Research On Seismic Imaging And Inversion Based On Compression Sensing

Seismic inversion and imaging methods can obtain geological structure and rock properties by using seismic records and well log data.It is the core technology of geophysical exploration and reservoir prediction.However,with the structure of the exploration area become more complex,the traditional seismic inversion and imaging methods cannot obtain satisfactory inversion results.Consequently,developing highresolution and high-efficient seismic inversion and imaging methods is meaningful in oil and gas exploration.To improve the accuracy and efficiency of seismic inversion and imaging,we analyze the traditional seismic inversion method and develop these methods by utilizing Bayesian statistical information.Moreover,we study the compressed sensing and use them in seismic inversion and imaging methods based on sparse constraints and convex optimization.The main research contents are shown as follows:(1)The seismic inversion theory based on the convolution model is studied in this paper.We introduce the frameworks of seismic inversion theory including non-statistical inversion framework and Bayesian inversion framework.Then,we analyze these frameworks and point out the problems of the non-statistical inversion and Bayesian inversion.(2)The seismic inversion model based on compressed sensing is studied in this paper.First,we introduce the compressed sensing.Then,by analyzing the relationship between compressed sensing and seismic inversion,we present the seismic inversion model based on compressed sensing.Besides,we summarize the seismic inversion algorithm,including the inversion method based on Frobenius norm constraint,the inversion method based on sparse norm constraint.(3)The traditional Bayesian inversion method always simulates acoustic impedance by Gaussian distribution.However,no research has proved that the statistical information of acoustic impedance obeys Gaussian distribution.To overcome this barrier,we proposed the Bayesian inversion method based on Gamma distribution.This novel approach provides a new idea of Bayesian seismic inversion.In this part,we show the statistical characteristics of impedance are non-Gaussian by the statistical parameters,QQ-plot,dynamic sample variance.Then,we utilize Gamma distribution to describe the statistical characteristics of impedance and verify Gamma distribution is more suitable than Gaussian distribution.According to this verification,we used Gamma distribution as a prior distribution in the Bayesian seismic forward model based on the convolution model.and utilize Markov Chain Monte Carlo method to build the inversion framework.the experiences of impedance inversion show the proposed method is feasible.(4)In the traditional Monte Carlo Markov Chain method,the sampling interval of Metropolis-Hastings sampling is fixed and the convergence criteria is missing.These problems reduce the accuracy and efficiency of inversion.To address these issues,we propose a seismic inversion method using Gaussian Metropolis–Hastings sampling with data driving.In this approach,we calculate acoustic impedance from well log data and statistics the statistical information of acoustic impedance,then we put the statistical information in Metropolis-Hastings sampling and control the sampling interval.Besides,we introduce convergence criteria in the Monte Carlo Markov Chain method.The experiences show the application of the statistical information can improve the accuracy of inversion result and the convergence criteria can reduce redundant operations.(5)Seismic inversion and imaging methods based on compressed sensing always use the first order total variant to provide sparse information.The application of the total variant leads to the staircase effect.The integer order difference operation of the total variant causes a scattering effect.To deal with these problems,we added sparse information by the second order total variant and replace integer order difference operation by fractional order difference operation.Then,we proposed a seismic inversion method based on the mixed second order fractional ATpV regularization.The text shows the sparse information of the second order total variant can relieve the staircase effect and the fractional order difference operation can alleviate the scattering effect.The inversion result of the proposed method has the highest accuracy than four traditional methods.(6)The traditional inversion method based on compressed sensing still has two defects.On the one hand,it lacks the information of sparse structure.On the other hand,the efficiency of the iterative algorithm is low.To overcome these defects,we proposed a seismic inversion method using second order overlapping group sparsity term and accelerated alternating direction method of multipliers iterative algorithm.In this approach,we include second order overlapping group sparsity in the inversion method and apply the accelerated alternating direction method of multipliers iterative algorithm to inverse the forward model.The results of experiences show that second order overlapping group sparsity can improve accuracy and the accelerated alternating direction method of multipliers can improve efficiency.The proposed method receives the highestaccuracy and highest-efficiency inversion results.