Folch y Marti Modelo de Caldera

Earth and Planetary Science Letters xxx (2009) xxx–xxx

EPSL-09681; No of Pages 8

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Earth and Planetary Science Letters

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Time-dependent chamber and vent conditions during explosivecaldera-forming eruptions

A. Folch a, J. Martí b,⁎a Earth Sciences Division, Barcelona Supercomputing Center—Centro Nacional de Supercomputación, Edifici Nexus II, c/ Jordi Girona 29, 08034 Barcelona, Spainb Institute of Earth Sciences “Jaume Almera” (IJA-CSIC), c/Lluís Solé Sabarís s/n, 08028 Barcelona, Spain

⁎ Corresponding author.E-mail address: [email protected] (J. Martí).

0012-821X/$ – see front matter © 2009 Published by Edoi:10.1016/j.epsl.2009.01.035

Please cite this article as: Folch, A., Martí, J.,Planet. Sci. Lett. (2009), doi:10.1016/j.epsl.2

a b s t r a c t
a r t i c l e i n f o
Article history:
We use a modified version Received 13 July 2008Received in revised form 25 January 2009Accepted 26 January 2009Available online xxxx
Editor: T.M. Harrison

Keywords:collapse calderasring faultmagma chambermodelling

of the CPIUC model [Macedonio, G., Neri, A., Martí, J., Folch, A., 2005. Temporalevolution of flow conditions in sustained explosive eruptions, Journal of Volcanology and GeothermalResearch, 143, 153-172] to simulate chamber and vent conditions during the different phases of a piston-likecaldera-forming eruption. Our idealized caldera-forming scenario assumes an initial central-vent conduitthat, after critical chamber decompression, migrates to a fissure-vent peripheral conduit(s). Furtherdecompression leads to final piston-like subsidence which stops only after the virtual destruction of themagmatic reservoir. The simulations find that the pressure at the conduit entrance drops during thedecompression phases at a rate depending on the conduit geometry, chamber volatile zonation andfragmentation threshold. The higher the volume contrast between the initial central-vent and the finalperipheral fissure-vent conduits, the higher the pressure drop and the jump in the mass eruption rate.Pressure increases back to lithostatic during piston subsidence while some compressible magma remainswithin the chamber. Finally, during the later phase, pressure experiments a gentle increase or decreasedepending on the balance between deposition of intra-caldera material and decrease in the contents ofvolatiles as deeper chamber levels are tapped.

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1. Introduction

The classical scenario for the formation of collapse calderas is thatof a magma chamber underpressurized below a critical value due tothe removal of magma during an eruption (e.g. Williams, 1941; Smithand Bailey, 1968; Druitt and Sparks, 1984; Martí et al., 2000). Analogueexperiments based on this evacuation scenario (e.g. Komuro, 1987;Marti et al., 1994; Roche et al., 2000; Acocella et al., 2000; Walter andTroll 2001; Lavalleé et al., 2004; Geyer et al., 2006) reproduce moststructural features like fractures, faults, or regions with different stressregimes, and provide a clear link between the aspect ratio of themagmatic reservoir and the resulting caldera morphology. In turn andcomplementary, a number of theoretical models try to assess thefraction of erupted mass or, equivalently, the chamber pressure drop,necessary to trigger the collapse depending on the chamber geometryand magma properties (Druitt and Sparks, 1984; Bower and Woods,1997; Martí et al., 2000; Roche and Druitt 2001). Other caldera-forming scenarios not conforming this classical view include collapseby opening of ring-faults due to regional doming beneath a shallowsill-like-shaped overpressurized reservoir (Komuro et al., 1984;Gudmundsson et al., 1997; Gudmundsson 1998) or faulting by

lsevier B.V.

Time-dependent chamber an009.01.035

chamber overpressure in a extensional regional stress filed (Gud-mundsson 1988; Gray and Monaghan, 2004).

