Gradual fault weakening with seismic slip: inferences from the seismic sequences of L'Aquila, 2009 and Northridge, 1994

We estimate seismological fracture energies from two subsets of events selected from the seismic sequences of L’Aquila (2009), and Northridge (1994): 57 and 16 selected events, respectively, including the main shocks. Following ABERCROMBIE and RICE (2005), we postulate that fracture energy (G) represents the post-failure integral of the dynamic weakening curve, which is described by the evolution of shear traction as a function of slip. Following a direct-wave approach, we compute mainshock-/aftershock-source spectral ratios, and analyze them using the approach proposed by MALAGNINI et al. (this issue, 2014) to infer corner frequencies and seismic moment. Our estimates of source parameters
(including fracture energies) are based on best-fit grid searches performed over empirical source spectral ratios. We quantify the source scaling of spectra from small and large earthquakes by using the MDAC formulation of WALTER and TAYLOR (2001). The source parameters presented in this paper must be considered as point source estimates representing averages calculated over specific ruptured portions of the fault area. In order to constrain the scaling of fracture energy with coseismic slip, we investigate two different slip-weakening functions to model the shear traction as a function of slip: (i) a power law, as suggested by ABERCROMBIE and RICE (2005), and (ii) an exponential decay.
Our results show that the exponential decay of stress on the fault allows a good fit between measured and predicted fracture energies, both for the main events and for their aftershocks, regardless of the significant differences in the energy budgets between the large (main) and small earthquakes (aftershocks). Using the power-law slip-weakening function would lead us to a very different situation: in our two investigated sequences, if the aftershock scaling is extrapolated to events with large slips, a power law (a la Abercrombie and Rice) would predict unrealistically large stress drops for large, main earthquakes. We conclude that the exponential stress evolution law has the advantage of avoiding unrealistic stress drops and unbounded fracture energies at large slip values, while still describing the abrupt shear-stress degradation observed in high-velocity laboratory experiments (e.g., DI TORO et al., 2011).