permeability controls on expansion and size distributions of...

Permeability controls on expansion and size distributionsof pyroclasts

A. C. Rust1 and K. V. Cashman2

Received 3 May 2011; revised 9 August 2011; accepted 12 August 2011; published 10 November 2011.

[1] We synthesize field and experimental data to evaluate relationships between thetextures and sizes of pyroclasts and the processes that shape them, with emphasis on therole of permeability. In (mafic) scoria, the important competition that determinespreserved vesicularity is between gas escape and magma expansion by bubble growth;post!fragmentation expansion occurs rapidly until the permeability increases substantially.In (silicic) pumice, the competition is between gas escape and fragmentation by bubbleoverpressure; sufficiently permeable regions allow gas escape although high viscosityhinders further expansion. Thus the preserved vesicularity of both pumice and scoria iscontrolled by the permeability threshold, the vesicularity at which there is an abrupt increasein permeability over a small increase in vesicularity, which appears to be !70–80%. Highpermeability thresholds may also explain the high fine ash content of silicic Plinianeruptions. At the local scale, magma ruptures because of stresses in viscous melt aroundexpanding isolated bubbles. Local control is illustrated by the correspondence between thesize distributions of the ash and of bubbles in individual pumice clasts of the 1980Mount St. Helens Plinian eruption: the medians and modes for grain and bubble sizes areof order tens of microns, and fractal dimensions are similar (3.1–3.2 for grains; 3.4 forbubbles). Fractal dimensions for total grain size distributions and bubble size distributionsin pumice from other silicic eruptions are similar (3.0–3.2, 2.9–3.9, respectively) and largerthan generated by crushing and grinding rocks. This suggests that fragmentation efficiencydepends on the balance between rates of magma decompression (overpressurization)and gas escape, which explains relationships between ash content and eruption rate. Insummary, the vesicularity distribution of pyroclasts places important constraints on thepermeability threshold of expanding magma, whereas the whole deposit grain sizedistribution of pyroclastic deposits places critical limits on the permeability structure of themagma at the point of fragmentation.

Citation: Rust, A. C., and K. V. Cashman (2011), Permeability controls on expansion and size distributions of pyroclasts,J. Geophys. Res., 116, B11202, doi:10.1029/2011JB008494.

1. Introduction

[2] An ongoing challenge in volcanology is to relateconditions of magma ascent to eruption style using infor-mation preserved in pyroclastic deposits. This approachassumes, with justification from theoretical and experimentalstudies, that factors such as magma viscosity, ascent rateand fragmentation mechanism affect measurable propertiesof pyroclasts, such as shape, vesicularity, permeability,bubble and crystal size distributions, as well as character-istics of the entire deposit (particularly the total grain sizedistribution). However, the physical characteristics of pyro-clastic deposits are typically considered in isolation fromdetailed studies of individual pyroclasts. Moreover, as detailed

studies of pyroclasts generally focus on cm!scale clasts, thereis the potential for a sample bias toward properties thatpreserve larger clasts (and therefore limit fragmentation); thispotential bias is of particular concern in deposits where mostof the magma foam was obliterated to ash.[3] Verhoogen [1951] first suggested a correlation between

the kinetics of bubble formation and the proportion of magmathat is fragmented to ash;Walker [1973, 1981] extended thisconcept by linking ash formation (fragmentation efficiency)to eruptive style. However, a theoretical basis for this rela-tionship is not well established. Dynamic fragmentationmodels typically predict only a threshold criterion for frag-mentation, using either a critical vesicularity [Sparks, 1978;Gardner et al., 1996;Kaminski and Jaupart, 1997] or a criticalshear rate beyond which the liquid magma crosses the glasstransition and behaves as a brittle solid [Dingwell, 1996;Papale, 1999], and not the resulting grain size distribution.In contrast, experiments that constrain relationships betweengrain size characteristics and fragmentation overpressure[e.g., Spieler et al., 2004; Kueppers et al., 2006] consider

1School of Earth Sciences, University of Bristol, Bristol, UK.2Department of Geological Sciences, University of Oregon, Eugene,

Oregon, USA.

Copyright 2011 by the American Geophysical Union.0148!0227/11/2011JB008494

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116, B11202, doi:10.1029/2011JB008494, 2011

B11202 1 of 17

http://dx.doi.org/10.1029/2011JB008494

initial vesicularity but not the dynamics of decompression!related vesiculation.[4] Here we examine magmatic fragmentation by relating

the physical characteristics of individual clasts (vesicularity,permeability, and vesicle size distributions) to the total grainsize distributions from which those individual clasts arederived. We focus particularly on magma permeability andthe relationship of permeability development to pyroclastpreservation and to the timing and efficiency of fragmen-tation. Specifically, we propose that the development of apermeability threshold, that is, a threshold vesicularity atwhich there is marked increase in permeability, plays acritical role both in limiting bubble expansion and in pre-venting fragmentation of magma that is too viscous toexpand. To explore these ideas, we first review data onmagma percolation thresholds as constrained by percolationtheory simulations, laboratory decompression experiments,and measurements of natural samples. We consider thereasons for apparent discrepancies in these data and thenexamine the role played by permeability in determining

(1) the vesicularity of pyroclasts and (2) the total grain sizedistribution (TGSD) of pyroclastic deposits.

2. Pyroclast Textures and Eruption Conditions:A Review

[5] The past decade has seen a tremendous increase indetailed measurements of the physical properties of pyr-oclasts and pyroclastic deposits. In Figure 1, we have com-piled mean (or modal, depending on available data) meltvesicularity (volume of vesicles/volume of vesicles and melt;i.e., bulk vesicularity corrected for phenocryst and matrixcrystal content) data for pyroclasts of relatively steady erup-tions that range in composition from basalt to rhyolite(see Table 1 for data sources). This compilation does notinclude vulcanian eruptions, which typically erupt clasts of awide range of vesicularities due to extensive pre!eruptiondegassing of relatively stagnant magma. We rank the data byreported mass eruption rate, although this provides the peak,not average, eruption condition. This compilation is strikingbecause, although the data do show a minimum vesicularityof !65–70%, there is no apparent relationship betweenvesicularity and either mass eruption rate (MER) or bulkcomposition. We note that our data differ from the compi-lation of Gardner et al. [1996], where mafic pyroclasts havelower vesicularities than silicic pyroclasts. The differencebetween these two assessments lies in the vesicularitymeasurements of mafic pyroclasts. H2O!rich mafic magmasoften have abundant microphenocrysts [e.g., Sable et al.,2006; Johnson et al., 2008; Erlund et al., 2010], whichGardner et al. [1996] did not include when correctingvesicularity for crystal content. From Figure 1 we concludethat, despite some evidence that clast vesicularity may becorrelated with MER in individual eruptions [e.g., Houghtonet al., 2010], this relationship does not appear to be gener-alizable and, in most circumstances, it is not possible todeduce even the order of magnitude of eruption intensityfrom clast vesicularity.[6] In contrast, there is a striking difference in the bubble

populations that create that vesicularity as shown with pho-tomicrographs in Figure 2 and bubble number density datain Figure 3 (see Table 1 for data sources). Silicic pumiceclasts tend to have fairly similar textures comprised of alarge number of very small bubbles (e.g., Figures 2a and 2b),regardless of eruption volume or intensity (Figure 3a). Vesic-ulation of silicic magma thus appears relatively insensitiveto eruption intensity and magnitude, perhaps because of thehigh supersaturations required for bubble nucleation in thesesystems [e.g., Mangan and Sisson, 2000]. In contrast, maficpyroclasts (e.g., Figure 2c) have bubble number densitiesthat increase with increasing eruption intensity [e.g., Mastin,1997; Sable et al., 2006] (Figure 3b). The most straight-forward interpretation of this trend is that vesiculation inmafic systems occurs under near!equilibrium conditions,such that the rate of bubble nucleation is controlled by therate of magma ascent (effective supersaturation), althoughdetailed interpretations of bubble number densities shouldalso take into account bubble coalescence. The exceptions tothe overall trend are the relatively high bubble number densitiesthat characterizes low energy episodic activity at Stromboli,Italy and Villarica, Chile [e.g., Lautze and Houghton, 2007;

Figure 1. Compilation of mean pyroclast melt vesicularity(volume vesicles/volume vesicles+glass) as a function ofmass eruption rate (MER). Samples labeled “Rhyolite” haverhyolitic glass but bulk compositions (including crystals)from dacite to rhyolite. The melt vesicularities are calculatedfrom reported bulk vesicularities (including the crystalvolumes) and crystallinity. In most cases, both phenocrystand groundmass crystallinity were given for individual sam-ples; where not reported individually, melt vesicularitieswere calculated from average crystallinities. Where densityor vesicularity distributions were provided rather than indi-vidual sample values, a single value was used representingthe mode of the vesicularity. Similarly, where MER esti-mates were given for each sampled deposit layer, the indi-vidual MERs are plotted; otherwise the peak MER for theentire deposit was used. The four basalt samples with meltvesicularity >90% are from the 122 BC Plinian eruptionof Etna for which the reported groundmass crystallinitiesare very high [Sable et al., 2006]. A possible explanationfor these outliers is post!fragmentation groundmass crys-tallization. Data sources and eruption dates are listed inTable 1.

RUST AND CASHMAN: MAGMA EXPANSION AND FRAGMENTATION B11202B11202

2 of 17

Figure 2. (a) Secondary!electron and (b–d) backscattered!electron photomicrographs of pyroclasts.Figures 2a and 2b show low!crystallinity pumice from the 7700 b.p. climactic Plinian eruption of MountMazama (Crater Lake), United States [Klug et al., 2002]. Figure 2c shows low crystallinity basaltic clastfrom the ca. 1800 AD Kaupulehu eruption, Hawaii [Kauahikaua et al., 2002]. Figure 2d shows crystal!rich basaltic pyroclast from a 1974 vulcanian eruptions of Fuego Volcano, Guatemala [Rose et al., 1978].

Table 1. Vesicularity and Bubble Number Density Data Sources for Figures 1 and 3

Eruption/Deposit Data Sources Figure 1 Label Figure 3 Label

Etna, Jan.–June 2000 Polacci et al. [2006] basalt b EtnaEtna, 122 BC Sable et al. [2006] basalt b EtnaMasaya, 60 ka Fontana Lapilli Costantini et al. [2009] Costantini et al. [2010] basalt b FontanaKilauea 1984–1986 Pu’u ’O’o fountains Mangan and Cashman [1996] basalt b HawaiiKilauea, 1790 Keanak!ko’i Ash Mastin [1997] Mastin et al. [2004] basalt b HawaiiKilauea 1991–1993 lava flows Cashman et al. [1994] ! b HawaiiKilauea, 1959 Kilauea Iki fountains Stovall [2009] Stovall et al. [2010] ! b HawaiiStromboli, 2002 Lautze and Houghton [2007] ! b StromboliVillarica, Nov. 2004 Gurioli et al. [2008] ! b VillaricaVesuvius, 79 EU1, EU2, EU3t Gurioli et al. [2005] trachyte a VesuviusPhlegraean Fields, 36 ka; fall of Campanian

Ignimbrite eruptionRosi et al. [1999] Polacci et al. [2003] trachyte a Vesuvius

Somma Vesuvius, 18000–19000 BP;Pomici de Base

Bertagnini et al. [1998] trachyte !

Askja, 1875 units B and D Carey et al. [2009] Sparks et al. [1981] rhyolite a AskjaMount Mazama, 7700 BP; climactic fall Klug et al. [2002] ! a MazamaSoufriere Hills, Montserrat 1997, Vulcanian Giachetti et al. [2010] ! a MontserratMount St. Helens, 1980 Cashman and McConnell [2005]; Klug and Cashman [1994] rhyolite a Mt. St. HelensPinatubo, 1991 climactic fallout Polacci et al. [2001] rhyolite a PinatuboTaupo, 1.8 ka Hatepe & Taupo Plinians,

Early & Taupo IgnimbritesHoughton et al. [2010] rhyolite a Taupo

Novarupta, 1912 episodes II and III,units C,D,F,G

Adams et al. [2006] rhyolite !