Regardless of the triggering mechanism, it is clear that theinitiation of a collapse caldera changes dramatically the ambientconditions in the magmatic reservoir and, simultaneously, providesnew paths for magma to reach the surface through peripheralconduits or fissures (Martí et al., in press). Such physical andgeometrical changes have a large impact on the conditions at thevent and modify the dynamics of the caldera-forming eruption. Aclassical example of these changes is the transition from plinian tolarge-scale ignimbritic eruption observed in the deposits of manycaldera-forming eruptions (Williams, 1941; Smith and Bailey, 1968;Druitt and Sparks, 1984; Newhall and Dzurisin, 1988; Geyer andMartí,2008, and references herein). Due to the tremendous destructivepotential of caldera-forming eruptions, the comprehension and quan-tification of these changes becomes a relevant issue to predict, troughmodelling, the dynamics of such events. Studies on the temporalevolution of the physical conditions at the vent during caldera-forming eruptions are, however, surprisingly scarce and almostlimited to fieldwork and to the analysis of the distribution of lithicsin the pyroclastic deposits (Hidreth and Mahood, 1986; Druitt andBacon, 1986; Suzuki-Kamata et al., 1993; Rosi et al., 1996; Pittari et al.,2008). The few existing theoretical models on caldera-formingeruptions (Druitt and Sparks, 1984; Bower and Woods, 1997;Gudmundsson 1998; Martí et al., 2000) are limited to the pre-collapse

d vent conditions during explosive caldera-forming eruptions, Earth

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phase and do not analyze the dynamics during the collapse. Here weextend the CPIUCmodel (Macedonio et al.; 2005) and use it to derive arough first-order approach for the chamber and vent(s) conditionsduring the whole caldera-forming eruptive sequence. It is importantto note in advance that caldera-forming eruptions are complexphenomena and may have very different behaviours due to a numberof reasons (Martí et al., 2008, in press). A detailed analysis of anyparticular case is out of the scope of this paper. Our final goal is toobtain, by means of simple modelling, general trends shared by theseparticular eruptions and to highlight the strong time variability ofrelevant physical parameters like pressure or mass eruption rate(MER). This is particularly critical for models on volcanic plumes andpyroclastic flows because, regardless their complexity, most simula-tions still assume time-independent boundary conditions at the vent.

2. Modelling scenario

We focus on the classical scenario of a piston-like coherentcollapse following the decompression of a shallow volatile-rich felsicmagma chamber (Druitt and Sparks, 1984; Martí et al., 2000) (Fig. 1).Our idealized sequence starts with an overpressurized chamber, withthe overpressure being caused by the exsolution of volatiles from afractional crystallization process and/or by the injection of freshmagma into the reservoir. When the chamber overpressure exceedsthe strength of the surrounding rocks an eruption is triggered trough asingle central-vent cylindrical conduit, leading to a progressivechamber withdrawal and decompression (Fig. 1a). The exact locationof the conduit relative to the chamber is not relevant to our model. It is

Fig. 1. Plan view and cross section schematic representation of the three-stage caldera-formcritical pressure drop ΔP1(−) is reached at t= t1 time subsidence of the reservoir roof starts, inmigration of the conduit from the central-vent to a fissure-vent (s) located along the margimarginal faults and the final formation of the bounding ring-fault. c) The piston-like block suassumed to flow along the same fissure-vent(s), which are the only parts of the ring-fault t

Please cite this article as: Folch, A., Martí, J., Time-dependent chamber anPlanet. Sci. Lett. (2009), doi:10.1016/j.epsl.2009.01.035

important to mention that, in most central-vent eruptions, chamberdecompression will lead to conduit closure, thus ending the eruptionafter removing only a small fraction of the chamber mass (Folch et al.,1998). The conditions for collapse caldera to form are hardly everreached because strict geometrical and mechanical constrains arerequired (e.g. Folch and Martí, 2004; Scandone and Acocella, 2007;Martí et al., 2008). In this paper we assume that these conditions areattained.

