RESEARCH ARTICLE

Eruptive versus non-eruptive behaviour of large calderas:the example of Campi Flegrei caldera (southern Italy)

Stefano Carlino & Renato Somma

Received: 20 February 2009 /Accepted: 20 April 2010# Springer-Verlag 2010

Abstract Caldera eruptions are among the most hazardousof natural phenomena. Many calderas around the world areactive and are characterised by recurrent uplift andsubsidence periods due to the dynamics of their magmareservoirs. These periods of unrest are, in some cases,accompanied by eruptions. At Campi Flegrei caldera (CFc),which is an area characterised by very high volcanic risk,the recurrence of this behaviour has stimulated the study ofthe rock rheology around the magma chamber, in order toestimate the likelihood of an eruption. This study considersdifferent scenarios of shallow crustal behaviour, taking intoaccount the earlier models of CFc ground deformation andcaldera eruptions, and including recent geophysical inves-tigations of the area. A semi-quantitative evaluation of thedifferent factors that lead to magma storage or to itseruption (such as magma chamber size, wall-rock viscosity,temperature, and regional tectonic strain rate) is reportedhere for elastic and viscoelastic conditions. Considering thelarge magmatic sources of the CFc ignimbrite eruptions(400–2,000 km3) and a wall-rock viscosity between 1018

and 1020 Pa s, the conditions for eruptive failure aredifficult to attain. Smaller source dimensions (a few cubickilometres) promote the condition for fracture (eruption)rather than for the flow of wall rock. We also analyse theinfluence of the regional extensional stress regime onmagma storage and eruptions, and the thermal stress as apossible source of caldera uplift. The present study also

emphasises the difficulty of distinguishing eruption andnon-eruption scenarios at CFc, since an unambiguousmodel that accounts for the rock rheology, magma-sourcedimensions and locations and regional stress field influen-ces is still lacking.

Keywords Campi Flegrei caldera . Caldera eruption . Yieldstrength .Magma storage . Viscous regime . Elastic regime .

Wall-rock viscosity

Introduction

The Campi Flegrei caldera (CFc) is roughly 12 km wide,with its centre located in the Bay of Pozzuoli, about 15 kmto the west of Naples (Fig. 1). The current caldera shape isthe result of two large collapses, the first of which wasprobably related to the Campanian Ignimbrite (CI; 150–200 km3 dense rock equivalent [DRE]; age, 39 ky BP) andthe second to the Neapolitan Yellow Tuff (NYT; 40 km3

DRE; age, 12–15.6 ky BP) eruptions (Rosi and Sbrana1987; Orsi et al. 1992, 1996; De Vivo et al. 2001; Rolandiet al. 2003; Deino et al. 2004). Since Roman times, the CFcarea has been characterised by slow aseismic subsidence, ata rate of about 1.1 to 2 cm y-1 (Dvorak and Mastrolorenzo1991; Bellucci et al. 2006), which has been interrupted byrecurring phases of rapid uplift that are generally accom-panied by intense seismicity. The study of sea-level markerson Roman coastal ruins has revealed historical groundmovements, with a Roman market-place (Serapis) that wasuncovered in AD 1750 in Pozzuoli being the subject ofmany studies (Dvorak and Mastrolorenzo 1991; Morhangeet al. 1999, 2006). Several phases of uplift have beenrecognised to have occurred in the Middle Ages, prior tothe Monte Nuovo eruption (AD 1538; 0.02 km3 DRE; Lirer

Editorial responsibility: M. Ripepe

S. Carlino (*) : R. SommaIstituto Nazionale di Geofisica e Vulcanologia (INGV),Sezione di Napoli, Osservatorio Vesuviano,Via Diocleziano 328,80124 Napoli, Italye-mail: stefano.carlino@ov.ingv.it

Bull VolcanolDOI 10.1007/s00445-010-0370-y

et al. 1987). More recently, two phases of uplift haveoccurred, during 1970–1972 and 1982–1984, when thetown of Pozzuoli was raised by 1.7 and 1.8 m,respectively. During the 1982–1984 unrest episodes,more than 15,000 shallow earthquakes (at 1–5 km indepth) with a maximum magnitude of 4.0 were recordedby the seismic stations of the Osservatorio Vesuviano(Fig. 2; Presti et al. 2004), and the ground uplift occurred

at an average rate of 0.3 cm d-1. The last episode of unrestindicated the possibility of an imminent eruption, forcingthe authorities to evacuate Pozzuoli; however, the unrestessentially ended in December 1984, without any eruptionoccurring (De Natale et al. 2001).

Studies of the unrest mechanism and caldera dynamicsusing different physical approaches are useful to provideassessments of the volcanic risks of this densely populatedarea. The key issue related to this unrest of CFc is the studyof the physical conditions necessary to trigger an eruption.This is correlated to the physical state of the rock (elastic,elasto-plastic, and viscoelastic) and to the causativedeformation processes at depth (magma, hydrothermalfluids, or a combination of both).

Some studies have presented elastic models of the 1970–1972 and 1982–1984 unrest (De Natale and Pingue 1993;Berrino et al. 1984; Berrino 1994; De Natale et al. 2001;Gottsmann et al. 2006), in which the deformation has beenrelated to the pressure increases in a shallow magmaticbody located below Pozzuoli. Many studies have highlight-ed the problems of modelling realistic values of overpres-sure to accommodate the uplift recorded during the CFcunrest without the occurrence of an eruption (Bianchi et al.1987; Quareni 1990; Bonafede 1991; De Natale et al. 1991,2001, 2006; Trasatti et al. 2005; Gottsmann et al. 2006).Using elasto-plastic and viscoelastic models, Trasatti et al.(2005) and Bonafede et al. (1986) showed that the values ofoverpressure are substantially lower than those obtainedusing elastic models.

More recently, Troise et al. (2007) and Amoruso et al.(2008) showed that a penny-shaped magma intrusion wasresponsible for part of the 1982–1984 uplift and for all ofthe recent minor uplift episodes. This intrusion wasprobably shallow (3–4 km in depth), with an overpressureof tens of MPa.

Despite our relatively good knowledge of the structureand rock properties of CFc (AGIP 1987; Zamora et al.1994; Rabaute et al. 2003; Judenherc and Zollo 2004,Vinciguerra et al. 2006; Zollo et al. 2008), hazard assess-ments for eruptions during the fast uplift phases appear tobe very difficult when compared with other centralvolcanoes that have been investigated (e.g. Mt. St. Helens,Soufriere Hills). In general, the physical state of the shallowcrust of caldera areas is characterised by high geothermalgradients, significant hot-fluid circulation, and voluminousstorage of magma, allowing non-elastic rock behaviour tooccur.

