Scattering and diffraction of elastic P- and S-waves by a spherical obstacle: A review of the classical solution
We re-derive the solution for scattering and diffraction of elastic waves by a single spherical obstacle. A complete catalog for the coefficients in the series’ expansions of scattered waves is presented. The classical solution is a superposition of incident and diffracted fields. Plane P- or S- wav...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2006 |
| País: | México |
| Institución: | UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO |
| Repositorio: | Geofísica Internacional |
| Idioma: | español inglés |
| OAI Identifier: | oai:revistagi.geofisica.unam.mx:article/218 |
| Acceso en línea: | http://revistagi.geofisica.unam.mx/index.php/RGI/article/view/218 |
| Access Level: | acceso abierto |
| Palabra clave: | Expansión difracción obstrucción esférica ondas elásticas funciones de Bessel y Hankel respuesta sísmica. Scattering diffraction spherical obstacle elastic waves Bessel and Hankel functions Bessel and Hankel func seismic response |
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Scattering and diffraction of elastic P- and S-waves by a spherical obstacle: A review of the classical solutionÁvila-Carrera, R.Sánchez-Sesma, F. J.Expansióndifracciónobstrucción esféricaondas elásticasfunciones de Bessel y Hankelrespuesta sísmica.Scatteringdiffractionspherical obstacleelastic wavesBessel and Hankel functionsBessel and Hankel funcseismic responseWe re-derive the solution for scattering and diffraction of elastic waves by a single spherical obstacle. A complete catalog for the coefficients in the series’ expansions of scattered waves is presented. The classical solution is a superposition of incident and diffracted fields. Plane P- or S- waves are assumed. They are expressed as expansions of spherical wave functions which are tested against exact results. The diffracted field is calculated from the analytical enforcing of boundary conditions at the scatterermatrix interface. The spherical obstacle is a cavity, an elastic inclusion or a fluid-filled zone. A complete set of wave functions is given in terms of spherical Bessel and Hankel radial functions. Legendre and trigonometric functions are used for the angular coordinates. Results are shown in time and frequency domains. Diffracted displacement amplitudes versus normalized frequency and radiation patterns at low, intermediate and high frequencies are reported. Synthetic seismograms for some relevant cases are computed.Rederivamos la solución para el cálculo de la difracción y dispersión de ondas elásticas por una obstrucción esférica. Se presenta un catálogo para los coeficientes en las expansiones de las series de las ondas difractadas. La solución clásica consiste en una superposición de los campos incidente y difractado. Se asumen ondas planas P y S. Ellas se expresan como expansiones de funciones de onda esféricas, las cuales son probadas contra resultados exactos. El campo difractado se calcula a partir de la imposición analítica de condiciones de frontera en la interfase matriz-difractor. La obstrucción puede ser una cavidad, una inclusión elástica o una esfera fluida. Se proporciona un conjunto completo de funciones de onda en términos de funciones radiales esféricas de Bessel y de Hankel. Para las coordenadas angulares se utilizan polinomios de Legendre y funciones trigonométricas. Se muestran resultados en el dominio del tiempo y la frecuencia. Reportamos espectros de amplitudes del desplazamiento contra la frecuencia normalizada y patrones de radiación en frecuencias bajas, medias y altas. Se calculan sismogramas sintéticos para algunos casos relevantes.Universidad Nacional Autónoma de México. Instituto de Geofísica2006-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://revistagi.geofisica.unam.mx/index.php/RGI/article/view/21810.22201/igeof.00167169p.2006.45.1.189Geofisica Internacional; Vol. 45 No. 1 (2006): January 1, 2006; 3-21Geofísica Internacional; Vol. 45 Núm. 1 (2006): Enero 1, 2006; 3-212954-436X0016-716910.22201/igeof.00167169p.2006.45.1reponame:Geofísica Internacionalinstname:UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICOinstacron:UNAMspaenghttp://revistagi.geofisica.unam.mx/index.php/RGI/article/view/218/207http://revistagi.geofisica.unam.mx/index.php/RGI/article/view/218/2505https://creativecommons.org/licenses/by-nc-sa/4.0/info:eu-repo/semantics/openAccessoai:revistagi.geofisica.unam.mx:article/2182024-08-16T17:31:49Z |
| dc.title.none.fl_str_mv |
Scattering and diffraction of elastic P- and S-waves by a spherical obstacle: A review of the classical solution |
| title |
Scattering and diffraction of elastic P- and S-waves by a spherical obstacle: A review of the classical solution |
