Chapter 2 Cyclic phenomena at the Soufrière Hills Volcano, Montserrat

Abstract Cycles of eruptive activity are generally interpreted as evidence of one or more mechanisms operating in equilibrium. Modulation of cycle characteristics thus reflects changes in the conditions affecting those mechanisms. This kind of semi-deterministic behaviour at the Soufrière Hills Volcano has occurred on multiple timescales and with a range of eruptive intensity. By documenting cyclic phenomena, it is possible to investigate the mechanisms that modulate the state of the eruption and examine conceptual models. Pattern recognition and model development allows some degree of short-term forecasting ability for volcanic activity. We report the cyclic eruptive phenomena that have occurred on Montserrat on scales of hours to centuries. We identify four dominant types of cyclicity: sub-daily variations in lava flux; sub-annual cycles in eruption intensity; multi-annual ‘on–off’ switching of lava extrusion; and multi-decadal recurrence of seismic crises. We exploit a wealth of multi-parameter datasets (including seismic, geodetic, thermal, archive and visual observations), and present the evidence and observations for each type of cyclicity, some of which are documented here for the first time. Wavelet time-series analysis is used to constrain cycle characteristics, where appropriate. We discuss the implications of these observations in understanding the eruptive mechanisms of the Soufrière Hills Volcano. Supplementary material: Details of all sub-daily cycles are listed in a supplementary table that is available at http://www.geolsoc.org.uk/SUP18700.

The eruption of the Soufrière Hills Volcano (SHV), Montserrat, has been characterized by significant variations in surface activity at multiple timescales. The eruption was preceded by several 'seismic crises' at about 30 year intervals (Wadge & Isaacs 1988). During the eruption, phases of lava extrusion lasting from months to years (Phases 1-5) have been interrupted by periods of relative quiescence of similar duration (Wadge et al. 2014b). Within each activity phase, variations in surface lava flux have been observed at scales of hours ) and weeks Costa et al. 2007). The occurrence of these and other examples of cycles have been associated with systematic processes; that is, processes that are derived intrinsically from non-random systems or mechanisms in the volcano. Observing and analysing cyclic phenomena in eruptions can thus serve to provide information to constrain the nature of those processes driving the eruption and to better understand future behaviour of the volcano.
Volcanic systems involve the generation and buoyant rise of magma, its storage and eruption. These systems are complex with some evidently non-linear processes involved (e.g. crystallization-induced rheological stiffening: Melnik & Sparks 1999), and the deterministic behaviour shown by cyclic behaviour at volcanoes like SHV is susceptible to divergent evolution caused by small variations in source conditions. This underlying tendency to chaotic dynamic behaviour renders prediction of future states impossible (Schuster & Just 2005). One of the concepts used in the mathematical analysis of such chaotic systems is that of intermittency, in which the time series follows a periodicity for some time but then fluctuates randomly from it, only to return to the periodic state later. This type of behaviour is apparent at times in sub-daily activity at the SHV.
Before discussing the evidence of various cyclic phenomena in detail, we must define what should be regarded under this umbrella term. For the purposes of this study, we consider a single cycle to be defined as a systematic variability through time in any observable parameter (e.g. number of seismically detected events) from an initial state, at an initial time, eventually returning to that state and followed by repeating behaviour. Recurrence may imply the existence of a mechanism or process that is able to reset and/or recharge at the end of each cycle ). In the simple case where a measured observable value oscillates in time like a sine wave, the cycle period could thus be measured, for example, from one peak to the next. In natural systems, of course, one would not necessarily expect the variation to be perfectly sinusoidal and often it is not (e.g. Melnik & Sparks 2005). Indeed, the shape and other characteristics of cycles, and how they change in time, may themselves be used to infer information about the source mechanism and its equilibrium state ). We revisit this topic in more detail later, with respect to observations made at the SHV.
Cycles might be observed at volcanoes through visual observations (usually at short timescales) but are often only clearly defined and quantified through visual or numerical inspection of time-series data. The eruption at the SHV is notable both for its duration and for the scrutiny with which it is routinely monitored by the Montserrat Volcano Observatory (MVO) and studied by the wider research community. The result is a rich, but fragmented collection of time-series data including seismic, deformation, gas, lava flux, thermal imagery and visual observation datasets. Where possible, we use a multi-parameter approach to define cyclic events at SHV, both to demonstrate their occurrence robustly and to understand their characteristics. The high sampling rate and sensitivity of the seismic monitoring network allows for short period (hours to months) cycles to be identified and analysed quantitatively. Seismic data are manipulated to generate derivative time-series data, such as Real-time Seismic Amplitude Measurement (RSAM: Murray & Endo 1992) with minute-scale resolution, and automatically or manually derived event counts of, for example, rockfall or long-period (LP) earthquake occurrence.
Other monitoring data can be integrated to characterize the nature of cyclic behaviour. The time resolution and sensitivity of available monitoring techniques are important considerations for recording and finding evidence of cyclic events. Tiltmeter measurements made in 1996-1997 (with a 10 min sampling interval) provided valuable geophysical evidence of cyclic processes (Voight et al. 1998). Deformation monitoring via permanent and episodic global positioning system (GPS) surveying, with daily resolution, has been used widely to interpret cycles at timescales of months to years (Odbert et al. 2014). The use of Electronic Distance Meter (EDM) measurements to assess baseline length changes around the flanks of SHV (typically at weekly to monthly intervals) has corroborated and complemented GPS deformation observations, especially in the near-field (Odbert et al. 2014). Routine sulphur dioxide (SO 2 ) monitoring has been undertaken on Montserrat since 1996 (Watson et al. 2000;Christopher et al. 2010) and has provided an average daily value, although higher-frequency sampling is possible during daylight hours at the cost of value uncertainty. Atmospheric SO 2 measurements can also be made via satellite remote sensing (Carn & Prata 2010) at daily intervals. The flux of erupting lava has been estimated using a variety of techniques (Odbert 2009), with an operational frequency of about 20 days for photogrammetric methods. Higher-frequency (c. hourly) volumetric flux monitoring has been demonstrated using All-weather Volcano Topography Imaging Sensor (AVTIS), a ground-based imaging radar (Wadge et al. 2014a). Regular visible and infrared imagery can be sampled frequently (c. 2 Hz) and analysed qualitatively or quantitatively. Often a combination of observations from multiple monitoring techniques is desirable for robust detection of eruptive cyclicity. We note specifically the value of visual observation logs in assimilating the other evidence, as well as sometimes serving as a quasi-quantitative dataset in their own right.
Often, the most easily measured property of a cycle is its period -the time from one point in a cycle's phase to the same point in the next cycle. The period (or, inversely, the frequency) of a cycle is sometimes the only metric that can be gleaned in absolute terms from the available data. In cases where quantitative data are available, the amplitude (the difference between the lowest and highest parts of the signal) and the shape of the cycle can also be measured, although care must be taken to account properly for the background noise that is inherent in most volcanological data. This is often accomplished using an appropriate filtering scheme. The amplitude of cycles corresponds to the intensity of activity, which, in turn, may be interdependent on cycle period. The shape of a cycle (e.g. how skewed or asymmetric it is) may also be used to characterize the process(es) driving periodic behaviour. A number of techniques may be used to ascertain cycle properties. Spectral analysis of a time series via the Fast Fourier Transform (FFT) can be applied to demonstrate the relative contribution of cyclic signals with different frequencies, and numerous algorithms exist to test results statistically against hypothetical noise models (Percival & Walden 1993). A drawback of FFT analysis of volcanic data is the assumption that the time series under analysis is stationary (i.e. the spectral content does not change in time); an assumption that is sometimes untrue at SHV. Spectrogram analysis uses FFT analysis over a series of contiguous or overlapping short time windows. Stationarity is then only required for the duration of each time window, and the spectral content of a window may be compared independently to that of the next window. Wavelet analysis provides a means of analysing a time series over a range of frequencies and time intervals, and requires no implicit assumption that a time series is stationary. Where possible, we use a combination of complementary timeseries analysis tools to identify the presence and properties of cycles in time-series data. We make no attempt here to analyse cyclicity in seismic data at waveform timescales (seconds to minutes); instead, we focus primarily on cycles in eruptive phenomena.
The occurrence of cyclic activity at SHV is evidence of systematic processes within the volcano. Achieving a better understanding of when and how these phenomena occur will help us to understand what causes them to start, change and cease. This has the lure of providing a route to being able to model and forecast deterministic or semi-deterministic processes in eruptions numerically. Here, we aim to present evidence of cyclic behaviour at the SHV at a range of timescales, and formally document the timing and characteristics of the cyclic volcanic phenomena. Where new data are available, we present time-series analysis from multi-parameter timeseries data, particularly from recent eruptive phases, when cyclic activity has been particularly prevalent. In this chapter, we discuss cycles according to their period: those occurring with periods of the order of hours (sub-daily), weeks to months, years and decades. We then discuss the observations generally, and outline a strategy for capturing and analysing cyclic behaviour optimally.

