Refining earthquake clustering models

Abstract

Assuming that earthquakes are the realization of a stochastic point process and that themagnitude distribution of all earthquakes is described by the Gutenberg-Richter law with aconstant b value, we model the occurrence rate density of earthquakes in space and time bymeans of an epidemic model. The occurrence rate density is computed by the sum oftwo terms, one representing the independent, or spontaneous activity, and the otherrepresenting the activity induced by previous earthquakes. While the first term dependsonly 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 Omorilaw for the time term, focusing our investigation on the magnitude and space terms. Weformulate two different hypotheses for each of them, and we find the respective maximumlikelihood parameters on the basis of the catalog of instrumental seismicity recorded in Italyfrom 1987 to 2000. The comparison of the respective likelihood computed for theseismicity recorded in 2001 provides a way for choosing the best model. The confidencelevel of our choice is then assessed by means of a Monte Carlo simulation on thevarioushypotheses. Our study shows that an inverse power density function is more reliablethan a normal density function for the space distribution and that the hypothesis ofscale invariance of aftershock productivity with respect to magnitude can be rejected withhigh confidence level. The final model is suitable for computing earthquake occurrenceprobability in real circumstances.