## Seismic source spectra and estimated stress drop derived from cohesive-zone models of circular subshear rupture

Yoshihiro Kaneko, & Peter M. ShearerPublished March 4, 2014, SCEC Contribution #1830

Earthquake stress drops are often estimated from far-field body-wave spectra using measurements of seismic moment, corner frequency, and a specific theoretical model of rupture behavior. The most widely-used model is from \citet{Madariaga76}, who performed finite-difference calculations for a singular crack radially expanding at a constant speed and showed that $\bar{f}_{\rm c} = k \beta/a$, where $\bar{f}_{\rm c}$ is spherically averaged corner frequency, $\beta$ is the shear-wave speed, $a$ is the radius of the circular source, and $k$ = 0.32 and 0.21 for $P$ and $S$ waves, respectively, assuming the rupture speed $V_{\rm r} = 0.9\beta$. Since stress in the Madariaga model is singular at the rupture front, the finite mesh size and smoothing procedures may have affected the resulting corner frequencies. Here we investigate the behavior of source spectra derived from dynamic models of a radially expanding rupture on a circular fault with a cohesive zone that prevents a stress singularity at the rupture front. We find that in the small-scale yielding limit where the cohesive-zone size becomes much smaller than the source dimension, $P$- and $S$-wave corner frequencies of far-field body-wave spectra are systematically larger than those predicted by \citet{Madariaga76}. In particular, the model with rupture speed $V_{\rm r} = 0.9\beta$ shows that $k = 0.38$ for $P$ waves and $k = 0.26$ for $S$ waves, which are 19 and 24 percent larger, respectively, than those of \citet{Madariaga76}. Thus for these ruptures, the application of the Madariaga model overestimates stress drops by a factor of 1.7. In addition, the large dependence of corner frequency on take-off angle relative to the source suggests that measurements from a small number of seismic stations are unlikely to produce unbiased estimates of spherically averaged corner frequency.

**Key Words**

earthquake dynamics, earthquake source observations, dynamics and mechanics of faulting

**Citation**

Kaneko, Y., & Shearer, P. M. (2014). Seismic source spectra and estimated stress drop derived from cohesive-zone models of circular subshear rupture. *Geophysical Journal International*, 197(2), 1002-1015. doi: 10.1093/gji/ggu030.

**Related Projects & Working Groups**

Earthquake Forecasting and Predictability