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dc.contributor.authorLiu, Qiancheng
dc.contributor.authorPeter, Daniel
dc.date.accessioned2019-07-29T08:55:25Z
dc.date.available2019-07-29T08:55:25Z
dc.date.issued2019-05-02
dc.identifier.citationLiu, Q., & Peter, D. (2019). Square-root variable metric based elastic full-waveform inversion—Part 2: uncertainty estimation. Geophysical Journal International, 218(2), 1100–1120. doi:10.1093/gji/ggz137
dc.identifier.doi10.1093/gji/ggz137
dc.identifier.urihttp://hdl.handle.net/10754/656218
dc.description.abstractIn our first paper (Part 1) about the square-root variable metric (SRVM) method we presented the basic theory and validation of the inverse algorithm applicable to large-scale seismic data inversions. In this second paper (Part 2) about the SRVM method, the objective is to estimate the resolution and uncertainty of the inverted resulting geophysical model. Bayesian inference allows estimating the posterior model distribution from its prior distribution and likelihood function. These distributions, when being linear and Gaussian, can be mathematically characterized by their covariance matrices. However, it is prohibitive to explicitly construct and store the covariance in large-scale practical problems. In Part 1, we applied the SRVM method to elastic full-waveform inversion in a matrix-free vector version. This new algorithm allows accessing the posterior covariance by reconstructing the inverseHessian with memory-Affordable vector series. The focus of this paper is on extracting quantitative and statistical information from the inverse Hessian for quality assessment of the inverted seismic model by FWI. To operate on the inverse Hessian more efficiently, we compute its eigenvalues and eigenvectors with randomized singular value decomposition. Furthermore, we collect point-spread functions from the Hessian in an efficient way. The posterior standard deviation quantitatively measures the uncertainties of the posterior model. 2-D Gaussian random samplers will help to visually compare both the prior and posterior distributions. We highlight our method on several numerical examples and demonstrate an uncertainty estimation analysis applicable to large-scale inversions.
dc.description.sponsorshipThe authors are grateful to editor Jean Virieux and reviewer Andreas Fichtner and an anonymous reviewer for improving the initial manuscript. The authors are grateful to Carl Tape for inspiring discussions and valuable inputs to improve the manuscript. 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.
dc.publisherOxford University Press (OUP)
dc.relation.urlhttps://academic.oup.com/gji/article/218/2/1100/5497300
dc.rightsThis is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectWaveform inversion
dc.subjectComputational seismology
dc.subjectSeismic tomography
dc.titleSquare-root variable metric based elastic full-waveform inversion-Part 2: Uncertainty estimation
dc.typeArticle
dc.contributor.departmentEarth Science and Engineering
dc.contributor.departmentEarth Science and Engineering Program
dc.contributor.departmentExtreme Computing Research Center
dc.contributor.departmentPhysical Science and Engineering (PSE) Division
dc.identifier.journalGeophysical Journal International
dc.eprint.versionPublisher's Version/PDF
kaust.personLiu, Qiancheng
kaust.personPeter, Daniel
kaust.grant.numberUAPN#2605-CRG4
refterms.dateFOA2019-07-29T08:56:27Z
kaust.acknowledged.supportUnitExtreme Computing Research Center
kaust.acknowledged.supportUnitInformation Technology
kaust.acknowledged.supportUnitOffice of Sponsored Research


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This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
Except where otherwise noted, this item's license is described as This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.