Sparse inversion-based seismic random noise attenuation via self-paced learning

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Seismic random noise reduction is an important task in seismic data processing at the Chinese loess plateau area, which benefits the geologic structure interpretation and further reservoir prediction. The sparse inversion is one of the widely used tools for seismic random noise reduction, which is often solved via the sparse approximation with a regularization term. The ℓ1 norm and total variation (TV) regularization term are two commonly used regularization terms. However, the ℓ1 norm is only a relaxation of the ℓ0 norm, which cannot always provide a sparse result. The TV regularization term may provide unexpected staircase artifacts. To avoid these disadvantages, we proposed a workflow for seismic random noise reduction by using the self-paced learning (SPL) scheme and a sparse representation (i.e. the continuous wavelet transform, CWT) with a mixed norm regularization, which includes the ℓp norm and the TV regularization. In the implementation, the SPL, which is inspired by human cognitive learning, is introduced to avoid the bad minima of the non-convex cost function. The SPL can first select the high signal-to-noise ratio (SNR) seismic data and then gradually select the low SNR seismic data into the proposed workflow. Moreover, the generalized Beta wavelet (GBW) is adopted as the basic wavelet of the CWT to better match for seismic wavelets and then obtain a more localized time-frequency (TF) representation. It should be noted that the GBW can easily constitute a tight frame, which saves the calculation time. Synthetic and field data examples are adopted to demonstrate the effectiveness of the proposed workflow for effectively suppressing seismic random noises and accurately preserving valid seismic reflections.