Sub-daily cycles
On numerous occasions since the onset of lava extrusion in 1995, patterns in activity have been documented that describe regular cycles, with periods of between hours and tens of hours (collectively referred to herein as 'sub-daily' cycles). Strong sub-daily cyclicity in 1996-1997 was associated with regular, smallmoderate explosions, and generated well-defined ground deformation (near-field tilt) and seismic signals (Voight et al. 1998). Similar sub-daily cycles with approximately 8.5 h average periods were recognized in 1999-2000, and their evidence in seismic tremor and SO 2 data was reported by Young et al. (2003). The authors noted a lag of several tens of minutes from peaks in seismic energy release to peaks in gas flux. Cycles such as these were less evident in subsequent phases of extrusion until Phase 4b ( -2009( ) and particularly Phase 5 (2009, when activity was again marked by strong variability at sub-daily timescales . These cycles in eruptive activity deserve particular attention because they can provide operational insight for short-term hazard mitigation planning, and this has been exploited by the MVO throughout the eruption.

Phase 5 cyclicity: 2009 -2010
Sub-daily cycles in the intensity of surface activity (mainly rockfalls and ash venting) developed shortly after the onset of dome growth in October 2009 and, as the cycles continued and intensified, became a defining feature of Phase 5 extrusion. In general, two forms of cyclic seismicity were observed. Figure 2.1 shows typical Phase 5 seismicity, with dominant signals from rockfalls (c. 0.5-5 min duration, cigar-shaped signals), hybrid earthquakes (short, low-amplitude signals) and tremor (c. 20 -90 min duration, continuous, low-amplitude signals). Figure 2.1a shows an example of cyclic seismicity that features frequent hybrid earthquakes that merge to form continuous tremor. Tremor signals ( Fig. 2.1a, b) were often associated with visible venting of ash and gases (so-called 'ash venting') around the summit of the lava dome; assumedly in the locale of the active lava extrusion vent. Rockfall and pyroclastic flow signals (RF, identified collectively) are generated by mass-wasting events, typically originating high on the lava dome. Figure 2.1 also shows bunching of RF events around the ash-venting episode and this combination of surface activity was commonly observed throughout Phase 5. Some example photographs of both types of activity are given by Cole et al. (2014a). Both panels in Figure 2.1 demonstrate the recurrence of ash venting at regular intervals (with c. 7 and 6 h-cycle periods on 1 November and 17 December 2009, respectively). Contributions from ash-venting-related tremor and RF signals dominated the seismic data stream for most of Phase 5 (see . Peaks in surface activity such as these usually lasted between about 0.5 and 4 h.
To analyse the occurrence and variation in sub-daily cyclicity throughout Phase 5, we consider the RSAM envelope of the seismic signal as a proxy for the intensity of surface activity. Usually it is possible to obtain RSAM from a single, representative seismic station. However, owing to intermittent failures across the network that are typical during periods of intense activity, we derived a normalized, network-averaged RSAM (or NARSAM:  to obtain a continuous time series. NARSAM is calculated using a weighted average of RSAM data from the seismic network. Weightings are determined through empirical adjustment, aiming to minimize biases in the network and maintain long-term consistency in the NARSAM time series. Figure 2.2a shows the NARSAM time series derived for Phase 5, clearly illustrating the changes in eruption intensity. The occurrence and characteristics of periodic signals in a time series may be analysed via the Continuous Wavelet Transform (CWT: Percival & Walden 2000;). Wavelet analysis provides a convenient method to measure how well correlated a time series is with the shape of the chosen wavelet in multiple domains (time and frequency). We adopt the Morlet wavelet -shaped like a decaying sine wave -to measure how similar the NARSAM time series is to a sine-wave-like signal for a range of frequencies. Large positive CWT values correspond to strong, positive correlation with the wavelet (i.e. relating to a peak in the time series) and large negative values correspond to strong anti-correlations. Values close to 0 indicate weak correlations. Persistence through time of regular high transform values for a given pseudo-period is therefore evidence of cyclicity in the time series. The CWT value for a fixed pseudo-period thus corresponds with the phase of the cycle in the data. We note that the cycles in the NARSAM time series do not necessarily resemble sine waves but that the choice of wavelet is suitable for such analyses without requiring specific a priori knowledge of the system generating the time series (Trauth 2006). Figure 2.2b shows the Morlet CWT for the NARSAM time series, indicating strong transform values at a range of pseudoperiods. Occasional elevated CWT values in October and November 2009 show the presence of sub-daily cycles with periods of between about 4 and 14 h. The most intense cycles of Phase 5 developed after 20 November (indicated by a green, dashed line). These had periods of about 5 h for around 2 weeks, at which point the periods began to increase. This is shown by an approximately linear transition of peak transform magnitude up to about 9 h by 8 January 2010, when there was a large Vulcanian explosion (details reported by Cole et al. 2014b). In the week that followed, which included two more explosions on 10 and 11 January, surface activity was markedly less well organized and this is reflected in the reduction of CWT magnitude in Figure 2.2b after 8 January 2010. Cyclic activity resumed at a variable, and generally lower, intensity, with a period of around 6 h from 11 January onwards. The period then began to lengthen once again to approximately 11 h by 5 February. Several isolated Vulcanian explosions occurred throughout this period (8, 10 and 11 January, and 5 and 8 February: Cole et al. 2014b), and there was demonstrable disruption to the sub-daily mechanism following the events on 8 January, and 5 and 8 February. A reduction in cycle period (from c. 10 to c. 7 h) and increase in intensity occurred over the approximately 2 days immediately preceding the partial dome collapse and end of Phase 5 (Stinton et al. Changes in the nature of the cycles can be tracked through Phase 5 by considering asymmetry and relative intensity ('asymmetry' is used here to describe the degree to which an RSAM cycle is skewed). Figure 2.2c shows the stages of each cycle during which tremor (and, by proxy, ash venting) was ongoing. As the tremor signal partly defines the RSAM cyclicity, it naturally follows that tremor typically began before the cycle peak and ended after it. However, Figure 2.2c shows that some asymmetry developed in this sequence, particularly in the middle episode of Phase 5. During the period of intense, approximately 5 h cycles, the most intense part of each cycle was towards the end of the ash-venting event. It is notable that the severity of this asymmetry diminished gradually before the cycles' period started to lengthen. The relative intensity of cycles can be analysed by considering the ratio between their peak amplitude and their period. In a case where the time-averaged intensity of the eruption is constant (e.g. constant lava flux), the ratio would remain approximately constant such that a shorter, higher-amplitude cycle could be considered equivalent to a longer, low-amplitude cycle. Following the assumption that each sub-daily cycle was due to the repeating action of the same mechanism(s), the ratio shown in Figure 2.2d may be considered as a proxy of eruption intensity. The general trend indicates a relatively constant background level of intensity that becomes elevated by nearly an order of magnitude around the end of November, immediately before the development of long, asymmetrical ash-venting events. The level of intensity decays to the background level in the latter part of the second episode, as cycles lengthen and become less intense.
