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Journal of Volcanology and Geothermal Research 180 (2009) 81–88
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Journal of Volcanology and Geothermal Research
j ourna l homepage: www.e lsev ie r.com/ locate / jvo lgeores
Degassing at low magma-viscosity volcanoes: Quantifying the transition betweenpassive bubble-burst and Strombolian eruption
M.R. James ⁎, S.J. Lane, L. Wilson, S.B. CorderLancaster Environment Centre, Environmental Science Division, Lancaster University, Lancaster LA1 4YQ, UK
⁎ Corresponding author. Tel.: +44 1524 593571; fax: +E-mail address: [email protected] (M.R. Jame
0377-0273/$ – see front matter © 2008 Elsevier B.V. Aldoi:10.1016/j.jvolgeores.2008.09.002
a b s t r a c t
a r t i c l e i n f oArticle history:
At many volcanoes, low ma Received 2 January 2008Accepted 1 September 2008Available online 9 September 2008Index words:8414 Eruption mechanisms andflow emplacement8445 Experimental volcanism8419 Volcano monitoring
Keywords:Strombolian eruptionpuffingpassive degassinggas slugoverpressure
gma-viscosities allow persistent degassing over a range of styles from explosiveStrombolian activity to gas ‘puffing’ and passive degassing. It is generally accepted that Strombolianeruptions reflect the bursting of large bubbles (gas slugs) at the magma surface and that relatively quiescent‘puffing’ indicates the presence of significantly smaller bubbles or slugs. Here, we address this qualitativerange and derive a dimensionless parameter, Pslim⁎ , to quantify and distinguish different regimes of ‘burstvigour’. For Pslim⁎ ≤1, ‘passive’ activity is anticipated and measurable parameters such as infrasonic amplitudewill be small. For Pslim⁎ N1, bursting slugs will be energetic, and surface effects are anticipated to increase withincreasing Pslim⁎ . Various physical parameters recorded during laboratory experiments and simulated throughnumerical models are shown to demonstrate the same trends when parameterised by Pslim⁎ . Hence, Pslim⁎
provides a straightforward relationship between changes in measurable surface effects and the system'ssubsurface physical parameters and, for energetic activity of a particular system, burst effects are shown to beproportional to the square root of the gas mass involved. Effect magnitudes are also shown to be a function ofatmospheric pressure and application of Pslim⁎ parameterisation to planetary scenarios produces results inline with our current understanding of planetary volcanism.
© 2008 Elsevier B.V. All rights reserved.
1. Introduction
The manner in which magma degasses is a controlling process oneruption style and, at terrestrial basaltic and other lowmagma-viscosityvolcanoes, styles vary from passive degassing to violent fire fountaining(Parfitt and Wilson, 1995). In order to understand more about theseprocesses, persistently active volcanoes such as Stromboli are con-venient targets for study. At Stromboli, activity generally encompassesthe range of passive degassing (weak, but quasi-continuousflow (Harrisand Ripepe, 2007)), through ‘puffing’ (gas emission as discrete packages(Ripepe et al., 2002; Harris and Ripepe, 2007)) to Strombolian eruptions(Chouet et al., 1974; Blackburn et al., 1976) and, despite the growingwealth of surface geophysical data (including video, seismic, thermal,radar and infrasonic datasets (Ripepe and Marchetti, 2002; Urbanskiet al., 2002; Chouet et al., 2003; Dubosclard et al., 2004; Ripepe et al.,2002, 2005; Auger et al., 2006; Marchetti et al., 2006; Gerst et al., inpress)) the relationships between themagnitude of these events and thesub-surface conditions remains either poorly constrained or qualitative.Here, we consider the part of the degassing spectrum over which thesurface style reflects the arrival of large individual bubbles or gas slugs atthe surface. More energetic fountaining activity, during which largebubbles are sufficiently close to interact and coalesce, or there is a
44 1524 593985.s).
l rights reserved.
significant net upward flux of magma (Wilson and Head, 1981; Parfitt,2004), are not considered.
For a first-order model to relate sub-surface parameters to themagnitude of surface measurements recorded at eruption (or ‘bubbleburst’, e.g. infrasonic data and ejecta velocities), we assume that theobserved magnitudes are a function of the overpressure in theascending gas bubble when it arrives at the surface. This may beintuitive when considering infrasonic data, but possibly less so forother measures such as seismic data, for which overpressuremay onlyact as a proxy for the relevant dynamics. As any gas bubble rises in aliquid, it tries to expand to be in equilibrium with the surroundingfluid-static pressure. If this could always be achieved successfullythen, neglecting surface tension which provides an insignificantcontribution to metre-sized bubbles in this type of system (Seyfriedand Freundt, 2000), all bursting bubbles would contain gas at close toatmospheric pressure and no energetic eruptions would be produced.However, this is not the case and expanding bubbles are hindered byviscous and inertial forces (Sparks, 1978; Proussevitch et al., 1993;Vergniolle, 1998; James et al., 2008) resulting from the dynamics ofthe expansion and are consequently overpressured.
