Deblending and interpolation of subsampled blended seismic data based on damped randomized singular spectrum analysis

When compared to traditional seismic data acquisition, irregular blended acquisition significantly promotes the acquisition efficiency. Yet, the blending noise of subsampled blended data introduces new obstacles for the subsequent processing of seismic data. Due to the predictability of linear events in the frequency–space domain, the constructed Hankel matrices exhibit low-rank characteristics. However, the blending noise of subsampled blended data increases the rank, so deblending and interpolation can be implemented via rank-reduction algorithms such as the singular spectrum analysis. The significant computing cost of the singular value decomposition, however, makes the traditional singular spectrum analysis inefficient. An alternative algorithm, known as the randomized singular spectrum analysis, employs the randomized singular value decomposition instead of the traditional singular value decomposition for rank-reduction. The randomized singular spectrum analysis significantly enhances the efficiency of the decomposition process, particularly when dealing with large Hankel matrices. There still remains some random noise when using the singular spectrum analysis or randomized singular spectrum analysis for subsampled blended data, because the noise subspace and signal subspace are coupled together. Thus, we incorporate a damping operator into the randomized singular value decomposition and propose a novel damped randomized singular spectrum analysis method. The damped randomized singular spectrum analysis combines the advantages of the randomized singular value decomposition and the damping operator to enhance the computational efficiency and suppress the remaining noise. Moreover, an iterative projected gradient descent strategy is introduced to achieve deblended and interpolated seismic data for subsequent processing. Examples from synthetic data and field data are used to demonstrate the effectiveness and superiority of the proposed damped randomized singular spectrum analysis method, which enhances the accuracy and efficiency during simultaneous deblending and interpolation.