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Journal of Volcanology and Geothermal Research 175 (2008) 156–167
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Journal of Volcanology and Geothermal Research
j ourna l homepage: www.e lsev ie r.com/ locate / jvo lgeores
MND(microlite number density) water exsolution rate meter
A. Toramaru a,⁎, S. Noguchi a,c, S. Oyoshihara b, A. Tsune a,d
a Department of Earth and Planetary Sciences, Kyushu University, Higashiku, 6-10-1 Hakozaki, Fukuoka 812-8581, Japanb Department of Earth Sciences, Kanazawa University, Kakuma, Kanazawa 920-11, Ishikawa, Japanc Volcano Research Center, Earthquake Research Institute, University of Tokyo, 1-1-1, Yayoi, Bunkyo, Tokyo 113-0032, Japand Sakurajima Museum, Furusato-machi 1078, Kagoshima, 891-1544, Japan
⁎ Corresponding author. Tel.: +81 92 642 4354; fax: +E-mail address: [email protected] (A. To
0377-0273/$ – see front matter © 2008 Elsevier B.V. Aldoi:10.1016/j.jvolgeores.2008.03.035
A B S T R A C T
A R T I C L E I N F OArticle history:
Microlites in effusive or py Accepted 24 March 2008Available online 22 April 2008Keywords:microlite number densitywater exsolution ratedecompression rateascent ratedome eruptionsexplosive eruption
roclastic rocks are possible indicators of water exsolution. In particular, themicrolite number density (MND) is considered to be a function of the rate of water exsolution from melt. Inthis paper, we have constructed a MND water exsolution rate meter based on the recent results of theory,experiments and the natural observation of crystallization kinetics. The MND method accounts for the effectsof melt composition and water content on the diffusivity of crytallizing components in melt. By using thismeter, we can estimate the water exsolution rate at the microlite nucleation depth from a MND valueprovided the crystal phase (plagioclase or clinopyroxene) is known. We applied the meter to the case of the1991–1995 dome eruption at Unzen and the 1986B subplinian eruption at Izu-Oshima. We obtained thewater exsolution rates in the range of 6.1×10−6 to 2.8×10−5 (wt.%/s) approximately at 70 (MPa) for Unzen(plagioclase MND=1014 to 1015 (m−3)) and 1.1×10−3 to 1.1×10−1 (wt.%/s) for Izu-Oshima (pyroxeneMND=1015 to 1017(m3)). Under the assumption of equilibrium vesiculation and steady state flow, thecorresponding decompression rate and ascent velocity are calculated in the range of 240 to 1100 (Pa/s) and0.014 to 0.068 (m/s) for Unzen and 1.2×104 to 1.3×106 (Pa/s) and 1.3 to 133 (m/s) for Izu-Oshima. Thiscontrast in the ascent velocity at the microlite nucleation depth is closely related to the reason why Unzenand Izu-Oshima revealed the different eruption styles, namely, dome growth and explosive eruption,respectively.
© 2008 Elsevier B.V. All rights reserved.
1. Introduction
Since the pioneeringworks ofWilson and coworkers (Wilson et al.,1978, 1980), the modeling of conduit flow has undergone significantenhancement. We can now obtain a graphical output of the steadystate ascent velocity of magma in the conduit through the Internetgiven the chemical composition and phenocryst contents (Mastin andGhiorso, 2000). Further, the effects of the crystal content andvesiculation on the transient behavior of conduit magmas have beenstudied (Melnik and Sparks,1999;Wylie et al., 1999). In addition, it hasbeen recognized that the transition between explosive and non-explosive eruptions is controlled by the ascent velocity in the conduitand degassing from the magma column due to a permeable flow(Jaupart and Allégre, 1991; Woods and Koyaguchi, 1994). Hence, thetheoretical flow behavior has been well understood during thisdecade, although important issues such as magma fragmentation,propagation of vesiculation, and unsteady flow problems remainunsolved. On the other hand, only Rutherford and Hill (1993)succeeded in the quantitative estimation of the flow dynamics based
81 92 642 2684.ramaru).
l rights reserved.
on the decompression-induced breakdown rim of the amphibole inthe case of the 1980–1986 Mount St. Helens eruptions. The currentstatus of the studies on conduit dynamics reveals a lack of naturalevidence for theory. This suggests that modeling studies are ratherpredominant and direct observations or quantitative estimations ofconduit flow dynamics using the erupted materials are required.
Microlites with sizes of b100 µm are typically present in lava,bomb, ash, pumice, and scoria originating from various volcaniceruption styles with a wide range of magma chemistry (Castro andMercer, 2004; Geschwind and Rutherford, 1995; Noguchi et al., 2006;Pallister et al., 1996; Polacci et al., 2001; Taddeucci et al., 2004).Plagioclase (most common), alkali feldspar, quartz, orthopyroxene,clinopyroxene, olivine (rare), amphibole (rare), and Fe–Ti oxide are thephases of microlites. It is considered that the microlites originate fromsupercooling or an increase in the liquidus temperature due to waterexsolution or vesiculation induced by magma decompression (e.g.Cashman and Blundy, 2000). Therefore, by examining the linkbetween the decompression process and the formation of microlites,we can obtain information on magma ascent and the resulting waterexsolution processes from the chemical and textural characteristics ofmicrolites. This background has stimulated the current activities suchas experimental (Blundy and Cashman, 2001; Hammer and Ruther-ford, 2002; Couch et al., 2003a,b) and numerical (Hort, 1998) works.
Fig. 1. Plot of log(MND) vs SiO2 content. MND data are compiled for plagioclase andpyroxenemicrolites in various volcanic rocks (Redoubt byWolf and Eichelberger (1997),Merapi by Hammer et al. (2000), Pinatubo by Hammer et al. (1999), Mount St. Helens byCashman (1992), and Unzen by Noguchi et al. (2008-this issue). MND at the margin ofmafic dikes is obtained from Gray (1970, 1978). Other data correspond to unpublisheddata of the authors.)
Fig. 2. Effects of H2O or Pw on diopside (Di)-anorthite (An) eutectic system. EDi–Andenotes the eutectic point at Pw=10 kbar. CEDi–An and TEDi–An indicate the composition andtemperature of EDi–An (Yoder, 1965; Kushiro, 1979).