The present study is based on earlier models of CFcground deformation (Bonafede et al. 1986; Bonafede 1991;De Natale et al. 2001; Trasatti et al. 2005) and calderaeruptions (Jellinek and De Paolo 2003), and we analysehere the relationships between the different behaviours ofthe crust (elastic, plastic, and viscoelastic) and the con-

Fig. 1 The Campi Flegrei area. Dashed lines: the caldera rims,produced by larger eruptions (modified after Bellucci et al. 2006),within which uplift and subsidence phases have occurred since Romantimes. Circles: locations of deep wells (AGIP 1987)

Fig. 2 Depth-section locations obtained for 270 earthquakes duringthe last two Campi Flegrei unrest periods of 1970–1972 and 1982–1984 (after Presti et al. 2004)

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ditions necessary for eruption versus magma storage forboth shallow and deep sources. We also evaluate theinfluence of regional extensional stress on magma storageand thermal stresses as contributors to the uplift of thecaldera. However, the purpose of the present study is not toprovide a formal fit to the observed displacements, butrather to understand the behaviour of the wall rock, shouldthere be future caldera reactivation, and the conditions thatmight lead to a future eruption, which is crucial for volcanicrisk assessment of this highly populated area.

The earlier models of ground deformationand the debate on the CFc unrest

The pattern of ground deformation recorded during the1970–1972 and 1982–1984 unrests shows an almostcircular shape that is centred on Pozzuoli. The verticaldeformation decays radially by about 95% over 3 km fromthe point of maximum uplift (De Natale et al. 2006). Usingan isotropic point-source elastic model (Mogi 1958),Berrino et al. (1984) interpreted this pattern of deformationas the effects of a shallow magma chamber that is subjectedto an overpressure of hundreds of mega Pascal. However,the idea of such a magmatic source as a direct mechanismthat produces the uplift at CFc has changed since theseearlier times. There have now been different seismicsurveys of Vp/Vs and Vp velocities in the shallow crust ofCFc, and these have recognised that, below Pozzuoli Bay,there is a complex system of a shallow aquifer (water/gas-saturated and fractured rock; Aster and Meyer 1988;Vanorio et al. 2005; Saccorotti et al. 2007). This aquiferhas an almost cylindrical shape, and it is 1 km in diameterand located at about 3 km in depth, below which the criticalwater/vapour equilibrium occurs (De Natale et al. 2006).The thermodynamic variations (i.e. the arrival of newmagma or hot fluids) of the magmatic system below suchan aquifer will generate changes in the temperatures andpressures of the water system, thus producing grounddeformation (Bonafede et al. 1986; Gaeta et al. 1998).According to this concept, De Natale et al. (2001, 2006)inferred that during these last two crises, the onset of thefast deformation that showed non-linear behaviour is due toincreases in the temperatures and pressures within themagma chamber, the top of which is located at a minimumdepth of about 4 km.

Subsequently, the thermodynamic variations within themagma chamber are buffered by the water system,producing its migration, and hence supplying the largestcontribute to the uplift. Trasatti et al. (2005) presented amodel in which the ground deformation was explained bythe elasto-plastic behaviour of the shallow crust, consid-ering a lower plastic threshold within the caldera, and

consequently, a lower effective rigidity of the innercaldera. The elasto-plastic behaviour was in good agree-ment with the deformation pattern, with the source locatedat about 5 km in depth and characterised by anoverpressure of 40–50 MPa.

Battaglia et al. (2006) provided a good fit to the 1980–1984 deformation pattern, which, during the uplift period,appeared to be due to a horizontal penny-shaped sourcewith an average density close to that of the hydrothermalfluids, while the source that provided the best fit for thedeflation period (1990–1995) was a vertical spheroid withthe same average density. According to the gravity changes,Amoruso et al. (2008) also indicated that the deformationpattern that occurred during the 1982–1984 unrest wasproduced by a shallow penny-shaped magma intrusion,although they ruled out the hydrothermal fluid as theprimary cause of the deformation. However, this last studydid not model the deflation period following the 1982–1984crisis (Amoruso et al. 2008), which is fundamental to fullyunderstand the rheology of the rock and the unrestdynamics. Lima et al. (2009) interpreted the unrest at CFcas a consequence of aqueous fluid exolution during magmasolidification at different timescales. Fluid transport and theconcomitant propagation of hydrofractures, as the fluidexpands from lithostatic to hydrostatic pressure during thedecompression, thus lead to ground-surface displacement(Lima et al. 2009).

The CFc uplift has generally been accompanied byintense seismicity, with about 15,000 events recordedduring the 1982–1984 period (Aster and Meyer 1988;Vanorio et al. 2005). These earthquakes terminated abruptlyat 3.5 to 4.0 km in depth (Fig. 2), suggesting a transitionfrom brittle to ductile behaviour (Hill 1992). This transitionwas also inferred both by the P-SV conversion from activeshots in the Gulf of Pozzuoli and the regional seismicity(Ferrucci et al. 1992), and by the teleseismic waves thatcrossed the caldera (De Natale et al. 2001). Over the last30 years of the seismic monitoring of CFc, the seismicityhas occurred during the periods of fast uplift, while therehas been seismic quiescence during the low subsidencephases.

The controversy relating to what is the source (magma,hydrothermal, or hybrid) that generates the deformation atCFc still continues. The non-uniqueness of the physicalmodels adopted in the literature is provided by the differentinterpretations of the available geophysical data. Forinstance, the inversion of both gravity and deformationdata from the 1982–1984 unrest fits well with sources ofdifferent natures and shapes: magmatic or hydrothermalspherical sources in a viscoelastic or plastic medium;penny-shaped hydrothermal sources in an elastic half-space; and penny-shaped magma intrusions in a layeredelastic half-space. Geophysical investigations have also

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excluded the presence of melt formations down to about7.5 km in depth (Vanorio et al. 2005; Zollo et al. 2008),although the methods used in these investigations did notallow the defining of a shallow magma body with a volumeless than 1 km3.

The phases of rapid inflation have been well-explainedusing all of the above models, while the subsidence phasesthat follow the uplift at rates greater than the secularsubsidence have only been modelled by Battaglia et al.(2006), in terms of the radial outwards migration ofhydrothermal fluids. Hybrid model sources have also beenproposed, in which magma intrusion occurs at the begin-ning of each period of unrest and produces perturbations ofthe geothermal system (De Natale et al. 2001; Battaglia etal. 2006). In this case, the deformation would mainly bedue to upward fluid migration and only to a minor extent tomagma intrusion. This presence of both magma andhydrothermal fluids thus creates difficulties for the model-ling of the CFc unrest. Nevertheless, understanding magma/fluid dynamic interactions in the caldera is a crucial aspect,as these can produce different precursors that would lead tovarious eruptives scenarios.

Another useful approach to assess the possibility oferuptions during the CFc unrest is to have an understandingthe rheology of the rock surrounding the magmatic and/orhybrid source. Indeed, the temperatures, pressures and yieldstrengths of the rock itself will strongly influence itsbehaviour, which will vary from elastic to plastic, orviscous. These different conditions will be taken intoaccount in the following discussion, as they can producerock fracturing and dyke propagation (eruption) or magmastorage (no eruption).

