Seismic random noise reduction via generalized beta wavelet and mixed norm

Seismic random noise reduction is an important task in seismic data processing at the Chinese Ordos 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 l(1) norm and Total Variation (TV) regularization are two commonly used techniques in the sparse transform-based random noise reduction methods. However, the l(1) norm is only a relaxation of the l(0) norm, which cannot always provide a sparse result. The TV-based methods may lead to an undesirable staircase result. To avoid these disadvantages, we propose a workflow for seismic random noise reduction by using a sparse representation (i.e. the Continuous Wavelet Transform, CWT) with a mixed norm regularization. In the implementation, the Generalized Beta Wavelet (GBW) is first adopted as the basic wavelet of the CWT to better match seismic wavelets and then obtain a more localized time-frequency representation. It should be noted that the GBW can easily constitute a tight frame, which saves the calculation time when solving the proposed optimization model. Then, the mixed norm regularization, including the lp norm and the TV regularization, is introduced in this paper, which not only overcomes the disadvantages of the two regularization solvers, but also accurately preserves the valid seismic reflections. Finally, synthetic data, 3D post-stack field data and Common Reflection Point (CRP) gather data examples from the Ordos Basin are adopted to demonstrate the effectiveness of the proposed workflow. The denoising results denote that the proposed method can suppress some random noise to improve the signal-to-noise ratio and protect the continuity of the seismic events. Furthermore, the proposed method can maintain the real amplitude of seismic signals to highlight the small-scale faults and the potential oil and gas reservoirs.