Earthquake location based on the gradient method and on minima of beams of directions

Autores
Gershanik, Simón
Año de publicación
1973
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Earthquake location is usually made by means of the Gauss-Newton iterative method, known in seismology as the Geiger method. As this method may fail to be efficient in some cases, attention is turned to the possibilities offered to the problem by the gradient method, which is always convergent, and, when properly used, may lead to the vicinity of the solution after a few iterations. But in the vicinity of the solution, the gradient method becomes slowly convergent. Therefore, in addition, another convergent method based on the minimum value, g , of the sum of the squared residuals taken on a beam of directions, is presented. In it the sum g is approximated by a polynomial of Laplace spherical harmonics. The new method includes the gradient method as a particular case; it is well suited in the vicinity of the solution and may lead quickly to it.
Facultad de Ciencias Astronómicas y Geofísicas
Materia
Geofísica
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/138933
Acceder
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network_name_str SEDICI (UNLP)
spelling Earthquake location based on the gradient method and on minima of beams of directionsGershanik, SimónGeofísicaEarthquake location is usually made by means of the Gauss-Newton iterative method, known in seismology as the Geiger method. As this method may fail to be efficient in some cases, attention is turned to the possibilities offered to the problem by the gradient method, which is always convergent, and, when properly used, may lead to the vicinity of the solution after a few iterations. But in the vicinity of the solution, the gradient method becomes slowly convergent. Therefore, in addition, another convergent method based on the minimum value, g , of the sum of the squared residuals taken on a beam of directions, is presented. In it the sum g is approximated by a polynomial of Laplace spherical harmonics. The new method includes the gradient method as a particular case; it is well suited in the vicinity of the solution and may lead quickly to it.Facultad de Ciencias Astronómicas y Geofísicas1973-10-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf1829-1840http://sedici.unlp.edu.ar/handle/10915/138933enginfo:eu-repo/semantics/altIdentifier/issn/1943-3573info:eu-repo/semantics/altIdentifier/issn/0037-1106info:eu-repo/semantics/altIdentifier/doi/10.1785/bssa0630051829info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2026-01-14T13:56:44Zoai:sedici.unlp.edu.ar:10915/138933Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292026-01-14 13:56:44.536SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Earthquake location based on the gradient method and on minima of beams of directions
title Earthquake location based on the gradient method and on minima of beams of directions
spellingShingle Earthquake location based on the gradient method and on minima of beams of directions
Gershanik, Simón
Geofísica
title_short Earthquake location based on the gradient method and on minima of beams of directions
title_full Earthquake location based on the gradient method and on minima of beams of directions
title_fullStr Earthquake location based on the gradient method and on minima of beams of directions
title_full_unstemmed Earthquake location based on the gradient method and on minima of beams of directions
title_sort Earthquake location based on the gradient method and on minima of beams of directions
dc.creator.none.fl_str_mv Gershanik, Simón
author Gershanik, Simón
author_facet Gershanik, Simón
author_role author
dc.subject.none.fl_str_mv Geofísica
topic Geofísica
dc.description.none.fl_txt_mv Earthquake location is usually made by means of the Gauss-Newton iterative method, known in seismology as the Geiger method. As this method may fail to be efficient in some cases, attention is turned to the possibilities offered to the problem by the gradient method, which is always convergent, and, when properly used, may lead to the vicinity of the solution after a few iterations. But in the vicinity of the solution, the gradient method becomes slowly convergent. Therefore, in addition, another convergent method based on the minimum value, g , of the sum of the squared residuals taken on a beam of directions, is presented. In it the sum g is approximated by a polynomial of Laplace spherical harmonics. The new method includes the gradient method as a particular case; it is well suited in the vicinity of the solution and may lead quickly to it.
Facultad de Ciencias Astronómicas y Geofísicas
description Earthquake location is usually made by means of the Gauss-Newton iterative method, known in seismology as the Geiger method. As this method may fail to be efficient in some cases, attention is turned to the possibilities offered to the problem by the gradient method, which is always convergent, and, when properly used, may lead to the vicinity of the solution after a few iterations. But in the vicinity of the solution, the gradient method becomes slowly convergent. Therefore, in addition, another convergent method based on the minimum value, g , of the sum of the squared residuals taken on a beam of directions, is presented. In it the sum g is approximated by a polynomial of Laplace spherical harmonics. The new method includes the gradient method as a particular case; it is well suited in the vicinity of the solution and may lead quickly to it.
publishDate 1973
dc.date.none.fl_str_mv 1973-10-01
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://sedici.unlp.edu.ar/handle/10915/138933
url http://sedici.unlp.edu.ar/handle/10915/138933
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/1943-3573
info:eu-repo/semantics/altIdentifier/issn/0037-1106
info:eu-repo/semantics/altIdentifier/doi/10.1785/bssa0630051829
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.format.none.fl_str_mv application/pdf
1829-1840
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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