Deconvolution with curvelet‐domain sparsity

Abstract

We use the recently introduced multiscale and multidirectional curvelet transform to exploit the continuity along reflectors for cases in which the assumption of spiky reflectivity may not hold. We show that such type of seismic reflectivity is sparse in the curvelet‐domain. This curvelet‐domain compression of reflectivity opens new perspectives towards solving classical problems in seismic processing including the deconvolution problem. In this paper, we present a formulation that seeks curvelet‐domain sparsity for non‐spiky reflectivity and we compare our results with those of spiky deconvolution.