Bull. Volcanol. Soc. Japan
Vol. /, (,**1) No. /, pp. ,1-ῌ,13

ArticleSource Mechanisms of Harmonic Tremors at Sakurajima Volcano
Takeshi TAMEGURIῌ, Sukir MARYANTOῌῌ and Masato IGUCHIῌ
(Received, November ,+, ,**0 ; Accepted, August ,+, ,**1)
Source mechanisms of harmonic tremors observed after B-type earthquake swarm (HTB) and those immediately after explosive eruption (HTE) at Sakurajima are estimated by inversion of root mean square (RMS) seismic
amplitudes of - components at / stations. HTB and HTE had a similar source mechanism that indicates isotropic
components of more than /*ῌ. Source depths of the HTB and HTE correspond to the location of a gas pocket
formed at uppermost part of the conduit. We infer that HTB is generated by resonance of the gas pocket formed
after swarm of B-type earthquake and that HTE is related with resonance of the gas pocket of which top ispartially collapsed by the explosion.
Key words : harmonic tremor, moment tensor, Sakurajima volcano+. Introduction
Eruptive activity with Vulcanian style has continued
at the summit crater, Minamidake of Sakurajima since+3//. Harmonic tremor (C-type tremor) have been
observed in active eruptive stages at Sakurajima volcano(Kamo et al., +311 ; Nishi, +32.), and are characterized
by regular peaks of spectra, composed of fundamental
frequency and its overtones from analyses of spectrum
and particle motion (e.g. Kakuta and Idegami, +31* ;Kamo et al., +311). As a result, the harmonic tremors
are classiﬁed into two types. One is the tremors observed several hours after B-type earthquake swarm(HTB) and the other is the tremors observed a few
minutes after explosive eruption (HTE). Peak frequencies of HTB are constant in duration of vibration.
In contrast, those of HTE gradually increase (Maryanto
et al., ,**/). During +32,῍,**,, 33- HTBs occurredand only / HTEs were recorded. HTEs were rareharmonic tremor at Sakurajima volcano.
Mechanisms of harmonic tremors have been investigated by analyses of spectra at other volcanoes. Harmonic tremor at Semeru volcano was caused by repetitive triggering sources at shallow part (Schlindwein
et al., +33/). Hellweg (,***) proposed that harmonic
tremor at Lascar volcano was excited by movement ofwater and gases near the surface. These studies discussed mechanisms on regular repetition of triggering
source for harmonic tremors ; however source mechanism of the trigger source has not been investigated.
Radiation pattern or moment tensor of the harmonic,. Data
Seismograms at / stations ranging +.1῍... km fromthe active crater (Fig. +) are used for analyses. At .
stations, three-component short-period seismometers(natural period T*ῌ+ s, damping constant hῌ+.*) areinstalled in boreholes at depths of 2/ to ,3* m. Station
HIK is equipped with the seismometers installed on thesurface in vaults. One horizontal component seismometer is set parallel to the direction from the station to thesummit crater (longitudinal component) and the otheris set perpendicular to the direction (tangential component). Velocity seismograms recorded before ,**+
were digitized with an A/D resolution of +, bit and asampling rate of ,** Hz from analog magnetic tapes.
Seismic signals recorded after ,**+ were recoded with
an A/D resolution of ,, bit and a sampling rate of ,**Hz.

῍ Sakurajima Volcano Research Center, Disaster Preven-

University, Jln. Veteran ++, Malang, Indonesia.

tion Research Institute, Kyoto University, SakurajimaYokoyama, Kagoshima 23+῍+.+3, Japan.
῍῍ Department of Physics, Faculty of Science, Brawijaya

Corresponding author : Takeshi Tameguri
e-mail : tamekuri@svo.dpri.kyoto-u.ac.jp

tremors were also practically not reported. And also,
their source locations were inferred at shallow parts
near the surface, but the depths were not quantitatively
determined in the previous studies. Maryanto et al.
(,**/) indicated that Rayleigh waves were dominant inharmonic tremors at Sakurajima volcano from analysesof particle motion.
In this study, we estimate moment tensor and source
depths of the two kinds of harmonic tremors, HTB and
HTE, at Sakurajima volcano from spatial distributionsof RMS seismic amplitudes. We further discuss common and di#erent factors in their source mechanisms.

274

Takeshi TAMEGURI, Sukir MARYANTO and Masato IGUCHI

Fig. +. Location of seismic stations. Solid circles
denote stations used for analyses. SVRC means
Sakurajima Volcano Research Center.

