声波完全匹配层吸收边界条件的改进算法

Improved algorithm for absorbing boundary condition of acoustic perfectly matched layer

（大庆石油学院地球科学学院，黑龙江大庆163318）

College of Earth Science, Daqing Petroleum Institute, Daqing 163318, China

传统位移形式的声波完全匹配层（PML）吸收边界条件以三分裂位移参量来构建，需要求解时间3阶导数，计算量大，计算时间长。为此，提出了一种改进的声波分裂PML吸收边界条件。阐述了传统和改进的PML吸收边界条件的构建原理，通过数值模拟讨论了改进和传统的PML吸收边界以及低阶Higdon吸收边界对边界反射的吸收效果。结果表明，低阶Higdon吸收边界条件吸收效果较差，在波场快照和模拟记录中存在较强的边界反射；改进的PML吸收边界条件与传统的PML吸收边界条件效果相当，均能有效地吸收衰减任意角度的边界反射波。改进算法用褶积近似运算代替时间3阶导数的求解，因此简化了计算过程，减少了计算量，是一种高效稳健的算法。

The absorbing boundary condition of acoustic perfectly matched layer (PML) in traditional displacement form should be established by three splitting displacement parameters and the third-order time derivative needs to be solved, which leads to a large computation amount and long computation time. Aiming at this problem, we proposed an improved acoustic splitting PML absorbing boundary condition. The establishment principles of traditional and improved PML absorbing boundary condition were described. Through numerical simulation, the absorbing effect of improved and traditional PML absorbing boundary and low-order Higdon absorbing boundary on boundary reflection was discussed. The results show that the absorbing effect of low-order Higdon absorbing boundary condition is undesirable and relatively strong boundary reflection exists in wave field snapshot and analog recording; the effect of traditional and improved PML absorbing boundary conditions are similar, which can effectively absorb and attenuate the boundary reflections from any angle. In the improved algorithm, the computation of three-order time derivative is replaced by convolution approximate calculation, which simplifies the computation process and reduces computation amount, and is high effective and robust.