The second key contribution to cyclicity in the RSAM record was the seismicity associated with RF events. Visual observations recorded the increased frequency of RFs coincident with ash venting. We can analyse the timing of RF events and ash venting to build up a type description of sub-daily cycles in Phase 5. Figure 2.3 shows the distribution of RF events around their respective RSAM peaks for events between 1 December 2009 and 8 January 2010. The histogram demonstrates the increase in rate of RF events by a factor of 3-4 in time intervals prior to and immediately after the RSAM peak. This demonstrates the variable rate in RF occurrence but is, in part, an intrinsic result of the RSAM calculation method. We consider that the peaks in RF frequency identify peaks in surface lava flux; as a batch of lava is extruded rapidly onto the lava dome, the stability of new and preemplaced lava masses is reduced compared to when there is little or no supply. The result would be an increase in generation of mass-wasting events from around the vent area. This argument is corroborated by more detailed evidence recorded during Phase 5. The unprecedented volume and height of the lava dome at this time meant that material could be shed from the lava dome into all major drainages around the volcano . Typically, RFs would occur in a dominant direction at any given time (as discussed later), but on numerous occasions multiple, moderate -large pyroclastic flows were formed simultaneously that travelled in different -often opposite -directions. These observations were a first at the SHV, and we interpret them as being more definitive evidence of RF generation driven by increased lava flux from a vent close to the summit of a nearly symmetrical lava dome. The occurrence of multi-directional RF events was also more common around the RSAM peaks, but we note that the proportion of pyroclastic flows that were multi-directional is greater at the cycle peak than at other times ( Fig. 2.3).
Finally, Figure 2.3 shows measurements of the ratio between hydrogen chloride and sulphur dioxide (HCl:SO 2 ) in the volcano's gas plume, recorded using a Fourier Transform Infrared (FTIR) spectrometer near the end of Phase 5. Each data point is averaged from a session consisting of tens to hundreds of individual scans. Although few data points are available, owing to instrument failure, we note that the highest measurements were made approximately coincident to cycle peaks and the lowest measurements made closer to the cycle trough. Indications from individual scans suggest that, where high ratios are observed, they are only sustained for a short period. Oppenheimer et al. (2002) reported variations in HCl:SO 2 from 1996 to 1998, interpreting increases in the ratio as the result of an increase in degassing from an andesite source (generating HCl) and/or a decrease in degassing of a basaltic source (generating SO 2 ). As the basaltic source is typically assumed to be from deep in the system, short-term ratio variations would then tend to be dominated by variable andesite magma degassing. Edmonds et al. (2001) associated high HCl:SO 2 ratios with elevated extrusion rate. Without independent absolute gas flux data for either species (routine SO 2 monitoring networks were out of service throughout most of Phase 5), we are unable to distinguish between the two contributions from the ratio data.
Common characteristics of sub-daily cyclicity that were typical (although not ubiquitous) of Phase 5 can be summarized as follows. Background seismicity prior to each cycle would be at a low level -dominated by smaller RF events owing to the instability of the active lava dome. The start of a cycle would be marked by the onset of continuous ash venting from near the summit of the lava dome and concomitant seismic tremor -reflected by increased RSAM. The rate and size of RF events would grow such that the combined activity generated a crescendo in RSAM. The RF frequency and ash-venting intensity then decayed. This decay would sometimes occur more suddenly than the onset, yielding an asymmetrical cycle. The surface activity would then return to the background state with no tremor and occasional RFs. The peak in activity typically lasted between about 0.5 and 4 h, perhaps accompanied by gas efflux with elevated HCl:SO 2 , and would repeat every 4-14 h. At times when cycle period was short, ash venting from the volcano was near continuous (e.g. early December, Fig. 2.2c).
We interpret this generalized sequence of events to be the surface expression of large variations in surface lava flux over the timescales of minutes to hours. Similar interpretations have been made from observations of sub-daily tilt cycles during 1997 Wylie et al. 1999;Widiwijayanti et al. 2005;Green et al. 2006;Costa et al. 2007;Lensky et al. 2008;). The mechanisms inferred from tilt data were generally thought of as pressurization in the shallow conduit ) as lava flow is restricted owing to the formation of a viscous lava plug formed by degassing-induced crystallization. At a critical pressure, the plug fails and is ejected from the conduit, often along with vigorous ash emission. The resulting pressure reduction promoted degassing in the conduit lava and the cycle repeated. We consider that the same mechanism would explain the sub-daily cyclicity  observed in Phase 5, and, perhaps, at earlier times in the eruption. The resulting surface observation is a reduction or cessation of lava extrusion from the vent as conduit flow is restricted, followed by a surge in lava flux during the plug-ejection phase. The onset of venting indicates the beginning of plug failure, as trapped gases that have exsolved from the lava plug are released. The structural failure allows the lava to be forced from the vent, generating RF activity. The pressure driving plug ejection is relaxed such that venting and the supply of fresh lava to form RFs subsides, and then the process resets. It appears that the cyclic activity can occur with a range of intensity from those with minimal visible surface activity up to cycles that culminated in Vulcanian explosions (e.g. . Given the sequence of events described above, we note particularly that surface efflux of lava varies significantly even during highly active periods of activity on the volcano. Indeed, if it were assumed that all of the lava erupted during Phase 5 (c. 74 Mm 3 : Stinton et al. 2014a) was extruded in this fashion (i.e. during ash-venting events, which accounted for 20% of the duration of Phase 5) and that the surface flux was 0 between cycle peaks, the actual surface flux of lava during active extrusion would be approximately 35 m 3 s 21 . Such extrusion rates would be sustained only for a short time (minutes to tens of minutes) and would not be detectable via conventional flux estimation methods (Odbert 2009). The long-term average flux for Phase 5 was 6.8 m 3 s 21 ).

