Uncertainty quantification of {FWI} images.

@inproceedings{Guizar2026RM,
 abstract = {Full-Waveform Inversion (FWI) provides high-resolution estimates of subsurface physical properties by exploiting the kinematic and dynamic information contained in seismic waveforms. However, its high dimensionality, nonlinearity, and non-uniqueness make uncertainty quantification essential for assessing the reliability of the recovered model. In this work, we investigate reduced-rank Hessian-based approaches for estimating posterior uncertainty following acoustic FWI. A P-wave velocity model is first recovered using 100 iterations of the limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) algorithm with a strong-Wolfe line search. Posterior covariance is subsequently approximated using truncated representations of the Hessian or inverse Hessian, with reduced subspaces constructed from either randomized probing or optimization-history vectors. The results reveal substantial differences between the tested approximations. Randomized Hessian probing provides the most numerically stable estimates, with well-conditioned projected systems. Increasing the approximation rank from 50 to 100 improves the representation of data-informed directions, reducing the minimum posterior standard deviation from 692.19 to 685.05 ms−1, relative to a prior standard deviation of 700 ms−1. In contrast, history-based approximations become severely ill-conditioned. The Hessian and inverse-Hessian formulations also exhibit fundamentally different truncation behaviour: incomplete Hessian approximations remain close to the prior covariance and therefore tend to overestimate uncertainty, whereas incomplete inverse-Hessian approximations strongly underestimate posterior uncertainty because only the retained covariance modes contribute to the estimate. A higher-rank randomized experiment at rank 800 confirms these contrasting trends but indicates that several hundred modes remain insufficient to recover the complete posterior covariance of the high-dimensional FWI problem. Overall, randomized Hessian probing provides the most robust characterization of spatial confidence among the approaches investigated and highlights both the capabilities and limitations of low-rank uncertainty quantification in large-scale FWI.},
 author = {Guizar Alfaro, Jorge and Cupillard, Paul},
 booktitle = {2026 {RING} meeting},
 language = {en},
 pages = {246--267},
 publisher = {ASGA},
 title = {Uncertainty quantification of {FWI} images.},
 year = {2026}
}