f Modelling waves in discontinuous media - uniformly converging schemes

In numerical modeling of elastic wave propagation, it is a known fact that standard numerical simulation schemes, such as e.g. finite differences and (pseudo-) spectral methods, suffer from numerical errors caused by discontinuities in material proporties. In computations this is typically seen as noisy waves trailing the shear waves (figure left). Since the most interenting parts of geological structures are usually the areas of discontinuities, it is of major importance to develop accurate methods for wave modeling over discontinuities.