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Abstract: (Multichannel) Singular spectrum analysis is considered as one of the most effective methods for seismic incoherent noise suppression. It utilizes the low-rank feature of seismic signal and regards the noise suppression as a low-rank reconstruction problem. However, in some cases the seismic geophones receive some erratic disturbances and the amplitudes are dramatically larger than other receivers. The presence of this kind of noise, called erratic noise, makes singular spectrum analysis?(SSA) reconstruction unstable and has undesirable effects on the final results. We robustify the low-rank reconstruction of seismic data by a reweighted damped SSA (RD-SSA) method. It incorporates the damped SSA, an improved version of SSA, into a reweighted framework. The damping operator is used to weaken the artificial disturbance introduced by the low-rank projection of both erratic and random noise. The central idea of the RD-SSA method is to iteratively approximate the observed data with the quadratic norm for the first iteration and the Tukeys bisquare norm for the rest iterations. The RD-SSA method can suppress seismic incoherent noise and keep the reconstruction process robust to the erratic disturbance. The feasibility of RD-SSA is validated via both synthetic and field data examples.