Curvelet‐domain matched filtering with frequency‐domain regularization and an application to primary‐multiple separation

Abstract

In Herrmann et al. (2008a), it is shown that zero‐order pseudod‐ifferential operators, which model the migration‐demigration operator and the operator mapping the predicted multiples to the true multiples, can be represented by a diagonal weighting in the curvelet domain. In that paper, a smoothness constraint was introduced in the phase space of the operator in order to regularize the solution to make it unique. In this paper, we use recent results in Demanet and Ying (2008) on the discrete symbol calculus to impose a further smoothness constraint, this time in the frequency domain. It is found that with this additional constraint, faster convergence is realized. Results on a synthetic pseudodifferential operator as well as on an example of primary‐multiple separation in seismic data are included, comparing the model with and without the new smoothness constraint, from which it is found that results of improved quality are also obtained.