Journal of Natural Disaster Science, Volume 38，Number 1，2017，pp65-83

Quantification of seismic and acoustic waves to characterize the 2014 and2015 eruptions of Kuchinoerabujima Volcano, Japan
Haruhisa Nakamichi, Masato Iguchi, Takeshi Tameguri, and Tadaomi Sonoda
Sakurajima Volcano Research Center, Disaster Prevention Research Institute, Kyoto University,（Received : Oct. 14, 2016

Accepted : May 29, 2017）

Abstract
At Kuchinoerabujima Volcano located in southwest Japan, eruptions occurred on August 3, 2014, andMay 29 and June 18, 2015. We evaluated the seismic and acoustic waves excited by these eruptions tocharacterize the eruptions. First, we estimated the eruption durations at a single station. The durations
were 50 s, 6 min, and 6 min for the eruptions on August 3, 2014, and May 29 and June 18, 2015,
respectively. The seismic and acoustic waveforms of the 2014 eruption have spindle shapes, while thewaveforms of the 2015 eruptions have initial impulsive phases followed by weak arrivals. These three
eruptions were phreatomagmatic in nature, as suggested by geological surveys. Second, we estimatedthe seismic and acoustic energies of the eruptions. The seismic and acoustic energies of the 2014
eruption were 1.88 GJ and 0.21 GJ, respectively. The seismic and acoustic energies of the eruption on
May 29, 2015 were 0.36 GJ and 2.2 GJ, respectively; and the seismic and acoustic energies of theeruption on June 18, 2015 were 0.3 GJ and 0.06 GJ, respectively. Third, we estimated the counter single
force excited by the eruptions on May 29 and June 18 by using seismic waveform matching at a
broadband station. The pulse width and amount of the counter force were lined on the scaling line for a
conduit pressure of 6 MPa. For the 2014 eruption, the short duration and spindle-like waveforms may
reflect that the eruption was short lived and initially weak, gradually becoming violent and forming
fissures, while the 2015 eruptions did not form new fissures.
Keywords：Kuchinoerabujima Volcano, seismic wave, infrasound, energy, single force

1. Introduction
To understand the eruption process and evaluate volcano hazards, it is important to quantify the amountof materials ejected by an eruption. The eruption column height is commonly used as an indicator of thesize of an eruption, because the discharge rate of ejected materials is approximately and empirically
proportional to the fourth power of the maximum column height (e.g., Sparks et al., 1997; Mastin et al.,2009), and the measurement is timely. However, the column height is strongly influenced by weather
conditions, especially the temperature gradient and wind speed (Wilson and Walker, 1987; Glaze andBaloga, 1996; Graf et al., 1999). The maximum column height is usually measured by visual inspections
with direct observations or remote cameras and is sometimes verified by radar and satellite
measurements. However, it is sometimes difficult to measure the maximum column due to bad weather.
A much better estimation of the amount of ejected materials is generally obtained by conducting ageological field survey. Ash-fall deposit measurements are conducted at several points at different
distances and azimuths from an eruption source. The volume of the fallout deposit is estimated by using
the relationship between the area covered by ash and the thickness of the fall deposit (e.g., Pyle, 1989).
However, deposit measurement is labor-intensive and time consuming.
Eruptions generally generate seismic and acoustic waves, the magnitudes and durations of which
may reflect not only the total mass and volume of erupted materials but also the explosivity of theeruptions. The amplitude of a volcanic tremor is empirically related to the volume of the ejectedmaterials (McNutt, 1994). McNutt and Nishimura (2008) proposed that the average discharge rate is thevalue of the total volume of ejected ash from an eruption divided by the duration of an eruption estimatedby the eruption tremor. Iguchi (2016) found that the monthly sum of ash weights correlates well with65

H.NAKAMICHI, M.IGUCHI, T.TAMEGURI, T.SONODA

the monthly sum of the seismic spectral amplitudes for the eruptions of Sakurajima Volcano andconstructed an empirical relationship between seismic amplitudes and ejected ash. Prejean and Brodsky(2011) applied the method for estimating the discharge rate using a single force obtained by a seismic
waveform analysis (Brodsky et al., 1999) to estimate the column heights of Plinian and Vulcanianeruptions. The discharge rate has been estimated based on infrasound data for explosive eruptions using
the relationship between pressure disturbances and density multiplied by the volumetric accelerationfrom monopole sources (e.g., Johnson et al., 2004). Seismic and acoustic observations can capture
signals from eruptions in a timely manner and are, therefore, important in the evaluation of seismic andacoustic waves for obtaining the size of an eruption, its explosivity, and its eruption process.
Kuchinoerabujima Volcano, southwest Japan (Fig. 1), has repeated phreatic andphreatomagmatic eruptions within the past 100 years following the oldest documented eruption in 1841
(Geshi and Kobayashi, 2007). Recently, the volcano erupted once in 2014 and twice in 2015. Since twoof the three eruptions occurred during bad weather, it was difficult to evaluate the size and explosivityof the eruptions. It is important to determine the size and explosivity of an eruption as soon as possible
even if weather conditions are poor and visual information of the eruption is not available. An
observation system near an active volcano generally has a few seismometers and infrasoundmicrophones. In this study, we evaluate the durations of the eruption and released energy based onseismic and infrasound records and the counter single forces for each eruption, which can be related toeruption size, strength, and process, by a single station.

Fig.1. Location of Kuchinoerabujima (Left) and station distribution at Kuchinoerabujima(Right). Web camera located at KEMN, with the lens pointed to Shindake crater. The
infrasound sensor (microphone) is located at KUCM (plus mark). Open inverted triangles
and open squares indicate seismic stations that belong to the Japan Meteorological Agency
and National Research Institute for Earth Science and Disaster Resilience, respectively.

