Episodic transport of discrete magma batches beneath Aso volcano
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Episodic transport of discrete magma batches beneath Aso volcano Jieming Niu ( j.niu@ucl.ac.uk ) University College London https://orcid.org/0000-0002-4481-022X Teh-Ru Song Department of Earth Sciences, University College London Article Keywords: Trans-crustal Magma Plumbing System, Long-term Volcanic Output, Short-term Eruption Dynamics, Episodic Long-period Tremors, Synchronous Deformation Events, Brittle-to-ductile Transition Rheology Posted Date: May 26th, 2021 DOI: https://doi.org/10.21203/rs.3.rs-408334/v1 License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License Version of Record: A version of this preprint was published at Nature Communications on September 21st, 2021. See the published version at https://doi.org/10.1038/s41467-021-25883-y.
Title: Episodic transport of discrete magma batches beneath Aso volcano
Authors: Jieming Niu1*, Teh-Ru Alex Song1†
Affiliations:
1
Seismological Laboratory, Department of Earth Sciences, University College London, WC1E 6BT,
5 London, United Kingdom.
*Correspondence to: j.niu@ucl.ac.uk.
Summary: Magma ascent, storage, and discharge in the trans-crustal magma plumbing system are key to
long-term volcanic output and short-term eruption dynamics. Petrological analytics, geodetic
deformations and mechanical modeling have shaped the current understanding of magma transport.
10 However, due to the lack of observations, how a distinct magma batch transports from a crystal-rich mush
region to a crystal-poor pool with eruptible magma remains enigmatic. Through stacking of tilt and
seismic waveform data, we find that episodic long-period tremors (LPTs) located near sea level beneath
the Aso volcano are accompanied by a synchronous deformation event, which initiates ~50 seconds
before individual LPT event and concludes seconds after. The episodic deformation source corresponds to
15 either an inflation or a deflation event located ~3 km below sea level, with a major volumetric component
(50-440 cubic meters per event) and a minor high-angle normal-fault component. We suggest that these
deformation events likely represent short-lived, episodic upward transport of discrete magma batches
accompanied by high-angle shear failure near the roof of the inferred magma chamber at relatively high
temperature, whereas their recurrences, potentially composition dependent, are regulated by the brittle-to-
20 ductile transition rheology under low differential stress and high strain rate due to the surge of magma
from below, regulating long-term volcanic output rate. The magma ascent velocity, decompression rates,
and cumulative magma output deduced from the episodic deformation events before recent eruptions in
Aso volcano are compatible with retrospective observations of the eruption style, tephra fallouts, and
plume heights, promising real-time evaluation of upcoming eruptions.
1
Main Text:
Theoretical considerations have shown that the ascending of a magma batch is likely dictated by
the density contrast between magma and surrounding rock, the excess pressure in the magma reservoir,
5 and magma viscosity1. More recent developments on magma transport and storage emphasize a trans-
crustal magmatic plumbing system consisting of relatively long-lived crystal-rich mushes and shorter
time-scale crystal-poor pools that were eventually tapped by eruptions2,3. However, the key process of
distinct magma transport from the crystal-rich mush to the crystal-poor pool is not well known, even
though it is intimately linked to magma ascent and discharge, controlling short-term eruption dynamics
10 and long-term volcanic output.
Numerous petrological means have been utilized to interrogate magma ascent4, including recent
chemical diffusion based geospeedometers5–9. However, these advancements rely on retroactive analysis
of eruption products, which cannot be obtained in real-time during unrest or before eruptions.
Furthermore, these estimates do not resolve the volume or duration of distinct magma ascent. Magma
15 ascent inferred from the migration of seismicity can be difficult as seismicity rarely follows simple
upward movement and the progression of seismicity could indicate conduit formation or propagating of
pressure through existing magma, rather than magma ascent1,10,11.
Ground deformation detected from geodetic means (e.g., InSAR, GNSS, tiltmeter, strainmeter)
provides invaluable insight into the average rate of magma supply12–14. However, except few instances
20 where syn-eruptive deformation of 0.1-10 microstrain over hours or less are reported15–17, the documented
pre-eruptive ground deformation is typically on the order of millimeter to centimeter, microstrain, or
microradian over days, weeks, or months and they do not offer a direct assessment on the nature of a
2
distinct magma ascent, potentially operating at a much shorter duration, higher frequency or/and smaller
volume.
Seismic resonances with periods of 0.2-200 s have been widely detected near shallow conduits or
reservoirs (e.g., < 2 km) in diverse volcanic systems18,19. They are often stationary and repetitive,
5 responding to internal processes accompanying magma ascent or/and the build-up of conduit
overpressure, including degassing, heat transfer and vaporization, change in the fluid pressure, or/and
unsteady magma transport of a deeper origin. The repetitive nature of shallow seismic resonance permits
the use of stacking to tease out small deformation signal20–22 that are otherwise undetected.