Sub-daily cycles since 1995
In light of the Phase 5 analysis and reports from earlier phases (e.g. Voight et al. 1998;Young et al. 2003), we revisited archive data and compiled the evidence of sub-daily cyclicity throughout the eruption at the SHV. Our catalogue was derived by reexamination of seismic data, as well as incorporating existing compilations (e.g. Thompson 2001;Dunkley et al. 2003). Cyclic activity is evident in most types of seismicity, with the notable exception of volcano-tectonic (VT) earthquakes. Episodes of continuous tremor have also been cyclic ('banded tremor'), although many of these actually result from the merging of frequent, small hybrid earthquakes (Neuberg et al. 1998). It has not been possible to analyse the entire eruption using a single dataset, such as a whole-eruption RSAM, owing to frequent changes in the seismic network (changing instrumentation and locations). The properties of the cycles were therefore estimated using shorter periods of RSAM data that were generated from suitable available data or, failing that, hourly counts of various earthquake types.
We identified 42 distinct episodes of cyclic activity, lasting between 1 and 153 days (Table 2.1). Several of these episodes can be divided into separate sub-episodes, characterized by notable changes in either the type of seismicity or the character of the cycles. For each episode or sub-episode (denoted by a lowercase suffix), we list the minimum, median and maximum cycle period. We note a slight tendency for sub-daily cycles to be asymmetric, with the RSAM peak usually closer to the end of the cycle, suggesting a similar pattern to observations from Phase 5. Figure 2.4 illustrates the occurrence of sub-daily cycles, as summarized in Table 2.1, throughout the eruption. Although the most pronounced cycles occurred in Phases 1 and 5, it is notable that there is evidence for similar events in all of the eruptive phases. Only two episodes of cyclicity took place when no extrusion was ongoing. The first, in September 1995, occurred before any liquid lava had been extruded, although it coincided with the extrusion of an old lava spine. With these exceptions, all of the cycles have been associated with ongoing lava extrusion and later are summarized for each multi-annual cycle. The period of cycles has varied throughout the eruption, as shown in Figure 2.4. There have been occurrences when the average cycle period has varied systematically over a series of sub-daily cycle episodes. For example, in early 1997, the average cycle period increased, indicating an apparent negative correlation with lava flux changes. The opposite correlation has been observed at other specific times in the eruption. However, cycles with shorter periods tend to correspond to periods of high average lava flux in general (Fig. 2.4).
The variety of the cyclic activity listed in Table 2.1 is remarkable, and may be evidence of multiple causal mechanisms or changing conditions under which a single mechanism operates. A common observation to all of the cycles is their association with near-surface activity. Cycles in low-frequency (LF) seismicity (i.e. hybrid and LP earthquakes) in 1996-1997 were associated with near-dome tilt cycles (Voight et al. 1998). Similar deformation has probably occurred at other times during the eruption but has not been captured owing to an absence of near-field deformation monitoring since 1997 (see Odbert et al. 2014). Magma fracturing is interpreted as a trigger for LF earthquakes, generated by interface waves between magma and the conduit walls (De Angelis & Henton 2011; Thomas & Neuberg 2012). Cycles in LF earthquakes located about 1500 m below the lava dome have been associated with stick -slip flow in the conduit (e.g. Neuberg et al. 2006); LF events were observed to occur during the depressurization phase of a stick -slip (no flow -flow) cycle ( fig. 3 of Neuberg et al. 2006), although we note that the exact timing of these occurrences in early eruption data may be complicated by instrument clock errors. Cycles in rockfall activity may be generated by deformation of the dome or regular changes in the lava extrusion rate.
The presence and characteristics of sub-daily cycles in activity have been modulated by the occurrence of significant volcanic events, such as explosions or dome collapses. Repeating cycles are evidence of the existence of a system whose boundary conditions are maintained within a certain degree of equilibrium ). Significant disruption to this equilibrium state, and, therefore, to the boundary conditions of the mechanism(s) generating cyclic activity, would therefore have the potential to alter that activity -either by effecting a change in the intensity or period of cycles, or by causing them to stop or start. Regular sub-daily cycles observed in late December 2008-2 January 2009 had a near-constant period of about 4 h. In the few cycles immediately preceding the Vulcanian explosion of 2 January 2009, the period shortened to about 3 h (Stewart et al. 2009). Earlier, we noted lengthening of sub-daily cycles in the weeks preceding the January and February 2010 explosions of Phase 5. Before the dome collapse of 25 June 1997, the sub-daily cycle, measured by tiltmeter, had an average period of about 10 h, which was reduced to about 7 h immediately after (Widiwijayanti et al. 2005). A post-collapse offset in the tilt pattern was interpreted by Widiwijayanti et al. (2005) to result from the additive effects of the unloading of dome surcharge and the pressure drop in the shallow magma system. Costa et al. (2012) modelled such a change in terms of an unloading depressurization forcing a stick -slip mechanism.

