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The rise and fall of periodic ‘drumbeat’ seismicity at Tungurahua
volcano, Ecuador
Andrew F. Bell (1), Stephen Hernandez (2), H. Elizabeth Gaunt (2), Patricia Mothes
(2), Mario Ruiz (2), Daniel Sierra (2), and Santiago Aguaiza (2)
(1) School of GeoSciences, University of Edinburgh, Edinburgh, U.K.,
(2) Instituto Geofisico, Escuela Politécnica Nacional, Quito, Ecuador
Key words: volcanic seismicity; long period earthquakes; drumbeat earthquakes;
conduit processes; volcano deformation; volcano degassing
Abstract
Highly periodic ‘drumbeat’ long period (LP) earthquakes have been described from
several andesitic and dacitic volcanoes, commonly accompanying incremental ascent
and effusion of viscous magma. However, the processes controlling the occurrence
and characteristics of drumbeat, and LP earthquakes more generally, remain
contested. Here we use new quantitative tools to describe the emergence, evolution,
and degradation of drumbeat LP seismicity at the andesitic Tungurahua volcano,
Ecuador, in April 2015. The signals were recorded during an episode of minor
explosive activity and ash emission, without lava effusion, and are the first to be
reported at Tungurahua during the ongoing 17 years of eruption. Following four days
of high levels of continuous and ‘pulsed’ tremor, highly-periodic LP earthquakes first
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appear on 10 April. Over the next four days, inter-event times and event amplitudes
evolve through a series of step-wise transitions between stable behaviours, each
involving a decrease in the degree of periodicity. Families of similar waveforms
persist before, during, and after drumbeat activity, but the activity levels of different
families change coincidentally with transitions in event rate, amplitude, and
periodicity. A complex micro-seismicity ‘initiation’ sequence shows pulse-like and
stepwise changes in inter-event times and amplitudes in the hours preceding the onset
of drumbeat activity that indicate a partial de-coupling between event size and rate.
The observations increase the phenomenology of drumbeat LP earthquakes, and
suggest that at Tungurahua they result from gas flux and rapid depressurization
controlled by shear failure of the margins of the ascending magma column.
1 Introduction
On 10 April 2015 a swarm of long period (LP) earthquakes with unusually regular
and persistent inter-event times and amplitudes was recorded by the monitoring
network of the Instituto Geofísico of the Escuela Politécnica Nacional (IGEPN) at
Tungurahua volcano, Ecuador (Fig. 1). Such characteristics appear similar to the
highly periodic ‘drumbeat’ earthquakes notably accompanying dome growth at Mount
St Helens (Iverson et al., 2006; Moran et al., 2008), and also reported from effusive
episodes at a range of andesitic and dacitic volcanoes including: Redoubt (Buurman et
al., 2013; Ketner and Power, 2013) and Augustine (Buurman and West, 2010; Power
and Lalla, 2010), USA; Soufriere Hills, Montserrat (Rowe et al., 2004; White et al.,
1998); and Guagua Pichincha (García-Aristizábal et al., 2007; Villagómez, 2000) and
Reventador (Lees et al., 2008), Ecuador. However, only relatively modest explosive 2
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activity and ash emission was observed at Tungurahua at this time, and neither
drumbeat-like signals nor dome emplacement had been reported since the eruption
began in 1999.
Volcanic seismicity allows insights into otherwise hidden physical processes
controlling eruptive activity at volcanoes, and is a key indicator of the state of
volcanic unrest (Sparks, 2003). LP earthquakes are often associated with the onset of,
and changes in, eruptive activity (Chouet, 1996; McNutt, 1996). Consequently,
knowledge of the source mechanisms for LP earthquakes is important for
understanding underlying physical processes and improved eruption forecasting.
Strong path effects present a challenge for traditional waveform inversion techniques
(Bean et al., 2013), and a diverse range of source mechanisms have been proposed for
apparently similar waveforms (Chouet and Matoza, 2013; McNutt, 2005). The
drumbeat phenomenon is a special case of LP seismicity, and as such offers the
possibility of fundamental insights into the origin of LP earthquakes. However,
observations come from only a small number of volcanoes and a narrow range of
eruptive conditions and magma rheologies, with few statistical measures available to
quantitatively characterize and compare activity across distinct systems.
The data from Tungurahua in April 2015 provide an important new opportunity to
investigate the occurrence attributes of LP earthquakes and the origins of drumbeat
seismicity. We present analyses of multi-parametric monitoring data, event statistics,
and seismic waveforms, revealing a complex evolution of variably periodic seismicity
unreported from other volcanoes, significantly broadening drumbeat phenomenology.
We suggest an LP source mechanism involving injection and depressurization of
pulses of ash-laden gas into a resonating fracture network, but where the timing of
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escape is regulated by local mechanical failure of the margins of the ascending
magma column.
First we summarise current of understanding of the origin of LP seismicity and
drumbeat earthquakes and introduce Tungurahua volcano. We then describe the data
recorded by the geophysical and geochemical monitoring network of the IGEPN
during April 2015, the nature of some of the recorded seismic waveforms, and
detailed event occurrence statistics. Finally, we discuss possible interpretations of
these data in terms of physical processes controlling earthquake generation, magma
ascent, and gas flux at Tungurahua, and implications for related volcanic systems.
1.1 LP earthquake source processes
LP earthquakes are characterized by energy concentrated between 1-5 Hz,
emergent onsets, and extended coda often dominated by a restricted range of
frequencies (Chouet, 1996). Models for LP earthquake generation generally require
two components: an initial excitation or trigger mechanism; and a subsequent
resonance or scattering of the waveform. Proposed excitation mechanisms for
andesitic volcanoes typically invoke either gas or magma movement with subsequent
resonances within a fluid-filled crack (Chouet, 1996) or the magma column (Neuberg
et al., 2000).
