Seismic Signal Denoising Based Onmulti-scale Geometric Analysis

Due to the limitations of acquisition environment and instrument performance,the collected seismic signals are often accompanied by strong noise,which brings great difficulties to subsequent processing and interpretation.Therefore,the study of seismic signal denoising is of great significance.Multiscale Geometric Analysis(MGA)has received extensive attention in recent years.Various MGA algorithms have shown strong performance and development potential in the field of seismic signal denoising.MGA algorithms such as Shearlet transform,Contourlet transform and Curvelet transform have been widely used in the field of signal processing.Non-Local Means(NLM)is a classic signal denoising algorithm,while distribution-free False Discovery Rate(FDR)is a statistical algorithm.Denoising effect is well improved when both NLM and FDR are applied respectively to the transformation domain to process the transformation coefficients.Non-Local Bayes(NL-Bayes)is also a classic denoising algorithms,which combining with denoising algorithms to transformation domain also improve denoising performance.This paper studies and improves NLM,FDR,NL-Bayes and other algorithms under the framework of MGA.The main research contents are as following:(1)Denoising of seismic signals based on NLM in Shearlet domainApplying NLM in the Shearlet transform domain to denoise the seismic signals,NLM first performs non-downsampling Shearlet transform on the seismic signals,followed by Principal Component Analysis(PCA)on Shearlet coefficients that approximately follow the generalized Gaussian distribution.NLM is then applied to process the Shearlet coefficients,and finally performs inverse Shearlet transform on the new Shearlet coefficients to obtain the denoised seismic signals.By the means of denoising artificial and actual marine seismic signals,the comparison denoising results with NLM,Shearlet hard threshold and Wiener filtering through the Peak Signal-to-Noise Ratio(PSNR),Mean Square Error(MSE),and Structural Similarity Index(SSIM)show that the algorithm in this paper is at better denoising effect than the other three denoising algorithms under low noise conditions.Therefore,the proposed algorithm is feasible for denoising seismic signals.(2)Denoising of seismic signals based on distribution-free FDR in Contourlet domainNon-Sub Sampled Contourlet Transform(NSCT)is combined with distribution-free FDR to denoise seismic signals.This algorithm uses NSCT to transform the original seismic signal.Since the down-sampling operation in the Contourlet transform is cancelled,it can effectively cancel the pseudo Gibbs phenomenon in the signal.A freely distributed FDR-based seismic signal denoising algorithm in Contourlet domain is proposed.The algorithm first performs NSCT processing on the original seismic signal,and introduces a freely distributed FDR algorithm in the Contourlet domain to process the Contourlet coefficients.Taking advantage of when the noise of Contourlet coefficients approaches zero and large effective signal coefficients,each level of Contourlet coefficients is used as a set of null hypotheses to be tested.First,it is hypothesised that all Contourlet coefficients are generated by noise,and then it is found that some coefficients are indeed not generated by noise.Therefore,these findings show correct discovery(signal)and false discovery(noise).Controlling the size of the FDR is able to control the proportion of false discoveries,hence to increase the proportion of correct discoveries.The threshold is then used to process the Contourlet coefficient,and the final denoising result can be obtained through inverse transformation.Denoising experiments are performed on synthetic seismic signals and marine seismic signals.The measured results such as PSNR,MSE,SSIM and experimental results show that the proposed algorithm has the best denoising effect.(3)Denoising of seismic signals based on Curvelet transform and non-local BayesianCurvelet transform well describes the geometric characteristics of seismic signals,and NL-Bayes has strong denoising ability.Combining the advantages of both,a seismic signal denoising algorithm combining Curvelet transform and NL-Bayes is proposed.The algorithm first uses Curvelet transform to obtain Curvelet coefficients,calculates the noise standard deviation and sets the threshold,and then processes Curvelet coefficients,followed by inverse transforms to obtain Curvelet transform denoising results.Then the original seismic signal is denoised using NL-Bayes to obtain the NL-Bayes denoising result.Finally,a weighted aggregation algorithm is used to perform weighted aggregation of the two denoising results,so that the final denoising result can combine the advantages of both.Based on denoising experiments on artificial and marine seismic signals,the superiority of the proposed algorithm is demonstrated based on metrics such as PSNR,MSE,SSIM and visual effects.