Adaptive Dictionary Learning-based Sparsity-promoting Regularization For Full-waveform Inversion

Full-waveform inversion(FWI)is a highly nonlinear and ill-posed inverse problem,which needs proper regularization to produce reliable results.Among numerous regularization strategies,Tikhonov regularization(sometimes called l2-norm regularization)is certainly one of the most popular,which is to use a smooth(differentiable)quadratic constraints.As a result,FWI with the Tikhonov regularization tends to produce a regularized solution that is overly smooth.Another category of regularization methods are the l1-norm sparsi-ty-promoting regularization based on the sparsity of model coefficients in a predetermined transform domain or dictionary.One important regularization in this category is the well known Total Variation(TV)regularization.TV regularization enforces that the sparsity of solutions in the model-derivative domain,and thus causes inversion results to suffer from the undesired staircase effect.Recently,the sparsity-promoting methods based on dictionary learning have been introduced to FWI problem,and these methods demonstrate significantly improving the quality of the inversion than l1-norm regularization using fixed transforms.Therefore,this paper proposes an adaptive dictionary learning-based sparsity promot-ing regularization for full-waveform inversion,called Adaptive Sparsity-promoting Regulari-zation-based Iterative inversion strategy,or ASRI-FWI method for short.Combining L-BFGS algorithm and l1-norm regularization method based on adaptive dictionary learning,the smooth background change and clear geophysical model parameter interface are reconstruct-ed.The main research contents include the following aspects:Firstly,starting from the forward modeling of full waveform inversion,the finite differ-ence method is constructed to solve the wave equation.In addition,the source function and boundary condition of forward modeling are introduced,and the corresponding solution method is given.Secondly,under the background of waveform inversion,dictionary learning is introduced into FWI process,in which dictionary is learned from many small imaging patches taken from the optimal velocity model obtained at previous L-BFGS iterations.In the end,the algorithm proposed in this paper is introduced.Algorithm is mainly introduced the two key steps:the optimization problem of the L-BFGS algorithm and the method of diction-ary learning.,and to specify other steps.We test our proposed method on a smoothed Mar-mousi model,an BG Compass model,and an SEG/EAGE salt model.From these experiments,we conclude that the proposed ASRI-FWI method achieves better performance than the FWI with TV regularization method.