Seismic Velocity Estimation in the Curvelet Domain

Curvelets can be seen from the geophysical point of view as the representation of local plane waves. They are known to efficiently decompose any seismic gathers and possibly imaging operators. We study here how curvelets can be useful for velocity estimation. In that context, we first show that the Differential Semblance Optimization technique has a very simple expression in the curvelet domain. We then derive the gradient of the cost function, still in the curvelet domain. An application on a 2-D synthetic data set, generated in a smooth heterogeneous model and with a complex reflectivity, demonstrates the usefulness of curvelets to derive how the velocity model can be improved to better focalize energy in the sub-surface after migration.