Uncertainty Quantification in Full Waveform Inversion with Gradient Flows in Probability Space
Abstract
We study the problem of Uncertainty Quantification (UQ) in full waveform inversion (FWI), a computationally intensive and ill-posed nonlinear inverse problem. Adopting a Bayesian approach, we demonstrate how the theory of gradient flows in the space of probability measures provides a principled foundation for sampling the posterior distribution and, in turn, quantifying uncertainties. We explain how the discretization of gradient flows connects to established Bayesian inference techniques used in seismic imaging. Relying on the Wasserstein-Fisher-Rao metric, we derive a variational inference scheme using a Gaussian mixture approximation, and propose numerical strategies, including adaptive time-stepping and preconditioning, to efficiently capture the posterior geometry. We demonstrate the scheme's accuracy and efficiency on a challenging Bayesian FWI benchmark, highlighting its ability to mitigate cycle-skipping. This interdisciplinary article aims to bring a fresh perspective to the uncertainty quantification problem in FWI. It reveals how the gradient flow perspective, rooted in optimal transport, paves the way toward global sampling algorithms at a controlled computational cost.
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BibTeX
@misc{marchner2026uncertainty,
title = {{Uncertainty Quantification in Full Waveform Inversion with Gradient Flows in Probability Space}},
author = {Philippe Marchner and Ludovic Métivier and Romain Brossier},
howpublished = {HAL},
year = {2026},
month = sep,
url = {https://hal.science/hal-05759497v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Uncertainty Quantification in Full Waveform Inversion with Gradient Flows in Probability Space
AU - Philippe Marchner
AU - Ludovic Métivier
AU - Romain Brossier
PY - 2026
DA - 2026/09/16
PB - HAL
UR - https://hal.science/hal-05759497v1
AB - We study the problem of Uncertainty Quantification (UQ) in full waveform inversion (FWI), a computationally intensive and ill-posed nonlinear inverse problem. Adopting a Bayesian approach, we demonstrate how the theory of gradient flows in the space of probability measures provides a principled foundation for sampling the posterior distribution and, in turn, quantifying uncertainties. We explain how the discretization of gradient flows connects to established Bayesian inference techniques used in seismic imaging. Relying on the Wasserstein-Fisher-Rao metric, we derive a variational inference scheme using a Gaussian mixture approximation, and propose numerical strategies, including adaptive time-stepping and preconditioning, to efficiently capture the posterior geometry. We demonstrate the scheme's accuracy and efficiency on a challenging Bayesian FWI benchmark, highlighting its ability to mitigate cycle-skipping. This interdisciplinary article aims to bring a fresh perspective to the uncertainty quantification problem in FWI. It reveals how the gradient flow perspective, rooted in optimal transport, paves the way toward global sampling algorithms at a controlled computational cost.
ER -