Random Noise Attenuation of Common Offset Gathers Using Iteratively Reweighted $\ell_{2,1}$ Norm Minimization

Abstract

Sparse representation (SR)-based denoising method attenuates random seismic noise trace-by-trace, which may not be able to employ the coherency between neighboring traces. To address this, we propose a multiple measurement vector (MMV)-based algorithm for robust denoising of multichannel seismic gathers. Seismic reflectors in common offset gather (COG) is characterized by horizontal events, which satisfy the common sparsity assumption, making it ideal for the MMV approach. $\ell _{2,1}$ -norm regularization, which enforces two constraints on source matrix, i.e., temporal sparsity and the horizontal continuity, is then adopted in the MMV model to stabilize the lateral variation between channels. Besides, $\ell _{2,1}$ -norm regularization provides a reasonable intrinsic structure to reduce the multisolution of the algorithm. Celebrating the strengths of iteratively reweighted (IR), we present a novel MMV algorithm, IR $\ell _{2,1}$ norm minimization (IR- $\ell _{2,1}$ ), that further improves the performance. The formulated IR- $\ell _{2,1}$ can be minimized by the alternating direction method of multipliers. Both synthetic and field data applications confirm the effectiveness of the proposed denoising method.