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Efficient Bayesian uncertainty estimation in linear finite fault inversion with positivity constraints by employing a log-normal prior

Benavente, Roberto; Dettmer, Jan; Cummins, Phil; Sambridge, Malcolm

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Obtaining slip distributions for earthquakes results in an ill-posed inverse problem. While this implies that only limited and uncertain information can be recovered from the data, inferences are typically made based only on a single regularized model. Here, we develop an inversion approach that can quantify uncertainties in a Bayesian probabilistic framework for the finite fault inversion (FFI) problem. The approach is suitably efficient for rapid source characterization and includes...[Show more]

dc.contributor.authorBenavente, Roberto
dc.contributor.authorDettmer, Jan
dc.contributor.authorCummins, Phil
dc.contributor.authorSambridge, Malcolm
dc.date.accessioned2020-02-17T03:22:49Z
dc.date.available2020-02-17T03:22:49Z
dc.identifier.issn0956-540X
dc.identifier.urihttp://hdl.handle.net/1885/201719
dc.description.abstractObtaining slip distributions for earthquakes results in an ill-posed inverse problem. While this implies that only limited and uncertain information can be recovered from the data, inferences are typically made based only on a single regularized model. Here, we develop an inversion approach that can quantify uncertainties in a Bayesian probabilistic framework for the finite fault inversion (FFI) problem. The approach is suitably efficient for rapid source characterization and includes positivity constraints for model parameters, a common practice in FFI, via coordinate transformation to logarithmic space. The resulting inverse problem is nonlinear and the most probable solution can be obtained by iterative linearization. In addition, model uncertainties are quantified by approximating the posterior probability distribution by a Gaussian distribution in logarithmic space. This procedure is straightforward since an analytic expression for the Hessian of the objective function is obtained. In addition to positivity, we apply smoothness regularization to the model in logarithmic space. Simulations based on surface wave data show that smoothing in logarithmic space penalizes abrupt slip changes less than smoothing in linear space. Even so, the main slip features of models that are smooth in linear space are recovered well with logarithmic smoothing. Our synthetic experiments also show that, for the data set we consider, uncertainty is low at the shallow portion of the fault and increases with depth. In addition, a simulation with a large station azimuthal gap of 180° significantly increases the slip uncertainties. Further, the marginal posterior probabilities obtained from our approximate method are compared with numerical Markov Chain Monte Carlo sampling. We conclude that the Gaussian approximation is reasonable and meaningful inferences can be obtained from it. Finally, we apply the new approach to observed surface wave records from the great Illapel earthquake (Chile, 2015, Mw = 8.3). The location and amplitude of our inferred peak slip is consistent with other published solutions but the spatial slip distribution is more compact, likely because of the logarithmic regularization. We also find a minor slip patch downdip, mainly in an oblique direction, which is poorly resolved compared to the main slip patch and may be an artefact. We conclude that quantifying uncertainties of finite slip models is crucial for their meaningful interpretation, and therefore rapid uncertainty quantification can be critical if such models are to be used for emergency response.
dc.format.mimetypeapplication/pdf
dc.language.isoen_AU
dc.publisherOxford University Press
dc.rights© The Author(s) 2019. Published by Oxford University Press on behalf of The Royal Astronomical Society.
dc.sourceGeophysical Journal International
dc.titleEfficient Bayesian uncertainty estimation in linear finite fault inversion with positivity constraints by employing a log-normal prior
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume217
dc.date.issued2019
local.identifier.absfor040407 - Seismology and Seismic Exploration
local.identifier.ariespublicationu3102795xPUB2049
local.publisher.urlhttp://www.oxfordjournals.org/
local.type.statusPublished Version
local.contributor.affiliationBenavente, Roberto, National Research Center for Integrated Natural Disaster Management (CIGIDEN)
local.contributor.affiliationDettmer, Jan, University of Calgary
local.contributor.affiliationCummins, Phil, College of Science, ANU
local.contributor.affiliationSambridge, Malcolm, College of Science, ANU
local.bibliographicCitation.issue1
local.bibliographicCitation.startpage469
local.bibliographicCitation.lastpage484
local.identifier.doi10.1093/gji/ggz044
local.identifier.absseo970104 - Expanding Knowledge in the Earth Sciences
dc.date.updated2019-11-25T07:33:22Z
local.identifier.thomsonID4.65603E+11
dcterms.accessRightsOpen Access
dc.provenancehttp://sherpa.ac.uk/romeo/issn/0956-540X/..."author can archive publisher's version/PDF" from SHERPA/RoMEO site (as at 17/02/2020). This article has been accepted for publication in Geophysical Journal International ©: The Author(s) 2019. Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.
CollectionsANU Research Publications

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