Seismic Data Reconstruction Based On Compressive Sensing And SPGL1 Algorithm

The requirement of seismic data is raised continuously in actual production with the development of seismic exploration technology.However,with the exploration and expansion of the scope of exploration area more and more complex surface conditions,these factors will cause the data is incomplete,irregular,and bring great difficulty to the subsequent seismic data processing,at the same time,it would increase the cost of field construction.Therefore,seismic data reconstruction technology is particularly important.The compressed sensing theory brings a new idea for seismic data acquisition and processing.Based on this theoretical framework,incomplete data can be reconstructed even if the sampling frequency is lower than Nyquist's.There are three main elements to realize the theory: signal sparsity,incoherence of measurement matrix and dictionary matrix,and efficient reconstruction algorithm.Based on these three points,this paper discusses the influence of different sparse representation methods on data reconstruction results.The results of numerical experiments proved that curvelet transform is better than Fourier transform has the outstanding ability of sparse representation,this paper introduces the construction of measurement matrix mathematics theory,and using rules to owe sampling and random sampling Jitter and undersampling three sampling methods to rebuild of synthetic seismic records,the results proved that the sampling points phase Jitter undersampling can obtain better recovery effect at the same time,after in Marmousi model of numerical experiment,the Jitter sampling method increases the sampling condition,ensure all near the shot point sampling,greatly enhance the signal-to-noise ratio data.In this paper,SPGL1 algorithm is used for seismic data reconstruction.The algorithm is obtained by solving multiple Lasso subproblems based tracking denoising problem's solution,in solving optimization problems involving noise estimation and selection of the number of iterations,this article studied these two parameters on the result of data reconstruction,and according to the preliminary conclusion defines the efficiency value formula,through the formula can effectively estimate the optimal parameter selection range.In this paper,a new RWSPGL1 method is proposed to solve the problem of weighted L1 norm minimization by introducing weight functions related to signal characteristics,which improves the efficiency of seismic data reconstruction and saves a lot of time cost.In addition,the data accuracy obtained by RWSPGL1 method is slightly higher than that of SPGL1.In the numerical test of Marmousi model,the velocity model obtained by using full waveform inversion method is compared in this paper,and the result proves that RWSPGL1 has better reconstruction performance.