Let ΔP0(+) be reservoir overpressure at the eruption onset, wherethe positive sign indicates overpressure with respect to lithostatic andthe subscript indicates the time instant t= t0. Assuming that the con-ditions to maintain the conduit open are verified, chamber decom-pression occurs during the initial central-vent phase until a criticalvalue for the onset of the collapse is reached (Fig. 1b). Analoguemodels (e.g. Acocella et al., 2000; Geyer et al., 2006) find that thecollapse process starts with the appearance of tensional fractures atsurface followed by a ground-down flexure, the nucleation at depth ofinner outward dipping bell-shaped reverse faults that propagateupwards to the surface, and, finally, the nucleation and developmentof the bounding ring-fault set that ultimately permits the coherentpiston-like block to subside (Fig.1c). It follows from these experimentsthat there is a certain pressure drop between the onset of the collapseat time t1 (when the chamber underpressure is ΔP1(−)) (Fig. 1b) and theonset of the piston subsidence at time t2 (when the chamberunderpressure is ΔP1

(−)) (Fig. 1c). Here, the former instant is assimi-lated to the appearance of tensional fractures at surface, whereas thelatter is associated with the complete development of the ring-fault.For simplicity we assume that when the chamber underpressure

ing scenario. a) A central-vent eruption decompresses the magma chamber. b) When avolving the appearance of tensional fractures at surface, ground-down flexure, and thenal fractures. Decompression continues until time t= t2 allowing the progression of thebsides until the virtual destruction of the magma chamber. During subsidence magma ishat act as a conduit.



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equals ΔP1(−) the conduit “instantaneously” migrates from the initial

central-vent to a peripheral fissure or set of fissures that may, or maynot, grow in length or change its location along the forming ring-faultduring the time interval (t1, t2). This transition from a single central-vent to a peripheral fissure-vent(s) is a characteristic feature of manycaldera-forming eruptions (Williams, 1941; Smith and Bailey, 1968;Bacon,1983; Lipman,1984,1997).Well documented examples include,for example, the eruption of the Bishop Tuff (Long Valley caldera) fromsuccessive vents migrating along the ring-fault (Hidreth and Mahood,1986; Wilson and Hildreth, 1997), the ejection of the climacticignimbrite from multiple vents along a ring-fracture system at CraterLake caldera (Suzuki-Kamata et al., 1993), the emplacement of large-scale ignimbrites at the Taupo volcanic centre (Cole et al., 1998), or thecontemporaneous emission from multiple vents that led to theemplacement of the Campanian Ignimbrite deposits at Campi Flegreicaldera (Rosi et al., 1996). Finally, at times greater than t2, during thepiston subsidence phase, we assume that the peripheral fissure-vent(s) remain unmodified. Pressure inside the magma chamber increasesduring this stage up to a value equal to the load of the piston inresponse to the compressive effect of the subsiding block (Martí et al.,2000). We also take into account the increase of load caused by theemplacement of intra-caldera products. In summary, we divide thecaldera-forming scenario in three stages: an initial central-vent phase(with a pressure drop from to ΔP0

(+) to ΔP1(−)), a transitional fissure-

vent(s) phase (with a pressure drop from to ΔP1(−) to ΔP2

(−)), and a finalphase associated with the collapse sensu stricto in which the piston-like block subsides.

3. The physical model

The above three-steps scenario has been simulated using theCPIUC model (Macedonio et al., 2005). CPIUC tracks the evolution offundamental flow variables in the chamber plus conduit systemduring eruptions of volatile-rich magmas. The chamber modelassumes a homogeneous magma composition but allows for verticalgradients in volatiles (chamber zonation) and for arbitrary chambergeometries. The conduit model is based on the averaged mass andmomentum balance equations and assumes homogeneous flow and aconstant Mach number at the vent. Bubble nucleation occursinstantaneously when pressure drops below the nucleation pressuregiven by a solubility law, and a simple fragmentation criteria based onthe gas volume fraction (Sparks, 1978) allows themixture to fragment.Conduit geometry is characterized by the wall friction coefficient Fw(Gilberti and Wilson, 1990), defined as the pressure drop due tomagma friction against the conduit walls. For details concerning themodel see Macedonio et al. (2005). The main advantage of CPIUC isthat it gives a first-order approach and allows to identify the role ofthe different input parameters and to assess which aspects deservefurther detailed study. We stress that results of the model must beconsidered with caution because of the several simplifying assump-tions. Major limitations include the presence of a single volatile com-ponent (water in our case), the equilibrium degassing, the simplicityof the fragmentation criterion (based on the gas void fraction ratherthan on the more realistic strain-rate-dependent glass transition), andthe conduit geometry. In the original version, CPIUC considered onlyvertical cylindrical conduits, for which Fw=−8uµ/r2, where µ is themixture viscosity, u is the mixture ascending velocity in the conduit,and r is the conduit radius.