2. The 2014 and 2015 eruptions of Kuchinoerabujima Volcano
Kuchinoerabujima is an andesitic volcanic island located to the south off Kyushu Island, Japan (Fig. 1).
Several magmatic eruptions occurred during 1931–34 and 1966–76 at Shindake crater, one of the central
cones (Geshi and Kobayashi, 2007). Although no eruption occurred during the 34 years since the fissure
eruption east of Shindake crater on September 28, 1980, an explosive eruption occurred at Shindakecrater on August 3, 2014 (hereinafter termed the 2014 eruption). Additional explosive eruptions
occurred at the crater on May 29 and June 18, 2015, and we refer to them as the 2015A and 2015B
eruptions, respectively. The explosive eruptions blew up the hydrothermally-altered materials and alsoa part of the intruded magma (Geshi et al., 2016). When the 2014 eruption occurred, Typhoon No. 12
was approaching the Ryukyu Islands, including Kuchinoerabujima, and it was windy around the island

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with the summit covered with clouds. Fortunately, no one was climbing the summit because of the badweather (One student party had cancelled their plan to climb). Under the prevailing windy weather
conditions, the ash column of the 2014 eruption rose to a height of 0.8 km from the rim of the crater anddrifted in the NNE direction, which was witnessed by the distant view camera at station KEMN (Fig. 1)(Japan Meteorological Agency, 2014). The pyroclastic density current (PDC) of the 2014 eruption
flowed down to ~2 km from the crater (Geshi et al., 2016). The 2015A eruption occurred during fineweather, and its ash column reached at least 9 km above the crater rim, which was witnessed by the
distant view camera at Yakushima (Fig. 1) (Japan Meteorological Agency, 2015). Its PDC flowed downfrom the summit area and reached a point ~3 km from the crater beyond the coastal line (Geshi et al.,2016). The 2015B eruption occurred during bad weather, so the height of the eruption column is
unknown. However, information about the direction of the eruption cloud was obtained. The PDC
current of the 2015B eruption with cloud cover around the summit was not observed by the distant view
camera at station KEMN. Lapilli fall was observed ~9 km ENE from the summit, and the ash fall was
distributed in the northern part of Yakushima and Tanegashima (Fig. 1) (Japan Meteorological Agency,2015).
3. Seismic and infrasound observation

Table 1. Operation status of seismic and infrasound stations during the three eruptions
StationSeismometer

Microphone

August 3, 2014

May 29, 2015

June 18, 2015

AroundShindake

Broadband Akashi V907
Short-period Akashi
J21-3DNA

NA

Operated until
the time of theeruption
Operated

Not operated

Not operated

Operated

Operated

Operated

Operated, but
communicationinterrupted
Only verticalcomponent
operated
Operated

Only verticalcomponent
operated
Only verticalcomponent
operated
Not operated
due to outage

Operated, but
communicationinterrupted,
and sensor
tiltedOperated

Operated

KUCM

Hakusan
SI-103U(until Jan.
21, 2015)
Hakusan
SI-104
Aco 7144

KEHT

Borehole Akashi JTS,
natural period of 1 s

KER4

Short-period L4C-3D,
natural period of 1 s

NA

KCFV

Broadband Trillium 240

NA

KCNV

Broadband Trillium 240

NA

KYKF

Broadband STS-2

NA

Only verticalcomponent
operated
Operated, butdata nottransmitted to
SVRC
Operated, butdata nottransmitted to
SVRC
Operated

Operated

Sakurajima Volcano Observatory (currently Sakurajima Volcano Research Center (SVRC)) began
continuous seismic observation at Kuchinoerabujima with a short-period three-component seismometerat 0.4 km west from Shindake crater in 1992. Three broadband seismometers were additionally installedaround the crater in May 2002 by the observatory. Japan Meteorological Agency (JMA) also beganseismic observations with one station near the crater in 1999 and added three stations around the craterin 2004. Both institutes also have seismic and infrasound stations on the flank of the volcano (Fig. 1 andTable 1). The National Research Institute for Earth Science and Disaster Resilience (NIED) was

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H.NAKAMICHI, M.IGUCHI, T.TAMEGURI, T.SONODA

constructing two stations (KCFV and KCNV) on the flank in 2014 and started retrieving broadband
seismic data on May 22, sending data to JMA beginning on August 7. However, the installation of
borehole seismometers and tiltmeters at the two NIED stations was halted by the 2014 eruption.
Infrasound sensors are deployed at stations KUCM of SVRC, and two stations of JMA (at KEHT andnear KUCM). We did not use these two JMA infrasound records, because the records of the 2015A
eruption are saturated at KEHT and have abnormally small amplitude at the other site. The three
institutes, SVRC, JMA, and NIED, have been sharing data since the 2014 eruption using the JDX net(Takano et al., 2008), a system for exchanging and distributing real-time seismic data over the JGN and
SINET high-speed networks in Japan (Urushidani and Matsukata, 2008). KYKF station located atYakushima (Fig. 1) is one of a nation-wide broadband seismic network (F-net) of stations (Okada et al.,2004).
The stations around the summit were destroyed due to the scattered ballistic blocks of the 2014
eruption (Geshi et al., 2016). The seismic waves excited by the eruption were obtained at the stations
until the ballistic blocks bombarded the stations (Iguchi et al., 2017). Since the 2015A eruption, datatransmissions from the stations on the flank have been frequently interrupted to SVRC due to outages
at the settlements on Kuchinoerabujima by landslides and lahars. Table 1 shows a list of stations used inthis study, indicating the models of the seismometers and infrasound microphones and the data retrieval
status. There is no period when data from all stations are available for the 2014, 2015A, and 2015B
eruptions. In this study, therefore, we use limited numbers of stations for analyzing the seismic andacoustic waves excited by the eruptions.
4. Characteristics of seismic and acoustic waves and estimation of duration of eruptions
We estimate the durations of the eruptions using the seismic and acoustic waves associated with theeruptions. We carefully investigated the characteristics of the waveforms from all available data of thestations as shown in Fig. 1 and Table 1. Figure 2 shows examples of the seismic and acoustic waveforms
associated with the eruptions. The duration of an eruption is defined as follows: (1) The onset time of
the infrasound signal excited by the eruption is measured. (2) The termination time of the infrasoundsignal is measured by judging whether the signal level is above the background noise. (3) The durationof the infrasound signal is equal to the time difference between the onset and termination times but isrounded off to the nearest 10 s. (4) The corresponding signal on a vertical component seismogram isalso inspected using the same procedure as that for the infrasound signal. However, it is difficult todefine the termination time of the seismic signal of the eruption because the seismogram is contaminatedwith the seismic events that occur beneath and around the volcano. For example, several small seismic
events are seen before and after the infrasonic signal arrivals (see Fig. 2a). Therefore, we adopt the
duration of the infrasound signal as the duration of the eruption. As a result, the durations are 50 s, 6min, and 6 min for the 2014, 2015A, and 2015B eruptions, respectively (Fig. 2). The 6-min duration of
the 2015A eruption is consistent with the witness report (Uhira and Toriyama, 2015), documenting thatstrong explosive activity of the 2015A eruption ended within 10 min, followed by a low and continuous
emission of steam. The infrasound record of the 2014 eruption is very noisy due to microseism excitedby Typhoon No. 12; therefore, the record is filtered in a pass-band greater than or equal to 0.5 Hz (Fig.
2b).