Unfortunately, estimating this overpressure directly for relativelylarge and rapidly moving gas slugs is non-trivial and, although valuescan be calculated numerically by dynamic slug ascent models(Vergniolle, 1998; James et al., 2008), these models do not considerany near-surface effects. Consequently, their results provide insight
82 M.R. James et al. / Journal of Volcanology and Geothermal Research 180 (2009) 81–88
into model sensitivity to different parameters but are subject tosignificant uncertainty if used to provide absolute values for burstconditions. The approach adopted here is to develop a straightforwardparameter which reflects how far a gas slug within a system must befrom a theoretical limiting state calculated from assuming staticpressures alone (i.e. zero bubble overpressure). As such, withoutactually modelling the dynamic processes involved, the parameterreflects the importance of the dynamics and thus acts as a proxy forthe degree of over-pressurisation at burst and, consequently, can beused to assess the variability of measurable effects during differentbubble bursts at a system. This approach therefore offers astraightforward link between geophysical observables, such asinfrasonic amplitude, and changes in the sub-surface physical proper-ties of the system such as the slug gas mass.
To derive the parameter, we first define a straightforward model ofan ascending gas slug in which the only pressure changes accountedfor are those resulting from changes in the liquid static head, and anypressures resulting from the dynamics of the system are explicitlyexcluded. Analysis of this model demonstrates that, within a system,for gas slugs greater than a specific size (or gas mass), decompressingand expanding as they ascend, there is a theoretical pressure belowwhich no stable solution for slug length can be calculated; this is aregion of parameter space for which no real solutions to this staticpressure model exist. Consequently, for such gas slugs to exist atpressures less than this limit, dynamic pressurisation must besignificant. The theoretical limiting static pressure is then used toderive the dimensionless parameter which relates changes inpotential burst overpressures of a system to its sub-surface para-meters. Finally, we test this parameterisation using previouslypublished experimental and dynamic modelling results and discussits implications for extraterrestrial activity.
2. Canonical static pressure model
In order to maintain a straightforward approach from which ascaling parameter can be derived, we first envisage the simplestpossible conduit model, comprising a constant volume of liquid in acylindrical vertical tube of radius rc (Fig. 1). An ascending gas slug isrepresented as a cylindrical region of gas of fixed radius rs, with rsbrc,
Fig. 1. Canonical representation of a gas slug within a cylindrical conduit, includingsymbols used within Eqs. (1)–(13) (see text for details). Liquid regions are shaded greyand unshaded areas represent gas regions (the slug and surface atmosphere) under (a)arbitrary starting conditions and (b) at some subsequent time.
to account for the thickness of the liquid film which must fall aroundthe slug body as it to ascends. Such a representation, in which slugradius is constant and minor effects such as surface tension andcurvature of the slug nose and base are neglected, is supported byexperimental observation and its applicability has been demonstratedwith successful numerical models which include dynamic effects(James et al., 2008). At this point, it is stressed that it is not intendedhere to produce a working model for ascending slugs, rather anidealised end-member scenario from which the significance of theneglected dynamic effects can be assessed.
The gas pressure in the slug is defined by conditions at the slugnose. This is in common with dynamic models (Vergniolle, 1998;James et al., 2008), in which the gas–liquid interface at the slug nosecouples both the static and the dynamic fluid pressures generated inthe overlying liquid, into the slug. However here, given that alldynamically induced pressures are explicitly excluded, the gaspressure in the slug, P, is equal to the liquid pressure at the slugnose boundary, Plsn, as given by the static liquid pressure alone
Plsn ¼ Psurf þ ρgh ð1Þ
where Psurf is the gas (atmospheric) pressure at the liquid uppersurface, ρ is the liquid density, g is the acceleration due to gravity andh is the length of the liquid column on top of the slug (Fig. 1). In orderto maintain our straightforward approach from which an analyticalsolution and a dimensionless parameter can be derived, the gas ismodelled as an ideal gas under isothermal conditions. Although anumerical solution for amodel assuming adiabatic expansion could bedetermined, this would not permit the derivation of a straightforwardparameter. The use of an isothermal approach is also supported by theresults and is discussed further, later in this section. Consequently, atany point during the slug ascent, with P=Plsn, and the gas assumed tobe ideal and isothermal,
Psurf þ ρgh0ð ÞL0 ¼ Psurf þ ρghð ÞL ð2Þwhere L is the slug length, and the zero subscripts denote arbitraryinitial length and depth starting conditions for the slug. Consideringconservation of liquid volume within the system,
h0πr2c þ L0π r2c − r2s
� � ¼ hþ sð Þπr2c þ Lπ r2c − r2s
� � ð3Þ
given s as the distance between the slug base and its initial position(Fig. 1). Simplification of Eq. (2) allows h to be expressed as
h ¼ h0 − sþ L0 − Lð ÞA′ ð4Þwhere A' =1−(rs/rc)2. (If comparing the model here with the dynamicmodel of James et al. (2008), note the difference in the definition of A',that increases the conciseness within this work). Substituting for h inEq. (3) provides a quadratic for the slug length,
AVL2 −Psurfρg
þ h0 − sþ A′L0
� �Lþ Psurf
ρgþ h0
� �L0 ¼ 0 ð5Þ
the real, positive root of which describes L as a function of s and theother physical parameters.
