Unsplit complex frequency-shifted PML implementation using auxiliary differential equations for seismic wave modeling

The complex-frequency-shifted perfectly matched layer (CFS-PML) technique can efficiently absorb near-grazing incident waves. In seismic wave modeling, CFS-PML has been implemented by the first-order-accuracy convolutional PML technique or second-order-accuracy recursive convolution PML technique. Both use different algorithms than the numerical scheme for the interior domain to update auxiliary memory variables in the PML and thus cannot be used directly with higher-order time-marching schemes. We work with an unsplit-field CFS-PML implementation using auxiliary differential equations (ADEs) to update the auxiliary memory variables. This ADE CFS-PML results in complete first-order differential equations. Thus, the numerical scheme for the interior domain can be used to solve ADE CFS-PML equations. We have implemented ADE CFS-PML in the finite-difference time-domain method and in anonstaggered-grid finite-difference method with the fourth-order Runge-Kutta scheme, demonstrating its straightforward impleme...