Adaptive multiscale MCMC algorithm for uncertainty quantification in seismic parameter estimation

Handle URI:
http://hdl.handle.net/10754/593349
Title:
Adaptive multiscale MCMC algorithm for uncertainty quantification in seismic parameter estimation
Authors:
Tan, Xiaosi; Gibson, Richard L.; Leung, Wing Tat; Efendiev, Yalchin R. ( 0000-0001-9626-303X )
Abstract:
Formulating an inverse problem in a Bayesian framework has several major advantages (Sen and Stoffa, 1996). It allows finding multiple solutions subject to flexible a priori information and performing uncertainty quantification in the inverse problem. In this paper, we consider Bayesian inversion for the parameter estimation in seismic wave propagation. The Bayes' theorem allows writing the posterior distribution via the likelihood function and the prior distribution where the latter represents our prior knowledge about physical properties. One of the popular algorithms for sampling this posterior distribution is Markov chain Monte Carlo (MCMC), which involves making proposals and calculating their acceptance probabilities. However, for large-scale problems, MCMC is prohibitevely expensive as it requires many forward runs. In this paper, we propose a multilevel MCMC algorithm that employs multilevel forward simulations. Multilevel forward simulations are derived using Generalized Multiscale Finite Element Methods that we have proposed earlier (Efendiev et al., 2013a; Chung et al., 2013). Our overall Bayesian inversion approach provides a substantial speed-up both in the process of the sampling via preconditioning using approximate posteriors and the computation of the forward problems for different proposals by using the adaptive nature of multiscale methods. These aspects of the method are discussed n the paper. This paper is motivated by earlier work of M. Sen and his collaborators (Hong and Sen, 2007; Hong, 2008) who proposed the development of efficient MCMC techniques for seismic applications. In the paper, we present some preliminary numerical results.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Xiaosi Tan*, Richard L. Gibson Jr., Wing Tat Leung, and Yalchin Efendiev (2014) Adaptive multiscale MCMC algorithm for uncertainty quantification in seismic parameter estimation. SEG Technical Program Expanded Abstracts 2014: pp. 4665-4669. doi: 10.1190/segam2014-1256.1
Publisher:
Society of Exploration Geophysicists
Journal:
SEG Technical Program Expanded Abstracts 2014
Issue Date:
5-Aug-2014
DOI:
10.1190/segam2014-1256.1
Type:
Article
Additional Links:
http://library.seg.org/doi/abs/10.1190/segam2014-1256.1
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorTan, Xiaosien
dc.contributor.authorGibson, Richard L.en
dc.contributor.authorLeung, Wing Taten
dc.contributor.authorEfendiev, Yalchin R.en
dc.date.accessioned2016-01-13T09:57:43Zen
dc.date.available2016-01-13T09:57:43Zen
dc.date.issued2014-08-05en
dc.identifier.citationXiaosi Tan*, Richard L. Gibson Jr., Wing Tat Leung, and Yalchin Efendiev (2014) Adaptive multiscale MCMC algorithm for uncertainty quantification in seismic parameter estimation. SEG Technical Program Expanded Abstracts 2014: pp. 4665-4669. doi: 10.1190/segam2014-1256.1en
dc.identifier.doi10.1190/segam2014-1256.1en
dc.identifier.urihttp://hdl.handle.net/10754/593349en
dc.description.abstractFormulating an inverse problem in a Bayesian framework has several major advantages (Sen and Stoffa, 1996). It allows finding multiple solutions subject to flexible a priori information and performing uncertainty quantification in the inverse problem. In this paper, we consider Bayesian inversion for the parameter estimation in seismic wave propagation. The Bayes' theorem allows writing the posterior distribution via the likelihood function and the prior distribution where the latter represents our prior knowledge about physical properties. One of the popular algorithms for sampling this posterior distribution is Markov chain Monte Carlo (MCMC), which involves making proposals and calculating their acceptance probabilities. However, for large-scale problems, MCMC is prohibitevely expensive as it requires many forward runs. In this paper, we propose a multilevel MCMC algorithm that employs multilevel forward simulations. Multilevel forward simulations are derived using Generalized Multiscale Finite Element Methods that we have proposed earlier (Efendiev et al., 2013a; Chung et al., 2013). Our overall Bayesian inversion approach provides a substantial speed-up both in the process of the sampling via preconditioning using approximate posteriors and the computation of the forward problems for different proposals by using the adaptive nature of multiscale methods. These aspects of the method are discussed n the paper. This paper is motivated by earlier work of M. Sen and his collaborators (Hong and Sen, 2007; Hong, 2008) who proposed the development of efficient MCMC techniques for seismic applications. In the paper, we present some preliminary numerical results.en
dc.language.isoenen
dc.publisherSociety of Exploration Geophysicistsen
dc.relation.urlhttp://library.seg.org/doi/abs/10.1190/segam2014-1256.1en
dc.rightsArchived with thanks to SEG Technical Program Expanded Abstracts 2014en
dc.subjectfinite elementen
dc.subjectinversionen
dc.subjectseismicen
dc.titleAdaptive multiscale MCMC algorithm for uncertainty quantification in seismic parameter estimationen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalSEG Technical Program Expanded Abstracts 2014en
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionTexas A & M Universityen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
kaust.authorEfendiev, Yalchin R.en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.