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Fig.2. Comparison of short-period seismic and infrasound waveforms (black lines) and theirenvelope (gray lines) of the 2014 and 2015 eruptions. (a) (b) seismic and infrasound recordof the 2014 eruption, respectively. (c) (d) seismic and infrasound record of the 2015A
eruption, respectively. (e) (f) seismic and infrasound record of the 2015B eruption,
respectively. All records are unfiltered, except for the infrasound record (b) of the 2014
eruption, which is filtered in a pass-band greater than or equal to 0.5 Hz. The envelopes
are shown in log scale.
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The overall shapes of the infrasound and seismic waveforms of the three eruptions are different,
although the three eruptions are commonly categorized as phreatomagmatic eruptions (Geshi et al.,2016). Figure 3 shows the infrasound and vertical seismic records for the three eruptions. The infrasoundrecord of the 2014 eruption is filtered in a pass-band greater than or equal to 0.5 Hz (Fig. 3a). The
envelope of the infrasound and seismic waves is spindle-like for the 2014 eruption (Fig. 3a, d). This
spindle-like shape was also found on the seismic signal associated with the 2014 phreatic eruption at
Mt. Ontake (Kato et al., 2015). However, the shapes of the 2015A and 2015B eruptions are different
from that of the 2014 eruption and have an impulsive large first arrival phase, which is followed bylong-tail small amplitude arrival phases (Fig. 3b, c, e, f). This pattern is found on both the infrasoundand seismic waveforms and is also found on small Vulcanian eruptions (e.g., Fee and Matoza, 2013;
Yamada et al., 2016). The characteristics of the waveforms of the 2015 eruptions are somewhat different,
as the acoustic wave of the 2015A eruption has clear secondary impulsive and minor third phases about
2 s and 5 s after the first impulsive phase, respectively (Arrows in Fig. 3b). The first, secondary andthird phases of the infrasound record correspond to those of the seismic record, but the first andsecondary seismic phases overlap each other and the third is obscure (Fig. 3e). The maximum amplitudesof the infrasound signals of the three eruptions are different, while there is no significant difference
between those of the seismic signals (Fig. 3d, e, f). The infrasound maximum amplitude of the 2015A
eruption is 230 Pa, and the minimum is -110 Pa (Fig. 3b). This amplitude variation is much larger thanthose of the 2014 and 2015B eruptions (Fig. 3a, c).

Fig.3. Comparison of short-period seismic and infrasound waveforms of the 2014 and 2015
eruptions. (a), (b) and (c) are infrasound records of the 2014, 2015A and 2015B eruptions,
respectively. (d), (e) and (f) are vertical seismic records of the 2014, 2015A and 2015B
eruptions, respectively. All records are unfiltered, except for the infrasound record (a) of
the 2014 eruption, which is filtered in a pass-band greater than or equal to 0.5 Hz. Note thatthe arrival time differences between seismic and infrasound waves are about 5, 10 and 20 s
for the 2014, 2015A and 2015B eruptions, respectively.
Note that the arrival time difference between the seismic and infrasound signals is about 5 s forthe 2014 eruption while those for 2015A and 2015B are about 10 and 20 s, respectively (Fig. 3).
Comparing arrival times of seismic waves of distant regional earthquakes for the stations in the island,
we did not find any significant time differences between them and any timing problem due to GPS timecorrection failure. The arrival time difference of the infrasound signals between KUCM and KEHT was
2.7, 0.9 and 1.3 s for the 2014, 2015A and 2015B eruptions, respectively. Considering the sound speedof 0.34 km/s and station distances from the crater, the arrival time difference was estimated to be 1.4 s.
The arrival time difference is partially explained by the difference of station distances between KUCM
and KEHT. However, it is impossible to explain the change of the time difference between the seismic
and infrasound signals from 5 to 20 s for the 2014 and 2015 eruptions. Although detailed discussions of
the change are beyond the scope of this paper, the change of the time difference could reflect a change

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in physical properties and/or a migration of the seismic source in the conduit, as suggested for explosions
at Stromboli (Ripepe et al., 2001).
5. Seismic and acoustic energy
Seismic energy is calculated from the time integral of the squared velocity of the seismogram. Assuming
an isotropic source at the top of a homogeneous half space, the seismic energy in terms of body waves
is shown by Johnson and Aster (2005) as:
𝐸#$%#&%' = 2𝜋𝑟 , 𝜌$./01 𝑐$./01

