Some limitations for the applicability of the ray method in elastodynamics
Autor(a) principal: | |
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Data de Publicação: | 1997 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFBA |
Texto Completo: | http://www.repositorio.ufba.br/ri/handle/ri/3373 |
Resumo: | The ray method in the frequency domain describes the asymptotic behavior of the wave field for large frequencies which is not, in general, uniform with respect to the distance between the source and the point of observation. This implies that one can face situations in which the results obtained by the ray method may not be reliable for large distances from the source, if the dominant frequency is not high enough. In this paper we present two examples of such a type of problem for rather simple elastodynamic problems: a homogeneous medium; and a constant gradient velocity medium without interfaces. For both cases, the sources are assumed to be represented by two successive terms of the ray series, and therefore there are no point sources problems in our study. To this end we employ the following criterion of validity of the ray method: the absolute value of the ratio of the second term of the ray series to the first one must be less than unity. This criterion turns out to be sensitive to the radius of curvature of the initial wave front and to the initial distribution of the amplitude (or energy) along it. In the worst case of an initially planar wave front with nonuniform distribution of the amplitude, the second term of the ray series increases very fast. This gives rise to strong limitations to the use of the ray method with respect to distance if the frequency is fixed, or with respect to frequency for large distances. The depolarization phenomenon in both cases is discussed as well. |
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Popov, Mikhail M.Oliveira, S.Popov, Mikhail M.Oliveira, S.2011-10-18T12:04:58Z2011-10-18T12:04:58Z19970102-261Xhttp://www.repositorio.ufba.br/ri/handle/ri/3373v.15, n.3The ray method in the frequency domain describes the asymptotic behavior of the wave field for large frequencies which is not, in general, uniform with respect to the distance between the source and the point of observation. This implies that one can face situations in which the results obtained by the ray method may not be reliable for large distances from the source, if the dominant frequency is not high enough. In this paper we present two examples of such a type of problem for rather simple elastodynamic problems: a homogeneous medium; and a constant gradient velocity medium without interfaces. For both cases, the sources are assumed to be represented by two successive terms of the ray series, and therefore there are no point sources problems in our study. To this end we employ the following criterion of validity of the ray method: the absolute value of the ratio of the second term of the ray series to the first one must be less than unity. This criterion turns out to be sensitive to the radius of curvature of the initial wave front and to the initial distribution of the amplitude (or energy) along it. In the worst case of an initially planar wave front with nonuniform distribution of the amplitude, the second term of the ray series increases very fast. This gives rise to strong limitations to the use of the ray method with respect to distance if the frequency is fixed, or with respect to frequency for large distances. The depolarization phenomenon in both cases is discussed as well.Submitted by Santiago Fabio (fabio.ssantiago@hotmail.com) on 2011-10-18T12:04:58Z No. of bitstreams: 1 fabio 201212.pdf: 472509 bytes, checksum: 71f17130399933c55ffbdd5f5d7d4bb5 (MD5)Made available in DSpace on 2011-10-18T12:04:58Z (GMT). No. of bitstreams: 1 fabio 201212.pdf: 472509 bytes, checksum: 71f17130399933c55ffbdd5f5d7d4bb5 (MD5) Previous issue date: 1997São PauloRevista Brasileira de GeofísicaRay methodElastodynamicsValidity of asymptoticsMétodo do raioElastodinâmicaValidade da aproximação assintóticaSome limitations for the applicability of the ray method in elastodynamicsRevista Brasileira de Geofísicainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleengreponame:Repositório Institucional da UFBAinstname:Universidade Federal da Bahia (UFBA)instacron:UFBAinfo:eu-repo/semantics/openAccessORIGINALfabio 201212.pdffabio 201212.pdfapplication/pdf472509https://repositorio.ufba.br/bitstream/ri/3373/1/fabio%20201212.pdf71f17130399933c55ffbdd5f5d7d4bb5MD51LICENSElicense.txtlicense.txttext/plain1906https://repositorio.ufba.br/bitstream/ri/3373/2/license.txt9e83543cb7f824d3fe20bef42d83aa99MD52TEXTfabio 201212.pdf.txtfabio 201212.pdf.txtExtracted texttext/plain41912https://repositorio.ufba.br/bitstream/ri/3373/3/fabio%20201212.pdf.txtbeeaa51d9da8c6e2b4b5c22e9d0ae7fbMD53ri/33732022-07-05 14:03:29.428oai:repositorio.ufba.br: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Repositório InstitucionalPUBhttp://192.188.11.11:8080/oai/requestopendoar:19322022-07-05T17:03:29Repositório Institucional da UFBA - Universidade Federal da Bahia (UFBA)false |
