The Effects of Variable and Constant Rupture Velocity on the Generation of High-Frequency Radiation from Earthquakes

Abstract

A viewpoint exists that generation of seismic high frequencies results from sudden movements of ruptures, experiencing episodes of acceleration/deceleration. We investigated this effect theoretically for (1) the far field of a small near-line source and (2) the near field of a large fault computed exactly from the representation integral. The results indicate that, in both cases, the strength of the high-frequency radiation and the spectral fall-off for ruptures moving with constant positive or negative acceleration, as well as with regularly changing acceleration, are variable: depending on the parameters, they can exceed, be similar to, or fall below the levels produced by constant-velocity propagation. The directivity spectral levels for the scenarios of constant (positive or negative) acceleration, acceleration modulated by an orderly function, or constant velocity are fully controlled by regular interference: a particular high-frequency slope seen is an artifact of the case-specific interference. Randomization of rupture speed suppresses regular interference and creates an appearance of high-frequency generation by irregularity in the velocity, while in reality it is due to the elimination of artifacts. Realistic ruptures will always have a random component in their travel times, depending on fault and material properties, and will always exhibit elevated high-frequency content with respect to an idealized constant-velocity scenario. The conclusion is that interpreting this phenomenon as high-frequency generation by rupture irregularity would be incorrect. The additional ${\omega }^{-1}$ spectral roll-off, typically attributed to fault finiteness, is a consequence of the constant-velocity assumption. Removing the latter flattens the spectrum, even for a finite fault.