The singular spectrum analysis (SSA) method can detect the low-rank structure of data and therefore has become a powerful tool in seismic data processing and analysis. In particular, the SSA method can effectively suppress seismic random noise according to the different behaviors of coherent signal and random noise in the singular spectrum. However, there has been much research and experimentation indicating that the basic SSA method performs poorly when the noise becomes erratic. One of the reasons is that the quadratic misfit adopted in SSA is sensitive to non-Gaussian disturbances. One solution to this problem is to iteratively reweight the low-rank approximation of using the SSA method and finally achieve a particular kind of robust misfit. The low-rank approximation is robustified in this study by a more direct strategy, which consists of two main steps, prediction and elimination, and is called the two-step SSA method. The whole algorithm only runs the SSA filtering twice and hence is more computationally efficient compared to the iteratively reweighted SSA technique. The two-step SSA method adopts two criteria to calculate a weighting matrix and predict the erratic disturbance. This strategy also can be generalized into an iterative reweighting-based technique (e.g., the iteratively reweighted SSA technique) for robust denoising. The performance of the proposed two-step SSA method is tested using simulated and real seismic data. The results demonstrate its feasibility.

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