Characterise the non-uniqueness in full-waveform inversion by using the square-root variable metric based null-space shuttle

Abstract
Full-waveform inversion is an ill-posed inverse problem, with non-unique solutions. We examine its non-uniqueness by exploring the null-space shuttle, which can generate an ensemble of data-fitting solutions efficiently. We construct this shuttle based on a quasi-Newton method, the square-root variable-metric (SRVM) method. This method enables a retrieval of the inverse data-misfit Hessian after the SRVM-based elastic FWI converges. Combining SRVM with randomised singular value decomposition (SVD), we obtain the eigenvector subspaces of the inverse data-misfit Hessian. The first one among them is considered to determine the null space of the elastic FWI result. Using the SRVM-based null-space shuttle we can modify the inverted result a posteriori in a highly efficient manner without corrupting data misfit. Also, because the SRVM method is embedded through elastic FWI, our method can be extended to multi-parameter problems. We confirm and highlight our methods with the elastic Marmousi example.

Citation
Liu, Q., & Peter, D. (2019). Characterise the Non-Uniqueness in Full-Waveform Inversion by Using the Square-Root Variable Metric Based Null-Space Shuttle. 81st EAGE Conference and Exhibition 2019. doi:10.3997/2214-4609.201901222

Acknowledgements
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.

Publisher
EAGE Publications

Conference/Event Name
81st EAGE Conference and Exhibition 2019

DOI
10.3997/2214-4609.201901222

Additional Links
http://www.earthdoc.org/publication/publicationdetails/?publication=97880

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