An unsplit complex-frequency-shifted PML based on matchedZ-transform for FDTD modelling of seismic wave equations

The perfectly matched layer (PML) is an efficient absorbing boundary condition for mitigating undesired reflections in seismic wave modelling. However, the performance of the conventional split-field PML (S-PML) is severely reduced at grazing incidence. Very low frequency waves and evanescent waves can also cause spurious reflections on the PML interface. Such problems could be circumvented by using the complex-frequency-shifted (CFS) stretching tensor in the PML. However, it is difficult to adopt the CFS stretching tensor in the S-PML. A matched Z-transform PML (MZT-PML) technique applied in electromagnetic modelling results in a complete unsplit-field form. In this paper, we show that the MZT-PML can easily implement the CFS stretching tensor and be adopted for elastic wave finite-difference time-domain modelling. The numerical tests in an elongated model illustrate that the complex-frequency-shifted matched Z-transform perfectly matched layer (CFS MZT-PML) can substantially improve performance by eliminating the spurious reflections at grazing incidence. The numerical stability of the CFS MZT-PML is verified by long time computation of the total energy. Also, we conduct a numerical test in a two-layer heterogeneous model showing that the CFS MZT-PML can also be used to simulate efficiently the wave propagation in more complex structures.