A hybrid PML formulation for the 2D three-field dynamic poroelastic equations

Abstract

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 introduces a novel hybrid PML formulation for arbitrary poroelastic domains. Instead of using ADEs, this formulation utilizes time-history variables to reduce the number of unknowns and mathematical operations. The modification of the PDEs to account for the PML is limited to the PML domain only, resulting in smaller matrices while maintaining the governing equations in the interior domain and preserving the temporal structure of the problem. The hybrid approach introduces three scalar variables localized within the PML domain.The proposed formulation was 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 method. The article also discusses the applicability of the method to complex media and its extension to the Multiaxial PML formulation.The codes used for the simulations are available for download from https://github.com/hmella/POROUS-HYBRID-PML.