In Fig. 2, solutions of Eq. (5) are illustrated alongside data fromlaboratory experiments in which the position of ascending slugs weretracked by video (see Section 3 for experimental details). Slug expansionwasvaried betweenexperimentsbychanging the surfacepressure usinga vacuum system. With s defined (using a linear fit to the appropriatevideo data) and the slug length, L, calculated (Eq. (5)), the position of theslug nose is thus determined and the position of the liquid surface(upper curve) can be calculated from conservation of liquid volume(Eq. (3)). For the relatively high surface pressure experiment (involvingonly a relatively small slug expansion, Fig. 2d), the static modelreproduces the evolution of the slug well. However, for the low surfacepressure experiments (involving large slug expansions), the model
Fig. 2. The ascent of a gas slugs during laboratory experiments as shown by video data(symbols), the static pressure model (solutions to Eq. (5), black curves) and a dynamicmodel (grey curves, (James et al., 2008)). The experiments were carried out with thereduced surface pressures given ineachpanel generatedbyavacuumpump, inorder tovarythe amount of gas expansion during the slug ascent. The vertical positions of the liquidsurface, slug nose and slug base are plotted. Note the steadyascent rate of the slug base andthe near-surface acceleration of the slug nose; these are standard features of rapidlydecompressing ascending gas slugs (James et al., 2008). The superimposed model curvesshow the results of solvingEq. (5) fordifferent valuesof the slugbaseheight, s, andusing thedynamic model of James et al. (2008), for the appropriate surface pressure and theexperimental parameters, ρ=862 kg m−3, g=9.81 m s−2, h0≈1.3 m, L0≈0.03 m (precisevalues varied slightly between experiments) andA'=0.466. See Section 3 for derivation andexplanation of Pslim⁎ .
83M.R. James et al. / Journal of Volcanology and Geothermal Research 180 (2009) 81–88
reproduces the slug motion reasonably at depth, but increasingly over-estimates the expansion as the surface is approached. These over-estimates by the static model thus illustrate the increasing importanceof dynamic processes in maintaining pressure within the slug as itapproaches the surface.
In order to confirm that this is indeed an effect of the dynamics(rather than from the assumption of isothermal, not adiabatic,expansion), results from a dynamic model (James et al., 2008) arealso plotted for each experiment (grey curves). This dynamic modelaccounts for the inertia and viscosity of the overlying fluid (see Jameset al. (2008) for details) and was run using isothermal conditions andparameter values identical to those in the static model. Thus, thedifferences between the static and dynamic model results reflect onlythe influence of the physical dynamics and are not influenced by anythermodynamic considerations. Interestingly, James et al. (2008)found that models using adiabatic conditions always fitted the datapoorly with respect to those assuming isothermal conditions.Although this has yet to be fully understood, it does support our useof isothermal conditionswithin the straightforward approach adoptedhere. Fig. 2 also shows that, not only does the dynamic model fit thedata very well, but for conditions of significant slug expansion, thedifferences between the static and the dynamic model results (andhence the relative magnitude of the dynamic effects) are considerable.
The results given in Fig. 2 illustrate the key feature of the staticmodel on which the static pressure-limit parameterisation derived inthis work is based. In Fig. 2 (a) and (b), the model curves for the liquidsurface and the slug nose stop (at t≈3.2 s) significantly before theyintersect, indicating that the model could not simulate the arrival ofthe slug at the liquid surface. This reflects a region of parameter spacefor which Eq. (5) has no real roots and, in the case of Fig. 2a, this regioncovers values of h less than 14.8 cm in the simulated experiment. Atslug positions above this (i.e. smaller values of h), there would beinsufficient liquid above the slug to maintain a static pressure balancewith the gas in the slug and to fill the liquid annulus surrounding it.Hence, the highest position of the slug realisable within the staticpressure model (a point termed here the static pressure limit, and forwhich we subsequently assign the subscript 'slim') is given by the lastreal root of Eq. (5). It is the gas pressure in the slug at this theoreticalpoint on which we base the parameterisation elaborated below.
3. A static pressure-limit parameterisation
Although the parameter of interest can be derived directly fromexamination of the last real roots of Eq. (5), the same concept can beapproached more intuitively by considering the stability of a slug, atany position, to a small perturbation, ΔL, in its length. For this analysis,the slug base is considered to be stationary, and the lengthperturbations are accommodated by small changes in the position ofthe slug's nose. Such a disturbance will change the liquid depth abovethe slug nose in order to accommodate the additional liquid volumerequired in the annulus surrounding the slug body. Consequently, thestatic liquid pressure at the slug nose will be reduced to P′lsn where
PVlsn ¼ Plsn − ρgΔLA′: ð6Þ
Inside the slug, ideal isothermal expansion of the gas will reducethe pressure to P′, where
PV Lþ ΔLð Þ ¼ PL ð7Þ
with the pre-perturbation pressure and length values given by P and Lrespectively. Given that P=Plsn, Eq. (7) can be rearranged as
PV¼ PlsnLLþ ΔL
: ð8Þ
Fig. 3. Slug burst data from laboratory experiments. The magnitudes of pressure (black)and apparatus displacement (gray) transients recorded during burst events are plotted.In (a) results are shown from experiments carried out over a range of surface pressuresusing UG19 (filled symbols) and UG20 (open symbols) oils as the liquid phase and a gasinjection volume of 6 ml. The magnitudes of the measured effects demonstrate strongincreases at surface pressures between ~100 and 1000 Pa. At smaller values, themagnitudes plateau, perhaps reflecting the fact that, as pressures decrease, the actualgas masses involved become sufficiently small that this counteracts the increasingamounts of expansion involved. In (b) results are given from experiments (using UG19)with surface pressures of 300 Pa (circles) and 1000 Pa (squares) for a range of initialstarting volumes of the gas slug.
