wilding-etal-2004-jgr-subglacial-quench (1).pdf

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rate. The development of polygonal fractures duringquenching will greatly increase the surface area of hot lavaavailable to transfer heat conductively to the surroundingwater. However, empirical calculations suggest that theprocess may be counteracted by the decrease in convectiveflux resulting from the development of a thick glass rind[Tuffen et al., 2002b]. Therefore there is no simple correla-

tion between the development and density of fractures inlavas in subglacial volcanic landforms, overall heat flux,and ice melting rate.

[4] Thermodynamic models can be used to evaluate themechanism of emplacement of subglacial volcanic depositsand to estimate the melting rate of ice [Hoskuldsson andSparks, 1997;Tuffen et al., 2002b].Wilson and Head[2002]developed a model for the emplacement of subglacialbasalts which emphasizes the influence of dissolved vola-tiles in controlling the eruption style. According to thatmodel, at the rapid strain rates expected during meltpropagation in a fracture, basaltic magma may either intrudethe overlying ice as a dyke or else spread sideways as a sill

at the rock-ice interface. The precise emplacement style isprobably affected by a combination of the magma chamberpressure gradient and magma buoyancy. For rapid emplace-ment rates of1 m s1 [Wilson and Head, 2002], there islittle time for much melting of the surrounding ice, and thedyke is briefly supported. Extensive melting follows veryshortly afterward, however, and the now unsupported dykecollapses as a rubble pile within an ice-confined void thatfills with water and becomes the locus of the continuingeruption. If the magma is emplaced as a sill, the lateralmovement of magma can result in more efficient melting ofthe surrounding ice because the extremely thin (subcentim-eter) initial layer of magma can transfer heat more effec-tively to the overlying ice via intervening meltwater. In bothdyke and sill eruptions the eruptive style may changedramatically if the vault becomes hydraulically connectedto the atmosphere, perhaps via subglacial tunnels connectedto a nearby ice margin. The confining pressure over the ventwill thus drop rapidly to atmospheric, i.e., much less thanthe volatile saturation pressure of the magma (3 MPa fortypical basalt water contents [Wilson and Head, 2002]).Volatiles (H2O and CO2) are then explosively exsolved,causing magma disruption and fire fountain activity. In thatevent, ice would be expected to melt rapidly; blocks of icemay even become entrained in the magma column, poten-tially precipitating more violent phreatomagmatic eruptionsand brittle collapse of the ice vault roof.

[5] The generation of meltwater during subglacial erup-tions can be modelled using versions of the Carslaw and

Jaeger [1959] model for the conduction of heat in twoinfinite half spaces. This model can be used to calculate thethickness of chilled crust generated on the surface of theerupted magma and also to calculate the heat flux throughthat surface as a function of time. It is straightforward tofurther calculate the thermal energy released and the amountof ice that can be conductively melted around the magma.The rates of meltwater generation in subglacial eruptionshave been estimated by two versions of the Carslaw and

Jaeger [1959] model, that of Hoskuldsson and Sparks[1997], and also that of Wilson and Head[2002], althoughthe consequences of meltwater generation are addresseddifferently in the two models. The melting rates were

estimated to be as high as 140 m day1. However, theserates are much slower than those observed in recent erup-tions (e.g., Gjalp, Iceland, in 1996 [Gudmundsson et al.,1997] and Deception Island, Antarctica, in 1969 [Smellie,2002]). Gudmundsson et al. [1997] and Gudmundsson[2004] appealed to fragmentation of magma to increasethe rapidity of the thermal flux between magma and water/

ice, whereas Smellie [Smellie, 2002; Tuffen et al., 2002b]invoked a role for juvenile gases and steam generated fromgroundwater. The two mechanisms are not mutually exclu-sive and may operate within the same eruption. What isrequired is an independent method of testing the publishedthermal models to assess why natural eruptions seem to beassociated with the unusually rapid and more completerelease of thermal energy from the magma than can cur-rently be predicted theoretically. It is difficult to determinethe cooling history of a subglacial volcanic edifice, as therecan be no preserved record of any hot gases, and there areno published descriptions of the volcanic products (frag-mented magma or intact lava pillows) formed over the vent

in the earliest stages of an eruption. Conversely, thequenched glass structure can retain evidence of its thermalhistory and potentially can be used to extract a numericalvalue of cooling rate if the structural relaxation of theglass can be modelled [Gottsmann and Dingwell, 2001;Gottsmann et al., 2002; Wilding et al., 2000; Wilding et al.,1996a; Wilding et al., 1996b]. It is the purpose of thispaper to demonstrate that sensible values of the thermalhistory of subglacial volcanic rocks can be derived usingquenched glass structure and that the data can be used tocalibrate and test the published thermal models.

