Earth and Planetary Science Letters 388 (2014) 166–174

Contents lists available at ScienceDirect

Earth and Planetary Science Letters

www.elsevier.com/locate/epsl

The influence of cooling, crystallisation and re-meltingon the interpretation of geodetic signals in volcanic systems

Luca Caricchi a,b,∗, Juliet Biggs b, Catherine Annen b, Susanna Ebmeier b

a Section of Earth and Environmental Sciences, University of Geneva, Rue des Maraîchers 13, CH-1205, Geneva, Switzerlandb School of Earth Sciences, University of Bristol, Wills Memorial Building, Queen’s Road, Bristol, BS8 1RJ, UK

a r t i c l e i n f o a b s t r a c t

Article history:Received 4 May 2013Received in revised form 9 October 2013Accepted 1 December 2013Available online xxxxEditor: L. Stixrude

Keywords:geodetic signalspetrologythermal modelling

Deformation of volcanic edifices is typically attributed to the movement of magma within the volcanicplumbing system, but a wide range of magmatic processes are capable of producing significant volumevariations and may also produce deformation. In order to understand the evolution of magmatic systemsprior to eruption and correctly interpret monitoring signals, it is necessary to quantify the patterns andtimescales of surface deformation that processes such as crystallisation, degassing and expansion of thehydrothermal system can produce. We show how the combination of petrology and thermal modellingcan be applied to geodetic observations to identify the processes occurring in a magmatic reservoirduring volcanic unrest. Thermal modelling and petrology were used to determine the timescales andvolumetric variations associated with cooling, crystallisation and gas exsolution. These calculations canbe performed rapidly and highlight the most likely processes responsible for the variation of a setof monitoring parameters. We then consider the magnitude and timescales of deformation producedby other processes occurring within the vicinity of an active magma system. We apply these modelsto a time series of geodetic data spanning the period between the 1997 and 2008 eruptions ofOkmok volcano, Aleutians, examining scenarios involving crystallisation, degassing and remelting of thecrystallising shallow magmatic body and including a viscoelastic shell or hydrothermal system. Thegeodetic observations are consistent with the injection of a water-saturated basalt, followed by minorcrystallisation and degassing. Other scenarios are not compatible either with the magnitude or rate ofthe deformation signals.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

Driven by the increasing availability of satellite technology suchas InSAR and GPS, the number of volcanoes for which geodeticmeasurements exist is growing rapidly, as is the spatial and tempo-ral resolution of those measurements (e.g. Sparks et al., 2012). Theglobal catalogue of volcanoes known to be deforming now exceedsone hundred (Fournier et al., 2010), but remarkably few of these fitsimple cycles of magma chamber recharge and discharge within anelastic medium. A new paradigm is required. In this paper, we cou-ple existing thermal models with petrologic constraints to estimatethe contributions of crystallisation and degassing on the magni-tude and time scales of surface deformation. We then consider thetimescale and magnitude of other processes, such as perturbationof the hydrothermal system and evolution of the physical prop-

* Corresponding author at: Section of Earth and Environmental Sciences, Univer-sity of Geneva, Rue des Maraîchers 13, CH-1205, Geneva, Switzerland. Tel.: +41 2237 96 630.

E-mail address: luca.caricchi@unige.ch (L. Caricchi).

0012-821X/$ – see front matter © 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.epsl.2013.12.002

erties of the crust, which are known to play a role in controllingdeformation in regions of active volcanism.

Of over a hundred volcanoes known to be deforming, roughlytwenty volcanoes are thought to be undergoing long-term sub-sidence (Table 1). This has been attributed to the cooling andcrystallisation of magma bodies (e.g. Medicine Lake; Poland et al.,2006) or associated hydrothermal activity (e.g. Kiska; Lu et al.,2010; Lu and Dzurisin, 2010). Sudden pulses of uplift are typicallylinked to magmatic intrusions (e.g. Three Sisters; Wicks, 2002),but discrete pulses of subsidence (e.g. Suswa; Biggs et al., 2009)are more challenging to explain. In several cases, exponentiallydecaying subsidence is observed immediately following pulses ofinflation (e.g. Okmok; Fournier, 2008; Fournier et al., 2009; Alutu;Biggs et al., 2011). The diversity of these observations illustratesthat we must consider not only the spatial pattern and magnitudeof the deformation, but also its temporal evolution if we are toidentify the processes driving volcanic unrest.

In this paper, we use Okmok volcano, Alaska (Fig. 1A) as a casestudy because a 15-year geodetic record including InSAR, contin-uous and campaign GPS measurements is available. The time se-ries, shown in Fig. 1B, covers major eruptions in 1997 and 2008and provides detailed time-series of inter-eruptive deformation

L. Caricchi et al. / Earth and Planetary Science Letters 388 (2014) 166–174 167

Table 1Global compilation of subsiding volcanoes.

Volcano Methodandcoverage

Rate(cm/yr)

Diameter(km)

Inferreddepth(km)

References

Aniakchak I: 92–02 1.3 (const.) 10 ∼4 Kwoun et al., 2006

Askja L: 83–98 5 (83–98), <25 3.2–3.8 Sturkell et al., 2006;Pagli et al., 2006;de Zeeuw-van Dalfsen et al., 2012

G: 93–98 2.5–3.0 (00–09),decayingI: 92–00

CampiFlegrei

G: 85–05 1.4–2.8,(decaying1985–)

∼12 2–4.2 Fernandez et al., 2001;Lundgren et al., 2001;Gottsmann et al., 2006.

I: 93–96

Cerro Blanco I: 92–00 1.8–2.5(decaying)

<30 <4.8 Pritchard and Simons, 2004

Copahue∗ I: 02–08 2 (const.) 2–3 ∼4 Euillades et al., 2008; Fournier et al., 2010;Velez et al., 2011

Fisher Caldera G: 99–01 – >10 >1.6 Mann and Freymueller, 2003

Kiska∗ I: 95–01 1.6 3 <1 Lu et al., 2002

Krafla L: 89– 5 (89–92) ∼10 1.5–2.5 Sigmundsson et al., 1997;de Zeeuw-van Dalfsen et al., 2006;Sturkell et al., 2008

G: 93–95 0.3 (00–05)G: 00–05I: 92–

MedicineLake

G: 96–04 ∼0.9–1.2 ∼12 – Dzurisin et al., 2002;Poland et al., 2006L: 54, 89,

90, 99I: 93–00

Sakurajima L ∼0.1 (79–) Oct-20 – Dvorak and Dzurisin, 1997;Mogi, 1958;Yokoyama, 1986.

Okmok I: 92–12 Variable ∼8 03-Apr Miyagi et al., 2004; Lu et al., 1998, 2000, 2005,2010; Lu and Dzurisin, 2010; Mann et al., 2002;Fournier et al., 2009; Biggs et al., 2010

G: 00–12 (Fig. 1)

The table lists the details of the observation method and temporal coverage, the rate and temporal behaviour of the subsidence, the diameter of the deformation patternand the estimated source depth. Okmok volcano is given for comparison. G—GPS, I—InSAR, L—Leveling. ∗ refers to volcanoes at which the deformation has been attributed tohydrothermal processes.

