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dc.contributor.authorLong, Quan
dc.contributor.authorMotamed, Mohammad
dc.contributor.authorTempone, Raul
dc.date.accessioned2015-08-03T12:35:45Z
dc.date.available2015-08-03T12:35:45Z
dc.date.issued2015-07
dc.identifier.issn00457825
dc.identifier.doi10.1016/j.cma.2015.03.021
dc.identifier.urihttp://hdl.handle.net/10754/564190
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.
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.
dc.publisherElsevier BV
dc.relation.urlhttp://arxiv.org/abs/arXiv:1502.07873v1
dc.subjectBayesian experimental design
dc.subjectInformation gain
dc.subjectLaplace approximation
dc.subjectMonte Carlo sampling
dc.subjectSeismic source inversion
dc.subjectSparse quadrature
dc.titleFast Bayesian optimal experimental design for seismic source inversion
dc.typeArticle
dc.contributor.departmentCenter for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentStochastic Numerics Research Group
dc.identifier.journalComputer Methods in Applied Mechanics and Engineering
dc.contributor.institutionDepartment of Mathematics and Statistics, The University of New Mexico, United States
dc.contributor.institutionInstitute for Computational Engineering and Sciences, The University of Texas at Austin, United States
dc.identifier.arxividarXiv:1502.07873
kaust.personLong, Quan
kaust.personTempone, Raul
dc.versionv1
refterms.dateFOA2017-07-01T00:00:00Z
dc.date.posted2015-02-27


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