3
4

𝑆 , 𝑈 𝑡 , 𝑑𝑡

(1)where r is the source station distance, 𝜌$./01 is the density of the medium, 𝑐$./01 is the body wave
propagation speed, S is the site response, U(t) is the seismic velocity amplitude, and t is the time. Here
S is assumed to be 1 because the site effect is not evaluated in this study. The term A is the attenuation
factor of seismic energy defined by:
𝐴 𝑟 = 𝑒 ;,<=/ ('?@ABC D)(2)

where f is the predominant frequency of the seismic wave, and Q is the quality factor.
Low-amplitude infrasound propagates with an energy density that is proportional to the square of theexcess pressure ( ∆𝑃 ) divided by the air density ( 𝜌.0&H# ) and sound speed ( 𝑐.0&H# ). Assuming
isotropic radiation, as from a point source monopole, the acoustic energy is shown by Johnson (2003)
and Johnson and Aster (2005) to be:
𝐸.'HI#0%' =,</ J
K@BLMN '@BLMN∆𝑃 𝑡 , 𝑑𝑡(3)Both seismic and acoustic signals are filtered with a two-pole Butterworth band-pass filter of 0.5–12 Hz.
This pass-band is the same as that used for seismic waves excited by Strombolian eruptions at Karmsky
and Erebus Volcanoes (Johnson and Aster, 2005) and Vulcanian eruptions of Popocatépetl Volcano(Arámbula-Mendoza et al., 2013). Here, we assume the parameters as 𝜌$./01 = 2000 kg/m3, 𝑐.0&H# =2.5 km/s, f = 6 Hz, which is the center of the pass-band, and Q = 65 for the seismic energy, and as
𝜌.0&H# = 1.2 kg/m3, 𝑐.0&H# = 0.34 km/s for the acoustic energy. The seismic energy can depend on
the parameters; therefore, we will discuss the dependency later. To characterize the acoustic energy
corresponding to the eruptions, we integrate over a time window spanning the entire duration of theacoustic transient. The integral is calculated from the signal onset until the time when both seismic andacoustic amplitude have decayed to background levels. The seismic energy for each component of theseismogram is calculated, and we sum the three-components of the seismic energy to obtain the threecomponent seismic energy.
Figure 4 shows the acoustic and seismic energy rate (energy per second) and their cumulative energy(total acoustic and seismic energy) for the three eruptions. For the 2014 eruption, there are three acoustic
energy arrivals and the middle one is the largest (Fig. 4a top), reflecting the spindle-like shape waveform(Fig. 3a). Two distinct seismic energy arrivals are found; the first one corresponds to the acoustic energy
arrivals, but the second one does not (Fig. 4a middle lower). For the 2015A eruption, two distinct
acoustic energy arrivals exist and correspond to two distinct seismic energy arrivals (Fig. 4b top andmiddle lower). However, there are minor seismic energy arrivals following the distinct arrivals (Fig. 4b
middle lower), while this is not the case for the acoustic energy (Fig. 4b top). For the 2015B eruption,
one distinct energy arrival commonly exists, and the arrival is followed by minor energy arrivals forboth seismic and acoustic energies. Note that the arrival time difference between the acoustic andseismic energy peaks is about 5 s for the 2014 eruption while those for 2015A and 2015B are about 10
and 20 s, as shown previously in Fig. 3. It is difficult to explain the time differences by the travel timesof seismic waves. Because the horizontal distances from Shindake crater to the stations are different and71

H.NAKAMICHI, M.IGUCHI, T.TAMEGURI, T.SONODA

are 2.35 km, 1.5 km, and 1.6 km for stations KEHT, KCFV, and KCNV, respectively, the time differenceof the travel times is less than 0.3 s.

Fig.4. Sismic and acoustic and cumulative seismic and acoustic energies for the (a) 2014, (b)2015A, and (c) 2015B eruptions. For each eruption, acoustic energy, cumulative
acoustic energy, seismic energy, and cumulative seismic energy are shown from the
top to the bottom. For the seismic energy, red, green, and blue lines show vertical,
north-south and east-west components, and black lines show the total of the threecomponents.
The total cumulative acoustic and seismic energies are measured at flat levels of the cumulative
energy flux (Fig. 4 middle, upper, and bottom). The total cumulative acoustic energy is 0.212 GJ, 2.20
GJ, and 0.0648 GJ for the 2014, 2015A, and 2015B eruptions, respectively. The total cumulative seismicenergy is 1.88 GJ, 0.358 GJ, and 0.296 GJ for the 2014, 2015A, and 2015B eruptions, respectively. The
sum of both total cumulative seismic energies is 2.09 GJ, 2.55 GJ, and 0.361 GJ for the 2014, 2015A,
and 2015B eruptions, respectively.
The volcanic acoustic-seismic ratio (VASR) is the ratio of the acoustic to seismic energies(Johnson and Aster, 2005), 𝜂 = 𝐸.'HI#0%' 𝐸#$%#&%' . The VASR is a non-dimensional parameter, which
may be related to different explosion mechanisms, and their physical interpretations may be useful incomparing processes at an individual or various volcanoes (Johnson and Aster, 2005). The VASR values
for the 2014, 2015A, and 2015B eruptions are 0.11, 6.1, and 0.22, respectively. Figure 5 shows
comparisons between the total cumulative acoustic and seismic energies, and the slope corresponds to
VASR. The colored hatched regions correspond to the seismic and acoustic energies for Strombolian
eruptions at Karymsky and Erebus (Johnson and Aster, 2005), and the pluses correspond to those for
Vulcanian eruptions at Popocatépetl, Mexico (Arámbula-Mendoza et al., 2013). Because Vulcanianeruptions are more energetic than Strombolian eruptions, the seismic and acoustic energies of the
Vulcanian eruptions are greater than those of the Strombolian eruptions. The data points for the 2014
and 2015 eruptions at Kuchinoerabujima are located in the region of the Vulcanian eruptions at
Popocatépetl.

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Fig.5. Comparison between total seismic and acoustic energies for the (a) 2014, (b) 2015A, and(c) 2015B eruptions. Each inclined line has a constant volcanic acoustic-seismic ratio(VASR). The black triangle, open circle and open diamond correspond to the 2014, 2015A,
and 2015B eruptions, respectively. The colored hatched oval regions roughly trace the total
seismic and acoustic energies for explosive eruptions at other volcanoes. The gray andbrown regions show Strombolian eruptions at Karymsky, Russia, and Erebus, Antarctica(Johnson and Aster, 2005). The pluses show moderate Vulcanian eruptions at Popocatépetl,
Mexico (Arámbula-Mendoza et al., 2013).