1.2. Structural Relaxation and Fictive Temperature

[6] Any natural or synthetic glass retains a record of itsthermal history in the quenched structure [Dingwell, 1995;

Moynihan, 1995; Scherer, 1990]. The quenched structure isresolved by analyzing any structurally dependent property,such as the volume or enthalpy, and the most convenientway of doing this is to introduce the concept of a fictivetemperature (Tf) [Moynihan et al., 1991; Narayanaswamy,1971, 1988; Tool, 1946]. Fictive temperature relates anystructure-dependent physical property (e.g., enthalpy) to atemperature at which that property would be in equilibriumand has units of temperature (K). Fictive temperature is thusa proxy for the equilibrium temperature of a structuralconfiguration and will differ from the ambient temperaturein the glassy state [Tool, 1946]. The fictive temperature is

used to extract the thermal history by observing the struc-tural relaxation to a new equilibrium as the glass is reheated.If the fictive temperature is equated with enthalpy (H), thenthe relaxation process can be observed directly throughdifferential scanning calorimetry (DSC) measurements,where the first temperature derivative of enthalpy, heatcapacity at constant pressure (Cp), is used. Such calorimetrymeasurements, applied to volcanic glasses, show a largerange of apparent cooling rates from a few degrees per dayto more rapid rates of up to 25 K s1 [Wilding et al., 2000,1996a]. The more rapid rates are consistent with ratesderived from other geospeedometry methods and alsofrom rates estimated from simple thermal models.

[7] In this contribution we use a series of DSC experi-ments on two rhyolitic glasses from two subglacial edifices

B08201 WILDING ET AL.: COOLING PROCESS IN RHYOLITE GLASSES

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in Iceland in order to evaluate their thermal history, correlatetheir cooling rate with a surface flux, and assess thepotential effect on the generation of meltwater. To constrainthe thermal history of the two glass samples, a large numberof repeated calorimetry measurements were made onaliquots from them, so that the distribution of fictive

temperatures in the relatively small glass samples couldbe evaluated. These data are used to evaluate the contribu-

tions of different cooling processes to the overall thermalhistory which have been shown to be complex [Tuffen et al.,2002b].

[8] The concept of fictive temperature and the relatedstructural relaxation time is used in the classic description ofglass formation. The liquid state is defined as a regimewhere any structural response to temperature is rapid,

reflecting a short relaxation time. A glass state is wherethe structure responds more slowly (i.e., the structuralrelaxation time is long) and may never achieve equilibrium.From this definition the fictive temperature is dependent onthe structural relaxation time (t), which is the ratio of theelastic bulk modulus (G) to the shear viscosity [Dingwell,1995; Dingwell and Webb, 1990], or the Maxwell relation[Maxwell, 1867]. The elastic bulk modulus remains constantfor silicate liquids [Webb and Dingwell, 1995], and so thestructural relaxation time of silicate liquids is proportionalto shear viscosity [Dingwell and Webb, 1990]. At hightemperatures the relaxation time is rapid, and the responseof the liquid to fluctuations in temperature is an equilibrium

one defining a stable liquid field by Tf = T; that is, theliquid structure is in equilibrium with the ambient temper-ature (Figure 1). When the glass-forming liquid is cooled,the structural relaxation time, t, increases and the liquidstructure (Tf) falls out of the Tf= Tequilibrium (Figure 1).The liquid can still partly relax (t> t), however, but not toan equilibrium structure. This departure fromTf=Tdependson cooling rate and occurs at a higher temperature forrapidly quenched liquids. Continued decrease in the ambi-ent temperature results in progressively longer relaxationtimes until a temperature is reached when fictive tempera-ture can no longer change (t t). This final value of fictivetemperature is that frozen into the quenched glass(Figure 1) [Moynihan, 1995].

[9] The fictive temperature and relaxation time are inti-mately related. To derive the thermal history of any glass,the fictive temperature and relaxation time must be mea-sured together, since it is the relaxation of fictive temper-ature that is characteristic of the cooling process. Enthalpy(H) is directly related to fictive temperature, and therelaxation process can therefore be investigated throughDSC. The first temperature derivative of the fictive temper-ature corresponds to the normalized heat capacity,

Cp ffiDH

DT

DTf

DT : 1

[10] The frozen thermal history of the glass is evaluatedby reheating the glass at a known heating rate. This processis also shown in Figure 1. As the glass is reheated, therelaxation time (t) becomes shorter relative to observationtime until a temperature is reached at which the structurecan begin to relax to a new, lower temperature equilibriumvalue. The new equilibrium is not reached, however,because the relaxation time is still long (Figure 1). Astemperature is increased further, the relaxation timebecomes shorter, while the temperature of the new structuralequilibrium (Tf = T) also increases. At a point where theequilibrium Tfexceeds that of the partly relaxed sample, theTf relaxes toward a higher fictive temperature (Figures 1

and 2). This hysteresis in Tfversus Tevolution depends onthe prior cooling rate and the heating rate. The relaxation of

