Hiroyuki Fujiwara and Kojiro Irikura
High-frequency seismic wave radiation from antiplane cohesive zone model and f _max as source effect
Bulletin of the Seismological Society of America (August 1991), 81(4):1115-1128

Abstract:
While a high-frequency cutoff, f _max is widely observed in strong-motion seismic data, there is no consensus on whether it is due to source processes or to attenuation and scattering of high-frequency radiation in the crust or near the surface. To investigate the ability of source processes to control f _max we use a standard antiplane crack propagation formalism to numerically model the effect of rupture nucleation and arrest on high-frequency radiation based on a simple physical hypothesis, a slip-weakening model. We model rupture arrest due to three types of inhomogeneity: (1) a strong portion of rupture medium (barrier); (2) a drop in the pre-existing stress distribution of rupture medium; and (3) a finite length of unruptured medium (asperity) lying between previous ruptures. For cases (2) and (3) high frequencies fall off more steeply than omega (super -2) and f _max cannot be properly defined. For case (1), we find that f _max = V _f L _f IL _i ² , where V _f is the final crack velocity, L _f is the final rupture length, and L _i is the initial crack size. We extrapolate this result to the rupture for a three-dimensional model and try to explain observed f _max . If we assume that an earthquake is a single crack, L _i is large for a large earthquake. However, if we assume that an earthquake is made up of set of cracks and asperities, f _max will be determined by the interaction of small cracks and barriers. If the distribution of these cracks and asperities is independent of source size, then f _max will be nearly constant for all earthquakes.