This paper presents a new approach to a local time-space grid refinement for a staggered-grid finite-difference simulation of waves. The approach is based on approximation of a wave equation at the interface where two grids are coupled. As no interpolation or projection techniques are used, the finite-difference scheme preserves second order of convergence. We have proved that this approach is low-reflecting, the artificial reflections are about 10???4 of an incident wave. We have also shown that if a successive refinement is applied, i.e. temporal and spatial steps are refined at different interfaces, this approach is stable