Figure 1. (a) Evolution of fictive temperature withtemperature. The fictive temperature (structure) of threeglasses is shown for three different cooling rates. Thedeparture from the equilibrium liquid (Tf = T) occurs athigher temperatures for rapid cooling rates, and the frozenvalues of fictive temperature are higher for more rapidlycooled glass. The relaxation paths for glasses reheated, at5 K min1, through the glass transition temperature to thestable liquid field (dotted lines) are also shown. (b) Theevolution of derivative fictive temperature on reheating. Forthe same three samples in Figure 1a the reheating paths are

shown with derivative fictive temperature, DTf/DT, if Tf isequated with enthalpy. These curves are the same as thosethat would be obtained from DSC measurements if the heatcapacity were normalized. Dashed line denotes glass cooledat 2.5 K min1.


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a glass passing into the liquid field is modelled using theKohlrausch-Williams-Watt (KWW) function:

P P0exp t

t

b: 2

[11] Heret is the characteristic relaxation time, tis timeandb is a constant (0 350 mthick. It comprises a very poorly exposed pedestal mainlycomposed of massive, poorly sorted phreatoplinian asherupted within a moist but drained englacial vault and a

flat-topped subaerial rhyolite lava cap. At least three addi-tional coeval rhyolite lavas are also present and exposedmainly on a low platform on the east side of the main massif(lavas C, D, and E from Tuffen et al. [2002a]; Figure 3).Lava D comprises three lava bodies, which share similarlithological characteristics and were probably coerupted.They occupy a prominent north-south trending break inslope formed by flow-banded obsidian lava with a subaerialcarapace of pumiceous and obsidian breccia. Sample JS.1.1was obtained at the eastern margin of a prominent columnarjointed obsidian lava lobe within lava D [Tuffen et al.,2002a]. The precise position of the original outer surface ofthe lava lobe in relation to the sample is unknown, but it is

likely to be within a few to several decimeters of thesampling position. The obsidian lava was possibly separated

from the enclosing ice walls by a fragmental layer, not nowpreserved. The sampled lobe consists of dark grey perlitizedflow-banded obsidian, which makes up the bulk of theexposure. The obsidian contains up to 80% bead-like relictsof black glass set in altered pale grey glass. The upstandingmorphology of the columnar jointed obsidian lobe is inter-preted to be an original ice contact feature, with the rhyolite

magma chilling rapidly against former ice walls of theenclosing glacier that dipped steeply east away from theedifice. Abundant meltwater probably caused the pervasiveperlitic alteration, most likely while the lava was still hot.

2.2. Sample JS.2.1

[14] The outcrop at Blahnukur represents a much smallervolume (400 m thick[Tuffen et al., 2001]. It comprises a basal glacial sedimen-tary unit overlain by a variety of monomict juvenile brecciasthat include numerous irregular columnar jointed lava lobesand cogenetic feeders. Unlike the Rau*ufossafjoll outcrop,

there is no evidence that the Blahnukur volcano was eversubaerial during its eruption. There is no subaerial lavacap and the outcrop lacks a flat top; it is thus not a rhyolitetuya. Glassy juvenile fragments in the breccias were formedroughly in situ, mainly by water quenching of the volatile-poor magma, but larg e sect ions of the edifice wereremobilized by a variety of mechanisms, mainly gravita-tional collapse of the growing volcanic pile, with evidencefor both hot and cold emplacement. Like Rau*ufossafjoll,the englacial vault was probably drained but moist, withabundant meltwater. The lava lobes are thought to havebeen injected into and molded and chilled in contact withthe overlying glacier. They are characterized by thick,obsidian surfaces that enclose massive microcrystallinerhyolite interiors; perlitization is largely confined to thelobe bases. Sample JS.2.1 was obtained from a columnarjointed lava lobe at the base of a stream section in Grnagil[Tuffen et al., 2001]. The lobe is part of a large-scale brecciaunit interpreted to have formed by brittle failure and massslumping of a cold section of the edifice. The sample is aflow-banded obsidian obtained 10 cm within the columnarjointed outcrop. The lobe is apparently in (obscured) contactwith dense obsidian breccia. Because the lobe has beendisplaced from its original position during slumping, it isunclear how close the sample site was located to the originallobe surface, although they were probably not separated bymore than a few decimeters.

3. Experimental Methods

[15] Heat capacity data were used to establish the firsttemperature derivative of fictive temperature, approximatedto DTf/DT (Figure 1b). Heat capacity data were collectedusing a Setaram DSC111 differential scanning calorimeter.Samples (200 mg) of glass were placed in platinum boatsand heated to 983 K at rates of 520 K min1. An emptyplatinum boat was placed in the reference position, and theinstrument was calibrated using a-Al2O3 powder. The heatcapacity curves fora-Al2O3(National Institute of Standardsand Technology) were used to calculate sensitivity curves

for each scan rate. Corrections for the heat capacity of theplatinum boats were made by heating empty boats for the


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same sequence of scan rates. Heat capacity curves were thencalculated using these corrections. According to the fictivetemperature concept, the liquid field is defined by DTf/DT=1 and the glass field DTf/DT= 0 (Tf= constant; Figure 1).The heat capacity curves are normalized by fitting linearcurves to the glass and liquid portions of the heat capacitytrace so that the same relations apply.