Here we report new observations that manifest a causal relationship between repetitive shallow
10 seismic resonances (i.e., shallow hydrothermal reservoir) and deformation within the deeper plumbing
system beneath Aso, an andesitic volcano in Japan23–25. Specifically, we focus investigation against the
very long-period signal (~15 s period) located in a fluid-filled crack-like conduit near sea level beneath
the active Naka-dake first crater26–31 (Fig. 1a). Following the nomenclature established in earlier studies,
we refer to the very long-period signal as long-period tremor (LPT) hereafter. Critically, LPT is known to
15 occur during the quiescence and active period27,29,31, offering a unique opportunity to methodically
explore discrete magma ascents over the entire eruption cycle in 2011-2016.
LPT and synchronous tilt/displacement offset
We analyze seismic and tilt waveform recorded by the fundamental volcano observation network,
or V-net32, which is equipped with collocated surface broadband seismic sensors (Nanometrics 240, ~250
20 s natural period) and borehole tiltmeters (~1 nanoradian resolution)33. Before the 8th Oct 2016
phreatomagmatic eruption34, we observe two anomalously large LPT events that occurred about 2-3
3
minutes before the eruption (Fig. 1b). Tilt offsets accompanying the two LPT events can be readily
observed at all four V-net stations (Fig. 1b). At station N.ASHV, the east-west tilt offset accompanying
the two events reach ~58 nrad and ~88 nrad, respectively.
We manually check tilt and vertical displacement waveforms of other events in the LPT catalog31
5 and discover similar observations in several instances (Fig. S1). In general, the tilt and displacement
offsets at station N.ASHV can be either east-down and vertical-up or west-down and vertical-down, but
the amplitude is typically much smaller than those accompanying the two LPT events before the 2016
eruption. As shown in Fig. 1b, there are several striking differences between the signal of LPT and the tilt
offset. First, the tilt offset at station N.ASHV is much stronger in the east-west component than that in the
10 north-south component, whereas the LPT signal in the north-south component is much stronger than that
in the east-west component. Secondly, the east-west tilt offset at station N.ASHV is much stronger than
that at station N.ASIV, but the LPT signal at station N.ASHV is much weaker than that at station
N.ASIV. These observations strongly indicate that the source of the tilt offset is spatially separated from
the LPT source, possibly closer to station N.ASHV than the source of LPT, which is near the active Naka-
15 dake first crater (see also Fig. 1a).
Discovery of the inflation/deflation event beneath Aso volcano
To systematically examine the presence and the stability of such synchronous signals, we
implement the matched-filter technique31,35 against all LPT events during the 2011-2016 Aso eruption
cycle31. The first of the two LPT events (Event 1) before the 2016 eruption is selected as the reference
20 template event, and we cross-correlate tilt and seismic waveform data of each LPT event against the
template waveforms in the ultra-long period band of 50-250 s, which allows us to effectively detect
possible displacement or tilt offset in the near-field (see also Material and Method). Specifically, we
4
gather detections with the same sign of cross-correlation coefficient in a given calendar time window to
produce waveform stacks and compute bootstrap uncertainties36.
Here we present two global waveform stacks of the highest quality at station N.ASHV during the
volcanic unrest in January 2011-August 2014 (Fig. 2a) and the intermittent Strombolian eruptions in
5 October 2014-April 2015 (Fig. 2b), respectively. During the volcanic unrest, we observe an upward
displacement offset and a predominantly east-down tilt offset (Fig. 2a). During the 2014 Strombolian
eruption, we observe a downward displacement offset and a predominantly west-down tilt offset (Fig.
2b). While the amplitude of the LPT differs by a factor of ~3 between the two episodes, the waveform
offset is relatively steady, i.e., ~1 !" in the vertical displacement and ~1 nrad in the east-west tilt,
10 respectively. Small bootstrap uncertainties of the global waveform stacks suggest the prevalence of the
signal that is synchronous with LPT. Here we refer to the signal associated with an upward (downward)
displacement offset as the inflation (deflation) event.
While it is well documented that LPT is often accompanied by short-period tremors (SPTs, ~0.5-1
s period) located near the top of the LPT source region18,27,37, as demonstrated in Fig. 2, the
15 inflation/deflation event occurs ~60 seconds earlier than SPT or LPT, providing a causal source of
internal triggering. While SPT precedes LPT by ~10 seconds, the peak energy of SPT envelopes arrives
~10 seconds after the LPT onset. The inflation (deflation) event, LPT, and SPT end approximately at the
same time. Observations of inflation/deflation events can also be made in other stations or high-quality
monthly waveform stacks (Fig. S2). Notably, the tilt offsets can remain relatively constant over 30
20 minutes (Fig. S3). We also measure the displacement and tilt amplitude ratio between stations N.ASHV
and N.ASIV in the ultra-long period band of 100-200 s (Fig. S4) against all monthly stacks (Fig. S5-S10).
The stability of these observational attributes indicates that repetitive inflation and deflation events share
generally the same proximity with a relatively stationary source region.
