Group Sparse BPFA-TV Algorithm For Seismic Noise Suppression

Seismic data is often subject to severe random noise.Low signal-to-noise ratio data seriously hinders the identification and extraction of the effective signal,further affecting the imaging of underground structures and the interpretation of seismic data.When dealing with seismic data,it is often faced with the suppression of non-stationary seismic noise,of which the intensity of random noise changes with time and space.The local area has a large noise intensity.Some events are attenuated and distorted under strong noise interference.Therefore,it is of great significance to find a suitable algorithm to suppress non-stationary seismic random noise and restore seismic signal.The Beta-Bernoulli process factor analysis(BPFA)is a nonparametric Bayesian dictionary learning algorithm.The Beta-Bernoulli process as a nonparametric dictionary learning prior can achieve sparse representation of dictionary elements.At the same time,the algorithm updates dictionary weights and noise variance from Gaussian posterior distribution.However,under the influence of strong noise,the obtained global noise variance is inaccurate,which affects the estimation of the feature dictionary.Further,the suppression of noise and the recovery of the signal will be affected.In order to overcome the impact of strong random noise on online dictionary learning,we propose a Beta-Bernoulli process factor analysis algorithm based on total variation constraints(BPFA-TV).BPFA-TV algorithm achieves random noise suppression and signal recovery in seismic under the constraints of BPFA and total variation.BPFA-TV algorithm uses the BPFA dictionary to learn complex structural features of signal in seismic data,thereby improving the accuracy of structural features.At the same time,the total variation regularization term suppresses random noise in the process of noise reduction,effectively alleviating the interference of local strong noise on dictionary learning.The learned dictionary can better characterize seismic signal.We use the ADMM algorithm to solve the BPFA-TV optimization problem,iteratively updating the BPFA term,total variation term,and signal reconstruction term,in order to recover the seismic signal from strong random noise.The results of the simulated and real seismic data show that the BPFA-TV algorithm improves the recovery of seismic signal and suppresses strong seismic noise.To solve the problem of nonstationary random noise,a Beta Bernoulli processfactor analysis algorithm based on group sparse total variation constraints(GBPFA-TV)is proposed in this paper.In the process of updating the dictionary,BPFA algorithm needs to infer noise variance.The accuracy of parameters directly affects the learning of signal features in the dictionary,and then affects the effect of noise reduction.Considering the characteristics of spatiotemporal variation of random noise variance in non-stationary seismic,it is concluded that only one global variance can not represent the characteristics of seismic noise.Therefore,the adaptability of BPFA to non-stationary noise is improved by combining the group sparse characteristics of seismic signal.GBPFA-TV algorithm classifies the noisy data according to the noise level.Each group of data is processed by BPFA-TV algorithm.A dictionary with clearer texture structure and richer signal characteristics can be learned to realize sparse representation of the signal.Finally,each group of data is reconstructed to the original position to get the denoised seismic signal.The processing results of seismic data show that the GBPFA-TV algorithm not only suppresses non-stationary seismic noise,but also restores the seismic signals.