Three dimensional seismic data reconstruction based on truncated nuclear norm

• Published in: Journal of applied geophysics 2023-07, Vol.214, p.105049, Article 105049
• Main Authors: He, Jingfei, Wang, Yanyan, Zhou, Yatong
• Format: Article
• Language: English
• Subjects: Hankel structure matrix; Matrix completion; Rank reduction; Truncated nuclear norm
• ISSN: 0926-9851; 1879-1859
• DOI: 10.1016/j.jappgeo.2023.105049

The rank reduction method is widely used to reconstruct three dimensional (3D) seismic data. The traditional multichannel singular spectrum analysis (MSSA) utilizes truncated singular value decomposition (TSVD) to approximately solve the rank function of the block Hankel structure matrix constructed by frequency slices of seismic data. However, the TSVD algorithm discards all nonzero singular values except a few largest singular values and ignores the useful seismic information in small nonzero singular values. To further utilize the seismic data information contained in these small singular values, this paper proposes a method to recover 3D seismic data with truncated nuclear norm (TNN). The proposed method imposes different constraints on large singular values and small singular values. Essentially, the TNN is closer to the rank function than the TSVD. Finally, the proposed model is addressed by the alternating direction method of multipliers, and closed-form solutions are used to update the optimization variables. The experimental results demonstrate that the proposed method achieves superior reconstruction results than the traditional MSSA method. •Truncated nuclear norm is used to recover 3D seismic data by further utilizing useful information in small singular values.•Different constraints are imposed on large singular values and small singular values of the generated block Hankel matrix.•The closed-form solutions are used to update the optimization variables.