84 M.R. James et al. / Journal of Volcanology and Geothermal Research 180 (2009) 81–88
Now, subsequent to such a length perturbation, if P′lsnNP′ then thenet force on the slug nose boundary will be restorative and theperturbation will be damped. However, if P′lsnbP′, then the perturba-tion will grow; the slug cannot be deemed stable under purely staticpressure conditions and would expand until the surface is reached.This scenario represents the condition of imaginary roots in Eq. (5).Expanding the stable case (P′lsnNP′) using Eqs. (6) and (8) leads to
Plsn N ρgAV Lþ ΔLð Þ ð9Þ
which, as ΔL→0, can be used to define the limiting criterionrepresenting the lowest pressure, Pslim, at which a slug would remainstable in the absence of dynamic effects:
Pslim ¼ ρgAVLslim: ð10Þ
By noting that the use of an isothermal ideal gas provides therelationship PslimLslim=P0L0, where P0 is the initial slug gas pressure(i.e. P0=Psurf+ρgh0), Pslim can then also be defined in terms of thearbitrary slug initial conditions:
Pslim ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiρgAVP0L0:
pð11Þ
So, Eq. (11) gives the slug gas pressure immediately prior to failureof the static pressure model, after which the slug cannot be describedunder the assumption of purely static conditions, and hence dynamicpressurisation must be important. Using an equivalent to Eq. (1), thisstatic pressure limit can also be given in terms of the liquid heightabove the slug nose;
hslim ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiAVP0L0ρg
s−Psurfρg
: ð12Þ
For a system of constant geometry, temperature and gas chemistry,the product P0L0 will be proportional to the slug gas mass. Thus, largerslugs, with larger Pslim and hslim values that represent greaterpressures and depths at which the static pressure model fails, mustbe further from a stable static pressure solution as they reach thesurface. They should, therefore, have greater dynamically generatedoverpressures at burst and vigorous eruptive events would beanticipated. Slugs with smaller gas masses (and hence smaller P0L0)have smaller Pslim and hslim values. For slugs with Pslim valuesapproaching that of the surface atmospheric pressure and corre-sponding hslim values tending to zero, slug overpressure at the surfaceand event vigour would also be expected to approach zero or, morelikely, to be small and controlled by other factors such as surfacetension or near-surface fluid dynamics. Consequently, Pslim has thepotential to link changes in the burst ‘vigour’ of a system to changes inthe gas masses involved. Note that, as continuous functions of P0L0,calculated Pslim values can be less than atmospheric pressure, andhslim values can be negative. Although such values have no physicalmeaning, they would reflect the increasing ‘stability’ of a system andthe increasing distance in parameter space from the likelihood of anenergetic burst.
In order to compare laboratory and real planetary scenarios, Pslimcan be non-dimensionalised by defining Pslim⁎ as the ratio between theslug pressure at the static limit and the surface pressure,
P⁎slim ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiρgAVL0P0
pPsurf
: ð13Þ
Pslim⁎ thus defines a parameter space in which gas slugs with Pslim⁎ ≤1have a static pressure solution at the surface and burst events areanticipated to be relatively low energy and, for gas slugs with Pslim⁎ N1,a surface static pressure solution does not exist and slugs must be
significantly dynamically overpressured as they burst. As Pslim⁎ valuesincrease, the ‘vigour’ of bursts is anticipated to do likewise.
4. Burst magnitudes: experiments and results
In order to ascertain the effectiveness of Eq. (13) for parameterisingthe effects of slug bursts, we plot measured ‘effects’ from laboratoryexperiments and from numerical models against calculated Pslim⁎
values.The laboratory experiments were carried out in a vertical glass
tube (of internal diameter 2.55 cm) mounted on a force sensor (whichwas calibrated for displacement to account for resonance effects(James et al., 2006)) with pressure transducers (Honeywell, P163)mounted within the tube, ~1 m above the liquid level. In order tocreate slug expansions similar to those observed at volcanoes, the topof the tube was connected to a vacuum pump, allowing the liquidsurface pressure to be reduced (i.e. varying Psurf between ~1 and105 Pa), and hence a wide range of Pslim⁎ values to be explored. Slugswere introduced by injecting gas (at near-equilibrium pressure) intothe apparatus base by syringe, under a liquid head of ~1.7 m.Experiments were carried out using two liquids (Edwards vacuum oilsUG19 and UG20 with densities and viscosities of 862 and 867 kg m−3
and 0.16 and 0.28 Pa s, respectively) and a range of initial gas slug sizes(injected gas volumes of between 1 and 49 cm3).
85M.R. James et al. / Journal of Volcanology and Geothermal Research 180 (2009) 81–88
From the recorded data, the slug-burst ‘effects’ extracted were thesize of the pressure pulse above the liquid surface produced by theburst, and the magnitude of the accompanying apparatus verticaldisplacement. In Fig. 3, these data are plotted against surface pressurefor experiments carried out at various surface pressures, and againstinitial slug length for experiments involving various initial gasvolumes.
The changes produced in the measured displacement and pressuretransients track each other closely, suggesting that they are measur-able results of the same process. However, the changes resulting fromvarying Psurf and L0 cannot be directly compared within Fig. 3,highlighting the requirement for a more general parameter such asPslim⁎ , against which the effect magnitudes can be plotted.
