Numerical Simulation of Wave Equation Using the Finite Difference Method with Variable Refined Grid in Complex Near-surface Condition

Abstract

Abstract The horizontal layered refined grid is adopted in the conventional finite difference method (FDM) of variable refined grid for the numerical simulation of wave equation. But, the method cannot well adapt to the characteristics of undulated topography and the variation of velocity structure in near-surface region. To solve this problem, a numerical simulation of wave equation using FDM with undulated variable refined grid is proposed in this paper. The grids are generated according to the undulated topography and the spatial distribution of velocity in the near-surface region from low-velocity to the high-velocity layer. For ensuring the accuracy while taking into account the computational efficiency, the FDM with variable coefficient in above grids is used to discretize the acoustic wave equation. The numerical evaluation and example show that the same accuracy as the method using fine grid can be obtained by the new method. However, its computational time is only 43.6% of the one spent by the fine grid. Furthermore, the new method can also stably adapt to the real complex loess plateau near-surface model in a working area of Ordos Basins.