(Lu et al., 2010; Lu and Dzurisin, 2010; Fournier et al., 2009;Biggs et al., 2010). The petrology of this system is well charac-terised, which is fundamental for quantifying the volumetric vari-ations associated with crystallisation and eventual exsolution ofvolatiles from the residual melt phase.

Following a magma intrusion, each part of a magma body willexperience a unique cooling history depending on the depth ofemplacement, thermal state of the crust, and magma composition,which ultimately controls the variation of crystallinity and volumewith decreasing temperature. Cooling leads to magma crystallisa-tion and because minerals are generally denser than the melt fromwhich they crystallise, to a decrease in volume (Lange, 1994). Therate of crystallisation, and therefore of volumetric variation, is afunction of the shape, area and volume of the cooling magma in-trusion, the thermal state of the surrounding rocks and the amountof latent heat released during crystallisation. Hence thermal mod-elling is necessary to calculate the appropriate rates of magmacontraction or expansion that could be the source of deformationobserved in volcanic systems. In volatile bearing magmas, crystalli-sation is accompanied by a relative enrichment of volatiles in theresidual melt. Once the saturation limit is reached, volatiles exsolvefrom the residual melt generating gas bubbles (second boiling) andleading to a volumetric increase of the crystallising magma. Thevariations of magma density during cooling control the rate andmagnitude of volumetric variation and thus surface deformation.Any model of subsidence in a magmatic system must thereforeincorporate not only appropriate thermal models, but also petro-logical information on the relationships between temperature andmelt/crystal/volatile fractions.

Here we focus on three scenarios that could be envisaged toexplain the sequence of inflation and deflation signals observedat Okmok between 1997 and 2008: (1) injection of basalt in the

country rock followed by crystallisation; (2) injection of H2O bear-ing basalt followed by cooling and degassing; (3) interaction be-tween the injected H2O bearing basalt and a partially crystallisedandesitic magma that may be present in the system as a residuumof previous eruptions (Finney et al., 2008). Here crystallisation,melting and gas exsolution are considered to have only volumetriceffects:

(1) In the first scenario, cooling of a volatile-undersaturatedmagma produces volumetric contraction with an associatedsubsidence rate that can vary depending on the ratio betweenthe density of the crystallising phases and the density of theresidual melt along the crystallisation sequence, the shape anddimensions of the magma intrusion, the magma compositionand the thermal state of the crust.

(2) If the magma present in a reservoir is volatile saturated, crys-tallisation leads to the exsolution of gas bubbles, which, inturn, within years, results in an inflation signal not relatedto magma injection and eventual subsidence if the systembecomes permeable and gas can be expelled from the subvol-canic reservoir.

(3) For the last scenario, the injection of a volatile-saturatedmagma into a crystal mush can potentially cause partial re-melting of the host. In this case, volatiles released from theinjected magma can potentially be resorbed by the volatile-undersaturated melt produced by re-melting. The result is in-flation (exsolution) followed by subsidence (resorption) but nosignificant degassing observable at the surface.

In the following, we show how geodetic measurements, de-tailed petrology, and thermal modelling can be combined to iden-tify the most likely processes occurring in a magmatic reservoir

168 L. Caricchi et al. / Earth and Planetary Science Letters 388 (2014) 166–174

Fig. 1. (A) Map showing the location of Okmok volcano and the position of the GPSstations (after Fournier et al., 2009). (B) Variation of volume in the Okmok mag-matic system between 1997 and 2008 (after Biggs et al., 2010). The volumes wereobtained by inverting InSAR, continuous and campaign GPS signals using a fixed-position Mogi model. The deflation observed between 2005 and 2006 correspondsto about 10% of the total volume increase in the system and is the subject of thisstudy.

and eventually preceding an eruption. Finally, we consider thethermal effects of the injection of magma on the surroundingcrust. In some cases, the increase in temperature is sufficient toremelt the rocks surrounding the intrusion, but even smaller in-creases in temperature will alter the rheology of cold country rock.This has led to the concept of a viscoelastic shell surroundingthe magma reservoir (e.g. Dragoni and Magnanensi, 1989). Fur-thermore, hot magma reservoirs are typically associated with hy-drothermal systems and a change in temperature is likely to alterthe pattern of fluid circulation. Both these processes may producegeodetic signals and/or affect the rate of inflation/deflation.

1.1. Case study: Okmok volcano

Okmok is a shield volcano located on Umnak Island in the Aleu-tian Chain (Fig. 1), and it has erupted every 10–20 years for thepast 200 years (Miller et al., 1998). In 1997, the eruption originatedfrom Cone A (Fig. 1A) and produced a basaltic lava flow 5 km longand tens of meters thick (Lu et al., 2003), while the 2008 eruptionproduced new vents located near Cone D (Fig. 1A) and producedmainly basaltic-andesite tephra, as a result of magma interactionwith the water table (Larsen et al., 2013). The 10-km diametersummit caldera was formed by eruptions 12,000 and 2050 years

ago (Miller and Smith, 1975; Beget et al., 2005), which depositeddominantly andesitic ash-flow units.

The petrological characterisation of the products places con-straints on the interaction between magmas injected at depth andthose residing in the shallower part of the system and suggestsa chemically stratified magmatic system at depths of 2.5–5 km.The most evolved products seem located in the shallowest partof the systems and more basaltic magmas occupy its deepest por-tions. The temperature in the plumbing system varies from 850 to1125 ◦C, with water contents ranging from 2 to less than 6 wt%(Finney et al., 2008).

Geodetic observations began at Okmok volcano in 1992 andsince then a combination of campaign and continuous GPS and In-SAR have been used to measure the surface deformation (Lu et al.,1998, 2000, 2005, 2010; Miyagi et al., 2004; Fournier et al., 2009;Lu and Dzurisin, 2010; Mann et al., 2002; Freymueller and Kauf-man, 2010). The broad pattern is that of rapid, metre-scale sub-sidence during the 1997 and 2008 eruptions and uplift duringinter-eruptive periods (pre 1997 and 1998–2008). All GPS and In-SAR displacements can be reproduced well using a simple pointsource model (Mogi, 1958) at a depth of 3.4 km (Biggs et al., 2010;Lu et al., 2010; Lu and Dzurisin, 2010; Fournier et al., 2009) al-though more complex rheologies and geometries have also beenproposed (Masterlark, 2007; Masterlark et al., 2010).

Biggs et al. (2010) combined campaign and continuous GPSwith InSAR to produce a time-series of volume flux, which spansthe entire geodetic record (1992–2007) and captures both the spa-tial resolution of InSAR and the temporal resolution of the contin-uous GPS. There are significant variations in the rate of uplift andperiods of minor subsidence not associated with eruption (Fig. 1B;Fournier et al., 2009; Biggs et al., 2010). Uplift in 1992–1995 wasfollowed by subsidence in 1995–1996 preceding the 1997 erup-tion. Uplift resumed from 1997 to 2002 followed by a major pulseof uplift in 2002–2004. The 2002–2004 uplift can be further sub-divided into two sub-periods of uplift (summer 2002 to late 2003,and spring–summer 2004) interposed by a short repose or possiblysubsidence in early 2004. A further period of subsidence followedin 2004–2005. The volcano then entered a 3-year period of quies-cence that ended with a 6–7 month period of inflation leading tothe eruption in July 2008.