Figure , shows examples of waveforms at HTB andHTE. We analyzed + minute records (+0 h +, m +/ s+0 h +- m +/ s) of HTB on July ,*, +33*, which continued about , hours from +. h (JST), and 0 minuterecords of HTE that started at ++ h +3 m following an
explosive eruption occurred on ++ h +/ m on October ++,The HTE continued for +, minutes.
Waveforms of the HTB and HTE observed at /stations are shown in Fig. -. The HTB and HTE havethe largest amplitudes at station HIK, the closest station
to the crater. Amplitudes decrease with distance fromthe crater. The amplitudes of horizontal component
are larger than those of vertical component and longitudinal components have the largest amplitudes, except
station KOM.
Spectra calculated for +* seconds records of the HTB
and HTE at station HIK are shown in Fig. .. The
spectra of HTB have clear dominant peaks at +.0 Hz, -.,Hz, ..2 Hz, 0.. Hz and 2.* Hz. The peak at +.0 Hz isfundamental mode the others are its overtones. Dominant peaks of the spectra of HTE appear at +.0 Hz, -.,Hz, ..2 Hz, 0.. Hz, and 2.* Hz. Waveforms processedby band-pass ﬁlter with a band width of ῌ*.*/ Hz offundamental (f+) and second mode (f,) at station HIK
are shown in Fig. /. The amplitudes of vertical components of HTB and HTE are almost stable. Wave
trains with spindle shape of duration of a few to +*seconds appear in horizontal components. The amplitudes of the fundamental mode of HTE are larger thanthose of the second mode. In contrast, the amplitudesof the second mode of HTB are larger than those of thefundamental mode. The HTB may be generated by asource which has two fundamental frequencies of f+ andf,.
-. Analysis
Moment tensor solution of the harmonic tremors are

Fig. ,. Seismograms of harmonic tremors. The seismograms are observed by a vertical component ofseismometer at station HIK. (a) HTB occurredon July ,*, +33*. (b) Explosion earthquake occurred at ++ : +/ on October ++, ,**, and HTE
started at ++ : +3.

estimated by inversion of RMS amplitudes of . s time
window, because it is di$cult to detect common phasesof harmonic tremors among the / stations and it is
impossible to apply a conventional waveform inversion
method to obtain the moment tensor. By using thedata of RMS amplitudes, we can evaluate an average
moment tensor solution for the given window. Here,fundamental and second modes of harmonic tremors
are analyzed, because amplitudes of higher mode aresmall at far stations from the crater. Peak frequenciesof the fundamental and second modes of HTB are
nearly constant. RMS amplitudes are calculated fromseismograms band-pass ﬁltered by +.//ῌ+.0/ Hz (f+) andSource Mechanisms of Harmonic Tremors at Sakurajima Volcano

Fig. -. Examples of --component velocity waveformsof harmonic tremors at / stations. (a) HTB from
+0 : +, : // to +0 : +- : +/ on July ,*, +33*. (b)HTE from ++ : ,+ : ** to ++ : ,+ : ,* on October++, ,**,.

Fig. .. Spectra of harmonic tremors. The spectra
were obtained from +*s-seismograms at station
HIK shown in Fig. -. (a) Spectra of HTB from
+0 : +, : //. (b) Spectra of HTE from ++ : ,+ : **.

those ﬁltered by -.+/ῌ-.,/ Hz (f,) for HTB. Fundamental frequency of HTE increased +.* to ,.0 Hz intime window of analysis. So, center frequency ofband-pass ﬁlter with band width of ῌ*.*/ Hz ischanged corresponding to dominant peak frequencies.
In order to remove local site e#ect at each station, thewaveform amplitudes were corrected by a site ampliﬁcation factor, which is deﬁned as the average of ampli-

275

Fig. /. Examples of waveform band-pass ﬁltered at f+
and f, with band width of ῌ*.*/ Hz. Seismograms are observed at station HIK. (a) HTB
from +0 : +, : // to +0 : +- : +/ on July ,*, +33*.
(b) HTE from ++ : +3 : ** to ++ : +3 : ,* on
October ++, ,**,.

tude ratio of teleseismic earthquakes with frequencies of+ῌ- Hz. The site correction factors, which are theinverse of the ampliﬁcation factors, at stations HIK,
ARI, HAR and KAB referring to KOM are *.3/, *.0.,+..2 and *.20, respectively.
We modiﬁed the waveform inversion method (Kikuchi
and Kanamori, +33+) so as to use RMS amplitudes.
Green’s functions to reproduce synthetic waveforms arecalculated by the method of Hisada (+33.). The depthsof seismometer are taken into account in the calculation. A homogeneous half-space with Vp῎,./ km/s, Vs
῎+... km/s, and a density of ,./῍+*- kg/m- (Iguchi,+33.) is assumed to calculate the Green’s functions.
Synthetic RMS amplitudes are calculated from synthetic waveforms predicted from sinusoidal source timefunctions with frequencies of the fundamental and second
modes. The synthetic waves are band-pass ﬁltered withthe same frequency bands as the observed waveforms.
It is assumed that epicenter of harmonic tremor is thesummit crater, because amplitudes of HTB and HTE
are the largest at station HIK, which is the closest
station to the crater (Fig. -). The moment tensor
inversion is conducted for . cases of source depths : ,.*,+.*, *./ and *.- km. In this analysis, RMS amplitudes
are obtained in . s windows. In order to conﬁrm validity of the length of time window, we test the inversion
method in case of , s and 2 s time windows. Similar
results are obtained to those of . s window.

