dc.contributor.advisor Omre, Karl Henning nb_NO dc.contributor.author Lindberg, David nb_NO dc.date.accessioned 2014-12-19T13:58:39Z dc.date.available 2014-12-19T13:58:39Z dc.date.created 2010-09-30 nb_NO dc.date.issued 2010 nb_NO dc.identifier 354281 nb_NO dc.identifier ntnudaim:5735 nb_NO dc.identifier.uri http://hdl.handle.net/11250/258753 dc.description.abstract In this thesis, we solve the seismic inverse problem in a Bayesian setting and perform the associated model parameter estimation. The subsurface rock layers are represented by categorical variables, which depends on some response variables. The observations recorded appear as a convolution of these response variables. We thus assess the categorical variables' posterior distribution based on a prior distribution and a convolved likelihood distribution. Assuming that the prior model follows a Markov chain, the full model becomes a hidden Markov model. In the associated Posterior-Prior deconvolution algorithm, we approximate the convolved likelihood in order to use the recursive forward-backward algorithm. The prior and likelihood distributions are parameter dependent, and two parameter estimation approaches are discussed. Both estimation methods make use of the marginal likelihood distribution, which can be computed during the forward-backward algorithm.In two thorough test studies, we perform parameter estimation in the likelihood. Approximate posterior models, based on the respective parameter estimates, are computed by Posterior-Prior deconvolution algorithms for different orders. The signal-to-noise ratio, a ratio between the observation mean and variance, is found to be of importance. The results are generally more reliable for large values of this ratio. A more realistic seismic example is also introduced, with a more complex model description. The posterior model approximations are here more poor, due to under-estimation of the noise parameter. nb_NO dc.language eng nb_NO dc.publisher Institutt for matematiske fag nb_NO dc.subject ntnudaim:5735 no_NO dc.subject SIF3 fysikk og matematikk no_NO dc.subject Industriell matematikk no_NO dc.title Parameter estimation in convolved categorical models nb_NO dc.type Master thesis nb_NO dc.source.pagenumber 106 nb_NO dc.contributor.department Norges teknisk-naturvitenskapelige universitet, Fakultet for informasjonsteknologi, matematikk og elektroteknikk, Institutt for matematiske fag nb_NO
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