Research On Some Issues Of Seismic Data Reconstruction Based On Compressed Sensing

Seismic reconstruction is necessary before the attribute analysis and geological interpretation due to the complexity of acquisition and processing of seismic data.By the reconstruction,the effective signal is enhanced while the negative parts are suppressed for subsequent processing.Seismic data with high quality can effectivly improve the accuracy of seismic exploration,reduce the cost of oil and gas production.As an important processing in geophysical prospecting direction,seismic data reconstruction has always attracted a lot of attention.Compressed sensing put forward new sampling model that sparse signal can be accurately reconstructed by data lower than Nyquist sampling frequency.The theory shows many available directions for seismic reconstruction.New sparse model can be constructed to reduce the multiplicity of the solutions and to improve the stability and reliability of the reconstruction based on the statistical charaterstica of seismic data.Our goal is to reconstruct the seismic data by using compressed sensing related sparse representation method,recovery algorithm and signal modeling,mainly including the following aspects:(1)The sparse representation of signals and its reconstruction algorithm with sparse constraint are studied,such as wavelet transform,multiscale geometric analysis and dictionary learning.By comparing the principle of wavelet and Curvelet,it is shown that the Curvelet transform has better ability of sparse representation for two dimensional or high dimensional signal.At the same time,according to the different construction methods,this paper expounds the advantages of the Shearlet transform as the sparse transform kernel in seismic processing.In addition,the dictionary learning is a kind of adaptive sparse representation method in which rational use of training data can further enhance its effect.Sparse reconstruction is a distinct feature of compressed sensing compared with traditional signal reconstruction methods.Sparse constraint limits the scope of solution space,which is helpful to obtain the reconstruction results which are more consistent with prior features.By improving the sparse model,the negative effects of the reconstruction process can be suppressed.The effect of the original algorithm can be improved by extracting a priori information of the signal.(3)A joint regularization method to suppress random noise of seismic data is presented.At first,the reason of the transform domain threshold denoising method is analyzed,and it mainly depends on the good ability of sparse representation.Followed by an analysis of the effect of Gibbs,the idea of total variation regularization is presented.Finally,a joint regularization method is put forward to reduce the adverse effects of the transform domain thresholding method and improve the random noise suppression effect.By adding different levels of noise on simulated data,it shows that the new method can combine the regularization term with their advantages with better separation of signal and noise while keep the waveform signal structure at the same time.(4)A new method with directional total variation constraint in Shearlet domain for suppressing random noise is proposed.Using the directional information of the signal,the directional total variation can obtain better result in noise suppression.By means of the direction sensitivity of the Shearlet,the seismic records are decomposed into subbands with explicit directional features in which directional total variation is taken to attenuate random noise.The proposed method can effectively improve the scene of the directional full variation and improve the signal noise ratio(SNR).(5)A time-varying wavelet estimation method based on improved online dictionary learning is presented.The wavelet is modeled as a linear superposition of a series of basic waveforms.The weights of each component are extracted by the sparse representation of seismic traces.Then the residual after filtering is projected onto the atoms to achieve online dictionary updating.The method can effectively estimate time-varying wavelet without estimating wavelet phase.It is more flexible and can effectively deal with the new training data.At the same time,easy to classify the training data,the seismic data quality is a more effective.At the same time,it can improve the robustness by using filtering operator.This method has achieved good results in both theoretical and practical data experiments.(6)A reflection coefficient inversion method based on spectral compressed sensing is presented.The number of reflection coefficient with large amplitude is sparse compared with sampling points.This article introduces parity decomposition which turns directly inversion into even and odd series inversion.Due to time window treatment,the observation results of frequency domain division may not directly fall in the frequency domain response of the reflection coefficient.According to spectral compressed sensin model,refinement dictionary is contructed.Two series are solved respectively by spectral compressed sensing.The final result is obtained by superposition of the two series.Compared with traditional methods,the proposed method can significantly improve the resolution of the reflection coefficient.The reconstructed seismic data in this study is more superior than that from classical method which is the basis for seismic data interpretation and exploration.The process can improve the reservoir prediction and the success rate of exploration.In addition,the proposed new model and recovery algorithm are all related with compressed sensing which also enrich its theory and application system.