Wave propagation in heterogeneous media: Effects of fine-scale heterogeneity

We study the multiple scattering effects caused by fine-scale heterogeneity. For this purpose, it is unreasonable to rely on a linearization of the dependency of the wavefield in the parameters that describe the medium. Therefore, the only tools that correctly model wave propagation are based on the numerical solution of the (two-way) wave equation by finite differences or finite elements. A fine grid provides a straightforward approach to account for fine-scale heterogeneity. In this situation, there is no need for high-order schemes. Variational methods allow us to exhibit a numerical scheme that accounts for heterogeneity and that is, by construction, stable, provided a stability condition is fulfilled. This condition is a sufficient-stability condition contrary to the classical necessary-stability conditions. In addition, general mathematical results prove the finite-difference solution is close to the solution of the wave equation when the grid is fine enough. The multiple scattering effects caused by fine-scale heterogeneity are very important. In particular, we observe that imaging the so-computed synthetic data by standard migration techniques (that assume a linearization of the above-mentioned dependency) shows a strongly noise-corrupted image. This illustrates the importance of preprocessing data to remove the effect of multiple scattering. We try to improve the signal-to-noise ratio by removing multiples related to the free surface. Although significant noise reduction is achieved, even more sophisticated preprocessing is required to obtain a clear image of the subsurface.