157A. Toramaru et al. / Journal of Volcanology and Geothermal Research 175 (2008) 156–167
HighMND (microlite number density) values are a characteristic ofmicrolites. In Fig. 1, the MND data compiled for various eruption stylesand chemical compositions are shown as functions of the SiO2 contentand the crystal phases. We observe that the MND values are in therange of 104 to 109 (mm−3) or 1013 to 1018 (m−3). For comparison, thehighest crystal number density (104 mm−3) or 1013 m−3)) of thegroundmass at themargin (distance of 1 mm to 1 cm from the contact,just inside the chilled margin) in mafic dikes (Gray, 1970, 1978) is alsoshown. Since the groundmass crystal number densities of the dikessystematically vary with the distance from the margin, therebyreflecting the cooling rate variation (Gray,1970,1978; Toramaru, 2001)(see later), it is evident that the groundmass crystals are formed due tocooling by the country rocks. The MND values of some basalticandesitic and andesitic rocks are very high, as seen in Fig. 1. If we try toexplain these MNDs on the basis of the cooling-induced crystal-lization, it appears that a higher cooling rate corresponding to adistance of less than 1 mm from the contact between the countryrocks and dikes, where a chilled margin is normally formed, isrequired. Although the effects of the melt composition and theeffective cooling rate could be offset with a more accurate examina-tion, these high MNDs suggest that the microlites in the effusive orpyroclastic rocks are not formed by cooling. Rather, they are formed bysupersaturation due to the effect of water exsolution on the increase inthe liquidus temperature during the decompression and vesiculationof magmas.
In this paper, we focus on the MND as an indicator of the waterexsolution or the decompression rate, and develop a new method forthe quantitative estimation of the water exsolution rate from theMND. First, we demonstrate the fundamental aspects of phasediagrams by using some simple water-bearing and realistic systemsto examine the microlite formation process, by emphasizing on theanalogy between the cooling-induced and the decompression-induced crystallization. Second, we describe a procedure to constructaMNDwater exsolution ratemeter, derive an equation to calculate thewater exsolution rate from the MND data, and extend the MND waterexsolution rate meter to estimate the decompression rate and ascentvelocity. Third, we address the validity and limitation of the MNDmethod by applying it to the Izu-Oshima 1986B subplinian eruption.Lastly, we illustrate the method by using the 1991–1995 Unzeneruptions as an example.
2. Construction of the MND water exsolution rate meter
2.1. Analogy between the decompression-induced crystallization and thecooling-induced crystallization
In this section, we address the assumption on which the waterexsolution rate meter is constructed. The basic assumption is theequivalence between the decompression-induced crystallization andthe cooling-induced crystallization. The liquidi of the crystallizingphases are influenced by the water content. This effect is essential forthe decompression-induced crystallization of microlites. Fig. 2 showsthe effects of H2O or the water-saturation pressure PW on the diopside(Di)-anorthite (An) eutectic system (Yoder, 1965; Kushiro, 1979) as asimple example of phase diagrams for minerals that are common tothe groundmass of volcanic rocks such as plagioclase and pyroxene.This figure indicates that both the cooling (thick arrow from point Q)and water exsolution (arrow from the liquidus curves at PW=5 kbar)by decompression have the same effect that brings the system to thesupersaturated state for the crystallized mineral in a similar manner.Therefore, we can apply quantitative understanding on the crystal-lization kinetics by cooling to that on the decompression-inducedcrystallization. The difference between cooling and decompression isthat the effect of water on the liquidus depends on the phase of themineral. For instance, it is found that the effect of the water-saturationpressure on the liquidus of anorthite is more intensive than that on thediopside one (this is clearly shown by the difference of b value, seelater in detail). Therefore, the eutectic composition shifts toward theanorthite-rich component with an increase in PW. In other words, at alow pressure PW, plagioclase tends to crystallize first. Hence, thecomposition CEDi–An and temperature TEDi–An of the eutectic point EEDi–Anof the binary system consisting of anhydrous minerals are functions ofthe water content or water-saturation pressure.
The combination of an anhydrous mineral and water results in aeutectic systemsuch as albite (another endmemberof plagioclase) andH2O, as reported by Yoder (1976). The difference between this systemand the solid–solid eutectic system is the negative slope of the phaseboundary of liquid(L) / liquid+H2O(vapor)(L+V), which is due to thenegative H2O-exsolution heat. The composition CEAb–Wand temperatureTEAb–W of the eutectic point EAb–W of the anhydrous solid+H2O binarysystem are also functions of the confining pressure.
An important feature is that all the phase boundaries and eutectic orcotectic pointsmovewith a change in the confining pressure. To observe
Table 1Water-free melt compositions assumed for Unzen dacite and Izu-Oshima basalticandesite
Unzen⁎ Izu-Oshima⁎⁎
SiO2 68.14 54.62TiO2 0.57 1.27Al2O3 15.08 14.55FeO 3.78 13.33MnO 0.09 0.20MgO 1.80 4.20CaO 4.10 9.20Na2O 3.51 2.06K2O 2.78 0.47P2O5 0.14 0.10Total 100.0 100.0
⁎Data from Nakada and Motomura (1999).⁎⁎Data from Fujii et al. (1988).
Fig. 3. (a)The eutectic temperature, TEA–W, in albite–H2O, anorthite–H2O and diopside–H2Osystems as a function of pressure (BurnhamandDavis,1974;Yoder,1965;Hodges,1974). (b)Comparison between plagioclase liquidi by experiments and those by MELTS calculationsfor groundmass and bulk compositions of the Unzen 1991–1995 eruptions. Bulkexperiment is from Holtz et al. (2005). Groundmass experiments from Sato et al. (1999).Note that curves other than Pl for bulk composition have similar slopes. The experimentalliquidi approximate few points of data satisfying the water-saturated condition.
158 A. Toramaru et al. / Journal of Volcanology and Geothermal Research 175 (2008) 156–167
this, in Fig. 3a, we show the eutectic temperature TESolid–W in albite–,anorthite–, and diopside–H2O systems (Burnham and Davis, 1974;Yoder, 1965; Hodges, 1974) as a function of the confining pressure(=water-saturation pressure). Plagioclase and clinopyroxene liquidi forrealistic multicomponent melts (Unzen dacite and Izu-Oshima basalticandesite; see Table 1 for their compositions), which are calculated byMELTS, (Ghiorso et al., 1983; Ghiorso and Sack, 1995) are also drawn. Itshould be noted that the plagioclase liquidus decreases with PWirrespective of the melt composition, whereas the clinopyroxeneliquidus increases in the case of the Unzen dacite and decreases in thecase of the Izu-Oshima basaltic andesite. This confirms that theplagioclase in the Unzen dacite is the product of the decompression-induced crystallization; it also accounts for the absence or rarity ofclinopyroxene in the groundmass. On the other hand, both the
plagioclase and clinopyroxene in the Izu-Oshima basaltic andesite arepossibly the products of decompression-induced crystallization.
