Journal of Natural Disaster Science, Volume 37，Number 2，2016，pp91-103

Seismic inversion analysis of the 2014 and 2015 Kuchinoerabujima volcanic eruptions,using F-net broadband seismometers
Takanori Matsuzawa1, Takumi Matsumoto1 and Toshikazu Tanada1
1

National Research Institute for Earth Science and Disaster Resilience
Address: 3-1 Tennodai, Tsukuba, Ibaraki 305-0006, JAPAN（Received: Sep.1, 2016 Accepted: Oct.21, 2016）

Short Running Title:
Seismic inversion of Kuchinoerabujima eruption

Abstract
We observed long-period seismic waves excited by eruptions in 2014 and 2015 at Kuchinoerabujima
Volcano, Japan. The propagations of seismic waves were clearly recognized in F-net seismograms insouthwest Japan. The excitation force of three eruptions was analyzed using F-net broadband seismometers.
The analysis of source time functions of three-component single force shows that vertical force is dominant
in the eruptions at 12:24 on Aug. 3, 2014, and at 12:09 on May 29, 2015 (local time). In addition to thevertical force, lateral force in the north-south direction was also dominant in the eruption at 9:59 on May
29, 2015. This suggests that the mechanism of this eruption is different from the other two eruptions. The
lateral force may be related to the momentum exchange by the emission of deposits inclined to the northsouth direction.

Keywords: Kuchinoerabujima Volcano, Eruption, Single force, Seismic Inversion
1.

INTRODUCTION

Long-period seismic wave excitations are sometimes observed in volcanic eruptions. To reveal themechanism of eruptions, the excitation force is estimated by a seismic inversion technique. For example,
lateral force is estimated in the 1980 St. Helens eruption, and attributed to a landslide followed by a lateralblast (Kanamori and Given, 1982). In the 1989 Izu-Oshima volcanic eruptions, vertical single force andvector dipoles are estimated, and interpreted as the force caused by the sliding down of the lava, and thevolumetric change in cracks or extended magma reservoirs, respectively (Takeo et al., 1990). In the 2010
eruption with caldera formation on Miyake Island, the very-long-period seismic signal is explained by apiston model (Kumagai et al., 2001). In the eruptions of Asama Volcano in 2004, downward and subsequent
upward vertical force are interpreted as a result of removal of capping and viscous drag force by ascending
magma, respectively (Ohminato et al., 2006). As in these studies, analysis of the seismic excitation source
is useful for discussing the eruption process.
Kuchinoerabujima Volcano is located in the south of Kyushu Island, Japan (Fig. 1). This volcano
consists of several edifices. Shintake and Furutake Volcanos in Kuchinoerabujima have repeatedly erupted
in the last 10,000 years. Lithic tephra indicates that these are Vulcanian-type and phreatomagmatic eruptions(Geshi and Kobayashi, 2006). Historical records since 1841 show that eruptions occurred at or around
Shintake crater, and repeated at intervals of tens of years (Geshi and Kobayashi, 2006; Japan Meteorological
Agency (JMA), 2013). In very recent years, an explosive eruption from the Shintake crater was observed at91

T.MATSUZAWA, T.MATSUMOTO, T.TANADA

12:24 on Aug. 3, 2014 (local time; i.e., UTC+9) (JMA, 2014). In the following year, an explosive eruption
at Shintake crater occurred at 9:59 on May 29, 2015 (JMA, 2015a). Due to this eruption, the residents ofKuchinoerabu Island were evacuated from the island. The plume height of this eruption reached more than
9000 m above the rim of the crater (JMA, 2015a). At about 12:09 on the same day, another eruption wasobserved (Japan Coast Guard, 2015). Eruptions were also observed at 12:17 and 16:31 on Jun. 18, 2015,
and at 9:43 on Jun. 19, 2015 (JMA, 2015b) at Kuchinoerabujima Volcano. Hereinafter, we call the eruptionsat 12:24 on Aug. 3, 2014, at 9:59 on May 29, 2015, and at 12:09 on the same day as Eruption A, B, and C,
respectively. We analyze these three eruptions in this paper.

