Integral Modelling of Propagation of Incident Waves in a Laterally Varying Medium : an Exploration in the Frequency Domain

ABSTRACT: In this work we present a formalism that intends to solve the problem of modeling wave propagation in the context of seismic inversion. The formalism is based on the linear perturbation theory of Cauchy’s equations. Based on the foregoing, we derived an equivalent Helmholtz equation for th...

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Autores:
Muñoz Cuartas, Juan Carlos
Atehortúa Jiménez, Anyeres Neider
Avendaño Pérez, Sheryl Karina
Tipo de recurso:
Article of investigation
Fecha de publicación:
2018
Institución:
Universidad de Antioquia
Repositorio:
Repositorio UdeA
Idioma:
eng
OAI Identifier:
oai:bibliotecadigital.udea.edu.co:10495/30950
Acceso en línea:
https://hdl.handle.net/10495/30950
Palabra clave:
Perturbación (matemáticas)
Perturbation (mathematics)
Propagación de ondas
Wave propagation
Análisis funcional
Functional analysis
Series de Neumann
Neumann series
Rights
openAccess
License
http://creativecommons.org/licenses/by-nc-sa/2.5/co/
id UDEA2_163e2af384619972687c2452d4ff497f
oai_identifier_str oai:bibliotecadigital.udea.edu.co:10495/30950
network_acronym_str UDEA2
network_name_str Repositorio UdeA
repository_id_str
dc.title.spa.fl_str_mv Integral Modelling of Propagation of Incident Waves in a Laterally Varying Medium : an Exploration in the Frequency Domain
dc.title.alternative.spa.fl_str_mv Modelado integral de propagación de ondas incidentes en medios con gradientes laterales : una exploración en el dominio de la frecuencia
title Integral Modelling of Propagation of Incident Waves in a Laterally Varying Medium : an Exploration in the Frequency Domain
spellingShingle Integral Modelling of Propagation of Incident Waves in a Laterally Varying Medium : an Exploration in the Frequency Domain
Perturbación (matemáticas)
Perturbation (mathematics)
Propagación de ondas
Wave propagation
Análisis funcional
Functional analysis
Series de Neumann
Neumann series
title_short Integral Modelling of Propagation of Incident Waves in a Laterally Varying Medium : an Exploration in the Frequency Domain
title_full Integral Modelling of Propagation of Incident Waves in a Laterally Varying Medium : an Exploration in the Frequency Domain
title_fullStr Integral Modelling of Propagation of Incident Waves in a Laterally Varying Medium : an Exploration in the Frequency Domain
title_full_unstemmed Integral Modelling of Propagation of Incident Waves in a Laterally Varying Medium : an Exploration in the Frequency Domain
title_sort Integral Modelling of Propagation of Incident Waves in a Laterally Varying Medium : an Exploration in the Frequency Domain
dc.creator.fl_str_mv Muñoz Cuartas, Juan Carlos
Atehortúa Jiménez, Anyeres Neider
Avendaño Pérez, Sheryl Karina
dc.contributor.author.none.fl_str_mv Muñoz Cuartas, Juan Carlos
Atehortúa Jiménez, Anyeres Neider
Avendaño Pérez, Sheryl Karina
dc.subject.lemb.none.fl_str_mv Perturbación (matemáticas)
Perturbation (mathematics)
Propagación de ondas
Wave propagation
Análisis funcional
Functional analysis
topic Perturbación (matemáticas)
Perturbation (mathematics)
Propagación de ondas
Wave propagation
Análisis funcional
Functional analysis
Series de Neumann
Neumann series
dc.subject.proposal.spa.fl_str_mv Series de Neumann
Neumann series
description ABSTRACT: In this work we present a formalism that intends to solve the problem of modeling wave propagation in the context of seismic inversion. The formalism is based on the linear perturbation theory of Cauchy’s equations. Based on the foregoing, we derived an equivalent Helmholtz equation for the propagation of waves in a variable density media. Then, we defined a solution, by using the boundary conditions on a half plane. This solution is of an integral nature and resembles expansion in a Neumann series. We implemented the solution of the first terms in the series, considering only the incident wavefield and neglecting the reflections. We show how this approximation works in different media that include lateral in homogeneities in the velocity. The method presented hereunder is intended as a first step in the modelling process for the full wavefield, to be used in seismic inversion methods, Full Waveform Inversion, for example.
