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## Seismic Energy and Stress-Drop Parameters for a Composite Source Model

John G. Anderson

Published February 1997, SCEC Contribution #317

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 (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 > 2 Δσs. The radiated energy in the S wave is EsCS = 0.233 CE (Δσd /μ) Μ0, where Μ0 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 ~ 0.44 CE Δσd . The Orowan stress drop (Δσo) is Δσo = 0.486 Δσd . The root-mean-square (rms) stress drop (Δσrms) is Δσrms = Δσd IΘ1/2Μ0 / Μοσ(Rmax)1/2(fc/f0)1/2, where f0 is corner frequency of the earthquake, Μοσ(Rmax) and fc are the moment and corner frequency of the largest subevent, and IΘ1/2 is a dimensionless constant approximately equal to 1.7. Finally, the Savage-Wood ratio (SWR) is given by SWR~ CEΔσd / Δσs. These results clarify the relationships among all of the stress parameters in the context of a complex fault, showing the critical role of the subevent stess 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.

Fault zones weakened by the presence of high-pressure fluids
have a predicted stress orientation signature. This
signature has been observed for the first time, providing
evidence for approximately lithostatic fluid pressures in
the San Andreas fault zone in southern California.
High-pressure fluids appear to extend into the surrounding
rock. The width of the inferred high fluid-pressure zone
scales with the width of the interseismic strain
accumulation, indicating that repeated strain-related
fracturing and crack sealing has created low-permeability
barriers which seal fluids into the network of currently
active fractures. These fluids may play a significant
role in the rupture dynamics of major earthquakes.

Citation
Anderson, J. G. (1997). Seismic Energy and Stress-Drop Parameters for a Composite Source Model. Bulletin of the Seismological Society of America, 87(1), 85-96.