Shallow LP earthquakes at Galeras volcano have been interpreted as resulting from
the release of a pulse of pressurized gas from the magma column, dilating and
exciting cracks in an andesite dome (Gil-Cruz and Chouet, 1997). A similar model
was proposed for LP earthquakes at Tungurahua (Molina et al., 2004). However,
numerical models of LP earthquake generation through gas-driven crack resonance
place specific constraints on the required crack dimensions and impedance contrast
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between fluid and solid phases (Kumagai and Chouet, 2001). Concerns as to the
feasibility of these criteria under common volcanic conditions supported the
development of models where LP earthquakes are excited by magma failure during
incremental ascent. Motivated by observations of fractures in fossil volcanic conduits
(Tuffen et al., 2003), LP earthquakes at Soufriere Hills volcano were interpreted as
resulting from the shear failure of ascending magma near the column margins (De
Angelis and Henton, 2011; Neuberg et al., 2006). However, there remain outstanding
questions about the maximum amplitudes of events that can be generated by magma
failure (Tuffen and Dingwell, 2005) and minimum magma healing times (Yoshimura
and Nakamura, 2010). A ‘dry’ excitation mechanism has also been suggested for
shallow LP earthquakes, involving slow shear failure of the edifice at low confining
pressure, and a strong scattering effect (Bean et al., 2013).
1.2 Drumbeat seismicity
Earthquake interactions and triggering mean that most tectonic earthquakes are
clustered in time (Touati et al., 2011). The null-hypothesis for volcano-tectonic
earthquakes is clustered or independently (Poisson) distributed events in time (Bell et
al., 2011); however, exceptionally, highly periodic (anti-clustered) LP or hybrid
‘drumbeat’ earthquakes have been reported (Buurman et al., 2013; Buurman and
West, 2010; Iverson et al., 2006; Lees et al., 2008; Villagómez, 2000; White et al.,
1998). Drumbeat earthquakes are characterised by a restricted range of inter-event
times and amplitudes compared to more typical activity, and highly similar
waveforms. These properties require a persistent source location, a non-destructible or
rapidly renewing mechanism, and a physical system involving small oscillatory
deviations from near equilibrium conditions (Iverson et al., 2006; Moran et al., 2008).
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The 2004-2008 eruption of a de-gassed lava spine at the dacitic Mount St Helens
was accompanied by large numbers of highly periodic LP and hybrid earthquakes
(Moran et al., 2008). Inter-event times were commonly close to 100 s, within the
range of 30 s to 300 s, and shifted slowly in time (Iverson, 2008). Source depths were
estimated as less than 500 m. As drumbeat occurrence coincided with steady-state
viscous lava extrusion, models for the earthquake source included stick-slip of the
plug margins (Iverson et al., 2006) and magma failure (Kennedy and Russell, 2012).
Periodic oscillations in plug velocity resulted from a balance between magma ascent
and plug weight and momentum, damped by friction at the plug margin and
accommodated by compression of ascending compliant gas-rich magma (Iverson,
2008). However, relatively poor correlation between extrusion rate and earthquake
inter-event times (Moran et al., 2008), source mechanisms from waveform inversions
(Waite et al., 2008), and considerations of the maximum size event for stick-slip
source mechanisms, gave rise to an alternative LP model involving repeated
pressurization and collapse of a water- or steam-filled sub-horizontal crack located
around 200 m depth (Waite et al., 2008).
Neuberg et al. (2006) interpret periodic LP earthquake inter-event times
accompanying dome emplacement at Soufriere Hills volcano in terms of a brittle
magma failure model. Each earthquake represents an increment of magma ascent,
raising fresh un-fractured magma into a ‘seismogenic window’. Periodic earthquake
inter-event times will emerge if the magma ascent rate, failure strength, and slip
distance remain constant or slowly changing. Experimental studies suggest that
frictional melting may enhance the periodic stick-slip process, especially at dacitic
systems (Kendrick et al., 2014). Steadily decreasing periodic inter-event times are
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observed prior to the onset of explosive events, possibly resulting from increasing
magma ascent rates (Neuberg et al., 2000).
1.3 Tungurahua volcano
Tungurahua is a 5,023 m high stratovolcano located in the Eastern Cordillera of the
Andes of Ecuador. Historically it is one of the most active volcanoes in the northern
Andes (Samaniego et al., 2011). Tungurahua has been in a state of eruption since
October 1999, producing andesite of a relatively unchanging bulk composition
(Samaniego et al., 2011). Eruptive behaviour has been characterized by episodes of
explosive strombolian or vulcanian activity of a few months duration, interspersed by
repose episodes involving only weak steam and ash emissions or total quiescence
(Arellano et al., 2008; Hidalgo et al., 2015). At no time in the eruption has effusive
dome emplacement occurred, though short lava flows were produced in 2006 and
2014. The IGEPN has monitored the eruption with a comprehensive multi-parametric
network. Seismicity has been dominated by swarms of LP earthquakes, with smaller
numbers of hybrid and VT earthquakes, along with episodes of continuous tremor and
explosions. Typical patterns of seismicity involve an increase in the rate of LP
earthquakes a few hours or days before the onset of new explosive activity, sometimes
preceded by small VT or hybrid earthquake swarms. The rate of LP earthquakes then
decrease as activity wanes. These episodes are often accompanied by cycles of
increasing and decreasing radial tilt, but many such cycles also occur with little or no
eruptive or seismic activity. By the start of April 2015, Tungurahua had experienced
its longest repose period of the current eruption, following the end of the preceding
vulcanian episode in September 2014. A longer-term inflation signal was recorded
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from January 2015, suggesting progressive pressurization of the magmatic system
and/or gradual, piecemeal magma ascent.