publishDate 2018
dc.date.issued.none.fl_str_mv 2018
dc.date.accessioned.none.fl_str_mv 2022-09-28T02:53:44Z
dc.date.available.none.fl_str_mv 2022-09-28T02:53:44Z
dc.type.spa.fl_str_mv info:eu-repo/semantics/article
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dc.type.hasversion.spa.fl_str_mv info:eu-repo/semantics/publishedVersion
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dc.type.local.spa.fl_str_mv Artículo de investigación
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status_str publishedVersion
dc.identifier.citation.spa.fl_str_mv Atehortúa-Jiménez, Anyeres N, Muñoz-Cuartas, J. C, & Avendaño, Sheryl. (2018). Integral Modelling of Propagation of Incident Waves in a Laterally Varying Medium: an Exploration in the Frequency Domain. CT&F - Ciencia, Tecnología y Futuro , 8 (2), 33-45. https://doi.org/10.29047/01225383.79
dc.identifier.issn.none.fl_str_mv 0122-5383
dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/10495/30950
dc.identifier.doi.none.fl_str_mv 10.29047/01225383.79
dc.identifier.eissn.none.fl_str_mv 2382-4581
identifier_str_mv Atehortúa-Jiménez, Anyeres N, Muñoz-Cuartas, J. C, & Avendaño, Sheryl. (2018). Integral Modelling of Propagation of Incident Waves in a Laterally Varying Medium: an Exploration in the Frequency Domain. CT&F - Ciencia, Tecnología y Futuro , 8 (2), 33-45. https://doi.org/10.29047/01225383.79
0122-5383
10.29047/01225383.79
2382-4581
url https://hdl.handle.net/10495/30950
dc.language.iso.spa.fl_str_mv eng
language eng
dc.relation.ispartofjournalabbrev.spa.fl_str_mv CT&F - Ciencia, Tecnología y Futuro
dc.rights.spa.fl_str_mv info:eu-repo/semantics/openAccess
dc.rights.uri.*.fl_str_mv http://creativecommons.org/licenses/by-nc-sa/2.5/co/
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dc.format.extent.spa.fl_str_mv 13
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dc.publisher.spa.fl_str_mv ECOPETROL - Instituto Colombiano del Petróleo
dc.publisher.group.spa.fl_str_mv Grupo de Física y Astrofísica Computacional (FACOM)
dc.publisher.place.spa.fl_str_mv Bucaramanga, Colombia
institution Universidad de Antioquia
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spelling Muñoz Cuartas, Juan CarlosAtehortúa Jiménez, Anyeres NeiderAvendaño Pérez, Sheryl Karina2022-09-28T02:53:44Z2022-09-28T02:53:44Z2018Atehortúa-Jiménez, Anyeres N, Muñoz-Cuartas, J. C, & Avendaño, Sheryl. (2018). Integral Modelling of Propagation of Incident Waves in a Laterally Varying Medium: an Exploration in the Frequency Domain. CT&F - Ciencia, Tecnología y Futuro , 8 (2), 33-45. https://doi.org/10.29047/01225383.790122-5383https://hdl.handle.net/10495/3095010.29047/01225383.792382-4581ABSTRACT: In this work we present a formalism that intends to solve the problem of modeling wave propagation in the context of seismic inversion. The formalism is based on the linear perturbation theory of Cauchy’s equations. Based on the foregoing, we derived an equivalent Helmholtz equation for the propagation of waves in a variable density media. Then, we defined a solution, by using the boundary conditions on a half plane. This solution is of an integral nature and resembles expansion in a Neumann series. We implemented the solution of the first terms in the series, considering only the incident wavefield and neglecting the reflections. We show how this approximation works in different media that include lateral in homogeneities in the velocity. The method presented hereunder is intended as a first step in the modelling process for the full wavefield, to be used in seismic inversion methods, Full Waveform Inversion, for example.RESUMEN: En esta investigación presentamos un formalismo que pretende contribuir al modelado de la propagación de ondas en el contexto de la inversión sísmica. El formalismo está basado en la teoría de perturbaciones lineales a las ecuaciones de Cauchy. Basados en este procedimiento derivamos una versión de la ecuación de Helmholtz que describe la propagación de ondas en un medio con densidad variable. Luego hallamos una solución en la cual se emplean condiciones de frontera de un plano semi infinito. Tal solución es expresada en forma de integral y recuerda la expansión en series de Neumann. Nosotros implementamos la solución del primer término de la serie, que considera únicamente el campo de onda incidente, sin considerar las reflexiones de onda. Mostramos que esta aproximación funciona en diferentes medios que incluyen variaciones in-homogeneidades laterales en el perfil de velocidad. Este método es presentado como un primer paso en el proceso de modelado del campo de onda completo el cual puede ser usado en métodos de inversión sísmica tales como "Inversión de onda completa", Full Waveform Inversion, (FWI).COL003826213application/pdfengECOPETROL - Instituto Colombiano del PetróleoGrupo de Física y Astrofísica Computacional (FACOM)Bucaramanga, Colombiainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_2df8fbb1https://purl.org/redcol/resource_type/ARTArtículo de investigaciónhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/2.5/co/http://purl.org/coar/access_right/c_abf2https://creativecommons.org/licenses/by-nc-sa/4.0/Integral Modelling of Propagation of Incident Waves in a Laterally Varying Medium : an Exploration in the Frequency DomainModelado integral de propagación de ondas incidentes en medios con gradientes laterales : una exploración en el dominio de la frecuenciaPerturbación (matemáticas)Perturbation (mathematics)Propagación de ondasWave propagationAnálisis funcionalFunctional analysisSeries de NeumannNeumann seriesCT&F - Ciencia, Tecnología y FuturoCT&F - Ciencia, Tecnología y Futuro334582ORIGINALMuñozJC_2018_IntegralModellingPropagation.pdfMuñozJC_2018_IntegralModellingPropagation.pdfArtículo de investigaciónapplication/pdf5342087https://bibliotecadigital.udea.edu.co/bitstream/10495/30950/1/Mun%cc%83ozJC_2018_IntegralModellingPropagation.pdf5603a1b1f18522fc905a7130254dc978MD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-81051https://bibliotecadigital.udea.edu.co/bitstream/10495/30950/2/license_rdfe2060682c9c70d4d30c83c51448f4eedMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://bibliotecadigital.udea.edu.co/bitstream/10495/30950/3/license.txt8a4605be74aa9ea9d79846c1fba20a33MD5310495/30950oai:bibliotecadigital.udea.edu.co:10495/309502022-09-27 21:53:45.081Repositorio Institucional Universidad de Antioquiaandres.perez@udea.edu.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