Mount St. Helens, 1800 AD, 1480 AD,2700 BP, 3500 PB

Gardner et al. [1996] rhyolite !

Bishop Tuff eruption, 770 ka, Long Valley Roberge, unpublished data (see Table S1 of the auxiliary material) rhyolite !Newberry, 1300 BP fall deposit Rust and Cashman [2007] rhyolite !Santorini, Minoan age Phase I (Plinian) Wilson and Houghton [1990] rhyolite !


3 of 17

Gurioli et al., 2008]. This discrepancy can be explained bythe tendency of these crystal!rich and near!static magmas totrap small bubbles within dense crystal networks [Belienet al., 2010].[7] Additionally, there is a pronounced difference in the

total grain size distributions (TGSDs) of the deposits in whichthese pyroclasts are found. Figure 4 shows a compilation ofTGSDs from fall deposits that represent a range of eruptivestyles and intensities (plinian, subplinian, vulcanian, violentStrombolian, Strombolian, and Hawaiian) (Table 2). Regard-less of eruption style and deposit type, sorting during transportand settling means that the TGSD of pyroclasts generated byan eruption cannot be assessed from the grain size distri-bution of any single sample, and so each TGSD is based oncompilation of grain size data from numerous locations [e.g.,Carey and Sigurdsson, 1982; Bonadonna and Houghton,

2005]. The data are shown in Figure 4 as cumulativecurves, a representation of TGSD data that highlights thewide range in both median grain size (d50 marked by thehorizontal line at 50%) and the shape of the grain size dis-tribution (a steeper slope reflects a smaller standard devia-tion in grain size). High intensity silicic (Plinian) depositshave TGSDs with median grain sizes <100 mm and standarddeviations of ! 1 log unit [(d16 " d84)/2]. In contrast, lowintensity mafic eruptions (Strombolian and Hawaiian) areunimodal with large median grain sizes (>0.1 m). Interest-ingly, eruptions that are intermediate in both intensity andcomposition also have TGSDs that are intermediate inmediangrain size and distribution shape.[8] To a first approximation, then, the contrasting char-

acters of Figures 1, 3, and 4 suggest that pyroclast vesicu-larity is independent of eruption style (excluding vulcanianeruptions) and fragmentation conditions, that bubble numberdensity is sensitive to eruption intensity (magma ascentrate) for low crystallinity mafic magmas only (i.e., viscosity isimportant), and that the total grain size distribution (frag-mentation efficiency) is strongly controlled by eruptionconditions. Of these, pyroclast vesicularity has long beenviewed as providing insight into the state of the magma at thetime of fragmentation [e.g., Verhoogen, 1951; Sparks, 1978;Houghton and Wilson, 1989], and thus the lack of correlationbetween vesicularity, eruption intensity, and TGSD is per-haps the most puzzling.[9] As magma ascends (decompresses), bubbles of dom-

inantly H2O and/or CO2 nucleate and grow at a rate deter-mined by the kinetics of vesiculation and the speed ofdecompression. Bubble formation and growth cause themagma to expand and accelerate; these two processes,expansion and acceleration, form the core of fragmentationtheories. As noted above, there have been two proposedcriteria for fragmentation: a critical vesicularity and a criticalstrain rate. The vesicularity criterion for fragmentation sug-gests that magma fragments when a critical vesicularity isattained; in silicic Plinian eruptions the vesicularity criterionhas variously be placed at 60% [Kaminski and Jaupart,1997], 64% [Gardner et al., 1996] and 75–83% [Sparks,1978] based on the observed range of vesicularity in pre-served pumice clasts. The lower values derive from theminimum preserved vesicularities; this minimum limitassumes that higher preserved vesicularities record post!fragmentation expansion prior to quenching. The strain ratecriterion for fragmentation derives from experimental studiesthat show a threshold in deformation properties (from ductileto brittle) at high strain rates [Webb and Dingwell, 1990].Both fragmentation criteria require ascending magma toexpand until the point of fragmentation, which requires thatthe volume of gas in the component bubbles increases bydecompression and volatile exsolution faster than it escapesby permeable flow through pathways of interconnectedbubbles [Klug and Cashman, 1996]. A permeability crite-rion for fragmentation further suggests that (1) the size andabundance of pumice clasts in a deposit should reflect thepermeability structure of the bulk mixture at the time offragmentation; (2) the size and abundance of ash in a depositshould reflect the bubble size distribution of isolated (non!permeable) bubbles; and therefore (3) the vesicularity ofpreserved clasts provides important information about the

Figure 3. Bubble number densities plotted as a function ofmass eruption rate for (a) silicic and (b) mafic eruptions.Note the dramatic increase in bubble number density withincreasing eruption intensity for most of the mafic samplesuites. Exceptions include Stromboli and Villarica, whicherupt crystal!rich pyroclasts from near!static magma col-umns under conditions of persistent degassing and eruptiveactivity; the high number density of small bubbles in thesesamples probably represents trapping of small bubbleswithin the crystal mush [e.g., Belien et al., 2010]. Datasources and eruption dates are listed in Table 1.


4 of 17

development of permeable pathways within vesiculatingmagma. We explore these relationships below.

3. Permeability Thresholds and Vesiculation

[10] Much like a hole in a balloon can make it impossibleto further inflate, the development of permeability will dras-tically slow magma expansion despite continued decom-pression and volatile exsolution. We hypothesize that magmais preserved as (silicic) pumice or (mafic) scoria when it istoo permeable to either continue expanding or fragment. Acorollary to this hypothesis is that the vesicularity (!) ofmost pumice and scoria clasts will be similar to the thresholdvesicularity at which there is an abrupt increase in perme-ability. The location of the permeability threshold, knownas the percolation threshold in percolation theory (which hasthe additional constraint that the permeability is zero belowthe threshold vesicularity), has been variably placed at! ! 30%(from numerical simulations [e.g., Garboczi et al., 1995]),

!60% (from measurements on obsidian flows [Eichelbergeret al., 1986]), !70% (from numerical simulations of sys-tems with power law bubble size distributions [Gaonac’het al., 2003]), and 60–80% (from decompression experi-ments [Namiki and Manga, 2008; Takeuchi et al., 2008,2009]). Below we review and unify these seemingly contra-dictory data and consider their relevance to permeabilitydevelopment during magma decompression.

3.1. Percolation Theory[11] Percolation theory predicts that vesiculating magma

will be impermeable until the vesicularity, !, reaches athreshold value !c (the percolation threshold), at whichpoint the bubbles form an interconnected network [e.g.,Blower, 2001]. When ! is slightly greater than !c, perme-ability (k) increases rapidly with increasing ! following apower law relationship:

k / !! !c" #b; "1#

Figure 4. Total grain size distributions (TGSDs) for pyroclastic deposits produced by eruptions thatrange in composition from basaltic to rhyolitic, and in style, grouped as Hawaiian!Strombolian, Vulcanian!Violent Strombolian, and Plinian!subPlinian. Intersections of TGSD with the dashed line indicate mediangrain sizes by mass. Data sources and eruption dates are listed in Table 2.

Table 2. Data Sources Total Grain Size Distributions of Fall Deposits Plotted in Figures 4 and 10

Eruption Data Source Figure 4 Label D Value Figure 10

Hw!StKilauea, 1959 Kilauea Iki Parfitt [1998] Kilauea !Stromboli 1988–1991 Ripepe et al. [1993] Stromboli !

Vul!VSCerro Negro, 1971 Rose et al. [1973] Cerro Negro !Fuego, 1974 fall only Rose et al. [2008] Fuego !Heimaey, 1973 Self et al. [1974] Heimaey !Izu!Oshima, 1986, TB!2, climactic Mannen [2006] Izu!Oshima !Ruapehu, June 1996 Bonadonna and Houghton [2005] Ruapehu !

Pl!subPlEl Chichon 1982 Rose and Durant [2009] El Chichon 1a 3.1

El Chichon 3a 3.2Mt. St. Helens, May 18, 1980 Plinianb Carey and Sigurdsson [1982] MSH 3.2Mt. Spurr, Aug. 1992 Durant and Rose [2009] Spurr!Aug 3.0Mt. Spurr, Sept. 1993 Spurr!Sept 3.2

aHere 1 and 3 refer to labels in Rose and Durant [2009] related to weighting of material outside the 2 mm isopach.bThe same data are also shown in Figure 9 along with data from same eruption from Rose and Durant [2009] with D value of 3.1.


5 of 17

where b depends on pore geometry [e.g., Wright et al.,2009]. Standard percolation theory shows that if uniformspheres are placed randomly in a much larger sample vol-ume and the spheres are allowed to overlap (connect), then acluster of touching and overlapping spheres will span thesample volume at ! = !c = 28.5 vol% [e.g., Sahimi, 1994].For this reason some studies have assumed that magmabecomes permeable at ! ! 30% [e.g., Candela, 1991;Polacci et al., 2008], and others fit permeability data frompyroclasts to a power law k (!) relationship with !c ! 30%[e.g., Mueller et al., 2005; Saar and Manga, 1999]. How-ever, numerical simulations also show that the percolationthreshold may be reduced by bubble deformation into non!aligned prolate or oblate ellipsoids [Garboczi et al., 1995],or when solid phases (crystals) occupy space that is notavailable to bubbles [Walsh and Saar, 2008]; alternatively,power law bubble size distributions can substantially increase!c [Gaonac’h et al., 2003].

3.2. Permeability in Experiments[12] Recent decompression experiments, using both rhy-

olite melt [Takeuchi et al., 2005, 2008, 2009] and bubble!bearing corn syrup with viscosity comparable to basalt[Namiki and Manga, 2008], provide important insightsinto permeability development in vesiculating magma. Anadvantage of laboratory experiments is that the compositionand decompression history of the magma or analog material

are known and controlled. Experimental results indicatepermeability thresholds that exceed 65% (Figure 5). Thesehigh permeability thresholds can be explained using kineticarguments when rhyolite is decompressed at extremely rapidrates (>4 MPa/s) [e.g., Takeuchi et al., 2005, 2008], becausehigh supersaturations and resulting bursts of homogeneousbubble nucleation are expected to limit time for coalescenceand delay permeability development [Mangan and Sisson,2000, 2005]. However, differences in decompression ratealone cannot account for the high permeability thresholdobserved in laboratory decompression experiments. For exam-ple, Takeuchi et al. [2009] decompressed hydrous rhyolite(4.7 wt% H2O) from 180 MPa to 5–30 MPa at constant ratesof 0.002, 0.005 and 0.05 MPa/s, which overlap withdecompression rates estimated for effusive eruptions. In theseexperiments, all samples with ! # 78% were almost imper-meable (k < 10"15 m2); additionally, although more coales-cence was observed at slower decompression rates, thebubble coalescence was local and thus increased the aver-age bubble size and heterogeneity of bubble size distribu-tions without generating span!wise vesicle connectivity.Then k increased by two orders of magnitude as the porosityincreased from 78 to 80% (Figure 5b). Concurrent with theabrupt permeability increase was an abrupt increase in theconnected porosity (as opposed to isolated, unconnectedbubbles) measured by water impregnation, which indicatesthat full connectivity of the gas phase was achieved.

Figure 5. Permeability (k) versus vesicularity (!) for natural samples (circles and squares), and experi-ments (triangles; white triangles represent experiments where the permeability was less than the detectionlimit and so actual permeabilities plotted are maxima as indicated by downward arrows). (a) Permeabilityof mafic vesicular pyroclasts as a function of bulk vesicularity (volume vesicles / total volume of vesicles,glass and crystals): Stromboli scoria [Mueller et al., 2005] and Stromboli “biondo” [Mueller et al., 2008]and scoria from cones of central Oregon [Saar and Manga, 1999]. Black curves are fits to the data withequation (1) for three percolation thresholds. Triangles mark permeability data from decompressionexperiments of syrup [Namiki and Manga, 2008]. (b) Permeability of rhyolite dome and pyroclast samplesfrom Inyo Domes (squares [Eichelberger et al., 1986]), and pumice of the climactic air fall of the 6845 BPeruption of Mt. Mazama (circles [Klug and Cashman, 1996]). Triangles are data from decompressionexperiments with rhyolite melt [Takeuchi et al., 2009]. All curves in this figure are equation (1) with b = 2,except for the 3 black curves in Figure 5a where b was a fit parameter (minimizing squared residuals in k)with b = 2.8, 4.7, 9.7 for !c = 40, 30, 0 with R2 = 0.89, 0.91, 0.91, respectively.


