中文摘要：

完全匹配层（perfectly matched layer，PML）是一种高效的吸收边界条件，对体波和面波都有非常好的吸收效果，被广泛应用于弹性波数值模拟。针对二维弹性动力学问题，基于PML最大反射系数的理论推导，对PML衰减函数中的参数取值进行了优化分析。首先基于复伸展坐标变换，给出了一种适用于二阶弹性波动方程的非分裂吸收边界条件；然后通过求解平面P-SV波的波数，得到了非分裂完全匹配层反射系数的解析表达式；最后采用COLLINO给出的衰减函数形式，令PML最大反射系数为最小，得到了衰减函数中PML的厚度、理论反射系数以及最大反射系数之间的相互关系。通过数值算例分析了PML最大反射系数的变化规律，为PML参数的选择和优化提供了理论依据。

英文摘要：

Perfectly matched layer （PML） is a high-efficiency absorbing boundary condition （ABC） to body waves and sur- face waves, and is widely applied to the numerical simulation of the elastic wave. Considering the two-dimensional elastic dy- namic problems, on the basis o~ the theoretical solution of PML＇s maximum reflection codficient, we carry out optimization a- nalysis on the parameters selection for the attenuation function in the PML. Primarily, based on the complex-stretching-coor- dinate transform,we deduced one kind of the unsplit absorbing boundary condition appropriate for the second-order elastic wave equation. Then by solving the wave number of plane P-SV waves, we obtained the analytical expression of maximum re- flection coefficient of the PML. We chose the attenuation function form proposed by Francis Collino, by ordering the maxi- mum reflection coefficient approaching the minimum value, and eventually obtained the mutual relations of the PML＇ s thick- ness, the theoretical reflection coefficient and the maximum reflection coefficient. Finally, we analyzed the variation rule of PML＇ s maximum reflection coefficient by nunaerical testing, which provided theoretical guidance for the selection and optimi- zation of PML＇ s parameters.