Source location and mechanism
5
Following the Bayesian source inversion approach by Fukuda and Johnson38, we measure the
vertical displacement, horizontal displacement (Fig. S11, see Method), and horizontal tilt offsets of the
reference event (Event 1) and invert the source location and mechanism (Fig. 3a-c, see also Material and
Method). We find that the source is located at a depth of ~3 km below sea level, ~2 km west of the Naka-
5 dake first crater (Fig. 1a, Fig. 3a-d, see also Table S2). The reference event has a moment magnitude Mw
= 3.3 with a predominantly volumetric component (~80%) and a minor dip-slip (normal-fault) component
of ~ 20% (Fig. 1a, Fig. S12, Table S2). The corresponding volume change is ~25,800 m3 (see Method).
The nature of inflation/deflation event in a renewed plumbing system beneath Aso volcano
The source of the inflation/deflation event is located near the inferred magma chamber39,40 (Fig. 1a)
10 but at a shallower depth. It is also near the upper end of a high conductivity anomaly41. We suggest that
the source of the inflation/deflation event corresponds to a shallow magma storage zone (SMSZ) beneath
the Aso volcano, connecting the source of LPT in the shallow conduit from above and the magma
chamber from below (Fig. 3d), suggesting that these episodic deformation events likely represent
instantaneous upward transport of a distinct magma batch near the roof of the inferred magma chamber.
15 We consider that the upward transport of a discrete magma batch only occurs in a short episode of
~ 50-100 s near the roof of a partially molten zone filled with crystal-rich magma, accompanied by high-
angle shear failure. Since the temperature at the depth of SMSZ (~3 km) beneath Aso volcano reaches
500º C42,43, the recurrences of these deformation events are likely regulated by the brittle-to-ductile
transition, under high temperature and high strain-rate44 due to the surge of magma from below, possibly
20 facilitated by ductile fracturing45 or/and magma mixing in the mush46. The deformation event ends as the
system returns to the ductile regime as a result of the shear-stress release or/and decreasing magma supply
(i.e., lower strain rate). As elaborated in the next session, the transport of discrete magma batches does not
exclude volatiles that may readily exist in the top of the mush region47.
6
We suggest that, when the inflow (outflow) is higher than the outflow (inflow), there is a net
volume increase (decrease) in the SMSZ and we observe an inflation (deflation) event (Fig. 3e, Fig. 3g).
When the inflow is approximately equal to the outflow, there is negligible net volume change in the
SMSZ and we observe a negligible offset in tilt or displacement (Fig. 3f). As shown in Fig. 4a, we
5 observe predominantly inflation events during intense unrest in July and August 2014. Right after the ash
eruption at the end of August 2014, we observe events with a negligible net offset in September 2014.
During the intermittent Strombolian eruptions (e.g., November 2014, March 2015), we observe
predominantly deflation events. After the pyroclastic cone collapsed in early May 2015, we again observe
inflation events in May and June 2015. While the deflation events dominate in late 2015 and most of
10 2016, two anomalously large inflation events occur just minutes before the 2016 phreatomagmatic
eruption (Fig. 1b).
These systematic observations also point to a robust and intimate link between surface volcanic
activities and the state of the SMSZ. The prominence of inflation (deflation) events corresponds to a
lower (higher) outgassing potential (Fig. 4b), equivalently a higher (lower) proportion of pressurization
15 LPT in the shallow conduit31, and a lower (higher) SO2 emission (Fig. 4c). Finally, the depth of the SMSZ
is very consistent with the highest gas saturation pressure of melt inclusions in scoria (~80-118 MPa, or 2-
3.5 km below sea level)23, supporting the hypothesis that the magma (and gas) are likely transferred from
a deeper reservoir48 (i.e., a crystal-rich mush) and temporarily stalled in the SMSZ (i.e., a crystal-poor
pool), which serves as a preparation zone for the storage and upward transport before upcoming
20 eruptions.
Implications of the inflation/deflation event on magma/gas transport and upcoming magmatic
eruption beneath Aso volcano
Single-event volume change (rate) versus long-term volume change rate
7
Our new observations suggest that the upward transport of magma/gas from the magma chamber
toward the surface is a stepwise process in an episodic fashion. Since the source is repetitive, the volume
change associated with individual inflation/deflation events can be obtained by scaling the tilt amplitude
of each event against that of the reference event. For example, the east-west tilt of the reference event at
5 station N.ASHV is ~58 nrad, corresponding to a volume increase of ~25,800 m3. The typical east-west tilt
in the global stacks is only about ~1 nrad (Fig. 2), which translates to a volume change of ~440 m3 per
event, or the size of a typical swimming pool.
We systematically measure the tilt amplitude of the monthly stacks (Fig.S13, see also Material
and Method) and estimate the volume change per event, which can be ~50 m3 in the subset of the lowest
10 signal-to-noise ratio (Fig. S14). The monthly volume change is obtained by multiplying the volume
change per event against the event number (Fig. S14) and the cumulative volume change over 2011-2016
is illustrated in Fig. 4a.