6 of 17

3.3. Permeability of Natural Samples[13] The permeability threshold of magma depends not

only on the geometry of the bubble populations, but alsoon the rates of film thinning and rupture required to formapertures between adjacent bubbles. To characterize per-meability thresholds, we examine the limited porosity andpermeability data available for suites of natural samples thatspan the threshold interval.[14] Permeability development in mafic magma is illus-

trated by permeability data for basaltic scoria from Stromboli,Italy [Mueller et al., 2005, 2008] and cinder cone eruptionsof central Oregon [Saar and Manga, 1999]. These data showthat permeability increases by over two orders of magnitudeas the porosity increases from about 45 to 70% (Figure 5a).Although a power law relation with !c ! 30% fits these data[Saar and Manga, 1999; Mueller et al., 2005], !c is notuniquely constrained and we conclude that the only robustconstraint on permeability threshold provided by these datais that !c < 46%, the porosity of the least!vesicular sample.Similarly, permeability measurements on a suite of breadcrustbomb samples fromGuagua Pichincha volcano [Wright et al.,2007] constrain the permeability threshold to <40% for slowexpansion of this dacite magma. An important observationabout these basalt scoria and dacite bomb samples, however,is that all except the most vesicular sample from Stromboliare highly crystalline (>25%) and thus the permeabilitythreshold would be higher if vesicularity were calculated for acrystal!free liquid [Melnik and Sparks, 2002;Walsh and Saar,2008]. That vesicle growth was affected by smaller ground-mass crystals is illustrated by the complex, multilobate bubbleshapes that are commonly seen in scoria (e.g., Figure 2d).[15] There are considerably more data on the permeability

of silicic than mafic samples. However, Plinian pumiceclasts typically have high vesicularities (Figure 1) and per-meability data tend to cluster at k ! 10"12±1 m2 (Figure 5b). Aunique sample set of Obsidian Dome rhyolite was obtainedby drilling; these samples, which cover a wide range invesicularity, define a permeability threshold of about 60%vesicularity [Eichelberger et al., 1986] (Figure 5b). Unfor-tunately, however, this threshold is defined by only a fewsamples and there is no accompanying textural information.Lower permeability thresholds for natural sample suites oflow!crystallinity silicic pyroclasts are observed in data setswith samples that have textures indicative of partial bubblecollapse [e.g.,Rust andCashman, 2004;Mueller et al., 2005],where k (!) is likely hysteretic with respect to expansionversus collapse [Rust and Cashman, 2004; Michaut et al.,2009].[16] The paucity of natural data available to constrain the

permeability threshold for primary vesiculation of magma isnot surprising given the very small vesicularity interval overwhich the rapid increase in permeability occurs. The corollaryof this observation, however, is that this rapid permeabilityincrease will drastically limit bubble expansion beyond thisthreshold. In fact, samples of crystal!poor silicic pumicerarely have porosities <70% [e.g., Klug and Cashman, 1996;Mueller et al., 2005; Wright et al., 2009] (Figure 5b), whichsuggests that the permeability threshold for these samplesmust also be $70%. This interpretation is supported by thehigh permeabilities (log k = "12 ± 0.5m2) of all silicic pumicesamples (crystal!poor and crystal!rich) from (sub)Plinian fall

deposits, which indicate that the permeability threshold hadbeen exceeded. Moreover, studies that quantify samplecrystallinity, in addition to vesicularity, show a similarporosity threshold for the melt phase of crystal!rich pumicesamples [e.g., Bouvet de Maisonneuve et al., 2009].

3.4. Combining Observations, Experimentsand Theory[17] The discrepancy between permeability thresholds

from percolation theory (!c ! 30% for randomly placedmonodisperse spheres), the high permeability thresholdsobserved in decompression experiments (!c > 70%), and thehigh porosity of crystal!poor pumice samples (! > 70%)suggests that standard percolation theory does not ade-quately model key aspects of magma vesiculation. In par-ticular, it does not take into account either the bulk volumeincrease during vesiculation or the time required to thin thefilms that separate individual bubbles. In percolation theory,spheres (or ellipsoids) are randomly placed in a volume, withthe analog bubbles effectively replacing melt (and portionsof other bubbles if the bubbles overlap). This approachseems reasonable for modeling crystallization where crystalshave similar density to the melt, melt volume is replacedby crystal volume, nucleation is often heterogeneous, andtouching crystals can adhere or otherwise impede motion. Incontrast, bubble formation within vesiculatingmagma changesthe volume (and density) of magma as each growing bubblepushes surrounding melt and bubbles away from its center.Furthermore, gas percolation through a foam requires notjust that spanning networks of bubbles (almost) touch butalso that the neighboring bubbles begin to coalesce andcreate apertures in the melt films between bubbles. There hasbeen some attempt to account for bubble coalescence innumerical simulations; for example, Blower [2001] requiresthat simulated bubbles overlap by some prescribed degreebefore they are considered connected for gas flow. However,the extent of bubble overlap required to account for actualcoalescence delay is unclear, and the assumption of sta-tionary bubble positions is still unrealistic. In short, the!30% threshold obtained from standard percolation theoryprovides only the minimum allowable porosity at whichconnected bubble networks may (theoretically) form duringvesiculation.[18] There are numerous examples showing that bubble!

bearing fluids can reach ! > 30% without becoming per-meable. Natural and synthesized closed!cell (non!permeable)foams abound in materials where liquid films are stabilizedeither by surfactants (e.g., soap foams and beer head) or byhigh fluid viscosities (e.g., popcorn, insulating foam,expanded graphite); these foams commonly reach porositiesin excess of 50%, and may reach porosities >90% withoutspan!wise pore connectivity [e.g., Celzard and Marêché,2002]. Therefore it is not extraordinary that vesiculatingmagma will also have percolation thresholds that are bothvariable and much greater than 30%, particularly whenmagmatic foams may contain both bubbles and crystals withdifferent shapes, sizes and size distributions.[19] One example of a discrepancy between experiments,

theory and natural samples is provided by scoria clasts withmoderate vesicularities (! $ 46%) that have well!connectedpores and are permeable (k ! 10"13 m2), yet decompressionexperiments of syrup of comparable viscosity [Namiki and


7 of 17

Manga, 2008] suggest a permeability threshold at about! = 70% (Figure 5). Here the high (typically 25–30%)microphenocryst content of most mafic scoria [e.g., Sableet al., 2006; Erlund et al., 2010; Johnson et al., 2008]probably lowers the apparent porosity of the permeabilitythreshold because connected bubble pathways can form onlywithin the melt [Melnik and Sparks, 2002; Walsh and Saar,2008]. In fact, pyroclasts produced by eruptions of crystal!poor basaltic melts of Hawaii typically have high porosities(>70%; Figure 1).[20] Another control on permeability thresholds in natural

systems is the shearing that occurs within volcanic conduits[Okumura et al., 2009]. Shear deforms bubbles [Rust andManga, 2002] and anisotropic bubble shapes can reducetheoretical percolation thresholds [e.g., Garboczi et al.,1995]. Of greater significance, however, is shear!inducedbubble coalescence. Torsional deformation experiments onbubble!bearing rhyolite melt [Okumura et al., 2006, 2008,2009] demonstrate that simple shear can enhance bubblecoalescence for vesicularity as low as 20%, can reduce per-meability thresholds to 30–40%, and can increase perme-ability by several orders of magnitude at ! = 60%. Evidencefor pervasive shear in natural systems includes descriptionsof pumice samples as ‘frustratingly’ heterogeneous andubiquitous microscopic shear zones (Figure 6) within pumicethat is macroscopically isotropic [e.g., Klug and Cashman,1996; Klug et al., 2002; Wright and Weinberg, 2009]. Alsocommon are tube pumice samples that show both extensivebubble elongation and elevated permeabilities along elon-gation directions [Wright et al., 2006, 2009] that has beeninterpreted as evidence for shear along conduit margins.However, the general dominance of macroscopically isotropicpumice over tube pumice in pyroclastic deposits (particu-larly in fallout deposits) suggests that most magma is notsubstantially affected by conduit margin shear, perhapsbecause the shear!thinning effect of bubbles on magma

rheology concentrates strain into narrow marginal zones[e.g., Llewellin and Manga, 2005].

4. Pumice Vesicularity Records the PermeabilityThreshold

[21] In the discussion presented above, we show that thepermeability threshold is not a single number, but insteadmay be a function of a number of variables, includingexpansion rate, melt viscosity, shear stresses, and the pres-ence of other phases. Here we argue that, under manyconditions, the vesicularity of pyroclasts provides a goodapproximation of the permeability threshold. We start byreturning to the limited range of pyroclast vesicularityillustrated by Figure 1.[22] One way to view these data is to assume that pyroclast

vesicularity is determined by the time available for post!fragmentation expansion prior to quenching [e.g., Thomaset al., 1994; Gardner et al., 1996; Kaminski and Jaupart,1997]. In the absence of permeable gas escape, post!fragmentation pyroclast expansion can be substantial for meltviscosity less than about 105–106 Pa s. For higher viscosities,expansion slows and is effectively prevented for viscositygreater than 109 Pa s. In fact, Thomas et al. [1994] concludedthat rhyolite pumice from Bishop, Taupo and Minoan Plinianeruptions could expand from ! = 60% to the typical pumicevesicularities of 78% in less than a second after fragmenta-tion. From this calculation they inferred rapid clast coolingby entrained air to prevent pumice expansion beyond therange of vesicularities observed in the deposits. However,their assumption that the magma is impermeable means thatcalculated magma expansion times are minima. Moreover,although subsequent evidence from pumice oxidation [Taitet al., 1998] indicates that fragmented clasts remain at hightemperatures for much longer than the expansion times cal-culated by Thomas et al. [1994], these calculations demon-strate that expansion of basaltic magma, or rhyolite magmawith substantial water still dissolved in the melt (!1.5 wt%)[e.g.,Hort andGardner, 2000;Blundy andCashman, 2005], istoo rapid to be limited by cooling if the magma is effectivelyimpermeable. From this we conclude that impermeable frag-ments generated during magmatic Plinian eruptions couldexpand to at least the vesicularity of the permeability thresholdbefore quenching.[23] To summarize, the rarity of low!crystallinity pumice

with ! < 70% in the deposits of relatively steady siliciceruptions, combined with evidence of permeability thresh-olds greater than 70% in laboratory decompression experi-ments, indicate both a percolation threshold near 70% and arapid increase in permeability at the percolation thresholdthat limits expansion beyond this vesicularity. We thereforeconclude that pumice vesicularity provides an approximatemeasure of the permeability (and percolation) threshold invesiculating magma, and, as a corollary, attainment of thepermeability threshold must be approximately coincidentwith fragmentation under most eruption conditions.

5. Beyond the Permeability Threshold

[24] The analysis presented above provides a generalexplanation for the limited range of pyroclast vesicularitiesobserved in eruptive deposits but does not explain the

Figure 6. Scanning electron microscope image of a pumiceclast from Monte Pilato (Italy) that illustrates local variabil-ity in bubble shape and size possibly caused by small!scaledifferences in bubble expansion and gas escape properties.Vertical dimension is 97 microns.


