Seismic Noise Suppression And Interpolation Method Based On Low Dimensional Manifold In Framelet Transform Domain

Seismic exploration is the main means of exploring underground oil and gas resources.Due to the complex structure of the earth,seismic exploration will produce and accompany with various noises in every stage of seismic signal generation,transmission and acquisition.In addition,in the actual seismic exploration,geophone faults are easily caused by poor environment and difficult acquisition conditions,and there are missing traces in seismic records,which affects the continuity of seismic events.Therefore,suppressing random noise in seismic data can keep effective seismic signal as much as possible in the reconstructed seismic data,which is helpful to improve the accuracy of seismic signal processing and subsequent interpretation.LDMM based signal estimation method assumes that the signals to be estimated are distributed on the low dimensional manifold in a certain embedded space,while the noise is irroutinely distributed everywhere in the new space,and then the signal with the lowest dimension is searched as the signal estimation.Because LDMM method only considers the similarity of the seismic events between blocks and ignores the continuity difference between the seismic events and noise in the data blocks.To solve this problem,this dissertation proposes a low-dimensional manifold model based on weighted framelet transformation(WF-LDMM).Combining LDMM with framelet transformation,the low-dimensional constraint is improved to the concentration constraint of framelet transform coefficients of the Hankel matrix of the data.In the new space,a data that is closest to the data to be processed and has the most concentrated framelet coefficients of Hankel matrix,and finally the denoising and interpolation of data are realized.On the one hand,WF-LDMM algorithm uses the feature vector of Laplacian feature map as the non-local basis of framelet transform to fully excavate the similarity of signals between data blocks.On the other hand,the local basis of framelet transformation is constructed based on matrix decomposition algorithm,so as to mine the continuous feature of signal in detail.In addition,this dissertation further studies the concentration of the framelet transformation coefficient of the seismic events,and designs a weight function according to the energy decay speed of the coefficients on the local basis of the noisy data.When WF-LDMM is minimized,more energy is concentrated on the corner of the framelet transformation coefficient matrix,so as to realize seismic data denoising and missing trace recovery.In this dissertation,synthetic data and real seismic data are used to verify the effectiveness of the proposed algorithm in denoising and missing trace recovery.The results show that this algorithm can effectively suppress Gaussian and desert noises that are common in seismic data,and make seismic events more clear and coherent.Compared with the more commonly used Principal Component Analysis(PCA)dimensionality reduction method and curvelet transform denoising method,the proposed method has more obvious denoising effect and can retain the effective signal more completely.At the same time,the results of the seismic data with 25% and 50%missing traces show that the proposed method can completely recover the missing traces in seismic data,and the recovered traces are optimal in amplitude and frequency compared with other methods.