Linearised versus Nonlinear Estimates of Uncertainty in Full Waveform Inversion

Clicks: 4
ID: 318891
2026
Free PDF
Article Quality & Performance Metrics
Overall Quality
Not rated
Combines reader engagement with the AI quality analysis. This article has not been analysed, so there is no overall score — reader engagement is measured and shown alongside.
AI Quality Assessment
Not analyzed
Readership in this journal
Steady

Ranked #115 of 222 articles by views in geophysical journal international

Most read Least read

Bar heights use a square-root scale. Only the 120 most-read articles are drawn; the journal has 222 in total.

Mint this article as an NFT
Not yet minted

Create a permanent, verifiable on-chain record of this article on the Scimatic Network. The NFT is held in your Journament account, and you can withdraw it to your own wallet at any time.

5 SUSD one-off · no wallet required
Sign in to mint
Abstract
Summary Seismic full waveform inversion (FWI) is a powerful technique that uses seismic waveform data to generate high resolution images of the Earth’s interior. However, significant uncertainty exists in all FWI solutions due to imperfect acquisition geometries, inherent noise in the data, nonlinearity of the forward problem, and the under-determined nature of real-world tomographic problems in which the target is heterogeneous over all length scales. Probabilistic Bayesian FWI addresses this non-uniqueness by estimating the entire family of possible model solutions and thus the solution uncertainty, described by the so-called posterior probability density function (pdf) over model parameter values. The posterior pdf can be estimated using nonlinear inversion methods to quantify full uncertainties, including those created by nonlinearity in the physics. Alternatively, by linearising (approximating) the physics relating parameters and observations around a chosen reference model solution, the posterior pdf is usually approximated by a compact distribution centred around the maximum a posteriori solution, typically a Gaussian pdf. This is referred to as the linearised method. In this work, we apply both nonlinear and linearised methods to 2D acoustic Bayesian FWI problems. We use one variational inference algorithm for the nonlinear case, in which a transformed Gaussian distribution is optimised to approximate the unknown, full posterior pdf, and a second, independent nonlinear variational algorithm – Stein variational gradient descent – for comparison. The results of both are then compared with those from a linearised, locally-Gaussian based method. The results show that while both the linearised and nonlinear methods recover the posterior mean models accurately, they exhibit different posterior uncertainty structures, especially around layer interfaces, due to the linearisation of wave physics. The differences become most obvious in partially constrained regions of the model, where posterior solutions are constrained jointly by data, prior information, and the nonlinearity of wave physics rather than being dominated by any single factor. We also demonstrate that linearised uncertainty estimates are significantly less accurate: they provide far less accurate fits to observed waveform data, and yield biased estimates of inferred or interpreted meta-properties such as volumes of geological bodies. This work therefore motivates the application of fully nonlinear inversion methods in Bayesian FWI if either accurate uncertainty estimates over parameters, or inferred or interpreted meta-properties are important.
Reference Key
openalex_W7166116207 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Xuebin Zhao, Andrew Curtis
Journal geophysical journal international
Year 2026
DOI
10.1093/gji/ggag248
URL
https://doi.org/10.1093/gji/ggag248
Keywords Keywords not found

Citations

No citations found. To add a citation, contact the admin at info@scimatic.org

Comments

No comments yet. Be the first to comment on this article.