Regularized Full-Waveform Inversion With Shearlet Transform and Total Generalized Variation

Full-waveform inversion (FWI) is a powerful method of reconstructing subsurface properties during seismic exploration. However, it is difficult for FWI to accurately describe a subsurface model with sharp surfaces and smooth variations because of the highly nonlinear and ill-posed problems associated with FWI. We first propose a novel FWI with shearlet transform and total generalized variation (TGV) regularization on a subsurface model to alleviate this challenge. Shearlet transform is particularly well adapted to preserve the abundant geometric information of models by representing anisotropic features such as curves and edges; however, it often induces the boundary effect, leading to a resolution reduction. To address shearlet transform drawbacks, we employ TGV to reduce the artifacts by involving various order derivatives to adjust different degrees of smoothness. The proposed regularization scheme is robust to the noise of the observed data during the inversion process. Using the simple synthetic, Society of Exploration Geophysicists (SEG)/European Association of Geoscientists and Engineers (EAGE) overthrust, Marmousi, and modified 2004 BP models, we demonstrate that the proposed method reconstructs subsurface geophysical models with sharp interfaces and smooth background variations more accurately than the conventional methods without any regularization and those with only the total variation (TV) regularization, TGV regularization, and shearlet transform regularization.