In order to extend the ranges of values used up to thoseappropriate to volcano-scales, two sets of computational fluiddynamic (CFD) simulations were carried out using the commercialsoftware package Flow3D (see James et al. (2008) for modellingdetails). Firstly, the laboratory experiments were modelled to validatethe CFD calculations against the experimental data. A second suite ofsimulations was then run with volcano-appropriate parameters(ρ=2600 kg m−3, h0=50 m, magma viscosity=500 Pa s, Psurf =105 kPa,and rc=1.5 m). For the simulations, in order to avoid uncertaintiesrelated to modelling the final rupture of the bubble nose, bubble
Fig. 4. The variation of burst effects with systems parameterised by Pslim⁎ . The key provides dethe magnitude of transient pressure changes Pb, and apparatus displacements, Szb (in micronout using UG19 liquid with a viscosity, µ, of 0.16 Pa s. Effect magnitudes for experiments usingvalue that, interestingly, is the similar to the ratio of the liquid viscosities. For CFD simulationThe grey dashed line represents a gradient of 1. For low values of Pslim⁎ , and consequently smatransducer noise levels. With the log scaling, null-results, where an effect cannot be discernedsurface tension, bursting film thicknesses and the decay of the liquid velocity field around t
pressure at burst has not been used as a measurable ‘effect’. Instead,and as a close equivalent to the apparatus displacements recordedduring the laboratory experiments, the magnitude of the net verticalforce transient during burst (as measured over the entire computa-tional domain) has been used. This results from the liquid motions(encompassing shear forces acting on the vertical walls of the conduitand pressure forces at the base of the domain) and not from any gasmotions. Unlike bubble pressure, which increasingly rapidlyapproaches atmospheric pressure as the slug approaches the surface,force transients peak during the burst process. Therefore, maximumforce is straightforward to obtain and, because it is due to bulk liquidmotions and unlikely to be significantly affected by uncertainties in therelatively thin liquid layer associated with the burst, it is thoughtto be the most reliable ‘burst effect’ parameter to use for the CFDsimulations.
In Fig. 4, the experimental data and the simulations are combinedby calculating Pslim⁎ values for the abscissa coordinates. In order tocompare the ‘effect magnitude’ data from the different systems, linearscaling of the different ordinate ‘effect’ values (the force, pressure anddisplacement magnitudes) was also carried out, as detailed in thekey. This scaling is required because, although Pslim⁎ can be used forquantitative analysis of variations within one type of burst vigourmeasurement of any one system, it cannot scale effect magnitudes
tails of the property used as ‘burst effect’ for each data type. For laboratory experiments,s) recorded at slug burst are used. Except where mentioned, experiments were carriedUG20 (0.28 Pa s) are smaller and have been scaled for comparison bymultiplying by 2, as, the burst effect used is the transient net vertical force calculated on the entire domain.ll burst effects, scatter increases in the data due to the effect magnitudes being similar toabove the noise level, cannot be plotted. In fact, null effects are not anticipated becausehe slug will always produce some effect (James et al., 2004).
86 M.R. James et al. / Journal of Volcanology and Geothermal Research 180 (2009) 81–88
between different proxies for burst vigour (for example, betweenseismic and infrasonic amplitudes) or between systems that differ byparameters not included in Pslim⁎ (e.g. viscosity). In Fig. 4, the dataobtained by varying either initial slug size (e.g. Fig. 3b) or the surfacepressure (e.g. Fig. 3a) demonstrate the same trends, with similargradients that change at Pslim⁎ values of approximately 1 to 3.
5. Discussion
Fig. 4 demonstrates that parameterisation by Pslim⁎ allows theregion of relatively passive degassing behaviour (equivalent to‘puffing’ at Stromboli) to be distinguished from that in whichsignificant overpressures have to exist during slug burst. This couldrepresent a change in the measured ‘burst behaviour’within one flowregime; i.e., within the slug flow regime, two regions of different‘eruption’ behaviour may be identified. The theoretical transitionoccurs at Pslim⁎ =1, and experimental and numerical simulationsconfirm that a gradual change in the relationship betweenmeasurableburst effects and Pslim⁎ occurs between Pslim⁎ values of 1 and 3 (Fig. 4),with bursts at smaller Pslim⁎ values producing very weak effects.
At Stromboli, good evidence for the presence of two regimes hasbeen shown within continuously collected infrasonic data. For datacollected between January 2003 and December 2005 (which recorded3.7×106 infrasonic events), Marchetti et al. (2006) demonstrate thepresence of two trends when the number of infrasonic transients isplotted against the infrasonic pressure, and they associate these with‘gas bursting’ events (that probably represent the previously identi-fied ‘puffing’ regime (Ripepe and Gordeev, 1999; Harris and Ripepe,2007)) and ‘explosion’ events. Marchetti et al. (2006) interpret thetrend change as indicating that gas bursting and explosions are not theresult of a single scale-invariant process. However, given the gradientchange shown in our data (Fig. 4), we suggest that these regimes couldbe considered as regions of different controlling parameters withinwhat is basically the same process: the bursting of gas bubblesascending in the slug flow regime.
In our experiments, for relatively small effects, measurement noiserepresents a significant scatter when plotted on the log scale of Fig. 4.However, the scatter lies below the line representative of measuredeffects for Pslim⁎ N3 (the grey dashed line in Fig. 4), suggesting that effectmagnitudes are being governed by processes different from thosecontrolling the more energetic bursts. For low-energy bursts, it isprobable that viscous and surface tension film drainage phenomenaare important (e.g. Debrégeas et al., 1998), whereas for Pslim⁎ N3, due tothe expansion velocities involved, bursts will be controlled by inertiaand the dynamic fluid flowaround the slug nose (James et al., 2008). Inorder to estimate the approximate maximum size of gas slugs thatcould be considered to burst within a low-energy ‘puffing’ regime(Ripepe and Gordeev, 1999; Harris and Ripepe, 2007), Eq. (10) can beused with Pslim⁎ values between 1 and 3 (and noting that Pslim=Pslim⁎ Psurf), representing the range for the maximum as suggested byboth theory and experiment. For a conduit radius of 1.5 m, andassuming a falling liquid film thickness of ~0.5 m (i.e. rc-rs=0.5 m,(Batchelor, 1967; Vergniolle, 1998; James et al., 2008)), which isappropriate for a magma viscosity of 1 kPa s, this gives maximum slug
Table 1Transitional gas masses between energetic and non-energetic bubble bursts for different pl
Earth V
Subaerial Mid-ocean ridge⁎ P
Acceleration due to gravity, (m s−2) 9.81 9.81 8Atmospheric pressure, (Pa) 105 3×107 9Transitional gas mass (kg) 4 2×105 3
For all calculations, rc=1.5 m, rs=1.0 m (appropriate to a magma viscosity of ~1 kPa s) and ρassuming pure water vapour at 1300 K.⁎This scenario is represented by terrestrial conditions but with an elevated ‘atmospheric’ p†These values are for illustrative purposes only, actual pressures would be smaller.