8 of 17

variations in vesicularity and pumice textures that have beenabundantly described in the literature. To address more subtleaspects of clast degassing, we need to examine the evolutionof pumice textures beyond the permeability threshold. Ourdiscussion revolves around concepts of local versus bulkpermeability. Magma permeability is measured as a bulkproperty averaged over a representative volume that quanti-fies the ease of gas percolation through the pore space.However, gas will flow through some pathways more easilythan others. Additionally, some bubbles will remain isolatedafter sample!spanning networks have formed. These localvariations in permeability can explain both increases anddecreases in vesicularity after the permeability threshold hasbeen reached.[25] Expansion can continue after the permeability

threshold is reached either when there are isolated bubbles,including new bubbles nucleating and growing in meltpockets between larger bubbles [e.g.,Mangan and Cashman,1996; Polacci et al., 2009; Lautze and Houghton, 2007], orif the rate of gas expansion in response to decompressionand exsolution exceeds the rate of gas escape by permeableflow. To illustrate the latter effect, we compare the charac-teristic timescale for gas escape by permeable flow, R

2 "gas

DPk , tothe timescale for expansion, "melt

DP , where R is the radius of theclast, DP/R is the pressure gradient driving gas out of thesample, and mgas and mmelt are the gas and melt viscosities.Gas escape will dominate expansion for

kR2 >

"gas

"melt; "2#

as illustrated in Figure 7 for mgas = 10"5 Pa s and a range ofmelt viscosities. In Figure 7, each diagonal line separatesconditions where gas escape dominates from conditions

where bubble growth dominates for a particular melt vis-cosity, based on equation (2). Although equation (2) providesonly order of magnitude estimates, it illustrates the impor-tance of both melt viscosity and magma permeability indetermining clast vesicularity. It also suggests that themaximum vesicularity of clasts depends not only on k(!) butalso on both the melt viscosity and the size of the fragmentsgenerated by the initial breaking apart of the magma.[26] The role of melt viscosity is illustrated by comparison

of pyroclast textures with predictions of equation (2). Typicalbasaltic eruptions are dominated by clasts of centimeters orlarger in size (Figure 4); Figure 7 shows that expansiondominates for mmelt = 100 Pa s and permeability of k =10"12 m2, consistent with textural evidence for expansionof low crystallinity basaltic clasts in Hawaiian fountains[Mangan and Cashman, 1996; Stovall et al., 2010]. However,Figure 7 predicts that gas escape will dominate over expan-sion even for the highest permeability scoria clasts (Figure 5a:k = 5.65 ! 10"11 m2; mmelt = 100 Pa s) when the clast radiusis less than a few centimeters (i.e., typical scoria clast sizes;c.f. Figure 4). In contrast, the viscosity of rhyolite, even with2 wt% dissolved water (e.g., mmelt = 107 Pa s), is highenough that gas escape always dominates over expansion(up to clasts a meter in radius) assuming the permeability oftypical pumice (k ! 10"12 m2). This calculation supports theargument made by Klug and Cashman [1996] that theimportant competition in permeable silicic magma is notbetween gas escape and expansion but rather between gasescape and overpressure, which can induce fragmentation.An important exception are bombs for which the larger sizefavors expansion over escape and also allows the center toremain hot for longer than lapilli [e.g., Tait et al., 1998]. Inthis case, post!fragmentation expansion is accompanied byextensive bubble coalescence, which is evidenced by largeinterior cavities, smooth aperture boundaries and remnantfilaments of former melt films [Klug et al., 2002]. Pyroclaststhat have experienced late!stage coalescence have poly-modal vesicle volume distributions and high (85–90%)vesicularities [e.g., Whitham and Sparks, 1986; Klug et al.,2002; Stovall et al., 2010].[27] Just as an increase in bulk permeability slows bulk

expansion, local variations in gas connectivity, where gascan flow through some gas pathways more readily thanothers, may produce different pressures and expansion ratesof bubbles within vesiculating magma. Additionally, well!connected bubble pathways may actually collapse if theyhave low internal pressures relative to adjacent bubbledomains, even when the bulk magma is expanding. Evi-dence for this process may lie in localized bands of elongate(and in some cases cuspate) bubbles that are common insilicic pumice clasts [e.g., Klug et al., 2002; Gurioli et al.,2005; Houghton et al., 2010]. Another example may bethat of Wright and Weinberg [2009], who describe bands ofsmall elongate bubbles that are interspersed around domainsof subequant bubbles. Although they interpret these texturesto represent shear localization, with bubble breakup gener-ating smaller bubble sizes, their descriptions of “variedshear band orientation and shear sense that do not definea sample!wide kinematic pattern” suggest an alternativeexplanation involving differential bubble expansion: perhapsthe complex variations in shear sense and band orientationsformed when poorly connected bubble clusters expanded,

Figure 7. Conditions for gas escape by permeably flowthrough magma versus expansion of bubble by viscousdeformation of surrounding melt (see text for details). Eachstraight diagonal line indicates the conditions for which thegas escape timescale and the viscous expansion timescaleare equal for a given melt viscosity. Gas escape is favoredby high magma permeability, short length scale for gas flow,and high melt (or melt+crystals) viscosity.


9 of 17

thereby driving shearing and bubble deformation in bandsbetween these expanding clusters. This alternative expla-nation is based on the observation that bubble growthrequires deformation of the melt around each bubble (andbulk volumetric strain). For this reason, a round bubbleshould not necessarily be equated with a low strain rate if themagma is expanding. Importantly, generation of such het-erogeneous textures would require very complex heteroge-nous flow [e.g., Wright and Weinberg, 2009] if there wereno differential bubble expansion.

6. Permeability and Fragmentation

[28] Bubble expansion increases magma vesicularity,accelerates magma ascent, and stresses the melt aroundbubbles, all of which may contribute to magma fragmenta-tion, whereby bubbly magma is transformed into a gas phasewith dispersed liquid or solid particles. Therefore gas escapedue to magma permeability, which reduces the rate ofbubble expansion, should affect the conditions required formagma fragmentation.[29] Experiments, theoretical calculations and the observed

angularity of pumice clasts all suggest that fragmentation insilicic Plinian eruptions occurs by brittle processes, wherethe melt breaks when either a critical bubble overpressure orstrain rate is exceeded. Fragmentation by overpressurerequires a decompression timescale that is shorter than thetimescale for bubble expansion by viscous deformationof surrounding melt, whereas fragmentation by strain rateoccurs if the reciprocal of the strain rate is shorter than therelaxation time of the melt. Theoretical and numericalstudies of bubble overpressure generally consider pressurein individual isolated (not connected) bubbles [Barclay et al.,1995; Sparks et al., 1994; Lensky et al., 2004; Navon et al.,1998], whereas models of strain rate!induced fragmenta-tion consider the strain rate on scales much larger thanindividual bubbles [Papale, 1999; Gonnermann and Manga,2003]. However, if the strain rates on the bubble scaledominate, then critical stress and critical strain rate criteriaare not fundamentally different: larger stresses generatelarger strain rates in the melt around expanding bubbles.Also important are the potential role of viscoelasticity,which complicates predicted relationships between stressand strain rate [Ichihara, 2008; Ittai et al., 2010], and thedrastic increase in rhyolite melt viscosity with progressivewater exsolution at !1 wt % H2O [Hess and Dingwell, 1996;Sparks et al., 1994], which will both impede bubble expan-sion and generate large vertical pressure gradients (by con-servation of mass; the flow does not slow down as theviscosity increases with height).[30] If the magma is locally permeable at the time of

fragmentation, high rates of gas loss by permeable flow willlimit magma expansion (vesicularity; e.g., Figure 1); thiswill lower both resulting strain rates in the surrounding meltand overpressure within individual bubbles. Thus regardlessof whether the most appropriate fragmentation criterion iscritical vesicularity, strain rate or bubble overpressure, highmagma permeability will impede fragmentation. The effectof permeability on fragmentation can be seen in unloadingexperiments [Mueller et al., 2005, 2008], where brittle frag-mentation of high permeability samples requires largerpressure drops than for low permeability samples.

[31] To further explore the importance of magma perme-ability in fragmentation of high viscosity magma, we com-pare a timescale for gas escape to a decompression timescalethat is the minimum needed to generate overpressure forfragmentation. In particular, we compare the timescale fordegassing by permeable flow for a pressure difference (DP)of 1 MPa over a length scale L, to the timescale to generatean overpressure of 1 MPa in isolated bubbles by externaldecompression without bubble expansion (i.e., the end!member case of non!permeable and extremely viscousmagma). The latter timescale is

DPdP=dt

$ 1 MPadP=dt

;

where dP/dt is the decompression rate. For simplicity weconsider only percolation of a “gas” (often actually asupercritical fluid) with the density and viscosity of H2O at800°C at two pressures: 25 MPa (rgas = 53 kg/m3 and mgas =4.2 ! 10"5 Pa s) and 0.1 MPa (rgas = 0.20 kg/m3 and mgas =4.0 ! 10"5 Pa s). Note that during decompression, the gasviscosity remains nearly constant but the density decreases;this means that resistance to open!system degassing willdiminish with ascent, even for constant magma permeabil-ity, if gas inertia is significant.[32] Our analysis shows that gas escape is most effective

for shorter length scales (smaller clasts), lower decompres-sion rates and greater magma permeabilities (Figure 8a).When the gas flow follows Darcy’s law (the gas viscositydominates resistance to percolation), the gas escape time-scale is

L2 "gas

DPk;

we assume mgas = 4 ! 10"5 Pa s. Under these conditions, atypical pumice permeability of k = 2 ! 10"12 m2 and dP/dt =1 MPa/s, yields comparable overpressure and gas escapetime scales for L = 0.2 m; length scales are reduced foreither lower permeabilities or higher decompression rates,and can be used to define limiting permeabilities for ashformation.[33] However, if decompression is sufficiently fast, gas

flow rates may be high enough that inertia may also beimportant in resisting flow through the magma pore space[Rust and Cashman, 2004]. Here

DPL

$"gas

k# %

$gask2

#2; "3#

where DP/L is the gas pressure gradient, v is the volumetricflow rate of gas per unit cross!sectional area of magma, k isthe viscous (Darcian) permeability and k2 is the inertialpermeability. Viscous and inertial effects on gas flow arecombined in Figure 8b using a gas escape time of L/v, wherev is determined from solving equation 3 with k and k2 valuesfrom measurements on 2.54 ! 2.54 cm cores of naturalpumice [Rust and Cashman, 2004] (k = 2 ! 10"13 to 3 !10"12 m2 and k2 = 1 ! 10"9 to 2 ! 10"7 m). We know thatthese pumice clasts evaded complete fragmentation to ashduring eruption; Figure 8b shows that the clast size and


10 of 17

permeability range is consistent with gas escape rates suf-ficient to prevent overpressure!driven fragmentation for alength scale of several centimeters or less.

[34] To summarize, Figures 8a and 8b show that smallerpyroclasts are expected for faster decompression ratesand lower permeabilities [e.g., Klug and Cashman, 1996;Mueller et al., 2005, 2008]. This analysis thus provides ageneral framework for relating the fragmentation efficiencyto the physical state (vesicularity and permeability) of themagma at the time of fragmentation. Note however, that atthe scale of individual bubbles, the larger!scale permeabilityof the magma is not a good measure of the local resistanceto gas escape.

