Scaling of the Tremor Source

The scaling of the tremor source quantifies the striking differences between tremor and regular earthquakes and offers clues on the underlying physics of this lately-discovered phenomenon. Recently, a compilation of various different types of slow slip events by Ide et al. (2007) suggested that durations of such events are linearly proportional to their seismic moments. Here I conduct a systematic study of source scaling of non-volcanic tremor using a consistent data stream for the September 2005 Cascadia ETS. Day-long horizontal-component seismograms from the small-aperture PA array above the Cascadia subduction zone are integrated, corrected for gain, and filtered from 1 to 5 Hz to highlight the tremor. Then envelopes of the horizontal records are stacked and lightly smoothed (low-passed below a varying frequency of 0.03 to 0.002 Hz). Tremor events are defined as intervals during which the envelope is greater than a threshold level. Durations of tremor events thus defined range from ~100 s to several hours. The envelopes of the tremor events are treated as time functions (moment- rates). Preliminary analysis of the shapes of the tremor time functions suggests a modest tendency for negative skewness - on average, these tremor events end slightly more abruptly than they start. An increasing peakedness (kurtosis) of the larger events is also seen. Moment of the tremor events is estimated assuming the signal consists of far-field direct S-waves emanating from the plate boundary below the array. I find that event duration is proportional to M00.85. This result does not depend on the absolute estimation of moment and appears robust - over a range of thresholds and smoothing periods, the exponent varies from 0.80 to 0.88, being commonly between 0.82 and 0.86. This allows for modest growth of the amplitude of tremor events with duration, which is clearly seen in the envelopes. This scaling contrasts strongly with that of regular earthquakes, which follow duration proportional to M00.33 over many orders of magnitude, and for which amplitudes grow strongly with increasing moment. That scaling occurs due to the rough proportionality of fault displacement, length, and width, and the imposition of a roughly constant value of rupture velocity by the dynamic stress propagation associated with earthquakes. One or more of these factors must be missing from tremor generation, and constraints on the spatial parameters will be useful in interpreting the scaling relation. The total moment released via tremor on a representative vigorous day of the 2005 ETS corresponds to that of a M5.3 earthquake. This suggests that the majority of slip in an ETS period occurs silently, without generating seismic signals in the bandwidth in which tremor is typically detected.