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

TL;DR

This paper introduces two novel PML formulations for simulating wave propagation in 2D poroelastic media, reducing computational complexity while maintaining accuracy, and demonstrates their effectiveness through geophysical numerical experiments.

Contribution

The paper presents a fully-mixed PML formulation with time-history variables and a hybrid PML form that confines variables to the PML domain, improving efficiency and accuracy in poroelastic wave simulations.

Findings

The formulations accurately simulate wave propagation in poroelastic media.

The hybrid PML reduces matrix size and computational resources.

Results outperform simpler ABCs and match extended domain solutions.

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 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}.