Sub-annual cycles
At various times since 1995, observations have indicated the presence of cyclic activity with a period of around 5-8 weeks (collectively considered here under the umbrella term '50 day cycles', although the actual period varied). The first such occurrences were recognized by Voight et al. (1998), who identified two complete cycles, plus part of a third, in near-vent tiltmeter data recorded during Phase 1, between May and August 1997.  also reported the characteristically abrupt onset of each cycle, often associated with a major volcanic event such as a dome collapse and with intense swarms of hybrid seismicity that gradually decayed in intensity and was commonly followed by explosions. Following the destruction of the tilt network in  (Kokelaar 2002;Young et al. 2002).
There was a notable interaction between the 50 day cycles and sub-daily cycles discussed earlier; the abrupt onset of the longer cycles would coincide with increased amplitude and frequency of inflation cycles, identified in tiltmeter inflation trends and explosion occurrence . The observations of 1997 have become recognized as the 'type' examples of 50 day cycles, to which other cases are compared hereafter. Similarity in estimated extruded lava volumes recorded for each of the five cycles (Table 2.2) prompted the suggestion that, perhaps, cycles were controlled by a volume capacitor . The overprinting of shorter, sub-daily cycles on 50 day cycles in 1997 demonstrates how it is possible for the surface expression of the longer cycles to be swamped by shorter-term variability. A single '50 day' cycle was identified in Phase 2 from 23 November 1999 to 8 January 2000 (Young et al. 2003), and several were recognized in the Phase 3 data ). In the absence of tilt data, 50 day cycles might be indicated by sudden increases in seismic or surface activity; initial earthquake swarms (hybrid, LP or VT); changes in the character of sub-daily cycles, if present; periods during which approximately 30 Mm 3 lava is extruded; ground deformation signals; and changes in the orientation of dome growth. Figure 2.5 shows an illustrative analysis of seismic data recorded during the whole eruption, indicating the occurrences of sub-annual cyclicity. We use the total triggered seismic event count here as an indicator of the daily level of activity during the eruption. This metric is one of the few quantitative measures that can encompass different types of event (e.g. volcanic earthquakes, rockfalls, pyroclastic flows) and was relatively consistently derived throughout the eruption. We note, however, that such simplistic interpretation of these data can be misleading and present these analyses as an indication of activity rather than as a quantitative proxy. The complete seismic count time-series record is shown in Figure 2.5a.
The second panel (Fig. 2.5b) shows the Morlet CWT power of this total event-count time series for pseudo-periods up to 28 weeks. The white dashed line indicates the 50 day pseudo-period.     Watts et al. (2002). ‡ Refers to cycle numbering allocated by Loughlin et al. (2010), also illustrated in (Fig. 2.6). § Estimation interpolated from volume series in Figure 2.9; HY, hybrid seismicity; LP, long-period seismicity; VT, volcano-tectonic seismicity; RF, rockfalls; DRE, Dense Rock Equivalent.
At various stages of the eruption there have been repeating cycles with high transform power (yellow -red colours) at these periods. This indicates a strong positive correlation between the time series and a sine-wave-like wavelet with a frequency of 1/50 days. The peak values in the CWT plot, along the dashed white line, indicate the timing of the 'peak' of the cycles in the data. Conversely, the troughs in the time-series cycles correspond to large negative values in the transform, which are not as readily identified using this colour scale. To highlight this point, Figure 2.5c shows the Morlet wavelet transform power of the seismic count time series at a scale equivalent to a 50 day pseudo-period; that is, the transform power along the white dashed line. The peaks, circled in red, indicate the timing of the peak of 50 day cycles, with absolute transform power exceeding 100. However, the period of cycles in the time-series data is not constant; deviation from the 50 day period line reduces transform power at that scale. Figure 2.5b, c may be used together to assess the existence and significance of 50 day cyclicity in the seismic count data. The five cycles between 17 May 1997 and 7 February 1998 -documented by   (Table 2.2) -are represented by highmagnitude transform values, showing strong wavelet correlation (Fig. 2.5c). Transform peaks are generally within a few days of the observed cycles (Table 2.2). There is evidence from this analysis of 50 day cycles throughout the eruption, although it is notable that few cycles were identified in 'real time' until Phase 5, when the magnitude of the cycles was comparable to those in Phase 1. The cycles identified in Figure 2.5c during Phase 2 are listed in Table 2.2. With the exception of the cycles documented during Phase 1 and one during Phase 2 (discussed above), subannual cycles were generally not noted at the time in the MVO observations log, indicating that their surface expression was not well defined. Without such independent observations, the timings in Table 2.2 should be regarded as speculative. The volume estimates for the Phase 2 cycles have a lower average (c. 14 Mm 3 ) than the typical 20-30 Mm 3 range reported in Phases 1, 3 and 5. This reflects the apparently lower level of average extrusion rate during Phase 2 (relative to Phases 1 and 3) and may be an artefact of the observations then (see  or may represent different dynamic conditions during Phase 2. Out of a possible 10 or 11 cycles that could have occurred in Phase 3, there is evidence from LF seismic swarms for at least six. These are indicated in black in Figure 2.6. The onset of these cycles was mainly identified using seismic swarms based on evidence compiled from MVO reports for Phase 3 (Bass et al. 2005(Bass et al. , 2006Loughlin et al. 2006;Hards et al. 2007a, b) and Ryan et al. (2010). Cycles 3, 4 and 5 ( Fig. 2.6, Table 2.2) also began with notable increases in lava flux. Banded tremor with 4 h periodicity occurred at the start of cycle 3. The end of cycle 3 is taken as 5 April 2006, which was identified as a point of changed behaviour based on AVTIS measurements and increased rockfall seismicity ). The three seismic swarms of 20 May, 25 June and 18 August 2006 could mark cycle boundaries (Fig. 2.6), but none is definitive. The wholesale collapse of 20 May 2006 may have changed the system equilibrium. Loughlin et al. (2010) defined 10 'major eruptive cycles' within Phase 3 largely using observed switches in dome growth direction (in red,  The wavelet analysis of seismic event count in Figure 2.5 can assist in reconciling these various interpretations, indicating that transform power is elevated at multiple frequencies. In fact, it appears that there is some concordance between the two approaches to identifying cycles, with pairs of the Loughlin et al. (2010) cycles fitting approximately into seismic-swarm cycles 3, 4 and 5. This fit is illustrated in Figure 2.6 and Table 2.2. The peaks of approximately 50 day cycles identified through wavelet analysis are included in Table 2.2 for comparison to those identified through independent compilation of MVO records. Although both sets of dates are based largely on seismic data, there are some notable differences. The 50 day cycles at this time were, again, relatively weakly defined, accounting for much of the ambiguity in defining precise time bounds of each cycle. The wavelet-picked start dates for the cycles tend to be a few days later than those picked based on LF seismicity alone. This is understandable in physical terms if there is a lag in the build-up of rockfall seismicity following increased lava flux at the start of the cycle (e.g. cycles 1, 4, 5 and 6 of Fig. 2.6).
Phase 4 comprised two short periods of lava extrusion, lasting about 62 (poorly constrained) and 33 days. Although these phases were too brief to exhibit multiple occurrences of 50 day cycles, it is reasonable to speculate that a common forcing mechanism controlled the duration of extrusion.
Phase 5 demonstrated marked fluctuations in activity with an approximately 50 day period. Initially, marked switches in the location of lava lobe growth highlighted changing dynamics during the phase. Later, evidence from trends in sub-daily cycle period and intensity (Fig. 2.2), and ground deformation, indicated changes that coincided with three distinct peaks in rockfall activity . Table 2.2 gives the timing of the three approximately 50 day cycles (also termed 'episodes') of Phase 5. Figure 2.7 shows some of the monitoring data used to classify these cycles. Changes in the focus of lava extrusion and lobe development are reflected in thermal imagery data. By stacking a series of images recorded using a thermal infrared video camera, it is possible to assess trends in emplacement of hot deposits, which are typically shed more readily from actively growing parts of the lava dome. Figure 2.7b shows that the earliest Phase 5 activity was focused in the NE sector of the volcano, later switching to the west (and south, which is out of view). Activity switched back towards the northern flanks in the second. This pattern can also be seen in the high-resolution spaceborne radar image mapping of pyroclastic flow deposits from Phase 5 . Figure 2.7c illustrates at least two cyclic trends in deformation velocity observed during Phase 5. Flank deflation (represented here by negative displacement) appears more rapid at the onset of cycles 1 and 2, slowing later in the cycle. Similar observations were made at several continuously operating GPS stations and their character bears resemblance to the 50 day tilt cycles recorded in 1997 . The daily rockfall count is also shown. The abundance of multi-parameter data collected during Phase 5 allows detailed examination of these cycles, and identification of the transition point from one cycle to the next. The times given in Table 2.2 therefore indicate the onset of the cycles, each of which developed gradually at first and then accelerated.
The peak of each of the cycles may be estimated as the value obtained through CWT analysis of the seismic time series (Fig. 2.5, italic entries in Table 2.2). Although similar in duration and demonstrating comparable sub-daily cyclicity (Fig. 2.5), the 50 day cycles of Phase 5 differed from those in Phase 1 in that VT and hybrid seismicity was markedly lower. The only significant peak in VT earthquakes occurred immediately preceding the onset of Phase 5 extrusion . Peaks in hybrid seismicity occurred around 1 and 28 November, during the first and second 50 day cycle, respectively. We note, however, that there has been a general observation of declining VT and hybrid seismicity throughout the eruption.
The similarity of Phase 5 cycles with those of Phase 1, and those now apparent at other stages of the eruption, would suggest that a common process has resulted in modulation of eruptive activity with a period of about 50 days. It is reasonable to interpret these observations as evidence of a persistent capacitor mechanism in the volcanic system that has been able to operate at different  Table 2.2). The cycles identified by Loughlin et al. (2010), mainly on the basis of visual observations, are shown in red (cycle number above the line, date below the line). Grey bars indicate the peaks of wavelet-identified cycles, as in Figure 2.5. times throughout the eruption. Costa et al. (2007) proposed a model in which the capacitor is an elastic-walled dyke joined to a cylindrical conduit above. Hautmann et al. (2009) modelled the elastic storage and release of magma in a dyke, and demonstrated that such conduit geometry could explain surface flux and deformation data. Recent analyses of SO 2 flux time series have revealed comparable 50 day cycles in degassing data (Nicholson et al. 2013). Degassing cycles are offset in time but demonstrably correlated with cycles in seismicity, deformation and lava extrusion, which will provide additional constraint on future models of causative processes.

