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

Abstract

AbstractThis 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 (Δσd) that is independent of the static stress drop (Δσs). In the model, Δσd is intended to represent the effective dynamic stress, and it does this well when Δσd > 2Δσs. The radiated energy in the S wave is ECSS = 0.233 CE (Δσd/μ) M0, where M0 is the seismic moment of the earthquake, μ is shear modulus, and CE is a dimensionless parameter that equals unity when Δσd > 2Δσs. The apparent stress (σa) is σa = 0.243 CE Δσd. The effective stress is σe ≈ 0.44CE Δσd. The Orowan stress drop (Δσo) is Δσo = 0.486 Δσd. The root-mean-square (rms) stress drop (Δσrms) is Δσrms = ΔσdI1/2θM0/Mos(Rmax)1/2 (fc/fo)1/2, where f0 is corner frequency of the earthquake, Mos (Rmax) and fc are the moment and corner frequency of the largest subevent, and I1/2θ is a dimensionless constant approximately equal to 1.7. Finally, the Savage-Wood ratio (SWR) is given by SWR ≈ CE Δσd/2 Δσs. 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.