An unsplit convolutional perfectly matched layer technique improved at grazing incidence for the viscoelastic wave equation

In the context of the simulation of wave propagation, the perfectly matched layer (PML) absorbing boundary layer has proven to be efficient to absorb non-grazing incidence waves. However, the classical discrete PML cannot efficiently absorb waves reaching the absorbing layer at grazing incidence. This is observed, for instance, in the case of thin mesh slices, or in the case of sources located close to the absorbing boundaries or receivers located at large offset. In order to improve the PML efficiency at grazing incidence we derive an unsplit convolutional PML (CPML) for a fourth-order staggered finite-difference numerical scheme applied to the 3-D viscoelastic seismic wave equation. The time marching equations of the standard linear solid mechanisms used do not need to be split and only the memory variables associated with velocity derivatives are stored at each time step. This is important in the case of more than one damping mechanism. Memory storage is reduced by more than 70 per cent in the PML regions in 3-D simulations compared to split PMLs optimized at grazing incidence. We validate the technique based on a benchmark performed in a thin mesh slice.