Full-Waveform Inversion Using a Learned Regularization

Full-waveform inversion (FWI) is an efficient technique for capturing the subsurface physical features by iteratively minimizing the misfit between simulated and observed seismograms. As such a problem is ill-posed, a significant ingredient for a satisfactory solution is to incorporate desirable priors. Most traditional regularized FWI approaches suffer from the nonadaptiveness and sensitivity of regularizers. Deep-learning-assisted inversion methods can use pretrained priors or parametric network priors as regularizers. We develop a novel FWI method based on a physics-constrained iterative algorithm with a learned regularization (FWIPLR). The introduced framework easily enables high-quality inversion by integrating two complementary terms: the physical constraints of the imaging system characterized by its forward model and a priori knowledge of the expected results characterized by a deep convolutional neural network (CNN)-based regularizer. In particular, the advanced CNN denoiser, which corresponds to an implicit regularization term, is first trained with large-scale natural images and then fine-tuned with small-scale geological images. Such a transfer learning strategy seems appealing as it makes FWIPLR more generic to distinct geological models. To stabilize the optimization, we use the spectral normalization instead of batch normalization to impose Lipschitz constraint on the networks. We validate the method effectiveness on Marmousi, overthrust, and 2004 BP models. The comparable results illustrate the ability of FWIPLR for producing high-resolution subsurface structures compared with total variation (TV)-regularized FWI, conventional denoiser, and other CNN denoiser-regularized FWI; in particular, when the initial model is inaccurate, data lose low-frequency information or model contains high-contrast media.