2 Data and methods
2.1 Monitoring data
Seismic, deformation, and gas flux data for Tungurahua are recorded by the
monitoring network of the IGEPN. The seismicity was best recorded at the nearest 1
Hz short-period vertical component seismometer located at station ‘RETU’, at 3900 m
elevation. Primary seismic data manipulation was undertaken using the Obspy python
library (Krischer et al., 2015). During drumbeat activity, the high similarity of
waveforms and persistent periodicity indicates that earthquakes originate from closely
located sources, and therefore the amplitude recorded at RETU is a reasonable
approximation of relative event size. Data from RETU was used to determine 15
minute relative seismic amplitude (RSAM), identify event waveform characteristics,
and picked to provide a detailed event catalogue. A catalogue of located events (Fig.
2) and magnitudes was generated using the broader IGEPN seismic network.
However, a low signal-to-noise ratio meant that many events were too small to
identify on most of the other stations around the volcano and in combination with
emergent onsets, means that location uncertainties are significant. Radial tilt data was
recorded by a biaxial tiltmeter station located at RETU, and SO2 flux measurements
made by a DOAS station in Pillate village, located W of the edifice (Hidalgo et al.,
2015). Infrasound measurements recorded no significant signals during April 2015,
unlike some previous unrest episodes (Ruiz et al., 2006).
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2.2 Statistical methods
We define the ‘periodicity’ of earthquake occurrence times as the ratio between the
mean and standard deviation of the inter-event times. For events that are randomly
distributed in time, with constant average rate λ (i.e. a Poisson process) the inter-event
times, τ , follow an exponential distribution with a probability distribution function
f ( τ ; λ )= λ e−λτ for τ>0, mean μ=1/ λ, and variance σ 2=1/ λ2. For such data, the mean
inter-event time provides the maximum likelihood estimate of the model parameter,
allowing a comparison between data and model. Therefore, the periodicity, μ/σ=1,
equivalent to the coefficient of variation for the earthquake rate. The variance of inter-
event times for earthquakes that are clustered in time (e.g. mainshock-aftershock
sequences or swarm activity) will be relatively high, giving values of periodicity less
than 1. The variance of highly periodic (anti-clustered) earthquakes will be relatively
small, resulting in periodicity values greater than 1.
2.3 Cluster analysis
We use a two-stage clustering algorithm to identify families of repeating events
(Green and Neuberg, 2006; Rodgers et al., 2016, 2013). The process involves: (1) an
initial grouping stage based on individual maximum pair cross-correlations exceeding
a specified threshold value; and (2) a secondary family coalescence stage using the
average waveform for each family in Stage 1, and a second, higher, threshold value.
Although we find the details of family inter-relations is strongly dependent on the
choice of threshold parameters and starting event, several key observations are robust
and independent of these choices. For consistency with other studies, we show results
using values of 0.7 and 0.8 for the first and second threshold values, respectively.
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3 Observations and results
3.1 Evolution of the April 2015 unrest episode
A large increase in seismic activity and the onset of moderate ash emissions on 6
April 2015 marked the start of a new unrest episode (Fig. 3). RSAM increased rapidly
at 08:30 on 6 April 2015 (all times given in UTC), indicating an increase in the level
of seismic activity (Fig. 3b). It remained elevated, though with transient pulse-like
increases and short periods of quiescence, for the duration of unrest. To the level of
resolution permitted by daily gas flux measurements, trends in RSAM broadly track
those in SO2 flux (Fig. 3b). Tilt data follows a cycle of increasing and decreasing
radial tilt through the unrest, with an increasing trend starting two days before the
elevated RSAM, and a maximum increase of 200 microradians by 20 April (Fig. 3c).
Overall seismicity levels begin to decrease from 13 April, with lower rates of LP
earthquakes and intermittent tremor. Two small explosions are reported on 6 April
(Fig. 3c), a slightly larger explosion on 16 April sending an ash column to 3000 m
above the crater, and several small explosions were registered on 24 April. Intense ash
and vapour emissions were noted from 6 April to 9 April, with a resurgence of
emissions coinciding with the onset of drumbeat earthquakes on 10 April (Fig. 3a).
Early in the unrest, from 6 April to 8 April, seismic activity is dominated by a
continuum of tremor-like signals, ranging from near-continuous amplitude tremor
(Fig. 4a) to ‘pulsed tremor’, where the amplitude oscillates with persistent periods of
between 30 s and 50 s (Fig. 4b). Generally, the amplitude increases and decreases
gradually through each pulse, but some pulses have relatively sharp increases in
amplitude similar to the onset of individual LP earthquakes, suggesting a continuum
of behaviour between the two signal types. Pulse rates tend to increase (i.e. inter-pulse
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times decrease) as amplitudes increase. However, continuous tremor does not emerge
as a result of an increase in rate, and consequent overlapping, of pulses or
earthquakes. Rather, the continuous signal emerges as a result of a combination of
increasing duration and broadening of individual pulses. Clear harmonics or gliding
frequencies are not observed during this episode. From about 12:00 on 7 April,
individual tremor pulses become progressively but erratically more impulsive (Fig.
4c). Inter-event times are similar to those between tremor pulses, though amplitudes
are more variable. Discrete LP events become increasingly prominent on 8 April and
9 April, and dominate the activity from 10 April.
Overall activity levels decreased early on 9 April, with lower RSAM values than
observed since the start of unrest. After 24 hours of this relative quiescence, an
episode of highly periodic and persistent drumbeat earthquakes began at 05:14 on 10
April (Fig. 5). These events have similar frequency content to the preceding tremor
(between 1 Hz and 6 Hz, harmonic, with main peak at 3 Hz; Supplemental Fig. 2),
and have durations of 20 s to 30 s (Fig. 1, 4d). There is no evidence for a
systematically higher frequency onset. After 12 hours of very constant inter-event
times and amplitudes, seismicity evolved over one hour to a second phase of
drumbeat earthquakes (Fig. 6), with longer inter-event times and higher amplitudes
(Fig. 4e), but otherwise similar characteristics (Supplemental Fig. 2). During this
second phase of drumbeat activity, an additional continuous tremor signal was
intermittently present. These tremor episodes last several minutes, their start and
finish is often coincident with the timing of individual LP earthquakes, and shares a
similar frequency content. A third phase of drumbeat activity, with longer and more
variable inter-event times, followed approximately 20 hours later.