6. Single force analysis
In this section, a single force analysis is conducted for comparison of the size of eruptions. Here weanalyze the 2015A and 2015B eruptions, because the 2014 eruption formed several fissures around
Shindake crater as described previously (Geshi et al., 2016) and its source mechanisms might not be
explained by a single force. When the 2015A eruption occurred on May 29, 2015, two broadband seismic
stations, KCFV and KCNV, were operating (Table 1). However, in this study, the broadband
seismograms of KCNV of the 2015A eruption were not used for the analysis because the tilt step
response of a broadband seismometer was shown in the record, as shown in a comparable experiment
between a tiltmeter and a broadband seismometer (Aoyama, 2008). The tilt step may be generated byfallen ballistic blocks of the eruption around KCNV station. When the 2015B eruption occurred on June18, 2015, only one broadband station (KCNV) operated (Table 1).
The seismic wave excited by the 2015A eruption is dominant in the frequency band of 0.1–1 Hz,
and its dominant frequency is 0.8 Hz, which is evaluated by consulting its power spectrum of thebroadband record at KCFV station. To understand the nature of the first arrival phase of the seismic
record of the 2015A eruption, we plot the particle motion for the first arrival phase of the seismic recordin Fig. 6. To avoid the influence of high-frequency noise and low-frequency fluctuation, the records ofvertical, radial, and transverse components were band-pass filtered between 0.1–1 Hz. We find that theradial linear motion of particles in the radial-transverse plane and the retrograde motion of particles fromwell-expressed ellipses in the vertical-radial plane are characteristics of Rayleigh waves. By using thesame band-pass filter, we also find that the first arrival phase of the seismic record of the 2015B eruption
has characteristics of Rayleigh waves. We focus on the first arrival phases and do not discuss the highfrequency later arrival phases for the 2015A and 2015B eruptions.

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Fig.6. Waveforms and particle motions recorded at KCFV station filtered in the 0.1 - 1 Hz bandfor the beginning of the 2015A eruption at 9:59 JST on May 29, 2015. (a) Filtered vertical,
radial, and transverse waveforms. The radial direction is from Shindake crater to the station;
the transverse direction is perpendicular to the radial direction and clockwise. Particle
motions of the signals within the windows marked by vertical gray dashed lines are plottedin (b). Particle trajectories start at the circles and end at the triangles. (b) On the left panel,
the north-south motion is plotted versus the east-west motion. The middle and right panels,
where transverse and vertical motions, respectively, are plotted against radial motion,
display retrograde motion of Rayleigh waves.
The Rayleigh nature of the seismic wave representing the first arrival phase allows us to use themethodology of modeling the first arrival phase as a Lamb’s pulse with an estimation of the counter
force of the eruption (Kanamori and Given, 1983). This nature is also reported for explosion earthquakes
at Mt. Asama (Nishimura and Hamaguchi, 1993; Nishimura and Uchida, 2005), Mt. Tokachi (Nishimura,1995), Mt. Colima (Zobin et al., 2006a, 2006b), and Mt. Popocatépetl (Cruz-Atienza et al., 2001). We
estimate the amount of force at the eruption source and the time width of the force by comparing thethree-component broadband seismograms at KCFV and KCNV to their theoretical ones for the 2015A
and 2015B eruptions, respectively. The epicenter of the force is fixed at the center of Shindake crater,
but the depth of the force is variable and grid-searched by the following procedure.

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Table 2. One-dimensional structure of densities, P- and S-wave velocities, and quality factors. The
structure as shown with values in parentheses at Layers 1 and 2 is used for station KCNV.
Layer

Density (g/cm3)

VP (km/s)

VS (km/s)

QP

QS

Thickness (km)11.91 (2.36)

2.00 (3.80)

0.61 (2.11)

50 (100)

30 (50)0.2

22.25 (2.36)

3.10 (3.80)

1.50 (2.11)

80 (100)

40 (50)

0.2

3

2.36

3.80

2.11

100

50

0.2

4

2.39

4.00

2.28

100

50

0.4

5

2.43

4.30

2.52

100

50

0.5

6

2.48

4.60

2.74

150

80

0.5

7

2.53

5.00

3.01

150

80

0.5

8

2.58

5.30

3.19

200

100

1.5

9

2.70

5.96

3.52

220

100

2.0

10

2.72

6.02

3.56

250

110

2.0

11

2.74

6.10

3.60

250

110

2.0

12

2.76

6.18

3.63

330

150

2.0

Fig.7. Velocity and density structures used for calculation of synthetic waveforms for KCFV
(black lines) and KCNV (grey lines at a depth of 0–0.4 km corresponding to Layers 1 and
2, see Table 2).

75

H.NAKAMICHI, M.IGUCHI, T.TAMEGURI, T.SONODA

We calculated the time domain synthetic seismograms excited by a single vertical pulse ofcounter force F originating at depth D beneath the crater and recorded at distances of 1.5 km and 1.65
km, between the crater and KCFV and KCNV stations, respectively (Fig. 1). Depth D = 0 km is defined
to be the heights (0.16 km and 0.18 km above sea level) of station KCFV and KCNV, respectively. We
use the discrete wavenumber method (Bouchon, 1979, 1981) and the reflection and transmission
coefficient matrices (Kennett and Kerry, 1979) for calculating the synthetic waves using a flat layered
one-dimensional (1-D) structure (Table 2 and Fig. 7). The 1-D VP structure is extracted from results ofthe 2004 active source experiment (Iguchi et al., 2005). The 1-D VS and density structure are converted
band-pass filtered between 0.1–1 Hz. The squared error of the vertical and radial components between
the observed and synthetic waveforms is calculated for a 2-s time window (number of samples: Ns = 41)
that contains the first arrival phase. Note that a transverse component is not excited by the synthetic
calculation, because the counter source is a vertical direction force and axially symmetric, and the 1-D
structure is assumed. Squared error E follows the definition by Ohminato et al. (1998) for the single
station case as follows:
𝐸=