Figure 1 Squares are F-net stations used in the waveform inversion. The black and gray triangles show thelocation of Kuchinoerabujima Volcano (Shintake Crater) and Aso Volcano, respectively.
2.

SEISMIC DATAThe National Research Institute for Earth Science and Disaster Resilience (NIED) operates a nation-wide
broadband seismic network called F-net (Okada et al., 2004). At the F-net stations, Streckeisen STS-1, 2, or
2.5 broadband sensors are installed in tunnels. Figure 2 shows the seismic data of F-net at the time oferuptions. In Eruption A, B, and C, propagations of long-period (more than 10 s) seismic signals arerecognized even at a distance of hundreds of kilometers from Kuchinoerabujima Volcano (Fig. 2(a), (b), and(c)). We note that all seismic data in the analysis and figures are prepared after correction of the instrumental
response.
KYKF station is located on Yakushima Island next to Kuchinoerabu Island (Fig. 1). The distancefrom the crater to KYKF is about 20 km. Seismic signals of eruptions were clearly observed in the broadband
seismograms. Figure 3 shows the seismograms and the particle motions in a horizontal plane at KYKF.
Particle motions of Eruption A and C are almost in the radial (east-to-west) direction. The particle motionof Eruption B is dominant in the transverse (north-to-south) direction. This suggests that the direction of theapplied force in Eruption B is different from the other eruptions.
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Seismograms of Eruption A are slightly noisy in the whole of Japan even before the eruption (Fig.
2(a)). In Fig. 3, the linearity of the particle motion of Eruption A is less clear than those of the other eruptions.
An MW 6.9 earthquake occurred at 00:22 (UTC) in the Micronesia region before Eruption A. The
seismograms of Eruption A, as in Fig. 2 and 3, seem to be affected by the coda part of surface waves excitedby this far-field earthquake.

Figure 2 UD-component seismograms of F-net at the time of eruptions. Seismograms are band-pass filtered
between 10 s and 20 s. The vertical position of each trace is based on the distance from
Kuchinoerabujima Volcano. The scale of the amplitude of waveforms is the same in all panels.
Each panel shows the eruption at (a) 12:24 on Aug. 3, 2014 (Eruption A), (b) 9:59 on May 29,2015 (Eruption B), (c) 12:09 on May 29, 2015 (Eruption C), (d) 12:17 on Jun. 18, 2015, (e) 16:31,
Jun. 18, 2015, and (f) 9:43 on Jun. 19, 2015. The propagations of seismic waves were recognizedin (a), (b), and (c), as indicated by black tilted arrows. Aso long-period events, which weredetected by a matched filter technique (Matsuzawa et al., 2015), are indicated by gray tilted arrows.
In the left panels, the locations of F-net stations are shown by squares. The locations ofKuchinoerabujima Volcano and Aso Volcano are indicated by a black and a gray triangle in thesame map, respectively.
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T.MATSUZAWA, T.MATSUMOTO, T.TANADA

Figure 3 Seismograms at KYKF. (a), (c), and (e) are three-component seismograms at Eruption A, B, andC, respectively. (b), (d), and (f) are particle motion in the horizontal plane of (a), (c), and (e),respectively. All seismograms are band-pass filtered between 10 and 100 s.