For a typical source duration of ~100 s (Fig. 2), the single-event volume change rate estimated
from the global stacks or the monthly stacks is ~0.5-4.4 m3/s or ~0.03-0.13 km3/year which is ~2 orders of
15 magnitude higher than the average volume change rate in 2011-2013 (i.e., ~10-4 km3/year) and in late
2014 (~1.3×10-3 km3/year), the geodetic deflation rate of the magma chamber at a greater depth (i.e.,
~2.5 × 10-4 km3/year over several decades)49,50 and Aso post-caldera output rates (i.e., ~0.001
km3/year)24,25,51 (Fig. 4d). We hypothesize that the volume change rate associated with individual
inflation/deflation event marks the instantaneous magma transport rate of a distinct magma batch,
20 whereas the recurrence interval modulates the averaged transport rate, reconciling the magma transport
over multiple timescales. This hypothesis reconciles similar disparities noted in basaltic volcanic systems
such as Kilauea52 and silicic volcanic systems such as Mount St. Helens53.
8Cumulative volume change in SMSZ before the eruption vs. the size of upcoming magmatic eruptions?
Considering a magma density of 2500 kg/m3, we convert the net volume change DV shown in
Fig. 4a to the net mass change in the SMSZ. There is a good agreement between the total mass change in
the SMSZ before the 2014 eruption and the mass of tephra fallout54,55 (Fig. 4e), consistent with a minimal
5 effect of magma compressibility on the estimate of DV. While the net volume change DV in the SMSZ
can be due to magma (DVmagma) or/and gas (DVgas), our observation shown in Fig. 4e is consistent with the
scenario where DVmagma >> DVgas before the 2014 eruption. However, the net volume change in the SMSZ
during/after the 2014 Strombolian eruption episode is 6-8 times larger than that before the eruption (Fig.
4e). Such a discrepancy is consistent with DVmagmaestimate the ascent velocity near the SMSZ of ~0.14-0.41 m/s and the decompression rate of ~0.004-
0.011 MPa/s, which is comparable to syn-eruptive decompression rates estimated by melt embayment and
water-in-olivine studies in basaltic eruptions5,6 and theoretical estimates for the strombolian eruption58
(Fig. 5).
5 Using a magma density of 2500 kg/m3, we convert the single-event volume change rate (~0.5-4.4
m3/s) to the mass flow rate of ~1,250-11,000 kg/s (Fig. 5). Since the Strombolian eruptions in Aso are
intermittent, the averaged mass discharge rate estimated by tephra deposits of the 2014 Strombolian
eruption (i.e., ~25-430 kg/s)55 is likely lower than the instantaneous mass discharge rate. Assuming only
small percentages (i.e., 5%) of the entire eruption duration24, the magma discharge rate of the 2014
10 eruption is ~500-8,600 kg/s, which is reasonably comparable to the estimated single-event mass flow rate
in the SMSZ. While the estimated mass flow rate in Aso is lower than those estimated in basaltic
eruptions by an order of magnitude (Fig. 5), such a difference is consistent with the disparity in the
average volcanic output rate between basaltic eruptions and andesitic eruptions59 (Fig. 4d).
In contrast, the two anomalously large inflation events ~2-3 minutes before the 2016
15 phreatomagmatic explosion corresponds to a much higher volume change rate of ~860-1,300 m3/s over a
30 s duration. The estimated mass flow rate is ~2.2-3.3×106 kg/s (Fig. 5) and the estimated ascent
velocity and decompression rate near the SMSZ are also much higher at ~7 m/s and ~0.2 MPa/s,
respectively, indicating a much larger overpressure. These results are similar to other explosive basaltic
eruptions6–8 (Fig. 5). Considering the tephra mass and the duration of the 2016 phreatomagmatic
20 explosion of 160-260 s, the total mass discharge rate is 2.7-4.1x106 kg/s60, comparable to our inferred
mass flow rate in the SMSZ. Using the empirical scaling between the mass discharge rate and the plume
height61, the mass flow rate in the SMSZ before the 2016 eruption projects a plume height of ~10 km,
consistent with observations56,62,63.
10Perspective and outlook
In essence, we show that repetitive shallow resonances provide a pathway to unravel magma flows
deep in the magma plumbing system (Fig.6). Specifically, discrete magma transport between crystal-rich
mush and crystal-poor pool could be accommodated by episodic deformation event accompanied by high-
5 angle normal faulting in a high strain-rate, low differential stress regime governed by the brittle-ductile
transition rheology. The duration of each deformation event (~ 50 s) is much longer than what is expected
for crustal earthquakes of similar size and such a slow deformation, to some extent, is analogous to slow-
slip events observed worldwide in the subduction zone interface or in the deep crust64,65, where the
rheological condition and fluid pressure are likely similar to that near the chamber roof, or the top of the
10 mush region..
