| Finite difference is one of the popular methods for seismic wavefield modeling, since its record may contain abundant information and the algorithm is easy to be realized. The traditional finite difference algorithm has the problem of instability and/or 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 method of decreasing grid steps is adopted usually, but which makes the computing time longer and computer memory be wasted.To solve the above problem, based on the foundation of the preceding related research, a varying grid algorithm in the longitudinal direction is introduced and improved in this paper, which is easy to be realized without wave-field interpolation, can improve computation efficiency, and save memory resources efficiently compared with traditional one. For verifying the validity of algorithm, several practical models are tested. Compared with the traditional finite difference algorithm from the aspect of simulation precision, computation efficiency and memory requirement, the results indicate that the new method is much better than the conventional one, and can decrease numerical dispersion effectively, which is regarded as an effective improvement over the traditional one.Compared with the perfectly matched layer (PML) absorbing boundary condition algorithm, it is proved that the varying grid one in the vertically direction has the similar realization thoughts. There is good transition relationship between them, which offers a possibility to realize varying grid perfectly matched layer (PML) absorbing boundary condition in the future. Through quantitative comparison among the transparent boundary, paraxial approximations absorbing boundary and PML one, and calculation by 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.
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