lengths of ~7−21m,with associatedwater vapourmasses of ~4−33kg.These values are in line with the values of 10−40 kg estimated byHarris and Ripepe (2007) from thermal data on gas puffing events atStromboli (which may be upper bounds because atmospheric airentrained into the puffs was included in the analyses (Harris andRipepe, 2007)). Thus we regard our approach to be fully consistentwith these fieldmeasurements. However, we note that, through A', theresults are sensitive to the magma viscosity, which is poorlyconstrained at Stromboli, with estimated values ranging from 300 to15 kPa s (Vergniolle et al., 1996; Metrich et al., 2001).
For Pslim⁎ N~3, Fig. 4 demonstrates that there is a strong relationshipbetween Pslim⁎ and the measurable effects used here. The dashed greyline indicates a slope of 1, i.e. a linear relationship between (effectmagnitude/Psurf) and Pslim⁎ . With Pslim⁎ dependent on only a fewvariables (Eq. (13)), most of whichwill usually be relatively constant atany one volcano, this parameterisation thus provides a directrelationship between geophysical data and variations in fundamentalphysical parameters such as the effective initial slug length andpressure (L0 and P0). Furthermore, with the product L0P0 beingproportional to slug mass, and noting that on Earth atmosphericpressure is reasonably constant, then for energetic bursts, assumingno significant changes in magma properties (i.e. maintaining ρ and A'constant), measurable effects are proportional to the square root of thegas mass involved.
This result, from our straightforward pressure parameterisation, isin line with results frommore complex dynamic models of slug ascent(e.g. Fig. 6 of James et al., 2008) and, although Pslim⁎ does not providean absolute scaling (i.e. gasmass as a direct function of specific seismicor infrasonic amplitudes), it could be used to help identify changes indegassing rates from such indirect geophysical data. Note that ourmodelling (both experimental and theoretical) was effectively madeat or near the source so, for field data, standard procedures to accountfor measurement path effects would be required. Additional con-straints to help quantify absolute gas masses could include thermaldata from plumes (Harris and Ripepe, 2007) or independent estimatesof P0 obtained from rapid FTIR monitoring of the erupted gases (Allardet al., 2005; Oppenheimer et al., 2006; Burton et al., 2007). Such gasmeasurements provide insight into the depth at which the gas ceasedto maintain chemical equilibrium with the melt, which should be areasonable indicator for the start of slug ascent.
It is important to reiterate that, although our theoretical approachis based on slug gas pressure, the results appear to be applicable toother geophysical characteristics of burst events. This is illustrated bythe fact that force and displacement data also fall on the trend in Fig. 4.CFD modelling (James et al., 2008) shows that viscous shear forcesexerted by the liquid on the conduit wall play a fundamental role inthe overall vertical force exerted during slug ascent and burst. Thus, inthis case, and assumedly because slug pressure and liquid velocitiesare inextricably linked, the pressure-related parameterization isproviding a good proxy for the viscous and inertial processes directlyresponsible for the measured forces.
Finally, the inclusion of both gravity and surface pressure withinPslim⁎ allows its application to a variety of planetary environments(Table 1). This illustrates that the subaerial terrestrial case, for which
anetary scenarios
enus Mars Io Moon
lains Uplands Plains Volcanoes
.87 8.87 3.72 8.87 1.80 1.63×106 4×106 600 60 1† 1†
×104 7×103 10−4 10−6 10−9 10−9
=2600 kg m−3. The transitional point is given by Pslim⁎ =1 and gas mass was calculated
ressure, equivalent to a water depth of ~2500 m.
87M.R. James et al. / Journal of Volcanology and Geothermal Research 180 (2009) 81–88
the transition between relatively low and high burst vigour occurs onthe kilogram-scale of gas mass, is relatively isolated from other end-member scenarios. The need for significant gas accumulation, con-sistent with Table 1, in a magma reservoir to allow explosive eruptiveactivity in the submarine environment on Earth has been explored byHead and Wilson (2003). On Venus, the high atmospheric pressuressuppress vigorous gas expansion unless extremely large gas massesare involved, here requiring extreme pre-eruption concentration ofgas into the upper part of a magma reservoir (Head andWilson,1992).In contrast, for low atmospheric pressure bodies such as Mars, andnear-zero pressures such as on Io and our Moon, ‘passive’ degassing issuggested to occur at only very small gas masses. However, thesemagnitudes would not be sufficient to form slugs, invalidating theinitial assumptions in the analysis. Consequently, no ‘passive’ regimewould exist and all activity would be deemed to be explosive. There isstrong evidence that most if not all of the current eruptions on Ioinvolve an explosive component at the vent, even when the mostobvious product of the eruption is a lava flow (Davies, 2007). Thesituation is less clear-cut for the ancient eruptions that took place onthe Moon; some can be documented to have been violently explosive(Head et al., 2002), involving carbon monoxide produced in apressure-dependent chemical reduction reaction (Fogel and Ruther-ford, 1995) as their volatile phase, but in other cases the fluid nature ofthe erupted lavas led to drowning of all potential evidence of near-vent explosive deposits. In the case of Mars, the possible identificationof explosively-generated particles by one of the Mars ExplorationRover vehicles (Squyres et al., 2007) has instigated a new awareness ofthe likely importance of explosive activity there (Wilson and Head,2007).
