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Authors: Console, R.* 
Murru, M.* 
Catalli, F.* 
Falcone, G.* 
Title: Real time forecasts through an earthquake clustering model constrained by the rate-and-state constitutive law compared with a purely stochastic ETAS model
Issue Date: Jan-2007
Series/Report no.: 1/78 (2007)
Keywords: rate and state
Subject Classification01. Atmosphere::01.02. Ionosphere::01.02.03. Forecasts 
Abstract: We propose an earthquake clustering model based on the popular concept of epidemic models. In these models every earthquake can be regarded as both triggered by previous events and as a potential triggering event for subsequent earthquakes (Ogata 1988, 1998; Ogata and Zhuang 2006 and reference therein; Console and Murru 2001; Console et al. 2003; Console et al. 2006a, 2006b; Helmstetter and Sornette 2002a, 2002b, 2003 for reviews; and Vere-Jones 2006 for review on the use of stochastic models for earthquake occurrence). The occurrence- rate density at any time and geographical location is computed by the contribution of every previous event using a kernel function that takes into proper account: (a) the magnitude of the triggering earthquake, (b) the spatial distance from the triggering event, and (c) the time interval between the triggering event and the instant considered for the computation. The magnitude distribution adopted here is the Gutenberg-Richter law (Gutenberg and Richter 1944). The above-mentioned criteria are implemented through the introduction of the rate-and-state constitutive law in a previously existing epidemic algorithm. The validity of the model can be tested in an exercise of realtime forecast.
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