Bayesian analysisof a probability distribution for local intensity attenuation
Main Article Content
Abstract
Intensity attenuation and its variation as a function of the distance and earthquake size is still a critical issue in evaluating seismic hazard. We present a method that allows us to incorporate additional information from the historical earthquake felt reports in the probability estimation of local intensity attenuation. The approach is based on two ideas: a) standard intensity versus epicentral distance relationships constitute an unnecessary filter between observations and estimates; and b) the intensity decay process is affected by many, scarcely known elements (the physical parameters of the source, propagation path effects, building vulnerability, the semi-qualitative character of macroseismic scales, etc.). Hence intensity decay should be treated as a random variable as is the macroseismic intensity. We assume here that decay, defined on the set {0,1, ..., I0}, follows a binomial distribution with parameters (I0, p); p depends on the distance from the epicenter and is related to the probability
of null decay at that distance. According to the Bayesian approach this p parameter is, in turn, a Beta random variable. The observations related to earthquakes with their epicenter outside the area concerned, but belonging to homogeneous zones, are used as prior knowledge of the phenomenon, while the data points of events inside
the area are used to update the estimates through the posterior means of the quantities involved. Our methodology
is described in detail in an application to the Umbria-Marche area in Central Italy. The data sets examined are the macroseismic intensity database DOM4.1 and the zonation ZS.4, both compiled by the Italian Group for
Defence against Earthquakes (GNDT). The method is validated by comparing the observed and the estimated intensity data points of the Camerino (28/07/1799) and of the Colfiorito (26/09/1997) earthquakes.
of null decay at that distance. According to the Bayesian approach this p parameter is, in turn, a Beta random variable. The observations related to earthquakes with their epicenter outside the area concerned, but belonging to homogeneous zones, are used as prior knowledge of the phenomenon, while the data points of events inside
the area are used to update the estimates through the posterior means of the quantities involved. Our methodology
is described in detail in an application to the Umbria-Marche area in Central Italy. The data sets examined are the macroseismic intensity database DOM4.1 and the zonation ZS.4, both compiled by the Italian Group for
Defence against Earthquakes (GNDT). The method is validated by comparing the observed and the estimated intensity data points of the Camerino (28/07/1799) and of the Colfiorito (26/09/1997) earthquakes.
Article Details
How to Cite
Rotondi, R. and Zonno, G. (2004) “Bayesian analysisof a probability distribution for local intensity attenuation”, Annals of Geophysics, 47(5). doi: 10.4401/ag-3356.
Issue
Section
OLD
Open-Access License
No Permission Required
Istituto Nazionale di Geofisica e Vulcanologia applies the Creative Commons Attribution License (CCAL) to all works we publish.
Under the CCAL, authors retain ownership of the copyright for their article, but authors allow anyone to download, reuse, reprint, modify, distribute, so long as the original authors and source are cited. No permission is required from the authors or the publishers.
In most cases, appropriate attribution can be provided by simply citing the original article.
If the item you plan to reuse is not part of a published article (e.g., a featured issue image), then please indicate the originator of the work, and the volume, issue, and date of the journal in which the item appeared. For any reuse or redistribution of a work, you must also make clear the license terms under which the work was published.
This broad license was developed to facilitate open access to, and free use of, original works of all types. Applying this standard license to your own work will ensure your right to make your work freely and openly available. For queries about the license, please contact ann.geophys@ingv.it.