Data and constraints on the behaviour of the CFc crust

Layering and rheology of the CFc crust

Although there is no direct evidence of changes in crustalrheology beneath CFc, the geophysical data that are availablehave allowed the identification of several crust discontinuities(Judenherc and Zollo 2004; Vanorio et al. 2005; Zollo et al.2008). Due to the large number of physical parameters thatcan affect the rock behaviour (e.g. temperatures, pressures,fluid circulation, strain rates, rock rigidities, and differentiallyapplied stresses), only preliminary assumptions can be madeabout crust discontinuities and their relationships with therock rheology of CFc. Despite this, the integration of thetemperatures measured within wells that go down to about3 km (AGIP 1987) with the seismic data represents a reliableconstraint for crustal rheology assessment.

The seismic surveys performed in the Bay of Pozzuoliand the Gulf of Naples have recognised different velocity

transitions from shallow depths down to 15 to 20 km. Atshallow depths, a high Vp/Vi anomaly has been located at0.5 to 1 km in depth, which, together with the character-istics of shallow seismicity in the CFc area, suggests thepresence of rock containing fluids in the liquid phase(Vanorio et al. 2005; Saccorotti et al. 2007). The behaviourof the shallow crust is mainly elastic, as testified by theoccurrence of the majority of the earthquakes down to 2 to3 km in depth. The purely elastic conditions probablypersist down to about 3 km in depth, where the temper-atures approach the elastic limit of ∼350°C. Considering thestrain rate associated with the last rapid uplift that occurredat CFc, of about 5×10-12 s-1, at temperatures above 300°Cthe rock would show a plastic behaviour (Hill 1992;Jellinek and De Paolo 2003). Between 2 and 4 km in depththe rock might display an intermediate behaviour betweenelastic and plastic, or viscoelastic (Bonafede et al. 1986;Trasatti et al. 2005). A further Vp/Vs transition has beenlocated at about 2.7 km in depth, where the rock is probablygas- or brine-saturated (Judenherc and Zollo 2004). Weassume that a brittle to ductile transition is located at about4 km in depth, where the temperatures approach more than500°C, and below which earthquakes occasionally occur(Hill 1992). Since a melt formation down to 4 to 5 km wasruled out by Vanorio et al. (2005) and Zollo et al. (2003),who recognised a low Vp/Vs ratio below the caldera, thequestion still remains the same: where is the magmaactually located? A magmatic body has been inferred froma high-resolution seismic reflection dataset for the Bay ofPozzuoli, which shows a partial melting zone beneath CFcat a depth of 7.5 to 8.0 km (Zollo et al. 2008). A similarmagma body was recognised by Zollo et al. (1996) at about12 km beneath Vesuvius. The boundaries of both of theseextensive magmatic bodies have not been well-defined:Zollo et al. (2008) inferred that the horizontal extension ofthe low-velocity layer beneath CFc should be not less than30 km2, with a thickness of about 1 km (minimum volume,30 km3 ) and a melt fraction between 65% and 90%. In aprevious study, Judenherc and Zollo (2004) suggested theoccurrence of a wider magma chamber (∼2,000 km3) thatwas located at a minimum depth of about 6 km, and whichfed the CI eruption. The lack of evidence of such largemagma volumes located at shallow depths thus suggests thatthey may have solidified, when compared with the volumeof the melt layer inferred from the seismic data (De Natale etal. 2006). Wohletz et al. (1999) used thermal models for theevolution of the CFc magmatic system, and they inferredthat, at present, there is a roughly 450 km3 magma chamberthat is located at a depth of about 4 km. Also in this case, thepercentage of melt must be very small (volume, ≤1 km3),since this has not been revealed by seismic surveys.

The depth at which the melting might occur can also beindirectly inferred from the geothermal gradients recorded

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within the AGIP wells that have been drilled in the CFcarea (AGIP 1987). Extrapolation of the average geothermalgradients to below the critical point of the water (∼3 km indepth) and under a pure conduction thermal regime and aroughly linear gradient, shows that the onset of melting canoccur at different depths below CFc (Fig. 3). Only themaximum geothermal gradient of 220°C km-1, which wasrecorded within the MF 1 well (see Fig. 3), would allowmelting to occur at the same depth as that calculated byZollo et al. (2008; 7.5 km), with a melt fraction above 60%.Considering this gradient, the onset of the melt would takeplace at 5 km in depth, although the melt fraction should bevery low, as it has not been seen by seismic tomography.The percentage of melt calculated by Zollo et al. (2008)appears to be very high when compared with the meltfractions inferred from seismic surveys of other activevolcanic areas. For instance, beneath the active AxialVolcano (Juan de Fuca mid-ocean ridge), the melt fractionof the magma chamber was evaluated at 5%, to a maximumof 25% (West et al. 2001). If this is correct, the presence ofsuch a high melt fraction beneath CFc (65–90%) does notrule out the occurrence of large-scale convective overturn inthe melting zone (Rayleigh 1916), although further con-straints to its horizontal and vertical extension will beessential to understand the physical conditions of this layer.

Moreover, a very sharp transition of more than 1 km s-1

(for Vp) at a depth of about 4 km has been related to the

continuation of the carbonatic layer beneath Pozzuoli Bay(Judenherc and Zollo 2004; Zollo et al. 2008). Zollo et al.(2008) located the melt zone to below the carbonaticbedrock. If this melt zone represents the residual magmachamber which fed the CI and/or NYT eruptions, evidencefor carbonatic lithologies should be found within thedeposits of these eruptions; however, this was not the case.Also, carbonatic rock was not encountered during thedrilling down to about 3 km in the CFc area. Conversely,carbonatic rock was found at Vesuvius in the Trecase well(2 km in depth) and also within the pyroclastic deposits ofthe main plinian eruptions of Vesuvius, testifying to themagma drainage through carbonatic bedrock. We believethat it is unlikely that the eruption conditions at CFc wouldnot have drained out carbonate xenoliths belonging to avery extensive layer above a magma chamber during theignimbrite eruptions.

The existence of a carbonatic layer at 4 km in depth(Zollo et al. 2008), together with the absence of carbonaticlithology within pyroclastic deposits, suggest anotherpossible scenario in which the magma reservoir that hasfed the main eruptions of CFc is located above thiscarbonatic layer (buoyancy level). If the magma exists atthis depth, it is certain that it will be solidified or in theform of a ‘mush’, with a low percentage of melt, as theresolution of seismic surveys is greater than 1 km.Although this localisation to the top of the carbonatic rock

Fig. 3 Extrapolations (dottedlines) of the average geothermalgradients below the critical pointof water (∼3 km in depth),where the thermal regime is dueto pure conduction. Solid lines:the actual temperaturesmeasured within the wells (seeFig. 1 for well locations).Typical solidus and liquiduscurves for the crust are alsoshown, with the percentages ofmelt. A geothermal gradient of220°C km-1 (Mofete 1 well)allows the melt (>50%) to occurat the same depth (7.5 km) asthat calculated by Zollo et al.(2008). See text for details

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is still uncertain, this is important because it represents apotential zone of magma storage due to the minimal densitydifferences with respect to the mafic melts (neutral buoy-ancy level). A rock density of 2,600 kg m-3 is inferred bygravimetric surveys at a depth of 4 km (AGIP 1987), and asthis represents the average density of both the silicate meltsand the carbonatic rock (Wohlenberg 1982; Spera 2000),this makes the distinction between them difficult whenusing only the seismic data. Furthermore, at this depth, theVp and Vs seismic wave velocities are also very similar.Thus, it is also possible that the carbonatic layer is deeper.

