10 Ư ΣƵνέƤƱƩƯ ƴηƲ Ε.Γ.Ε., 15-17 ΑưƱƩƫίƯƵ 2004, ΘƥƳƳαƫƯνίƪη 10 th G.S.G. Congress, 15-17 April 2004, Thessaloniki, Greece 631 PRECURSORY ACCELERATION OF SEISMICITY: FROM THE THEORETICAL ELEGANCE TO THE PRACTICAL DIFFICULTIES A.Tzanis, Department of Geophysics – Geothermy, University of Athens, Panepistimiopoli, 15784 Zografou, Greece, e-mail atzanis@geol.uoa.gr . F. Vallianatos, Department of Natural Resources and Natural Environment, Technological Educational Institute of Crete, Romanou 3, 731 33 Chania, Greece, e-mail: fvallian@chania.teicrete.gr. ABSTRACT It has been credibly argued that the earthquake generation process is a critical phenomenon culminating with a large event that corresponds to some critical point. In this view, a great earth- quake represents the end of a cycle on its associated fault network and the beginning of a new one. The dynamic organization of the fault network evolves as the cycle progresses and a great earth- quake becomes more probable, thereby rendering possible the prediction of the cycle’s end by monitoring the approach of the fault network toward a critical state. This process may be described by a power-law time-to-failure scaling of the cumulative Benioff strain, of the form ε(t)=K+A(t f - t) m , where t f is the failure time of the large event and m is of the order 0.2 - 0.4. Observational evidence has confirmed the power-law scaling in many cases and has empirically determined that the critical exponent m is typically of the order 0.3. There are also two theoretical predictions for its value. Ben- Zion and Lyakhovsky (2002) give m=1/3. Rundle et al. (2000) relate the behaviour of seismicity prior to a large earthquake to the excitation in proximity of a spinodal instability and show that the power-law activation associated with the spinodal instability is essentially identical to the power-law acceleration of Benioff strain observed prior to earthquakes, with m=0.25. In the present work, we outline a theoretical framework to derive the time-to-failure power-law from basic principles. We use energy conservation in a faulted crustal volume undergoing stress changes and we assume that the fault system obeys a fractal / hierarchical distribution law. Fur- thermore, we assume that the precursory seismic activation extends over a broad area around the impending failure and rapidly converges to the rupture zone as a function of the time-to-failure. By considering the analytic conditions near the time of failure, we derive the time-to-failure power-law and show that the critical exponent m is a function of the fractal dimension and that the cumulative precursory crustal deformation (A) is a function of the energy supplied to the system and the size of the rupture. The fractallity of the fault system is a necessary condition for the appearance of power- law acceleration in the seismic release rates. We note that this approach is based on first principles and gives a clear interpretation of the empirical parameters involved in equation (1). On the basis of these results, it is possible to explain a set of empirical laws derived by other researchers (e.g. Papazachos et al., 2002), in terms of a plausible physical framework. Furthermore, by considering the relationship of the instantaneous Benioff strain rate with respect to the mean Benioff strain rate, it is possible to construct approxi- mate analytical expressions to estimate the magnitude and time of failure of the impending earth- quake. More recently, the CP earthquake concept has gained support from the development of regional seismicity models with realistic fault geometry that show accelerating seismicity before large events. Essentially, these models involve stress transfer to the fault network during the cycle such, that the region of accelerating seismicity will scale with the size of the culminating event, as for in- stance in Bowman and King (2001). It is thus possible to understand the observed characteristics of distributed accelerating seismicity in terms of a simple process of increasing tectonic stress in a re- gion already subjected to stress inhomogeneities at all scale lengths. Then, the region of accelerat- ing seismic release is associated with the region defined by the stress field required to rupture a fault with a specified orientation and rake; it is thus possible to incorporate tectonic information into the analysis.