Seismic energy and stress-drop parameters for a composite source model

This article examines relationships among radiated energy and several stress-drop parameters that are used to describe earthquake faulting. This is done in the context of a composite source model that has been quite successful, in its ability to reproduce statistical characteristics of strong-motion accelerograms. The main feature of the composite source model is a superposition of subevents with a fractal distribution of sizes, but all with the same subevent stress drop (Delta sigma(d)) that is independent of the static stress drop (Delta sigma(s)). In the model, Delta sigma(d) is intended to represent the effective dynamic stress, and it does this well when Delta sigma(d) > 2 Delta sigma(s). The radiated energy in the S wave is E(S)(CS) = 0.233 C-E (Delta sigma(d)/mu) M(0), where M(0) is the seismic moment of the earthquake, mu is shear modulus, and C-E is a dimensionless parameter that equals unity when Delta sigma(d) > 2 Delta sigma(s). The apparent stress (sigma(a)) is sigma(a) = 0.243 C-E Delta sigma(d). The effective stress is sigma(e) approximate to 0.44 C-E Delta sigma(d). The Orowan stress drop (Delta sigma(o)) is Delta sigma(o) = 0.486 Delta sigma(d). The root-mean-square (rms) stress drop (Delta sigma(rms)) is Delta sigma(rms) = Delta sigma(d)I(theta)(1/2) M(0)/M(os)(R(max))(1/2) (f(c)/f(o))(1/2), where f, is corner frequency of the earthquake, M(os) (R(max)) and f(c) are the moment and corner frequency of the largest subevent, and I-theta(1/2) is a dimensionless constant approximately equal to 1.7. Finally, the Savage-Wood ratio (SWR) is given by SWR approximate to C-E Delta sigma(d)/2 Delta sigma(s). These results clarify the relationships among all of these stress parameters in the context of a complex fault, showing the critical role of the subevent stress drop. They also provide an additional tool for energy, stress, and Savage-Wood ratio estimation. Since the process of modeling strong motion with the composite source uses realistic Green's functions, estimates of energy and stress parameters using this model are expected to have a good correction for wave propagation.