6. Summary
A canonical model of an ascending gas slug in equilibriumwith thelocal static pressure is presented and used to distinguish regions ofparameter space for which a slug could reach the magma surface witha gas pressure close to that of atmospheric, from parameter spaceregions inwhich it must be significantly dynamically overpressured atburst. This approach provides a dimensionless parameter, Pslim⁎ , thatcan be used to relate the variability in burst vigour of the system tochanges in the gas masses involved. Plotting the magnitude of various‘burst effects’ (obtained from laboratory experiments and CFDmodels) against Pslim⁎ illustrates the two regimes with a gradientchange (Fig. 4). For parameters appropriate to Stromboli, gas slugsreleased during ‘gas puffing’ style degassing, associated with muchsmaller ‘burst effects’ than Strombolian eruptions, are predicted tohave masses less than of order 10 kg. For more vigorous Strombolianeruptions, geophysical metrics of slug burst are expected to scale withthe square root of the gas mass involved.
Acknowledgements
MRJ was supported by the Royal Society and SC by LancasterUniversity. Two anonymous referees are thanked for their commentson an early version of the manuscript which helped clarify the text.M. Ichihara and E. Llewellin provided further valuable reviews. We areparticularly indebted to E. Llewellin who described the derivationfrom a small perturbation of slug length used here, which resulted in asignificant simplification of our original approach.
References
Allard, P., Burton, M., Mure, F., 2005. Spectroscopic evidence for a lava fountain drivenby previously accumulated magmatic gas. Nature 433 (7024), 407–410.
Auger, E., D'Auria, L., Martini, M., Chouet, B., Dawson, P., 2006. Real-timemonitoring andmassive inversion of source parameters of very long period seismic signals: anapplication to Stromboli Volcano, Italy. Geophysical Research Letters 33 (4), L04301.
Batchelor, G.K., 1967. An introduction to fluid dynamics. Cambridge University Press,Cambridge. 615 pp.
Blackburn, E.A., Wilson, L., Sparks, R.S.J., 1976. Mechanics and dynamics of Strombolianactivity. Journal of the Geological Society London 132, 429–440.
Burton, M., Allard, P., Mure, F., La Spina, A., 2007. Magmatic gas composition reveals thesource depth of slug-driven Strombolian explosive activity. Science 317 (5835),227–230.
Chouet, B., Dawson, P., Ohminato, T., Martini, M., Saccorotti, G., Giudicepietro, F., DeLuca, G., Milana, G., Scarpa, R., 2003. Source mechanisms of explosions at StromboliVolcano, Italy, determined from moment-tensor inversions of very-long-perioddata. Journal of Geophysical Research-Solid Earth 108 (B1), 2019.
Chouet, B., Hamisevicz, N., McGetchin, T.R., 1974. Photoballistics of volcanic jet activityat Stromboli, Italy. Journal of Geophysical Research 79 (32), 4961–4976.
Davies, A.G., 2007. Volcanism on Io: A comparison with Earth. Cambridge UniversityPress. 355 pp.
Debrégeas, G., de Gennes, P.G., Brochard-Wyart, F., 1998. The life and death of “bare”viscous bubbles. Science 279 (5357), 1704–1707.
Dubosclard, G., Donnadieu, F., Allard, P., Cordesses, R., Hervier, C., Coltelli, M., Privitera,E., Kornprobst, J., 2004. Doppler radar sounding of volcanic eruption dynamics atMount Etna. Bulletin of Volcanology 66 (5), 443–456.
Fogel, R.A., Rutherford, M.J., 1995. Magmatic volatiles in primitive lunar glasses. 1. FTIRand EPMA analyses of Apollo 15 green and yellow glasses and revision of thevolatile-assisted fire-fountain theory. Geochimica et Cosmochimica Acta 59 (1),201–215.
Gerst, A.,Hort,M., Kyle, P.R. andVöge,M., inpress. 4Dvelocityof Strombolian eruptions andman-made explosions derived from multiple Doppler radar instruments. Journal ofVolcanology and Geothermal Research. doi:10.1016/j.jvolgeores.2008.05.022.
Harris, A., Ripepe, M., 2007. Temperature and dynamics of degassing at Stromboli.Journal of Geophysical Research-Solid Earth 112 (B3).
Head, J.W., Wilson, L., 1992. Magma reservoirs and neutral buoyancy zones on Venus —implications for the formation and evolution of volcanic landforms. Journal ofGeophysical Research-Planets 97 (E3), 3877–3903.
Head, J.W., Wilson, L., 2003. Deep submarine pyroclastic eruptions: theory andpredicted landforms and deposits. Journal of Volcanology and Geothermal Research121 (3-4), 155–193.
Head, J.W., Wilson, L., Weitz, C.M., 2002. Dark ring in southwestern Orientale Basin:Origin as a single pyroclastic eruption. Journal of Geophysical Research-Planets 107(E1), 5001. doi:10.1029/2000JE001438.