Propagations of small seismic waves are also found in Fig. 2 (b), (c), and (e) at the time without
eruptions. These did not originate from the Kuchinoerabu region, but from the Aso volcanic region. They
are interpreted as long-period events in Aso Volcano (Kaneshima et al., 1996). As indicated by the grayarrows in Fig. 2, long-period events are detected at 10:07, 12:08, and 12:13 on May 29, 2015, and 16:30 on
Jun. 18, 2015 by a matched filter technique using F-net data (Matsuzawa et al., 2015). These detected times
correspond to the start of propagations of seismic waves from the Aso region.
After Eruption C, three eruptions have been reported as described in the previous section. Figure 2(d), (e), and (f) show the waveforms around the time of these reported eruptions. However, clear
propagations from Kuchinoerabujima Volcano are not recognized in these three eruptions at F-net stations.
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It is difficult to analyze such very small seismic sources of these eruptions using only F-net data. Therefore,
we analyzed the eruptions with clear seismic signals (i.e., Eruption A, B, and C) in this paper.
3. INVERSION METHOD

We estimate the source time functions of excitation force using a waveform inversion method to reveal themechanisms in eruptions and adopt a discrete wavenumber integral method (Takeo, 1985; Takeo et al., 1990)
to calculate synthetic waveforms. The same laterally layered seismic structure is assumed as that in F-net(Kubo et al., 2002).
In this analysis, source time functions of three-component single force are estimated simultaneously
by least squares inversion with a smoothing constraint. Each component of source time functions isexpressed by a first order B-spline function that is spanned by half-overlapped basis functions (Fig. 4).

Figure 4 Schematic image of basis functions in the inversion analysis. Each component of single force isexpressed by a linear combination of the B-spline basis functions that are half-overlapped. The
time interval of each basis function is 1 s. In the analysis except for Fig. 5(c), the total source
duration is 100 s.

The number of basis functions, N , is 100 in our result except for the case in Fig. 5(c). In a discrete form,
the synthetic waveform of the j -th component at the i -th station by the single force applied in the k -th
direction is expressed as
K ,Nd ij(syn ) (t m ) = ∑ g ijk (t m − τ l )sk (τ l )(1).

k =1,l =1

g ijk (t ) is the synthetic waveform, when the source time function is a unit basis function. sk (t ) is a source
time function and indicates the amount of applied force. K is the number of force directions (e.g., K = 3
for three-component force). N is the number of points of the source time function. This is easily extended
to the case of the moment tensor source, replacing sk (t ) and g ijk (t ) with the moment rate function of thek -th basis moment tensor and the synthetic waveform excited by a unit basis source time function of thecorresponding moment tensor, respectively. In addition, waveforms by a mixed source of single force andmoment tensor source are expressed by a simple summation of two equations in these two cases.
In this inversion analysis, the sampling interval of source time function is the same as the decimatedinterval of the observed waveforms ( ∆t =1 s). Therefore, t m and τ l are given as95

T.MATSUZAWA, T.MATSUMOTO, T.TANADAt m = (m − 1)∆t , τ l = (l − 1)∆t

( m = 1,  , M , l = 1,  , N )(2).
M is the number of data points in each decimated observed waveform, and 180 in this analysis except forthe case in Fig. 5(c). We assume that g ijk (t ) is zero for t < 0 or t > L∆t ( L = 80 in this study).
Waveform data and source time functions are written in a vector form as

d = [d11 (t1 ),, d11 (t M ), d12 (t1 ), , d IJ (t M )](3),

s = [s1 (τ 1 ),  , s1 (τ N ), s2 (τ 1 ),   , s K (τ N )]

(4),

T

and

T

respectively. I and J are the number of used stations and number of components of each sensor,
respectively. Using these vectors, the observation equation is written as

d = Gs(5).

Here, G is an IJM × KN size matrix. The matrix coefficients of G are given by (1).
In this analysis, a smoothing constraint is introduced, as the second order difference is zero. This is expressedin an equation assk (τ l −1 ) − 2 sk (τ l ) + sk (τ l +1 ) = 0( k = 1,  , K , l = 1,  , N )(6).

For convenience, sk (τ 0 ) and sk (τ N +1 ) are assumed to be zero in the above equation. The set of Equation(6) for all k and l is written in matrix form as

Fs = 0(7).

Combining this constraint, the observation equation is modified tod (obs)  G 
 =  s
0  α F (8).