276

Takeshi TAMEGURI, Sukir MARYANTO and Masato IGUCHI

Fig. 0. Examples of results of the inversion. Assumed
source time function and obtained moment tensor
components are shown in left side. Fitness ofsynthetic RMS amplitudes to observed ones areplotted in right side. (a) Fundamental frequency
of HTB. (b) Second mode of HTB. (c) Fundamental frequency of HTE. (b) Second mode of
HTE.

.. Results
Examples of inversion results are shown in Fig. 0.
Result for f+ of HTB shows that a vertical dipole isdominant, non-diagonal components are ,*ῌ of Mzz
component, and diagonal components have same polarity. These represent a volume change of the source.
Moment tensor solution for f, of HTB is similar to thatof f+. Peak to peak amplitude of the moment rates forf+ and f, are +.2ῌ+*0 Nm/s and -.2ῌ+*0 Nm/s, respectively. Synthetic RMS amplitudes assuming source
depth of *./ km are best ﬁtted to the observed ones witha residual of *.*1. Result for f+ of HTE is almost sameas that of HTB, indicating dominant vertical dipole anddiagonal components with a same polarity. Non-diagonal components are ,/ῌ of Mzz component. Moment
tensor solution for f, of HTE are similar to that of f+.
Peak to peak amplitude of the moment rates for f+ andf, are *.1ῌ+*2 Nm/s and *.-ῌ+*2 Nm/s, respectively.
Source depth of *.- km gives the best result.
Next, moment tensor components are decomposed toisotropic, compensated linear vector dipole (CLVD ;Knopo# and Randall, +31*), and double couple (DC)parts using the method of Horálek et al. (,**,), andtemporal changes of the three parts and moment-rates
are investigated (Fig. 1). Isotropic components for f+of HTB are /*῍0*ῌ, and CLVD and DC components
are about ,*ῌ. The three components for f, are about
0*ῌ, ,*῍-*ῌ, and +*ῌ, respectively. Moment-rates
for f+ ﬂuctuate, ranging from -.,ῌ+*0 to ..+ῌ+*0 Nm/
s and moment-rates for f, decrease from 3./ῌ+*0 Nm/sin the same analysis window. Isotropic components
for f+ of HTE are /*῍1*ῌ, and CLVD and DC compo-

Fig. 1. Moment-rate and moment tensor components.
Circles, triangles, and squares represent percentages of isotropic, CLVD, and DC components ofmoment tensor, respectively. (a) Fundamental frequency of HTB. (b) Second mode of HTB. (c)Fundamental frequency of HTE. (b) Second modeof HTE.

nents are about ,*ῌ and +*῍,*ῌ, respectively. The
three components for f, are about 0*ῌ, ,*῍-*ῌ, and+*ῌ, respectively. Moment-rates for f+ are stable until++h,-m, ranging *.0ῌ+*2 to *.3ῌ+*2 Nm/s and increased to ,..ῌ+*2῍-.+ῌ+*2 Nm/s from ++ h ,. m.
Moment-rates for f, range from *./ῌ+*1 to 3./ῌ+*1
Nm/s. Although the moment-rates change in the analysis window, a ratio of the three parts is stable.
Source depths of HTB and HTE are estimated to be*./ km and *.- km, respectively, beneath the crater in all
analysis windows. In order to examine the accuracy ofthe estimated source depths, moment tensor inversions
are done for source depths ranging from *.+ km to ,.*km with increment of *.+ km, using the seismograms of
HTB at +0 h +, m // s and HTE at ++ h ,+ m ** s. The
source depths of HTB and HTE as minimizing theresidual between observed RMS amplitude and synthet-Source Mechanisms of Harmonic Tremors at Sakurajima Volcano

277

Fig. 3. Conceptual models of HTB and HTE. (a)HTB. +) Volcanic conduit is ﬁlled with magma
including gas during B-type earthquake swarm. ,)The magma reaching crater bottom becomes solidiﬁed lava dome by cooling and a gas pocket isformed beneath the lava dome. HTB is generated
by resonance of the gas pocket. (b) HTE. +)An explosion occurs, partially collapsing the lava
dome. ,) HTE is generated by resonance of gas
pocket during gas release from small vent of thelava dome.
Fig. 2. Residuals of RMS amplitudes between observed
and synthetics plotted against source depths. Upperand lower ﬁgures are HTB and HTE, respectively.