dc.title.pt_BR.fl_str_mv |
Some limitations for the applicability of the ray method in elastodynamics |
dc.title.alternative.pt_BR.fl_str_mv |
Revista Brasileira de Geofísica |
title |
Some limitations for the applicability of the ray method in elastodynamics |
spellingShingle |
Some limitations for the applicability of the ray method in elastodynamics Popov, Mikhail M. Ray method Elastodynamics Validity of asymptotics Método do raio Elastodinâmica Validade da aproximação assintótica |
title_short |
Some limitations for the applicability of the ray method in elastodynamics |
title_full |
Some limitations for the applicability of the ray method in elastodynamics |
title_fullStr |
Some limitations for the applicability of the ray method in elastodynamics |
title_full_unstemmed |
Some limitations for the applicability of the ray method in elastodynamics |
title_sort |
Some limitations for the applicability of the ray method in elastodynamics |
author |
Popov, Mikhail M. |
author_facet |
Popov, Mikhail M. Oliveira, S. |
author_role |
author |
author2 |
Oliveira, S. |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Popov, Mikhail M. Oliveira, S. Popov, Mikhail M. Oliveira, S. |
dc.subject.por.fl_str_mv |
Ray method Elastodynamics Validity of asymptotics Método do raio Elastodinâmica Validade da aproximação assintótica |
topic |
Ray method Elastodynamics Validity of asymptotics Método do raio Elastodinâmica Validade da aproximação assintótica |
description |
The ray method in the frequency domain describes the asymptotic behavior of the wave field for large frequencies which is not, in general, uniform with respect to the distance between the source and the point of observation. This implies that one can face situations in which the results obtained by the ray method may not be reliable for large distances from the source, if the dominant frequency is not high enough. In this paper we present two examples of such a type of problem for rather simple elastodynamic problems: a homogeneous medium; and a constant gradient velocity medium without interfaces. For both cases, the sources are assumed to be represented by two successive terms of the ray series, and therefore there are no point sources problems in our study. To this end we employ the following criterion of validity of the ray method: the absolute value of the ratio of the second term of the ray series to the first one must be less than unity. This criterion turns out to be sensitive to the radius of curvature of the initial wave front and to the initial distribution of the amplitude (or energy) along it. In the worst case of an initially planar wave front with nonuniform distribution of the amplitude, the second term of the ray series increases very fast. This gives rise to strong limitations to the use of the ray method with respect to distance if the frequency is fixed, or with respect to frequency for large distances. The depolarization phenomenon in both cases is discussed as well. |
publishDate |
1997 |
dc.date.issued.fl_str_mv |
1997 |
dc.date.accessioned.fl_str_mv |
2011-10-18T12:04:58Z |
dc.date.available.fl_str_mv |
2011-10-18T12:04:58Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://www.repositorio.ufba.br/ri/handle/ri/3373 |
dc.identifier.issn.none.fl_str_mv |
0102-261X |
dc.identifier.number.pt_BR.fl_str_mv |
v.15, n.3 |
identifier_str_mv |
0102-261X v.15, n.3 |
url |
http://www.repositorio.ufba.br/ri/handle/ri/3373 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Revista Brasileira de Geofísica |
publisher.none.fl_str_mv |
Revista Brasileira de Geofísica |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UFBA instname:Universidade Federal da Bahia (UFBA) instacron:UFBA |
instname_str |
Universidade Federal da Bahia (UFBA) |
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UFBA |
institution |
UFBA |
reponame_str |
Repositório Institucional da UFBA |
collection |
Repositório Institucional da UFBA |
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