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Close inspection of the seismic data from RETU reveals a complex sequence of
even lower amplitude periodic LP earthquakes preceding the onset of the more
prominent drumbeat activity (Fig. 1, 5). From around 06:00 on 9 April, RSAM was
very low until a high amplitude LP earthquake at 01:21 10 April (Fig. 5). The event
was located by the IGEPN seismic network, centrally below the volcano, with a
magnitude of 1.6 and depth of 6± 1.5 km. The earthquake was followed by a swarm
of LP micro-seismicity, increasing in amplitude and rate for 20 minutes, and returning
to background levels over a further 20 minutes (Fig. 5). At 03:40, a second large LP
earthquake was recorded, with a magnitude of 1.8 and the same depth. This
earthquake was immediately followed by a sharp increase in the amplitude and rate of
LP micro-seismicity, with no diminution in rate or amplitude with time. The
seismicity was periodic, with a mean inter-event time of 54 s, and a mean amplitude
less than half of that during the initial phase of drumbeats. A third prominent but
somewhat smaller LP earthquake is recorded at 05:14, 1.5 hours after the start of the
second micro-seismicity swarm. An immediate stepwise increase in both amplitude
and rate signalled the onset of the first prolonged drumbeat phase. Though uncertain,
the depth of these events coincide with the initiation depths of deep ‘decompression’
events which trigger ascending pressure waves and shallow explosions, recorded in
2010 at Tungurahua (Kumagai et al., 2011).
3.2 Event data and statistics
4805 LP earthquakes were manually picked from the data recorded at RETU
between 6 April and 13 April. Root-mean-square amplitudes, inter-event times, and
the periodicity of these events are shown in Fig. 6 for the period of most significant
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LP earthquake activity from 9 – 12 April. On the basis of distributions of earthquake
amplitudes, inter-event times, and periodicity, we define three distinct phases of
quasi-stationary drumbeat activity (Fig. 6), all with average periodicities consistently
higher than that expected for a Poisson process (above the 95% boot-strapped
confidence interval). Phase 1, from 05:14 to 17:00 on 10 April, is the most highly
periodic. The inter-event time distribution is strongly depleted in short and long inter-
event times compared to the best-fitting exponential distribution, with a mean inter-
event time of 32 s (Fig. 6d). The range of amplitudes is reduced compared to earlier
and later activity. Ten of these earthquakes are recorded in the IGEPN regional
earthquake catalogue, with a magnitude range of 1.0-1.5 (mean of 1.1). Phase 2 lasts
from 17:00 on 10 April to 13:00 on the 11 April. Compared to Phase 1, Phase 2 has
higher average amplitudes (approximately double), longer inter-event times (mean of
74 s, approximately double), and lower periodicity (Fig. 6). Sixteen of these
earthquakes are recorded in the IGEPN catalogue with a magnitude range of 1.2-1.5
(mean 1.4). The transition between Phase 1 and Phase 2 of the drumbeat seismicity is
gradational, occurring over approximately one hour. Phase 3, from 13:00 on 11 April
to 12:00 on 12 April, has a lower periodicity again, but still systematically above 1.0,
so more periodic than a Poisson process. The amplitudes are similar to those in Phase
2, though with a slight increase in the proportion of small events, and a lower mean
event rate (Fig. 6). Event rates fall at around 12:00 on 12 April, marking the end of
prominent drumbeat activity with an episode of continuous tremor (though
occasionally periodic inter-event times re-emerge for short times).
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3.3 Waveform similarity and families
All 4805 picked events at RETU were cross-correlated to determine the extent and
properties of waveform similarity. Cross-correlation values were calculated using
waveforms of 25 seconds duration, filtered between 0.1 and 10 Hz. Many highly
similar waveforms are observed throughout the unrest episode. Some pairs of events
have cross-correlation values above 0.9, suggesting that persistent earthquake source
locations are active for extended periods of time (likely within a few hundred meters
or less (Green and Neuberg, 2006), despite the highly variable catalogue locations).
Similar waveforms are observed with substantially different amplitudes.
Cluster analysis shows that 1789 (37%) events belong to a family of two events or
more (Fig. 7a), and 1135 (24%) events belong to one of the 5 families containing 50
events or more (Fig. 7b). This proportion is quite low compared to other studies
(Green and Neuberg, 2006; Hotovec et al., 2013; Thelen et al., 2011), especially
considering their highly periodic nature. Families persist across significant changes in
periodicity, event amplitude and event rate, and all are active during the main
drumbeat episode. The standout results from the cluster analysis are: (1) activity in the
two largest families begins on 7 April, three days before the main drumbeat activity,
and continues through to the 12 April when periodicity has returned close to Poisson
values; (2) changes in relative family activity correspond closely to transitions
between phases; (3) a large number of small families emerge and die-out during Phase
1, the most periodic phase. Periodicity is highest when determined for all events and
low for individual families (Supplemental Fig. 1). The periodicities of individual
families are low (1.0 or less), whether consider for the full episode or within
individual phases. This observation suggests that the generation of periodic inter-
event times does not require an identical energy source for successive earthquakes. 14
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Sources can switch between families from one cycle to the next, as well as evolving
more systematically with time. Many of the LP earthquakes during the onset process
belong to some of the same families as those in the main drumbeat activity (Fig. 7b),
even though the event amplitudes are much lower. These observations support a
complex population of both persistent and transient sources that are releasing seismic
energy as part of drumbeat activity.