Multi-annual cycles
A striking feature of the SHV eruption has been the intermittency of lava extrusion (Wadge et al. 2014b). Between 1995 and the time of writing there have been five major phases of extrusion (Phases 1-5: Table 2.3), each followed by a period of repose when no lava was erupted (Pauses 1 -5). The 'on -off' nature of extrusion on Montserrat is, perhaps, the most obviously apparent cyclic feature of the eruption. Within each phase, lava flux has varied considerably, as we have already discussed, and Phases 2 and 4 were each interrupted by brief periods of no extrusion (Table 2.3). Whether or not these interruptions should be classed as pauses in their own right becomes a matter of semantics, but in this section we shall treat them as secondary to the main extrusive trends. Taking this into account, the average duration of lava extrusion phases has been 1.7 years and the average pause interval (including the current state) has been 1.4 years.  (Odbert et al. 2014) have been a striking feature of the eruption. Pauses in lava extrusion have been accompanied by near-linear inflation of the volcanic edifice, while near-linear deflationary signals were recorded during extrusive phases. Several authors have used such deformation measurements to investigate the cause of the repeating inflation cycles; these are summarized by Odbert et al. (2014) and will not be discussed in depth here. However, a commonly accepted inference is that approximately 1-3 yearly cycles have been controlled by the recharging of a shallow magma reservoir (top at c. 5 km) until it reaches a state where it is ready to erupt and sustain another extrusive phase (e.g. Foroozan et al. 2011).
An interesting observation of Figure 2.8 is an apparent bimodal distribution in pause and phase duration; Phases 4 and 5, and the pauses preceding them, were each considerably shorter than the three earlier phases and pauses. These observations raise the question of whether the preconceived inferences of shallow reservoir recharge are valid or, alternatively, whether the volcanic system underwent some fundamental change between Phases 3 and 4. Perhaps Phases 4 and 5 are the combined effect of a repetition of the mechanism that triggered the first three extrusive phases. In this case, it would appear that the energy available to drive this fourth phase of eruption was significantly less than on previous occasions. However, the activity during Phases 4b and 5 was notably vigorous (Wadge et al. 2014b) in comparison to earlier phases, which suggests some change in the mechanisms feeding the eruption. Figure 2.9 shows the comparative evolution of Phases 1, 2, 3 and 5 in terms of the normalized cumulative volume of lava extruded. While the time series for Phase 5 is less well populated due to the shorter duration of extrusion, it is evident that the onset of lava extrusion had a much higher initial flux. By contrast, Phases 1 and 3 began gradually, with flux becoming about constant in the middle part of each phase . Phase 2 had a higher initial flux than 1 and 3 but a lower average flux (Table 2.3), which was maintained at a relatively constant rate. All of these phases showed a period of waning output at the end. Like Phase 5, Phase 4b was short-lived, with high average flux (Table 2.3). The characteristic distinction demonstrated to date, therefore, is that prolonged extrusion phases (1-3) began with low lava flux and continued for 2-3 years, whereas shorter phases (4b and 5) were marked by higher flux but lasted only a few months on average. This distinction would support the conclusion that there was, indeed, some change in the eruptive mechanism between Phases 3 and 4. However, there is no evidence that this will not change again if activity resumes. The elapsed time since the end of Phase 5 has already surpassed the duration of the first two pauses at the time of writing (November 2012).
In addition to the phases of extrusion, there is other evidence of cyclic activity at similar timescales. Nicholson et al. (2013) suggest that LP cycles of SO 2 flux may have occurred, with a period of between about 2 and 3 years. The authors note that there has been no apparent correspondence between SO 2 and phases of lava extrusion since 1995, and attribute the cycles to storage and release of gas in the volcanic system that is somewhat independent of extrusion dynamics.

Multi-decadal cycles
The occurrence of repeating 'volcano-seismic crises' at approximately 30 year intervals was noted prior to the onset of the 1995 eruption (Shepherd et al. 1971;Wadge & Isaacs 1987. Typically, the crises were defined by significant seismic activity and sometimes elevated fumarolic activity. We have revisited the available data and written records, and have identified several other episodes of unrest. It is notable that some misleading inferences pertaining to some of these events have begun to become entrained in recent literature, and we attempt to present the original evidence for discussion. Montserrat was first encountered by Europeans in 1493 but there is little written record of natural events prior to the nineteenth century. Therefore, there is no evidence to either support or dismiss earlier occurrences. Some of the historical evidence is ambiguous or fleeting in detail and must be interpreted with care. In this section, we present the evidence of historical seismic crises and attempt to constrain their timing, given the available information (Table 2.4). The differences in how each crisis was monitored and recorded make it difficult to directly compare separate events. However, we are confident that at least three and possibly four seismic crises occurred prior to 1995. Figure 2.10 illustrates the timing of crisis events, and shows the intensity of all seismic events (volcanic and tectonic) felt on Montserrat for the same period. Also shown are two VT swarms that occurred in the 1970s and 1980s. These were smaller in intensity and do not share other characteristics with the dominant seismic crises. We thus consider that they were probably not the same type of phenomenon and exclude them from the following discussion.

1840s
There is some circumstantial evidence that a volcano-seismic crisis occurred in the 1840s. English (1930), who more extensively documented some of the early narrative about Montserrat, recorded that the Gages soufrière (fumarole) came into existence between 1840 and 1850. He speculated that it probably formed as a result of the great regional earthquake of 8 February 1843. This event was probably the last major interplate thrust earthquake in the northern half of the Lesser Antilles subduction zone (Bernard & Lambert 1988). Its likely location is shown in Wadge et al. (2014b, fig. 1.1). However, in a report from his October 1810 visit to Montserrat, Nugent (1811) described Galway's soufrière in detail and remarked that he understood there to be a similar fumarole, 'on the side of the mountain not more than a mile distant in a straight line ' (p. 189). This may have been Gages soufrière, and Shepherd et al. (2003) interpreted this account as evidence that the Gages soufrière predated the 1843 earthquake.
It may be significant that English (1930) noted Gages soufrière at all, referring to it as, 'the only one usually seen by visitors' (p. 5). In contrast, accounts of visits shortly before 1843 (Coleridge 1825;Martin 1837) appear to describe Galway's soufrière as though it is the only one on Montserrat. This, perhaps, suggests that the Gages fumarole was reactivated or became more active in the 1840s, possibly in connection with a volcano-seismic crisis. While increased seismicity has commonly been associated with volcanic unrest and fumarole activity, none was mentioned by English (1930). However, the aftershock sequence that inevitably followed the large (M . 8) 1843 earthquake would have generated frequent felt earthquakes, probably precluding awareness of volcano seismicity for several years.

-1900
Evidence of a volcano-seismic crisis around the turn of the twentieth century was recorded in the contemporary newspaper articles and Commissioners' reports discussed by Sapper (1903) and Perret (1939). Felt and damaging earthquakes were documented at Gages, Tar River, Harris and other parts of the east -west belt between Centre Hills and Soufrière Hills. Most commentators, including Robson (1964), report that seismic activity began on 23 April 1897. However, Milne (1902) documented 'many small earthquakes' following heavy rain on 29 November 1896 and went on to note that, 'For forty years before there had been but few noticeable shocks. Since the rainfall the springs give off more gas, and silver is blackened three miles away ' (p. 152). Major damage to stone-built churches and houses, and roadblocking landslides were common, particularly in 1898 and on 20 October 1900 (Perret 1939).
The end of the crisis is less clear still, and has been reported variously as 1898, 1899and 1900. MacGregor (1938  reports of ongoing activity until 1902 but these were deemed to probably be incorrect by Powell (1937). Feuillet et al. (2011) argued, on the basis of Coulomb stress modelling, that the 1843 earthquake imparted a large stress on the Montserrat -Bouillante Fault System running through Montserrat to Guadeloupe and that this was the source of the trigger for the significant regional earthquake near Guadeloupe on 29 April 1897, and perhaps the initiation of volcano-seismic activity on Montserrat 1 week earlier.

