Full Waveform Inversion Method Based On Dictionary Learning And Improved Total Variational Regularization

Geophysical exploration uses the collected data to calculate the underground physical parameters and judge the underground structure.Full Waveform inversion(FWI)has great development potential as a high resolution inversion imaging method.FWI uses kinematic and dynamic information in prestack seismic wave field to reveal structural details and lithology information in complex geological background.In mathematics,FWI is a highly ill-conditioned nonlinear problem,and the inversion results lack continuous dependence on the observed data,so it is easy to fall into the local minimum.The disadvantages of FWI are especially evident in the face of complex geological structures with smooth features and sharp boundaries.Regularization technique keeps the stability of FWI inversion results by mining the prior information of recorded data.In recent years,sparse promoted regularization has attracted extensive attention in the field of inverse problems.In order to obtain stable and high-precision inversion results at reasonable computational cost,three different sparse facilitation FWI algorithms are proposed in this thesis.The specific work is summarized as follows:(1)A modified orthant-wise limited memory quasi-newton method is proposed to solve the corresponding regularization target functional of FWI with mixed regularization.Numerical experiments are carried out on the modified Marmousi model with complex structure and BG Compass model,and the results show that t modified orthant-wise limited memory quasi-newton method proposed in this thesis has obvious advantages in computational efficiency and quantitative analysis compared with the FWI and limited memory quasi-newton method without regularization.(2)To overcome the step artifacts caused by total variational regularization,a new hybrid regularization FWI method is proposed,which combines non-convex second-order total variational regularization with sparse total variational regularization of overlapping groups.The non-convex second-order algorithm is used to reduce the staircase artifacts,while the overlapping group sparse total variational regularization can improve the edge recovery quality.The frequency expansion strategy and adaptive regularization parameter selection alternate direction multiplier algorithm are used to implement the regularization method for FWI problems in frequency domain.Compared with classical total variational regularization,the new hybrid regularization FWI method has advantages both in quality and quantity.(3)Based on the local sparsity and non-local similarity of geological images,a new sparse facilitated FWI computing framework is proposed.First,the dictionary-based learning of principal component analysis(PCA)groups similarity guided image blocks from noise approximation images(estimated results from using local optimization methods)and learned dictionaries.Secondly,sparse representation and non-local similarity are introduced as regularization terms.Finally,the relative total variational algorithm is used to eliminate the residual errors in the reconstructed model.The new inversion strategy combines the external optimization knowledge of the model with the inherent local sparsity and non-local self-similar priors to invert the parameters of the geological model.Experimental results show that the proposed method is superior to the total variational FWI method and the sparse facilitation FWI method in curve-wave domain both qualitatively and quantitatively.