J
PVW

TN
Q
S
UVW IP R∆0 ;IP R∆0J
TNQ
J
PVW UVW IP R∆0

J(4)

where 𝑢YZ 𝑝∆𝑡 represents the p-th sample of the n-th data component and 𝑢Y\ 𝑝∆𝑡 represents the pth sample of the n-th component of the synthetic waveforms. We change the three parameters of depthD, pulse width t, and amount of force F to seek the minimum of squared error E. Depth D varies from0.01 to 0.25 km with an interval of 0.01 km, from 0.25 to 0.4 km with an interval of 0.05 km, and from
0.4 to 1 km with an interval of 0.1 km. Pulse width t varies from 0.2 to 2.0 s with an interval of 0.1 s.
Force F varies at 5 × 109, 1 × 1010, 1.5 × 1010, 2 × 1010, 5 × 1010, and 1 × 1011 N. Finally, we find thebest-fit model with the minimum squared error of E = 0.546 and E = 0.469 for the 2015A and 2015B
eruptions, respectively. For the 2015A eruption, the best-fit parameters of D, t, and F are 0.19 km, 0.9s, and 1.5 × 1010 N, respectively. For the 2015B eruption, parameters D, t, and F are 0.16 km, 1.6 s, and5 × 1010 N, respectively. Taking into account the height of the station, source depths D for the 2015A
and 2015B eruptions are 30 m and 0 m below sea level, respectively. Figure 8 shows a comparison
between the observed and synthetic waveforms, which are band-pass filtered between 0.1–1 Hz. The
synthetic waveforms are calculated for the best-fit parameters. The good fit between the observed andsynthetic waveforms for vertical and radial components indicates that the observed features are fairly

Fig.8. Waveform matches obtained by the single force analysis. (a) Station KCFV of the 2015A
eruption. (b) Station KCNV of the 2015B eruption. Solid black and dashed gray lines epresent
the observed and best-fit synthetic seismograms, respectively.
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Journal of Natural Disaster Science, Volume 38，Number 1，2017，pp65-83

well reproduced by the synthetic waveforms calculated for the best-fit solutions of both eruptions.
However, discrepancies in the waveform fits may occur because the source may not be simply
represented by a vertical single force or unknown structure, and a topographic effect may exist. The
unmolded source, unknown structure, and topography will be taken into account in future waveform
fittings, which are beyond the scope of this study.
In order to verify the obtained best-fit parameters, we compare the observed and synthetic
waveforms for KYKF station. The observed waveforms at KYKF are corrected with the response of theSTS-2 broadband seismometer and band-pass filtered between 4 and 40 s to reduce long-period
microseisms excited by ocean waves. Since the velocity structure between Kuchinoerabujima andYakushima Island is unknown, it is difficult to match observed and synthetic seismograms of KYKF
station for the eruption earthquakes. Therefore, we just compare the amplitudes between the observed
and synthetic waves for the 2015A eruption. We do not compare the amplitudes for the 2015B eruption,
because the long-period (>10 s) seismic signals excited by the 2014B eruption are not clear at KYKF
station (Matsuzawa et al., 2016). The amplitudes of the radial component of the response-corrected andfiltered seismograms are about ±1.5 µm/s for the first arrival phase of the 2015A eruption. For thesynthetic calculation, depth D, pulse width t, and force F are fixed to 0.19 km, 0.9 s and 1.5 × 1010 N,
respectively. The amplitude of the filtered synthetic radial waveform is ±1.9 µm/s. Since the difference
between the observed and synthetic seismic amplitudes is not significant, the best-fit parameters areverified by the records from KYKF station.
7. Discussion
Estimation of seismic energy can depend on the assumed parameters. Here we evaluate the dependencyof quality factor Q and body wave propagation speed cearth. For volcanic regions, quality factor Q varies
from 10 to 100 at shallow depths, which is less than 5 km (e.g., Clawson et al., 1989). Johnson and Aster(2005) and Arámbula-Mendoza et al. (2013) adopted the quality factor value of Q = 10, which is thelowest value of Q. To evaluate the dependency, we calculate the seismic energy by using several sets ofquality factors and speeds as shown in Table 3. The seismic signals are filtered with the same band-passfilter of 0.5–12 Hz. Seismic energy is calculated for the case of a body wave propagation speed cearth =1.4 km/s corresponding to the S-wave velocity at shallow layers (Layers 1 and 2 shown in Table 2),
although the original energy calculation is performed using a wave-speed value corresponding to the Pwave velocity at the shallow layers. The dependency of the propagation speed of the seismic wave type
is not significant compared to the dependency of the quality factor. The largest difference exists between
the quality factors of Q = 10 and others. For example, there is about 10 times difference between Case
1 and 2. Therefore, the seismic energy might be an overestimate for the case of Q = 10.

Table 3. Comparison between cumulative seismic energies and assumed parameters.
Case

Quality factor

cearth (km/s)