These considerations highlight the complex evidenceprovided by the geophysical data of CFc and the non-uniqueness of the solutions. Accordingly, two maininterpretations of the composition and behaviour of thecrust below CFc can be proposed (Fig. 4a, b). In both cases,the magma chamber that fed the CI and NYT eruptionswould be located above the carbonatic layer. In the firstinterpretation (Fig. 4a), this magma chamber is located at7.5 to 8.0 km in depth, according to a low-velocity zone(Zollo et al. 2008). After the CFc collapse, the magmawould have migrated upwards as dykes and re-equilibratedat a shallower depth (3–4 km; Mangiacapra et al. 2008),forming small magma batches, which would produce minoreruptions. These magma batches should have a low meltfraction according to the seismic data. In the secondinterpretation (Fig. 4b), the CI and NYT magma chamberwould be located at the shallower depth (4 km), and itwould contain a significant proportion of crystals, whichwould increase the bulk viscosity of the magma by severalorders of magnitude above its value as a liquid. Alterna-tively, this magma chamber is formed by a solid zone thatcontains local batches of molten rock that do not exceed1 km3 in volume. The minor volcanic activity after the CFccollapse would have been fed by the residual melt duringthe magma chamber cooling.

The deeper melt layer can also be characterised by aconvective regime, instead of a stationary magma body(Cubellis et al. 2002). Indeed, for a horizontal fluid layer,vigorous convection can occur if the thickness of this layeris about 1 km; the temperature difference between its topand bottom is about 100°C, and the magma viscosity rangesbetween 107 and 1012 Pa s (Rayleigh 1916). With boththese interpretations, at the shallower levels of 1 to 2 km indepth, the hydrothermal fluids can participate in the unrest(Bonafede 1991; Gaeta et al. 1998; De Natale et al. 2001;Battaglia et al. 2006).

The geophysical and geochemical investigations of CFchave also shown that its unrest can be driven by bothdeeper magma and shallower geothermal system dynamics(a hybrid source). This process occurs within a layeredcrust with a high geothermal gradient; thus, the behaviourof the crust during the unrest can be very different, varying

from viscous or plastic at a deeper and hotter level (wherethe magma chamber is located), to elastic or elasto-plasticat a shallower and relatively colder level (where rockfracturing, gas circulation and geothermal fluids occur).These behaviours will be taken into account in thefollowing analysis, to evaluate the possibility of magmarising to the surface in the elasto-plastic and the viscoelasticcases.

Elasto-plastic behaviour

Experimental data for triaxial compression have shownthat, above the yield point, rock shows either brittle failureor plastic flow, which depends on the temperatures andconfining pressures (Johnson 1970). As both the temper-atures and confining pressures increase, the rock behaviourdevelops into the plastic. The conditions for the onset ofplasticity at CFc during the periods of unrest are promotedby the high geothermal gradient (∼150°C·km-1), the fluidcirculation and the heterogeneity of the rock (Aster andMeyer 1988; Zollo et al. 2003; Trasatti et al. 2005). Trasattiet al. (2005) constrained the source depth and theoverpressure of CFc, assuming that, under confiningpressure, the rock can deform elastically up to the yieldpoint (corresponding to the yield stress, σ0) and flowplastically once this stress has been attained. In thefollowing case, we assume the crust behaviour during theuplift to be perfectly elastic from 0 to 2 km in depth and tobe elastic-perfectly plastic (strain hardening is neglected)below this depth, where the temperatures overcome theelastic limit. The source of deformation (magma and/orfluids) is located within the elasto-plastic layer (at 2–4 kmin depth). Within this layer, the elastic or plastic behaviouris controlled by the value of the applied strain, with respectto the yield strength of the rock.

Under the confining pressure and elasto-plastic condi-tions, the loading–unloading experimental data have shownthat the stress–strain relationships follow a characteristicpath (Jaeger and Cook 1969; Johnson 1970; Billington andTate 1981). During the loading, the linear elastic relation isσ=Eε. At the yield point (σ=σ0), the stress–strain curve isindependent of the stress rate, while ε can be arbitrarilylarge (Turcotte and Schubert 2001). At the yield point,additional stress is constantly released by the flow strain.Upon unloading, the rock behaves elastically again. Whenthe applied stress is reduced to the initial conditions, theelastic strain is recovered, while the plastic strain remains.Using this stress–strain cycle described here, we studied the1982–1984 uplift (1.8 m) and the subsequent 1984–2004slow subsidence (about 0.8 m) (De Natale et al. 2006;Bellucci et al. 2006): these deformations are concentrated ina roughly circular area centred on Pozzuoli Bay, with a

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maximum radius of 7 km (Trasatti et al. 2005). The 0.8 mof subsidence was recovered over about 20 years, at adecay rate from about 160 mm y-1 (13 mm month-1) toabout 30 mm y-1 (2.5 mm month-1). These values also

contain the contributions of the secular slow subsidence of1.1 to 2.0 cm y-1 (average, 1.5 cm y-1). Subtracting theseaverage values for the period 1984–2004 from the 0.8 m ofsubsidence, we obtain 0.6 m. This can be reasonably

Fig. 4 Cartoons representingthe two possible geological andrheological stratifications of thecrust below CFc, as inferredfrom the geophysical data. a Azoned magma chamber (CI andNYT eruptions) is located at 7.5to 8.0 km in depth, just abovethe limestone. Dyke intrusionsform small magma batches atshallow depths. b A residualmagma chamber of CI and NYTeruptions is located at about4 km in depth, above the lime-stone (with melt volume<1 km3), while the melt layer islocated at 7.5 to 8.0 km in depth(Zollo et al., 2008). If this layeris sufficiently thick and the meltfraction is high, convectiveregimes can occur. In bothcases, the variations in temper-atures and pressures within thechamber can produce upwardfluid migration into the shallowzones. The tectonic extensionεex and the magma influx Qin

are also shown. See text fordetails

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assumed as the amount of elastic contribution that wasrecovered during the subsidence (Bellucci et al. 2006). Theremaining part of the permanent deformation can beascribed to the plastic deformation that occurred withinthe deeper layer (2–4 km in depth). Therefore, we assumethe value of 0.6 m as the yield point (elastic–plasticthreshold). We also assume that, after the rapid uplift(1982–1984), the elastic relaxation of the crust is completewhen the subsidence velocity becomes similar to thesecular velocity. This occurred at the end of the periodunder consideration (i.e. in 2004).