7. Permeability Controls on Total Grain SizeDistributions

[35] The analysis above leads us to hypothesize that silicicmagma preserved as pumice was too permeable to fragmentand that primary ash forms from bubble overpressure in rel-atively low permeability magma. This hypothesis is consis-tent with the observation that eruptions of different intensity(and bulk composition) have similar pyroclast vesicularity(Figure 1) and permeability (Figure 5) but very differentfragmentation efficiencies (Figure 4). A corollary of thishypothesis is that the length scales of both isolated bubblesand connected bubble pathways within the magma at thetime of fragmentation should constrain the total grain sizedistribution (TGSD) of the resulting deposit. In particular,we hypothesize that the size of ash, which are bubble!wallshards, will be of the same order of magnitude as the bub-bles in the magma, extending the suggestion of Sparks andWilson [1976] that ash particles finer than a few microns arerare because smaller bubbles cannot form.[36] To test this corollary we compare the physical char-

acteristics of the total grain size distribution of the pyro-clastic deposit produced by the May 18, 1980 eruption ofMount St. Helens with the vesicle characteristics of indi-vidual pumice clasts from the deposit. The deposit isexceptionally well characterized, particularly in the smallergrain sizes, because of premature ash fallout by particleaggregation [Carey and Sigurdsson, 1982]. To quantify thegrain size characteristics in a way that can be compareddirectly with the bubble population preserved in pyroclasts,we must convert mass distributions to particle number. Wedo this for the Mount St. Helens deposit using TGSD esti-mates (in mass %) from both Carey and Sigurdsson [1982]and Rose and Durant [2009]. We use component analysis[Carey and Sigurdsson, 1982] to estimate the bulk densitiesappropriate for each size class (see Table S2 of the auxiliarymaterial), from which we calculate the number of grains inthe size class.1 Number!based cumulative distributions showpower law behavior, with power law exponents (fractaldimensions, D) of 3.2 [Carey and Sigurdsson, 1982] and 3.1[Rose and Durant, 2009, Figure 9]. These high power lawexponents are similar to results from other studies [e.g.,Kaminski and Jaupart, 1998] and indicate that the smallparticle sizes comprise the bulk of the deposit, consistent withthe small (mass!based) median grain size of the Mount St.Helens TGSD (!15 mm; Figure 4). However, there is anoutstanding question of whether these particles are the result ofprimary or secondary fragmentation. Kaminski and Jaupart

Figure 8. Conditions for generation of gas overpressure of1 MPa in isolated bubbles in a viscous magma (too viscousfor significant bubble growth on the timescale of decom-pression) versus gas pressure release by gas escape throughpermeable magma during magma decompression (see textfor details). Gas escape is favored by a short length scale(L) and slow decompression rate and high magma perme-ability. Each (a) straight or (b) slightly curved diagonal lineindicates the conditions for which the characteristic time-scale for generating a gas overpressure of 1 MPa equalsthe characteristic timescale for gas escape with pressuregradient 1 MPa /L for a particular magma permeability.In Figure 8a only the gas viscosity (4 ! 10"5 Pa s) is includedin the resistance to gas escape and each line is for a differentmagma Darcian permeability (k). In Figure 8b both gas iner-tia and viscosity are taken into account and each line corre-sponds to the calculation using the pair of Darcian andinertial permeabilities from one of the seven pumice samplesmeasured by Rust and Cashman [2004]. The gas viscosityand density employed for the gas escape timescale calcula-tions correspond to H2O at 800°C at 25 MPa (black) or0.1 MPa (gray). Note that the density of H2O at 800°C at0.1 MPa is sufficiently low that its inertia can be neglectedbut at 25 MPa inertia dominates the gas escape time scale.

1Auxiliary materials are available in the HTML. doi:10.1029/2011JB008494.


11 of 17

[1998] argued that the abundant fine particles must reflectsecondary fragmentation, because the fractal dimension issubstantially higher than that expect for brittle fragmentation[e.g., Turcotte, 1986; Kueppers et al., 2006]. However, thisinterpretation does not take into account the potential roleof expansion of individual bubbles in the fragmentationprocess.[37] To examine fragmentation under conditions of

magma expansion, we compare the TGSDs above to bubblesize distributions (BSDs) of selected pumice samples fromthe May 18, 1980, Mount St. Helens eruption [Klug andCashman, 1994]. As noted by Rose and Durant [2009],the TGSD and pumice BSD have approximately the samemodes: the same size of particles and bubbles dominatesvolumetrically. We find that the medians and modes of thedeposit grains (both mass! and volume!based) and thepumice bubbles are all within the range of 10–90 microns.When plotted as cumulative bubble number density, theBSDs are remarkably similar to the TGSD, and show powerlaw size distributions with D values of 3.4, which is similarto, although somewhat higher than, those of the TGSDs(Figure 9). The similarity in medians and modes, and thehigh D values of both the TGSDs and BSDs compared tofragmentation theory for crushing and experiments decom-pressing static volcanic samples [Turcotte, 1986; Kuepperset al., 2006], suggest that fine particles in the deposit aregenetically related to the bubble population, thereby sup-porting the hypothesis that the initial bubble populationexerted a primary control on the fragmentation process.

Furthermore, the observation that the power law exponentfor the bubbles exceeds that of the particles is consistentwith the concept that the larger pyroclastic fragments areformed by connected bubble networks rather than individualisolated bubbles (i.e. the largest clasts were not formed bythe bursting of individual single large bubbles). Addition-ally, although bubbles preserved within pumice might havebeen modified by post!fragmentation expansion or coales-cence, these processes would decrease, rather than increase,D values. Importantly, the reference volumes for TGSD(total volume of pyroclasts) and BSD (volume of vesicule!free pyroclasts) differ and therefore are expected to deviatewith increasing grain size (i.e., when grains contain multiplebubbles).[38] We are not aware of other silicic deposits where

both the TGSD and BSDs are as well constrained as forMt. St. Helens 1980. However, we can convert the TGSDdata from Figure 4 into number density data in the same waythat we converted the Mount St. Helens data (densities arelisted in Table S2 of the auxiliary material). Figure 10 showsthat these other deposits also have power law distributionswith exponents (D values) of 3.0–3.2 (Table 2). Most datasets are slightly concave!down, which could be real or couldreflect difficulties in fully representing the smallest (and to alesser extent the largest) clasts of an eruption, as discussedby Kaminski and Jaupart [1998]. Available BSD data forsilicic pumice clasts also show power law bubble size dis-tributions with D > 3 (with one exception from a crystal!richVulcanian pumice deposit that has D $ 2.9; Table 3). Wetherefore conclude that the high measured D values for bothTGSDs and BSDs is not an accident, but instead supports adirect relationship between the kinetics of vesiculation(which controls the BSD), the conditions under which thepermeability threshold is reached (which controls the scaleand geometry of developing pore pathways), and the con-ditions and products of fragmentation (and resulting TGSD).

Figure 9. Comparison of total grain size distribution(TGSD) for Mount St. Helens, May 18, 1980 and the bubblesize distribution (BSD) for two pumice clasts (one white andone gray) from the same deposit. The data are fit with N =Cd"D, where C and D are constants. The D values are shownin the figure legend; for clarity only the line for the fit to theblack squares is shown. For BSD N is the number of bubblesper m3 of vesicle!free magma with diameter larger than d.For TGSD,N is the number of clasts with diameter (calculatedfrom a sphere of the same volume as the clast) larger than dper m3 of pyroclasts (including vesicles). Data from Roseand Durant [2009] (R&D), Carey and Sigurdsson [1982](C&S), and Klug and Cashman [1994]; data sources are alsolisted in Tables 2 and 3. Densities of clasts, based on Careyand Sigurdsson [1982], are listed in Table S2 of the auxiliarymaterial.

Figure 10. Power law TGSDs for Plinian and subPlinianeruptions shown in Figure 4. Note the similarity in powerlaw slope (D = 3.1–3.2) for these distributions (Table 2).The dotted line is the same power law fit to the Mt. St.Helens data with D = 3.2 as shown in Figure 9. Data sourcesare listed in Table 2; clast densities are in Table S2 of theauxiliary material.


12 of 17

[39] To place these data in a different context, we contrastthe TGSDs and BSDs of silicic deposits with those ofHawaiian fire fountains. Mass!based TGSDs have beenestimated for the pyroclast deposit produced by the com-bined 17 phases of the 1959 eruption of Kilauea Iki [Parfitt,1998; Richter et al., 1970] (Figure 4). For simplicity, weconvert these mass data to clast numbers assuming a con-stant density of 2000 kg/m3. The resulting cumulative par-ticle number distribution only shows a power law behaviorfor clasts smaller than 0.032 m, and the D value of 1.1 ismuch lower than for silicic deposits (Figure 11a). Instead, itis well described by two different log linear distributions(Figure 11b). When deformed, low viscosity melt tends to

flow rather than break brittley into pieces; for this reason,fragmentation in Hawaiian fire fountains is most likelycaused by instabilities within the accelerating fluid [e.g.,Mangan and Cashman, 1996; Shimozuru, 1994]. Thisfragmentation mechanism has been demonstrated experi-mentally [Kaminski and Jaupart, 1998; Zimanowski et al.,1997], where fluid instabilities also generate up to three dif-ferent populations of particles with log linear distributions.[40] Inspection of bubbles preserved in basaltic fountain

pyroclasts from Phase 1 of the 1959Kilauea Iki [Stovall et al.,2010] and the 1984–1986 Pu’u ’O’o eruptions [Mangan andCashman, 1996] shows (1) that bubble size distributionsfor the two eruptions differ substantially, (2) that neitherresembles the Kilauea Iki TGSD, and (3) that neither followthe simple power law distribution seen in silicic pumice(Figures 11c and 11d) [see also Shimano and Nakada, 2006;Mattsson, 2010]. First, the difference in bubble size dis-tributions is consistent with bubble number density datashown in Figure 3. The K"lauea Iki eruption involved highermass eruption rates (as recorded by both high fire fountainheights and high bubble number densities, [e.g., Stovall et al.,2010] than the Puu Oo episodes sampled by Mangan andCashman [1996]. As illustrated above, more rapid ascentof basaltic magma generates more small bubbles (highernucleation rate), consistent with the numerous small bubbles

Table 3. D Values for Power Law Fits to Cumulative Bubble SizeDistributions in Silicic Pumice

Eruption Data Source D Value

Novarupta, 1912 Adams et al. [2006] 3.9Soufriere Hills 1997 Vulcanian

crystal!rich pumiceGiachetti et al. [2010] 2.9–3.4

Mount. St. Helens May 18 1980Plinian

Klug and Cashman [1994] 3.4

Mt Mazama, 7700 BP Crater Lake Klug et al. [2002] 3.3Vesuvius, 79 Shea et al. [2010] 3.4–3.6

Figure 11. (a and b) Cumulative grain size data for the 1959 fountaining eruption of Kilauea Iki, Hawaiirecalculated from Parfitt [1998]. For clasts smaller than 0.032 m, N and d are well related by a power law(gray line in Figure 11a) or a lognormal (gray dashed line in Figure 11b) fit but larger clasts are better!fitwith a different lognormal equation (black dashed line in Figure 11b) (c and d) Cumulative bubbles sizedata for scoria samples from the 1984–1996 Pu’u O’o fountains [Mangan and Cashman, 1996] and therinds and interiors of three clasts from Phase 1 of the 1959 Kakauea Iki eruption [Stovall et al., 2010].


13 of 17

preserved in the K"lauea Iki samples (Figures 11c and 11d,K"lauea Iki rind). Protracted expansion of larger clastswithin the high fountains also allowed extensive expansionof K"lauea Iki clast interiors (Figures 11c and 11d, K"laueaIki interior). Second, the very different scales of the basaltpyroclasts and their bubbles (compare axes of Figures 11aand 11c) supports the interpretation that fragmentation ofmagma in Hawaiian fire fountains is controlled by instabil-ities in the accelerating liquid jets rather than interaction ofexpanding bubbles [e.g., Mangan and Cashman, 1996].Finally, the absence of simple power law distributions in boththe BSDs and the TGSDs is a direct reflection of the complexbubble nucleation, expansion, and coalescence history (i.e.,point one) and the fragmentation process (e.g., point two)[Kaminski and Jaupart, 1998]. From these observations weconclude that fragmentation is not directly controlled by theisolated bubble population in Hawaiian fountains as it is intypical silicic (sub)Plinian eruptions.[41] More TGSD!BSD data sets of both silicic and

basaltic eruptions are required to test the hypotheses pre-sented here. TGSD are time!consuming to assemble andoften limited by exposure; for this reason, it would beconvenient if fragmentation efficiency (e.g., D values) couldbe assessed from the analysis of individual sites as proposedby Perugini et al. [2011] in a study of basaltic samples froma dissected cinder cone. However, we are cautious of thisapproach because it is not clear how much the local grainsize distribution is affected by sorting in the air and bygrain!size segregation during granular flow down the cindercone.