-1937
The first seismic crisis to be studied scientifically was the subject of a Royal Society expedition, reported by MacGregor (1938) and Powell (1938). However, by the time the expedition reached Montserrat, in the spring of 1936, the intensity of activity had greatly diminished. Nonetheless, over 1000 felt local earthquakes were reported -some strong enough to damage stone buildings, probably at Modified Mercalli Intensity VIII -making it the most intense of the crises seismically. Perret (1939) studied the crisis from 1934 onwards and noted its similarities to the previous crisis, including increased fumarolic degassing, especially hydrogen sulphide, from the Galway's and two Gages soufrières. Powell (1938) estimated that the hypocentre locations were spread along an east -west belt to the east of St George's Hill. The seismic record documented by Perret (1939) shows a gradual increase from 1934, peaking in May 1935. We consider that another, larger peak in the seismic event record in November 1935 must be contaminated by the aftershock sequence of a major regional earthquake, which occurred to the north of Montserrat on 10 November 1935. Perret (1939) reported that this event, and a subsequent sequence of earthquakes were located between Montserrat and the island of Redonda to the NW. He reported damage to buildings on Montserrat and a large landslide on Redonda. Activity declined through 1936 -1937 until it reached a very low level and the monitoring instrumentation was withdrawn.

-1967
The crisis starting in March 1966 and continuing until November 1967 was monitored using seismometers deployed by the University of the West Indies Seismic Research Unit (Shepherd et al. 1971). More than 700 earthquakes were recorded instrumentally, with locations across southern Montserrat in a WNW-trending band, and with depths between 3 and 13 km. The average depth of earthquakes decreased from 5 to 3 km between April and September 1966, and then increased to about 10 km by November 1967. Fewer than 50 felt earthquakes were reported and there were no reports of damaged buildings, suggesting a significantly lower intensity than the previous two crises.
Tilt measurements made at three sites indicated inflation of the volcanic edifice between July and October 1966, and a deflationary trend from January to March 1967, with rates of up to 0.3 mrad (c. 0.6 mm over 2 km) per day. No changes were reported in fumarolic activity, except that the heat flow decreased by a factor of 4 between late 1966 and 1 year later. Shepherd et al. (1971) interpreted the observations as the ascent of magma beneath SHV (or to its SE) until about August 1966, and subsequent magma descent.

-1985
The seismic network deployed in 1966 remained operational after the crisis had ended, and in 1977 it recorded the first of three episodes of VT earthquake swarms, followed by two more in 1978 and 1985 (Latchman 1995). Table 2.4 lists the dates of these swarms individually. The earthquakes were generally lower intensity (only a few were felt) and the VT swarms were much shorter than the earthquake swarms of earlier crises (days rather than years  (Robson 1964). We note that the absence of permanent instrumentation prior to 1966 may have precluded observation of earlier, low-intensity crises such as this because individual or sporadic felt earthquakes are a common occurrence in the Eastern Caribbean generally and would probably not warrant reporting.

1992-1995
The seismic crisis that immediately preceded the onset of the 1995 eruption at SHV was monitored instrumentally, but there were few other observations of the soufrières or deformation, for example. The seismicity of the crisis has not been reported in detail, although it has been summarized by numerous authors (Latchman 1995;Ambeh & Lynch 1996;Shepherd et al. 2003). In August and September 1992, there were three earthquake swarms, each comprising tens of individual events. Elevated seismic activity persisted, albeit at a lower rate, into 1994. The pre-eruption crisis reached its peak in November -December 1994 when the event rate exceeded 100 per day. Although earthquakes were more frequent than in the 1930s crisis, they were smaller in magnitude (fewer were felt). As this crisis transitioned into the phreatic onset of the 1995 SHV eruption, the seismicity grew steadily. Hypocentre locations were clustered beneath the SHV and to the east, and the larger events were at depths of 5 -9 km (Shepherd et al. 2003).

Overview of seismic crises
The events classified above as seismic crises share the common characteristics of being extended periods of VT seismicity with varying intensity. The intensity of the most recent crises (1966 -1967 and 1992-1995) was significantly less, based on felt events, than during the two previous crises. Figure 2.10 shows the temporal relationships between the periods of unrest discussed. A notable feature is that the frequency of occurrence of crisis is somewhat regular, and that the period reduces monotonically from 57 to 26 years in the two centuries approaching the onset of the 1995 SHV eruption if we include the 1840s crisis. Deformation of the volcano's flanks was recorded during the 1966-1967 crisis, but there are no equivalent observations during other episodes, so it is not known whether such activity was typical. Three of the four crises (excluding events of the 1840s) involved increased fumarolic activity, with observed increases in heat or gas flux. The notable exception was, again, the most recent crisis: no increase in fumarole intensity was reported during the 1992-1995 crisis, indicating that the volcano's hydrothermal system was not involved with the onset of the eruption (Boudon et al. 1998;Hammouya et al. 1998). Shepherd et al. (1971) concluded that the crises represented 'failed eruptions', in which magma did not reach the surface to erupt. This argument was supported by the eventual eruption of the SHV in 1995. There are two main aspects of the periodic nature of these events that are of interest to our discussion: the quasi-regular timing of the crises; and the duration of each episode.
Adopting the inferences of Shepherd et al. (1971), the processes driving the intrusion and ascent of magma beneath the volcano were modulated such that the 'active' part of each cycle recurred at approximately three-decade intervals. Several authors have drawn an association between large, felt regional earthquakes and volcanic activity on Montserrat. Figure 2.10 shows the timing of all regional earthquakes (MMI . IV) since 1825 and how intensely they were felt on Montserrat. This catalogue incorporates the events reported by Robson (1964) and subsequent updates (L. Lynch pers. comm. 2011). While most of the seismic events occur around the same time as volcanic unrest, the largest events post-date crisis onsets (i.e. in the 1840s and 1930s). We, therefore, reject regional tectonic earthquakes as the direct trigger of seismic crises but do not rule out the likely influence of major earthquakes on the regional stress field and, perhaps, the volcanic system generally.
The long period of recurrence is also indicative of a mechanism in the deep part of the volcanic system. Candidate mechanisms could include crustal (or, perhaps, mantle) processes. Such an example might be the injection or mixing of fresh basic magma into the bottom of the magmatic plumbing system, each time reinvigorating the shallower system, driving buoyant magma ascent and/or seismogenic reservoir or conduit processes. The absence of obvious progression from one crisis to the next may suggest that the three-decade mechanism reflects adjustment to the existing magmatic system rather than the genesis of a new one. After repeat 'attempts', these disturbances supply sufficient energy to the system to trigger the eventual eruption. Recurrent seismic crises have been a feature of many arc volcanoes (Lindsay et al. 2005); a greater understanding and record of these observations may serve in the interpretation of events at other potentially active volcanoes.
The duration of each seismic crisis ( Fig. 2.10, Table 2.4) was relatively constant, typically about 2-4 years. The consistency of this timing may reflect the process or sequence of processes operating at each occurrence. For example, one might expect that a similar batch of 'energy' (e.g. in the form of heat, magma,  gas) was involved for each crisis, resulting in a similar mechanical or hydrothermal response from the volcano each time. The apparent progressive decrease in the seismic energy involved in the crises could reflect a process where the same volume of crust was repeatedly subject to stresses of equivalent magnitude. Alternatively (or additionally), the country rock becoming more ductile (and less seismogenic) could be a result of progressive heating over the course of the repeated crises. Once SHV began erupting, the boundary conditions of the system changed. It is notable that the duration of each seismic crisis is slightly longer but similar in duration to the extrusive phases during the eruption. This may be coincidental, or may reflect a characteristic modulating frequency of the volcanic system between the source and the surface vent.

