Observational constraints on earthquake source scaling: Understanding the limits in resolution

I examine the resolution of the type of stress drop estimates that have been used to place observational constraints on the scaling of earthquake source processes. I first show that apparent stress and Brune stress drop are equivalent to within a constant given any source spectral decay between ??1.5 and ??3 (i.e., any plausible value) and so consistent scaling is expected for the two estimates. I then discuss the resolution and scaling of Brune stress drop estimates, in the context of empirical Green's function results from recent earthquake sequences, including the 1992 Joshua Tree, California, mainshock and its aftershocks. I show that no definitive scaling of stress drop with moment is revealed over the moment range 1019-1025; within this sequence, however, there is a tendency for moderate-sized (M 4-5) events to be characterized by high stress drops. However, well-resolved results for recent M > 6 events are inconsistent with any extrapolated stress increase with moment for the aftershocks. Focusing on comer frequency estimates for smaller (M < 3.5) events, I show that resolution is extremely limited even after empirical Green's function deconvolutions. A fundamental limitation to resolution is the paucity of good signal-to-noise at frequencies above 60 Hz, a limitation that will affect nearly all surficial recordings of ground motion in California and many other regions. Thus, while the best available observational results support a constant stress drop for moderate-to large-sized events, very little robust observational evidence exists to constrain the quantities that bear most critically on our understanding of source processes: stress drop values and stress drop scaling for small events.