Fast Bayesian optimal experimental design for seismic source inversion

Handle URI:
http://hdl.handle.net/10754/564190
Title:
Fast Bayesian optimal experimental design for seismic source inversion
Authors:
Long, Quan ( 0000-0002-0329-9437 ) ; Motamed, Mohammad; Tempone, Raul ( 0000-0003-1967-4446 )
Abstract:
We develop a fast method for optimally designing experiments in the context of statistical seismic source inversion. In particular, we efficiently compute the optimal number and locations of the receivers or seismographs. The seismic source is modeled by a point moment tensor multiplied by a time-dependent function. The parameters include the source location, moment tensor components, and start time and frequency in the time function. The forward problem is modeled by elastodynamic wave equations. We show that the Hessian of the cost functional, which is usually defined as the square of the weighted L2 norm of the difference between the experimental data and the simulated data, is proportional to the measurement time and the number of receivers. Consequently, the posterior distribution of the parameters, in a Bayesian setting, concentrates around the "true" parameters, and we can employ Laplace approximation and speed up the estimation of the expected Kullback-Leibler divergence (expected information gain), the optimality criterion in the experimental design procedure. Since the source parameters span several magnitudes, we use a scaling matrix for efficient control of the condition number of the original Hessian matrix. We use a second-order accurate finite difference method to compute the Hessian matrix and either sparse quadrature or Monte Carlo sampling to carry out numerical integration. We demonstrate the efficiency, accuracy, and applicability of our method on a two-dimensional seismic source inversion problem. © 2015 Elsevier B.V.
KAUST Department:
Center for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program; Stochastic Numerics Research Group
Publisher:
Elsevier BV
Journal:
Computer Methods in Applied Mechanics and Engineering
Issue Date:
Jul-2015
DOI:
10.1016/j.cma.2015.03.021
ARXIV:
arXiv:1502.07873
Type:
Article
ISSN:
00457825
Sponsors:
The authors are grateful for support from the Academic Excellency Alliance UT Austin-KAUST project-Uncertainty quantification for predictive modeling of the dissolution of porous and fractured media. Quan Long and Raul Tempone are members of the KAUST SRI Center for Uncertainty Quantification in Computational Science and Engineering.
Additional Links:
http://arxiv.org/abs/arXiv:1502.07873v1
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorLong, Quanen
dc.contributor.authorMotamed, Mohammaden
dc.contributor.authorTempone, Raulen
dc.date.accessioned2015-08-03T12:35:45Zen
dc.date.available2015-08-03T12:35:45Zen
dc.date.issued2015-07en
dc.identifier.issn00457825en
dc.identifier.doi10.1016/j.cma.2015.03.021en
dc.identifier.urihttp://hdl.handle.net/10754/564190en
dc.description.abstractWe develop a fast method for optimally designing experiments in the context of statistical seismic source inversion. In particular, we efficiently compute the optimal number and locations of the receivers or seismographs. The seismic source is modeled by a point moment tensor multiplied by a time-dependent function. The parameters include the source location, moment tensor components, and start time and frequency in the time function. The forward problem is modeled by elastodynamic wave equations. We show that the Hessian of the cost functional, which is usually defined as the square of the weighted L2 norm of the difference between the experimental data and the simulated data, is proportional to the measurement time and the number of receivers. Consequently, the posterior distribution of the parameters, in a Bayesian setting, concentrates around the "true" parameters, and we can employ Laplace approximation and speed up the estimation of the expected Kullback-Leibler divergence (expected information gain), the optimality criterion in the experimental design procedure. Since the source parameters span several magnitudes, we use a scaling matrix for efficient control of the condition number of the original Hessian matrix. We use a second-order accurate finite difference method to compute the Hessian matrix and either sparse quadrature or Monte Carlo sampling to carry out numerical integration. We demonstrate the efficiency, accuracy, and applicability of our method on a two-dimensional seismic source inversion problem. © 2015 Elsevier B.V.en
dc.description.sponsorshipThe authors are grateful for support from the Academic Excellency Alliance UT Austin-KAUST project-Uncertainty quantification for predictive modeling of the dissolution of porous and fractured media. Quan Long and Raul Tempone are members of the KAUST SRI Center for Uncertainty Quantification in Computational Science and Engineering.en
dc.publisherElsevier BVen
dc.relation.urlhttp://arxiv.org/abs/arXiv:1502.07873v1en
dc.subjectBayesian experimental designen
dc.subjectInformation gainen
dc.subjectLaplace approximationen
dc.subjectMonte Carlo samplingen
dc.subjectSeismic source inversionen
dc.subjectSparse quadratureen
dc.titleFast Bayesian optimal experimental design for seismic source inversionen
dc.typeArticleen
dc.contributor.departmentCenter for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)en
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentStochastic Numerics Research Groupen
dc.identifier.journalComputer Methods in Applied Mechanics and Engineeringen
dc.contributor.institutionDepartment of Mathematics and Statistics, The University of New Mexico, United Statesen
dc.contributor.institutionInstitute for Computational Engineering and Sciences, The University of Texas at Austin, United Statesen
dc.identifier.arxividarXiv:1502.07873en
kaust.authorLong, Quanen
kaust.authorTempone, Raulen
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