In this article, the curvilinear grid finite‐difference method is extended to simulate seismic‐wave propagation in 2D general anisotropic media with surface topography. In order to better describe the surface topography, the geological model is discretized in curvilinear coordinates by body‐conforming grids whose grid lines align with the surface topography. To implement the free‐surface boundary condition, we derive the analytical relationship between derivatives of velocity components for anisotropic media and use the compact finite‐difference scheme and traction‐image method. We fully validate the proposed method using complex topographic surface models and compare the synthetic waveforms with the spectral‐element method. The results show a good agreement between the two methods, confirming the validity of our method.

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