We have modified the original version of CPIUC to extend themodel to the different phases of our caldera-forming scenario. First,the geometry of the conduit is let to vary in time when the pressuredrop equals ΔP1(−) in order to model the transition from a central-ventconduit to a peripheral fissure-vent conduit(s). Fissure-vents areassumed to be vertical, a reasonable hypothesis in the context of acaldera-forming eruption (Folch and Martí, 2004; Martí et al., 2008).The modification of the model affects the friction coefficient in the


momentum equation, which for a fissure is Fw=−12uµ/w2, and thecross section of the conduit, which varies from to πr2 to Lw. In theexpressions above w and L are, respectively, the fissure width andthe fissure length. Fissure length is let to vary linearly in time betweentwo user-defined values during the transitional phase. This allows tosimulate the effect of a progressive enlargement of a peripheralfissure and/or the opening of multiple fissure-vents located along thenucleating ring-fault. Second, once the critical underpressure ΔP2

(−)

has been reached, the chamber roof is let to move downwards tosimulate the piston subsidence. This modification affects the chambergeometry (the chamber volume decreases) but not the conduitdimensions (width, length and depth) which, for simplicity, areassumed to be constant during the piston subsidence. Collapse goeson at a user-defined rate and pressure at the chamber top is deter-mined by mass conservation requirements (at any time slice theconduit mass flow rate times the time step must equal the massremoved by the combined effects of pressure variation and chambervolume decrease). Subsidence proceeds until a user-defined frac-tion of the chamber volume has been extruded. We consider values of80–90%, implying that the subsidence (i.e. the eruption) ceases onlyafter the total destruction of the chamber. This assumption issupported by multiple examples where collapses are followed by along period of repose, a new chamber rebuilding, and the initiation ofa new eruptive cycle (Self et al., 1986; Lipman, 1984; Newhall andDzurisin, 1988; Nairn et al., 1995; Marti and Gudmundsson, 2000) andalso from theoretical models (Martí et al., 2000).

4. Results

For a given temperature and magma composition, the eruptiondynamics in the CPIUC model is mainly controlled by the pressurevariations within the magmatic reservoir, the chamber and theconduit geometries, the mass fraction of volatiles and the thresholdvalues for fragmentation. We have performed different sets ofsimulations changing one of these input parameters within reason-able bounds to look into its effect on the pressure drop, MER, andpositions of the exsolution and fragmentation fronts. All the simu-lations assume the chocked-flow condition at the vent (Mach numberequal to 1) but we have verified that, the rest being equal, the Mach atoutflow has little influence on the pressure drop and MER. Aspreviously mentioned, the geometry of the chamber is, in our case, farfrom arbitrary. Analogue models (e.g. Roche et al., 2000) show that, inorder to have a coherent piston-like collapse, the chamber aspect ratio(chamber depth to extension ratio) must be in the range or lowerthan 0.7. This result is in agreement with numerical simulations (e.g.Gudmundsson et al., 1997; Burov and Guillou-Frottier, 1999; Folch andMartí, 2004; Hardy, 2008) which, in addition, identify also sill-likegeometries as the most likely to favour the formation of ring-faults. Inconcordance, we have limited the spectrum of simulations to thesechamber shapes and aspect ratios.