Fig. 3b shows the comparison between the plagioclase liquidus bythe MELTS calculation and by experiments (Hammer et al., 1999;Venezky and Rutherford, 1999; Holtz et al., 2005). From this figure it isfound that the MELTS yields liquidi that are systematically lower – by40 to 50 K – than the experiments. Although the experimental datathat these liquidi are based on are only at two pressure conditions forthe groundmass and bulk compositions, this difference is significant.Consequently it is expected that the estimation of the amount ofsupersaturation by the MELTS will have some error. Therefore, readersmight be led to believe that this difference significantly affects theMND method itself and the resultant values of the MND waterexsolution rate meter, if the MELTS is used. However, in the presentmodel, this discrepancy does not affect at all the water exsolution ratemeter and the resultant values of the water exsolution rate. This isbecause the MND water exsolution rate meter is controlled not by theamount of supersaturation but by the supersaturation rate, as long asthemicrolite nucleation occurs and is completed, asmentioned below.Therefore, only the slope of the liquidus in the P−T space is important.
2.2. Relationship between MND and increasing rate of liquidus
On the basis of the description presented in the previous section,the crystallization induced by water exsolution is equivalent to thatdue to simple cooling when the cooling rate |dT/dt| is replaced with anincreasing rate dTL/dt of liquidus due towater exsolution. In the case oflinear cooling crystallization of a binary eutectic system, a numericalsimulation (Toramaru, 1991, 2001) reveals that the MND is propor-tional to the 3/2 power of the cooling rate. Therefore we can expressMND or N (m−3) as a function of the increasing rate of dTL/dt (K/s) asfollows:
N ¼ adTLdt
� �3=2
; ð1Þ
where a is the kinetic factor. This is expressed as 103.5×C0 (16πγ3υ2/3kB
3T03)−1.7×(ϕ0kB
2T03D/4γ2υ2)−1.5, where C0, γ, υ, ϕ0, T0, kB , and D denote
the number of molecules of cyrstallizing components per unit volume,interfacial tension between the crystallizing phase and melt, volume ofthe crystallizing molecule, initial volume fraction of the crystallizingphase, initial liquidus of the crystallizingphase, Boltzmann constant andeffective diffusivity of the crystallizing component, respectively. Thenumerical factor 103.5 depends on the shape of the assumed liquidus ofthe crystallized phase in the binary eutectic system in the numericalexperiment (represented by a dimensionless parameter Δs/kB; Δs is thefusion entropy of the crystallizing phase per molecule) and the effect oflatent heat release (represented by the Stefan number St). In this paper,we do not determine the value of a using the data on these material
159A. Toramaru et al. / Journal of Volcanology and Geothermal Research 175 (2008) 156–167
properties (e.g., γ or v) and the value of the numerical factor calculatedin the numerical experiment. The reasons for this are as follows: (1) γ atthe nucleation stage is notwell constrained in the experiments; (2) υ is ahypothetical quantity, but not a propertywith the reality determined byexperiments; (3) the numerical factor 103.5 depends on the detailedshape of the liquidus curve in the cooling-induced crystallization, and itis still unclear how this value is influenced by the decompression-induced crystallization; (4) the numerical factor includes the uncer-tainty by the numerical solution. Despite the ambiguity of these values,we can understand the dependences of these properties on MND anduse the knowledge of them in constructing the MND rate meter.
It is significant that only the diffusivity of the crystallizingcomponent in melt has a remarkable dependence on the compositionof melt including H2O, and that other properties such as γ and υ haveno evident dependence on the composition and are effectively almostcanceled arithmetically. Therefore, we consider a as an adjustableconstant except for the SiO2 dependence of the diffusivity of thecrystallizing component. In addition, we must note here that we usethe equivalence between the cooling-induced crystallization and thedecompression-induced crystallization. In other words, the value of athat is determined for the cooling-induced crystallization can beapplied to the decompression-induced crystallization. According tothis, in the next subsection,we determine the value of a using dike datafrom the natural experiment of the cooling-induced crystallization.
The physics behind Eq. (1) can be interpreted by expressing thenucleation rate as a function of the degree of supersaturation. Generally,we consider that the nucleation rate responds nonlinearly to the degreeof supersaturation, as shown in Fig. 4. An increase in liquidus ΔTL raisesthe degree of supersaturation ΔS. In this figure, the instantaneousnucleation rate is determined for a certain value of ΔS. In the case of acontinuous change in temperature (cooling-induced) or liquidus(decompression-induced), the maximum nucleation rate Jmax that canbe achieved during the entire history of crystallization determines theMND. More importantly, Jmax should be different from the apparentmaximum rate of nucleation J0 which is determined by constant ΔSexperiments. In fact, Jmax is determined by the interplay between theincrease in ΔS due to the rising of liquidus and the decrease inΔS due tothe depletion of the crystallizing component resulting from the growthof nucleated crystals. It is known that Jmax is proportional to theincreasing rate of supersaturation, specifically, to the5/2powerof dTL/dt,Jmax∝(dTL/dt)5/2. The powerof 5/2 originates from the classical theory ofhomogeneous nucleation and the diffusion-limited growth in thenucleation stage. The MND is determined by the product of Jmax and
Fig. 4. Schematic figure showing nucleation rate as a function of the degree ofsupersaturation. The increase path of nucleation rate is controlled by the increase inliquidus or effective cooling. The decrease path is controlled by the depletion of thecrystallizing components.
nucleation duration δtn;N≈ Jmax×δtn. δtn is proportional to the time scaleof supersaturation or inversely proportional to dTL/dt. Hence, theMND isproportional to the 3/2 power of dTL/dt. The power 3/2 is related to thediffusion-controlled growth lawwhich is proportional to the square rootof time. A more detailed illustration is given in Toramaru (2001).