| spellingShingle |
Scattering and diffraction of elastic P- and S-waves by a spherical obstacle: A review of the classical solution Ávila-Carrera, R. Expansión difracción obstrucción esférica ondas elásticas funciones de Bessel y Hankel respuesta sísmica. Scattering diffraction spherical obstacle elastic waves Bessel and Hankel functions Bessel and Hankel func seismic response |
| title_short |
Scattering and diffraction of elastic P- and S-waves by a spherical obstacle: A review of the classical solution |
| title_full |
Scattering and diffraction of elastic P- and S-waves by a spherical obstacle: A review of the classical solution |
| title_fullStr |
Scattering and diffraction of elastic P- and S-waves by a spherical obstacle: A review of the classical solution |
| title_full_unstemmed |
Scattering and diffraction of elastic P- and S-waves by a spherical obstacle: A review of the classical solution |
| title_sort |
Scattering and diffraction of elastic P- and S-waves by a spherical obstacle: A review of the classical solution |
| dc.creator.none.fl_str_mv |
Ávila-Carrera, R. Sánchez-Sesma, F. J. |
| author |
Ávila-Carrera, R. |
| author_facet |
Ávila-Carrera, R. Sánchez-Sesma, F. J. |
| author_role |
author |
| author2 |
Sánchez-Sesma, F. J. |
| author2_role |
author |
| dc.subject.none.fl_str_mv |
Expansión difracción obstrucción esférica ondas elásticas funciones de Bessel y Hankel respuesta sísmica. Scattering diffraction spherical obstacle elastic waves Bessel and Hankel functions Bessel and Hankel func seismic response |
| topic |
Expansión difracción obstrucción esférica ondas elásticas funciones de Bessel y Hankel respuesta sísmica. Scattering diffraction spherical obstacle elastic waves Bessel and Hankel functions Bessel and Hankel func seismic response |
| description |
We re-derive the solution for scattering and diffraction of elastic waves by a single spherical obstacle. A complete catalog for the coefficients in the series’ expansions of scattered waves is presented. The classical solution is a superposition of incident and diffracted fields. Plane P- or S- waves are assumed. They are expressed as expansions of spherical wave functions which are tested against exact results. The diffracted field is calculated from the analytical enforcing of boundary conditions at the scatterermatrix interface. The spherical obstacle is a cavity, an elastic inclusion or a fluid-filled zone. A complete set of wave functions is given in terms of spherical Bessel and Hankel radial functions. Legendre and trigonometric functions are used for the angular coordinates. Results are shown in time and frequency domains. Diffracted displacement amplitudes versus normalized frequency and radiation patterns at low, intermediate and high frequencies are reported. Synthetic seismograms for some relevant cases are computed. |
| publishDate |
2006 |
| dc.date.none.fl_str_mv |
2006-01-01 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
| format |
article |
| status_str |
publishedVersion |
| dc.identifier.none.fl_str_mv |
http://revistagi.geofisica.unam.mx/index.php/RGI/article/view/218 10.22201/igeof.00167169p.2006.45.1.189 |
| url |
http://revistagi.geofisica.unam.mx/index.php/RGI/article/view/218 |
| identifier_str_mv |
10.22201/igeof.00167169p.2006.45.1.189 |
| dc.language.none.fl_str_mv |
spa eng |
| language |
spa eng |
| dc.relation.none.fl_str_mv |
http://revistagi.geofisica.unam.mx/index.php/RGI/article/view/218/207 http://revistagi.geofisica.unam.mx/index.php/RGI/article/view/218/2505 |
| dc.rights.none.fl_str_mv |
https://creativecommons.org/licenses/by-nc-sa/4.0/ info:eu-repo/semantics/openAccess |
| rights_invalid_str_mv |
https://creativecommons.org/licenses/by-nc-sa/4.0/ |
| eu_rights_str_mv |
openAccess |
| dc.format.none.fl_str_mv |
application/pdf |
| dc.publisher.none.fl_str_mv |
Universidad Nacional Autónoma de México. Instituto de Geofísica |
| publisher.none.fl_str_mv |
Universidad Nacional Autónoma de México. Instituto de Geofísica |
| dc.source.none.fl_str_mv |
Geofisica Internacional; Vol. 45 No. 1 (2006): January 1, 2006; 3-21 Geofísica Internacional; Vol. 45 Núm. 1 (2006): Enero 1, 2006; 3-21 2954-436X 0016-7169 10.22201/igeof.00167169p.2006.45.1 reponame:Geofísica Internacional instname:UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO instacron:UNAM |
| instname_str |
UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO |
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UNAM |
| institution |
UNAM |
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Geofísica Internacional |
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Geofísica Internacional |
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