8. Synthesis and Conclusions

[42] We started with basic observations about pyroclasttextures and deposit grain size distributions (Figures 1, 3,and 4) that raised fundamental questions about the role ofvesiculation in controlling fragmentation of magma of dif-ferent compositions and at different ascent rates. It has longbeen known that exsolving and expanding gases play a keyrole is driving volcanic eruptions [e.g., Verhoogen, 1951;Sparks, 1978] and that the permeability of magma andconduit wall rocks have important effects on the intensity andstyle of eruption [e.g., Eichelberger et al., 1986; Jaupart,1996]. In this paper we have presented data and scalingarguments that examine the role played by permeabilityin both fragmentation efficiency and post!fragmentationexpansion. We conclude that measured pyroclast vesicula-rities approximate the permeability threshold under mostconditions, because (1) permeability increases rapidly forvery small increases in porosity after span!wise bubble con-nectivity is achieved and therefore (2) bubble expansionbeyond the permeability threshold is limited in most casesby gas escape (Figure 6).[43] The relationship between permeability development

and fragmentation is more complicated. Magma ascentdrives volatile exsolution and vesiculation; bubble nucle-ation and growth causes the ascending magma to expand,thus accelerating magma ascent. Continued growth of bub-bles in ascending magma requires that gas volume be gen-erated faster than it escapes through interconnected bubblenetworks, but not so fast that the magma fragments to ash.Fragmentation can occur when (1) a critical overpressure

within individual bubbles is exceeded because viscous for-ces limit bubble expansion (particularly when H2O lossdrastically increases the melt viscosity and/or induces rapidcrystallization that changes the magma rheology), or (2) acritical local strain rate is exceeded. Fragmentation may bebrittle or ductile. Where fragmentation is brittle (siliciceruptions), magma permeability is key to preserving pumiceclasts. Where fragmentation is ductile, permeability is notas important for fragmentation because bubble expansionwill prevent substantial bubble overpressure. In both cases,however, pyroclast vesicularities should approximate (orslightly exceed) the magma permeability threshold. In thefirst case, the foam preserved as pumice is permeable atfragmentation and high melt viscosities hinder further bub-ble expansion; in the second case post!fragmentation expan-sion occurs rapidly only until the permeability threshold isreached, after which expansion is limited by gas loss as wellas cooling.[44] There are several interesting corollaries. As noted by

Verhoogen [1951], “differences in the behavior of eruptingvolcanoes may depend more on the kinetics of the processesinvolved than on original differences in composition, gascontent, depth, etc.” Differences in eruptive behavior thenlead to differences in the resulting eruptive products. Inexplosive eruptions, these differences are commonly mea-sured using the thickness and grain size distributions of theeruptive deposits [e.g., Walker, 1973; Pyle, 1989]. Alter-natively, these differences may be tracked using the physicalcharacteristics of erupted pyroclasts [e.g., Klug et al., 2002;Gurioli et al., 2005; Houghton et al., 2010]. Here we haveshown that these two views can be linked through consid-eration not only of bubble size distributions (BSDs) andbubble number densities but also of total grain size dis-tributions (TGSDs).[45] The close correspondence in power law behavior of

TGSDs and BSDs in silicic eruptions shows that the sizedistribution of the bubbles (and connected bubble pathways)exerts a first order control on the particle size distribution ofthe fragmented material. For this reason, fragmentation ofvesiculating magma generates very different grain size dis-tributions than fragmentation produced by crushing, grind-ing, or sudden decompression of static (not vesiculating)samples [e.g., Turcotte, 1986; Kaminski and Jaupart, 1998;Kueppers et al., 2006]. The kinetics of bubble nucleation area direct function of volatile supersaturation, which is con-trolled by magma decompression rate [e.g., Toramaru,2006] and surface tension [Mangan and Sisson, 2000,2005]. This direct link between conditions of magma ascentand the resulting bubble population suggests that the formermay be inferred from the latter if there are no kinetic barriersto nucleation (e.g., Figure 3b). Finally, the competitionbetween bubble nucleation and bubble growth (by eitherdiffusion or expansion) determines the form of the bubblesize distribution (e.g., unimodal, log linear, power law, etc.).Available data suggest that only crystal!poor viscous meltsgenerate simple power law bubble size distributions withD > 3, much larger than predicted for ‘Apollonian’ packingschemes [e.g., Blower et al., 2001]. It seems likely that thesehigh D values reflect rapid late!stage bubble nucleationbecause of large nucleation delays [e.g., Hurwitz and Navon,1994; Mangan and Sisson, 2000]. In contrast, low kineticbarriers to bubble nucleation in low viscosity mafic melts


14 of 17

produce more complicated bubble size distributions andbubble number densities that record ascent conditions.[46] To conclude, measurements of the textures, perme-

ability, and other physical properties of natural samplesprovide important insights into the permeability of magmas.The vesicularity (density) distribution of larger pyroclastsplaces important constraints on the permeability thresholdof expanding magma, whereas the whole deposit grain sizedistribution of pyroclastic deposits places critical limits onthe permeability structure of the magma at the point offragmentation. The correspondence between bubble sizedistribution and ash size distribution for the 1980 Mount St.Helens Plinian eruption suggests that stresses on the bubblescale are integral to ash formation, and that detailed studiesof individual well!constrained eruptive deposits could pro-vide critical information about fragmentation processes. Incontrast, the lack of correspondence between bubble sizeand grain size in K"lauea fire fountain deposits underlinesboth the rapid evolution of the bubble population inexpanding low viscosity melts and the absence of a directconnection between the bubble population and conditions offragmentation. Importantly, however, we have focused onlyon end!member cases of crystal!poor rhyolitic and basalticmagmas. A wide spectrum of magma compositions anderuptive styles (and corresponding TGSDs, BSDs, andcrystal size distributions) lies between these end!membersand presents important challenges for obtaining a completeunderstanding of eruption dynamics. In the case of the frag-mentation of a crystal!rich magma, both the sizes of crystalsand bubbles likely affect the total grain size distribution.

[47] Acknowledgments. We thank Michael Ryan, David Pyle, andShingo Takeuchi for thorough and helpful reviews and Julie Roberge forthe use of her unpublished data. A.C.R. was supported by a Royal SocietyURF (UF061403). K.V.C. was supported by NSF EAR1019848.

ReferencesAdams, N. K., B. F. Houghton, and W. Hildreth (2006), Abrupt transitionsduring sustained explosive eruptions: Examples from the 1912 eruptionof Novarupta, Alaska, Bull. Volcanol., 69(2), 189–206, doi:10.1007/s00445-006-0067-4.

Barclay, J., D. S. Riley, and R. S. J. Sparks (1995), Analytical models forbubble growth during decompression of high viscosity magmas, Bull.Volcanol., 57(6), 422–431.

Belien, I. B., K. V. Cashman, and A. W. Rempel (2010), Gas accumulationin particle!rich suspensions and implications for bubble populations incrystal!rich magma, Earth Planet. Sci. Lett., 297(1–2), 133–140,doi:10.1016/j.epsl.2010.06.014.

Bertagnini, A., P. Landi, M. Rosi, and A. Vigliargio (1998), The Pomici diBase plinian eruption of Somma!Vesuvius, J. Volcanol. Geotherm. Res.,83(3–4), 219–239, doi:10.1016/S0377-0273(98)00025-0.

Blower, J. D. (2001), A three!dimensional network model of permeabilityin vesicular material, Comput. Geosci., 27, 115–119, doi:10.1016/S0098-3004(00)00066-2.

Blower, J. D., J. P. Keating, H. M. Mader, and J. C. Phillips (2001), Inferringvolcanic degassing processes from vesicle size distributions, Geophys.Res. Lett., 28, 347–350, doi:10.1029/2000GL012188.

Blundy, J., and K. Cashman (2005), Rapid decompression!driven crystalli-zation recorded bymelt inclusions fromMount St. Helens volcano,Geology,33(10), 793–796, doi:10.1130/G21668.1.

Bonadonna, C., and B. F. Houghton (2005), Total grain!size distributionand volume of tephra!fall deposits, Bull. Volcanol., 67(5), 441–456,doi:10.1007/s00445-004-0386-2.

Bouvet de Maisonneuve, C., O. Bachmann, and A. Burgisser (2009), Char-acterization of juvenile pyroclasts from the Kos Plateau Tuff (Aegean

Arc): Insights into the eruptive dynamics of a large rhyolitic eruption,Bull. Volcanol., 71(6), 643–658, doi:10.1007/s00445-008-0250-x.

Candela, P. A. (1991), Physics of aqueous phase evolution in plutonicenvironments, Am. Mineral., 76, 1081–1091.

Carey, R. J., B. F. Houghton, and T. Thordarson (2009), Abrupt shiftsbetween wet and dry phases of the 1875 eruption of Askja Volcano:Microscopic evidence for macroscopic dynamics, J. Volcanol. Geotherm.Res., 184(3–4), 256–270, doi:10.1016/j.jvolgeores.2009.04.003.

Carey, S. N., and H. Sigurdsson (1982), Influence of particle aggregationon deposition of distal tephra from the May 18, 1980, eruption of MountSt!Helens Volcano, J Geophys Res., 87, 7061–7072.

Cashman, K. V., and S. M. McConnell (2005), Multiple levels of magmastorage during the 1980 eruptions of Mount St. Helens, WA, Bull Volcanol.,68(1), 57–75.

Cashman, K. V., M. T. Mangan, and S. Newman (1994), Surface degassingand modifications to vesicle size distributions in Kilauea basalt, J. Volcanol.Geotherm. Res., 61(1–2), 45–68, doi:10.1016/0377-0273(94)00015-8.

Celzard, A., and J. F. Mareche (2002), Fluid flow in highly porous aniso-tropic graphites, J. Phys. Condens. Matter, 14(6), 1119–1129,doi:10.1088/0953-8984/14/6/301.

Costantini, L., C. Bonadonna, B. F. Houghton, and H. Wehrmann (2009),New physical characterization of the Fontana Lapilli basaltic Plinianeruption, Nicaragua, Bull. Volcanol., 71(3), 337–355, doi:10.1007/s00445-008-0227-9.

Costantini, L., B. F. Houghton, and C. Bonadonna (2010), Constraints oneruption dynamics of basaltic explosive activity derived from chemicaland microtextural study: The example of the Fontana Lapilli Plinianeruption, Nicaragua, J. Volcanol. Geotherm. Res., 189(3–4), 207–224,doi:10.1016/j.jvolgeores.2009.11.008.

Dingwell, D. B. (1996), Volcanic dilemma: Flow or blow?, Science,273(5278), 1054–1055, doi:10.1126/science.273.5278.1054.

Durant, A. J., and W. I. Rose (2009), Sedimentological constraints onhydrometeor!enhanced particle deposition: 1992 Eruptions of Crater Peak,Alaska, J. Volcanol. Geotherm. Res., 186(1–2), 40–59, doi:10.1016/j.jvolgeores.2009.02.004.

Eichelberger, J. C., C. R. Carrigan, H. R. Westrich, and R. H. Price (1986),Non!explosive silicic volcanism, Nature, 323, 598–602, doi:10.1038/323598a0.

Erlund, E. J., K. V. Cashman, P. J. Wallace, L. Pioli, M. Rosi, E. Johnson,and H. D. Granados (2010), Compositional evolution of magma fromParicutin Volcano, Mexico: The tephra record, J. Volcanol. Geotherm.Res., 197(1–4), 167–187, doi:10.1016/j.jvolgeores.2009.09.015.

Gaonac’h, H., S. Lovejoy, and D. Schertzer (2003), Percolating magmasand explosive volcanism, Geophys. Res. Lett. , 30(11), 1559,doi:10.1029/2002GL016022.

Garboczi, E. J., K. A. Snyder, J. F. Douglas, and M. F. Thorpe (1995), Geo-metrical percolation threshold of overlapping ellipsoids, Phys. Rev. E, 52,819–828, doi:10.1103/PhysRevE.52.819.

