@article{epos1455,
          volume = {108},
          number = {B10},
           month = {October},
          author = {Rodolfo Console and Maura Murru and Anna Maria Lombardi},
           title = {Refining earthquake clustering models},
       publisher = {American Geophysical Union},
         journal = {Journal of Geophysical Research},
            year = {2003},
        keywords = {earthquake clustering, aftershocks, stochastic processes, hypothesis test, Italian
seismicity},
             url = {https://episodesplatform.eu/eprints/1455/},
        abstract = {Assuming that earthquakes are the realization of a stochastic point process and that the
magnitude distribution of all earthquakes is described by the Gutenberg-Richter law with a
constant b value, we model the occurrence rate density of earthquakes in space and time by
means of an epidemic model. The occurrence rate density is computed by the sum of
two terms, one representing the independent, or spontaneous activity, and the other
representing the activity induced by previous earthquakes. While the first term depends
only on space, the second one is factored into three terms that include the magnitude, time,
and location, respectively, of the past earthquakes. In this paper we use the modified Omori
law for the time term, focusing our investigation on the magnitude and space terms. We
formulate two different hypotheses for each of them, and we find the respective maximum
likelihood parameters on the basis of the catalog of instrumental seismicity recorded in Italy
from 1987 to 2000. The comparison of the respective likelihood computed for the
seismicity recorded in 2001 provides a way for choosing the best model. The confidence
level of our choice is then assessed by means of a Monte Carlo simulation on the
varioushypotheses. Our study shows that an inverse power density function is more reliable
than a normal density function for the space distribution and that the hypothesis of
scale invariance of aftershock productivity with respect to magnitude can be rejected with
high confidence level. The final model is suitable for computing earthquake occurrence
probability in real circumstances.}
}