On corner frequencies, attenuation, and low-frequency earthquakes

We have recently suggested that the nearly constant duration of low-frequency earthquakes (LFEs) (and, equivalently, the band limitation of tectonic tremor) manifests a moment-duration scaling that is fundamentally different from regular earthquakes and is most easily explained as rupture on asperities of roughly constant dimension. In that work, we employed qualitative arguments against potential bias by attenuation. Here we examine the role of attenuation more quantitatively through an analysis that avoids specification of particular source (e.g., Brune) models and relies on the particle velocity spectral maximum as the definition of apparent corner frequency. The analysis leads to the formal definition of a saturation frequency as the limiting value of apparent corner frequency as the true corner frequency tends infinity. The saturation frequency, a formal equivalent to f(max), can be used to set bounds on path-averaged quality factor Q. We apply these relations to deep crustal and intraslab earthquakes beneath Vancouver Island to estimate bulk crustal attenuation parameters that are subsequently used to correct apparent corner frequency measurements of LFEs reported in our earlier work. The attenuation bias due to bulk crustal structure is shown to be small, with negligible effect on the principal conclusions of that study. However, a review of laboratory and seismic refraction measurements of attenuation in oceanic basalts and evidence for high P-to-S LFE corner frequency ratios raises the possibility that strong, highly localized, near-source attenuation accompanying high pore-fluid pressures could cause the bandlimited nature of LFEs through the depletion of high frequencies.