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Magnitude–Frequency Distribution of Volcanic Explosion Earthquakes Nishimura et al. Earth, Planets and Space (2016) 68:125 DOI 10.1186/s40623-016-0505-2 LETTER Open Access Magnitude–frequency distribution of volcanic explosion earthquakes Takeshi Nishimura1*, Masato Iguchi2, Mohammad Hendrasto3, Hiroshi Aoyama4, Taishi Yamada4, Maurizio Ripepe5 and Riccardo Genco5 Abstract Magnitude–frequency distributions of volcanic explosion earthquakes that are associated with occurrences of vulcan- ian and strombolian eruptions, or gas burst activity, are examined at six active volcanoes. The magnitude–frequency distribution at Suwanosejima volcano, Japan, shows a power-law distribution, which implies self-similarity in the system, as is often observed in statistical characteristics of tectonic and volcanic earthquakes. On the other hand, the magnitude–frequency distributions at five other volcanoes, Sakurajima and Tokachi-dake in Japan, Semeru and Lokon in Indonesia, and Stromboli in Italy, are well explained by exponential distributions. The statistical features are consid- ered to reflect source size, as characterized by a volcanic conduit or chamber. Earthquake generation processes asso- ciated with vulcanian, strombolian and gas burst events are different from those of eruptions ejecting large amounts of pyroclasts, since the magnitude–frequency distribution of the volcanic explosivity index is generally explained by the power law. Keywords: Magnitude, Exponential distribution, Power law, Explosion Introduction magnitude–frequency distributions are often termed Volcanic explosion earthquakes (hereafter termed EXs) power laws, which are interpreted to be related to fractal are earthquakes that are observed in vulcanian and properties and self-similar systems. strombolian eruptions, or gas bursts, which often accom- Since Minakami’s pioneering work in 1960, magnitude– pany strong air shocks or infrasonic signals. A pioneer frequency distributions have been investigated at active study by Minakami (1960) first defined EXs, classifying volcanoes (e.g., Tanaka 1967; Shimozuru et al. 1971; Tan- volcanic earthquakes into four types: A-, B-type, explo- aka et al. 1972; Del Pezzo et al. 1974; Rowe et al. 2000). sion earthquake, and tremor. He indicated that EXs These previous studies often plotted the number of EXs at Sakurajima, Japan, follow Ishimoto–Iida’s formula versus amplitude in double-logarithmic graphs to esti- −m of n(A) = kA , where n(A) represents the number of mate m values. However, most of the figures presented earthquakes with a maximum amplitude of A, m is the seem not to be well matched with the Ishimoto–Iida’s coefficient called Ishimoto–Iida’s m value, and k is a formula (power law). For example, Tanaka (1967) pointed proportional coefficient (Ishimoto and Iida 1939). This out a break in the Ishimoto-Iida’s formula at large ampli- relationship is linked to the Gutenberg–Richter equa- tudes for EXs at Sakurajima and interpreted the break as tion (G–R eq.) that explains the magnitude–frequency related to crater size. Magnitude–frequency distributions distribution of earthquakes in general, and the m value of EXs associated with strombolian eruptions at Akita- is related to the b value in the G–R eq. as m = b + 1 Komagatake, Japan, were explained by combinations of (Asada et al. 1950; Suzuki 1953). These observed two power laws using two m values (Tanaka et al. 1972). Rowe et al. (2000) examined the magnitude–frequency distribution of EXs associated with frequent strombo- *Correspondence: [email protected] lian explosions within the summit crater lake at Erebus 1 Department of Geophysics, Graduate School of Science, Tohoku University, 6‑3 Aramaki‑aza Aoba, Aoba‑ku, Sendai 980‑8578, Japan volcano, Antarctica. They showed that the distribution Full list of author information is available at the end of the article follows an approximate power law with b value of about © 2016 The Author(s). This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Nishimura et al. Earth, Planets and Space (2016) 68:125 Page 2 of 12 1.7 and pointed out that an inflection in the cumulative Tokachi-dake. The Sakurajima Volcano Research Center distribution curve may be due to low detection level of (SVRC) of Kyoto University started seismic observation small events, distinct source populations or a preferred at Sakurajima in 1968. Since then, seismic signals have median bubble size. These previous studies indicate that been recorded with an S-1000 seismometer at Haruta- EXs do not follow a simple relation as represented by the yama (HRT) station, which is 2.7 km from the active Ishimoto–Iida’s