Abstract：Conventional finite difference numerical simulation of seismic waves employs regular grids in Cartesian coordinates to divide the calculated region. During simulating seismic wavefields under undulating surfaces, it is not only unfavorable to realize the free boundary conditions, but also prone to generate false scattered waves at the corners of the grid due to stepped grid approximation, thus affecting the simulation accuracy. To this end, the orthogonal body-fitted grid generation technique in computational fluid dynamics is introduced into the grid generation of viscoelastic media under undulating surfaces. The first-order velocity-stress equation in curvilinear coordinates is calculated by the optimized homologous grid finite difference method, and the point oscillation generated by the homologous grid difference is eliminated by the selective filtering method. The orthogonal body-fitted grid can accurately describe the undulating surface, and due to the orthogonality of the grid, free boundary conditions can be implemented without complicated coordinate transformation and interpolation operations. Numerical examples show that the numerical solutions obtained by this method are in good agreement with the analytical ones. By comparing the simulation results of the proposed method with those of the regular grid finite difference method, the proposed method can effectively eliminate the false scattered waves caused by the stepped grid in the condition of the same grid spacing, thus improving the numerical simulation accuracy. In addition, the simulation results of two-layers and three-layers viscoelastic medium models on undulating surfaces show that the proposed method is also applicable for complex models.
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