[16] In typical DSC experiments the sample size is200 mg, a very small fraction of a typical volcanic deposit.This implies that, potentially, each glass sample can have adifferent thermal history. Accordingly, in this study wereport the results of a series of heat capacity experiments,

on 200 mg aliquots from each of the two rhyolite obsidiansamples. Multiple (18 and 20) measurements from eachspecimen were taken, and the distribution of fictive temper-atures for each glass has been used to establish the influenceof annealing on the frozen structure retained in thequenched products.

[17] In previous studies, sets of kinetic parameters havebeen obtained for individual samples [Wilding et al.,1996a, 1996b]. In this study we have not used separatesets of parameters for each aliquot measurement, but wehave slightly modified this approach to take account of theminimal compositional differences within the sample sub-sets. There are 18 20 subsets of each bulk composition(JS.1.1 and JS.2.1), and the relaxation process of each, as

described by equation (2), will be similar. Therefore onlytwo sets of kinetic parameters, one for JS.1.1 and one forJS.2.1, are required. The extraction of fictive temperaturefor the 20 subset samples of JS.1.1 and JS.2.1 can beaccomplished more efficiently by modifying the calibrationstep. The specific kinetic parameters for each of the twobulk compositions JS.2.1 and JS.1.1 were obtained bymore extensive thermal treatments [Wilding et al., 1995] atcooling rates of 5, 10, 15, and 20 K min1. Once theseparameters were derived, subsequent measurements ofeach composition required only two heating steps; onewas the initial reheating to determine the fictive tempera-ture of the naturally cooled sample, and the other followed

a controlled cooling at 10 K min

1

for calibration. Thesemodified measurements were made with reheating rates of

10 K min1. An example of the quality of fit is shown inFigure 4.

4. Results

[18] The fictive temperatures modelled from the heatcapacity measurements for the 20 aliquots from JS.1.1 rangefrom 833 to 910 K, equivalent to apparent cooling rates of0.016 0.5 K min1. The ranges of kinetic parametersassociated with this glass composition are shown inTable 1. The sample has a relatively high glass transitiontemperature and an activation energy for viscous flow of330 kJ mol1. A consequence of the high activation energyis that the enthalpy release on structural relaxation is quitesmall, as is the associated calorimetric signal. The values offictive temperature modeled for the 20 glass aliquots fromJS.1.1 are skewed toward higher values of fictive temper-ature reflecting faster quench rates (Figure 5a).

[19] The glass transition temperature for sample JS.2.1 ismuch lower than that for JS.1.1. The onset is at750 K,and the mean value of fictive temperature is 745 K (Table 2).The activation energy for viscous flow, determined from thethermal treatments of these glass samples, is 299 kJ mol1.The differences between the activation energies of the twosamples indicate a difference in the temperature dependenceof viscous relaxation, consistent with minor compositional

differences between the two samples [Gottsmann et al.,2002; Martens et al., 1987; Stevenson et al., 1995]. Thedistribution of fictive temperatures for sample JS.2.1 ismore symmetrical about the mean value (Figure 5b). Therange in fictive temperature is from 722 to 769 K, equiv-alent to apparent quench rates of 0.0035 to 0.065 K min1

(Table 2).

5. Discussion

[20] The maximum quench rate for subglacial volcanismcan be estimated from the classic models of conduction ininfinite half spaces [Carslaw and Jaeger, 1959]. In this type

of analysis the solution to the conduction problem yields thetemperature as a function of time and distance from the

Table 1. Kinetic Parameters, Modeled Quench Rate, and Fictive Temperatures for JS.1.1

Run Number Log10t0/s 0.5 DH/(kJ mol1) 5 X 0.05 b 0.05 jqj/(K min

1) Tf/K 0.5

71 16 330 0.55 0.7 0.04 856.673 16 330 0.65 0.7 0.08 832.675 16 330 0.63 0.63 0.50 909.677 16 328 0.6 0.7 0.06 862.979 16 333 0.55 0.75 0.08 873.7

81 16 328 0.57 0.73 0.15 880.683 16 326 0.7 0.54 0.05 851.385 16 325 0.7 0.55 0.07 855.087 17 353 0.55 0.6 0.06 878.989 16 330 0.68 0.65 0.06 869.091 16 329 0.73 0.53 0.06 889.493 16 330 0.68 0.68 0.08 898.995 16 325 0.55 0.75 0.18 887.797 16 324 0.60 0.76 0.25 881.799 16 330 0.55 0.73 0.13 882.5101 16 325 0.6 0.78 0.11 865.9103 16 324 0.6 0.78 0.01 850.4105 16 328 0.55 0.75 0.50 896.7107 16 337 0.6 0.6 0.02 858.2109 17 358 0.5 0.5 0.02 851.3