2.3. Determination of a
The constant a can be determined by fitting the model predictionunder the assumption of conductive cooling (Toramaru, 2001), i.e., |dT/dt|∝y−2,whereydenotes thedistance fromthe contact of thedikes, to thenatural data on solidifiedmafic dikes. Fig. 5 compiles the data obtained byGray (1970, 1978) together with the model prediction lines. The modellines for plagioclase, pyroxene, and oxide are drawn with the followingcontrol point: MND=5 mm−3 for plagioclase, pyroxene and oxide at adistance of 103 mm. For 50 wt.% SiO2, which represents the compositionsof thesemafic dikes (normally negligiblewater contentCW=0wt.% can beassumed), the value of a is derived as 3×1015±1 for plagioclase, pyroxeneand oxide. The bound ±1 accounts for data dispersion.
It shouldbenoted thatadepends on SiO2 and thewater concentrationin the melt and temperature only through the diffusivity of thecrystallizing component D as a∝D−3/2, as argued in the last section. Inthis case, we consider that the crystallization components can berepresented by Si. Si diffusion is the slowest among the diffusivities ofmajor species in silicatemelts such as Ca and Al (Baker,1992; Liang et al.,1996a), and is controlled by themelt polymerization. The diffusivity of Siin silicatemeltsDSi is related to the viscosity of themelt η as ameasure ofmelt polymerization, by the following equation: DSi∝η−0.8 (Liang et al.,1996a). The viscosity of the silicate melt is constrained effectively as afunctionof the silica concentrationCSi,water contentCWand temperatureT as η=exp[0.46(CSi−72)−1.25CW+2×104/T] (Toramaru, 1995). Further-more, the temperature of magmas is correlated with CSi as T=103/(0.16+0.01CSi) (Toramaru,1995). Finally, fromthese relationships, it is found thatthe diffusivity of Si in silicate melts depends on CSi and CW, i.e., DSi∝exp(−0.53CSi+CW) (direct measurement by Baker (1991) shows the depen-dence on H2O by the term exp(0.77CW)). By considering the SiO2 andwater dependence of diffusivity, we obtain
a ¼ 3� 1015F1þ0:345DCSi�0:65CW ; ð2Þ
for plagioclase, pyroxene and oxide, where ΔCSi=CSi−50, and CSi andCW in wt.%. Then, we can plot the MND as a function of the effectivecooling rate, CSi, and CW from Eqs. (1) and (2), as shown in Fig. 6. Wecan estimate the increasing rate of the liquidus from theMND value asfollows:
dTLdt
¼ Na
� �2=3
ð3Þ
The dependence of theMND on distance (Fig. 5) can be explained bythe cooling-induced crystallization and not by the decompression-induced crystallization since the cooling rate because the decompres-sion rate does not systematically changes with the distance from themargin of the dikes. The model lines of pyroxene and oxide cansuccessfully account for the trendexhibited bymost of the observationaldata. On the other hand, the model line for plagioclase disagrees withthis approximate trend. However we think that this discrepancy is notimportant for the decompression-induced crystallization by the follow-ing reason. This discrepancy implies that the plagioclase nucleation incoolingdikes is controlledbyanucleation style that is different fromthatof a simple homogeneous nucleation, which is assumed to generate themodel prediction lines. The difference in the nucleation styles is possiblyrelated to the pre-nucleation condition. Normally, the initial watercontent of the mafic magmas that form the dikes is very low and thesemagmas vesiculate at shallower depths, resulting in a very small degreeof supersaturation for liquidus phase microlite nucleation (the
Fig. 6. MND of plagioclase as a function of SiO2 content for various effective coolingrates. (a)Cw=0wt.%. (b)Cw=3.5wt.%. Hatched area covers MND range in natural samplesin Fig. 1.
Fig. 5. Number density of groundmass minerals in dikes as a function of the distancefrom the contact (data obtained from Gray (1970, 1978)). (a) Plagioclase. Dashellipsoidal curve indicates the taret range of the microlite MND. (b) Pyroxene.(c) Oxide. The star symbol denotes the control point for a model prediction line (solidline).
160 A. Toramaru et al. / Journal of Volcanology and Geothermal Research 175 (2008) 156–167
supercooling required for nucleation is estimated to be approximately80 °C for the plagioclase of the Unzen 1991–1995 dacite: see theapplication section for details). The normative compositions of all thedikes reveal that plagioclase is the liquidus phase (Fig. 7). On the otherhand, pyroxene and oxide represent the second and third crystallizingphases, respectively, which are initially above their liquidi. Initially, inthe mafic dikes, plagioclase is slightly below the liquidus; however, itdoes not crystallize and forms molecular clusters. Thus, in comparisonwith the pre-existing cluster-free condition which is expected for thedecompression-induced crystallization, the number density of ground-mass plagioclase and the related crystal morphology formed by thecooling-induced nucleation with preexisting clusters are significantlyinsensitive to the cooling rate (Grove,1990; Sato,1995). This explains the
Fig. 7.Normative plots on the diopside–anorthite–albite ternary diagram formafic dikesreported by Gray (1978). The solid curve represents the cotectic line at 1 bar.
161A. Toramaru et al. / Journal of Volcanology and Geothermal Research 175 (2008) 156–167
reason for the difference between the distance dependences ofplagioclase MNDs and those of pyroxene and oxide in the coolingmafic dikes. In the case of the decompression-induced crystallization inextrusive rocks, we believe that plagioclase, pyroxene, and oxidemicrolites start to crystallize under super- or on-liquidus condition. Inconclusion, for plagioclase, pyroxene, and oxide, we can assume thesame dependence of the MND on the increasing rate of the liquidi (i.e.,the exponent 3/2).
