Rank-reduction based standard deviation estimation and shuttling for FWI

Full-waveform inversion (FWI) is capable of providing high-resolution Earth models, but quantifying uncertainty in these models remains a challenging and costly endeavour. The computational limitations of FWI mean that practical uncertainty estimates are necessarily based on highly incomplete information. This makes significant the difference between aggressive approaches, which systematically underestimate uncertainty, and conservative approaches, which systematically overestimate it. Here, we investigate an approach for inexpensive, conservative uncertainty quantification for high-dimensional FWI problems [1].  

 

This uncertainty quantification strategy is based on truncated singular value decomposition of the inverse problem Hessian. It takes as input a set of model and gradient pairs, which can, but do not have to be the inversion update history. This machinery can be used for both standard deviation estimation and hypothesis testing, using a targeted nullspace shuttling approach. In addition to its flexibility,  comparatively low cost and large-problem scaling, a key advantage of this approach is its conservativism; it provides a guarantee that the estimated uncertainty is greater than that which would be achieved with a full-rank Hessian estimate.

 

[1] Keating, S., Zunino, A., & Fichtner A, 2026. A comparison of rank-reduction strategies for uncertainty estimation in full-waveform inversion. Accepted for publication in Geophysical Journal International