The relation between LP earthquake periodicity and waveform similarity is
explored in Figure 8. For independent groups of 25 consecutive events, the average
maximum cross-correlation of all event pairs is plotted as a function of periodicity.
These results show that average waveform similarity increases with the degree of
periodicity, suggesting that persistent sources comprise more of the seismicity during
highly periodic episodes. The results from Tungurahua are compared to a small
sample of data from drumbeat activity at Mount St Helens (MSH), recorded at station
HSR on 15 December 2004 (Moran et al., 2008). The range of periodicity values for
activity at MSH on this day is similar to that of the Phase 1 drumbeats from
Tungurahua. However, the average waveform similarity is considerably higher at
MSH (0.7 to 0.8 at MSH compared to 0.35 to 0.45 during Phase 1 at Tungurahua),
consistent with the lower proportion of family events at Tungurahua compared to
MSH (Thelen et al., 2011). This pattern suggests more ‘singleton’ events (those not
belonging to any family at the 0.7 threshold), although a lower signal to noise level
may also be partly responsible.
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4 Discussion
As detailed in Section 3, the observations of highly-periodic persistent LP
seismicity at Tungurahua volcano in April 2015 broaden our understanding of the
phenomenology of drumbeat seismicity, including:
1. A complex but systematic evolution of drumbeat inter-event times,
amplitudes, and waveforms, between stable behaviours, involving:
a) step-wise instantaneous increases in both amplitudes and event rate
(e.g. at the start of Phase 1; Fig. 6a,b)
b) coupled increases in amplitudes and decreases in event rate (e.g.
during the transition from Phase 1 to Phase 2; Fig. 6a,b)
c) pulse-like transient increases in amplitudes and rates, in both pulsed
tremor and discrete earthquakes (Fig. 4)
2. A stepwise breakdown in periodicity, coincident with changes in inter-
event times and amplitudes, but without significant changes to earthquake
waveforms (Fig 6c; Fig. 7)
3. Similar waveforms for earthquakes with significantly different amplitudes
during periodic activity (Fig. 7)
4. A continuum of behaviour between discrete drumbeat LP earthquakes,
periodic pulsed tremor, and continuous tremor (Fig. 4)
5. Large changes in both the nature and amplitude of seismic activity with
little change in the daily tilt rate (Fig. 3; Fig. 6)
6. Eruptive activity dominated by modest levels of continuous ash emission,
with a few small explosions, and no lava effusion
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Considering the magma composition, absence of lava extrusion, and continuum
between tremor and discrete LP events, the two processes most likely to be playing a
significant role in the excitation mechanism for LP earthquakes at Tungurahua in
April 2015 are: (1) the flux and depressurization of (ash-laden) gases (e.g. Molina et
al., 2004); or (2) local shear failure of ascending magma (e.g. Neuberg et al., 2006). In
this context, we will now discuss some observations in more detail, and consider their
implications for the nature of the LP source mechanism, and the origin of drumbeat
seismicity.
4.1 Evolution of inter-event times, amplitudes, and periodicity
Periodic earthquake inter-event times are expected to result from a physical system
consisting of: (1) a steady ‘loading’ rate, i.e. of stress or pressure accumulation; (2) a
near-constant ‘failure’ strength at which the stress or pressure is released; and (3) a
near-constant slip or pressure drop (Shimazaki and Nakata, 1980). This system could
be based on the accumulation and release of gas pressure or shear-stress due to
magma ascent. If earthquake magnitude is dependent on the slip (Tuffen and
Dingwell, 2005) or pressure drop (Kumagai and Chouet, 2001, 2000), this physics
would suggest that periodic earthquakes should have highly similar magnitudes,
which is generally the case for other examples of drumbeat seismicity (Iverson, 2008).
This property is also observed during Phase 1 at Tungurahua, where both earthquake
inter-event times and amplitudes (recorded at RETU) have a low variance (aggregate
coefficient of variation, ‘COV ’, of 0.32 and 0.34, respectively). The transition to
Phase 2 is associated with a doubling of both the average inter-event time and average
amplitude, and so could be explained by an increase in the failure strength resulting in
the same loading rate being accommodated by less frequent, but larger events.
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However, the inter-event time variance considerably increases in Phase 2 (COV =0.58
, i.e. periodicity decreases), whereas that of the amplitudes remains relatively low (
COV =0.41). In Phase 3 the coefficient of variation for amplitudes (COV =0.60)
increases more than that for inter-event times (COV =0.65). These patterns suggest a
more complex correlation between inter-event times and event sizes than initially
apparent, and are inconsistent with a simple co-dependency on slip or pressure drop.
The complex correlation is also apparent at the onset of Phase 1, where average
inter-event times decrease and average event amplitudes increase suddenly (within
one inter-event time). In the context of the physics outlined above, this transition
cannot be explained by an increase in either the loading rate or failure strength, but
would require both to increase in tandem. Transient coupled increases in event rate
and amplitude during drumbeat earthquakes and pulsed-tremor require similar
systematic changes in both loading rate and failure strength over timescales of a few
minutes.
A shallowing of the source would result in an increased amplitude for the same
energy release. However, the high similarity of waveforms rules out significant
changes in source location. Changes in the radiation properties of the resonating
system, e.g. magma crystallinity, gas content, or viscosity, could also change
amplitudes (Collier et al., 2006). However, the variety of styles of changes in
amplitude documented here, including instantaneous ones, and without changes in
waveform frequency content, mean that we consider changes in the resonating system
are unlikely to be a primary control.
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4.2 Tremor – earthquake continuum
Continuous and discrete LP signals share many characteristics during this episode.
There is clear evidence for a transition from continuous tremor, through pulsed
tremor, to drumbeat earthquakes, characterised by increasing event discretization. The
transition involves the onset of individual events/pulses becoming more impulsive and
shorter duration coda (Fig. 4). The similar frequency content, duration, and inter-
event times, suggest a closely related excitation mechanism.