The deformation during the 1992–2005 period was associatedwith a single, static source, but the pre-, co- and post-eruptive de-formation associated with the 2008 eruption occurred in a newsource that changed in both location and geometry with time. De-flation during the 2008 eruption is attributed to pressure decreasein a source 2.1 km below sea level, notably shallower than thatassociated with the 1997 eruption. Deflation of a deep source cou-pled with re-inflation of a shallow change began a few weeks afterthe eruption.

This study focuses on the inter-eruptive deformation that oc-curred in 2002–2005. The peak uplift in 2003 corresponds to vol-ume change of 0.03 km3 while the subsequent deflation corre-sponds to a volume decrease of 0.003 km3, or 10% of the originalinput volume (Fig. 1B). Although the 2008 eruption will have sig-nificantly altered the patterns of magma storage only 6 years afterthe magma input, we run our models forward for 60 years to cap-ture processes occurring over longer timescales.

A previous study constrained the variations of volume and pres-sure responsible for the observed deformation using thermody-namic models to describe magma properties and a mechanicalmodel that accounts for the properties of the crust surroundingthe magma chamber (Fournier, 2008). By performing thermal mod-elling we can add temporal constraints and account for the ef-fects of magma properties on the deformation signals observed atOkmok between 1997 and 2008.

L. Caricchi et al. / Earth and Planetary Science Letters 388 (2014) 166–174 169

2. Methodology

2.1. Thermal modelling

A range of simulations were performed to model the injec-tion of basalt at 1075 ◦C (near-liquidus temperature of an arc-type water-saturated basalt similar to the basic magma erupted atOkmok; Wagner et al., 1995) at 4 km depth either in a cold crust(Tcrust = 150 ◦C) or in a reservoir of partially crystallised andesite(T = 850 ◦C, crystal fraction = 0.5; Moore et al., 1998). The evolu-tion of temperature for basalt, crust and andesitic magma was cal-culated using an explicit finite difference scheme (see Appendix A).The model includes heat transfer by conduction and latent heatproduced or absorbed by crystallisation or melting. The consump-tion of latent heat related to gas exsolution is neglected because itrepresents a relatively small contribution with respect to the la-tent heat released by crystallisation (Sahagian and Proussevitch,1996). The model uses cylindrical coordinates with temperaturesand melt fractions calculated on a 2D vertical slice of a 3D systemcharacterised by a rotational symmetry around its vertical axis. Theprogressive injection of basalt is simulated with discrete emplace-ment of successive magma pulses, which are wafer-shaped with adiameter of 400 m. Each injection is emplaced in the middle of theformer one to simulate the thickening of a sill-like body (Annen,2011). The effect of convection is not calculated in the thermalmodel, however will be considered later in the discussion of thetimescales of volumetric variations.

2.2. Petrology

In order to calculate volume changes caused by cooling, crys-tallisation, re-melting, it is necessary to have a complete descrip-tion of the crystal and gas volume fraction, as function of tem-perature for the different magmas present in system. Water is themost abundant gaseous phase in volcanic systems and hence theonly one considered here. We use petrological data from Wagneret al. (1995) and Moore et al. (1998) for arc basalts and an-desites from experiments performed at 1 kbar, temperatures be-tween 1100 and 800 ◦C and 3.15–4.05 wt% H2O (water saturatedconditions at 1 kbar for basalt and andesite respectively; Newmanand Lowenstern, 2002). The pressure condition was chosen be-cause it is consistent with the geodetic estimate of 3–4 km forthe magma chamber depth (e.g. Biggs et al., 2010; Fournier etal., 2009). To calculate the phase equilibria for the Okmok basaltcontaining 2 wt% H2O (such water content, and higher ones, aremeasured in melt inclusions for this volcano; Finney et al., 2008)and to extend the temperature range over which experimentaldata are present, we used the thermodynamic software MELTS(Ghiorso, 1985; Ghiorso and Sack, 1995). We first modelled thewater-saturated composition and compared the results with theexperimental data finding good agreement (Fig. 2A). Given thegood match, we used MELTS to compute the phase equilibria forthe Okmok magma containing 2 wt% H2O (Finney et al., 2008;Larsen et al., 2013). All the calculations were performed at a con-stant confining pressure of 1 kbar. MELTS was also used to calcu-late the density of the crystallising minerals, residual melt, and ex-cess gas volume present in the system (Fig. 2B and C). We then pa-rameterise the volume–temperature relationships and couple themwith the thermal model to trace the evolution of temperature andvolume associated with a magmatic injection for comparison withthe geodetic observations.

3. Volume balance

Analytic models of the geodetic observations suggest that thetotal uplift from 1997 could be explained with the injection of

Fig. 2. (A) Variation of crystal mass fraction with temperature for the different mag-mas used in the calculations. The diamonds are experimental data and the lineswere calculated using the MELTS software (Ghiorso, 1985; Ghiorso and Sack, 1995).(B) and (C) show the relative volumetric fraction of minerals and melt as functionof temperature calculated at a constant confining pressure of 1 kbar for a water sat-urated magma and a magma containing 2 wt% water, respectively. The variationsof magma relative volume during cooling are calculated assuming that excess wateris continuously removed from the magma (thick dashed line), and considering thatall the excess water is maintained in the magma and no outgassing occurs (thickblack line).

0.03 km3 of magma at depths of 3–4 km while the 2005–2006subsidence signal requires a volume decrease 0.003 km3 (10% of

170 L. Caricchi et al. / Earth and Planetary Science Letters 388 (2014) 166–174

the initial volume) in less than 1 year (Fig. 1; Biggs et al., 2010).The main target of our study is to determine the process respon-sible for this subsidence. All our calculations assume that the totalamount of magma injected in the system is the volume obtainedfrom the inversion of data recorded since 1997.

We start testing the hypothesis that the geodetic observa-tions are an elastic response to change in volumes related tomagma injection, cooling and crystallisation, gas exsolution andolder magma remelting. We numerically simulated the injectionof magma at a rate that approximates the increase of volume cal-culated from the inversion of the geodetic data. The results of thethermal modelling were used to calculate the possible volumetricvariations associated with magma cooling. Fig. 3 shows the dif-ferent effects of cooling, crystallisation, exsolution of gas from thecrystallising magma, and re-melting, on the volume of the subvol-canic reservoir.

These calculations provide both the magnitude and the rate ofvolumetric variations in time, which are fundamental to identify-ing the possible processes operating in the magmatic reservoir andresponsible for uplift or subsidence.

