Affected by complex environmental factors, the seismic data collected in desert area are disturbed by a large number of random noise, which makes the signal-to-noise ratio of seismic data low. Moreover, the frequency band of low frequency random noise will overlap with some effective signal bands, which is not conducive to the realization of signal-noise separation. Considering the problems mentioned above, a low-rank matrix approximation algorithm based on variational mode decomposition is proposed to suppress the random noise of desert seismic data. In this paper, we decompose the input signal into several low-rank mode components by the variational mode decomposition method, and extract the intrested low-rank components by solving the weighted nuclear norm minimization of the low-rank modes. The proposed method suppresses a large amount of low-frequency random noise in desert area, and solves the problem of separating part of effective signal from noise in the same frequency band. Through the comparative analysis with other methods in numerical simulation experiments on synthetic and actual seismic data in desert areas, the proposed method suppresses low-frequency noise effectively and recover the events continuously.


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