A temporal fourth-order scheme for the first-order acoustic wave equations

In this paper, we propose a temporal fourth-order scheme for solving the 2-D first-order acoustic wave equations with perfectly matched layers in time domain. For the temporal discretization, we approximate the velocity at mid-points and the pressure at grid points, then expand the velocity and pressure by Taylor series and replace the high-order temporal derivatives by spatial derivatives. For the spatial discretization, we apply the Fourier pseudospectral method based on conventional and staggered-grid schemes. The dispersion and stability of the new scheme are analysed, and numerical simulations are presented to confirm the robustness and efficiency of the scheme. The new scheme is eventually applied for the wavefield modelling and reverse time migration in bilayered and heterogeneous media to further verify its accuracy and efficiency.