Efficiency of perfectly matched layers for seismic wave modeling in second-order viscoelastic equations

Abstract

Summary In order to improve the perfectly matched layer (PML) efficiency in viscoelastic media, we first propose a split multi-axial PML (M-PML) and an unsplit convolutional PML (C-PML) in the second-order viscoelastic wave equations with the displacement as the only unknown. The advantage of these formulations is that it is easy and efficient to revise the existing codes of the second-order spectral element method (SEM) or finite-element method (FEM) with absorbing boundaries in a uniform equation, as well as more economical than the auxiliary differential equations PML. Three models which are easily suffered from late time instabilities are considered to validate our approaches. Through comparison the M-PML with C-PML efficiency of absorption and stability for long time simulation, it can be concluded that: (1) for an isotropic viscoelastic medium with high Poisson's ratio, the C-PML will be a sufficient choice for long time simulation because of its weak reflections and superior stability; (2) unlike the M-PML with high-order damping profile, the M-PML with second-order damping profile loses its stability in long time simulation for an isotropic viscoelastic medium; (3) in an anisotropic viscoelastic medium, the C-PML suffers from instabilities, while the M-PML with second-order damping profile can be a better choice for its superior stability and more acceptable weak reflections than the M-PML with high-order damping profile. The comparative analysis of the developed methods offers meaningful significance for long time seismic wave modeling in second-order viscoelastic wave equations.