Optimal Transport Regularization Applied to Full Waveform Inversion via Machine Learning
Full Waveform Inversion, Optimal Transport, Regularization, Machine Learning, Seismic Imaging
Full Waveform Inversion (FWI) is a seismic imaging technique that aims to reconstruct subsurface physical properties by minimizing the misfit between observed and simulated wavefields. However, FWI is often non-convex and ill-posed, usually affected by problems such as cycle-skipping or crosstalk. This thesis revisits a regularization framework for FWI based on optimal transport theory in order to mitigate these problems. Unlike conventional L2-based misfit measures, the Wasserstein metric exhibits improved convexity properties under translation and dilation, making it less sensitive to phase shifts and better suited to mitigate cycle-skipping. In order to make the Wasserstein distance computation tractable within the inversion loop, we employ a neural-network-based approximation inspired by the Kantorovich-Rubinstein dual formulation. The network is trained to estimate the distance between probability distributions associated with model parameters and well-log constraints. The proposed optimal transport regularization term is incorporated into the FWI objective function and evaluated through numerical experiments using a synthetic seismic setup based on the Marmousi model. Results for a single inversion parameter using common optimization methods indicate mild improvement in the Wasserstein-regularized inversion and suggest directions for future implementations.