3.1. Effect of crystallisation

The injection of magma is followed by cooling, which, in turn,leads to crystallisation of minerals with higher density than theinitial melt and in absence of gas, this would result in contraction.Petrological studies of Okmok, however, suggest that the magmain the magmatic system contains volatiles (Finney et al., 2008;Larsen et al., 2013). Therefore, for crystallisation to account for thedeflation, excess volatiles should be continuously removed fromthe system during crystallisation. This is physically difficult be-cause the presence of crystals tend to inhibit the buoyant rise ofbubbles in magma (Belien et al., 2010), even if deformation couldfacilitate the escape of gas bubbles (Caricchi et al., 2011). Assumingthat volatile saturation results in continuous degassing, a volumet-ric contraction of a volumetric contraction of 10% (i.e. a total vol-ume fraction of magma of 0.9; Figs. 2B and 3) would be achievedat a temperature of about 1000 ◦C (Fig. 2B; in the model basalticmagma is injected at its liquidus temperature of 1075 ◦C). At thistemperature the crystal mass fraction is 0.44. However, crystalli-sation cannot be responsible for the observed deflation becausethe thermal model shows that even with injection in relativelycold crust (150 ◦C, unlikely for an active system such as Okmok)more than 50 years are required for a volume of 0.03 km3 ofbasalt to cool to 1000 ◦C and account for the relative decrease ofvolume of 10% (Fig. 3A). Depending on the magma body geome-try and thickness, magma convection might accelerate cooling andcrystallisation. However, cooling of a convecting magma layer islimited by the capacity of the country rock to conduct away themagma heat. Analysis by Worster et al. (1990) of the solidificationof a convecting magma chamber cooled from above by conductionthrough the country rock indicates that the solidification time fora convecting magma layer is about half the time predicted by con-ductive cooling. Thus, even if the magma is vigorously convecting,crystallisation alone cannot explain a 10% volume contraction overless than 1 year from the end of the injection episode as recordedat Okmok (Fig. 1B).

3.2. Crystallisation, second boiling and gas release

The crystallisation-only model implies complete and continuousdegassing, yet crystals tend to trap gas bubbles (Belien et al., 2010).Alternative models may account for the delay between the end ofthe magma injection episode and the onset of degassing: (1) gasis initially trapped in the magma until bubble coalescence leads toa significant increase of permeability; (2) enough time is required

Fig. 3. Volume of crystal, melt and gas phases with time, normalised to the max-imum volume obtained from the inversion of geodetic data at the end of theinflation period. The first 8 years of the thermal modelling are inspired by thegeodetic records in the period 1997–2004. (A) H2O-saturated basalt injected intocrust at 150 ◦C. (B) Basalt containing 2 wt% H2O injected into crust at 150 ◦C.(C) H2O-saturated basalt injected into crust at 850 ◦C. Volume fraction–temperaturerelationships are taken from Fig. 2 and temperature–time relationships from thethermal model. The arrows in (A) show the necessary conditions for 10% deflationbased on two assumptions: (1) If we assume all gas is lost instantly, the volume ofmelt+crystal falls to 90% of the peak value 52 years after the start of injection (inthe year 1997). (2) If we assume the gas is stored in unconnected bubbles, the gasaccumulated accounts for 10% of the total volume by the time injection is complete.

L. Caricchi et al. / Earth and Planetary Science Letters 388 (2014) 166–174 171

for buoyant gas bubbles to rise and leave the system and the mag-matic reservoir starts to release the gas and deflates. Consideringfor simplicity that the excess gas at intrusion depth (3–4 km)is principally water, that the intruding fully molten basalt has adensity of 2700 kg/m3 (Lange, 1994) at 1075 ◦C and the molarvolume of H2O at these conditions is 110 cc/mol (Ghiorso, 1985;Ghiorso and Sack, 1995), approximately 0.6 wt% excess water hasto be released from the injected 0.03 km3 of basalt to account for avolume change of 0.003 km3 (i.e. 10% of the total injected volume).Fig. 3A shows that by the time the injection is completed, a rela-tive volume of 10% excess gas has already been accumulated in thesystem, the release of which would account for the deflation ob-served between 2005 and 2006. Considering that convection wouldhave increased the cooling rate of the basalt and also taking intoaccount the uncertainty on the recalculated volumes, the calcu-lated time is in good agreement with the time interval of almost10 years between the onset of magma injection and the beginningof deflation (Fig. 1).

Given the rate of deflation measured between 2005 and 2006,we can also calculate an approximate gas flux that would havebeen measured during this period. Considering a weight ratioS/H2O for the basalt of about 0.04 as measured in melt inclusionsin Okmok volcanic products (Zimmer et al., 2010), the mass of Sreleased daily would be a modest 100 tons. Clearly the reality liesbetween these end-member models and the timescale over whichthe gas would be released would depend on the mechanism of de-gassing. Additionally, the gas fluxes measured at the surface couldbe affected by the presence of a hydrothermal system and there-fore for such relatively small quantities of gas it may be difficult tolink degassing and deflation rates.

So far we have considered the injection of a water-saturatedbasalt. Fig. 2C shows that for a water undersaturated basalt con-taining 2 wt% H2O, no excess gas starts to accumulate in the sys-tem until the magma reaches an average temperature of 1050 ◦C.This could suggest that the first modest subsidence episode(2000–2002; Fig. 1B) following the first inflation event, could re-sult from cooling and crystallisation and the second uplift eventcould reflect the point at which the basalt reaches second boil-ing and expands (Fig. 2C). However, this is not physically possiblebecause if all the inflation would be produced by the volumetricexpansion of magma at depth, this would imply an expansion ofabout 200% (Fig. 1B), and the compressibility of gases at pressurescompatible with the depth of the magma chamber is not com-patible with such extreme increase of volume (Pitzer and Sterner,1994). On the other hand, the magnitude of the last inflation mea-sured between before the 2008 eruption could be explained by theexsolution of about 10 vol% volatiles from the magma. The thermalmodel indicates that the rate of inflation observed before eruptionis too elevated to be accounted for by the second boiling of magma(Figs. 1B and 3B).

In conclusion, (1) the deflation observed between 2005 and2006 cannot be explained by crystallisation alone and can onlybe explained by degassing if the injected magma was volatilesaturated. (2) The second inflation episodes cannot be related tosecond boiling. (3) The last minor inflation episode preceding theeruption occurred with higher rates than those that would be pro-duced by second boiling. Therefore our preferred explanation forthis last event is the injection of another, smaller, pulse of magmainto the magmatic system.

3.3. Interactions with host andesite

At frequently erupting volcanoes, new magma is likely to beinjected into a system that contains residual magma from pre-vious eruptions. At Okmok, a major caldera-forming eruption re-leased andesitic magma (Finney et al., 2008), which suggests the

presence of chemically evolved bodies of magma in the plumb-ing system. The magma erupted in 2008 had a more chemicallyevolved composition with respect to previous basaltic eruptions(Larsen et al., 2013), which could be related to interaction be-tween basaltic magma and more chemically evolved magmas. Weuse our thermal models to simulate the injection of basalt at1075 ◦C into an andesitic magma body at 850 ◦C with a crystalfraction of ∼0.5 (Moore et al., 1998; Fig. 2). We consider alsothat the excess gas in the andesite magma left the system in thetime preceding the unrest that started in 1997. The volume of0.03 km3 of basalt leads to the re-melting of about 0.005 km3 ofcrystals from the andesite producing a water-under-saturated melt(Fig. 3C). This figure is for conductive heat transfer between thebasalt and the andesite. We notice that convection of the basaltlayer and of the andesite would result in more basalt crystallis-ing and more andesite remelting (Huppert and Sparks, 1988). There-melting has two main effects on the deformation signals: (i) Be-cause the density of melt is lower than the density of crystals,partial re-melting produces an additional volume increase whichcontributes to the uplift signal (Fig. 3C). (ii) Excess volatiles re-leased from a water-saturated basalt can be resorbed by the re-molten andesite causing subsidence without any surface degassing.The volume of re-molten andesite is in fact sufficient to resorb theexcess water in the basalt and account for the total subsidencemeasured.

