Physical and stochastic models of earthquake clustering

The phenomenon of earthquake clustering, i.e., the increase of occurrence probability for seismic events close in space and time to other previous earthquakes, has been modeled both by statistical and physical processes.From a statistical viewpoint the so-called epidemic model (ETAS) introduced by Ogata in 1988 and its variations have become fairly well known in the seismological community. Tests on real seismicity and comparison with a plain time-independent Poissonian model through likelihood-based methods have reliably proved their validity.On the other hand, in the last decade many papers have been published on the so-called Coulomb stress change principle, based on the theory of elasticity, showing qualitatively that an increase of the Coulomb stress in a given area is usually associated with an increase of seismic activity. More specifically, the rate-and-state theory developed by Dieterich in the ′90s has been able to give a physical justification to the phenomenon known as Omori law. According to this law, a mainshock is followed by a series of aftershocks whose frequency decreases in time as an inverse power law.In this study we give an outline of the above-mentioned stochastic and physical models, and build up an approach by which these models can be merged in a single algorithm and statistically tested. The application to the seismicity of Japan from 1970 to 2003 shows that the new model incorporating the physical concept of the rate-and-state theory performs not worse than the purely stochastic model with two free parameters only. The numerical results obtained in these applications are related to physical characters of the model as the stress change produced by an earthquake close to its edges and to the A and σ parameters of the rate-and-state constitutive law.