Inexact augmented Lagrangian method-based full-waveform inversion with randomized singular value decomposition

Abstract

Abstract The main advantage of full-waveform inversion (FWI) is the ability to obtain useful subsurface structure information, such as velocity and density, from complex seismic data. We have developed a novel inversion algorithm to improve the capability of FWI to achieve high-resolution imaging, even under complex conditions caused by random noise contamination, initial model dependence, or the selection of parameters to be estimated. Our algorithm considers an effective image processing and dimension reduction tool, randomized singular value decomposition-weighted truncated nuclear norm regularization, for embedding FWI to achieve high-resolution imaging results. This algorithm obtains a truncated matrix approximating the original matrix by reducing the rank of the velocity increment matrix, thus achieving the truncation of noisy data, with the truncation range controlled by weighted truncated nuclear norm regularization. Subsequently, we employ an inexact augmented Lagrangian method algorithm in the optimization to compress the solution space range, thus relaxing the dependence of FWI and randomized singular value decomposition-weighted truncated nuclear norm regularization on the initial model and accelerating the convergence rate of the objective function. We tested on one set of synthetic data, and the results show that, compared with traditional FWI, our method can more effectively suppress the impact of random noise, thus obtaining higher resolution and more accurate subsurface model information. This work indicates that the combination of randomized singular value decomposition-weighted truncated nuclear norm regularization and FWI is an effective imaging strategy that can help to solve the challenges faced by traditional FWI.