Numerical Modeling Of Acoustic Wave Equation With Spatial Varying Meshes

Finite difference is one of the most popular methods for the forward modeling of wave equation, since its record may contain abundant information and the algorithm is easy to be realized. The traditional finite difference algorithm has the problems of instability and numerical dispersion when dealing with a model with low-speed surface medium or low/high speed interlayer. To get simulation results with higher precision, a normal method of decreasing grid steps is adopted. However, it makes the computing time longer and wastes computer memory.The conventional high order finite difference method based on acoustic wave equation is first introduced, and then the problems of the stability of finite difference method and numerical dispersion are discussed in detail and the perfectly matched layer boundary condition is used as the boundary condition for finite difference modeling. Through calculation of examples, the result shows that the perfectly matched layer absorbing boundary condition is better than other absorbing boundary conditions and is easy to be realized.To solve the above problems, a varying grid algorithm in the longitudinal direction is introduced and improved in this paper based on the foundation of the preceding related research. The algorithm is easy to be realized without wave-field interpolation and the computation efficiency is improved correspondingly, thus it saves memory resources efficiently compared to the traditional one.For verifying the validity of algorithm, five practical models are tested. Compared with the traditional finite difference algorithm from aspects of simulation precision, computation efficiency and memory requirement, the results indicate that the new method is much better than the conventional one, and it can decrease numerical dispersion effectively, which is regarded as an effective improvement over the traditional one.