Empirical Low-Rank Approximation for Seismic Noise Attenuation

• Published in: IEEE transactions on geoscience and remote sensing 2017-08, Vol.55 (8), p.4696-4711
• Main Authors: Yangkang Chen, Yatong Zhou, Wei Chen, Shaohuan Zu, Huang, Weilin, Dong Zhang
• Format: Article
• Language: English
• Subjects: Approximation; Approximation algorithms; Approximation method; Approximation methods; Attenuation; Components; Dimensions; Empirical low-rank decomposition; Empirical mode decomposition; empirical mode decomposition (EMD); Energy; Frequency-domain analysis; local similarity; Mathematical analysis; Mathematical models; Noise; Noise reduction; Random noise; Seismic data; seismic noise attenuation; Windows (intervals)
• ISSN: 0196-2892; 1558-0644
• DOI: 10.1109/TGRS.2017.2698342

The low-rank approximation method is one of the most effective approaches recently proposed for attenuating random noise in seismic data. However, the low-rank approximation approach assumes that the seismic data has low rank for its f - x domain Hankel matrix. This assumption is seldom satisfied for the complicated seismic data. Besides, the low-rank approximation approach is usually implemented in local windows in order to satisfy the principal assumption required by the algorithm itself. When implemented in local windows, the rank is even more difficult to choose because the seismic data is highly nonstationary in both time and spatial dimensions and the optimal rank for different local windows is not consistent with each other. In order to preserve enough useful energy, one needs to set a relatively large rank when implementing the low-rank approximation method, which makes the traditional method incapable of attenuating enough noise. Considering such difficulties described above, we propose an empirical low-rank approximation approach. We adaptively decompose the input data into several components that have truly low ranks via empirical mode decomposition. An interpretation of the proposed empirical low-rank approximation method is that we empirically decompose a multi-dip seismic image that is not of low rank into multiple single-dip seismic images that are low-rank individually. We use both synthetic and field data examples to demonstrate the superior performance of the proposed approach over traditional alternatives.