Unsplit perfectly matched layer absorbing boundary conditions for second-order poroelastic wave equations

Abstract

An unsplit perfectly matched layer (PML), an absorbing boundary condition, is proposed for the second-order Biot’s equations to simulate wave propagation in unbounded poroelastic media. The PML formulas are derived using a two-parameter complex stretching approach, resulting in a two-dimensional (2D) time-domain system which consists of four second-order displacement equations and six first-order auxiliary differential equations. The proposed PML was validated using three 2D benchmarks: (i) spurious reflection of PML at grazing incidence; (ii) application of PML in stratified porous media and (iii) the relationship between the material property and the stability of PML. The numerical results show that the outgoing body waves and surface waves can be effectively attenuated by the proposed PML with appropriate scaling factors and damping profiles. The proposed formulas are much more compact, making it more efficient in studying poroelastic wave phenomena in open domain.