formula or G–R eq. Such divergence of crater at Minami-dake. The amplitudes of seismic and the magnitude–frequency distribution is also found for acoustic signals for vulcanian explosions have been con- volcanic tremors. Benoit and McNutt (2003) analyzed tinuously cataloged; here we analyze the 49-year period duration times and amplitudes of volcanic tremors and from 1963 to 2011. Vulcanian explosions frequently followed exponential rather than power-law scaling. occurred at Minami-dake crater until 2007; however, the Although magnitude–frequency distributions provide volcanic activity reduced after 2000 (Iguchi 2013). Since some of the most basic and important information to 2008, Showa crater, which is about 0.5 km southeast of understanding explosive eruption processes, investiga- Minami-dake, has been activated, while there have been tions of the statistical characteristics of EXs are limited few explosions at Minami-dake (Iguchi et al. 2013). In the in number. In the present study, therefore, we examine following analysis, therefore, we separate Sakurajima data the magnitude–frequency distribution characteristics of into two periods, from 1968 to 1999 and from 2008 to EXs at different volcanoes. The EXs we analyze are those 2011. The former represents the characteristics of explo- associated with vulcanian and strombolian eruption sions at Minami-dake, while the latter represents Showa styles and gas bursts at Sakurajima, Suwanosejima, and crater. Tokachi-dake in Japan, Semeru and Lokon in Indonesia, Figure 2 shows frequency distributions of the maxi- and Stromboli in Italy. Note that Plinian style explosive mum amplitudes of EXs at Minami-dake and Showa cra- eruptions are associated with eruption tremors (e.g., ter. For Minami-dake, maximum amplitude of EXs ranges McNutt and Nishimura 2008) rather than EXs, and they up to 0.3 mm and the cumulative number of events is are not the target of the present study. Since EXs are con- 2584, while for Showa crater, maximum amplitude is sidered to be caused by rapid conduit pressure changes in about 0.1 mm, and the total number of events is 2633. volcanic explosions, magnitude–frequency distributions The double-logarithmic graphs for both craters are con- provide us with the basic statistical attributes of erup- vex, indicating that the Ishimoto–Iida’s formula may not tions and clues to understanding eruption dynamics. We explain the observed magnitude–frequency distributions. examine the magnitude–frequency distribution of EXs at On the other hand, the cumulative number of EXs plot- the six volcanoes identified above and discuss their rela- ted in semilogarithmic graphs is well fitted by a straight tionship to the volcanic systems. line. This suggests that the EX magnitude–frequency dis- tributions at Sakurajima follow exponential rather than Magnitude–frequency distributions power-law scaling. Vulcanian eruptions at volcanoes in Japan We analyze seismic data from Suwanosejima vol- Figure 1a shows the locations of the volcanoes we cano for the period from January to June 2010, during analyzed in Japan: Sakurajima, Suwanosejima and which time about 120 small vulcanian eruptions were ab c Fig. 1 Locations of volcanoes analyzed. a Japan, b Indonesia, and c Italy Nishimura et al. Earth, Planets and Space (2016) 68:125 Page 3 of 12 a b Fig. 2 Magnitude–frequency distributions of explosion earthquakes at Sakurajima volcano, Japan, for a 1963–1999 (Minami-dake crater) and b 2008–2011 (Showa crater). Left-hand graphs have log–log scale, and right-hand ones semilogarithmic. Parameters of Nb, r and a0 represent the num- ber of bins, correlation coefficients and characteristic amplitude of the exponential distribution. Regression lines and correlation coefficients are in red. Regression lines and correlation coefficients in blue are determined from data with the five lowest-amplitude bins removed observed. We examine raw seismograms from a broad- their maximum amplitudes from the raw broadband band seismometer (STS-2, Streckeisen) located at SWA seismometer records. Figure 3 plots the cumulative station, about 500 m south of the active crater (Iguchi number of EXs versus maximum seismic amplitude in et al. 2008). Volcanic tremors associated with continu- double-logarithmic and semilogarithmic graphs. Con- ous ash emission were often observed during the explo- trary to the Sakurajima, the magnitude–frequency dis- sive activity at Suwanosejima, and eruptive activities tribution plots as linear in the double-logarithmic graph sometimes ceased for several weeks or more (Nishimura for Suwanosejima, suggesting a power-law relationship et al. 2013).
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