Cumulative seismic energy
(GJ)
2014

2015A

2015B

1

10

1.4

19.0

1.27

1.15

2

65

1.4

1.31

0.230

0.186

3

100

1.4

1.10

0.206

0.166

4

10

2.5

8.43

0.931

0.800

5

65

2.5

1.88

0.358

0.296

6

100

2.5

1.71

0.336

0.270

77

H.NAKAMICHI, M.IGUCHI, T.TAMEGURI, T.SONODA

The 2014, 2015A, and 2015B eruptions commonly produced pyroclastic materials consisting ofa mixture of various types of rock fragments (Geshi et al., 2016). These eruptions blew up thehydrothermally-altered materials and also a part of the intruded magma, which is suggested by
precursory phenomena (Iguchi et al., 2017). The volcanic ashes are mainly composed of thehydrothermally-altered rock fragments. The lapilli consist of both fresh and crystalline rock fragments
and hydrothermally-altered lava fragments (Geshi et al., 2016). However, the difference between the2014 and 2015 eruptions is the formation of fissures. The 2014 eruption formed two eruption fissureswith north-south and ENE-WSW trends, which traced the eruption fissures formed in the 1931 eruption(Geshi et al., 2016). The 2015A and 2015B eruptions occurred at the bottom of Shindake crater.
Although the depth of Shindake crater increased after the eruptions, there was no significant change inthe horizontal outline of the crater, and the fractures formed by the 2014 eruption remained after the2015 eruptions (Geshi et al., 2016).
The duration and shape of the seismic and acoustic waveforms of the 2014 eruption are quite
different from those of the 2015A and 2015B eruptions. The difference may be related to the formationof fractures in Shindake crater. As described previously, the duration of the 2014 eruption was 50 s,much shorter than the 6 min durations of the 2015 eruptions (Fig. 2). The seismic and acoustic
waveforms of the 2014 eruption have a spindle-like shape (Fig. 3), suggesting that the eruption was
initially weak, gradually became violent, and then stopped. The eruption energy of the 2014 eruption
was largely used for forming new fractures and was also converted to seismic energy during theformation of the fractures. The remainder of the energy during and after the formation was converted toacoustic energy, resulting in the low VASR of 0.47 (Fig. 5). The seismic energies for the 2015 eruptions
were lower than those for the 2014 eruption, as no new fissures were formed in the crater by the 2015
eruptions. The seismic energy was roughly the same for the 2015A and 2015B eruptions, while theacoustic energy of the 2015A eruption was over 30 times larger than that of the 2015B eruption, resulting
in the high VASR value for the 2015A eruption (Figs. 4 and 5). Although both the 2015A and 2015B
eruptions had explosive eruption natures, the strength of the capped conduit (ballistics plug) below thecrater before the occurrence of the eruptions may have been different for both eruptions, as the strengthof the 2015A eruption was much larger than that of the 2015B eruption as seen in the difference of theacoustic energy and maximum amplitudes (Figs. 3 and 4).
In this study, we did not apply the single force method to the 2014 eruption, because we believethat the source mechanism of the 2014 eruption earthquake was not simply expressed by a single force
and possibly had shear faulting components. As described previously, the 2014 eruption formed fissures,
which may have been promoted by the structural instability of the edifice of Shindake (Geshi et al.,2016). Several eruption fissures had been formed by the previous 1931, 1945, and 1980 eruptions andwere promoted by the westward sliding of the edifice of Shindake (Geshi et al., 2016). This westward
sliding may be caused by an east-west extensional stress, which is supported by the normal fault typemechanisms with the WNW-ESE extension of the shallow volcano-tectonic (VT) earthquakes (Triastuty
et al., 2009). The source mechanisms of the 2014 eruption earthquake will be investigated considering
the normal faulting component in a future study.
As seen in the movie from the camera at KEMN station, the 2015A eruption initially ejectedvertically and then ejected an inclined blast in the NWN direction 5 s afterward. As seen in Fig. 6, theinitial arrival phase corresponds to the initial vertical ejection, but the arrival phase that corresponds tothe inclined blast is not clear. Matsuzawa et al. (2016) elucidated the vertical component of the single
force and the horizontal force component that is directed in a north-south direction and suggested that
this horizontal force corresponds to the blast. Therefore, the inclined counter force will be applied in a
future study as it is beyond the scope of this study. Matsuzawa et al. (2016) point out that the peak
amplitudes of the horizontal single force are similar to that of the vertical force, and, in addition, theinitial phase of the vertical force precedes that of the horizontal by several seconds. In our case, only the
initial phase is modeled. The discrepancy between the observed and synthetic waveforms for the verticaland radial components (Fig. 8) may be reduced by the waveform modeling taking into account the more
complex seismic sources, including an inclined force and or moment tensor and also the topographic
effects of the volcano edifice (e.g., Ohminato and Chouet, 1997).
Seismic waves excited by explosive eruptions have frequently been modeled by the waveform
inversion technique assuming a counter downward force (e.g., Kanamori et al., 1984; Nishimura andHamaguchi, 1993; Ohminato et al., 2006). As described previously, the seismic waves excited by the78

Journal of Natural Disaster Science, Volume 38，Number 1，2017，pp65-83

2015 eruptions are also modeled by the counter force model. Nishimura and Hamaguchi (1993)
proposed the relationship between the counter forces and pulse width using the following scaling law:log 𝐹 = 2 log 𝜏 + 2 log 𝑣 3 + log 𝑃 + log 𝜋 (5)where v is the initial particle velocity of the flow of the ejected materials of an eruption and P is theinitial pressure in a conduit before the eruption. The lines for the scaling law are shown for initialpressure P = 0.1, 1, and 10 MPa in Fig. 9. The counter forces and the pulse widths of the single forces
for the 2015A and 2015B eruptions are shown on the scaling line for the pressure of 6 MPa (Fig. 9). We
compare the results of the 2015A and 2015B eruptions with the results of several volcanoes around theworld (Fig. 9). The counter force and pulse width for the 2015A eruption are the same as that of the
Vulcanian eruptions of Tokachi-dake, Japan in 1989 (Nishimura, 1995; Kato et al., 2002). The counter
force and pulse width of the 2015B eruption are similar to those of the Vulcanian eruptions of Mt. Asama
in 1983 and 2004 (Nishimura and Uchida 2005; Ohminato et al., 2006) and Mt. Colima in 2003 (Zobin
et al., 2006a), 2004 and 2005 (Zobin et al., 2006b). The points of the counter forces and pulse widths
for the 2015 eruptions are located between the scaling lines for the pressure of 0.1–10 MPa (Fig. 9). The
2015A and 2015B eruptions lie in the higher-pressure regime, suggesting a higher internal pressure in
the conduit below the crater before the eruption occurred.

