Making f-x projection filters robust to erratic noise

Abstract

Summary Linear prediction filters are efficient for reducing random seismic noise but not for removing erratic noise. We propose a robust f-x projection filtering scheme for simultaneous erratic noise and Gaussian random noise attenuation. Instead of adopting the ℓ2 norm, as commonly used in the conventional design of f-x filters, we utilize the hybrid ℓ1/ℓ2 norm to penalize the energy of the additive noise. The estimation of the prediction error filter and the additive noise sequence are performed in an alternating fashion. First, the additive noise sequence is fixed and the prediction error filter is estimated via the least-squares solution of a system of linear equations. Then, the prediction error filter is fixed and the additive noise sequence is estimated through a cost function containing hybrid ℓ1/ℓ2 norm that prevents erratic noise to influence the final solution. Synthetic and field data examples are used to evaluate the performance of the proposed algorithm.