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Full waveform inversion (FWI) is a highly nonlinear and ill-posed problem. Onone hand, it can be easily trapped in a local minimum. On the other hand, theinversion results may exhibit strong artifacts and reduced resolution becauseof inadequate constraint from data. Proper regularizations are necessary toreduce such artifacts and steer the inversion towards a good direction. In thisstudy, we propose a novel adaptive sparsity-promoting regularization for FWI inthe model-derivative domain which exploits nonlocal similarity in the model.This regularization can be viewed as a generalization of total variation (TV)with multi-class learning-based dictionaries. The dictionaries incorporate theprior information of nonlocal similarity into the inversion, exploiting thefact that geological patterns at different places are similar to some others upto affine transformations (translation, rotation and scaling). Such nonlocalsimilarity priors effectively reduce the degrees of freedom in modelparameters, and may also mitigate the problem of local minima. The formulatedoptimization problem is solved by the Alternating Direction Method ofMultipliers (ADMM). By interpreting the iterative scheme, we find our methodclosely connected with image processing techniques and convolutional neuralnetworks (CNN). We test our proposed method on a modified BP 2004 velocitymodel and a smoothed Marmousi model. Compared with traditional FWI, ourtechnique can better reconstruct sharp edges such as salt body boundaries, andis also able to effectively reduce artifacts. Compared with TV, our result isless blocky and more geologically realistic. Quantitatively, our result has thehighest structural similarity index (SSIM) and also the lowest model meansquare error.

Full waveform inversion with nonlocal similarity and model-derivative domain adaptive sparsity-promoting regularization