4. Thermal effects on the surrounding crust

The previous section discusses the subsurface volume changescaused by the thermal evolution of a magma intrusion. In orderto link these processes to observations of surface deformation, wehave made the assumption of a purely elastic, homogeneous crustimplicit within the Mogi model (Mogi, 1958; Biggs et al., 2010). Inthis section, we discuss the effects of intrusions on the surround-ing crust and hydrothermal system. We use an energy balance todiscuss the thermal expansion associated with heat input into ahydrothermal system and use an analytic solution for the effectsof pressure change within a viscoelastic shell (Segall, 2010). Theresults allow us to estimate the direction and order of magnitudeof the deformation resulting from each mechanism independently.Multiple mechanisms may act together and feedbacks betweenthem, for example, crystallisation of a magma intrusion within aviscoelastic medium, would alter the spatial and temporal patternsof surface deformation hence we do not try to fit the data withany individual mechanism.

4.1. Rheology

The high-temperature environment around an active magmaticsystem favours a viscoelastic rheology over a purely elastic one,leading to a time-dependent response to volumetric and baro-metric variations in the plumbing system of an active volcano.Masterlark et al. (2010) constructed finite element models to simu-late subsidence associated with the 1997 eruption of Okmok basedon a magma reservoir that is surrounded by a viscoelastic rindof country rock embedded in an elastic domain, with the shal-low caldera fills represented by lower density and elastic mod-uli.

Here, we use a simpler analytic solution to consider the direc-tion, timescale and magnitude of deformation following a pressurechange of a magma reservoir surrounded by a viscoelastic rindwithin an elastic halfspace. The characteristic relaxation time, tr ,is given by the equation (Segall, 2010)

tr = 3η(1 − υ)R32

3μ(1 + ν)R3

1

172 L. Caricchi et al. / Earth and Planetary Science Letters 388 (2014) 166–174

where η is the viscosity of the shell; μ is the shear modulus; νis Poisson’s ratio; R1 is the radius of the chamber and R2 is theradius of the shell. The displacements have the same spatial distri-bution as for a Mogi source, but following the instantaneous elasticresponse, the displacements continue to increase at an exponen-tially decreasing rate that scales with tR (Segall, 2010).

An andesite at T = 850 ◦C with a crystal fraction of 0.5 wouldbe expected to have a Newtonian (i.e. maximum) viscosity ofthe order of 107–108 Pa s (considering a water saturated rhyoliticmelt; Giordano et al., 2008; Caricchi et al., 2007). Using this vis-cosity, even for shells 10 times wider than the magma reservoir(R2/R1 = 10), the relaxation time is still less than 1 s. From amonitoring perspective, any viscoelastic response from this part ofthe magma chamber would be included within the initial intru-sion. Further from the intrusion, the wall rock will remain solid,but may still behave viscoelastically and viscosities on the orderof 1017 are required to produce relaxation times on the order ofa year. The dimensions of the thermal aureole (and hence R2/R1)depends on the intrusion history: at low rates of emplacement,the thermal profile will be the same as for an individual intrusion,but if new magma is supplied before the previous batch has fullycooled, the thermal aureole will grow (Annen, 2011).

For the case under consideration, that of a magmatic intrusion,the post-intrusion viscoelastic response would be continued upliftat an exponentially decreasing rate. The rate at which this occurswill depend on the intrusion and eruption history of the magmachamber.

4.2. Hydrothermal system

A new influx of magma would also be expected to perturb thehydrothermal system. In a simple model, an increase in tempera-ture at the base would increase the energy of hydrothermal systemabove it. The total energy released can be calculated using:

E = ρb Vb(cb�Tb + L�X) (1)

For a volume of basalt, Vb of 0.03 km3 at 1075 ◦C cooling to1030 ◦C (�Tb = 45 K) causing 20% crystallisation (�X = 0.2)would release 1016 J. We assume the following constants: densityof basalt, ρb = 2700 kg m−3; specific heat capacity of basalt, cb =1000 J kg−1 K−1 (Robertson, 1988), and latent heat, L = 4 × 105 J(Bohrson and Spera, 2001).

Combining the equations for specific heat capacity with thosefor thermal expansion, shows that the overall volume change,�V w , is independent of the volume of water in the hydrothermalsystem.

�V w = αρb(cb�Tb + L�X)

ρw cwVb (2)

Thus for a basalt volume, Vb = 0.03 km3 and a temperaturecontrast, �Tb of 45 ◦C and thermal expansion coefficient of water,α = 0.01 K−1; gives a volume increase of 0.024 km3.

In the short term, the temperature change in a thin boundarylayer at the base could be considerably higher, driving a brief pe-riod of enhanced convection or causing a phase transition to steam,neither of which are addressed by these equations. More com-plex hydrothermal responses, such as intrusion-triggered changesin permeability leading to draining of the system are plausible, butrequire a full model of the hydrothermal system, which is beyondthe scope of this study.

For both a viscoelastic and hydrothermal scenarios, the initialresponse to intrusion would be additional uplift and hence thesemechanisms cannot explain the change from uplift to subsidenceobserved at Okmok. In fact, since they act in the opposite direc-tion, they are likely to reduce the magnitude of the subsidenceobserved, making our previous estimates minimum values.

5. Discussion

This paper details thermal and petrological calculations for vol-ume balances based on the geodetic record at Okmok volcanobut the concept may apply to other deforming volcanoes aroundthe world (Table 1). Like Okmok, geodetic measurements at thewell-studied calderas of Askja, Campi Flegrei and Sakurajima, cap-ture pulses of uplift followed by subsidence that last for severaldecades. Similarly, several volcanoes in the East African Rift showcomplex patterns of uplift and subsidence; for example, Alutu vol-cano shows two pulses of rapid uplift in 2004 and 2008 inter-spersed with gradual subsidence (Biggs et al., 2011). However, forthis system, the lack of petrological characterisation means thatequivalent volume-balanced calculations cannot be performed.

At volcanoes such as Medicine Lake, Krafla and Cerro Blanco,geodetic observations began during an extended period of subsi-dence, and we infer an intrusion prior to the geodetic record. Theseare caldera systems, where intrusions have been large enough toresult in long-lived subsidence signals and many show a slow de-cay in rate. For example, the 10-km wide subsidence pattern atKrafla caldera decreased in rate from 5 cm/yr in 1989–1992 to0.3 cm/yr in 2000–2005 (Sturkell et al., 2008). Traditionally, thesesubsidence signals have been attributed to drainage of magma (e.g.Askja, de Zeeuw-van Dalfsen et al., 2012) but the calculations pre-sented here suggest that volumetric changes associated with crys-tallisation in a cooling magma body could produce deformationpatterns of the required magnitude and duration. This may also betrue for the smaller areas of persistent shallow subsidence com-monly attributed to hydrothermal cooling e.g. Copahue (Velez etal., 2011) or Kiska (Lu et al., 2002), although the presence of ahydrothermal system may also effectively mask volume changesassociated with crystallisation and second boiling.