The contrast in the decompression rate (or the ascent velocity) and the mass flow rate inferred in
this report are strongly correlated with the eruption style in Aso, collaborating with theoretical
prediction66 and geological evidence67. As persistent shallow resonances in Aso have been documented
for almost a century31,68,69, establishing the amplitude scaling between the synchronous sources in Aso
15 will permit critical evaluations of pre-eruptive volume changes (or volume change rates) against the size
and style of historical eruptions even when modern geodetic and broadband seismic data are not available.
Since the mass discharge rate and the magma ascent velocity or decompression rate can only be
obtained retroactively after the eruptions5–10,67,70, new seismic observations reported here underscore the
possibility that, through real-time signal detection/processing and source analysis in volcanic systems
20 where repetitive shallow seismic resonances are routinely detected18,19, the volume change and volume
change rate (or mass flow rate) of episodic deformation similar to observations in Aso could facilitate in-
situ characterization of magma ascent and transport before upcoming eruptions. Such efforts can be
coupled with improved knowledge of external loading/unloading conditions67,71, continuous monitoring of
11degassing rate72 and the permeability/rheology of shallow conduit31,67 to facilitate diagnosing short-term
eruption potential.
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10
Acknowledgments: We gratefully thank NIED and JMA for providing us the high-quality waveform data
of V-net. We are also grateful to Prof. Mare Yamamoto and Prof. Takuhiro Ohkura for hosting J. Niu in
Aso Volcanic Observatory and Tohoku University during the early stage of this work, which helps
improve our understanding of the LPT and Aso volcanic system. The uses of the UCL Legion High-
15 Performance Computing Facility (Legion@UCL), the UCL Grace High-Performance Computing Facility
(Grace@UCL), the UCL Emerald High-Performance Computing Facility (Emerald@UCL), and
associated support services are acknowledged. Data processing and production of figures are
implemented in Python with relevant modules such as ObsPy and PyCUDA. Funding: J. Niu and T.-R.
A. Song are supported by the Natural Environment Research Council, UK (NE/ P001378/1 &
20 NE/T001372/1). Author contributions: J. Niu: Conceptualization, Methodology, Software, Validation,
Formal analysis, Investigation, Resources, Data curation, Writing - original draft, Visualization. T.-R. A.
Song: Conceptualization, Methodology, Validation, Formal analysis, Writing - review & editing,
Supervision, Project administration, Funding acquisition, Conceptualization.; Competing interests:
22Authors declare no competing interests. Data and materials availability: The waveform data can be
downloaded from https://www.hinet.bosai.go.jp. The LPT catalog published by Niu and Song (2020) and
all the codes used in this study are available upon request.
Supplementary Materials:
5 Methods
Figures S1-S14
Tables S1-S2
References (##-##)
23Figure 1. Aso volcano system and observations of tilt offset synchronous with LPT. (a) The
topographic relief near the Aso caldera is overlaid with collocated seismometer and tiltmeter (open
triangles), LPT source in the shallow crack-like conduit (thick bar), the geodetically inferred magma
5 chamber (open circle), and the low-velocity zone (dashed circle). The star marks the Naka-dake first
crater. The upper inset displays Aso volcano located in Kyushu island, southwest Japan. The source of the
tilt offset is marked as a red cross and it is referred to as a shallow magma storage zone (SMSZ). The
beach ball displays the deviatoric component of the source mechanism in SMSZ. (b) Tilt waveforms at
four V-net stations near the October 8, 2016 phreatomagmatic eruption. The waveforms are low-pass
10 filtered at 0.05 Hz with a 4th-order casual Butterworth filter. The linear trend determined in the first 10
minutes is used to remove the background trend. “Event 1” and “Event 2” denote the tilt offset that
occurred concurrently with two LPT events. Redline marks the timing of the 2016 eruption.
24Figure 2. Observations of inflation (a) and
deflation (b) waveform stacks against LPT and
5 SPT. Broadband tilt, displacement, and velocity of
global waveform stacks at station N.ASHV are
presented against LPT velocity waveforms (10-30 s)
and SPT envelopes (0.5-1 s). The bootstrap errors
are shown in yellow strips. These waveforms and
10 envelopes are aligned against the onset of SPT. To
preserve the phase of the long-period waveform (>
50 s), a 2nd-order acasual Butterworth filter is
implemented. We apply a 2nd-order causal
Butterworth filter to preserve the timing of the LPT
15 waveform (10-30 s) and SPT envelope (0.5-1 s).
25Figure 3. Source inversion result and a new conceptual framework of magma/gas transport in the
plumbing system beneath Aso volcano. (a), (b) and (c) compares data (black arrows) and synthetics (red
arrows) from the inverted source location and mechanism. Red cross marks the inverted source location
5 with a confidence level of 99%. Black, red and blue circles indicate the new Mogi magma chamber40,
BYA and BCU magma chambers49, respectively. Dashed circle marks the low-velocity zone39. (d) An
east-west cross section showing a conceptual diagram of magma/gas transport system beneath Aso
volcano. The inverted source, or the shallow magma storage zone (SMSZ), connects the LPT source in
the shallow conduit from above and the magma chamber from below. SPT source is shown directly above
10 the shallow conduit. The inset displays the volumetric and deviatoric components of the focal mechanism,
respectively, looking from the south. Blue dashed line indicates the brittle-ductile transition. (e), (f) and
(g) display the simplified flow conditions where the SMSZ suffers inflation, null volume change, or
26deflation, respectively. Waveform stacks representative of these three conditions are shown directly
below.
