Simultaneous random noise attenuation and three‐dimensional seismic‐data interpolation with faster adaptive rank reduction.

Rank‐reduction‐based simultaneous random noise attenuation and three‐dimensional seismic‐data interpolation has recently become a hot topic in reflection seismology. However, the rank of traditional methods is fixed without considering the variation of signal‐to‐noise ratio on different frequency components, leading to serious residual noise and further affecting the following processing and interpretation tasks. In addition, traditional methods also heavily rely on the application of singular value decomposition technique for rank reduction, which is proven to be computationally expensive for large‐scale data. Thus, a fast‐adaptive rank‐reduction method is proposed in this study. First, the information entropy theory is introduced to adaptively select the optimal rank at various frequencies by calculating the increment of singular entropy. Second, we propose a fast Random Block Krylov algorithm and a subspace multiplexing technique to replace the singular value decomposition algorithm used in traditional methods. The proposed method can significantly improve computational efficiency and yield better seismic‐data reconstruction performance than traditional methods. Applications of the proposed approach on both synthetic and field seismic data demonstrate its superior performance over a well‐known rank‐reduction‐based method, that is the random multi‐channel singular spectrum analysis, in terms of recovered signal‐to‐noise ratio and visual view. [ABSTRACT FROM AUTHOR]