Can observations of earthquake scaling constrain slip weakening?

S U M M A R Y We use observations of earthquake source parameters over a wide magnitude range (M W ∼ 0–7) to place constraints on constitutive fault weakening. The data suggest a scale dependence of apparent stress and stress drop; both may increase slightly with earthquake size. We show that this scale dependence need not imply any difference in fault zone properties for different sized earthquakes. We select 30 earthquakes well-recorded at 2.5 km depth at Cajon Pass, California. We use individual and empirical Green’s function spectral analysis to improve the resolution of source parameters, including static stress drop ( σ ) and total slip (S). We also measure radiated energy E S. We compare the Cajon Pass results with those from larger California earthquakes including aftershocks of the 1994 Northridge earthquake and confirm the results of Abercrombie (1995): μE S/M 0 σ (where μ = rigidity) and both E S/M 0 and σ increase as M 0 (and S) increases. Uncertainties remain large due to model assumptions and variations between possible models, and earthquake scale independence is possible within the resolution. Assuming that the average trends are real, we define a quantity G ′ = ( σ − 2μES/M 0)S/2 which is the total energy dissipation in friction and fracture minus σ 1S, where σ 1 is the final static stress. If σ 1 = σ d, the dynamic shear strength during the last increments of seismic slip, then G ′ = G, the fracture energy in a slip-weakening interpretation of dissipation. We find that G′ increases with S, from ∼103 J m−2 at S = 1 mm (M1 earthquakes) to 106– 107 J m−2 at S = 1 m (M6). We tentatively interpret these results within slip-weakening theory, assuming G ′ ≈ G. We consider the common assumption of a linear decrease of strength from the yield stress (σ p) with slip (s), up to a slip Dc. In this case, if either Dc, or more generally (σ p − σ d) Dc, increases with the final slip S we can match the observations, but this implies the unlikely result that the early weakening behaviour of the fault depends on the ultimate slip that the fault will sustain. We also find that a single slip-weakening function σ F(s) is able to match the observations, requiring no such correlation. Fitting G′ over S = 0.2 mm to 0.2 m with G ′ ∝ S1+n , we find n ∼ 0.3, implying a strength drop from peak σ p − σ F(S) ∝ Sn. This model also implies that slip weakening continues beyond the final slip S of typical earthquakes smaller than ∼ M6, and that the total strength drop σ p − σ d for large earthquakes is typically >20 MPa, larger than σ . The latter suggests that on average a fault is initially stressed below the peak strength, requiring stress concentration at the rupture front to propagate slipping.