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water-lava interface [Hoskuldsson and Sparks, 1997;Wilson

and Head, 2002]. Values of thermal diffusivity (2.88 106 m2 s1) and eruption temperature (1323 K) appropri-ate for rhyolite, and a water temperature of 273 K, are usedto calculate the temperature profile as a function of depthand time. The temperature in the first 1.5 cm of the lava-water interface will fall below the value of the calorimetricglass transition during the first 60 s of contact. Theinstantaneous quench rate calculated at the interfacedepends on both temperature and time. At the interfaceitself the quench rates are, as expected, very rapid (of theorder of 1200 K min1) and are much faster than thosepreviously reported for natural glasses, even though theDSC-based technique is robust enough to record such high

fictive temperatures. Further from the interface, within thefirst few centimeters, the quench rates are more moderateand range between 10 and 30 K min1. These values are

Table 2. Kinetic Parameters, Modeled Quench Rate, and Fictive Temperatures for JS.2.1

Run Number Log10t0/s 0.5 DH/(kJ mol1) 5 X 0.05 b 0.05 jqj/(K min

1) Tf/K 0.5

35 16.4 297 0.65 0.7 0.004 722.637 16.4 297 0.7 0.7 0.015 745.939 16.4 297 0.65 0.7 0.09 773.241 16.4 297 0.65 0.7 0.02 749.243 16.4 297 0.65 0.7 0.015 752.2

45 16.4 297 0.65 0.7 0.04 760.347 16.2 297 0.65 0.7 0.015 751.949 16.4 298 0.65 0.7 0.015 744.651 16.4 300 0.65 0.7 0.008 742.453 16.4 297 0.65 0.7 0.008 738.255 16.4 295 0.73 0.7 0.035 754.957 16.4 297 0.65 0.7 0.035 759.359 16.4 295 0.75 0.7 0.006 731.861 16.4 297 0.75 0.7 0.024 752.263 16.4 299 0.65 0.7 0.003 725.265 16.5 297 0.73 0.7 0.018 745.767 16.4 297 0.68 0.7 0.065 769.069 16.4 300 0.65 0.7 0.07 740.4

Figure 2. The modification of fictive temperature byisothermal annealing processes. A glass cooled at 25 Kmin1 has a fictive temperature of 853 K and is modified toa glass with a fictive temperature of 810 K (equivalent to a5 K min1 cooling rate) following the path shown. A glasswith a fictive temperature of 768.9 K (a cooling rate of

0.25 K min

1

) is shown modified to the same fictivetemperature, 810 K.

Figure 3. Locations of rhyolite samples obtained from theRau*ufossafjoll center and the Blahnukur locality withinthe Torfajokull rhyolite complex. (top) View looking southat a large upstanding obsidian lava lobe attached to theeastern margin of lava D, Rau*ufossafjoll [Tuffen et al.,2002a]. Sample JS.1.1 was obtained at the lower left marginof the outcrop shown. (bottom) View of a columnar jointedlava lobe in Grnagil stream valley, Blahnukur. Sample

JS.2.1 was obtained from the steep, dark-colored obsidiansurface to the left of the two people.


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more consistent with those of rapidly cooled glass frag-ments (25 K min1; [Wilding et al., 1996a]). The eruptiontemperature has limited influence on the cooling ratedetermined in this way, and so this maximum cooling rate

is equally applicable to basaltic and rhyolitic glass compo-sitions [Wilding et al., 2000].[21] The minimum expected value of quench rate is

determined from a critical quench rate that avoids crystalli-zation. This value can be determined from classic nucleationtheory [Debenedetti, 1996], in which a temperature-time-transformation (TTT) envelope is constructed (Figure 6).The temperature-time-transformation envelope is a plot ofthe structural relaxation time (t1) and the time taken tocrystallize a given volume fraction (t2), both of which areplotted as a function of temperature. The value of therelaxation time is again proportional to the shear viscosity,as described by the Maxwell relation. The time taken tocrystallize a given volume fraction is determined by the

degree of undercooling (i.e., the ratio of ambient temperatureto fusion temperature), the heat of fusion, and the liquidviscosity. This means that viscous liquids with low heats offusion can be cooled relatively slowly without crystalliza-tion, whereas rapid quench rates are necessary for low-viscosity liquids with a high heat of fusion. In Figure 6 theTTT envelope for albite is shown using available heat-of-fusion data and viscosity data [Cranmer and Uhlmann,1981; Stebbins et al., 1983] to estimate the approximatecritical quench rates expected for rhyolites. These datasuggest a rate of 0.05 K s1, yet the fictive temperaturesobtained for the glasses sampled as part of this study yieldvalues even lower than this minimum quench rate; for JS.1.1

the lowest quench rate is 0.0005 K s1

, whereas for JS.2.1,the value is 0.00005 K s1. These data suggest that the

apparent cooling rates recorded in the glass samples do notreflect the simple quenching of hot volcanic material incontact with cold water or even ice but have thermal historiesthat involve modification of the fictive temperature by anannealing process.

