Convolutional and Non-convolutional PMLs for High-order Schemes Optimized at Grazing Incidence for the Seismic Wave Equation

摘要

The perfectly matched layer (PML) absorbing boundary condition has proven to be very efficient from anumerical point of view for the elastic wave equation to absorb both body waves with nongrazingincidence and surface waves.However, at grazing incidence the classical discrete PML method suffers from large spurious reflectionsthat make it less efficient for instance in the case of very thin mesh slices, in the case of sources locatedclose to the edge of the mesh, and/or in the case of receivers located at very large offset.The PML can be improved at grazing incidence for the seismic wave equation based on unsplitconvolution (CPML) or non convolution techniques (ADE-PML/Auxiliary Differential Equations PML).Unsplit CPMLs for the velocity and stress formulation of the seismic wave equation are classicallycomputed based on a second-order finite-difference time scheme.To increase the accuracy of thealgorithm, particularly for long time periods, we implemented an unsplit non-convolutional high-ordertime-stepping version of ADE-PML. ADE-PML and CPML are equivalent at the second-order in time.Applications to purely elastic, anisotropic, poroelastic and viscoelastic thin slices in 2D/3D configurationsare shown.