Scale dependence in the dynamics of earthquake propagation: Evidence from seismological and geological observations

We attempt to reconcile current understanding of the earthquake energy balance with recent estimates of
fracture energy from seismological investigations and surface energy from geological observations. The
complex structure of real fault zones suggests that earthquakes in such fault structures are dominated by
scale-dependent processes.We present a model for an inelastic fault zone of finite thickness embedded in an
elastic crust represented at a macroscopic scale by a mathematical plane of zero thickness. The constitutive
properties of the fault zone are governed by physical processes controlling gouge and damage evolution at
meso- and micro-scale. However, in order to model and interpret seismological observations, we represent
dynamic fault weakening at the macroscopic scale in terms of traction evolution as a function of slip and
other internal variables defining a phenomenological friction or contact law on the virtual mathematical
plane. This contact law is designed to capture the main features of dynamic fault weakening during
earthquake rupture. In this study we assume that total shear traction is friction and corresponds to shear
resistance of the whole fault zone.We show that seismological observations, depending on finite and limited
wavelength and frequency bandwidth, can only provide an estimate of breakdown stress drop and
breakdown work (a more general definition of seismological fracture energy) representing a lower bound of
the total intrinsic power of dissipation on the fault zone. We emphasize that geological estimates of surface
energy can be compared with seismological estimates of breakdown work only if they are representative of
the same macroscopic scale. In this case, it emerges that, contrary to surface energy, seismological
breakdown work represents a non-negligible contribution to the earthquake energy budget.

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