At Soufriere Hills, increasing rates of periodic LP earthquakes merge to form
continuous LP tremor (Neuberg et al., 2000; Powell and Neuberg, 2003). At Redoubt,
gliding harmonic tremor is understood to result from a population of rapidly repeating
periodic LP earthquakes that are too small to be resolved individually (Buurman et al.,
2013; Dmitrieva et al., 2013; Hotovec et al., 2013). In both cases, tremor is interpreted
to result from the merger of rapidly repeating magma shear failure events. It is
difficult to reconcile this type of model with the observations here, where the
transition from tremor to discrete earthquakes occurs without significant changes in
inter-event times, but with a clear modification of the pulse/event waveform. These
observations instead suggest a change from a continuous to impulsive excitation
process.
In the case of a gas-driven excitation process, tremor could result from excitation
through persistent gas flux, involving turbulent or choked flow (Chouet et al., 1994),
and individual LP earthquakes could result from discrete flux or decompression
events (Molina et al., 2004), or different choked-flow regimes (Chouet et al., 1994).
Periodic earthquake inter-event times might result from a steady rate of gas pressure
increase and constant failure strength. However, it is not clear how this model can
explain the same ‘inter-pulse’ times for pulsed tremor, where continuous excitation 19
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seems more likely, possibly precluding gas pressure increases from provide a primary
control on inter-event times.
4.3 Combined magma and gas ascent model
4.3.1 Two phase models for periodic LP seismicity
LP earthquakes at Tungurahua in April 2015 reveal considerable complexity and
characteristics that we feel cannot be readily explained by a simple LP generation
model based on either: (a) magma ascent with repeated loading, shear failure, and slip
along column margins (e.g. Neuberg et al., 2006); or (b) gas ascent with trapping and
pressurization, failure, and escape (e.g. Molina et al., 2004). However, these ‘single-
phase’ models are end-members of a suite of potential models that consider both
magma and gas ascent. Such two-phase models have been proposed to explain the
episodic explosive behaviour of Santiaguito volcano, Guatemala. Johnson et al.
(2008) suggest a model involving shallow gas trapping and pressurization driving
dome inflation, but with LP earthquakes resulting from the momentum change
accompanying discrete dome ascent events. Holland et al. (2011) suggest an
alternative model, where magma ascent drives repeated shear failure of column
margins, but with LP earthquakes resulting from passive gas escape and explosive
decompression through the resulting transient fracture pathway. Importantly, these
models allow a greater independence between event timing and size. Here we
consider how this type of model may better explain our observations for activity at
Tungurahua.
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4.3.2 LP earthquakes resulting from shear failure and gas escape
In April 2015, steadily increasing radial tilt at RETU indicates likely magma ascent
(Fig. 3c), and gas flux is variably elevated through the episode (Fig. 3b). The
continuum from continuous and pulsed tremor, to discrete earthquakes, is most easily
explained by a source mechanism involving gas flux and depressurization (Chouet et
al., 1994; Molina et al., 2004). However, we suggest that the specific conduit
conditions and structure at the time led to an unusually strong coupling between gas
flux and periodic incremental magma ascent. Magma ascent from depth increases the
shear stress at a horizon of relatively high strength of the column margins, at a depth
controlled by the details of magma rheology and conduit structure (Fig. 9a). When
shear stress exceeds strength, magma failure and slip occurs (generating ash through
comminution and fragmentation), but here is either aseismic, or generates insufficient
energy to be resolved in the seismic signal recorded at RETU. Instead, through a
mechanism similar to that proposed by Holland et al. (2011), shear failure of the
column margins generates a transient degassing pathway, allowing gas escape. A
combination of gas flow and de-pressurization, in the confines of a shallower
resonating crack network, initiate an LP earthquake (Fig. 9b). At times of low gas
flux, incremental magma ascent and shear failure may well continue, but not generate
LP earthquakes above the magnitude detection threshold (about 0.5). Importantly, this
mechanism does not require successive LP earthquakes to originate from identical
sources to maintain periodic behaviour. During an increment of column ascent, gas
may escape from different locations around the magma column, resulting in small
changes in the waveform and the diversity of families seen during drumbeat activity.
At times of high gas flux, particularly early in the episode, gas pressure is
sufficiently high to maintain a continuous pathway, but with a flux modulated by 21
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small stress changes through each increment of magma ascent, giving rise to pulsed
tremor. As gas pressure falls, or perhaps some cracks become blocked with ash
(Molina et al., 2004), seismicity transitions to increasingly discrete LP earthquakes
controlled by the timing of slip events. This transition from continuous to discrete
excitation means that it is RSAM, not event rate, which generally correlates best with
gas flux data (Fig. 3).
The frequency content and quality factors of LP waveforms can be used to
constrain physical characteristics of the resonator element of the source mechanism
(Kumagai and Chouet, 2000). For LP earthquakes recorded at Tungurahua in 2001,
similar to those in April 2015, modelling by Molina et al (2004) suggests that crack
lengths of around 200 m are required for an ash-gas fluid. However, there is potential
for strong covariance between crack length and other model parameters including
depth and gas pressure, and other studies suggest lengths of tens to a few hundred
meters (Chouet and Matoza, 2013). These waveform characteristics fall within the
range analysed using a hydraulic crack model (Lipovsky and Dunham, 2015),
corresponding to fracture lengths of a few tens of metres, and half widths of a few
cms for a water filled crack in rock. Much greater crack dimensions are required for
cracks filled with basaltic or andesitic magmas.