2.4. Relationship between the increasing rate of liquidus and the waterexsolution rate
We determine the relationship between dTL/dt (K/s) and dCw/dt(wt.%/s) from the phase diagrams of the water-bearing systemspresented in the previous section. We assume the following linearrelationship:
dtLdt
¼ bj dCW
dT j ð4Þ
where b is the thermodynamic factor defined by |dTL/dCw|. Fig. 8 givesthe plot of the liquidi of plagioclase and clinopyroxene as functions ofCw (wt.%), which is calculated byMELTS. The linearity of TL(Cw) in Fig. 8suggests that the assumption of Eq. (4) is valid in the margin of error(see the later discussion). From this figure, b is calculated as follows:
b ¼ 40 ð5aÞ
for plagioclase in the Unzen dacite and Izu-Oshima basaltic andesite and
b ¼ 17 ð5bÞ
for the clinopyroxene in the Izu-Oshima basaltic andesite. The depen-dence of b on themelt composition for plagioclase seems to be negligiblejudging fromthe curve forUnzenand Izu-Oshima inFig. 8. Thebvalue andstability for pyroxene seems to depend on the melt composition; hence,the precise value of b should be determined by experiments using naturalsamples. However, experiments (e.g. Moore and Carmichael, 1998)at lower pressures – upto 3 kbar – cannot provide a detailed shape ofthe liquidus curvebecauseof thepaucityof experimental conditions in thePw−T space, although the value of b is similar to that of Eq. (5b).
We have to address the thermodynamic definition of b. According toBurnhammodelofwater-bearingalbite system (Burnham,1979),we can
Fig. 8. Liquidus temperatures of plagioclase and clinopyroxene in Unzen dacite and Izu-Oshima basaltic andesite as functions of water content.
write the liquidus of albite TL(Cw) as a function ofwater contentCw at thewater saturated state or eutectic temperature with water as follows.
TL CWð Þ ¼T0Dsþ K Cw
Cw0
� �2Δυ
Ds� kBln 1� CwCwo
� �2
where T0 is the melting temperature of the pure crystallizing phase;Cw0=12, the scale of water content (mole fraction of water 0.5corresponds to 6 wt.% at 200 MPa); Δs is the entropy of fusion permolecule; Δυ, the volume change (per molecule) of thecrystallizingsubstance during melting; K , the solubility constant for P=K (Cw/Cw0)2;and K=8×108 with Cw=6 wt.% at P=200 MPa (Burnham, 1975). b isrepresented by 2kB T0/(Cw0Δs) as a first order approximation. So thedifference in b is primarily caused by the difference in T0/Δs, which leadsto b=26.9 for diopside (Δs=(enthalpy of fusion, 34 kcal/mol)/TDi=1.43×10−22 (J/molecule) with TDi=1665 K), b=55.1 for anorthite(Δs=(enthalpy of fusion, 20 kcal/mol)/TAn=7.63×10−23 (J/molecule)with TAn=1830 K), and b=42.5 for albite (Δs=(enthalpy of fusion,15 kcal/mol)/TAb=7.53×10−23 (J/molecule) with TAn=1391 K) (represen-tative data from Weill et al. (1980)). The difference of these valuesbetweenpyroxeneandplagioclase in simple systemsare consistentwiththe MELTS calculations. Here, we adopt the values fromMELTS becausethe multicomponent effect is taken into account by more relevant way.
The second order term of TL(Cw) is (Δυ×K/(kB T0)−1+4kB/Δs)×kBT0/(Δs×CW0
2 ). Normally this value is negligibly smaller than the firstorder term by one or two orders of magnitude (−0.29 for diopside,−1.2 for anorthite and −1.4 for albite with Δυ=1.5×10−5 /6×1023(m3)).Thus, the linear approximation in Eq. (4) is valid.
2.5. Derivation of the MND water exsolution rate meter
The substitution of Eq. (4) in Eq. (1) results in the expression of theMND as a function of the water exsolution rate: N=a(b|dCw/dt|)3/2.Further, we obtain the water exsolution rate as a function of the MND:
jdCw
dt j ¼ kN23 ð6Þ
where k is defined by 1/(a2/3b); then,
k ¼ 1:2� 10�12�0:23DCSiþ0:43Cw ð7aÞ
for plagioclase, and
k ¼ 2:8� 10�12�0:23DCSiþ0:43Cw ð7bÞ
for pyroxene and oxide. These equations represent the MND waterexsolution rate meter proposed in this paper.
2.6. Derivation of the MND decompression rate meter
By assuming that the water exsolution is at equilibrium, we canestimate the decompression rates from the water solubility relationPw=5.6×106×Cw2 (5.6×106 is derived by K/Cw0
2 (Toramaru, 2006)) asfollows:
jdPwdt j ¼ cjdCw
dt j ð8Þ
where dPw/dt is in Pa/s and c is defined by |dPw/dCw| as follows
c ¼ 11:2� 106 � Cw: ð9Þ
By using Eq. (8) and Eq. (6), we obtain the relationship between thedecompression rate and the MND;
jdPwdt j ¼ cb
Na
� �2=3
ð10Þ
Fig. 9. Comparison of theMNDvs. the decompression rate between experiments andMNDdecompression rate meter developed in the present paper. (a) Solid squares indicate 3DMND calculated by (Nakamura, 2006) for MDE experiments by (Couch et al., 2003b). Solidline is the model prediction assuming CSi=71 wt.% and Cw=5 wt.%. (b) The experimentaldecompression rate vs the calculated decompression rate given experimental MND.
162 A. Toramaru et al. / Journal of Volcanology and Geothermal Research 175 (2008) 156–167
The decompression rate derived from this equation is the Lagrangianquantity attached with the material ascending within the conduit(Toramaru, 2006). Furthermore, when the decompression process is inthe steady state, the decompression rate at the microlite nucleationdepth zn is expressed as follows;
jdPdt jz¼zn¼ j dPwdt j
z¼zn¼ VnjdPdz jz¼zn
ð11Þ
where Vn denotes the ascent velocity at the microlite nucleation alongthe vertical axis; jdP=dzjz¼zn , represents the pressure gradient at thenucleation depth; and jdP=dzjz¼zn ¼ q � g;q denotes the bulk density ofthe vesiculated magma at the nucleation depth and g denotes thegravity acceleration. This argument is valid for the case that thevelocity gradient is negligible or as long as the microlite nucleationdoes not occur at the fragmentation level (Toramaru, 2006). Thus, fromthe decompression rate, we can estimate the ascent velocity at thenucleation depth as follows:
Vn ¼ 1qg jdPdz jz¼zn
ð12Þ
3. Applicability and limitation of the MND rate meter
3.1. Water exsolution rate vs. decompression rate
TheMNDratemeterdeveloped in the previous section exhibits someproblems, which result from the disequilibrium characteristics includedin the crystallization and vesiculation processes. It has been advocatedthat the vesiculation proceeds at disequilibrium (Larsen and Gardner,2004;Manganand Sisson, 2000). Sinceweneglect such a disequilibriumvesiculation, the present method is based on the assumption that thewater exsolution proceeds at the equilibrium rate in response to thechange in pressure. Nevertheless, the water exsolution rate is a truevalue as long as the MND is controlled by water exsolution and not bydecompression, irrespective of whether the vesiculation proceeds at theequilibrium. On the other hand, the decompression rate estimated bythe present method provides the minimum value because the decom-pression rate should be higher for the same value of MNDs observed innatural samples if the vesiculation is at disequilibrium.
