Square-Root Variable Metric based nullspace shuttle: a characterization of the non-uniqueness in elastic full-waveform inversion

Qiancheng Liu, Daniel Peter

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Full-waveform inversion (FWI) is for most geophysical applications an ill-posed inverse prob-16lem, with non-unique solutions. We examine its non-uniqueness by exploring the nullspace17shuttle, which can efficiently generate an ensemble of data-fitting solutions. We construct18this shuttle based on a quasi-Newton method, the square-root variable-metric (SRVM)19method. The latter provides access to the inverse data-misfit Hessian in FWI for large-scale20applications. Combining the SRVM method with a randomised singular value decomposi-21tion, we obtain the eigenvector subspaces of the inverse data-misfit Hessian. Its primary22eigenvalue and eigenvector are considered to determine the null space of inversion result.23Using the SRVM-based nullspace shuttle, we can modify the inverted result a posteriori24in a highly efficient manner without corrupting the data misfit. Also, because the SRVM25method is embedded through elastic FWI, our method can be extended to multi-parameter26problems. We confirm and highlight our approach with the elastic Marmousi example.
Original languageEnglish (US)
JournalJournal of Geophysical Research: Solid Earth
Issue number2
StatePublished - Jan 28 2020

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): UAPN#2605-CRG4
Acknowledgements: All data analyzed here are openly available. The MarmousiSRVM model can be found at https://zenodo.org/badge/latestdoi/125932696. The SeisflowSRVM codes can be found at https://zenodo.org/badge/latestdoi/125918416. The codes for null-space shuttle can be found at https://zenodo.org/badge/latestdoi/126001419. This work was supported by the King Abdullah University of Science & Technology (KAUST) Office of Sponsored Research (OSR) under award No. UAPN#2605-CRG4. Computational resources were provided by the Information Technology Division and Extreme Computing Research Center (ECRC) at KAUST.


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