Perfectly matched layer on curvilinear grid for the second-order seismic acoustic wave equation

A curvilinear-grid perfectly matched layer (PML) absorbing boundary condition for the second-order seismic acoustic wave equation is presented in this paper. The rectangular grids are transformed into curvilinear grids by using a mathematical mapping to fit the curvilinear boundary, and the original wave equation is reformulated under the curvilinear coordinate system. Based on the reformulated wave equation, theoretical expressions and analysis of the curvilinear-grid PML are given. Furthermore, PML model 1 with symmetric form and PML model 2 with asymmetric form are derived from the same acoustic wave equation. By combination with the finite difference (FD) method, these two models are applied to seismic wave modelling with surface topography. The results show that the absorption effect of these two models discretised by the same second-order time difference and second-order space difference are different, and the symmetric-form PML yields better modelling results than the asymmetric-form.