Performance of convolutional perfectly matched layers for pseudospectral time domain poroviscoelastic schemes

This paper presents an implementation of the convolutional perfectly matched layer for the velocity–stress formulation of poroviscoelastic equations in anisotropic media, with high-order time and space formulations. After its introduction by Bérenger in 1994 for Maxwellʹs equation, the perfectly matched layer (PML) quickly became the standard approach to absorb outgoing waves on a numerical mesh. Subsequent developments include generalization and formulation in terms of a convolutional operator and auxiliary differential equations that improve efficiency and allow for the implementation of high-order time integration schemes. In this work, a fourth-order Runge–Kutta scheme is employed. Also, with the convolutional formulation, the wavefields need not be split as in the original formalism. Such unsplit PMLs allow for the implementation with a pseudospectral operator as presented in this paper. Although efforts have been deployed for the optimization of PML parameters, such an approach is not always tractable, especially for seismic wave propagation because different types of waves interact with the medium. Hence, the performance of the implementation is evaluated through a series of numerical experiments. Tests are performed for waves impinging on the PML interface both at normal and grazing incidence, for both isotropic and anisotropic media. The results highlight the advantage of the convolutional formulation for waves at grazing incidence and show that anisotropic media require a larger number of absorbing layers to achieve performances comparable to those obtained in isotropic media.