4.3.3 Earthquakes as a function of gas flux, pressures, and column margin
conditions
In this conceptual model, earthquake size is controlled by the gas flux and pressure
drop, whereas the timing is controlled by the shear stress and strength at the column
margins. Constant rates of magma ascent and gas accumulation will result in constant
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rates of increase in shear stress and gas pressure. If margin failure strength and co-
event gas escape also remain constant, LP earthquakes will be periodic and equal
amplitude. Small variations in these parameters will result in quasi-periodic
earthquakes and a (narrow) range of amplitudes. An increase in the effective strength
of the conduit margin, or a slowing of magma ascent, will result in longer inter-event
times, allowing time for greater gas pressure increase, and hence larger amplitudes.
Inter-event times and amplitudes can have a higher degree of independence than a
magma failure or gas model alone, as shear stress is not directly dependent on gas
pressure, allowing for the varied statistical relations we observe.
Rather than a purely passive role, if the upward flow of gas is restricted by reduced
permeability at or close to the high strength horizon, the increasing gas pressure
between drumbeat earthquakes may influence the loading and failure cycles at the
column margins, potentially synchronizing variations in gas pressure with margin
shear stress, and enhancing the periodicity and repeatability of the process. Partly
synchronized fluctuations in gas pressure and shear-stress may help explain coupled
increases in event amplitude and rate during pulsed tremor activity, and during the
initiation of drumbeat activity (Fig. 5). The prominent larger earthquakes on 10 April
likely signify the re-activation of a deeper gas plumbing system and increased flux,
rather than a change in magma ascent rate. Co-drumbeat tremor (Fig. 4e), prominent
in Phase 2 where inter-event times are longer, may result from continuous gas flux
through a semi-permanent degassing pathway, intermittently opened and closed by
small stress changes associated with magma ascent.
The evolution in periodicity, waveform similarity, and amplitudes during drumbeat
activity suggest a progressive degradation of the coupled magma ascent-gas flux 23
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system. This could result from the increased load due to the gradual ascent of the
magma column, changes in the properties of the gas storage zone, the properties of the
column margin interface (Iverson, 2008), or evolution of the greater de-gassing
pathway (Molina et al., 2004). The stepwise rather than continuous changes in event
statistics are intriguing and suggest the existence of quasi-stable states. The close-to
doubling of inter-event time between Phase 1 and Phase 2 drumbeats could be chance,
but could perhaps reflect different harmonics of the partly-coupled periodic gas and
magma system.
4.3.4 Remarkable drumbeats during an unremarkable episode
The absence of prolonged, highly periodic drumbeat LP seismicity from the
previous 15 years of eruption suggests that some exceptional conditions are required,
despite in April 2015. Eruptive activity, other aspects of LP earthquake characteristics
and rates, RSAM, gas flux, and deformation signals, were all unremarkable during
this episode, and were well within the range of behaviours previously observed. The
only unusual factor was the long quiescence period since the preceding significant
explosive episode in October 2014. Therefore, it is likely that this quiescence played
some role in establishing the physical conditions necessary for drumbeat activity,
perhaps through extended healing of the magma column margins, or vertical growth
of a plug due to cooling and crystallization (Iverson, 2008). However, extended
quiescence and likely magma ascent together do not appear to be sufficient criteria to
explain drumbeat occurrence. The April 2015 increasing-decreasing tilt cycle was one
of four such cycles between March and June 2015 (Fig. 10). These pulses all had
similar tilt amplitudes and durations, but only the April 2015 episode was associated
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with significant LP seismicity. Gas fluxes also show cyclical behaviour with similar
period to tilt data between March and June 2015, and fairly closely correlates with
trends in daily RSAM. During April 2015, peak gas flux coincides with the increasing
phase of the tilt cycle. For all other cycles, increasing tilt phases are associated with
minimum gas flux. The coincidence of high gas flux with the ascent of magma after a
long period of repose is likely to have been an important factor in creating the
physical conditions necessary for drumbeat LP activity.
5 Conclusions
The unrest episode at Tungurahua in April 2015 provides valuable new
observations of highly-periodic LP seismic activity, and offers important insights into
possible LP earthquake source mechanisms and conduit processes. Drumbeat LP
seismicity occurred without viscous dome formation, or portending a large eruption.
Waveform characteristics show a gradual transition from continuous tremor to distinct
LP events, controlled by an increased discretization of individual pulses rather than
event rate changes. Inter-event times, amplitudes, and waveform-similarity metrics
allow quantitative analysis of changes in activity through the episode, and
comparisons with analogous activity at other volcanoes. These statistics reveal a range
of both step-wise and ‘pulsed’ changes in inter-event times, with coupled changes in
amplitude and periodicity. A series of activation steps precede the onset of the most
highly-periodic drumbeat activity, with a progressive, stepwise, breakdown in
periodicity over the following days and coincident with changes in inter-event times
and amplitudes.
Distinguishing between models for the source of LP earthquakes is challenging.
We feel that the balance of evidence available supports a two phase model for
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drumbeat seismicity for this episode, with earthquake excitation by gas flux and
depressurisation into a resonating crack network, but facilitated by the formation of
transient fracture pathways during incremental ascent of the magma column. At other
times, incremental magma ascent may occur without detectable LP earthquake
activity if gas flux is low, or not trapped within the column.
Acknowledgments
AFB was funded by a Carnegie trust research incentive grant. We would like to
thank Silvana Hidalgo for helpful comments and provision of gas flux data, and two
anonymous reviewers for constructive comments and suggestions that helped improve
the manuscript.
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Figure 1: Helicorder plot for vertical component short-period station RETU on 10
April 2015. Each line represents 30 minutes of data, running from left to right, and
from top to bottom. Seismic activity progressively increases after two higher
amplitude earthquakes at 01:21 and 03:40 UTC. First phase of highly periodic
drumbeat earthquakes begins sharply at 05:14. Transition to higher amplitude, less
frequent, less periodic drumbeat earthquakes occurs from about 17:00.