6. Conclusions

This paper demonstrates that thermal models can be used tolink petrological processes to deformation patterns on geodetictimescales. We examine candidate mechanisms for the 2005–2006period of subsidence at Okmok volcano. Although the volumechange associated with crystallisation alone is of the right mag-nitude, the timescale required is greater than the 9-year inter-val between injection and onset of deflation (Fig. 3). However,these timescales are compatible with a scenario where the defla-tion signal is linked to the degassing of excess volatiles producedby crystallisation of a water-saturated magma. The presence ofvolatile-saturated magma at a depth corresponding to the mag-matic reservoir of Okmok is confirmed by petrological evidences(Finney et al., 2008). In this case, the timescale of subsidencewould be controlled by the mechanism of degassing. Alterna-tively, re-melting of a partially crystalline andesite would generatea volatile under-saturated reservoir capable of resorbing the ex-cess volatiles without surface degassing. This study shows howan appropriate chemical characterisation of eruptive products, incombination with thermal modelling can be used to increase ourunderstanding of sub-volcanic processes from the interpretation ofgeodetic signals. A similar approach would help understanding theprocesses responsible for the subsidence observed in several vol-canic systems.

Appendix A. computation of temperatures and melt fractions

Energy conservation implies that:

ρc∂T

∂t+ ρL

∂ X

∂t= k∇T (1)

where ρ is density, T is temperature, t is time, L is latent heat ofcrystallisation, X is melt fraction, and k is conductivity, or

L. Caricchi et al. / Earth and Planetary Science Letters 388 (2014) 166–174 173

∂ H

∂t= k∇T (2)

with

H = ρcT + ρL X (3)

The forward finite difference expression of (2) on a squared grid incylindrical coordinates is:

H p+dti, j − H p

i, j

dt= k

r dr

[(T p

i−1, j − T pi, j

)(r − dr

2

)

+ (T p

i+1, j − T pi, j

)(r + dr

2

)+ (

T pi, j−1 − T p

i, j

)r

+ (T p

i, j+1 − T pi, j

)r

](4)

with subscripts i and j denoting the spatial position on the gridand superscript p denoting position in time. dt is the numericaltimescale. r is the distance to symmetry axis and dr is the lengthof a cell. To ensure numerical stability, dt < K/4 dr2, with the ther-mal diffusivity K = k/ρc.

To determine temperatures and melt fractions, we proceed asfollows:

With Ts , the solidus temperature:

H S = ρcTs (5)

T (H � Hs) = H

ρc(6)

and

X(H � Hs) = 0 (7)

For H > Hs , we use laboratory-determined temperatures and meltfraction to calculate the corresponding H with Eq. (3) and we as-sume that T –X–H relationship between laboratory data is linear,so that for any H calculated with Eq. (4), we can recover T and Xby linear interpolation. The Matlab code with H and the pressureP as input is as follows:%“labTemp” are experimental temperatures (Wagner et al., 1995, Green,%1973, Holloway and Burnham, 1972)%labTemp = [930 985 1000 1015 1035 1045 1050 1075];%“dT” is a correction for pressure of 75C per 2 kb (Beard and Lofgren,1989)dT = −(P−1)*75/2;labTemp = labTemp + dT;%“labMelt” is the set of experimental melt fractions corresponding tolabTemp %(Wagner et al., 1995; Green, 1973; Holloway and Burnham,1972)labMelt = [0 0.53 0.56 0.63 0.83 0.89 0.96 1];%“ labH” is calculated for the experimental pointslabH = ro *c.* labTemp + ro * L. * labMelt;%Temperatures T and melt fractions are interpolated between experimen-tal %points for input Hfor i = 1:length(labH) − 1

H1 = labH(i);H2 = labH(i + 1);T1 = labTemp(i);T2 = labTemp(i + 1);m1 = labMelt(i);m2 = labMelt(i + 1);index = logical(H > H1 & H <= H2);T(index) = T1 + ((T2 − T1)/(H2 − H1)).*(H(index) − H1);melt(index) = m1 + ((m2 − m1)/(H2 − H1)).*(H(index) − H1);

end

References

Annen, C., 2011. Implications of incremental emplacement of magma bodies formagma differentiation, thermal aureole dimensions and plutonism–volcanismrelationships. Tectonophysics 500, 3–10.

Beard, J.S., Lofgren, G.E., 1989. Effect of water on the composition of partial melts ofgreenstone and amphibolite. Science 244, 195–197.

Beget, J.E., Larsen, J.F., Neal, C.A., Nye, C.J., Schaefer, J.R., 2005. Preliminary volcano-hazard assessment for Okmok volcano, Umnak Island, Alaska. Alaska Division ofGeological & Geophysical Surveys Report of Investigation 2004-3, 32 pp.

Belien, I.B., Cashman, K.V., Rempel, A.W., 2010. Gas accumulation in particle-rich suspensions and implications for bubble populations in crystal-richmagma. Earth Planet. Sci. Lett. 297, 133–140. http://dx.doi.org/10.1016/j.epsl.2010.06.014.

Biggs, J., Anthony, E.Y., Ebinger, C.J., 2009. Multiple inflation and deflationevents at Kenyan volcanoes. East African Rift. Geology 37 (11), 979–982.http://dx.doi.org/10.1130/G30133A.1.

Biggs, J., Mothes, P., Ruiz, M., Amelung, F., Dixon, T.H., Baker, S., Hong, S.-H.,2010. Stratovolcano growth by co-eruptive intrusion: The 2008 eruption ofTungurahua Ecuador. Geophys. Res. Lett. 37, L21302. http://dx.doi.org/10.1029/2010GL044942.

Biggs, J., Bastow, I.D., Keir, D., Lewi, E., 2011. Pulses of deformation reveal frequentlyrecurring shallow magmatic activity beneath the Main Ethiopian Rift. Geochem.Geophys. Geosyst. 12. http://dx.doi.org/10.1029/2011GC003662.

Bohrson, W.A., Spera, F.J., 2001. Energy-constrained open-system magmatic pro-cesses I: General model and energy-constrained assimilation and fractional crys-tallization (EC-AFC) formulation. J. Petrol. 42 (5), 1019–1041.

Caricchi, L., Burlini, L., Ulmer, P., Gerya, T., Vassalli, M., Papale, P., 2007. Non-Newtonian rheology of crystal-bearing magmas and implications for magmaascent dynamics. Earth Planet. Sci. Lett. 264, 402–419. http://dx.doi.org/10.1016/j.epsl.2007.09.032.

Caricchi, L., Pommier, A., Pistone, M., Castro, J., Burgisser, A., Perugini, D., 2011.Strain-induced magma degassing: insights from simple-shear experiments onbubble bearing melts. Bull. Volcanol. 73 (9), 1245–1257. http://dx.doi.org/10.1007/s00445-011-0471-2.

de Zeeuw-van Dalfsen, E., Rymer, H., Williams-Jones, G., Sturkell, E., Sigmundsson,F., 2006. Integration of micro-gravity and geodetic data to constrain shallowsystem mass changes at Krafla Volcano, N Iceland. Bull. Volcanol. 68, 420–431.http://dx.doi.org/10.1007/s0445-005-0018-5.

de Zeeuw-van Dalfsen, E., Pedersen, R., Hooper, A., Sigmundsson, F., 2012.Subsidence of Askja caldera 2000–2009: Modelling of deformation pro-cesses at an extensional plate boundary, constrained by time series In-SAR analysis. J. Volcanol. Geotherm. Res. 213–214, 72–82. http://dx.doi.org/10.1016/j.jvolgeores.2011.11.004.