4.1. Reference case and general trend

Table 1 summarizes the model input values for a reference runwhich illustrates the predictions of the CPIUCmodel during the wholecaldera-forming sequence. Clearly, the quantitative results vary fromrun to run, but a general qualitative trend is found in all thesimulations. The reference run assumes an initial overpressure of15 MPa, migration to the fissure-vent when the underpressure is15 MPa, the initiation of subsidence after a drop of 40 MPa and, finally,the end of the eruption after removing 90% of the chamber mass.These critical pressure drops represent averaged natural values for thetensile and the shear strength of the crust in volcanic environments(Toulokian et al., 1981). Collapse velocity has been set to 30 m/h. Fig. 2shows the evolution of the pressure drop at the top of the chamber(conduit entrance). The transition from the central-vent to the fissure-



Table 1Input values for the reference run

Value Units Comments

Chamber Width 6 km The value of the chamber aspectratio is consistent with coherentpiston-like experimental collapses.

Height 2 kmDepth 4 kmAspect ratio 0.66 –

Conduit Radius (cylinder) 50 m The conduit is a cylinder during theinitial central-vent stage and afissure of constant length during thetransitional and subsidence phases.

Width (fissure) 25 mLength (fissure) 1 km

Pressure Lithostatic 95 MPa Value at the chamber topassuming an averaged rockdensity of 2420 kg/m3.

OverpressureΔP0

(+)15 MPa Representative value for the

host rock tensile strength.Drop ΔP1

(−) −15 MPaDrop ΔP2

(−) −40 MPa Representative value for thehost rock shear strength.

Magma Composition Rhyolitic –

Liquid density 2400 kg/m3

Temperature 900 °CCrystal contents 10% –

Crystal density 3000 kg/m3

Viscosity law – From Hess and Dingwell (1996)Volatile type H2O – Exsolution model from Zhang (1999)Volatile contents 4.25% – From 4.25% at the chamber top

to 3.25% at the chamber bottom.Fragmentationvoid fraction

0.75 –

Values are characteristic of natural systems but do not represent any specific eruption.


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vent occurs, for this particular simulation, after removing 2.4% of thechamber mass. During the transient stage, subsequent extrusion ofmagma trough the peripheral fissure yields to further decompressionbut at a different rate reflecting the difference in volume between theinitial central-vent conduit and the new fissure-vent conduit(s). Ingeneral, the higher the cross-section (volume) of the fissure-vent,the steepest the pressure drop. Since the CPIUC model assumes aninstantaneous adjustment of solubility to the ambient conditions, thedecompression phases are accompanied by a progressive deepening ofthe exsolution level (see Fig. 3). The situation changes dramatically at

Fig. 2.Model results for the reference run reported on Table 1. Left: evolution of the pressurethe beginning of the eruption. The most distinctive eruptive phases are marked. Percentageslithostatic pressure value is recovered during the subsidence, two end-member situationsdeposition. The calculated MER values are of the same order of magnitud than those estima


the onset of subsidence which, for this particular simulation, occursafter removing 8.9% of the chamber mass. The piston subsidencecompresses the remaining magma and progressively forces pressureto increase, reaching the lithostatic value (95 MPa) when 21.5% of thechamber mass has been erupted. The exsolution front in the chamberresponds to the pressure increase, shifts upwards, and eventuallyreaches the conduit, leaving the chamber full of undersaturated(incompressible) magma. We highlight that, in general, the lithostaticpressure at the chamber top is not constant but increases graduallydue to the emplacement of intra-caldera products. The two plotbranches in Figs. 2 and 3 correspond, respectively, to the end-membersituations inwhich all the eruptedmaterial fills the caldera depressionor is completely emplaced away from it.

During the initial central-vent phase, theMER decreases gently dueto the combined effect of the pressure drop (pressure differencebetween chamber and vent decreases gradually) and the inflow ofmagma less rich in volatiles as deeper levels of the reservoir are tapped.The opening of the fissure-vent(s) produces a sharp discontinuity ofthe MER which grows by almost an order of magnitude in response tothe changes in conduit geometry and volume (from cylindrical tofissure and from ≈0.01 km3 to 0.1 km3 in volume). Further decom-pression during the interval (t1, t2) is accompanied by a second MERdecrease until piston subsidence starts. Compression of the residualmagma increases theMERwhich reaches a plateau once the lithostaticequilibrium has been recovered. Depending on the balance betweenthe increase of lithostatic pressure by intra-caldera deposition (whichtends to increase the MER) and the decrease in volatiles due to tapingof deeper chamber levels (which tends to decrease theMER), the slopeof the plateau results slightly positive or negative (Fig. 2, branches aand b respectively).

