Please use this identifier to cite or link to this item: http://hdl.handle.net/2122/704
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dc.contributor.authorallLombardi, A. M.; Istituto Nazionale di Geofisica e Vulcanologia, Sezione Roma1, Roma, Italiaen
dc.date.accessioned2006-02-14T10:08:33Zen
dc.date.available2006-02-14T10:08:33Zen
dc.date.issued2002en
dc.identifier.urihttp://hdl.handle.net/2122/704en
dc.description.abstractAssuming that, in a catalog, all the earthquakes with magnitude larger than or equal to a cutoff magnitude M c follow the Gutenberg-Richter Law, the compatibility of this hypothesis with «Bath’s Law» is examined. Consi-dering the mainshock M 0 and the largest aftershock M 1 of a sequence respectively as the first and the second largest order statistic of a sample of independent and identically distributed exponential random variables, the distribution of M 0 , M 1 and of their difference D 1 is evaluated. In particular, it is analyzed as the distribution of D 1 changes when only the sequences with the magnitude of the mainshock above a second threshold M c*•M c are considered. It results that the distributions of M 0 , M 1 and D 1 depend on the difference M c*•M c and on the number of events in the sequence. Moreover, the expected value of D 1 increases with increasing of M c*•M c for every value of N. Then it is shown that «Bath’s Law» could be ascribed to selection of data caused by the two thresholds M c and M c* and that it has a qualitative agreement with the model proposed. Key words Assuming that, in a catalog, all the earthquakes with magnitude larger than or equal to a cutoff magnitude M c follow the Gutenberg-Richter Law, the compatibility of this hypothesis with «Bath’s Law» is examined. Consi-dering the mainshock M 0 and the largest aftershock M 1 of a sequence respectively as the first and the second largest order statistic of a sample of independent and identically distributed exponential random variables, the distribution of M 0 , M 1 and of their difference D 1 is evaluated. In particular, it is analyzed as the distribution of D 1 changes when only the sequences with the magnitude of the mainshock above a second threshold M c*•M c are considered. It results that the distributions of M 0 , M 1 and D 1 depend on the difference M c*•M c and on the number of events in the sequence. Moreover, the expected value of D 1 increases with increasing of M c*•M c for every value of N. Then it is shown that «Bath’s Law» could be ascribed to selection of data caused by the two thresholds M c and M c* and that it has a qualitative agreement with the model propose.en
dc.format.extent724784 bytesen
dc.format.mimetypeapplication/pdfen
dc.language.isoEnglishen
dc.publisher.nameINGVen
dc.relation.ispartofAnnals of Geophysicsen
dc.relation.ispartofseries3-4/45 (2002)en
dc.subjectmagnitude distributionen
dc.subjectcluster sizeen
dc.subjectb-valueen
dc.subjectorder statisticsen
dc.titleProbabilistic interpretationof «Bath's Law»en
dc.typearticleen
dc.description.statusPublisheden
dc.type.QualityControlPeer-revieweden
dc.subject.INGV04. Solid Earth::04.05. Geomagnetism::04.05.08. Instruments and techniquesen
dc.subject.INGV05. General::05.05. Mathematical geophysics::05.05.99. General or miscellaneousen
dc.description.journalTypeJCR Journalen
dc.description.fulltextopenen
dc.contributor.authorLombardi, A. M.en
dc.contributor.departmentIstituto Nazionale di Geofisica e Vulcanologia, Sezione Roma1, Roma, Italiaen
item.openairetypearticle-
item.cerifentitytypePublications-
item.languageiso639-1en-
item.grantfulltextopen-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.fulltextWith Fulltext-
crisitem.author.deptIstituto Nazionale di Geofisica e Vulcanologia (INGV), Sezione Roma1, Roma, Italia-
crisitem.author.orcid0000-0002-8326-7135-
crisitem.author.parentorgIstituto Nazionale di Geofisica e Vulcanologia-
crisitem.classification.parent04. Solid Earth-
crisitem.classification.parent05. General-
crisitem.department.parentorgIstituto Nazionale di Geofisica e Vulcanologia-
Appears in Collections:Annals of Geophysics
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