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High-frequency seismic wave radiation from antiplane cohesive zone model and f_max as source effect

NATIONAL RESEARCH INSTITUTE FOR EARTH SCIENCE AND DISASTER PREVENTION, TENNODAI, TSUKUBA 305 Japan
DISASTER PREVENTION RESEARCH INSTITUTE KYOTO UNIVERSITY, Japan

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 ^–2, and f_max cannot be properly defined. For case (1), we find that f_max = V_fL_f/L²_i, 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.