In this equation, α is a weighting parameter of the smoothing constraint (i.e., hyper parameter). The
observation equation with the constraint (8) is solved by a least squares method. As an optimized hyper
parameter, we choose α , which minimizes Akaike’s Bayesian Information Criterion (ABIC) (e.g., Yabuki
and Matsu’ura, 1992). The source of the synthetic waveform is assumed as a point source at a depth of 0.5
km in the Shintake crater. Observed and synthetic waveforms are band-pass filtered between 10 and 100 s.

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Figure 5 Result of the inversion analysis of Eruption A. (a), (c) Estimated source time function of threecomponent single force. (b), (d) Comparison of synthetic (thick dashed lines) and observed
waveforms (thin lines). (a) and (b) are the inversion result with the source duration of 100 s. The
length of fitted data is 180 s. (c) and (d) are the result in the case that the source duration and thelength of fitted data are limited to 30 s and 110 s, respectively.
4.

RESULTS

Figures 5, 6, and 7 show the results of estimated source time functions of Eruption A, B, and C, respectively.
Both the north-south and vertical components are dominant in Eruption B, while only the vertical component
is dominant in Eruption A and C. This means that seismic waves in Eruption A and C are mainly excited by
the vertical force. Seismic waves in Eruption B are also excited by the lateral force in the north-south
direction. In Eruption B, the peak amplitudes of the lateral single force are similar to that of the verticalforce. In addition, the rise of the vertical force precedes the lateral force. The results of the force directions
and the delayed lateral force of Eruption B suggest that the excitation force of Eruption B is different fromthe other two eruptions and is complex.

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T.MATSUZAWA, T.MATSUMOTO, T.TANADA

Figure 6 Result of the inversion analysis of Eruption B. (a) Estimated source time function of threecomponent single force. (b) Comparison of synthetic (thick dashed lines) and observed
waveforms (thin lines).

Figure 7 Result of the inversion analysis of Eruption C. (a) Estimated source time function of threecomponent single force. (b) Comparison of synthetic (thick dashed lines) and observed
waveforms (thin lines).
In Eruption A, force in the north-south direction is dominant in the longer period (more than 30 s), especiallyafter 30 s, while vertical force is dominant in the shorter period (10–20 s) within the first 30 s. The
propagating surface waves by Eruption A are dominant at the period from 10 to 20 s. Surface waves by the
far-field earthquake are dominant above 20 s at the time of Eruption A. Therefore, the longer-period lateralforce after 30 s apparently arises from the effect of the far-field earthquake. Figures 5(c) and (d) show theresult when the source duration is limited to the first 30 s. The characteristic waveform at KYKF is well
explained without the large lateral single force. In addition, the peak value of the estimated single force in
Fig. 5(c) is larger than that in Fig. 5(a), and also larger than those of Eruption B and C. The peak value in
Fig. 5(a) seems to be underestimated by the disturbance by the far-field earthquake. This is supported by
the peak amplitude of the seismic wave at KYKF that is larger than those of Eruption B and C (Fig. 3).
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5.

DISCUSSION

Our results show that both the lateral and vertical single forces are dominant in Eruption B. However, it isalso possible that other processes (e.g., earthquake, or crack opening) may occur in the eruption. As suchmechanisms are represented by moment tensor, therefore, we examined a seismic source with vertical single
force and six-component moment tensor. Figure 8 shows the result in this case. As the variance reduction(VR) is 80.2%, waveforms are relatively well explained. However, this is smaller than the VR of 84.5% in
the case of the three-component single force, although the number of model parameters in Fig. 8 is morethan double. This suggests that the contribution from the lateral single force is suitable for explaining theseismic waveforms.

Figure 8 Result of the inversion analysis of Eruption B considering a vertical single force and moment
tensors. (a) Estimated source time function of vertical single force and six moment sensors. (b)Comparison of synthetic (thick dashed lines) and observed waveforms (thin lines).

