Seismic Random Noise Simultaneous Attenuation in the Time–Frequency Domain Using Lp-Variation and γ Norm Constraint

Sparse low-rank denoising methods are widely applied for seismic random noise attenuation. Due to the poor structural sparsity and poor low rank of the traditional method, random noises, effective signal loss, and poor continuity still exist. To overcome these barriers, a multitrace seismic random noise simultaneous attenuation method in the time–frequency using the Lp-variation and ${\gamma }$ norm constraint is proposed. This approach uses Lp-variation regularization to describe the structural sparsity of seismic data in the time–frequency domain. The structural sparsity can obtain the structural similarity of adjacent traces in the time–frequency domain. This similarity can improve the continuity of events and can further suppress low-amplitude random noise. Besides, the approach utilizes the ${\gamma }$ norm to constrain the low rank of seismic data in the time–frequency domain. The ${\gamma }$ norm can obtain more low-rank information than the nuclear norm. More low-rank information can improve the overall suppression effect of random noise. The Lp-variation and ${\gamma }$ norm constraints are used to construct the objective function. The alternating direction method of multipliers algorithm, the difference of convex programming, and singular value decomposition are utilized to obtain the attenuation algorithm. Both synthetic and field data tests prove that the proposed method has better denoising and effective signal protection ability.