Entropic Unbalanced Optimal Transport: Application to Full-Waveform Inversion and Numerical Illustration
Miao YU — PhD Dissertation, Université de Paris, 2021
PhD Dissertation
Abstract
This doctoral dissertation explores the integration of entropic optimal transport theory into geophysical full waveform inversion (FWI). We develop and analyze a family of Sinkhorn divergence-based misfit functions as alternatives to the conventional L2 norm, with the goal of improving convergence robustness and mitigating the cycle-skipping problem in seismic inversion. The core contribution is a systematic comparison of optimal transport objectives — including W1, W2, GHK, and entropic/unbalanced variants — across synthetic and realistic inversion scenarios. This work represents one of the earliest applications of regularized OT distances to subsurface model optimization in seismic imaging, connecting mathematical optimal transport theory with large-scale geophysical computation.
Publicly available: HAL Open Archive — tel-03512143
Supervised by: Jean-Pierre Vilotte (IPGP) & Jean-David Benamou (INRIA)
Institution: Université de Paris (now Université Paris Cité), Institut de Physique du Globe de Paris (IPGP) / INRIA
Significance for EB-1A: This dissertation establishes original contributions at the intersection of mathematical optimal transport theory and geophysical inverse problems. The Sinkhorn divergence approach developed here has since gained broad interest in the computational geophysics community, reflecting the foundational nature of this theoretical contribution. Publicly archived and freely accessible.