4.2. Role of the chamber zonation

Previous theoretical models (e.g. Martí et al., 2000) have suggestedthat volatile-zoned chambers need to erupt a minor fraction of massthan volatile homogeneous reservoirs to reach the same pressuredrop. This phenomenon is illustrated in Fig. 4, which compares thereference run (poorly-zoned chamber, gradient in volatiles from 4.25%

drop at the top of the magma chamber. Drops are referred to the lithostatic pressure atindicate the chamber mass erupted at different phases. Left: MER versus time. Once theare shown: (a) maximum and (b) minimum (zero) roof load increase by intra-calderated for plinian and ignimbritic eruptions (e.g. Pyle, 2000).



Fig. 3.Model results for the reference run reported on Table 1. Depth of exsolution front (left) and fragmentation level (right) versus time. The initial depth of the chamber is 4 km. Thedepths of the chamber roof and base are indicated by discontinuous lines. In the CPIUC model, the exsolution level instantaneously fits to pressure variations.


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at top to 3.25% at bottom) with a simulation having a higher gradient(from 4.25% to 1.25%). In the poorly-zoned case piston subsidencestarts after removing 8.9% of mass, whereas only 4.8% is required forthe highly-zoned case. Highly-zoned reservoirs anticipate the collapsebut, in contrast, extend the duration of the subsidence phase becausethe plateau of the MER decays (Fig. 4b).

4.3. Role of the peripheral conduits

The dimension of the peripheral fissure-vent(s) is another impor-tant parameter for the eruption dynamics. Although the location ofthis conduit is not relevant to the CPIUCmodel, different scenarios can

Fig. 4. Effect of different volatile (water) gradients on the pressure drop at the top of the resertop, 1.25% at bottom) and (b) poorly-zoned (4.25% to 3.25%) chambers. The rest of paramet


be simulated by changing the length and/or the width of the fissure.One end-member case is that of a fissure with constant length, whichcould represent a single fixed peripheral vent or, alternatively, a ventthat migrates along the ring-fault keeping a similar size. The otherend-member situation is that of a ring-fissure that opens up to themaximum length (the projection of the chamber margins). This is ananalogue for a collapse with extrusion trough an annular-conduit, i.e.represents an extreme and rather unrealistic situation where thewhole ring-fault serves as a conduit. Legros et al. (2000) discussed theeffect of conduit geometries on fountains and pyroclastic flows. Aconclusion of their analysis was that perfectly annular ring-fissureconduits do not favour the formation of pyroclastic flows and, from

voir (left) and on the MER (right). Results are illustrated for (a) a highly-zoned (4.25% aters are as in Table 1.



Fig. 5. Effect of two different fissure-vent conduit geometries on the pressure drop (left) and MER (right). Results are for (a) a 25 m width fissure that grows in length from 100 to1000 m during the transition phase and (b) a 25 m width fissure of constant length (100 m). This could represent a single peripheral fissure-vent or the migration of a fissure-ventalong the ring-fault. The rest of parameters are as in Table 1. The jumps in the MER are marked (a) or smooth (b) depending on the differences between the volumes of the initialcentral-vent and the subsequent fissure-vent conduit(s). For visualization purposes, case (b) plot is cut after 150 h, when only 16% of the chamber mass has been removed.


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the occurrence of pyroclastic flows in virtually all caldera-formingeruptions, inferred that magma ascent should be mainly localised inmore restricted conduits or parts of the ring-fissure. In fact, lithicsdistribution studies in caldera deposits suggest that the opening of aneruption through ring faults is a progressive process and responds tothe successive opening of multiple vents along the ring-fracture, butnot to its instantaneous transformation into a homogeneous, singlering-fissure vent. In other words, even if the piston-like collapseoccurs along a ring fault, only parts it act as an eruption conduit.