27Figure 4. Characterization of the volume/mass change inside the SMSZ during the 2011-2016
eruption cycle (a) The accumulative net volume changes in the SMSZ. Dark inverse triangles mark the
onset of the 2014 Strombolian eruption, the 2015 and 2016 phreatomagmatic eruptions, whereas hatched
5 areas mark their eruption episodes. Grey inverse triangles indicate minor eruptions. ⊕, ⊖ and ⊙ mark
the episodes associated with observations of inflation event, deflation event and event of negligible offset,
respectively (see waveform stacks in the insets). ① and ② mark the time windows where the mass
changes in SMSZ before the 2014 and 2016 eruptions are calculated, respectively (see also Fig. 4e). (b)
Outgassing potential of the shallow conduit, or equivalently the moment ratio between pressurization and
10 depressurization LPTs31. A lower (higher) outgassing potential corresponds to a higher proportion of
pressurization (depressurization) LPT events. (c) The campaign SO2 emission from JMA
(https://www.data.jma.go.jp/svd/vois/data/fukuoka/rovdm/Asosan_rovdm/gas/gas.html). (d) The volume
change rates estimated by the inflation event (black crosses), the geodetic data (green cross), and
28geological analysis (blue cross). Average volcanic output rates from White et al.59 are shown in the pink
shaded regions. (e) The observed volcanic output of the 2014 Strombolian and 2016 phreatomagmatic
eruptions against the estimated mass change inside the SMSZ before the eruptions. ① and ② mark the
time windows in Fig. 4a where the mass changes in SMSZ before the 2014 and 2016 eruptions are
5 calculated, respectively.
29Figure 5. Comparisons of the mass flow rate and decompression rate from petrology and
seismology. Open circles and triangles mark the volume estimates from waveform stacks of inflation and
deflation events before the 2014 and 2016 eruptions (see details in the main text). Target crosses mark the
5 median volume estimates from the five subsets (Fig. S13a-e). Solid circles mark previous compilations in
basaltic volcanoes5, where the decompression rates are estimated from water diffusion in olivine or
embayment studies and the mass discharge rates are estimated from volcanic outputs or plume heights,
respectively. Contour lines display a theoretical estimate of decompression rate and mass flow rate
against fixed conduit radius (see equation 4 in Barth et al.5). Hatched areas show the mass discharge rate
10 of the 2014 and 2016 eruptions (see details in the main text). Dashed line indicates the boundary of
magmastatic-dominated and friction-dominated decompression after Barth et al.5.
30Figure 6. A conceptual diagram of episodic deformation in the chamber accompanying repetitive
shallow volcanic resonances, providing the glue to long-term volcanic output and short-term
magma ascent/discharge rates. Green solid bars indicate the global observations of the average volcanic
5 output rates over eruption cycles in geological time scale (~1 yr–1 Myr). Gray dashed bars indicate the
single-event magma ascent/discharge rate over a seismic time scale (~100 s). Composition, viscosity,
rheology and tectonic settings govern the recurrences of episodic deformation (red lines).
31Methods
1. Systematic detection using the matched filter (the inflation/deflation event)
A robust observation of the tilt or displacement offset shown in Fig. 1b and Fig. S1 requires a high
signal-to-noise ratio that is not routinely achievable. Instead, we measure the energy in the ultra-long-
5 period band and use it as a proxy for the static offset30. Here we use the matched filtered technique31,35 to
systematically examine the presence and the stability of such synchronous signals against the LPT event
catalog during the 2011-2016 Aso eruption cycle31.
The first of the two LPT events before the 2016 eruption (Event 1 in Fig.1) is selected as the
reference template event. The waveforms at two long-running stations, N.ASHV and N.ASIV, are cut in a
10 10-minute window centered at the LPT arrival time and filtered in the period band of 50-250 s using a 3rd-
order causal Butterworth filter to obtain the template waveforms. The waveforms of each LPT event are
processed in the same way as the reference event before the matched filter is applied to cross-correlate
waveform data against the template waveforms. To avoid the coupling between tilt and translation in the
horizontal components73, we only concern vertical-component seismic waveform data and borehole tilt
15 waveform data in the signal detection. Depending on the cross-correlation coefficient (CC) and signal-to-
noise ratio (SNR) between waveform data and the template waveforms (Table S1), the detection against
the entire LPT catalog of more than 200,000 events is divided into five subsets (I-V) (Table S2).
