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

Kaneko, Y, Shearer PM.  2014.  Seismic source spectra and estimated stress drop derived from cohesive-zone models of circular subshear rupture. Geophysical Journal International. 197:1002-1015.

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borehole, california, depth, dynamic rupture, Dynamics and, Earthquake dynamics, Earthquake source observations, earthquakes, energy, fault, mechanics of faulting, simulations, source parameters, source scaling relationships


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 behaviour. The most widely used model is from Madariaga in 1976, who performed finite-difference calculations for a singular crack radially expanding at a constant speed and showed that (f) over bar (c) = k beta/a, where (f) over bar (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-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 behaviour 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 the Madariaga model. In particular, the model with rupture speed V-r = 0.9 beta shows that k = 0.38 for P waves and k = 0.26 for S waves, which are 19 and 24 per cent larger, respectively, than those of Madariaga. 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.