It is likely that the equilibrium vesiculation occurs more sufficientlyin effusive eruptions than in explosive eruptionsbecause the acceleratedascent of magma in explosive eruptions facilitates the disequilibriumexsolution of H2O from melt. Therefore the application to the Unzendome-forming eruptions seems to be valid for both thewater exsolutionrate and the decompression rate. In Section 3.3,weprovide independentevidence to support that the estimation by the MND meter is alsoreasonable also for the explosive eruption of andesitic magmas.
The MND water exsolution rate meter assumes an idealistic crystal-lization in which microlite nucleation occurs as a single event duringdecompression-induced crystallization and finishes until the surface.Further in this crystallization, the heterogeneous nucleation is notdominated and other expected realistic processes such as continuousnucleation until the surface or extraordinarily retarded nucleation donot occur. However, in natural eruptions, it is likely that such idealisticsituations can be realized only for limited conditions. In fact we aresometimes able to observe pumice containing no microlites. Althoughthe origin of extraordinarily microlite-poor vesiculated samples has notyet been understood by experiments or theories, we can suggest twopossibilities. (1) The degree of disequilibrium between the pressure andwater content in themelt ismaintained at a high value so that thedegreeof supersaturation is insufficient formicrolitenucleation (disequilibriumvesiculation). (2)Microlite nucleation or growth is effectively hinderedby the high diffusivity or viscosity of the melt due to water depletion(glass formation). In both cases, we cannot apply the MND method tosuch extraordinarily microlite-poor samples.
3.2. Comparison with experiments
Recently, several studies on the decompression-induced crystal-lization kinetics (Couch et al., 2003a,b; Hammer and Rutherford, 2002),Couch et al. (2003b) carried out two series of decompressionexperiments: SDE (single step decompression) and MDE (multi-stepdecompression). The MND data for MDE experiments was compiled byNakamura (2006) who recalculated the 3D MND from the 2D originaldata, and correlated the 3D with the integrated decompression rate;these experiments replicated the continuous decompression withconstant rates. In Fig. 9a, we plot the 3D MND data versus thedecompression rate with the line indicating the relationship predictedby the MND decompression rate meter. Fig. 9b shows the comparisonbetween the experimental decompression rate and the calculated ratefor thegivenMND in theexperiments. Thisfigure shows that thepresentMND model can successfully explain the experimental MND by firstorder approximation. Thus the MND rate meter presented in this paperhas some amount of experimental basis for reliabilitywithin some error.
3.3. Application to the Izu-Oshima 1986B subplinian eruptions
It is important to compare other independent estimations orproxies for decompression rates with those given by the present MND
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rate meter. We provide the preliminary MND data for the Izu-Oshima1986B subplinian eruption for which eruption column height data as afunction of time by direct observation are available. Here, weperformed a chronological comparison of the MND decompressionrate and the observed column height as an indicator of the exitvelocities, and argue that theMNDmethod can be applied to explosiveas well as effusive eruptions.
The Izu-Oshima 1986B subplinian eruption was documented for itsgeophysical (e.g. Okubo andWatanabe,1989; Hashimoto and Tada,1990),petrological (e.g. Fujii et al.,1988), and geochemical (e.g. Hirabayashi et al.,1988) aspects. Fig.10a shows the change in the height of the columnwithtime (Abe and Takahashi, 1987). The groundmass compositions of scoria(rare phenocrysts) produced by the eruption are classified into andesitewith SiO2=54.5 to 58.5 wt.% (preliminary data by EPMA). The vesicle
Fig. 10. Temporal variation of the eruption column height for the Izu-Oshima 1986Bsubplinian eruption (Abe and Takahashi, 1987). (b) Temporal variation of textural typesof microlite: poor (A-type), intermediate, rich(B-type) for scoria sampled at 1.2 kmnorth (locality OI) from the craters and (c) 2 km east (locality UI). Deposits areapproximately 50 cm (OI) and 30 cm (UI) in thickness. Unit number indicates thestratigraphic position from the bottom.
texture varies fromsample to sample; fromspherical bubbles to coalescedvesicles with irregular interfaces. Tentative BNDs (bubble numberdensity) are around 1010 to 1013 (m−3). The microlite texture can beclassified into two types: A-type (microlite-poor (not extraordinarilypoor) and low MND) and B-type (microlite-rich and high MND) (Fig. 11).The transition between these two types is continuous; therefore theclassification is both qualitative and tentative. General A-type scoria has ahigher vesicularity with spherical bubbles whereas B-type scoria has alower vesicularitywith vesicles that are irregular in shape. The proportionofmicrolite textural types indicates thedominantdecompressionprocess;A-type: lower decompression rate, and B-type: higher decompressionrate. Fig. 10b and c show the chronological variation of the proportion ofeach type in the scoria sampleswith approximately the same size (10mmin diameter). From Fig. 10, we can recognize that the temporal change intexture which indicates a low-high-low variation in the decompressionrate with time correlates with the low-high-low variation in the columnheight, which suggests that the magmas producing a higher columnascent with a higher decompression rate and ascent velocity at themicrolite nucleation depth. An important fact is that themicrolite texturealso correlates with the groundmass composition: A-type scoria has ahigher in SiO2 content upto 58wt.%whereas B-type scoria has a relativelylow SiO2 content— around 55 wt.%.
