A Full-Waveform Inversion Method Based on Structural Tensor Constraints

Full-waveform inversion (FWI) is a method for obtaining velocity models. Because of its theoretical completeness, the final modeling results are often superior to those of velocity modeling methods such as stacking velocity analysis, migration velocity analysis, and velocity tomography. FWI usually takes the $L2$ norm of the residuals between observed and simulated data as the objective function. The current velocity model that best fits the observed data is obtained by solving the objective function. However, during FWI, there is a strong ill-posedness due to its limited conditions. To solve this problem, regularized constraints or gradient preconditioning methods are commonly introduced. In this article, we propose a regularization method that incorporates prior information, aiming to alleviate the aforementioned issues to some extent. This method adds a regularization term based on structural tensors to the original $L2$ norm objective function, introducing subsurface structural information in conventional regularized constraints of FWI. It smooths the velocity model along layer interfaces to ensure that the obtained inversion results are more consistent with the true velocity model. The inversion results from synthetic data of the Marmousi model and BP 2004 benchmark velocity model demonstrate the feasibility and effectiveness of this method. The noisy data FWI further demonstrates the robustness of this method. Moreover, the proposed method can better recover the small-scale structures in the velocity model and significantly improve the resolution of the velocity model.