The total strain at the end of the uplift (1.8 m) was 1×10-4 s-1, while the strain after 0.6 m of subsidence was 7×10-5 s-1; thus, we can deduce the elastic stress–strainrelation during the subsidence. To consider the horizontalstrain that produces the stretching of the crust and theconditions for dyke intrusion (crack opening), we approx-imate that at CFc the horizontal displacement was about40% of the vertical displacement (Mogi 1958; De Nataleet al. 2006). Following the theoretical path of the loading–unloading cycle for rock under elasto-plastic conditions,we set 0.6 m as the value of the elastic uplift where therock starts to develop plastic behaviour, such that the onset ofplasticity during the uplift occurs when the strain is 3.4×10-5 s-1 (Fig. 5). Thus, since the elastic uplift and subsidencepaths can be represented by the linear equation σ=Eε,starting from (x, y)=0 and assuming the initial conditions ofσt0=0, εt0=0, with E=43 GPa (Zamora et al. 1994; Rabauteet al. 2003), we can evaluate the stress corresponding to theelasto-plastic transition (the yield stress) as 10 MPa (Fig. 5).This is in agreement with the yield stress obtained forvolcanic rock (Haimson and Rummel 1982; Amadei andStephansson 1997; Gudmundsson and Brenner 2005).

Further evaluation of the yield stress of the rock at CFccan be carried out taking into account the seismic strainenergy that was released during the 1982–1984 period. Theenergy produced by the inflating of the magmatic or hybrid

source stored within a certain volume of rock was releasedas strain energy W. Following the von Mises criterion, theyield occurs when the strain energy associated withdistortion reaches a value that is characteristic of thematerial (Jaeger and Cook 1969). This is expressed by thefollowing equation:

W ¼ s20=6m ð1Þ

where the rigidity (μ) is set to 17 GPa (Zamora et al. 1994).The total strain energy Wt or potential energy stored in thebrittle layer below CFc is obtained by integrating over thewhole brittle volume (V):

Wt ¼ W � V ð2Þwhere V can be approximated to a cylinder with a 3-kmradius and a 3-km height (Rosi and Sbrana 1987; De Nataleet al. 2001). Considering that the 0.6 m uplift (the yieldpoint) was achieved about 18 months after the onset of theunrest (Barberi et al. 1984; Orsi et al. 1999), the seismicenergy (M) that was accumulated up to that time has beenevaluated as 2×1013 N m (Orsi et al. 1999). To obtain therelationship between this value and the correspondingbrittle deformation, we use the seismic efficiency, whichrepresents the ratio of the elastic energy and the energyrequired for the volumetric change due only to seismicfailure (McGarr 1976). The seismic efficiency at CFcduring the 1983 period has been calculated as about 1×10-2 (Yokoyama and Nazzaro 2002). Considering this ratioas being constant over the entire unrest period, the energyrelated to the brittle deformation (Mbr) was roughly 2×1011 N m. Assuming that, at the end of the elastic phase orat the onset of the plastic phase, Wt∼Mbr, using Eqs. (1) and(2), we obtain a yield stress σ0 of about 0.5 MPa.

The low value of the yield strength allows the rock to bein the plastic condition for relatively small values of theapplied stress. Thus, large deformations would be expected

Fig. 5 Ideal representation of thestress–strain path for the 1982–1984 uplift and the followingsubsidence (1984–2004), assum-ing that the medium behaves aselastic-perfectly plastic. σ0 repre-sents the value of the yield stress(10 MPa) at which the plasticbehaviour occurs (the yieldpoint). This point is assumed tobe attained when the uplift isequal to about 0.6 m. During theelastic phase, the stress–strainrelationship is represented by theequation σ=Eε (where E isYoung's modulus)

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also for relatively low increments in the magmatic sourcepressure once the yield-point threshold has been reached.This state can be arrived at only for the elasto-plastichypothesis. According to our assumptions, the amount ofmaximum horizontal strain (1×10-4 s-1) (maximum tensilestress), that corresponds to the end of the plastic phase wasnot sufficient to produce fracturing of the rock and magma-dyke intrusion.

Viscoelastic behaviour

In this section, we consider the behaviour of the wallrock around the magma body for both deep (>4 km) andshallow (<4 km) crusts, and the possibility of magmaintrusion, which is strongly related to both the overpres-sure within the magma chamber and the mechanicalresponse of the wall rock. We assume the simple case ofMaxwell viscoelastic rheology (Jellinek and De Paolo2003), and we describe the response of an extendedviscoelastic volume around the reservoir. At CFc, the highgeothermal gradient and the presence of incoherentvolcanic materials at shallow depths can produce effectiveviscosities in the order of several magnitudes lower thanthe characteristic values of rock (Bonafede et al. 1986;Zollo et al. 2008). Thus, viscoelastic effects can occur.Jellinek and De Paolo (2003) provided a simple expressionfor viscoelastic conditions that relates to the maximumoverpressure (Δpmax) of the source required to propagatemagma to the surface, the magma influx (Q), the wall-rockviscosity (μwr) and the source volume (V), such that:

Δpmax ¼ 2mwrQ

3Vð3Þ

Assuming the magma to be an incompressible fluid and thewall-rock behaviour as viscoelastic, with a constant viscosity(μwr), we can use Eq. (3) for both of the two cases of deeper(case 1) and shallower (case 2) magmatic sources. In case 1,we assume that, after the large ignimbrite eruptions (CI andNYT), the magma chamber was depressurised up to thelithostatic pressure. The released magma in this case is thatwhich represents the excess volume with respect to thelithostatic condition. The volumes of the CI and NYTeruption magma chambers (CI, 200 km3 DRE; age, 39 ky;NYT, 40 km3 DRE; age, 15.6 ky) are assumed to be 2,000and 400 km3, respectively (Smith 1979; Crisp 1984; Zollo etal. 2003; Wohletz et al. 1999). During the approximately23 ky that have elapsed since the CI and NYT eruptions,even though some cooling has occurred, the magma chamberhas probably been replenished with new magma (Pappalardoet al. 2002). This magma accumulation can producepressures greater than the lithostatic pressures. We assumethat the amount of magma that produced these conditions is