Fig.9. Relationship between the counter force of eruption F and the pulse width of single force t
for the explosion earthquakes for a group of volcanoes of the world. The relationships
between F and t for the 2015A and 2015B eruptions of Kuchinoerabujima are shown by
red and yellow triangles, respectively. The data for other earthquakes are shown for Colima
in 2003 (Zobin et al., 2006a), 2004 and 2005 (Zobin et al., 2006b) as open hexagons, for
Tokachi in 1989 (Nishimura, 1995; Kato et al., 2002) as open diamonds, for Asama in 1983
(Nishimura and Hamaguchi, 1993) and 2004 (Nishimura and Uchida, 2005; Ohminato etal., 2006) as black circles, for Popocatépetl (Cruz-Atienza et al., 2001) as black crosses, andfor Mount St. Helens in 1980 (Kanamori et al., 1984) as an open square. The solid lines ofscaling for three initial internal pressures of 0.1, 1, and 10 MPa proposed by Nishimura andHamaguchi (1993) are shown. The dashed line shows the scaling line for the pressure of 6
MPa.
Geshi et al. (2016) analyzed non-altered grains in the volcanic ash from the 2014 and 2015
eruptions and found that fresh glassy grains exist, and the water content in the glass is 1.2–1.6 wt.%.
79

H.NAKAMICHI, M.IGUCHI, T.TAMEGURI, T.SONODA

The presence of silica minerals in the grains suggests that the crystallization occurred at a low-pressure
condition of less than 10 MPa, and the water contents correspond to the water solubility in a rhyolitic
melt at 10–20 MPa (Geshi et al., 2016). This pressure corresponds to the lithostatic pressure at a depthof ~0.5–1 km, assuming the crustal density as 2000 kg/m3. The pressure corresponds to the pressure of
6 MPa estimated by the single force analysis of the seismic waves. The source depths of the 2015A and2015B eruptions estimated by the single force analysis are 30 m and 0 m below sea level, respectively,
roughly corresponding to the lithostatic pressure depth and to the depth of 0–100 m above sea level ofthe aquifer below Shindake that is suggested by the audio-frequency magneto-telluric survey (Kanda etal., 2010). Therefore, we interpreted that a magma head reached the aquifer below Shindake crater, waterin the aquifer suddenly vaporized and then phreatomagmatic eruptions occurred.
Following the method of Prejean and Brodsky (2011), we estimate the mass discharge rate fromthe amount of the estimated single force. Vertical force F on the Earth can be related to mass discharge
rate 𝑀 and volumetric discharge rate q using a momentum balance following Brodsky et al. (1999):
𝐹 = 𝑀𝑣 = 𝑞𝜌𝑣(6)where v is the velocity of material discharging from the vent and r is the dense rock equivalent (DRE)
density. Following Prejean and Brodsky (2011), we assume the vent exit speeds (v) to be 100–250 m/s.
Therefore, we obtain the mass discharge rate 𝑀 of 0.6–1.5 × 108 kg/s using the estimated vertical force
and Eq. (6) for the 2015A eruption. We do not discuss the 2015B eruption, because its column height
was not measured due to bad weather. If DRE density r is 2500 kg/m3, volumetric discharge rate q is
2.4–6 × 104 m3/s. Following the equation of Mastin et al. (2009), the empirical relationship between the
maximum column height in km above the vent and volumetric discharge rate q in m3/s is expressed as
𝐻 = 2𝑞 h.,j3 .

(7)

Using the volumetric discharge rate and Eq. (7), we obtain the maximum column height as 23–28 km
from the vent, which is much higher than the observed column height of 9 km. The significant
discrepancy between the estimated maximum column height and the observed one partially comes fromsuppression of the rising up of the eruption column due to a strong west-northwesterly wind of 14 m/s
blowing over Kuchinoerabujima at an altitude of 7.5 km (Tanaka and Iguchi, 2016).
We do not estimate the amount of ejected materials from the eruptions using the seismic andacoustic energies in this study. Systematic analyses of the seismic and acoustic energies and the force ofthe seismic waves for the eruptions need to be conducted along with ash sampling surveys and remotesensing to evaluate the amount of the ejected materials. A new relationship between the energies and theamount of the ejected materials will be established in future studies.
8. Conclusions
As a limited number of stations were available for the analysis, we estimated the seismic and acoustic
energies and durations of the eruptions. The durations of the eruptions were 50 s, 6 min, and 6 min forthe 2014, 2015A, and 2015B eruptions, respectively. Although the ejected materials of the 2014 and2015 eruptions were of phreatomagmatic origins, as suggested by geological surveys, the characteristicsof the seismic and acoustic waveforms were different. The seismic and acoustic waveforms of the 2014
eruption were expressed by spindle shapes, suggesting that the eruption was initially weak and graduallybecame violent; while the waveforms of the 2015A and 2015B eruptions were expressed by shapes
similar to a typical explosive eruption. The seismic and acoustic energies of the 2014 eruption were 1.88
GJ and 0.21 GJ, respectively. The seismic and acoustic energies of the 2015A eruption were 0.36 GJ and
2.2 GJ, respectively, and the seismic and acoustic energies of the 2015B eruption were 0.3 GJ and 0.06
GJ, respectively. We also estimated the counter single force excited by the 2015 eruptions by using
seismic waveform matching of a broadband seismometer. The depths of the counter force by the 2015
eruptions were near sea level. The pulse width and the amount of the force were lined on the scaling line
for the initial pressure of 6MPa. The energies of the seismic and acoustic waves of the eruptions and the80

Journal of Natural Disaster Science, Volume 38，Number 1，2017，pp65-83

source parameter can be related to the intensity of the explosivity of the eruption and the amount of theejected material. These parameters will be quantified in future studies.
Acknowledgements
We are very grateful to the staff of Sakurajima Volcano Research Center for maintaining the permanent
observation system of Kuchinoerabujima Volcano. NIED data have been managed by Drs. Toshikazu
Tanada and Hideki Ueda. Fukuoka Regional Headquarters of JMA provided the movies of the 2014 and2015 eruptions at KEMN station at Kuchinoerabujima. This work was supported by MEXT KAKENHI
Grant Number 15H05794 to M.I. and JSPS KAKENHI Grant Number 16K12849 to H.N., and by the
Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan, under its Earthquake
and Volcano Hazards Observation and Research Program. We are grateful to two anonymous reviewers
and a sub-editor for their constructive comments and suggestions.
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