Dragoni, M., Magnanensi, C., 1989. Displacement and stress produced by a pressur-ized, spherical magma chamber, surrounded by a viscoelastic shell. Phys. EarthPlanet. Inter. 56 (3), 316–328.

Dvorak, J., Dzurisin, D., 1997. Volcano geodesy: The search for magma reservoirs andthe formation of eruptive vents. Rev. Geophys. 35, 343–384.

Dzurisin, D., Poland, M.P., Bürgmann, R., 2002. Steady subsidence of Medicine Lakevolcano, northern California, revealed by repeated leveling surveys. J. Geophys.Res. 107 (B12), 2372. http://dx.doi.org/10.1029/2001JB000893.

Euillades, P.A., Velez, M.L., Meljem, M., Cadelli, A., Martinez-Diaz, J.J., 2008. DInSARSBAS data processing in the southern Andes: The Copahue-Agrio Caldera studycase. Paper presented at 4th Alexander von Humboldt International Conference.Eur. Geosci. Union, Santiago.

Fernandez, J., Tiampo, K.F., Rundle, J.B., 2001. Viscoelastic displacement and gravitychanges due to point magmatic intrusions in a gravitational layered solid earth.Geophys. J. Int. 146, 155–170.

Finney, B., Turner, S., Hawkesworth, C., Larsen, J., Nye, C., George, R., Binde-man, I., Eichelberger, J., 2008. Magmatic differentiation at an island-arccaldera: Okmok volcano, Aleutian Islands, Alaska. J. Petrol. 49 (5), 857–884.http://dx.doi.org/10.1093/petrology/egn008.

Fournier, T.J., 2008. Analysis and interpretation of volcano deformation in Alaska:studies from Okmok and Mt. Veniaminof volcanoes. PhD thesis. University ofAlaska, Faribanks.

Fournier, T., Freymueller, J., Cervelli, P., 2009. Tracking magma volume recovery atOkmok volcano using GPS and an unscented Kalman filter. J. Geophys. Res. 114(B2). http://dx.doi.org/10.1029/2008JB005837.

Fournier, T.J., Pritchard, M.E., Riddick, S.N., 2010. Duration, magnitude, and fre-quency of subaerial volcano deformation events: New results from Latin Amer-ica using InSAR and a global synthesis. Geochem. Geophys. Geosyst. 11 (1).http://dx.doi.org/10.1029/2009GC002558.

Freymueller, J.T., Kaufman, A.M., 2010. Changes in the magma system during the2008 eruption of Okmok volcano, Alaska, based on GPS measurements. J. Geo-phys. Res. 115, B12415. http://dx.doi.org/10.1029/2010JB007716. 14 pp.

Ghiorso, M.S., 1985. Chemical mass-transfer in magmatic processes. 1. Thermody-namic relations and numerical algorithms. Contrib. Mineral. Petrol. 90, 107–120.

Ghiorso, M.S., Sack, R.O., 1995. Chemical mass-transfer in magmatic processes. 4.A revised and internally consistent thermodynamic model for the interpolation

174 L. Caricchi et al. / Earth and Planetary Science Letters 388 (2014) 166–174

and extrapolation of liquid–solid equilibria in magmatic systems at elevated-temperatures and pressures. Contrib. Mineral. Petrol. 119, 197–212.

Giordano, D., Russell, J.K., Dingwell, D.B., 2008. Viscosity of magmatic liq-uids: A model. Earth Planet. Sci. Lett. 271, 123–134. http://dx.doi.org/10.1016/j.epsl.2008.03.038.

Gottsmann, J., Rymer, H., Berrino, G., 2006. Unrest at the Campi Flegrei caldera(Italy): A critical evaluation of source parameters from geodetic data inversion.J. Volcanol. Geotherm. Res. 150, 132–145.

Green, D.H., 1973. Experimental melting studies on a model upper mantle compo-sition at high pressure under water-saturated and water-undersaturated condi-tions. Tectonophysics 17, 285–297.

Holloway, J.R., Burnham, C.W., 1972. Melting relations of basalt with equilibriumwater pressure less than total pressure. J. Petrol. 13, 1–29.

Huppert, H.E., Sparks, R.S.J., 1988. The generation of granitic magmas by intrusionof basalt into continental crust. J. Petrol. 29 (3), 599–624.

Kwoun, O.I., Lu, Z., Neal, C., Wicks Jr., C., 2006. Quiescent deformation of the Ani-akchak Caldera, Alaska mapped by InSAR. Geology 34, 5–8. http://dx.doi.org/10.1130/G22015.1.

Lange, R.A., 1994. The effect of H2O, CO2 and F on the density and viscosity ofsilicate melts. In: Volatiles in Magmas. In: Rev. Mineral., vol. 30, pp. 331–369.

Larsen, J.F., Sliwinski, M.G., Nye, C., Cameron, C., Schafer, J.R., 2013. The 2008 erup-tion of Okmok volcano, Alaska: Petrological and geochemical constraints on thesubsurface magma plumbing system. J. Volcanol. Geotherm. Res. 264, 85–106.

Lu, Z., Dzurisin, D., 2010. Ground surface deformation patterns, magma sup-ply, and magma storage at Okmok volcano, Alaska, from InSAR analysis: 2.Coeruptive deflation, July–August 2008. J. Geophys. Res. 115. http://dx.doi.org/10.1029/2009JB006970.

Lu, Z., Mann, D., Freymueller, J., 1998. Satellite radar interferometry measuresdeformation at Okmok volcano. Trans. Am. Geophys. Union 79 (39), 461.http://dx.doi.org/10.1029/98EO00348.

Lu, Z., Mann, D., Freymueller, J.T., Meyer, D.J., 2000. Synthetic aperture radar inter-ferometry of Okmok volcano, Alaska: Radar observations. J. Geophys. Res. 105(B5), 10791. http://dx.doi.org/10.1029/2000JB900034.

Lu, Z., Masterlark, Tim, Power, John, Dzurisin, Daniel, Wicks, C.J., 2002. Subsidenceat Kiska volcano, Western Aleutians, detected by satellite radar interferometry.Geophys. Res. Lett. 29 (18), 2-1–2-4. http://dx.doi.org/10.1029/2002GL014948.

Lu, Z., Fielding, E., Patrick, M.R., Trautwein, C.M., 2003. Estimating lava volume byprecision combination of multiple baseline spaceborne and airborne interfero-metric synthetic aperture radar: The 1997 eruption of Okmok volcano, Alaska.IEEE Trans. Geosci. Remote Sens. 41 (6), 1428–1436.

Lu, Z., Masterlark, T., Dzurisin, D., 2005. Interferometric synthetic apertureradar study of Okmok volcano, Alaska, 1992–2003: Magma supply dynam-ics and postemplacement lava flow deformation. J. Geophys. Res. Solid Earth(1978–2012) 110 (B2). http://dx.doi.org/10.1029/2004JB003148.