In terms of the geological observation, it is suggested that the eruptions in 2014 and 2015 at
Kuchinoerabujima Volcano are directed blasts (Kobayashi, 2015; Kobayashi and Yamaguchi, 2015).
Kobayashi and Yamaguchi (2015) suggested that Eruption B was a lateral blast. Force in the north-south
direction in our result supports the occurrence of lateral blast in Eruption B, as the lateral mass movement
is suggested from the lateral single force. In addition, a blast in the lateral direction is reported in the99

T.MATSUZAWA, T.MATSUMOTO, T.TANADA

eruptions at the other volcanos (e.g., Kieffer, 1981; Kanamori and Given, 1982). In Eruption B, the rise of
the source time function in the vertical direction precedes that in the north-south direction by several seconds.
The delayed lateral force is also supported by the camera observed by JMA, which shows that Eruption B
is in the vertical direction at first, and then in the inclined direction after several seconds (e.g., Jiji Press,2015).
The excitation force of Eruption C was dominant in the vertical direction. This means that theexcitation force changed in each eruption even at the interval of two hours. Kobayashi and Yamaguchi(2015) suggest that blocking material on the crater caused a lateral blast in Eruption B. Perhaps, the material
has been removed from the crater by Eruption B. Then, the direction of Eruption C may be vertical again as
in Eruption A. In addition, the source time function of Eruption B is more complex and has a slightly higher
dominant frequency than those in the other eruptions. Such features may be related to the coexistence ofvertical and lateral blasts that are caused by the removal of blocking material at the crater.
In Eruption B, small long-period force is found both in the north-south and vertical direction from60 s to 80 s (Fig. 6(a)). This may also be attributed to the eruption. Kanamori and Given (1982) reported
that a large-scale landslide excited long-period seismic waves after a lateral blast in the 1980 St. Helens
eruption. However, this mechanism does not seem to be applicable to the excitation force of Eruption B, as
no large landslides were reported in this eruption. Deceleration or landing of laterally emitted deposits may
cause such momentum exchange from 60 s to 80 s, as found in the camera observation by JMA (e.g., Jiji
Press, 2015). Further study, including the location of sources, might reveal whether the source at each stage
is around the surface or in the deeper part.
Eruption B was larger than Eruption C, as confirmed by the satellite images (JMA, 2015c), while
the amplitudes of seismic excitation are similar. As single force excitation is interpreted as the momentum
exchange by mass movement, this suggests that a large fraction of mass movement in Eruption C occurred
below the surface. Eruption B or dike opening, which preceded Eruption C, might cause a low-pressure
region in the vent or magma chamber. Then, fluid movement or degassing from magma might flow into that
region from the deeper part. Further study on the depth and the detailed excitation mechanism would be
helpful to discuss this point.
Our obtained source time functions show oscillating behaviors. In Eruption C, for example,
maximum downward force is found after small downward force and moderate upward force. This may becaused by the uncertainty of the assumed Green’s function and microseismic noise, as the dominant periodof source time function is relatively short (typically 10–20 s). Data observed at close stations are likely tobe less affected by such effects due to the short path length. In a future study, an inversion analysis withclose stations might be suitable for discussing the details of the source time function (e.g., Ohminato et al.,2006). In that study, the topography of the island should be considered, while a laterally layered structure isassumed in this study that uses distant stations.
Another cause of such oscillation is the effect of the applied band-pass filter. Nakano et al. (2008)
pointed out that the obtained source time function is band-pass-filtered, when the filter is applied only tothe observed seismic waveforms. In this analysis, this effect can be avoided, as the same band-pass filter isapplied to both the observed and synthetic waveforms (Yagi, 2014). However, Yagi (2014) showed that theapplied band-pass filter indirectly affects the solution in the case of damped least squares inversion. As oursmoothing constraint is different from that in Yagi (2014), we briefly discuss the effect of band-pass filter,
replacing the term of constraint in (12), (13), and (14) in Yagi (2014). For simplicity, we assume continuousfunctions instead of a discrete form as in Yagi (2014). In the time domain, the inversion problem is attributed
to minimizing∞∞∑ ∫ B(t ) ∗ [g (t ) ∗ s (t ) − d (t )] dt + α ∑ ∫ s (t ) dt
2ijk

i , j ,k −∞

k

2

2

ij

k

(9).

