Full-Waveform Inversion with Unbalanced Optimal Transport Metric for Seismic Imaging

Abstract

Full-waveform inversion (FWI) is an effective method for obtaining high-resolution images of subsurface structures. Conventional full-waveform inversion, which uses the least-square norm $L_2$ to measure the mismatch between observed and synthetic seismograms, frequently suffers from cycle-skipping and local minimum problems. Derived from optimal transport theory, the Wasserstein metric has been proposed to mitigate cycle-skipping issue. However, due to the requirement for mass conservation, the classical quadratic Wasserstein metric is not ideally suited for FWI applications. In this study, we introduce two unbalanced optimal transport (UOT) distances for use in FWI: the regularized UOT and the unbalanced Sinkhorn divergence. An entropy regularization approach and a truncation approximation are employed to guarantee the efficiency of calculating distances and gradients. These unbalanced optimal transport distances preserve the desirable properties of the quadratic Wasserstein metric, particularly its convexity and insensitivity to noise, while overcoming issues related to mass conservation. We compare the unbalanced optimal transport distances with the $L_2$ distance and the classical quadratic Wasserstein metric using the Camembert model and the crustal root model. Our numerical experiments demonstrate the superiority of the unbalanced optimal transport distances over traditional methods.