ic one are estimated to be *./ km and *.- km, respectively (Fig. 2). The shallow source depths are appropriate, because local minimum in residuals is not recognized and amplitudes of body wave are small (Maryanto
et al., ,**/).
/. Discussion
Moment tensors of HTB and HTE at Sakurajima
volcano include isotropic component more than /*ῌ.
This indicates that the harmonic tremors are excited byrepetition of expansion and contraction of the source.
CLVD component having a vertical main axis is included by ,*ῌ in moment tensor. The source repeating expansion and contraction is dominated by vertical
dipole, as shown by dominant Mzz component. We
infer that the source of harmonic tremor is related tovertically dominated volume change of ﬂuid.
Source depths of HTB and HTE are estimated to be*./ km and *.- km, respectively. The depths correspondto the location of a gas pocket that are inferred from tilt
and strain steps caused by an instantaneous pressure
decrease reﬂecting the outbreak of a gas pocket at *./km beneath the crater (Ishihara, +33*). The depths

are also consistent with the location of the source oflong-period largest motion for explosion earthquakes(Tameguri et al., ,**,).
Figure 3 shows the conceptual models of HTB andHTE. Generating B-type earthquakes, magma ascends
to the crater bottom and ﬁlls the conduit (Iguchi +33. ;Fig. 3a-+). The magma reaching to crater bottom
forms a lava dome, which is a magma solidiﬁed bycooling from the surface. When gas is released frommagma beneath the lava dome, a gas pocket can beformed at uppermost part of conduit (Ishihara, +32/).
It is considered that harmonic tremor is generated byresonance of ﬂuid with boundary of large contrast of
impedance (Kamo et al., +311 ; Fujita and Ida, ,**-).
We infer that HTB after swarm of B-type earthquakes isgenerated by resonance of the gas pocket formed at
uppermost part of conduit (Fig. 3a-,). During theoccurrence of HTB, we observed weak gas emission
from crater which may play a role in driving source forgeneration of the HTB. On the other hand, HTE
occurs a few minutes after explosive eruption (Maryanto
et al., ,**/), indicating that the gas pocket sealed bylava dome is broken by an explosion (Ishihara, +32/ ;Tameguri et al., ,**,). If the gas pocket trapped beneath the crater is the resonance source generating
harmonic tremor, the harmonic tremor would not occur

278

Takeshi TAMEGURI, Sukir MARYANTO and Masato IGUCHI

after explosions. However, if the lava dome above thegas pocket is not completely destroyed (Fig. 3b-+), andvolcanic gas is released from a hole smaller than the sizeof gas pocket, the gas pocket that has a large impedancecontrast to the surrounding volcanic ediﬁce may play arole of the resonator (Fig. 3b-,). Increase in peakfrequencies of the HTE may be caused by decrease ofvolume of the gas pocket that is introduced by slow gas
release from the small hole after the explosion. The
moment-rates of HTE suddenly became large at ++ h ,m .* s (Fig. 1) when a seismic event similar to a B-type
earthquake occurred at this time as shown in Fig. ,.
This correlation suggests that resonance of the gas
pocket is excited by a seismic event. It is inferred that
HTB and HTE are excited by resonance of the same gas
pocket formed before an explosion, because the moment
tensor solutions of HTB and HTE are almost same.
The moment tensor solutions are dominated by vertical dipole (Mzz). The sources of harmonic tremors areapproximated by vertical vibration of a horizontallyextended thin source. Furthermore, the harmonic tremor is characterized by regular peaks of spectra, composed of fundamental frequency and its overtones.
Fujita and Ida (,**-) showed that the characteristics ofregular peaks of spectra are caused by resonance ofplanar inclusion. So, it is inferred that the source ofharmonic tremors is formed in a thin plane ﬁlled withgas between a lower part of the lava dome and the top ofmagma in the conduit.
0. Conclusions
The HTB and HTE show a same moment tensor
solution dominated by vertical dipole, and the source ischaracterized by repeating expansion and contraction.
The sources of harmonic tremors are approximated byvertical vibration of a horizontally extended thin source.
Source depths of *.-ῌ*./ km coincide with the depth ofgas pocket that inferred to be formed beneath the crater.
We suggest that the harmonic tremors are generated byresonance of the gas pocket.
Acknowledgement
We greatly thank the sta#s of Sakurajima Volcano
Research Center, Disaster Prevention Research Institute, Kyoto University, for maintenance of the observation system. We thank Dr. Takeshi Nishimura of
Tohoku University for discussion about the source
mechanism. Comments by Dr. Eisuke Fujita of National Research Institute for Earth Science and Disaster
Prevention, Dr. Haruhisa Nakamichi of Nagoya University, and Dr. Tomoki Tsutsui of Akita University
were very helpful to revise the manuscript.

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