[22] The modification of a glass structure by annealing iseasily demonstrated from the models of fictive temperature

as shown in Figure 2, which uses the Tool-Narayanaswamymodel [Crichton and Moynihan, 1988; Moynihan et al.,1991; Narayanaswamy, 1971, 1988]. The modification ofstructure involves an isothermal dwell at a temperaturewithin the glass transition where the relaxation time is shortenough to allow modification. If the dwell temperature istoo low, however, then no effective modification will occur.For example, in Figure 2, if the dwell temperature were tobe 600 K, then the relaxation time values would be 3.5107 s, and they would be even longer at room temperature(4.5 1025 s). The original fictive temperature would bemodified by isothermal annealing following paths similar tothose shown in Figure 2, depending on whether the dwell

temperature was above or below that of the rapidlyquenched glass (Figures 3 and 4).

[23] The distributions of fictive temperatures reportedhere for two rhyolite samples are assumed to reflect thesampling of the annealing path for the modification of an

Figure 4. Measured and modeled heat capacity curve forJS.2.1. This heat capacity curve is produced by the firstheating through the glass transition interval, and the shapeof the normalized curve reflects the relaxation of the frozen

fictive temperature. The modeled normalized heat capacitycurve is based on the kinetic parameters derived from thecalibration run performed after this first heating step. Theexperiment is matched to a cooling rate of 0.017 K min1

(Tf = 746 K). For reference, two other curves are shown,which have cooling rates of 0.05 K min1 (Tf= 763 K) and0.005 K min1 (Tf= 727 K).

Figure 5. (a) Distribution of fictive temperature for JS.1.1samples. The fictive temperatures for the 20 JS.1.1 glasssamples have a minimum at 832.6 K and maximum value of909.6 K. The mean value is 872.9 K, and the distributionis skewed to higher values. (b) Distribution of fictivetemperature for JS.2.1 samples. The 20 glass samples forJS.2.1 are shown with values between 722.6 and 773.2 K;the distribution is more symmetrical about the mean valueof 747.7 K. The fictive temperature and glass transition forthis sample are much lower for compositional reasons. In

both JS.1.1 and JS.2.1 the uncertainty in fictive temperaturevalues is 0.5 K.


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initially rapidly quenched value of fictive temperature.

The distribution of fictive temperatures will reflect thecharacteristic form of the annealing curve and will dependon both the kinetic parameters and dwell temperature.This is modelled by assuming that the initial fictivetemperature is fixed by a 25 K min1 quench rate, withdifferent values of fictive temperature determined by thekinetic parameters established for each individual compo-sition. As the glass is modified, we make the assumptionthat some portions of the sample are isolated from furtherrelaxation, and we simulate this by selecting 20 randomsamples from the time-dependent annealing curve. Thisresults in a distribution of values reflecting the progres-sion toward a final value of fictive temperature. Thelowest value of fictive temperature for each of the two

samples is assumed to represent the dwell temperatureand, using the constraints of dwell temperature, initial Tf[Crichton and Moynihan, 1988; Moynihan et al., 1991],and kinetic parameters (Tables 1 and 2), the time taken tomodify the glass structures can be calculated.

[24] For JS.1.1 the lowest value of fictive temperaturedetermined is 832 K. The approach to this value, plottedas a function of time, shows that it would take 8 hoursat 832 K to achieve the modified value of fictivetemperature (Figure 7a). The distribution of fictive tem-peratures for 20 random samples (Figure 7b) based onthis simple annealing process does not correspond withthe distribution of 20 samples reported from the DSC

measurements (Figures 5a and 6). The distribution of 20random samples taken for a single modification of fictive

temperatures is skewed toward low values, as shown

in Figure 7b when the annealing path comprises asingle step. The measured fictive temperatures forJS.1.1 (Figure 5) are skewed toward higher Tf valuesand suggest a more complex annealing process. Amultiple annealing step path with a series of isothermalsteps each 20 min long (Figure 7a) and with thetemperature reduced from 895 to 880 K by 20 Kincrements results in the distribution of values shownin Figure 7c. This distribution is more consistent withthat obtained from the DSC data (Figure 5a) and impliesa more complicated annealing process.

