Preconditioned BFGS-based Uncertainty Quantification in Elastic Full Waveform Inversion

Qiancheng Liu, Stephen Beller, Wenjie Lei, Daniel Peter, Jeroen Tromp

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


Full Waveform Inversion (FWI) has become an essential technique for mapping geophysical subsurface structures. However, proper uncertainty quantification is often lacking in current applications. In theory, uncertainty quantification is related to the inverse Hessian (or the posterior covariance matrix). Even for common geophysical inverse problems its calculation is beyond the computational and storage capacities of the largest high-performance computing systems. In this study, we amend the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm to perform uncertainty quantification for large-scale applications. For seismic inverse problems, the limited-memory BFGS (L-BFGS) method prevails as the most efficient quasi-Newton method. We aim to augment it further to obtain an approximate inverse Hessian for uncertainty quantification in FWI. To facilitate retrieval of the inverse Hessian, we combine BFGS (essentially a full-history L-BFGS) with randomized singular value decomposition to determine a low-rank approximation of the inverse Hessian. Setting the rank number equal to the number of iterations makes this solution efficient and memory-affordable even for large-scale problems. Furthermore, based on the Gauss-Newton method, we formulate different initial, diagonal Hessian matrices as preconditioners for the inverse scheme and compare their performances in elastic FWI applications. We highlight our approach with the elastic Marmousi benchmark model, demonstrating the applicability of preconditioned BFGS for large-scale FWI and uncertainty quantification.
Original languageEnglish (US)
JournalGeophysical Journal International
StatePublished - Sep 21 2021

Bibliographical note

KAUST Repository Item: Exported on 2021-09-28

ASJC Scopus subject areas

  • Geochemistry and Petrology
  • Geophysics


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