Fig. 6. Effect of two different fragmentation thresholds on the pressure drop (left) andMER (rand 0.90 (b) which represent, respectively, a poor and a rich pumice vesicularity. The rest o


Fig. 5 shows the results for a fissure of constant width (25 m) andlength (100 m) and for a fissure having the same width but a lengththat increases by an order of magnitude (from 100 m to 1 km) duringthe time slice (t1, t2). In both cases the pre-collapse cylindrical central-vent conduit is 50 m in diameter (cross section ≈2000 m2). For theCPIUC model, a varying-in-time fissure can represent a single fissurethat grows in length or a gradual opening of multiple fissure-vents atdifferent locations along the ring-fault. The largest the contrastbetween the size of the conduits the fastest the pressure drop and the

ight) plotted versus time. Results for a maximum allowed gas volume fraction of 0.60 (a)f parameters are as in Table 1.



Fig. 7. Effect of two different fragmentation thresholds on the depth of exsolution front (left) and fragmentation level (right) plotted versus time. Results for a maximum allowed gasvolume fraction of 0.60 (a) and 0.90 (b). The rest of parameters are as in Table 1. The depths of the chamber roof and base are indicated by discontinuous lines.


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sharpest the discontinuity in the MER that precedes the plateau phase(Fig. 5b).

4.4. Role of the fragmentation threshold

Finally, the effect of the fragmentation criterion, based on a maxi-mum allowed gas void fraction, is illustrated on Figs. 6 and 7. Thehigher the fragmentation threshold (i.e. the higher the vesicularity ofthe resulting pumices), the slower the pressure drop and the MER.

5. Summary

We have modified the CPIUC model in order to track chamber andvent conditions along the different stages of the caldera-formingscenario (central-vent conduit, transition to peripheral fissure-ventconduit(s), and piston-like subsidence). It is obvious that, in practise,eruptions can be very complex and dependent on several uncontrol-lable factors. Furthermore, predictions of first-ordermodels like CPIUCmust be interpreted on a semi-quantitative basis only. Notwithstand-ing this, simulations point out that parameters like pressure drop,MER or fragmentation level can experiment large variations duringthe successive phases of a caldera-forming eruption. This is of concernto more sophisticated sub-aerial models, which should change itsboundary conditions in time accordingly.

The quantitative results doobviously vary from run to rundependingon the input parameters but, nevertheless, a general common trend isfound. Pressure at the conduit entrancedrops during the decompressionphases at a rate which depends on conduit geometry, volatile contentsand fragmentation threshold. Highly-zoned chambers, large volumecontrasts between the central-vent conduit and the peripheral fissure-vent conduit(s), and low vesicularity of the resulting pumices produce afaster pressure drop and a sharper discontinuity in the MER. Duringthe piston-like subsidence stage pressure increases back to lithostaticand the MER experiments a plateau with a gentle slope of positive ornegative sign depending on the balance between the chamber zonationand the syn-eruptive deposition of intra-caldera material.

Unfortunately, MER data on explosive caldera-forming episodes,including a complete record from the central plinian to the ignimbritic


caldera collapse stages, are practically inexistent. This is in part due tothe lack of observational data on caldera eruptions and also to thevariable degree of preservation of caldera-forming deposits in thegeological record. In the few historical cases reported (e.g. Katmai andPinatubo, in Stix and Kobayashi, 2008) the calderas studied areinterpreted to have formed inmass at a late stage of the eruption, aftera significant proportion of magma has already been erupted and largeundepressures have developed in the chamber, which is not exactlythe general case modelled in our study. In these examples there is asignificant increase of MER from the plinian to the ignimbriticepisodes, but it does not substantially change when the bulk ofsubsidence occurs, since most of the ignimbrites had already beenerupted before the major collapse episodes were initiated. However,the validity of our model is supported by the comparison between thecalculated MER values and those estimated for a diversity of plinianand ignimbritic eruptions (e.g. Pyle, 2000), which are of the sameorder of magnitude.

Acknowledgements

This work has been partially funded by the EXPLORIS project(EVR1-2001-00047). JM is grateful for the MICINN grant PR2008-0207. We thank the careful reviews of two anonymous referees.

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Folch y Marti Modelo de Caldera