Gardner, J. E., R. M. E. Thomas, C. Jaupart, and S. Tait (1996), Fragmenta-tion of magma during Plinian volcanic eruptions, Bull. Volcanol., 58(2–3),144–162, doi:10.1007/s004450050132.

Giachetti, T., T. H. Druitt, A. Burgisser, L. Arbaret, and C. Galven (2010),Bubble nucleation, growth and coalescence during the 1997 Vulcanianexplosions of Soufriere Hills Volcano, Montserrat, J. Volcanol. Geotherm.Res., 193(3–4), 215–231, doi:10.1016/j.jvolgeores.2010.04.001.

Gonnermann, H., and M. Manga (2003), Explosive volcanism may notbe an inevitable consequence of magma fragmentation, Nature, 426,432–435, doi:10.1038/nature02138.

Gurioli, L., B. F. Houghton, K. V. Cashman, and R. Cioni (2005), Complexchanges in eruption dynamics during the 79 AD eruption of Vesuvius,Bull. Volcanol., 67(2), 144–159, doi:10.1007/s00445-004-0368-4.

Gurioli, L., A. J. L. Harris, B. F. Houghton, M. Polacci, and M. Ripepe(2008), Textural and geophysical characterization of explosive basalticactivity at Villarrica volcano, J. Geophys. Res., 113, B08206, doi:10.1029/2007JB005328.

Hess, K.!U., and D. B. Dingwell (1996), Viscosity of hydrous leucograniticmelts: A non!Arrhenian model, Am. Mineral., 81, 1297–1300.

Hort, M., and J. Gardner (2000), Constraints on cooling and degassing ofpumice during Plinian volcanic eruptions based on model calculations,J. Geophys. Res., 105, 25,981–26,001, doi:10.1029/2000JB900186.

Houghton, B. F., and C. J. N. Wilson (1989), A vesicularity index forpyroclastic deposits, Bull. Volcanol., 51(6), 451–462, doi:10.1007/BF01078811.

Houghton, B. F., R. J. Carey, K. V. Cashman, C. J. N. Wilson, B. J. Hobden,and J. E. Hammer (2010), Diverse patterns of ascent, degassing, and erup-tion of rhyolite magma during the 1.8 ka Taupo eruption, New Zealand:Evidence from clast vesicularity, J. Volcanol. Geotherm. Res., 195(1),31–47, doi:10.1016/j.jvolgeores.2010.06.002.


15 of 17

Hurwitz, S., and O. Navon (1994), Bubble nucleation in rhyolitic melts:Experiments at high!pressure, temperature, andwater!content,Earth Planet.Sci. Lett., 122(3–4), 267–280, doi:10.1016/0012-821X(94)90001-9.

Ichihara, M. (2008), Dynamics of a spherical viscoelastic shell: Implica-tions to a criterion for fragmentation/expansion of bubbly magma, EarthPlanet. Sci. Lett., 265(1–2), 18–32, doi:10.1016/j.epsl.2007.09.033.

Ittai, K., L. Vladimir, and N. Oded (2010), Bubble growth in visco!elasticmagma: Implications to magma fragmentation and bubble nucleation,Bull. Volcanol., 73(1), 39–54.

Jaupart, C. (1996), Physical models of volcanic eruptions, Chem. Geol.,128(1–4), 217–227, doi:10.1016/0009-2541(95)00175-1.

Johnson, E. R., P. J. Wallace, K. V. Cashman, H. D. Granados, and A. J. R.Kent (2008), Magmatic volatile contents and degassing!induced crystal-lization at Volcán Jorullo, Mexico: Implications for melt evolution andthe plumbing systems of monogenetic volcanoes, Earth Planet. Sci. Lett.,269(3–4), 478–487, doi:10.1016/j.epsl.2008.03.004.

Kaminski, E., and C. Jaupart (1997), Expansion and quenching of vesicularmagma fragments in Plinian eruptions, J. Geophys. Res., 102, 12,187–12,203,doi:10.1029/97JB00622.

Kaminski, E., and C. Jaupart (1998), The size distribution of pyroclasts andthe fragmentation sequence in explosive volcanic eruptions, J. Geophys.Res., 103, 29,759–29,779, doi:10.1029/98JB02795.

Kauahikaua, J., K. Cashman, D. Clague, D. Champion, and J. Hagstrum(2002), Emplacement of the most recent lava flows on Hualalai Volcano,Hawai’i, Bull. Volcanol., 64(3–4), 229–253, doi:10.1007/s00445-001-0196-8.

Klug, C., and K. V. Cashman (1994), Vesiculation of May 18, 1980, MountSt!Helens magma, Geology, 22(5), 468–472, doi:10.1130/0091-7613(1994)022<0468:VOMMSH>2.3.CO;2.

Klug, C., and K. V. Cashman (1996), Permeability development in vesiculat-ing magmas: Implications for fragmentation, Bull. Volcanol., 58(2–3),87–100, doi:10.1007/s004450050128.

Klug, C., K. V. Cashman, and C. R. Bacon (2002), Structure and physicalcharacteristics of pumice from the climactic eruption of Mount Mazama(Crater Lake), Oregon, Bull. Volcanol., 64(7), 486–501, doi:10.1007/s00445-002-0230-5.

Kueppers, U., D. Perugini, and D. B. Dingwell (2006), “Explosive energy”during volcanic eruptions from fractal analysis of pyroclasts, EarthPlanet. Sci. Lett., 248(3–4), 800–807, doi:10.1016/j.epsl.2006.06.033.

Lautze, N. C., and B. F. Houghton (2007), Linking variable explosionstyle and magma textures during 2002 at Stromboli volcano, Italy, Bull.Volcanol., 69(4), 445–460, doi:10.1007/s00445-006-0086-1.

Lensky, N., O. Navon, and V. Lyakhovsky (2004), Bubble growth duringdecompression of magma: Experimental and theoretical investigation,J. Volcanol. Geotherm. Res., 129(1–3), 7–22, doi:10.1016/S0377-0273(03)00229-4.

Llewellin, E., and M. Manga (2005), Bubble suspension rheology andimplications for conduit flow, J. Volcanol. Geotherm. Res., 143(1–3),205–217, doi:10.1016/j.jvolgeores.2004.09.018.

Mangan, M. T., and K. V. Cashman (1996), The structure of basaltic scoriaand reticulite and inferences for vesiculation, foam formation, and frag-mentation in lava fountains, J. Volcanol. Geotherm. Res., 73(1–2), 1–18,doi:10.1016/0377-0273(96)00018-2.

Mangan, M., and T. Sisson (2000), Delayed, disequilibrium degassing inrhyolite magma: Decompression experiments and implications for explo-sive volcanism, Earth Planet. Sci. Lett., 183(3–4), 441–455, doi:10.1016/S0012-821X(00)00299-5.

Mangan, M., and T. Sisson (2005), Evolution of melt!vapor surface tensionin silicic volcanic systems: Experiments with hydrous melts, J. Geophys.Res., 110, B01202, doi:10.1029/2004JB003215.

Mannen, K. (2006), Total grain size distribution of a mafic subpliniantephra, TB!2, from the 1986 Izu!Oshima eruption, Japan: An estimationbased on a theoretical model of tephra dispersal, J. Volcanol. Geotherm.Res., 155(1–2), 1–17, doi:10.1016/j.jvolgeores.2006.02.004.

Mastin, L. G. (1997), Evidence for water influx from a caldera lake duringthe explosive hydromagmatic eruption of 1790, Kilauea volcano, Hawaii,J. Geophys. Res., 102, 20,093–20,109, doi:10.1029/97JB01426.

Mastin, L. G., R. L. Christiansen, C. Thornber, J. Lowenstern, andM. Beeson(2004), What makes hydromagmatic eruptions violent? Some insightsfrom the Keanakako’i Ash, Kilauea Volcano, Hawai’i, J. Volcanol.Geotherm. Res., 137(1–3), 15–31, doi:10.1016/j.jvolgeores.2004.05.015.

Mattsson, H. B. (2010), Textural variation in juvenile pyroclasts from anemergent, Surtseyan!type, volcanic eruption: The Capelas tuff cone,Sao Miguel (Azores), J. Volcanol. Geotherm. Res., 189(1–2), 81–91,doi:10.1016/j.jvolgeores.2009.10.007.

Melnik, O., and R. S. J. Sparks (2002), Dynamics of magma ascent andlava extrusion at Soufriere Hills Volcano, Montserrat, in The Eruptionof Soufriere Hills Volcano, Montserrat, From 1995 to 1999, edited byT. H. Druitt and B. P. Kokelaar, pp. 153–171, Geol. Soc., London.

Michaut, C., D. Bercovici, and R. S. J. Sparks (2009), Ascent and compac-tion of gas rich magma and the effects of hysteretic permeability, EarthPlanet. Sci. Lett., 282(1–4), 258–267, doi:10.1016/j.epsl.2009.03.026.

Mueller, S., O. Melnik, O. Spieler, B. Scheu, and D. B. Dingwell (2005),Permeability and degassing of dome lavas undergoing rapid decompres-sion: An experimental determination, Bull. Volcanol., 67(6), 526–538,doi:10.1007/s00445-004-0392-4.

Mueller, S., B. Scheu, O. Spieler, and D. B. Dingwell (2008), Permeabilitycontrol on magma fragmentation, Geology, 36(5), 399–402, doi:10.1130/G24605A.1.

Namiki, A., and M. Manga (2008), Transition between fragmentation andpermeable outgassing of low viscosity magmas, J. Volcanol. Geotherm.Res., 169(1–2), 48–60, doi:10.1016/j.jvolgeores.2007.07.020.

Navon, O., A. Chekhmir, and V. Lyakhovsky (1998), Bubble growth inhighly viscous melts: Theory, experiments, and autoexplosivity of domelavas, Earth Planet. Sci. Lett., 160, 763–776, doi:10.1016/S0012-821X(98)00126-5.

Okumura, S., M. Nakamura, and A. Tsuchiyama (2006), Shear!inducedbubble coalescence in rhyolitic melts with low vesicularity, Geophys.Res. Lett., 33, L20316, doi:10.1029/2006GL027347.

Okumura, S., M. Nakamura, A. Tsuchiyama, T. Nakano, and K. Uesugi(2008), Evolution of bubble microstructure in sheared rhyolite: Forma-tion of a channel!like bubble network, J. Geophys. Res., 113, B07208,doi:10.1029/2007JB005362.

Okumura, S., M. Nakamura, S. Takeuchi, A. Tsuchiyama, T. Nakano, andK. Uesugi (2009), Magma deformation may induce non!explosive vol-canism via degassing through bubble networks, Earth Planet. Sci. Lett.,281(3–4), 267–274, doi:10.1016/j.epsl.2009.02.036.

Papale, P. (1999), Strain!induced magma fragmentation, Nature, 397,425–428, doi:10.1038/17109.

Parfitt, E. A. (1998), A study of clast size distribution, ash deposition andfragmentation in a Hawaiian!style volcanic eruption, J. Volcanol.Geotherm. Res., 84(3–4), 197–208, doi:10.1016/S0377-0273(98)00042-0.

Perugini, D., A. Speziali, L. Caricchi, and U. Kueppers (2011), Applicationof fractal fragmentation theory to natural pyroclastic deposits: Insightsinto volcanic explosivity of the Valentano scoria cone, J. Volcanol.Geotherm. Res., 202(3–4), 200–210.

Polacci, M., P. Papale, and M. Rosi (2001), Textural heterogeneities inpumices from the climactic eruption of Mount Pinatubo, 15 June 1991,and implications for magma ascent dynamics, Bull. Volcanol., 63(2–3),83–97, doi:10.1007/s004450000123.

Polacci, M., L. Pioli, and M. Rosi (2003), The Plinian phase of theCampanian Ignimbrite eruption (Phlegrean Fields, Italy): Evidence fromdensity measurements and textural characterization of pumice, Bull.Volcanol., 65(6), 418–432, doi:10.1007/s00445-002-0268-4.