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Figure 2: Topographic map and N-S and E-W cross-sections of Tungurahua volcano,
showing location of seismic stations (black triangles), Pillate DOAS station (red
square), and reported locations for earthquakes in the IGEPN catalogue during
different phases of drumbeat activity with depth error bars.
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Figure 3: Multi-parametric data recorded by the monitoring network of the IGEPN
during the unrest episode at Tungurahua, April 2015. (a) Overall evolution of seismic
activity, and temporal extent of subsequent figures. Periods of Ash emmission are
indicated by blue triangles, and relative activity level indicated by green shading. (b):
15 minute RSAM recorded at station RETU (black line), and daily maximum SO2
flux recorded at station Pillate. (c): Daily radial tilt recorded at station RETU (black
line) and 6 hourly numbers of LP earthquakes (dark green bars) and explosions (red
bars) as detected by the IGEPN seismic monitoring network. RSAM sharply increases
at the start of the unrest episode on 6 April and remains variably elevated until 29
April. Trends in gas flux are broadly similar to RSAM, though resolution is lower and
data are sensitive to changes in wind direction. Tilt follows a gradual increasing-
decreasing cycle, with initial small explosions starting early in the cycle. Rate of LP
earthquakes increases sharply on 10 April, marking the onset of drumbeat activity.
Lower rates of LP earthquakes continue through the later part of the episode.
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Figure 4: 10 minute vertical velocity time-series and spectrograms for some of the waveform types
recorded at station RETU in April 2015. (a) continuous tremor; (b) pulsed tremor; (c) tremor-LP
earthquake transition; (d) phase 1 drumbeats; (e) phase 2 drumbeats. All amplitudes are normalized to
the same value, so are directly comparable between figures. Phase 1 drumbeats and plused tremor share
similar inter-event times, but drumbeat LPs have more impulsive onsets. Increasingly impulsive onsets
of tremor pulses appear on 7 April, marking a progressive transition from tremor-dominated to LP
dominated seismicity. Note additional continuous tremor signal accompanying phase 2 drumbeats, the
amplitude of which increases and decreases at the same time as individual LP earthquakes.
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Figure 5: (a) Velocity time series for 6 hours of data recorded at RETU from 00:30 UTC on 10
April 2015 and documenting the initiation and onset of drumbeat activty. Dark blue line represents all
data; light blue line represents data filtered between 0.1 and 12 Hz, and averaged over 10 seconds. (b)
RMS velocity amplitudes, and (c) inter-event times (in seconds) for individual LP earthquakes. The
first higher amplitude earthquake at 01:21UTC is followed by a pulse-like increase and decrease in LP
event amplitude. The scond higher amplitude earthquake at 03:40 UTC is followed by a step-wise
increase in amplitude. A third step-wise increase in event amplitude and decrease in mean inter-event
time at 05:14 marks the start of persisent Phase 1 drumbeats.
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Figure 6: Left panels: RMS velocity amplitudes, inter-event times, and periodicity for LP
earthquakes picked from data from RETU, 9 – 12 April 2015. For amplitudes and inter-event times,
black circles represent individual values, red lines represent 30 minute averages. For periodicity, red
line represents 25 event average, horizontal dashed line and green bar indicates expected (mean, and
5% and 95% confidence limits) periodicity for a Poisson process. Vertical dashed lines indicate key
changes in activity. Right panel: inter-event time distributions for three major phases of drumbeat
activity. Circles and solid lines represent actual data. Dashed lines in corresponding colour represent
best-fitting exponential inter-event time distribution model for each phase.
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Figure 7: Families of similar earthquakes recorded at station RETU, 6-13 April 2015, determined
using a two-stage clustering algorithm with cross-correlation thresholds of 0.7 and 0.8. Top panel
shows all families; bottom panel shows only families containing 50 or more events. Black circles
depict occurrence time of events belonging to different families. Red lines indicate temporal extent of
each family. Family 0 consists of ‘singleton’ events that have no cross-correlations with other events
above the 0.7 threshold. Several families begin well in advance of drumbeat activity on 10 April, and
the start and end of some larger families coincide with changes in event rate and amplitude indicated by
vertical dashed lines. Phase 1 sees the emergence of many small short-lived families.
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Figure 8: Average waveform similarity (mean cross-correlation for all pair combinations of 25
consecutive events) as a function of inter-event time periodicity for 25 event windows during April
2015 unrest. Coloured circles represent data from three main LP drumbeat phases. Black crosses
represent data from outside those times. Green triangles represent comparitive data from drumbeat
activity at Mount St Helens recorded at station HSR on 15 December 2004. Vertical dashed line and
green bar indicates expected (mean, and 5% and 95% confidence limits) periodicity for a Poisson
process. Data reveals a correlation between periodicity and waveform similarity for Tungurahua,
though highly periodic Phase 1 data has a lower waveform similarity than the trend for Phases 2 and 3,
and for comparable periodicity data from Mount St Helens.
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Figure 9 Cartoon illustrating mechanism of LP earthquake generation during drumbeat activity in
April 2015 at Tungurahua. (a) Between earthquakes, magma ascent increases shear stress at high
strength horizon, and gas pressure increases beneath low permeability barrier. At time of high gas flux,
or during Phase 2 drumbeats, some gas may ascend past barrier, generating tremor. (b) As shear stress
exceeds strength, shear failure allows slip, an increment of column ascent, and generates a transient
degassing pathway. Gas escape and depressurization generates seismic energy, which resonates within
the shallower fracture network.
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Figure 10 Multi-parametric data recorded by the monitoring network of the IGEPN, March to June
2015. Daily radial tilt recorded at station RETU (black line), daily maximum SO2 flux recorded at
station Pillate (blue line), daily average RSAM (green shading) and daily numbers of LP earthquakes
(dark green bars) and explosions (red bars) as detected by the IGEPN seismic monitoring network.
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