James, M.R., Lane, S.J., Chouet, B., Gilbert, J.S., 2004. Pressure changes associated withthe ascent and bursting of gas slugs in liquid-filled vertical and inclined conduits.Journal of Volcanology and Geothermal Research 129 (1-3), 61–82.
James, M.R., Lane, S.J., Chouet, B.A., 2006. Gas slug ascent through changes in conduitdiameter: laboratory insights into a volcano-seismic source process in low-viscositymagmas. Journal of Geophysical Research-Solid Earth 111 (B5), B05201.doi:10.1029/2005JB003718.
James, M.R., Lane, S.J., Corder, S.B., 2008. Modelling the rapid near-surface expansion ofgas slugs in low viscosity magmas. In: Lane, S.J., Gilbert, J.S. (Eds.), Fluid motion involcanic conduits: A source of seismic and acoustic signals. Geological Society,London, pp. 147–167. Special Publications.
Marchetti, E., Ripepe, M., Ulivieri, G., 2006. Degassing dynamics at Stromboli Volcano:Insights from infrasonic activity, International Workshop: Physics of FluidOscillations in Volcanic Systems. Lancaster University. U.K. http://www.es.lancs.ac.uk/seismicflow/.
Metrich, N., Bertagnini, A., Landi, P., Rosi, M., 2001. Crystallization driven bydecompression and water loss at Stromboli volcano (Aeolian Islands, Italy). Journalof Petrology 42 (8), 1471–1490.
Oppenheimer, C., Bani, P., Calkins, J.A., Burton, M.R., Sawyer, G.M., 2006. Rapid FTIRsensing of volcanic gases released by Strombolian explosions at Yasur volcano,Vanuatu. Applied Physics. B, Lasers and Optics 85 (2-3), 453–460.
Parfitt, E.A., 2004. A discussion of the mechanisms of explosive basaltic eruptions.Journal of Volcanology and Geothermal Research 134 (1-2), 77–107.
Parfitt, E.A., Wilson, L., 1995. Explosive volcanic-eruptions 9. The transition betweenHawaiian-style lava fountaining and Strombolian explosive activity. GeophysicalJournal International 121 (1), 226–232.
Proussevitch, A.A., Sahagian, D.L., Anderson, A.T., 1993. Dynamics of diffusive bubble-growth in magmas — isothermal case. Journal of Geophysical Research-Solid Earth98 (B12), 22283–22307.
Ripepe, M., Gordeev, E., 1999. Gas bubble dynamics model for shallow volcanic tremorat Stromboli. Journal of Geophysical Research-Solid Earth 104 (B5), 10639–10654.
Ripepe, M., Marchetti, E., 2002. Array tracking of infrasonic sources at Strombolivolcano. Geophysical Research Letters 29 (22), 2076.
Ripepe, M., Harris, A.J.L., Carniel, R., 2002. Thermal, seismic and infrasonic evidences ofvariable degassing rates at Stromboli volcano. Journal of Volcanology andGeothermal Research 118 (3-4), 285–297.
Ripepe, M., Harris, A.J.L., Marchetti, E., 2005. Coupled thermal oscillations in explosiveactivity at different craters of Stromboli volcano. Geophysical Research Letters 32 (17),L17302.
Seyfried, R., Freundt, A., 2000. Experiments on conduit flow and eruption behavior ofbasaltic volcanic eruptions. Journal of Geophysical Research-Solid Earth 105 (B10),23727–23740.
Sparks, R.S.J., 1978. The dynamics of bubble formation and growth in magmas: a reviewand analysis. Journal of Volcanology and Geothermal Research 3, 1–37.
Squyres, S.W., Aharonson, O., Clark, B.C., Cohen, B.A., Crumpler, L., de Souza, P.A.,Farrand, W.H., Gellert, R., Grant, J., Grotzinger, J.P., Haldemann, A.F.C., Johnson, J.R.,Klingelhofer, G., Lewis, K.W., Li, R., McCoy, T., McEwen, A.S., McSween, H.Y., Ming,D.W., Moore, J.M., Morris, R.V., Parker, T.J., Rice, J.W., Ruff, S., Schmidt, M., Schroder,
88 M.R. James et al. / Journal of Volcanology and Geothermal Research 180 (2009) 81–88
C., Soderblom, L.A., Yen, A., 2007. Pyroclastic activity at home plate in Gusev Crater,Mars. Science 316 (5825), 738–742.
Urbanski, N.A., Voge, M., Seyfried, R., Rupke, L., Petersen, T., Hanebuth, T., Hort, M., 2002.Fifteen days of continuous activity survey at Stromboli volcano, Italy, in lateSeptember 2000: doppler radar, seismicity, infrared, soil humidity, and mapping ofthe crater region. International Journal of Earth Sciences 91 (4), 712–721.
Vergniolle, S., 1998. Modelling two-phase flow in a volcano., 13th Australasian FluidMechanics Conference, Aristoc. Offset, Monash Univ., Melbourne, Australia.
Vergniolle, S., Brandeis, G., Mareschal, J.C., 1996. Strombolian explosions.2.Eruptiondynamics determined from acoustic measurements. Journal of GeophysicalResearch-Solid Earth 101 (B9), 20449–20466.
Wilson, L., Head, J.W., 1981. Ascent and eruption of basaltic magma on the Earth andMoon. Journal of Geophysical Research 86, 2971–3001.
Wilson, L., Head, J.W., 2007. Explosive volcanic eruptions on Mars: tephra andaccretionary lapilli formation, dispersal and recognition in the geologic record.Journal of Volcanology and Geothermal Research 163 (1-4), 83–97.