Polacci, M., R. A. Corsaro, and D. Andronico (2006), Coupled textural andcompositional characterization of basaltic scoria: Insights into the transi-tion fromStrombolian to fire fountain activity atMount Etna, Italy,Geology,34(3), 201–204, doi:10.1130/G22318.1.

Polacci, M., D. R. Baker, L. P. Bai, and L. Mancini (2008), Large vesiclesrecord pathways of degassing at basaltic volcanoes, Bull. Volcanol., 70(9),1023–1029, doi:10.1007/s00445-007-0184-8.

Polacci, M., M. R. Burton, A. La Spina, F. Mure, S. Favretto, and F. Zanini(2009), The role of syn!eruptive vesiculation on explosive basaltic activ-ity at Mt. Etna, Italy, J. Volcanol. Geotherm. Res., 179(3–4), 265–269,doi:10.1016/j.jvolgeores.2008.11.026.

Pyle, D. M. (1989), The thickness, volume and grain size of tephra falldeposits, Bull. Volcanol., 51(1), 1–15, doi:10.1007/BF01086757.

Richter, D. H., J. P. Eaton, K. J. Murata, W. U. Ault, and H. L. Krivoy(1970), Chronological narrative of the 1959–1960 eruption of Kilaueavolcano, Hawaii, U.S. Geol. Surv. Prof. Pap., 537!E, 73.

Ripepe, M., M. Rossi, and G. Saccorotti (1993), Image processing of explo-sive activity at Stromboli, J. Volcanol. Geotherm. Res., 54(3–4), 335–351,doi:10.1016/0377-0273(93)90071-X.

Rose, W. I., and A. J. Durant (2009), Fine ash content of explosiveeruptions, J. Volcanol. Geotherm. Res., 186(1–2), 32–39, doi:10.1016/j.jvolgeores.2009.01.010.

Rose, W., S. Bonis, R. Stoiber, M. Keller, and T. Bickford (1973), Studiesof volcanic ash from two recent Central American eruptions,Bull. Volcanol.,37(3), 338–364, doi:10.1007/BF02597633.

Rose, W. I., A. T. Anderson Jr., L. G. Woodruff, and S. B. Bonis (1978),The October 1974 basaltic tephra from Fuego volcano: Description andhistory of the magma body, J. Volcanol. Geotherm. Res., 4(1–2), 3–53,doi:10.1016/0377-0273(78)90027-6.

Rose, W. I., S. Self, P. J. Murrow, C. Bonadonna, A. J. Durant, and G. G. J.Ernst (2008), Nature and significance of small volume fall deposits atcomposite volcanoes: Insights from the October 14, 1974 Fuego erup-tion, Guatemala, Bull. Volcanol., 70(9), 1043–1067, doi:10.1007/s00445-007-0187-5.


16 of 17

Rosi, M., L. Vezzoli, A. Castelmenzano, and G. Grieco (1999), Plinianpumice fall deposit of the Campanian Ignimbrite eruption (PhlegraeanFields, Italy), J. Volcanol. Geotherm. Res., 91(2–4), 179–198,doi:10.1016/S0377-0273(99)00035-9.

Rust, A. C., and K. V. Cashman (2004), Permeability of vesicular silicicmagma: Inertial and hysteresis effects, Earth Planet. Sci. Lett., 228(1–2),93–107, doi:10.1016/j.epsl.2004.09.025.

Rust, A. C., and K. V. Cashman (2007), Multiple origins of obsidian pyr-oclasts and implications for changes in the dynamics of the 1300 BPeruption of Newberry Volcano, USA, Bull. Volcanol., 69(8), 825–845,doi:10.1007/s00445-006-0111-4.

Rust, A. C., and M. Manga (2002), Bubble shapes and orientations inlow Re simple shear flow, J. Colloid Interface Sci., 249, 476–480,doi:10.1006/jcis.2002.8292.

Saar, M. O., and M. Manga (1999), Permeability!porosity relationship invesicular basalts, Geophys. Res. Lett., 26, 111–114, doi:10.1029/1998GL900256.

Sable, J. E., B. F. Houghton, P. Del Carlo, and M. Coltelli (2006), Changingconditions of magma ascent and fragmentation during the Etna 122 BCbasaltic Plinian eruption: Evidence from clast microtextures, J. Volcanol.Geotherm. Res. , 158(3–4), 333–354, doi:10.1016/j.jvolgeores.2006.07.006.

Sahimi, M. (1994), Applications of Percolation Theory, 258 pp., Taylorand Francis, London.

Self, S., R. S. J. Sparks, B. Booth, and G. P. L. Walker (1974), The 1973Heimaey strombolian scoria deposit, Iceland,Geol. Mag., 11(6), 539–548,doi:10.1017/S0016756800041583.

Shea, T., L. Gurioli, J. F. Larsen, B. F. Houghton, J. E. Hammer, and K. V.Cashman (2010), Linking experimental and natural vesicle textures inVesuvius 79AD white pumice, J. Volcanol. Geotherm. Res., 192(1–2),69–84, doi:10.1016/j.jvolgeores.2010.02.013.

Shimano, T., and S. Nakada (2006), Vesiculation path of ascending magmain the 1983 and the 2000 eruptions of Miyakejima volcano, Japan, Bull.Volcanol., 68(6), 549–566, doi:10.1007/s00445-005-0029-2.

Shimozuru, D. (1994), Physical parameters governing the formation ofPele’s hair and tears, Bull. Volcanol., 56(3), 217–219, doi:10.1007/BF00279606.

Sparks, R. J. S. (1978), The dynamics of bubble formation and growth inmagmas: A review and analysis, J. Volcanol. Geotherm. Res., 3(1–2),1–37, doi:10.1016/0377-0273(78)90002-1.

Sparks, R. J. S., and L. Wilson (1976), A model for the formation of ignim-brite by gravitational column collapse, J. Geol. Soc., 132(4), 441–451,doi:10.1144/gsjgs.132.4.0441.

Sparks, R. S. J., L. Wilson, and H. Sigurdsson (1981), The pyroclasticdeposits of the 1875 eruption of Askja, Iceland, Philos. Trans. R. SocA, 299(1447), 241–273, doi:10.1098/rsta.1981.0023.

Sparks, R. S. J., J. Barclay, C. Jaupart, H. M. Mader, and J. C. Phillips(1994), Physical aspects of magmatic degassing. 1. Experimental andtheoretical constraints on vesiculation, Volatiles Magmas, 30, 413–445.

Spieler, O., B. Kennedy, U. Kueppers, D. B. Dingwell, B. Scheu, andJ. Taddeucci (2004), The fragmentation threshold of pyroclastic rocks,Earth Planet . Sci . Let t . , 226(1–2), 139–148, doi :10.1016/ j .epsl.2004.07.016.

Stovall, W. K. (2009), Dynamics and processing during the 1959 KilaueaIki eruption, Ph.D. thesis, 168 pp., Univ. of Hawai’I, Honolulu.

Stovall, W., B. Houghton, H. Gonnermann, S. Fagents, and D. Swanson(2010), Eruption dynamics of Hawaiian!style fountains: The case studyof episode 1 of the K"lauea Iki 1959 eruption, Bull. Volcanol., 73(5),511–529.

Tait, S., R. Thomas, J. Gardner, and C. Jaupart (1998), Constraints on cool-ing rates and permeabilities of pumice in an explosive eruption jet fromcolour and magnetic mineralogy, J. Volcanol. Geotherm. Res., 86(1–4),79–91, doi:10.1016/S0377-0273(98)00075-4.

Takeuchi, S., S. Nakashima, A. Tomiya, and H. Shinohara (2005), Exper-imental constraints on the low gas permeability of vesicular magma dur-ing decompression, Geophys. Res. Lett., 32, L10312, doi:10.1029/2005GL022491.

Takeuchi, S., S. Nakashima, and A. Tomiya (2008), Permeability measure-ments of natural and experimental volcanic materials with a simple per-meameter: Toward an understanding of magmatic degassing processes,J. Volcanol. Geotherm. Res., 177(2), 329–339, doi:10.1016/j.jvolgeores.2008.05.010.

Takeuchi, S., A. Tomiya, and H. Shinohara (2009), Degassing conditionsfor permeable silicic magmas: Implications from decompression experi-ments with constant rates, Earth Planet. Sci. Lett., 283(1–4), 101–110,doi:10.1016/j.epsl.2009.04.001.

Thomas, N., C. Jaupert, and S. Vergniolle (1994), On the vesicularity ofpumice, J. Geophys. Res., 99, 15,633–15,644.

Toramaru, A. (2006), BND (bubble number density) decompression ratemeter for explosive volcanic eruptions, J. Volcanol. Geotherm. Res.,154(3–4), 303–316, doi:10.1016/j.jvolgeores.2006.03.027.

Turcotte, D. L. (1986), Fractals and fragmentation, J. Geophys. Res., 91,1921–1926, doi:10.1029/JB091iB02p01921.

Verhoogen, J. (1951), Mechanics of ash formation, Am. J. Sci., 249(10),729–739, doi:10.2475/ajs.249.10.729.

Walker, G. P. L. (1973), Explosive volcanic eruptions ! a new classificationscheme, Geol. Rundsch., 62, 431–446, doi:10.1007/BF01840108.

Walker, G. P. L. (1981), Generation and dispersal of fine ash and dustby volcanic eruptions, J. Volcanol. Geotherm. Res., 11(1), 81–92,doi:10.1016/0377-0273(81)90077-9.

Walsh, S. D. C., and M. O. Saar (2008), Magma yield stress and permeabil-ity: Insights from multiphase percolation theory, J. Volcanol. Geotherm.Res., 177(4), 1011–1019, doi:10.1016/j.jvolgeores.2008.07.009.

Webb, S. L., and D. B. Dingwell (1990), Non!Newtonian rheology of igne-ous melts at high stresses and strain rates: Experimental results for rhyolite,andesite, basalt, and nephelinite, J. Geophys. Res., 95, 15,695–15,701,doi:10.1029/JB095iB10p15695.

Whitham, A. G., and R. S. J. Sparks (1986), Pumice, Bull. Volcanol., 48(4),209–223, doi:10.1007/BF01087675.

Wilson, C., and B. Houghton (1990), Eruptive mechanisms in the Minoaneruption: Evidence from pumice vesicularity, in Thera and the AegeanWorld III, edited by D. Hardy, pp. 122–128, The Thera Foundation,London.

Wright, H. M. N., and R. F. Weinberg (2009), Strain localization in vesicularmagma: Implications for rheology and fragmentation, Geology, 37(11),1023–1026, doi:10.1130/G30199A.1.

Wright, H. M. N., J. J. Roberts, and K. V. Cashman (2006), Permeability ofanisotropic tube pumice: Model calculations and measurements,Geophys.Res. Lett., 33, L17316, doi:10.1029/2006GL027224.

Wright, H. M. N., K. V. Cashman, M. Rosi, and R. Cioni (2007), Bread-crust bombs as indicators of Vulcanian eruption dynamics at GuaguaPichincha volcano, Ecuador, Bull. Volcanol., 69(3), 281–300,doi:10.1007/s00445-006-0073-6.

Wright, H. M. N., K. V. Cashman, E. H. Gottesfeld, and J. J. Roberts(2009), Pore structure of volcanic clasts: Measurements of permeabilityand electrical conductivity, Earth Planet. Sci. Lett., 280(1–4), 93–104,doi:10.1016/j.epsl.2009.01.023.

Zimanowski, B., R. Buttner, V. Lorenz, and H. G. Hafele (1997), Fragmen-tation of basaltic melt in the course of explosive volcanism, J. Geophys.Res., 102, 803–814, doi:10.1029/96JB02935.

K. V. Cashman, Department of Geological Sciences, University ofOregon, Eugene, OR 97403!1272, USA.A. C. Rust, School of Earth Sciences, University of Bristol, Wills

Memorial Building, Queens Road, Bristol BS8 1RJ, UK. ([email protected])


17 of 17

permeability controls on expansion and size distributions of...

Documents