the same as that ejected during the NYT eruption. Themagma that erupted between the CI and the NYT has notbeen considered here, as it is negligible with respect to thatwhich was ejected during the NYT. Although it is not reallyknown whether magma influx within large chambers isroughly steady or is pulsatile, for simplicity here, weconsider the first case (a steady magma influx). Taking intoaccount the magma feeding of 40 km3 that occurred betweenthe CI and the NYT, we obtain an average magma influx Q=0.002 km3 y-1. This is in agreement with the average valuesinferred for other calderas (Smith 1979; Hill 1992; Battagliaet al. 1999). In case 2, we consider a shallower and smallersource that was associated with the last episodes of unrestduring the 1972–1974 and 1982–1984 crises. A volumerange from 0.5 to about 30 km3 is assumed, whichcorresponds to a spherical source of 0.5 to 2.0 km in radius,respectively. The fluid influx during the 1972–1974 and1982–1984 periods of unrest has been evaluated as from0.009 to 0.02 km3 y-1, respectively (Battaglia et al. 2006;Gottsmann et al. 2006). In our case here, we assume that,initially, this influx was due to the arrival of magma. In theequation, the viscosity is the most uncertain parameter toevaluate, as this spans over different orders of magnitude.Using experimental and theoretical curves for a point-sourceembedded in a viscoelastic homogeneous half-space, reliablevalues of viscosity for a CFc shallow crust have beenevaluated as ≥1×1018 Pa s (De Natale et al. 1991). The wall-rock viscosity around magma chambers of volcanic areas aregenerally evaluated at between 1×1016 and 1×1019 Pa s(Jellinek and De Paolo 2003). Thus, for CFc, we assume that1×1018 Pa s for the case of a shallow crust and 1×1019 Pa sfor the case of a deeper crust are quite consistent.

The results of the computation for cases 1 and 2 (Figs. 6and 7) can be interpreted in terms of elastic or viscousregimes once certain yield strength is set. The yield strengthof the CFc rock has been fixed as 10 MPa, which is atypical value for such a volcanic environment (Folch andMartí 1998; Pinel and Jaupart 2003). Thus, the wall rockbehaves roughly as in an elastic regime when Δpmax >yield strength, allowing rock failure and eruption, while thewall rock is in a viscous regime when Δpmax < yieldstrength, promoting magma storage and the growth of alarge magma chamber (Jellinek and De Paolo 2003).Therefore, the results show that for the deep magmaticsource (case 1; Fig. 6), the viscous regime prevails for all ofthe values of viscosity, while the elastic regime could occurif larger values of viscosity (>1×1020 Pa s) and smallerdimensions for the source occur. For the shallower source(case 2; Fig. 7), the elastic regime is dominant; indeed, for asource of 1 km in radius, the elastic regime could also occurat smaller values of viscosity (1×1018 Pa s) with respect tocase 1. The shallow source would be located between 3 and4 km in depth (De Natale et al. 2001; Battaglia et al. 2006,

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Amoruso et al. 2008). Of course, at shallower depths,conditions might prevail for which the contribution of theviscous deformation is much smaller than that of the elasticdeformation.

Furthermore, the failure of the rock that leads to aneruption could arise after a large deformation, whichcertainly contributes to the establishing of favourableconditions for magma ascent from the source towards thesurface (Morhange et al. 2006). Although there aredifficulties of establishing a direct correlation betweendeformation and eruptions, the eruptions will probably bepromoted by small dimensions of magmatic batches andrelatively low temperatures (high viscosities) of the wallrock. For instance, the 1538 AD Monte Nuovo eruption(0.025 km3 DRE; Lirer et al. 1987) followed several yearsof ground deformation (8–9 m of uplift; Parascandola1947). Before the eruption, the magma migrated to ashallow depth (∼30 MPa), forming a small batch(∼0.25 km3; Piochi et al. 2005). As Fig. 8 shows, theinflux of new magma into this small batch produced great

overpressure also for a low wall-rock viscosity, promotingelastic failure and eruption.

Eq. (3) provides the maximum pressure in the chamberfor uniform wall-rock viscosities. For elevated temperaturesand confining pressures, the rock could flow, following apower-law rheology. The rheology of wall rock is describedby the relationship (Carter and Tsenn 1987):

"� ¼ A s1 � s3ð Þne�G=RT ð4Þwhere A is a constant that is dependent on the material, G isthe activation energy for creep, R is the molar gas constant,T is the temperature, n is the power-law exponent, andσ1–σ3 is the deviatory stress. By using Eq. (3) and (4),Jellinek and De Paolo (2003) described the expression ofthe maximum chamber overpressure for the power-lawrheology, in which the deviatory stress was mechanicallyequivalent to the flow stress in the wall rock that assumed,in turn, a function of temperature and strain rate:

ΔPmax � 2

3

16QðtÞ81AVchðtÞ e

G=RT

� �1=n

ð5Þ

In Fig. 9, the maximum overpressure has been plottedversus the chamber volume (as for Fig. 6) for different

Fig. 7 Maximum overpressure (Δpmax) generated by a steadyincompressible fluid influx (Q) within a magmatic source, for differentvalues of Q (0.009, 0.02 km3 y-1) as a function of the spherical sourcevolume (V), the wall rocks of which have a constant viscosity (μwr).The range of viscosity are from 1×1018 to 1×1020 Pa s as illustrated.The horizontal solid line represents the probable value of the yieldstrength (ys) of the CFc rock above which fracturing occurs. Thevolume of the source corresponding to a 1-km radius is also shown(De Natale et al. 2001)

Fig. 6 Maximum magmatic source overpressure (Δpmax) generatedby a steady magma influx Q=0.002 km3 y-1 as a function of thespherical source, with different volumes (V) and a constant viscosityof the wall rock (μwr). The viscosity ranges between 1×1018 and 1×1020 Pa s. The more reliable values of the viscosity for CFc are around1×1019 Pa s (De Natale et al. 1991). The horizontal solid linerepresents the probable value of the yield strength (ys) of the CFc rockabove which fracturing occurs. If Δpmax>ys the source is roughly inan elastic regime, and fracturing and magma injection can lead tovolcanic eruption. When Δpmax<ys, the wall rocks are approximatelyin a viscous regime, which favours melt storage and growth of themagma chamber (Jellinek and De Paolo 2003). The reported minimumand maximum volumes represent the NYT and CI chamber volumes,respectively. Dashed line: the influence of magma buoyancy onoverpressure for a density contrast of 100 kg m-3. See text for details

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temperatures and for wall rock with power-law rheology,using Eq. (5). For a volcanic environment, we assume A=2×10-4 MPa-1.9 s-1; G=141 kJ mol-1; n=1.9 and thetemperature varying from 300°C to 900°C (Hansen and

Carter 1983; Jellinek and De Paolo 2003). As expected, thepure elastic regime occurs for temperatures above about300°C. At CFc, this temperature is likely to be reached atabout 2 km in depth. For temperatures of 600°C and 900°C(at about 4 and 6 km in depth, respectively), the behaviourof the wall rock is viscous.

