Multi-step damped multichannel singular spectrum analysis for simultaneous reconstruction and denoising of 3D seismic data (Publication with Expression of Concern. See vol. 16, pg. 1009, 2019)

Multichannel singular spectrum analysis (MSSA) is an effective approach for simultaneous seismic data reconstruction and denoising. MSSA utilizes truncated singular value decomposition (TSVD) to decompose the noisy signal into a signal subspace and a noise subspace and weighted projection onto convex sets (POCS)-like method to reconstruct the missing data in the appropriately constructed block Hankel matrix at each frequency slice. However, there still exists some residual noise in signal space due to two major factors: the deficiency of traditional TSVD and the iteratively inserted observed noisy data during the process of weighted POCS like iterations. In this paper, we first further extend the recently proposed damped MSSA (DMSSA) for random noise attenuation, which is more powerful in distinguishing between signal and noise, to simultaneous reconstruction and denoising. Then combined with DMSSA, we propose a multi-step strategy, named multi-step damped MSSA (MS-DMSSA), to efficiently reduce the inserted noise during the POCS like iterations, thus can improve the final performance of simultaneous reconstruction and denoising. Application of the MS-DMSSA approach on 3D synthetic and field seismic data demonstrates a better performance compared with the conventional MSSA approach.