A convex variational approach for multiple removal in seismic data

Due to complex subsurface structure properties, seismic records often suffer from coherent noises such as multiples. These undesired signals may hide the signal of interest, thus raising difficulties in interpretation. We propose a new variational framework based on Maximum A Posteriori (MAP) estimation. More precisely, the problem of multiple removal is formulated as a minimization problem involving time-varying filters, assuming that a disturbance signal template is available and the target signal is sparse in some orthonormal basis. We show that estimating multiples is equivalent to identifying filters and we propose to employ recently proposed convex optimization procedures based on proximity operators to solve the problem. The performance of the proposed approach as well as its robustness to noise is demonstrated on realistically simulated data.