The perfectly matched layer for acoustic waves in absorptive media

The perfectly matched layer (PML) was first introduced by Berenger as a material absorbing boundary condition (ABC) for electromagnetic waves. It was first proven by Chew and Liu that a fictitious elastic PML half-space also exists in solids, which completely absorbs elastic waves, in spite of the coupling between compressional and shear waves. The PML absorbing boundary condition provides much higher absorption than other previous ABCs in finite-difference methods. In this work, a method is presented to extend the perfectly matched layer to simulating acoustic wave propagation in absorptive media. This nonphysical material is used at the computational edge of a finite-difference time-domain (FDTD) algorithm as an ABC to truncate unbounded media. Two aspects of the acoustic PML are distinct: (a) For a perfectly matched layer in an intrinsically absorptive medium, an additional term involving the time-integrated pressure field has to be introduced to account for the coupling between the loss from the PML and the normal absorptive loss; (b) In contrast to the full elastodynamic problem, the acoustic PML requires a splitting only on the pressure field, but not on the particle velocity field. The FDTD algorithm is validated by analytical solutions and other numerical results for two- and three-dimensional problems. Unlike the previous ABCs, the PML ABC effectively absorbs outgoing waves at the computational edge even when a dipping interface intersects the outer boundary.