Buoyancy magma force

In the above analysis (case 1), the influence of thebuoyancy of large silicic magma on the overpressure ofthe magma source is neglected. However, additionalpressure can be supplied by the buoyancy forces, whichdepend on the density contrast (Δρ) between the magmaand the wall rock, and by the magma–chamber dimensions.As indicated above, the density ranges of the silicate meltsare between 2,500 and 2,600 kg m-3 (Wohlenberg 1982;Spera 2000), while rock densities of about 2,600 kg m-3

were located at depths of about 4 km in gravimetric surveys(AGIP 1987). If this value is associated with the carbonaticlayer (or with highly metamorphic carbonatic rock), thesilicate melts can be located within or above this, due to thebuoyancy force of the magma. Considering the densityrange of the silicate melts, the maximum density differencebetween the carbonatic rock and the magma can beapproximated to about 100 kg m-3. In the simple case of aspherical magma chamber that is composed of non-compressible melt, the chamber overpressure due to themagma buoyancy will increase vertically along the chamberwalls and reach its maximum (Δρgr, r=radius of chamber)at the top of the magma body (Jellinek and De Paolo 2003).Thus, the overpressure due to the density contrast betweenthe magma and the wall rock varies from 4.6 MPa for r=5 km, to 7.8 MPa for r=8 km, which correspond to magmachambers of 400 km3 (NYT) to 2,000 km3 (CI), respec-tively. The buoyancy overpressure as a function of themagma chamber volume is shown in Fig. 6 (dotted line);the influence of the buoyancy forces is not negligible, asthe line is positioned at the boundary between the viscousand elastic regimes.

The role of regional extension

The CFc area is characterised by tectonic extension, whichhas a strong influences on the migration of magma towardsthe surface. Indeed, tectonic extension can suppress dykeformation by increasing the volume of the chamber anddissipating the chamber overpressure. On the other hand,regional extensional stress can enhance dyke formation bystretching the roof rock at a rate that is sufficient to causetensile failure (Jellinek and De Paolo 2003).

The regional extension for the viscous regime willconstantly decrease the chamber overpressure along the

Fig. 9 Maximum overpressure (Δpmax) generated by a steadyincompressible fluid influx (Q) within a magmatic source, for Q=0.002 km3 y-1, as a function of the spherical source volume (V), thewall rocks of which have a power-law rheology

Fig. 8 Maximum overpressure versus source volume, as representedin Fig. 7, considering a magma source with a volume similar to that ofthe Monte Nuovo eruption (0.25 km3) and Q=0.008 km3 y-1

(0.025 km3 in about 3 y). For all of the values of viscosity, the wallrocks are in the elastic regime (eruption)

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plane perpendicular to the extensional direction. Thus, thearrival of new magma produces expansion of the chamber,generating overpressure only along the two sides of thechamber aligned with the extension direction. Considering achamber with an elliptical shape (Fig. 4a, b), the influx ofmagma (Qin) necessary to balance the negative chamberoverpressure in the plane perpendicular to the extensiondirection is given by Qin=εexV, where εex is the extensionaltectonic strain rate (Jellinek and De Paolo 2003). Typicalvalues of tectonic strain rate are in the range of 10-14–10-15 s-1

(Carter and Tsenn 1987). These values are also in agreementwith those inferred by the average extension rates data of thecentral and southern Apennines, Italy, over the last 18 ky(Roberts 2006; Papanikolaou and Roberts 2007). For a strainof 1×10-14 s-1, the magma influx necessary to balance thenegative overpressure is: Qin=0.0001 km3 y-1 for V=400 km3, and Qin=0.0006 km3 y-1 for V=2000 km3. Thesevalues are lower than the average values of the magma influx(Qin(m)=0.002 km3 y1) (Smith 1979; Hill 1992, Battaglia etal. 1999). The condition Qin(m)>Qin can produce overpres-sure within the magma chamber, which will then increase theprobability of eruption. Otherwise, the average estimation ofthe magma influx might be different from reality. Indeed, themagma input can be episodic, with sudden rapid pulses andhigher influx rates among relatively long periods ofquiescence and lower influx rates (Scandone et al. 2007). Itis also known that, once a chamber is sufficiently large,it becomes difficult to produce sufficient overpressure forrock failure, due to the steady and relatively low magmarate (Jellinek and De Paolo 2003). A well-knownpossibility is a quickly increased instead of a steadymagma influx, within a magma chamber with a relativelycold and rich gas/crystal content, which generates a rapidincrement of pressure that is faster than the temperatureincrement. This would allow the wall rock to maintain arelatively high viscosity with a prevalently brittle behav-iour (elastic regime, so eruption). The quicker the magmainput, the more elastic the rock response. For non-spherical chambers, the strains are concentrated locallyalong its edges, allowing fractures and dyke formationaround the periphery of the chamber (Gudmundsson andBrenner 2005). This mechanism can generate largeignimbrite eruptions and caldera collapse.

We can also propose another mechanism to generatecaldera eruptions in extensional tectonic regimes. When thevolume of the magma influx is not enough to balance thenegative chamber overpressure due to the extensionaltectonics of the area, the negative pressure within the chambercould result in roof collapse, triggering eruptions. This casecould occur at CFc if the strain rate associated with theregional extensional regime of the area is sufficiently large.This hypothesis is consistent with the velocity of the spreadingof the Tyrrhenian Sea, which is probably characterised by

sudden rapid pulses punctuated by relatively long periods oftectonic quiescence (Nicolosi et al. 2006). A stable conditionoccurs when a steady influx of magma balances the negativechamber overpressure (so that the net pressure is ∼0), whichproduces the conditions for magma accumulation and agradual increase in the temperatures of the wall rock, thebehaviour of which can become viscous (so eruption isinhibited; Jellinek and De Paolo 2003).

Thermal stress: another possible source of stress

As has been shown, the existence of magma batches is anecessary condition to generate hot fluid circulation andelevated geothermal gradients (Wohletz et al. 1999).Changes in the temperatures of magma reservoirs can leadto very large changes in pressure (i.e. thermal stress). Thisstress can be transferred up to the surface through differentmechanisms. Indeed, a temperature increase in a porousmedium containing a fluid phase can lead to a notableincrease in the pore fluid pressure, accompanied by gas/fluid migration towards the surface (De Natale et al. 1991).

For a confined volume of rock (dV=0; dP>0), thethermal stress is given by ΔpTH=(α2/β) dT, where α and βare the isothermal compressibility and volumetric coef-ficients of the thermal expansion, respectively. Typicalvalues of α and β for volcanic rock are 3×10-5 K-1 and 1×10-11 Pa-1, respectively (Turcotte and Schubert, 2001). Toproduce ground uplift and rock failure, the net pressure(Pnet) at a given depth must be larger than the lithostaticpressure (LP=ρgh) and the tensile strength of thesurrounding rock (Martì and Folch, 2005). Let us considerthe lithostatic pressure as negative and the upwardpressure due to thermal stress as positive; here, the netpressure is given by Pnet=ΔpTH−LP. It is assumed that thesource of pressure (hydrothermal fluids) is located atabout 4 km in depth (LP=∼100 MPa; ρ=2.6 Kg m-3), thebottom of which is in contact with the magmatic source. Inthis case, the thermal stress produced by the magma isquickly transmitted to the hydrothermal source by thepore-pressure increment. In Fig. 10, this net pressure (Pnet)is plotted against the temperature variation (ΔT) of themagmatic source. A positive ΔT of the hydrothermalsource of between 20°C and 30°C during the 1982–1984unrest has been estimated (Cioni et al. 1984; De Natale etal. 1991), which corresponds to sufficient thermal stress inthe magma batch for the onset of uplift. For a temperatureincrement less than about 35°C, the net pressure isnegative because the lithostatic pressure overcomes thethermal stress (no uplift). If the temperature increases bymore than 35°C, the thermal stress becomes greater thanthe lithostatic pressure, and the pressurisation of the hotmagmatic fluid allows the onset of ground uplift.