Conclusions
We have identified and catalogued the existence of cyclic behaviour in eruptive activity at the SHV at four timescales: sub-daily (hours), sub-annual (weeks), multi-annual and multi-decadal scales. Although the source mechanisms of these different cyclic signals are not the same, their existence is evidence of systematic behaviour at the volcano on a range of scales. It is generally understood that longer-period signals at volcanoes correspond to deeper processes, and this is borne out in the observations we have summarized.
Shallow (,1 -2 km) conduit processes are responsible for rapid fluctuations in lava flux over hours to tens of hours that have been detected, intermittently, throughout the eruption. These processes may include plug-formation, rheological stiffening, magma fracturing and stick -slip behaviour. Seismic and deformation observations suggest recurrent cycles with a period of around 50 days, and these have been interpreted in term of an elastic-walled dyke at a depth of between 1-2 and 5 km acting as a magma capacitor (Costa et al. 2007;Hautmann et al. 2009). Inflation -deflation cycles associated with crustal (6 -19 km) magma reservoir(s) are highly correlated with lava efflux cycles, with periods of a few years, although we note that this has changed in character somewhat in recent years. The longest cyclicity recognized is of three (or, perhaps, four) volcano-seismic crises recurring at about 30 year intervals, which may be caused by basic magma rising from depth (.20 km) in the SHV system.
In addition to the four cycle types, we have discussed there is some evidence of others in the long-term SHV record. Cyclic (c. 2 year) variations have been identified in SO 2 efflux that appear to be unrelated to extrusive activity. There is also some indication of a semi-annual -annual cycle in the seismicity/deformation record for Phase 2 (e.g. Fig. 2.5). Some of this behaviour could be forced externally by the global hydrological/atmospheric cycles. It is often impossible to separate the influence of such forcings in monitoring data. There is evidence that cyclic phenomena may also exist at timescales of minutes (Neuberg et al. 1998) and over 10 3 -10 4 years (Harford et al. 2002).
While it is clear that multiple different mechanisms can operate cyclically at SHV, it also seems apparent that there may be welldefined interactions between those mechanisms. The striking pattern of sub-daily cyclicity between late November 2009 and early January 2010 (Fig. 2.2), for example, corresponds to the second sub-annual cycle shown in Figure 2.7. The interaction between the sub-daily and sub-annual cycles over this time bear a remarkable resemblance to those recorded between 22 June and late July 1997 ). According to the elastic-walled dyke model of Costa et al. (2007), the magmatic pressure in the dyke is highest at the start of the 50 day cycle and, hence, it should be transmitted to the conduit experiencing the sub-daily cycles during this period. The short-period, high-amplitude, asymmetric character of these cycles (Fig. 2.2) is generally consistent with this.
The influence of a deeper, larger part of the volcanic system on a shallower system seems intuitive.  speculated that at least some of the cyclic behaviour seen at SHV may be controlled primarily by the volume capacitance of the mechanism(s). In the example outlined above, dyke deflation cycles -each associated with a 'batch' of magma approximately tens of million cubic metres in volume -evidently influence the character of cycles. The changing supply rate of magma from the dyke into the shallow conduit alters a critical boundary condition to the plug-formation process, and can thus affect a change in the rate of plug formation and ejection (e.g. Diller et al. 2006). Disruption to the state of equilibrium in which the cyclic mechanism operates thus precipitates a change in the character of the cyclicity. The reciprocal influence which the development of sub-daily cyclicity may have on deeper processes, if any, is less clear. It is conceivable that the changes in the time-averaged resistance of flow out of the dyke due to conduit mechanisms, for example, may feed back to modulate the development of longer period cycles. Perhaps interactions such as these have controlled the variable intensity of the sub-daily and sub-annual cyclicity throughout the eruption; the most clearly defined examples of both types of behaviour have been coincident (occurring in Phases 1 and 5).
Looking deeper in the volcanic system, the dyke inflation mechanism may interact with the reservoir inflation mechanism that feeds it, although the evidence for such a relationship is less clear. Higher-volume, deeper components of the magmatic plumbing system (e.g. the crustal reservoirs v. the intermediate dyke) are likely to exert greater overall control on the progression of the eruption because of their greater mechanical inertia (Melnik & Costa 2014). However, it is apparent that each of the processes, and the mechanisms by which they are able to feed back to one another, are important in determining surface volcanic activity. Another consideration is that the surface expression of any mechanisms operating on short timescales deeper in the system would probably be damped or buffered by shallower parts of the system and may not be able to generate a coherent or detectable surface signal.
Several key monitoring techniques have been vital to the identification and analysis of cyclic phenomena. Visual indications of varying surface activity often provide the earliest sign of cyclic activity at the volcano. Seismic data then offer a versatile means of summarizing activity at the volcano quantitatively. The timeaveraged amplitude of seismicity, represented by RSAM, is an indicator of the eruption intensity during phases of lava extrusion. This has proven to be a useful tool for short-term (hours to months) assessment of cyclicity at sub-daily timescales, when contributions from surface activity dominate the signal. Records of individually categorized events, such as rockfalls, tremor and various types of earthquake, have been exploited to demonstrate the existence of cyclic eruptive activity at longer timescales, and we identify numerous cycles that had previously not been detected.
However, seismic data alone cannot unambiguously identify eruptive cyclic phenomena. Evidence from other monitoring techniques and records can be used to corroborate seismic observations and vice versa. As the eruption has continued, the longevity and quality of monitoring data streams on MVO has grown. Recent eruptive episodes have generated a rich, multi-parameter dataset that allows close scrutiny of cyclic events. These observations demonstrate the value of multi-parametric observation. In order to capture cyclic phenomena, it is important to maintain a monitoring strategy with the appropriate coverage, resolution and sensitivity for the phenomena under observation. We have summarized some of the key observations from Phase 5, when strong cyclic activity was apparent at timescales of hours and weeks. SHV also has a small network of Sacks -Evertson dilatometers that have proven to be sensitive to strain transients associated with major explosive/collapse events (e.g. Chardot et al. 2010). Unfortunately, they are apparently located too far (.5 km) from the upper conduit of SHV to be able to detect any strain signals associated with the sub-daily cycles.
The observation and measurement of cyclic phenomena at volcanoes has obvious appeal. If it appears that the system(s) driving the eruption can operate under a deterministic regime, there exists potential to forecast future cyclic events. This has been achieved to some degree of success at short timescales when, for example, the expectation of an imminent increase in surface activity may be used to guide deployment of equipment or workers in the field. This has become possible in cases where the number of observed cycles has become large enough that some degree of confidence could be placed in simplistic first-order forecasting. However, for longer-term cycles, fewer data points are available on which to form the basis of a statistical forecast model. The continuation of robust and thorough monitoring programme at SHV will assist in strengthening our knowledge and understanding of cyclic phenomena. By understanding this element of activity on Montserrat, we move towards the ability to characterize deterministic mechanisms that control the state of eruption at a range of timescales.