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[1] 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.INDEX TERMS: 7223 Seismology: Seismic hazard assessment and prediction; 7230 Seismology: Seismicity and seismotectonics; 7260 Seismology: Theory and modeling; KEYWORDS: earthquake clustering, aftershocks, stochastic processes, hypothesis test, Italian seismicity Citation: Console, R., M. Murru, and A. M. Lombardi, Refining earthquake clustering models,

We present the first high-quality catalog of early aftershocks of the three mainshocks of the 2016 central Italy Amatrice-Visso-Norcia normal faulting sequence. We located 10,574 manually picked aftershocks with a robust probabilistic, non-linear method achieving a significant improvement in the solution accuracy and magnitude completeness with respect to previous studies. Aftershock distribution and relocated mainshocks give insight into the complex architecture of major causative and subsidiary faults, thus providing crucial constraints on multi-segment rupture models. We document reactivation and kinematic inversion of a WNW-dipping listric structure, referable to the inherited Mts Sibillini Thrust (MST) that controlled segmentation of the causative normal faults. Spatial partitioning of aftershocks evidences that the MST lateral ramp had a dual control on rupture propagation, behaving as a barrier for the Amatrice and Visso mainshocks, and later as an asperity for the Norcia mainshock. We hypothesize that the Visso mainshock re-activated also the deep part of an optimally oriented preexisting thrust. Aftershock patterns reveal that the Amatrice Mw5.4 aftershock and the Norcia mainshock ruptured two distinct antithetic faults 3–4 km apart. Therefore, our results suggest to consider both the MST cross structure and the subsidiary antithetic fault in the finite-fault source modelling of the Norcia earthquake.

[1] We describe the results of a prospective, real-time earthquake forecast experiment made during a seismic emergency. A M w 6.3 earthquake struck the city of L'Aquila, Italy on April 6, 2009, causing hundreds of deaths and vast damage. Immediately following this event, we began producing daily earthquake forecasts for the region, and we provided these forecasts to Civil Protection -the agency responsible for managing the emergency. The forecasts are based on a stochastic model that combines the Gutenberg-Richter distribution of earthquake magnitudes and power-law decay in space and time of triggered earthquakes. The results from the first month following the L'Aquila earthquake exhibit a good fit between forecasts and observations, indicating that accurate earthquake forecasting is now a realistic goal. Our experience with this experiment demonstrates an urgent need for a connection between probabilistic forecasts and decisionmaking in order to establish -before crises -quantitative and transparent protocols for decision support.

The concept of controllability of linear systems from control theory is applied to networks inspired by biology. A node is in this context controllable if an external signal can be applied which can adjust the level (e.g., protein concentration) of the node in a finite time to an arbitrary value, regardless of the levels of the other nodes. The property of being downstream of the node to which the input is applied turns out to be a necessary but not a sufficient condition for being controllable. An interpretation of the controllability matrix, when applied to networks, is also given. Finally, two case studies are provided in order to better explain the concepts, as well as some results for a gene regulatory network of fission yeast.