Research On AVO Inversion Algorithm Based On Nonconvex Optimization

As one of the frontier research topics in the application field of seismic signal processing and interpretation,AVO inversion can obtain reliable P-wave velocity,S-wave velocity and density estimation,from which subsurface lithological and fluid properties can be predicted.However,the AVO inverse problem is inherently an ill-posed problem.To help hydrocarbon detection and lithology identification activities,regularization technique plays a crucial role in AVO inverse problem.In reflection seismology,a sparse regularization indicates high resolution solutions.In general,high resolution inversion techniques are roughly classified as stochastic and deterministic inversion approaches.Compared with stochastic inversion approach,deterministic inversion approache attracts more attention due to its low computational expense.By using sparsity constraints in the sparse domain,deterministic inversion is an effective method to obtain high-resolution inversion results.Taking deterministic inversion and nonconvex sparse constraints as the starting point,this thesis focuses on the problem of highprecision and high-resolution AVO inversion.The proposed algorithms have good application in practical problems.The main contributions and innovations of this thesis are as follows:1 In order to improve the underestimation problem of L1 norm based total variation class regularization methods in AVO inversion,a class of smooth nonconvex functions with stronger sparsity-inducing property is used as the regularization function.This kind of nonconvex regularization methods can get more accurate inversion results in the region where the amplitude changes sharply.Simultaneously,traditional regularization parameter selection method uses same regularization parameters for different stratums.As a result,the regularization parameter is too small in the region of rapidly changing stratigraphy and is too large for smooth stratigraphy.To solve this problem,an adaptive individual weight-gain strategy is proposed to assign different regularization parameter weights with different stratums.Finally,a spectral PRP conjugate gradient algorithm combined with linear search step method is used to optimize the established model,and the convergence analysis of the proposed algorithm is given.2 Considering the problem of global convergence and robustness,a constrained ADMM with guaranteed convergence for nonconvex regularized robust AVO inversion is proposed.On the one hand,in order to solve the robustness problem and avoid the singularity of the loss function,a logarithmic absolute error function is used as the loss function.On the other hand,a class of nonconvex functions satisfying Kurdyka-Lojasiewica(KL)property is used as regularization term.At the same time,a new constrained ADMM algorithm is proposed to optimize the established multivariable objective function.Through the KL property,the theoretical analysis of convergence in the transform domain is given.The theoretical convergence analysis shows that the whole iterative sequence is a Cauchy sequence.3 The traditional data-driven AVO inversion algorithm uses K-SVD method for dictionary learning and sparse representation.Sparse coefficients sequence generated by K-SVD method may diverge,and then affect the convergence of the final inversion parameters.In addition,since OMP algorithm is a greedy algorithm,the computational effectiveness of the whole AVO inversion problem can not be guaranteed.The whole objective function of the traditional data-driven AVO inversion algorithm using L2 norm as the loss function will lead to robustness problems.To tackle abovementioned issues,a robust data-driven AVO inversion algorithm based on generalized nonconvex dictionary learning algorithm is proposed.In dictionary learning and sparse coding process,a class of nonconvex functions are used to replace L0 norm as the sparsity-inducing function.At the same time,a smoothed L1 norm with less computational cost is used as the loss function.Finally,the convergence analysis of the proposed algorithm is provided.In comparison with the conventional data-driven AVO inversion algorithm,the proposed algorithm is robust,convergent and computational efficiency.4 In traditional data-driven AVO inversion algorithm,the dictionary learning process and sparse representation process of P-wave velocity,S-wave velocity and density are carried out independently.It ignores the inter-relationship information among the different elastic parameters.Thus,the accuracy of the inversion result will not be anticipated,especially for density term.Considering the powerful representation ability for correlation signal based on quaternion algebra and the inter-relationship information among the different elastic parameters,we model the elastic parameters as a quaternionic signal.A quaternion sparse representation based data driven AVO inversion algorithm is proposed.The proposed algorithm naturally describes the complex characteristics of geological structure while preserve correlation information among the different elastic parameters.