Inaccurate treatment of sharp medium discontinuities introduces a significant error in finite-difference simulations of wave propagation. Such error can be significantly decreased if medium parameters are modified in the vicinity of the interface in some special way. Here we address the theory of how to modify the parameters to achieve the best accuracy. We perform the accuracy analysis of reflection and transmission coefficients and find the modification which provides the second order accuracy versus grid size for planar fluid-elastic and elastic interfaces parallel to the grid. Two widely used finite different schemes of the second and fourth orders are considered. We validate our theoretical results numerically.