2. Waveform stacking
After removing the mean and trend of raw seismic waveforms, we align and stack the waveforms
20 against the LPT event time to produce the waveform stacks, which greatly enhances the signal and
eliminates incoherent noise. To minimize the bias introduced by arbitrary spikes as well as the energy
from large earthquakes, we normalize raw velocity waveforms of the single event against their vertical
peak-to-peak velocity in the period band of 10-30 s at station N.ASHV before stacking. After stacking the
32normalized waveforms, the waveform stacks are multiplied by the median vertical peak-to-peak velocity
in the period band of 10-30 s to recover the amplitude of the waveform stack in a given month. The
bootstrap technique is used to quantify the uncertainties of the waveform stacks36. After deconvolving the
instrument response up to 1000 seconds, we remove the background mean in the first 150 sec of the
5 velocity waveform stacks, perform a causal low-pass filter, and integrate the velocity waveform stacks to
obtain displacement waveform stacks.
Regarding tilt waveform stacks, we first differentiate the raw tilt waveform to obtain the tilt-rate
waveform and apply the same data processing procedure as done against velocity waveforms. This
stacking procedure not only reduces noise but also helps remove unwanted bias associated with tides,
10 pressure, temperature, or rainfall, which are nonetheless trivial in the data window of 10 minutes.
3. Estimate the static displacement offset of the broadband seismometer
As the seismic recording is also sensitive to sensor tilt, it is often difficult to recover true
translational signal74. This tilt-related signal is often exhibited as a non-linear drift in the original
displacement seismogram74. Due to the projection of gravitational force into the horizontal axis, this
15 phenomenon is particularly severe in the horizontal components. Many approaches have been proposed to
separate translational and tilt signals in seismic recordings73,75–79. Here we estimate and remove the
nonlinear drift in the displacement seismogram by least-square fitting the portion of seismogram without
major signals with a polynomial function75,76.
The pre-event window is set to 20 s and the total duration of seismograms is 120 s. A 4th-order
20 polynomial function is used as suggested by Zhu76. After removing the non-linear drift (Fig. S11), the
displacement offset in the individual component is calculated by differing the average displacements in
the post-event (mean: (! , standard deviation: ) ! ) and pre-event (mean: (" , standard deviation: ) " )
windows as ( = (! − (" , with uncertainty, ) = ,() " )# + () ! )# .
33As indicated in the previous study78, the static displacement from this approach may be affected
by the selection of polynomial order and time window78. In our case, the determination of the time
window of the major signal of the reference event is relatively straightforward. As presented in Tab. S2,
the selection of polynomial order does not significantly change the estimations of the point-source
5 location and source geometry.
4. Source properties of the inflation/deflation event
We followed the mixed linear-nonlinear source inversion scheme in a Bayesian framework
proposed by Fukuda and Johnson38 to obtain the location and mechanism of the reference event (Event 1
in Fig. 1b). This mixed inversion method efficiently handles non-linear inversion problems when some of
10 the parameters are linearly related to the observations. The offsets of the vertical displacement, horizontal
displacement and horizontal tilt are modeled with Okada’s analytic deformation model for a point
source80.
4.1 Problem formulation
Considering a mixed linear-non-linear inversion problem38 associated with a point
15 dislocation/force source proposed by Okada80: 0 = 1(2)3 + 4 where 1(2) is the kernel matrix relating
non-linear model parameters, 2 = [6$ , 8$ , 9$ , :, ;]% (3-D Cartesian location of a point source with respect
to the Naka-dake first crater, strike and dip angles of the fault plane and crack plane), and linear model
parameters, 3& = ["$$ , "'$ , "() , "*+ ]% (the scalar moments of strike-slip, dip-slip, tensile crack and
explosion) or 3, = ["$$ , "'$ , "() , "*+ , =- , =. , =/ ]% (the scalar moments of strike-slip, dip-slip, tensile
20 crack and explosion, the magnitudes of forces towards east, north, and up directions), to the observation
vector, 0 = [0& , 0, , 00 ]% (vertical displacement, horizontal displacement, and horizontal tilt), with
normally distributed error, 4 = [4& , 4, , 40 ]% where 41 ∼ ?(@, A1 ) . B(2 minimum norm constraints (or
34Tikhonov regularization) are applied on the linear parameters, CD3 3C , where B = 2 if forces are
#
considered. Otherwise, B = 1.
An optimal solution can be found by minimizing an objective function Φ(2, 3) = ∑657! " [05 −
!
4 !
15 (2)3]% A8!
5 [05 − 15 (2)3] + ∑37! 9 " CD3 3C where )5 adjust relative weights of the multiple data sets
: ! #
#
#
5 in fitting the data; I3# adjust relative weights of regularization prior on 3. If B = 1, D! = J. If B = 2,
J 0 0 0
D! = K ;×; M and D# = N
0 0 0 J=×= O.
Following Fukuda and Johnson38, if assuming that the prior
probability density functions of the linear, non-linear and hyperparameters are uniform, the posterior
probability density function of the parameters given the data, P(2, 3, Q, R|0), can be given according to
Bayes’ theorem as below:
10 − ln P(2, 3, Q, R|0)
:
∝ W 2X5 ln )5 + W 2Y3 ln I3 + Φ(2, 3∗ )
6
57! 37!