[25] The distribution of fictive temperatures for sampleJS.2.1 is approximately symmetrical about the meanvalue of 745 K (Figure 5b). The mean value of fictive

temperature is much lower than the minimum valueobtained for sample JS.1.1. This may reflect eithercompositional differences between the two glasses ordifferences in their thermal histories. As in sampleJS.1.1 a single annealing step for the minimum valueof fictive temperature (740 K) does not result in thedistribution of fictive temperatures recorded in the glass(Figures 8a and 8b), and we assume that there aremultiple annealing steps and a gradual reduction in dwelltemperature. The distribution of fictive temperaturesreported from the DSC experiments (Figure 5b) couldbe achieved if the glass was held isothermally first at755 K for 3.33 hours (Figure 8a) and subsequently at

750, 745, 740, and 735 K for the same time increment.This more complicated annealing path would take

Figure 6. Temperature-time-transformation envelope for a glass-forming liquid. Classical nucleationtheory is used to plot the time taken to crystallize a given volume fraction (t2) as a function oftemperature. Also plotted is the structural relaxation time (t1) obtained by the Maxwell relation. Themodification of a fictive temperature from Tf1 to Tf2 is also shown (compare to Figure 2).


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16.5 hours, but the fictive temperatures recorded in theglass would have a distribution (Figure 8c) similar to thatobtained from the DSC measurements.

[26] Comparison of the modified paths for fictive tem-perature and the DSC data suggests that the studied sub-glacial rhyolite glasses were held at elevated temperaturesfor periods of up to 16.5 hours. This means that the surfaceheat flux for these erupted materials remained high forextended periods, with consequences for the water temper-ature surrounding these volcanic deposits. For many eruptedigneous rocks, including subglacial volcanic deposits, theCarslaw and Jaeger[1959] model has been used to estimatesurface fluxes and thicknesses of cooled crust. For eruptedrhyolites [Wilson and Head, 2002] these calculations indi-cate that a crust 0.4 m thick would develop within 8 hours

and the surface flux would decrease from 106

to104 W m2 s1. These values can be used in combinationwith the thermal parameters for water and ice to calculatethe thickness of ice melted, the temperature of the resultingmeltwater, and the possibility of convection within the ice-bound vaults [Hoskuldsson and Sparks, 1997; Tuffen et al.,2002b]. The estimates for the temperature of water [ Wilsonand Head, 2002] and the thickness of ice melted suggeststhat a thickness of ice 8 times that of the cooled crustcould melt during eruption and high water temperaturescould be maintained. The glass thermal histories suggest aslow overall cooling dominated by isothermal dwells. Thisoverall cooling is much slower than that obtained by theconductive model, although the values of surface heatflux are initially comparable with those calculated from

Figure 7. Modification of the fictive temperature for JS.1.1 glass by both single and multiple annealingsteps. (a) Annealing modeled following an initial, rapid cooling step of 25 K min1, using the kineticparameters for this sample (Table 1). (b) Distribution of fictive temperatures, skewed toward a value of840 K, if a single annealing step at 835 K is assumed. (c) Distribution ofTf, if an additional annealingstep is introduced (similar to that in Figure 5a).


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the Carslaw and Jaeger treatment [Roshenow et al., 1998].The analysis of the glass fictive temperatures suggestthat the surface heat flux remains higher for longer forthese subglacial rhyolites and that high melting rates(0.15 mm s1) would persist (Figure 9). These estimatesfor surface heat flux model are much greater than those

suggested for rhyolites by Hoskuldsson and Sparks [1997],even though the same parameters are used.

[27] Our interpretation of the thermal history of therhyolites therefore suggests that large volumes of ice couldbe melted very rapidly, particularly in the earliest stages oferuption (Figure 9), and will cause a corresponding rapidrise in the buildup (and likely subsequent discharge) ofmeltwater in a subglacial vault. This conclusion is supported

by both the models using isothermal spheres and also fromour calculations based on the conductive model.

Figure 8. Modification of fictive temperature for JS.2.1 glass by single and multiple annealingprocesses. (a) Isothermal annealing process for a glass cooled at 25 K min-1, modified with a singleannealing step (a decrease to 730 K), using the kinetic parameters in Table 2. (b) Histogram of fictivetemperatures, showing values are skewed toward higher values of fictive temperature. (c) A morecomplicated, multiple annealing step process resulting in a distribution of Tfmore consistent with themeasured values.


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[28] The persistence of elevated temperatures in theobsidians suggests that meltwater might be maintained inan ice-bound vault at relatively elevated temperatures,sufficient to drive vigorous convection prior to vault drain-ing. If these results are applicable to subglacial eruptionsgenerally, the present approach has the potential to provide

detailed information on the rate at which the vault grew byice retreat and drained through preexisting subglacial tun-nels [Smellie, 2000]. For example, melting by warm melt-water may be an order of magnitude more rapid thanmelting caused solely by mechanical energy of flowingwater at the pressure melting point [Clarke, 1982]. Thesurface heat flux from the simple thermal model ofCarslawand Jaeger [1959] suggests melting rates of ice consistentwith the values of 140 m per day obtained by Hoskuldssonand Sparks [1997]; however, these values are smallerthan those observed from field observations of basalticeruptions. For example, in the Gjalp eruption in 1996 ittook 30 hours to melt a 500 700 m thick ice sheet[Gudmundsson et al., 1997].

