Proper generalized decomposition solution of the parameterized Helmholtz problem: application to inverse geophysical problems

This is the peer reviewed version of the following article: [Signorini, M., Zlotnik, S., and Díez, P. (2017) Proper generalized decomposition solution of the parameterized Helmholtz problem: application to inverse geophysical problems. Int. J. Numer. Meth. Engng, 109: 1085–1102. doi: 10.1002/nme.531...

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Authors: Signorini, Marianna, Zlotnik, Sergio|||0000-0001-9674-8950, Díez, Pedro|||0000-0001-6464-6407
Format: article
Publication Date:2017
Country:España
Institution:Universitat Politècnica de Catalunya (UPC)
Repository:UPCommons. Portal del coneixement obert de la UPC
Language:English
OAI Identifier:oai:upcommons.upc.edu:2117/99875
Online Access:https://hdl.handle.net/2117/99875
https://dx.doi.org/10.1002/nme.5313
Access Level:Open access
Keyword:Seismology--Mathematics
parameterized Helmholtz problem
proper generalized decomposition (PGD)
parameter identification
inverse problems
seismic analysis
Sismologia -- Matemàtica
Àrees temàtiques de la UPC::Enginyeria civil::Geotècnia::Sismologia
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oai_identifier_str oai:upcommons.upc.edu:2117/99875
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spelling Proper generalized decomposition solution of the parameterized Helmholtz problem: application to inverse geophysical problemsSignorini, MariannaZlotnik, Sergio|||0000-0001-9674-8950Díez, Pedro|||0000-0001-6464-6407Seismology--Mathematicsparameterized Helmholtz problemproper generalized decomposition (PGD)parameter identificationinverse problemsseismic analysisSismologia -- MatemàticaÀrees temàtiques de la UPC::Enginyeria civil::Geotècnia::SismologiaThis is the peer reviewed version of the following article: [Signorini, M., Zlotnik, S., and Díez, P. (2017) Proper generalized decomposition solution of the parameterized Helmholtz problem: application to inverse geophysical problems. Int. J. Numer. Meth. Engng, 109: 1085–1102. doi: 10.1002/nme.5313], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.5313/full. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.The identification of the geological structure from seismic data is formulated as an inverse problem. The properties and the shape of the rock formations in the subsoil are described by material and geometric parameters, which are taken as input data for a predictive model. Here, the model is based on the Helmholtz equation, describing the acoustic response of the system for a given wave length. Thus, the inverse problem consists in identifying the values of these parameters such that the output of the model agrees the best with observations. This optimization algorithm requires multiple queries to the model with different values of the parameters. Reduced order models are especially well suited to significantly reduce the computational overhead of the multiple evaluations of the model. In particular, the proper generalized decomposition produces a solution explicitly stating the parametric dependence, where the parameters play the same role as the physical coordinates. A proper generalized decomposition solver is devised to inexpensively explore the parametric space along the iterative process. This exploration of the parametric space is in fact seen as a post-process of the generalized solution. The approach adopted demonstrates its viability when tested in two illustrative examples.Peer Reviewed20172017-02-0120172017-01-23journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/99875https://dx.doi.org/10.1002/nme.5313reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/998752026-05-27T15:37:01Z
dc.title.none.fl_str_mv Proper generalized decomposition solution of the parameterized Helmholtz problem: application to inverse geophysical problems
title Proper generalized decomposition solution of the parameterized Helmholtz problem: application to inverse geophysical problems
spellingShingle Proper generalized decomposition solution of the parameterized Helmholtz problem: application to inverse geophysical problems
Signorini, Marianna
Seismology--Mathematics
parameterized Helmholtz problem
proper generalized decomposition (PGD)
parameter identification
inverse problems
seismic analysis
Sismologia -- Matemàtica
Àrees temàtiques de la UPC::Enginyeria civil::Geotècnia::Sismologia
title_short Proper generalized decomposition solution of the parameterized Helmholtz problem: application to inverse geophysical problems
title_full Proper generalized decomposition solution of the parameterized Helmholtz problem: application to inverse geophysical problems
title_fullStr Proper generalized decomposition solution of the parameterized Helmholtz problem: application to inverse geophysical problems
title_full_unstemmed Proper generalized decomposition solution of the parameterized Helmholtz problem: application to inverse geophysical problems
title_sort Proper generalized decomposition solution of the parameterized Helmholtz problem: application to inverse geophysical problems
dc.creator.none.fl_str_mv Signorini, Marianna
Zlotnik, Sergio|||0000-0001-9674-8950
Díez, Pedro|||0000-0001-6464-6407
author Signorini, Marianna
author_facet Signorini, Marianna
Zlotnik, Sergio|||0000-0001-9674-8950
Díez, Pedro|||0000-0001-6464-6407
author_role author
author2 Zlotnik, Sergio|||0000-0001-9674-8950
Díez, Pedro|||0000-0001-6464-6407
author2_role author
author
dc.subject.none.fl_str_mv Seismology--Mathematics
parameterized Helmholtz problem
proper generalized decomposition (PGD)
parameter identification
inverse problems
seismic analysis
Sismologia -- Matemàtica
Àrees temàtiques de la UPC::Enginyeria civil::Geotècnia::Sismologia
topic Seismology--Mathematics
parameterized Helmholtz problem
proper generalized decomposition (PGD)
parameter identification
inverse problems
seismic analysis
Sismologia -- Matemàtica
Àrees temàtiques de la UPC::Enginyeria civil::Geotècnia::Sismologia
description This is the peer reviewed version of the following article: [Signorini, M., Zlotnik, S., and Díez, P. (2017) Proper generalized decomposition solution of the parameterized Helmholtz problem: application to inverse geophysical problems. Int. J. Numer. Meth. Engng, 109: 1085–1102. doi: 10.1002/nme.5313], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.5313/full. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
publishDate 2017
dc.date.none.fl_str_mv 2017
2017-02-01
2017
2017-01-23
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/99875
https://dx.doi.org/10.1002/nme.5313
url https://hdl.handle.net/2117/99875
https://dx.doi.org/10.1002/nme.5313
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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