Perfectly matched absorbing layer for modelling transient wave propagation in heterogeneous poroelastic media

Abstract

The perfectly matched layer (PML) has been demonstrated to be an efficient absorbing boundary for near-field wave simulation. For heterogeneous media, the property of the PML needs to be carefully specified to avoid numerical instability and artificial reflection because part of it lies at the discontinuous interface. Coupled acoustic-poroelastic (A-P) media or coupled elastic-poroelastic (E-P) media often arise in the field of geophysics. However, PMLs that appropriately terminate these heterogeneous poroelastic media are still lacking. The main purpose of this paper is to explore the application of unsplit PMLs for transient wave modeling in infinite, heterogeneous, coupled A-P media or coupled E-P media. To this end, a consistent derivation of memory-efficient PML formulations for the second-order Biot’s equations, elastic wave equations and acoustic wave equations is performed based on complex coordinate transformation using auxiliary differential equations. Furthermore, the interface boundary conditions inside the absorbing layer are rigorously derived for the considered A-P and E-P cases. Finally, the weak form of PML formulations for coupled poroelastic problems is presented. The finite element method is used to validate the proposed PML based on several two-dimensional benchmarks. The accuracy and stability of weak PML formulations are investigated. In particular, for coupled acoustic-poroelastic PML, two extreme (open-pore and sealed-pore) interface conditions are considered and PML results are compared with known analytical solutions. This study demonstrates the ability of the PML to effectively eliminate outgoing bulk waves and surface waves in coupled poroelastic media.