[29] Thus we suggest that rhyolites may remain hot forlonger than a simple conduction model suggests, and themost obvious possible contribution to this extendedthermal history is the release of the latent heat ofcrystallization. There is evidence for such a contributionfrom basaltic eruptions, in which high internal temper-atures and even temperature increases have been mea-sured in studies of advancing pahoehoe lava flows[Keszthelyi, 1995; Keszthelyi and Denlinger, 1996]. Thissuggestion is strongly supported by field evidence fromthe Blahnukur center, in which the lava lobes havethick obsidian glass rims enclosing microcrystallinerhyolite [Tuffen et al., 2001]. Similar microcrystalline

rhyolite cores are not described from lava D in theRau*ufossafjoll outcrop [Tuffen et al., 2002a]. However,

our results suggesting multiple isothermal dwells andenhanced surface heat flux imply that microcrystallinerhyolite may be present in lava D but is presumablyhidden at the current level of exposure. Additional studiesof other subglacial volcanic centers are required beforewe will understand better the role of the latent heat of

crystallization in the cooling history of subglacial volca-noes. Ideally, these studies should include independentobservations of indicators of cooling rate, such as thedistribution and density of lava surface fractures [Tuffenet al., 2002b].

6. Conclusions

[30] Relaxation geospeedometry has been used to esti-mate the thermal histories of two rhyolitic obsidian sam-ples. A series of 20 aliquots from each of the bulk sampleswas used to establish the range of apparent cooling ratesby modeling the relaxation of enthalpy through differentialscanning calorimetry (DSC) measurement. The cooling

rates range from 0.5 to 0.08 K min

1 for the sample withthe higher glass transition temperature (Tg; sample JS.1.1)and are between 0.065 and 0.0035 K min1 for the lowerTg sample (JS.2.1). These cooling rates are much slowerthan the estimated critical quench rates for rhyolitic liquidsand therefore cannot reflect the simple quenching oferupted material in cold water. The fictive temperaturecan be modified by any process that allows the partialrelaxation of glass structure, and the distribution of fictivetemperatures for the rhyolite obsidian samples investigatedsuggests such a structural modification.

[31] The distribution of the retained fictive temperaturesfor the obsidian samples indicates a modification of previ-

ously rapidly quenched glass. The initial quench rateestimated from simple conduction models is 35 K min1.

Figure 9. Surface flux for rhyolite calculated usingCarslaw and Jaeger[1959] model with an eruptiontemperature of 1173 K. The melting rates of ice for convective flux at different water temperatures,calculated according toHoskuldsson and Sparks[1997], are shown. These suggest rapid initial melting ofthe ice surrounding subglacial rhyolites.


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Modification of this initial value is obtained by maintainingthe glass at a fixed temperature for short time intervals.These isothermal dwells are used to estimate the distributionof fictive temperatures sampled by the calorimetry measure-ments, assuming a series of random samples along theannealing path. Surprisingly, the glass samples do not showevidence for a single annealing step but are apparently

cooled in a series of steps. On the basis of the calorimetricand model results of this study the fictive temperature forglass JS.1.1 could be explained if, on eruption, the magmainitially cooled to a glass at 35 K min1, after which point,cooling was arrested at885 K for a short time (0.5 hours),at which point temperature continued to fall slowly. Bycomparison, JS.2.1 appears to have cooled more graduallyfollowing an initial dwell at 750735 K. The temperature isreduced by a 5, 10, 15, and finally 20 K increment beforethe annealing is arrested. The annealing totals 16.5 hours.Although the cooling histories of samples JS.1.1 and JS.2.1show annealing of rapidly quenched samples, they do notrepresent components of a similar overall cooling trend. The

cooling histories are very different, although the reasons forthese differences are not yet apparent.

[32] Acknowledgments. We are grateful to Hugh Tuffen, DaveMcGarvie, and Jennie Gilbert for introducing the outcrops to JS and,together with Bruce Houghton, for creating fruitful discussion on subglacialeruptions of rhyolite magmas. DSC measurements were made in thethermochemistry facility of the University of California at Davis.

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edited by J. L. Smellie and M. G. Chapman, pp. 526, Geol. Soc.,London.

C. E. Lesher and M. C. Wilding, Department of Geology, University of

California at Davis, Room 4440, One Shields Avenue, Davis, CA 95616,USA. ([email protected]; [email protected])

S. Morgan, School of Earth Sciences, University of Leeds, Leeds LS29JT, UK. ([email protected])

J. L. Smellie, British Antarctic Survey, High Cross, Madingley Road,Cambridge CB3 0ET, UK. ([email protected])

L. Wilson, Environmental Science Department, Institute of Environ-mental and Natural Sciences, Lancaster University, Lancaster LA1 4YQ,UK. ([email protected])


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