k −∞

Here, ∗ and B(t ) mean convolution in the time domain and a response function of the band-pass filter,
100Journal of Natural Disaster Science, Volume 37，Number 2，2016，pp91-103

respectively. The smoothing constraint of the second order difference (Equation (6)) is expressed by thesecond order derivatives of the source time function. From Parseval’s theorem, this is equal to minimizing
∞

[

]

∞

∑ ∫ B(ω ) gijk (ω )sk (ω ) − d ij (ω ) dω + α 2 ∑ ∫ ω 4 sk (ω ) dω2

2

i , j ,k −∞

(10)

k −∞

in the frequency domain. Here, ⋅ (ω ) denotes the Fourier transformed function. Therefore, the source timefunction in the frequency domain is given by∑ B (ω )B(ω )g (ω )d (ω )∗sk (ω ) =

i, j
∗

∗
ijk

∗
ijk

∑ B (ω )B(ω )g (ω )g (ω ) + α ω
∗
ijk

2

ijk

i, j

In the above equation,∗∑ g (ω )d (ω )

ij

4

=

ij

i, j

α 2ω 4
(
)
(
)
+
g
ω
g
ω
∑
ijk
B ∗ (ω )B(ω )
i, j

(11).

∗
ijk

means a complex conjugate. As B (ω )B(ω ) << 1 out of the pass band,∗

α 2ω 4 [B ∗ (ω )B(ω )] becomes very large in the high frequency band. Therefore, the high frequency

component in the solution was reduced indirectly by the effect of the band-pass filter. The strength of thiseffect is controlled by the hyper parameter α . Such effect may also cause the small apparent oscillation in
our result due to the lack of the high frequency component.
Observations close to the volcano are sometimes unavailable due to natural hazards or other factors(e.g., human error). This risk increases when an eruption occurs. Some observations at stations close to
Kuchinoerabujima Volcano were disrupted by the eruptions (e.g., JMA, 2016). However, continuous
monitoring and analysis with F-net data are available even in such cases, as F-net sensors are widelydistributed in Japan and installed in places with a low-noise level that enables us to analyze small signals.
Analysis with distant seismic stations is important as an alternate monitoring method of volcanic activity,
when immediate analysis or monitoring is required, especially, in the case of lack or failure of data fromclose stations.

6.

CONCLUSIONS

When an eruption on Aug. 3, 2014 (Eruption A) and two eruptions on May 29, 2015 (Eruption B and C)
occurred in Kuchinoerabujima Volcano, the propagations of seismic waves were clearly recognized insouthwestern Japan in the F-net broadband data (Fig. 2). However, the propagations of seismic waves were
not clear at the time of the three eruptions on Jun. 18 and 19, 2015. This means that the excitation force of
these three eruptions was smaller than those of Eruption A, B, and C.We analyzed the seismic waves in
Eruption A, B, and C, and estimated the excitation force by the least squares inversion methodwith a smoothing constraint using F-net broadband data. The excitation force of Eruption A and
C was mainly in the vertical direction. In Eruption B, however, lateral force was also applied justafter the vertical force. This is consistent with the emission of deposits observed by a JMA camera(Jiji Press, 2015), and the suggestion from a geological study (Kobayashi and Yamaguchi, 2015)
Acknowledgements
We used the Generic Mapping Tools (Wessel and Smith, 1998) to prepare figures. This work is partially
supported by MEXT/JSPS KAKENHI, Grant-in-Aid for Special Purposes. We appreciate two anonymous
reviewers and a sub editor for their helpful comments.
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