ON THE DETERMINISTIC DESCRIPTION OF EARTHQUAKES

The quantitative estimate of earthquake damage due to ground shaking is of pivotal importance in geosciences, and its knowledge should hopefully lead to the formulation of improved strategies for seismic hazard assessment. Numerical models of the processes occurring during seismogenic faulting represent a powerful tool to explore realistic scenarios that are often far from being fully reproduced in laboratory experiments because of intrinsic, technical limitations. In this paper we discuss the prominent role of the fault governing model, which describes the behavior of the fault traction during a dynamic slip failure and accounts for the different, and potentially competing, chemical and physical dissipative mechanisms. We show in a comprehensive sketch the large number of constitutive models adopted in dynamic modeling of seismic events, and we emphasize their prominent features, limitations, and specific advantages. In a quantitative comparison, we show through numerical simulations that spontaneous dynamic ruptures obeying the idealized, linear slip-weakening (SW) equation and a more elaborated rate-and state-dependent friction law produce very similar results (in terms of rupture times, peaks slip velocity, developed slip, and stress drops), provided that the frictional parameters are adequately comparable and, more importantly, that the fracture energy density is the same. Our numerical experiments also illustrate that the different models predict fault slip velocity time histories characterized by a similar frequency content; a feeble predominance of high frequencies in the SW case emerges in the frequency ranges [0.3, 1] and [11, 50] Hz. These simulations clearly indicate that, even forgiving the frequency band limitation, it would be very difficult (virtually impossible) to discriminate between two different, but energetically identical, constitutive models, on the basis of the seismograms recorded after a natural earthquake.