In this paper, a curved grid with surface topography is mapped onto a rectangular grid with horizontal surface and second-order elastic wave equation is deduced by using coordinate mapping. For ensuring the stability of numerical modeling, one of the difficulties of elastic wavefield modeling is how to handle the free surface. In this paper, three kinds of free boundary conditions of the flat surface, including implicit and unilateral pseudo node and mixed free surface boundary conditions, are introduced and the concrete difference schemes are given. Numerical modeling results show that the second-order elastic wave equation modeling method with surface topography is effective and feasible, and different surface treatment methods have different influence on the stability, the implicit free boundary condition has the best stability of the other free boundary conditions.


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