attenuation function.