Lu, Z., Dzurisin, D., Biggs, J., Wicks Jr., C., McNutt, S., 2010. Ground surface de-formation patterns, magma supply, and magma storage at Okmok volcano,Alaska, from InSAR analysis: 1. Intereruption deformation, 1997–2008. J. Geo-phys. Res. 115. http://dx.doi.org/10.1029/2009JB006969.

Lundgren, P., Usai, S., Sansosti, E., Lanari, R., Tesauro, M., Fornaro, G., Berardino, P.,2001. Modeling surface deformation observed with synthetic aperture radar in-terferometry at Campi Flegrei caldera. J. Geophys. Res. 106 (B9), 19355–19366.

Mann, D., Freymueller, J., 2003. Volcanic and tectonic deformation on Unimak Islandin the Aleutian Arc, Alaska. J. Geophys. Res. 108 (B2), 2108. http://dx.doi.org/10.1029/2002JB001925.

Mann, D., Freymueller, J., Lu, Z., 2002. Deformation associated with the 1997 erup-tion of Okmok volcano, Alaska. J. Geophys. Res. 107 (B4), 2072.

Masterlark, T., 2007. Magma intrusion and deformation predictions: Sensitivi-ties to the Mogi assumptions. J. Geophys. Res. Solid Earth 112, B06419.http://dx.doi.org/10.1029/2006JB004860.

Masterlark, T., Haney, M., Dickinson, H., Fournier, T., Searcy, C., 2010. Rheologicand structural controls on the deformation of Okmok volcano, Alaska: FEMs,InSAR, and ambient noise tomography. J. Geophys. Res. 115. http://dx.doi.org/10.1029/2009JB006324.

Miller, T.P., Smith, R.L., 1975. Two caldera-forming eruptions on Umnak Island, east-ern Aleutian Islands. U.S. Geol. Surv. Circ. 733, 45.

Miller, T.P., McGimsey, R.G., Richter, D.H., Riehle, J.R., Nye, C.J., Yount, M.E., Dumoulin,J.A., 1998. Catalog of the historically active volcanoes of Alaska. U.S. Geol. Surv.Open-File Rep. 98-582, 104 pp.

Miyagi, Y., Freymueller, J.T., Kimata, F., Sato, T., Mann, D., 2004. Surface deformationcaused by shallow magmatic activity at Okmok volcano, Alaska, detected by GPScampaigns 2000–2002. Earth Planets Space 56 (12), E29–E32.

Mogi, K., 1958. Relations between the eruptions of various volcanoes and the de-formations of the ground surfaces around them. Bull. Earthq. Res. Inst. Univ.Tokyo 36, 99–134.

Moore, G., Vennemann, T., Carmichael, I., 1998. An empirical model for the solubilityof H2O in magmas to 3 kilobars. Am. Mineral. 83, 36–42.

Newman, S., Lowenstern, J.B., 2002. VOLATILECALC: a silicate melt-H2O–CO2 solu-tion model written in Visual Basic for excel. Comput. Geosci. 28 (5), 597–604.

Pagli, C., Sigmundsson, F., Árnadóttir, T., Einarsson, P., Sturkell, E., 2006. Deforma-tion of the Askja volcanic system: constraints on the deformation source fromcombined inversion of satellite radar interferograms and GPS measurements.J. Volcanol. Geotherm. Res. 152, 97–108.

Pitzer, K.S., Sterner, S.M., 1994. Equations of state valid continuously from zeroto extreme pressures for H2O and CO2. J. Chem. Phys. 101 (4), 3111–3116.http://dx.doi.org/10.1063/1.467624.

Poland, M., Burgmann, R., Dzunisin, D., Lisowski, M., Masterlark, T., Owen, S.,Fink, J., 2006. Constraints on the mechanism of long-term, steady subsi-dence at Medicine Lake volcano, northern California, from GPS, leveling,and InSAR. J. Volcanol. Geotherm. Res. 150, 55–78. http://dx.doi.org/10.1016/j.jvolgeores.2005.07.007.

Pritchard, M.E., Simons, M., 2004. An InSAR-based survey of volcanic deforma-tion in the southern Andes. Geophys. Res. Lett. 31, L15610. http://dx.doi.org/10.1029/2004GL020545.

Robertson, E.C., 1988. Thermal properties of rocks. U.S. Geol. Surv. Open-File Rep.88-441, 106 pp.

Sahagian, D.L., Proussevitch, A.A., 1996. Thermal effects of magma degassing. J. Vol-canol. Geotherm. Res. 74 (1–2), 19–38.

Segall, P., 2010. Earthquake and Volcano Deformation. Princeton University Press,ISBN 9780691133027.

Sigmundsson, F., Vadon, H., Massonet, D., 1997. Readjustment of the Krafla spreadingsegment to crustal rifting measured by satellite radar interferometry. Geophys.Res. Lett. 24, 1843–1846.

Sparks, R.S.J., Biggs, J., Neuberg, J.W., 2012. Monitoring Volcanoes. Science 335(6074), 1310–1311. http://dx.doi.org/10.1126/science.1219485.

Sturkell, E., Sigmundsson, F., Slunga, R., 2006. 1983–2003 decaying rate of deflationat Askja caldera: pressure decrease in an extensive magma plumbing system ata spreading plate boundary. Bull. Volcanol. 68, 727–735. 99–134.

Sturkell, E., Sigmundsson, F., Geirsson, H., Ólafsson, H., Theodórsson, T., 2008. Multi-ple volcano deformation sources in a post-rifting period: 1989–2005 behaviourof Krafla, Iceland constrained by levelling, tilt and GPS observations. J. Volcanol.Geotherm. Res. 177 (2), 405–417.

Velez, M.L., Euillades, P., Caselli, A., Blanco, M., Díaz, J.M., 2011. Deformation of Co-pahue volcano: Inversion of InSAR data using a genetic algorithm. J. Volcanol.Geotherm. Res. 202 (1), 117–126.

Wagner, T.P., DonnellyNolan, J.M., Grove, T.L., 1995. Evidence of hydrous differen-tiation and crystal accumulation in the low-MgO, high-Al2O3 lake basalt frommedicine lake volcano, California. Contrib. Mineral. Petrol. 121 (2), 201–216.

Wicks, C.W., 2002. Magmatic activity beneath the quiescent Three Sisters volcaniccenter, central Oregon Cascade Range, USA. Geophys. Res. Lett. 29 (7), 1122.http://dx.doi.org/10.1029/2001GL014205.

Worster, M.G., Huppert, H.E., Sparks, R.S.J., 1990. Convection and crystallization inmagma cooled from above. Earth Planet. Sci. Lett. 101, 78–89.

Yokoyama, I., 1986. Crustal deformation caused by the 1914 eruption of Sakura-jima volcano, Japan and its secular changes. J. Volcanol. Geotherm. Res. 30,283–302.

Zimmer, M.M., Plank, T., Hauri, E.H., Yogodzinski, G.M., Stelling, P., Larsen, J., Singer,B., Jicha, B., Mandeville, C., Nye, C.J., 2010. The role of water in generating thecalc-alkaline trend: new volatile data for aleutian magmas and a new tholeiiticindex. J. Petrol. 51 (12), 2411–2444. http://dx.doi.org/10.1093/petrology/egq062.