Eliminating Seismic Data Noise by Merging Nonlocal Enhanced Low-Rankness and Second-Order Gradient Smoothness

Seismic data are inevitably polluted by noise, which has a significant impact on subsequent applications. Currently, regularization-based methods that utilize interpretable data priors are widely used for eliminating seismic data noise. However, many existing methods are merely direct linear weighted combinations of regularization terms, resulting in the introduction of a series of balancing parameters. Moreover, these methods may fail to fully capture the complex curved structures that exist in seismic data. To handle the above problems, we propose a merged approach based on nonlocal enhanced low-rankness and second-order gradient smoothness (ELGS). The ELGS method simultaneously encodes multiple dimensional features of seismic data within a single term, including temporal evolution characteristics, geological spatial structural information, and self-repeating redundancy of seismic profiles, which minimizes the introduction of balancing parameters while effectively capturing the curved geological structures of seismic data. Specifically, the ELGS method maps low-dimensional seismic data to high-dimensional structural tensors by using a similar patch-matching framework and applies low-rank constraints to the second-order gradient tensors along each direction for each high-dimensional structural tensor. To solve the optimization problem faced by the developed ELGS approach, we design an algorithm based on the alternating direction multiplier method (ADMM). Numerous numerical experiments conducted on both synthetic and field seismic data show that our approach outperforms the related approaches in both quantitative measures and visual performance.