For quantitative estimation, we derive the value of k for the MNDwater-exsolution rate using CΔSi=8 wt.% for A-type and CΔSi=5 wt.%for B-type with the same water content (Cw=1 wt.%; this is ahypothetical value); and then,
kPyA ¼ 1:1� 10�13 ð13aÞ
for pyroxene microlite in A-type scoria, and
kPyB ¼ 5:4� 10�13 ð13bÞ
for pyroxene microlite in B-type scoria. Typical MND values of A-typeand B-type are 1015 and 1017(m3), respectively. These values and Eqs. (6),(13a,b) and (10) lead towater exsolution rates of 0.001wt.%/s for A-typescoria and 0.12 wt.%/s for B-type scoria and corresponding decompres-sion rates of 1.2×104 Pa/s for A-type and 1.3×106 Pa/s at the pyroxenemicrolite nucleation depth. These values are higher than those obtainedfor the Unzen dome eruption estimated in the next section, by aroundone to threeorders ofmagnitude. Further, usingEq. (12),we estimate theascent velocity to be 1.3 (m/s) for A-type scoria and 133 (m/s) for B-typescoriawithabulkdensityof 1000 (kg/m3). Finally, it shouldbenoted thatA-type and B-type scoriae (with similar sizes) are found with varyingproportions within the same stratigraphic height in the deposits at thesame locality for unknown reasons.
4. Application to the Unzen 1991–1995 eruptions
Since the application of the MND rate meter to the Unzen 1991–1995 dome eruptions is extensively described in Noguchi et al. (2008-this issue), here, we briefly address the summary of its application. Inorder to apply the MND water exsolution rate meter (Eq. (6)) to theplagioclase microlites of samples collected from the Unzen domeeruptions of 1991–1995, we substitute ΔCSi=18 and ΔCw=3.5 (seebelow) in Eqs. (6) and (7a). Then, we have
jdCw
dt j ¼ 2:8� 10�15N2=3pl ð14Þ
For the MND data obtained in the range of 1014 to 1015 (m−3)(Noguchi et al., 2008-this issue), this equation yields 6.1×10−6 and2.8×10−5 (wt.%/s) as the water exsolution rates. The bound of a, ±1, inEq. (2a) (or ±2/3 in k (Eq. (7a))) yields a lower bound multiplied by 0.2and an upper bound multiplied by 4.6 for the estimation.
In order to apply the MND decompression rate meter (Eq. (10) to theplagioclase microlites, we require the water content at the microlite
Fig.11. Photomicrographs andmanually traced gray scale images ofmicrolite texutes of the Izu-Oshima 1986B subplinian eruption. (a) A-type (reflected right, width=100 µm) from theuppermost part of OI. (b) gray scale image of (a). black=plagioclase, gray=clinopyroxene, white=glass. (c) B-type (same magnification as (a)) from the uppermost part of UI, (d)grayscale image of (c).
Fig. 12. Anorthite content of plagioclase at the liquidus as functions of the water contentin the Unzen dacite and Izu-Oshima basaltic andesite melts by the MELTS and byexperiments for the Soufriere Hills by Couch et al. (2003a). It should be noted that theanorthite content at Cw≈4.7 wt.% changes abruptly in the MELTS calculation; this is dueto a change in the precipitation sequences of clinopyroxene and plagioclase. Oxygenfugacity is assumed to be NNO+2 (Sato et al., 1999) for the MELTS calculation. Fourexperimental data were read in Fig. 4 of Couch et al. (2003a). Note that the anorthitecontent of 45 leads to 3.5 wt.% of thewater content according to the experimental result.
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nucleation for the determination of c (Eq. (9)). We use the anorthitecontent of the plagioclase microlites as an indicator of thewater contentat the nucleation. The anorthite content at the plagioclase nucleationdepends on the melt composition and water content, as shownexperimentally (e.g., Housh and Luhr, 1991; Couch et al., 2003a; Takagiet al., 2005). Based on this feature of the plagioclase composition, weestimate the water content at the plagioclase nucleation. At present,there is no experiment using the Unzen samples, in which An contentdata are systematically provided, sowe estimate the anorthite content ofplagioclase by experiments for Soufriere Hills Volcano, Montserrat,carried out by Couch et al. (2003a). Fig.12 shows the anorthite content ofplagioclase at the liquidus estimatedby the experiment and theMELTS inwhich most of the important thermodynamic data on the phaseequilibria for various compositions of melts are taken into account.From thisfigure, it can be recognized that theMELTS gives systematicallyhigh An content of liquidus plagioclase relative to experiments, thoughthe composition of starting material in experiments is slightly differentfrom the Unzen composition (see Noguchi et al., 2008-this issue). Thisdiscrepancy is not significant for the MND rate mater itself (the liquidusslope is essential), but it becomes important in estimating the watercontent at the nucleation of plagioclase microlite by the An content as afunction of thewater content. Herewe consult the experimental data byCouch et al. (2003a,b) for An content. From this figure and data of the Ancontent of plagioclase microlites (An≈45 for smaller microlites whichcontrol the MND), we obtain Cw=3.5(wt.%), which corresponds to asaturation pressure of 70 MPa (see Fig. 12).
Then, theMND decompression rate meter can bewritten as follows:
jdPWdt j ¼ 1:1� 10�7N2=3pl ð15Þ
By applying this equation to theMND data of the Unzen 1991–1995eruptions, we obtain the decompression rates ranging from 240 to
1100 (Pa/s). The estimated value has the bound (the lower and upperbounds are multiplied by 0.2 and 4.6, respectively).
Further, Eq. (12) yields the ascent velocities in the conduit as 0.015 to0.068 (m/s) for ρ=1684 (kg/m3) of the vesiculated magma in a closedsystem (melt density is assumed to be 2500(kg/m3)). By assuming a
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completely degassed magma (open system), i.e., ρ=2500(kg/m3), Vn isestimated to be 0.01–0.046 (m/s). The implication of these estimatedvalues of the water-exsolution rate, decompression rates, and ascentvelocities is discussed in greaterdetail inNoguchi et al. (2008-this issue).
5. Discussions
We address some issues related to the use of the MND waterexsolution rate meter and the problems involved in the assumptionsand method. First, in the case of Eq. (1), it is assumed that microlitenucleation occurs as a single event in a closed system. Although it isdifficult to verify this assumption from the textural evidence of theeruption products, we can examine the applicability of this assump-tion to the samples from the crystal size distribution (CSD). Theexponential distribution is considered to result from the nucleationand growth processes in a batch system (Marsh, 1998). On the otherhand, the power–law–type distribution is related tomultiple events ofnucleation or magmatic mixing (locally open system). Most of theUnzen samples used in the present study exhibit exponentialdistributions in lower size ranges where the size of microlites ischemically confirmed to be formed due to the decompression-inducedcrystallization (Noguchi et al., 2008-this issue).
