Double-pole unsplit complex-frequency-shifted multiaxial perfectly matched layer combined with strong-stability-preserved Runge-Kutta time discretization for seismic wave equation based on the discontinuous Galerkin method

Abstract

The classical complex-frequency-shifted perfectly matched layer (CFS-PML) technique has attracted widespread attention for seismic wave simulations. However, few studies have addressed the double-pole variant of the CFS-PML scheme. The double-pole CFS-PML has a stronger capacity to absorb near-grazing incident waves and evanescent waves than the classical CFS-PML. Using the discontinuous Galerkin (DG) method, we derive a double-pole unsplit auxiliary ordinary differential equation CFS-multiaxial PML (AODE CFS-MPML) formulation, which combines a fourth-order strong-stability-preserved Runge-Kutta time discretization for wavefield simulation on an unstructured grid. The double-pole unsplit CFS-MPML formulations are obtained by introducing auxiliary memory variables and AODEs. The original stress-velocity equations and the double-pole unsplit AODE CFS-MPML equations are all first-order hyperbolic systems and suitable for the DG method. The attenuative variables are added directly to the original seismic wave equations without changing their formats. In contrast to the split perfectly matched layer (PML), we avoid reformulating PML equations in the nonattenuative modeling region. The original seismic wave equation is solved in the nonattenuative modeling domain, whereas the double-pole unsplit AODE CFS-MPML equation is implemented in the PML absorbing region. Three numerical examples validate the performance of the double-pole unsplit AODE CFS-MPML technique. The isotropic and anisotropic experiments demonstrate that our developed double-pole unsplit AODE CFS-MPML is more stable and obtains more accurate solutions than the classical CFS-PML. The second example indicates the flexibility of the combination of the DG method with the double-pole CFS-MPML on undulating topography. The final example displays the applicability and effectiveness of our method in a 3D situation.