Apparent LFE Magnitude-Frequency Distributions and the Tremor Source

Abstract:

Over a decade since its discovery, it is disconcerting that we know so little about the kinematics of the tremor source. One could say we are hampered by low signal-to-noise ratio, but often the LFE signal is large and the "noise" is just other LFEs, often nearly co-located. Here we exploit this feature to better characterize the tremor source. A quick examination of LFE catalogs shows, unsurprisingly, that detected magnitudes are large when the background tremor amplitude is large. A simple interpretation is that small LFEs are missed when tremor is loud. An unanswered question is whether, in addition, there is a paucity of small LFEs when tremor is loud. Because we have both the LFE Green's function (from stacks) and some minimum bound on the overall LFE rate (from our catalogs), tremor waveforms provide a consistency check on any assumed magnitude-frequency (M-f) distribution.

Beneath southern Vancouver Island, the magnitudes of >10^5 LFEs range from about 1.2-2.4 (Bostock et al. 2015). Interpreted in terms of a power-law distribution, the b-value is >5. But missed small events make even this large value only a lower bound. Binning by background tremor amplitude, and assuming a time-invariant M-f distribution, the b-value increases to >7, implying (e.g.) more than 10 million M>1.2 events for every M=2.2 event. Such numbers are inconsistent with the observed modest increase in tremor amplitude with LFE magnitude, as well as with geodetically-allowable slips. Similar considerations apply to exponential and log-normal moment-frequency distributions. Our preliminary interpretation is that when LFE magnitudes are large, the same portion of the fault is producing larger LFEs, rather than a greater rate of LFEs pulled from the same distribution. If correct, this distinguishes LFEs from repeating earthquakes, where larger background fault slip rates lead not to larger earthquakes but to more frequent earthquakes of similar magnitude. One possible explanation, that LFEs represent the high-frequency end of a continuous spectrum of slip rates, and that large LFEs are just those where more of the slip occurs in the tremor frequency band, finds no support from stacked templates, in that the corner frequencies of both large- and small-magnitude LFEs are very similar (~2 Hz) and lie within our bandpass.