A Well-posed PML Absorbing Boundary Condition For 2D Acoustic Wave Equation

An perfectly matched layers absorbing boundary condition (PML) with an unsplit field is derived for the acoustic wave equation by introducing the auxiliary variables and their associated partial differential equations. Unlike the conventional split-variable PML which is only weakly well-posed, the unsplit PML is proven to be strongly well-posed. Both the split-field PML (SPML) and the well-posed PML (WPML) are tested on a homogeneous velocity model by applying the 2-4 staggeredgrid finite-difference scheme. Test results are compared with those by Cerjan’s sponge zone absorbing boundary condition. The comparison indicates that WPML and SPML have almost the same performance and are significantly more effective and efficient in absorbing spurious reflections. The advantage of WPML over SPML is that it is theorectically more robust.