Acoustic reverse time migration and perfectly matched layer in boundary-conforming grids by elliptic method

Traditionally, finite difference method is chosen as a fast and accurate solution method for numerical simulation of wave equation. However, finite difference method faces obstacles when surface topography and irregular interfaces exist. Boundary-conforming grids by the elliptic method provide an optimal choice for finite difference wavefield simulation in complicated domains containing not only surface topography but also irregular interfaces. By such grids, the calculations of spatial derivatives are transformed by a chain rule into those in the regular computational space, where traditional finite difference schemes are still applicable. Boundary-conforming grids are superior to other irregular grid methods, such as interpolation method, mapping method and unstructured grids, on the aspects of generality, in accuracy and stability. This paper comprehensively applies the elliptic method and acoustic wave equation simulation, reverse time migration, perfectly matched layers in such boundary-conforming grids. The two-dimensional acoustic wave equation is compactly reformulated in boundary-conforming grids by the elliptic method for forward modeling and reverse time migration, and the symmetric and compact form of perfectly matched layers expressed in curvilinear coordinate system are applied to suppress artificial reflections. A stable and explicit second order accuracy finite difference method is used for discretization. Two models are presented to evaluate the ability of boundary-conforming grids to deal with surface topography and complex interfaces, and to demonstrate the feasibility of wavefield propagation and reverse time migration. Comparisons between the numerical simulations with and without the perfectly matched layers are performed to show the effect of the reformulated perfectly matched layer.