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The crust temperature strongly controls how the defor-mation of the rock occurs (elastic or non-elastic). Settingthe maximum value of the yield strength of the rock at10 MPa (Folch and Martí 1998; Pinel and Jaupart 2003)and assuming a progressive temperature increment, ΔT, ofthe magmatic source, the elastic conditions might occurover a very narrow range of temperature variation (about35–38°C), during which the stress is maintained below theyield strength. As the temperature increases, the thermalstress overcomes the yield strength, which then allows theonset of plastic deformation. Since the plastic state of therock makes fracture propagation difficult, although criticalvalues of the pressure (Pnet>yield strength) are attained(Jellinek and De Paolo 2003), the injection of magma froma deep reservoir through fractures in the elastic crust abovemight be suppressed.

Discussion and conclusions

By considering previous CFc unrest models and calderaeruptions, we have evaluated the strength of the rock forelasto-plastic behaviour and the conditions for eruption or

magma storage for both shallow and deep magmaticsources at CFc for the viscoelastic case. When the elasto-plastic conditions for the 1982–1984 uplift are considered,relative low yield strengths are obtained (0.5–10 MPa).These values will be related to the particular physical stateof the crust below CFc, which is characterised by hightemperatures, intense fracturing, and circulation of hotfluids. This allows the shallow rock to enter the plasticdomain if it is subjected to low increases in the stress. Thus,large deformation can be expected also without eruption.

We have also considered the case of wall-rock behaviouraround a magmatic source by using the viscoelastic modelobtained by Jellinek and De Paolo (2003). This modelconsiders two different behaviours, elastic and viscous, andtakes into account the viscosity of the wall rock, the volumeof the source and the overpressure generated by the magmainflux. Considering a magmatic source for CFc of at least450 km3 (Wohletz et al. 1999) and a wall-rock viscosityfrom 1018–1020 Pa s, it is difficult to attain the conditionsfor eruptive failure. These conditions are further inhibitedfor larger magmatic sources (2,000 km3; the CI magmachamber). Since a reliable value of wall-rock viscosity forCFc is around 1×1019 Pa s (De Natale et al. 1991), the

Fig. 10 Pressure Pnet versus temperature variations, ΔT, from 0°Cto 100°C. The Pnet is calculated as the differences between ΔpTH=(α2/β)dT (the thermal stress) and the lithostatic pressure PL. Thelatter is considered negative. Dotted line: the yield strength of theCFc rock. When the Pnet overcomes the lithostatic pressure, uplift ofthe ground occurs; if the pressure Pnet is exceeded by the lithostaticpressure (LP=ρgh) plus the tensile strength of surrounding rocks, the

circumstances for plastic deformation or eruptive failure occur.Under substantial confining pressures and high temperatures, therocks deform plastically rather than elastically. In this case, elasticbehaviour occurs for a very narrow range of temperature variation,while plastic deformation dominates for temperature variations ofmore than about 38°C

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likelihood of eruptions for such a large magma chamberneed to be correlated with other variables, such as, sourcedimension, regional stress field, and high rates of magmainflux.

Considering the rheology of the rock around an over-pressurised shallower and smaller source (of about 1 kmradius; De Natale et al. 2001, Battaglia et al. 2006;Amoruso et al. 2008), we have shown that the elasticregime of the wall rock dominates for all of the values ofviscosity (1018–1020 Pa s). At CFc, this condition mighthave triggered eruptions, as for instance, during the last1970–72 and 1982–84 unrests, whereas their presentabsence might be ascribed to different factors, such as alesser viscosity of the wall rock due to its higher temper-atures (viscous regime) or the lack of magma intrusionaccording to the hypothesis of fluid migration as the sourceof ground uplift.

In general, the above considerations show that theconditions that would favour eruptions are the highviscosity of the rock around the magmatic source and thesmall dimension of the source itself. These circumstanceswould promote the fracturing of the wall rock and dykeinjection towards the surface. In contrast, higher temper-atures and lower viscosities of the wall rock would inhibitthe propagation of magma up to the surface; theseconditions occur for larger magma chambers (hundreds ofcubic kilometres).

In addition, the extensional regime of the CFc areawould promote a rising of magma from deeper sources anda decrease in the chamber pressure along the planeperpendicular to the extensional direction. This overpres-sure within the chamber can occur when the magma influxrate is sufficiently high to overcome the negative pressuredue to the extensional rate.

Finally, an alternative efficient mechanism for theperiodic inflation and deflation of CFc without eruptionscan be seen as the pore pressure increases due to thermalvariations within the deep magmatic source (thermal stress;De Natale et al. 2001). We show that temperature variationsof more than 35°C within a deep magmatic source canproduce the thermal stress that is sufficient for the uplift ofthe caldera. This process probably occurs in the plastic orviscous domain and might involve the circulation ofgeothermal fluids.

The present study has emphasised the difficulty ofunderstanding how to discriminate between the conditionsfor eruption or non-eruption at CFc. For instance, the seismic,deformation and gravity monitoring data provide the moreimportant evidence for volcanic activity renewal, but theirinterpretation is complicated by the non-uniqueness of thesolutions that generate the CFc unrest. Otherwise, thereactivation of volcanic activity of large calderas might takeplace without clear precursors, as occurred during the 1994

Rabaul caldera eruption (McKee et al. 1995; De Natale et al.2001). Under other conditions, no eruption would happen,even after long periods of seismic activity and largedeformation of the caldera, as in the case of the 1970–1972and 1982–1984 CFc unrest.

The complexity of the problem is related to anunderstanding of the particular physical state of the crustand particularly to the location and dimension of themagma reservoir, the rheology around the magma reservoir,the type of magma feeding and the influence of the regionalstress field and the strain rate in the area. The lack of acomprehensive model that can take all of these features intoaccount produces the uncertainties in the evaluations ofboth short-term and long-term volcanic eruption forecasts.

Acknowledgments We are grateful to Giuseppe De Natale foruseful discussions and suggestions. We also thank the referees C.Giunchi and C.R.J. Kilburn and the executive editor John Stix for theirhelpful comments that greatly improved the quality of the final draft.

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