Duration‐amplitude distribution of volcanic tremor

Abstract

[1] The duration-amplitude distribution of volcanic tremor was examined in eight volcanoes and one geothermal area. An exponential model, implying a scale-bound source process, is found to be a better fit to the data than a power law (scale invariant) model. The exponential model well describes tremor associated with magmatic and phreatic eruptions, shallow and deep source regions, and geothermal sources. We tested the exponential model described by:ÀlD R , where d is the duration of tremor greater than or equal to a particular amplitude D R , d t is the total duration of tremor, and the inverse of l is the characteristic amplitude of the distribution. l À1 takes on values between 0.003 and 7.7 cm 2 . Our results show that the characteristic amplitude for eruptive tremor is greater than for noneruptive tremor, that for deep tremor is greater than for shallow tremor, and that for tremor associated with magmatic eruptions is greater than for tremor associated with phreatic eruptions. The exponential scaling of tremor suggests that tremor is not simply composed of a series of low-frequency events closely spaced in time. Further, the exponential scaling requires the source to be scale bound; the amplitude variations of tremor are distributed about a constant characteristic amplitude. We propose that exponential scaling of tremor amplitude is caused by fixed source geometry driven by variable excess pressures. The exponential scaling of tremor demonstrates that tremor source processes are fundamentally different from those for earthquakes.

Using volcanic tremor for eruption forecasting at White Island volcano (Whakaari), New Zealand

“…Instead, these distributions better fit an exponential model (Fig. 7b, Table 4), as predicted by Benoit et al (2003). They still present some non-linearity, with a generally steeper slope at high amplitudes.…”

“…Aki and Koyanagi (1981) proposed that the durationamplitude of deep tremor at Kilauea follows an exponential model implying a unique length scale for the tremor generating process which could be the average size of the conduit. This observation was later extended to other volcanoes and tremor types (Benoit et al, 2003). The last study also highlighted the possible change in slope of the duration-amplitude distribution or a change to a power law distribution if brittle fracture occurs, and the observation of several slopes in the distribution when several tremor generating processes are present.…”

“…Finally, we conducted a tremor scaling analysis (Benoit et al, 2003) to shed light on the number and potential nature of the processes involved. Aki and Koyanagi (1981) proposed that the durationamplitude of deep tremor at Kilauea follows an exponential model implying a unique length scale for the tremor generating process which could be the average size of the conduit.…”

Magnitude–frequency distribution of volcanic explosion earthquakes

“…Such divergence of the magnitude-frequency distribution is also found for volcanic tremors. Benoit and McNutt (2003) analyzed duration times and amplitudes of volcanic tremors and followed exponential rather than power-law scaling.…”

An approach to source characterization of tremor signals associated with eruptions and lahars

“…Quantifying the sources of these signals is important for understanding the dynamic processes associated with eruptions and lahars and for monitoring volcanic activity. Reduced displacement (D R ), a measurable quantity defined by Aki and Koyanagi (1981), has been used in various studies of tremor signals (e.g., Fehler 1983;McNutt 1992;Alparone et al 2003;Benoit et al 2003). McNutt (1994) showed that the volcanic explosivity index (VEI; Newhall and Self 1982) is correlated with D R estimated for eruption tremor, although McNutt (2004) later showed that there is a wide range of D R values for each VEI.…”