Seismic Data Compression And Reconstruction In Wavelet Domain Based On Bayesian Compressive Sensing

With the rapid development of petroleum geophysical exploration technology,seismic exploration instruments are moving towards multidimensional,multi-compo-net,multi-parameter and high-resolution,which makes the data of seismic exploration increase exponentially and needs much higher data transfer rate to ensure the real time of the data,otherwise it will affect the construction efficiency and exploration resolution.Especially,the seismic exploration instrument has changed from wired transmission to wireless transmission,which is widely used now.In the face of the real time recovery of massive data,the limitation of channel bandwidth and so on.How to improve the real-time transmission ability of massive data of seismic exploration system has become the research hotspot and the core problem to be solved.Among them,the research on compression and reconstruction of seismic data is particularly urgent.Data compression can reduce the amount of data from the source of transmission,improve the efficiency of network transmission of exploration system,improve the real-time processing speed of data and save the storage space.Because of the restriction of the traditional Shannon sampling theorem,most of the existing compression schemes are to transform and encode the field data to eliminate its redundancy,thus achieving the compression effect,and then recovering the original data by decoding and the inverse transform.However,this kind of compression and reconstruction scheme needs to operate the complete seismic data,which is not only inefficient,but also easy to waste the hardware resources.Moreover,decoding is the inverse operation of coding,and the correlation between coding and decoding algorithms is too strong.It is difficult to meet the demand of real-time compression and high-precision reconstruction at the same time.To solve above problems,in this paper,a new seismic data compression and reconstruction scheme is proposed based on the theory of compressive sensing?CS?.In the process of seismic data compression,the chaotic Bernoulli measurement matrix is constructed by using Logistic chaotic sequence,and then the sparse coefficient of seismic data after wavelet transform is measured by the measurement matrix.Because the compression measurement process is essentially a simple matrix and vector multiplication operation,the method of constructing the measurement matrix is used to compress the data,the calculation speed will be very fast,and the real-time performance of data compression will be better.When the seismic data is recovered,the observed values after compression measurement are transmitted or stored,and when the complete seismic data are processed,the reconstruction algorithm is used to restore them.In the process of seismic data reconstruction,we use Bayesian wavelet tree-structured compression sensing reconstruction algorithm?BTSWCS?.Firstly,a hierarchical Bayesian CS priori model is constructed according to the statistical characteristics of wavelet tree structure.Then the Markov chain Monte Carlo?MCMC?method is used to estimate the parameters of the model.Variational Bayesian reasoning is used to replace the MCMC method to improve the convergence speed of the algorithm.The reconstruction algorithm based on Bayesian theory has good anti-noise performance and high reconstruction accuracy.The actual seismic data processing results show that the CBMM constructed in this paper has shorter compression time than the set partitioning in hierarchical trees algorithm?SPIHT?When the same data is compressed and the compression ratio is the same.When CBMM compresses data with a total sampling point is⁸2,the compression time can be shortened to level10^-5.In other words,if the sampling rate of the seismograph is 1KHz,the CBMM measurement matrix can compress the 0.25second collected data by seismograph in real time.For the actual data processing of sampling points2¹⁴,in the case of low SNR,BTSWCS algorithm reconstruction effect is superior to common greedy iterative algorithm.The PSNR of the reconstruction results can be more than 70 dB,and the reconstruction error can be less than 0.05,PSNR can be improved by at least 5 dB.Synthesis of the above research results,in the process of seismic exploration,the method of constructing CBMM is used to compress the seismic data in real time,then the compressed data is transmitted and stored.Finally,the complete data is reconstructed with high accuracy by using the BTSWCS algorithm.It can effectively relieve the pressure of massive seismic data transmission.