Numerical Simulation Of Anti-dispersion Finite-difference Scheme For Wave Equations And Adaptive Grid

The forward simulation of finite difference method for the wave equation is of great significance for understanding the rules of seismic wave propagation and guiding geological interpretation of seismic data.The inherent numerical dispersion of finite difference method especially in the forward simulation of near sueface is a serious interference to the useful wave field;reduce the resolution of wave field simulation.So,a new efficient numerical simulation method,an adaptive grid,different mesh size in different areas is imperative,and has become the focus of seismic wave simulation.In order to eliminate the numerical dispersion,this paper makes a preliminary analysis on the cause of dispersion,then combining the mean value theorem with the difference methods and leads up to the time discrete anti-dispersive wave equations though the discrete processing to wave equations.According to the different proportion of group and phase velocity,we make the theoretical dispersion curves and obtain the optimal parameter when they are approximately equal.At the same time,in order to improve the computational efficiency,this paper proposes an adaptive grid algorithm.First of all,the region is divided into the coarse grids,then find out the region where need a grid refinement according to the comparison between the speed of coarse grid node and the preset threshold.It can easily refine the grids at the time of dividing the grids according to the medium speed,without the wave field interpolation.Meanwhile,easy to implement,and also save computation time and computer memory.As for the nodes of the grid at the transition,making the second Taylor expansion to the wave equation with a solution of Laplasse operator,so as to avoid the interpolation of the instability and computational complexity.Last,the model experiments:the weakening effect of anti-dispersion algorithm to numerical dispersion is obvious.the results of two order and four order accuracy after anti-dispersion correction are better than before and higher precision,two order precision after correction of even up to simulate the effect of the traditional four order.In combination with the adaptive grid,no matter the simple or complex geological model method,adaptive method does not need to wave field interpolation,and can spread well simulated in the condition of complex surface acoustic wave,significantly reduces the calculation amount,weaken the dispersion,improve simulation accuracy.Perfectly matched layer absorbing boundary can absorb the artificial boundary effectively,the wave propagation was simulated successfully.