{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "name": "Philippe Marchner"
    },
    {
      "name": "Ludovic Métivier"
    },
    {
      "name": "Romain Brossier"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/adgf1trkb0jj5.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "adgf1trkb0jj5",
  "issns": [],
  "landing_url": "https://hal.science/hal-05759497v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "0.sdu"
    ],
    [
      "hal",
      "0.stat"
    ],
    [
      "hal",
      "1.math.math-oc"
    ],
    [
      "hal",
      "1.sdu.stu"
    ],
    [
      "hal",
      "2.sdu.stu.gp"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05759497/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/adgf1trkb0jj5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:37Z",
      "native_id": "hal-05759497",
      "source": "hal",
      "url": "https://hal.science/hal-05759497v1"
    }
  ],
  "subjects": [
    {
      "field": "earth",
      "origin": "hal:2.sdu.stu.gp",
      "subfield": "geophysics"
    },
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-oc",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "hal:0.stat",
      "subfield": "statistics"
    }
  ],
  "title": "Uncertainty Quantification in Full Waveform Inversion with Gradient Flows in Probability Space",
  "title_text": "Uncertainty Quantification in Full Waveform Inversion with Gradient Flows in Probability Space",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:37Z",
  "url": "https://research.draconitic.com/paper/adgf1trkb0jj5",
  "venue": "HAL",
  "versions": []
}