1 1 %
5 15 (2) + W # D3 D3 Z
:
+ ln ZW # 1%5 (2)A8!
6
)5 I3
57! 37!
where 3∗ is the weighted damped least-square solution of the linear parameter given the nonlinear and
hyperparameters, 2 , Q and R ; X5 is the number of samples in [ (2 data set; Y3 is the number of
15 parameters efficiently regulated by \(2 prior constraint. If B = 1, Y! = 4. If B = 2, Y! = 4 and Y# = 3.
To tackle the weights between displacement and tilt, we first normalize the kernel matrix 1(2),
the observation vector 0 and the covariance matrix A by the absolute of observation vector as _ =
1/|(! | ⋯ 0
` ⋮ ⋱ ⋮ e, 1? (2) = _1(2), 0? = _0 , and A? = _A_@ . Then, by utilizing Cholesky
0 ⋯ 1/|(. |
35factorization, we equalize the weight difference among the observations as A? = f@ f , 0?? = f0? ,
1?? (2) = f1′(2) . Then, if let ) #5 = 1 , we can rewrite the objective function as Φ(2, 3) =
(h − i3)@ (h − i3) where h = [0?? , @]% and i = j1?? (2), $ , ⋯ , %k . In this case, the posterior
%
B B
9 9$ %
probability density function of the parameters can be re-written as − ln P(2, 3, R|0) ∝ ∑:37! 2Y3 ln I3 +
Φ(2, 3∗ ) + lnli@ il where 3∗ = mi@ in i h.
8& @
5
4.2 Synthetic static displacement/tilt calculation
Synthetic displacements and tilts from a point dislocation source in a homogeneous half space are
calculated following Okada80. Following Legrand et al.30, we set the P velocity of 1500 m/s, S-velocity of
800 m/s and the density of 1700 kg/m3 , respectively. To evaluate the significance of the single force
10 component, we also calculate synthetic displacement and tilt from a point force source following
equations 1-2 in Okada80. To take into account the station elevation (i.e., typically 600 m above sea level),
we set the station elevation as the free surface and the depth of the source is adjusted accordingly in the
calculation of synthetics81. Since the borehole tiltmeter is typically about 100 meters below the surface,
we calculate synthetic tilts at the borehole depth.
15 4.3 Bayesian inference of model parameters
We first use differential evolution method82 to find the global minimum of −ln P(2, 3, R|0). This
step is repeated for hundreds of times with the randomly assigned initial values. A consistently converged
minimum is regarded as the global minimum. Subsequently, we use an ensemble Monte Carlo Markov
Chain method83,84 to sample the posterior probability density function. The starting values of ensemble
20 Markov chains of o(2 parameter are randomly assigned according to the global minimum by a normal
distribution, ?(6C , |6C |), where 6C ∈ {2, 3, R}. This step is also repeated for multiple times to evaluate
the convergence of independent Markov chains. Finally, the posterior probability density functions of the
parameters are combined from multiple independent chains (Fig.S12). The moment-tensor representation
36of the source can be reconstructed from the moments of strike-slip, dip-slip, tensile crack and explosion
by following equation 3.21 in Aki and Richard85.
5. Estimating volume change
5.1 Volume change of the reference event
5 As the strike-slip and dip-slip components do not experience any volume changes, the volume
change associated with the reference event is estimated by only considering the tensile crack and
explosion components. Following Okada80, the eigenvalue of tensile-crack moment tensor is !DE =
"() [1,1,1 + 2 !⁄s]% and the eigenvalue of explosion moment tensor is !*+ = "*+ [1,1,1]% . Following
equation 16 in Kawakastu and Yamamoto18, the volume change associated with the tensile crack
10 component is "uF() = "() /s where s is Lame constant. Following equations 10-11 in Kawakastu and
Yamamoto18, the volume change associated with the explosion component in the presence of the
confining pressure of the surrounding elastic medium is "uF*+ = "*+ /(s + 2!) where ! is shear
modulus. Hence, the ‘Mogi volume’ change associated with the reference event is "uF = "uF*+ + "uF() .
If assuming s = 2.737 xyz and ! = 1.088 xyz , |uF = ~25840 "= (Tab.S2, a 4th-order polynomial
15 function).
5.2 Estimate volume change from monthly tilt waveform stacks
Following the note in section 5.1, the Mogi volume change corresponding to a 1-nrad tilt at
N.ASHV.LE is ~440 m3. However, unlike the reference event, the static tilt offset in the monthly stacks
can be difficult to measure directly in the time domain. As the duration of the tilt offset is typically ~100 s
20 or less, the amplitude of the tilt-rate spectra plateaus in the near-field at the very long-period (i.e., >1000
s), corresponding to the amplitude of the tilt (Fig. S13). We zero-pad the stacked waveform 10,000s
before the start of the tilt-rate time series and compute the tilt-rate amplitude spectra. The amplitude at the
period of 10,000 s is used as a proxy for the static offset, which is scaled against the tilt of the reference
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