Simulation of wave propagation in poroelastic half-spaces presents a common challenge in fields like geomechanics and biomechanics, requiring Absorbing Boundary Conditions (ABCs) at the semi-infinite space boundaries. Perfectly Matched Layers (PML) are a popular choice due to their excellent wave absorption properties. However, PML implementation can lead to problems with unknown stresses or strains, time convolutions, or PDE systems with Auxiliary Differential Equations (ADEs), which increases computational complexity and resource consumption. This article presents two new PML formulations for arbitrary poroelastic domains. The first formulation is a fully-mixed form that employs time-history variables instead of ADEs, reducing the number of unknowns and mathematical operations. The second formulation is a hybrid form that restricts the fully-mixed formulation to the PML domain, resulting in smaller matrices for the solver while preserving governing equations in the interior domain. The fully-mixed formulation introduces three scalar variables over the whole domain, whereas the hybrid form confines them to the PML domain. The proposed formulations were tested in three numerical experiments in geophysics using realistic parameters for soft sites with free surfaces. The results were compared with numerical solutions from extended domains and simpler ABCs, such as paraxial approximation, demonstrating the accuracy, efficiency, and precision of the proposed methods. The article also discusses the applicability of these methods to complex media and their extension to the Multiaxial PML formulation. The codes for the simulations are available for download from \url{https://github.com/hmella/POROUS-HYBRID-PML}.

翻译：模拟孔隙弹性半空间中的波传播是地质力学和生物力学等领域面临的常见挑战，需要在半无限空间边界处采用吸收边界条件。完美匹配层因其优异的波吸收性能而成为常用选择。然而，PML的实现可能导致未知应力或应变、时间卷积或带有辅助微分方程的偏微分方程组等问题，从而增加计算复杂性和资源消耗。本文针对任意孔隙弹性域提出了两种新的PML公式。第一种是全混合形式，采用时间历史变量替代辅助微分方程，减少了未知量和数学运算量。第二种是混合形式，将全混合公式限制在PML域内，从而在保持内部域控制方程的同时，为求解器生成更小的矩阵。全混合公式在整个域中引入三个标量变量，而混合形式则将其限制在PML域内。通过三个地球物理数值实验对所提出的公式进行了测试，实验中采用具有自由表面的软土场地真实参数。将结果与扩展域和更简单吸收边界条件（如旁轴近似）的数值解进行了比较，证明了所提出方法的准确性、效率和精度。本文还讨论了这些方法在复杂介质中的适用性及其在多轴PML公式中的扩展。模拟代码可从 \url{https://github.com/hmella/POROUS-HYBRID-PML} 下载。