It is well known that some of the open systems in chemicalengineering produce an exponential distribution. However, it is unlikelythat microlites with sizes less than several tens of µm can cause a fluiddynamic size segregation in such highly viscous magmas. Thus, webelieve that a single event of microlite nucleation occurred in the Unzensamples used in the present analysis.
In order to estimate the kinetic factor a or k, we use the crystal-lization data on the water-poor mafic dikes. The effect of the bulkcomposition of melts on the diffusivities is considered in theestimation. a includes the effects of the latent heat release and theshape of liquidus curves of plagioclase and pyroxene in the anhydrouscomposition-temperature space (as shown in Fig. 2). However theseeffects are parametrically taken into account by the kinetica factor afrom the numerical study (Toramaru, 2001).
Actually, melts, plagioclase, and other microlite minerals such aspyroxene form a multicomponent system. However, the growth rate ofsuch solid solution minerals is influenced only by the diffusion of theslowest species in the melt and not by the (coupled) diffusion processwithin the crystal. Muncill and Lasaga (1987, 1988) attempted to solvethis diffusion effect in themelt by incorporating it into the viscosity termof the growth rate by assuming a reaction-limitedmechanism. Themostaccurate method is to solve the multicomponent diffusion in the meltsurrounding a growing crystal and then include this effect into theMNDformulation. However, this procedure does not appear to be successfulbecause the nature of multicomponent diffusion still requires under-standing, as shown recently bymany related articles (Chakraborty et al.,1995a,b; Liang et al., 1996a,b, 1997; Richter et al., 1998; Mungall et al.,1998; Mungall, 2002), and because the growth rate of a solid-solutionnucleus with a critical size has not been formulated thus far. Therefore,to avoid the ambiguity and uncertainty induced by the inclusion of thiscomplex process, we selected a method in which the diffusion effect istaken into account solely by the Si diffusion,which is the slowest speciesin commonmelts. This method was based on the result of Baker (1992)and Liang et al. (1996a) that silicon diffusion is the slowest process indacite and rhyolite. Si diffusionwas incorporated into themodel throughthe viscosity, similar to Muncill and Lasaga; but the Stokes–Einsteinrelation is broken in the relation used in the present model which maybe more realistic as pointed out by Muncill and Lasaga (1988). Thus, webelieve that the simplification adopted in the present paper allowsreaders to realize the influence of the composition on the MND ratemeter through the physical properties more clearly.
A recent experiment (Hammer, 2004) suggests that the interfacialenergy of the crystal/melt interface is effectively reduced by theaddition of water. The effect of the water content on the interfacial
energy is not taken into account in the evaluation of a. In addition, thechemical composition of crystals and melts may affect the interfacialenergy. In this study, we consider that γ has no strong systematicdependence on composition, and the bound of a involves theseuncertainties. However in the future, we should aim to determine aaccurately from the precise values of physical properties andlaboratory experiments, and to confirm Eq. (1).
A key factor in the estimation of the water exsolution rate is theevaluation of the liquidus curve as a function of the waterconcentration in the melt. Hence, we recommend, if possible, thatthe value of slope |dTL/dCw| should be determined from experimentsusing natural samples of a target eruption, although in the presentpaper, we have used MELTS for the estimation. The thermodynamicmeaning of the slope is discussed in the Section 2.4.
It is important to determine the water content at the microlitenucleation or the pressure for the calculation of k. With this regards, weconsulted the experimental results using the different compositionrather than the METLS calculation. The MELTS provides the reasonableslopes of phase boundaries owing to the thermodynamic data onwhichit is based. However in estimating the water content from the anorthitecontent of plagioclase microlite, the absolute value estimated foranorthite content appears to have some ambiguity. Thus the experi-ments is highly desired to determine the anorthite content as functionofthe water content at the water-saturated state for the target eruption.With regards to pyroxene, we also need to carry out experiments fornucleation condition because of no manner to estimate the nucleationcondition (pressure or water content).
The coupling between the vesiculation and crystallization can beexpected because the vesiculation makes the system supersaturatedfor the crystallizing components, which in turn makes the systemsupersaturated for the volatile components. The vesiculation that isenhanced by crystallization accelerates the crystallization. The super-saturated and disequilibrium state for both crystallization andvesiculation continues until the crystallization and water exsolutionare completed. However, such an achievement of the reaction is notaccomplished in natural products by effusive and explosive eruptions.Thus, a precise interpretation of the texture of volcanic rocks requiresa rigorous understanding of the coupling of vesiculation and crystal-lization during the later stages.
We now comment on the relation between the decompression rateestimated using the BND (bubble number density) decompression ratemeter (Toramaru, 2006) and the MND meter. The BND estimates thedecompression rate at the bubble nucleation depth, whereas the MNDestimates it at themicrolite nucleation depth. Hence, the BND estimatesthe decompression rate in a deeper part of the conduit. Thus, we candetermine the change in the decompression rate along the magmaascent in the conduit using both the BND andMND decompression ratemeters.
6. Conclusions
We have developed a method using the MND (microlite numberdensity) to quantitatively estimate the water exsolution rate, decom-pression rate, and ascent velocity at the microlite nucleation depth.This method assumes the equivalence between the cooling-inducedcrystallization and the decompression-induced crystallization. On thebasis of this assumption, we have determined the kinetic factorcontrolling the relationship between the MND and the waterexsolution rate by observing the natural experiment of crystallizationin mafic dikes. In order to incorporate the effect of the meltcomposition we take into account the diffusivity in the melt as afunction of the viscosity, which depends on the melt composition. Thethermodynamic factor controlling the relation between the liquidusand dissolved water content is examined in order to develop the MNDwater exsolution rate meter. The validity of this method is supportedby a comparison with the experiments and the independent evidence
166 A. Toramaru et al. / Journal of Volcanology and Geothermal Research 175 (2008) 156–167
from the chronologically well documented Izu-Oshima 1986B sub-plinian eruption. In the MND decompression rate meter, certainlimitations arise with regard to the disequilibrium vesiculation and inthe determination of the kinetic constant; these limitations has beenaddressed. The application of this method to the Unzen 1991–1995dome forming eruptions is briefly summarized.
Acknowledgments
This study was partially supported by a Grant-in-Aid for ScientificResearch from MEXT (No.14080202 and No.17340131) and the MEXTproject “Unzen Volcano: International Cooperative Research withScientific Drilling for Understanding Eruption Mechanisms andMagmatic Activity”.
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