A simple and testable model for earthquake clustering

Citation
R. Console et M. Murru, A simple and testable model for earthquake clustering, J GEO R-SOL, 106(B5), 2001, pp. 8699-8711
Citations number
20
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Earth Sciences
Journal title
JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH
ISSN journal
2169-9313 → ACNP
Volume
106
Issue
B5
Year of publication
2001
Pages
8699 - 8711
Database
ISI
SICI code
0148-0227(20010510)106:B5<8699:ASATMF>2.0.ZU;2-D
Abstract
Earthquakes are regarded as the realization of a point process modeled by a generalized Poisson distribution. We assume that the Gutenberg-Richter law describes the magnitude distribution of all the earthquakes in a sample, w ith a constant b value. We model the occurrence rate density of earthquakes in space and time as the sum of two terms, one representing the independen t, or spontaneous, activity and the other representing the activity induced by previous earthquakes. The first term depends only on space and is model ed by a continuous function of the geometrical coordinates, obtained by smo othing the discrete distribution of the past instrumental seismicity. The s econd term also depends on time, and it is factorized in two terms that dep end on the space distance (according to an isotropic normal distribution) a nd on the time difference (according to the generalized Omori law), respect ively, from the past earthquakes. Knowing the expected rate density, the li kelihood of any realization of the process (actually represented by an eart hquake catalog) can be computed straightforwardly. This algorithm was used in two ways: (1) during the learning phase, for the maximum likelihood esti mate of the few free parameters of the model, and (2) for hypothesis testin g. For the learning phase we used the catalog of Italian seismicity (M grea ter than or equal to3.5) from May 1976 to December 1998. The model was test ed on a new and independent data set (January-December 1999). We demonstrat ed for this short time period that in the Italian region this time-dependen t model has a significantly better performance than a stationary Poisson mo del, even if its likelihood is computed excluding the obvious component of main shock-aftershock interaction.