Can observations of earthquake scaling constrain slip weakening?

SUMMARY 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 .W ecompare 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/ 2w hich is the total energy dissipation in friction and fracture minus σ 1 S ,w here 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.