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.
Numericalmodels 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.