Abstract

While a high-frequency cutoff, fmax, 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 fmax, 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 ω−2, and fmax cannot be properly defined. For case (1), we find that fmax = VfLf/L2i, where Vf is the final crack velocity, Lf is the final rupture length, and Li is the initial crack size. We extrapolate this result to the rupture for a three-dimensional model and try to explain observed fmax. If we assume that an earthquake is a single crack, Li is large for a large earthquake. However, if we assume that an earthquake is made up of set of cracks and asperities, fmax 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 fmax will be nearly constant for all earthquakes.

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