Abstract:To solve the problem of the conventional grid difference scheme is difficult to be applied to the complex medium in the numerical simulation of seismic wave field. This paper utilizes the compact staggered finite difference scheme in the numerical simulation of the viscous acoustic wave equation for the first time. Furthermore, we compared the simulation results with acoustic equations in simulation accuracy, dispersion relation, and stability analysis. The theoretical results illustrated that: ① To achieve the same difference accuracy, the number of nodes required by compact staggered grid is less than conventional central difference and staggered difference schemes. Moreover, the computational efficiency of compact staggered finite difference schemes is higher. ② Compared with the conventional staggered and central difference schemes, the truncation error of the compact difference is minor and with lower numerical dispersion. So it is applicable for coarse grid calculation. ③ Under the same difference accuracy, the time grid size of the compact difference scheme is smaller, and the stability condition is stricter. ④ The Perfect matching layer can effectively absorb boundary reflection using the compact staggered difference scheme . Finally, the numerical simulation of the viscous acoustic wave equation and the analysis of wave field characteristics were conducted on the homogeneous medium model, horizontally layered medium model, and Marmousi model. The experimental results demonstrate the practicability and effectiveness of the proposed method for the numerical simulation of complex media, with high simulation accuracy and computational efficiency.