Permeability evolution during non-isothermal compaction in volcanic conduits and tuffisite veins: Implications for pressure monitoring of volcanic edifices

28 July 2021

Original Citation:

Permeability evolution during non-isothermal compaction in volcanic conduits and tuffisite veins: Implications for

pressure monitoring of volcanic edifices

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DOI:10.1016/j.epsl.2019.115783

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Contents lists available atScienceDirect

Earth

and

Planetary

Science

Letters

www.elsevier.com/locate/epsl

Permeability

evolution

during

non-isothermal

compaction

in

volcanic

conduits

and

tuffisite

veins:

Implications

for

pressure

monitoring

of

volcanic

edifices

S. Kolzenburg

a

,

b

,

c

,

∗

, A.G. Ryan

d

, J.K. Russell

d

a_{Ludwig-Maximilians-UniversityMunich,DepartmentofEarthandEnvironmentalSciences,SectionforMineralogy,PetrologyandGeochemistry,Theresienstraße}

41,80333München,Germany

b_{McGillUniversity,DepartmentofEarthandPlanetarySciences,3450UniversityStreet,H3A0E8Montreal,Quebec,Canada} c_{UniversityatBuffalo,DepartmentofGeology,126CookeHall,Buffalo,NY14260,UnitedStatesofAmerica}

d_{VolcanologyandPetrologyLaboratory,Earth,OceanandAtmosphericSciences,UniversityofBritishColumbia,2020-2207MainMall,Vancouver,V6T1Z4,}

Canada

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received26January2019

Receivedinrevisedform15August2019 Accepted16August2019

Availableonline11September2019 Editor: T.A.Mather

Keywords: volcanomonitoring thermalmodeling welding compaction viscoussintering permeability

Explosive volcanic eruptions are destructive geological phenomena that pose hazards of significant socioeconomic impactand potential lossoflife. Effectiveriskmitigationand decisionmakingpriorto andduringvolcaniccrisesrequirereal-timemonitoringofgasoverpressure–thesinglemostimportant drivingforceforexplosiveeruptions.Developmentandreleaseofgasoverpressureareregulatedbygas lossthroughpermeablepathwaysthatareinherentlytransient.

Here, we use geometry-dependent conductive cooling models, in concert with the most up-to-date welding and permeability models, to assess the potential for “freezing in” permeability within (1) conduit-fillingpyroclasticdepositsand(2)tuffisiteveinswithintheedifice.Wefindthatbothgeometry and dimension of each deposit dictate its thermal evolution and, with that, its transient outgassing capacity. Rapid cooling of thin sheet-like tuffisite veins preserves high porositiesand permeabilities. Incontrast,widecylindricalconduit-filling depositscoolslowlyandpermeabilityisannihilatedovera period ofminutestohours.Thishighlightsthat conduit-fillingdeposits losetheiroutgassing capacity throughwelding,whiletuffisiteveins(previouslythoughttorapidlyseal)canformlong-livedoutgassing features.Weusethemodelresultstocalculatethetimedependentgasflowpartitioningbetweenboth degassinglithologies.Basedonthereconstructedoutgassingpatternweoutlinethepotentialtousethe gasflowbalancebetweenthecentralconduitanddistalfumarolesfedbytuffisiteveinsasasimpletool tomonitorgasoverpressurewithinavolcanicedifice.

©2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

Explosivevolcaniceruptionsaredestructivegeological phenom-enathat posehazardsofsignificant socioeconomic impact (pyro-clastic flows, tephra dispersal) and potential loss of life. Risk is especially highin densely populated areas wheremonitoring in-frastructureisscarce.Effectiveriskmitigationanddecisionmaking priortoandduringvolcaniccrisesrequirereal-timemonitoringof gasoverpressure–thesinglemostimportantdrivingforcefor ex-plosiveeruptions.

*

Correspondingauthorat:Ludwig-Maximilians-UniversityMunich,Department ofEarthand EnvironmentalSciences, SectionforMineralogy,Petrologyand Geo-chemistry,Theresienstraße41,80333München,Germany.

E-mailaddress:[email protected](S. Kolzenburg).

All silicatemeltsexsolve volatilesduring ascent anderuption. Volcanicoverpressure develops whenthe volume ofgas released fromthe magma exceeds theoutgassing capacityof thevolcanic

system which, itself, depends on sustained permeable pathways

(Farquharsonetal., 2017b; Jaupart andAllègre,1991).When this (over)-pressure exceeds the strength of the confining rock mass, portions of the edifice fail, resulting in rapid decompression of themagmaandexplosiveeruption(AlidibirovandDingwell,1996; Rutherfordetal.,1985)

Permeable pathways (i.e. networks of interconnected void

space, includingbubbles, cracks andspacesbetweencrystals and

clasts) permit exsolved gases to vent from the magma through

the volcanic edifice. The abundance and outgassing capacity of

permeable materials therefore moderates gas pressurization and reduces the potential for explosive eruption (Castro et al.,2012;

https://doi.org/10.1016/j.epsl.2019.115783

0012-821X/©2019TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBY-NC-NDlicense (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Farquharson et al., 2017b; Jaupart and Allègre, 1991; Kennedy et al., 2010; Kolzenburg andRussell, 2014). Permeable pathways

can includeconnectedbubble networksin theascending magma

(KlugandCashman,1996; Rust andCashman, 2004), networksof cracksandvoidspacesinthepyroclasticmaterialthatfillthe vol-canic conduit (Chevalier et al., 2017; Eichelberger et al., 1986; Kennedy et al., 2010; Kolzenburg and Russell, 2014), and tuff-isiteveins,representingvolcanichydro-fracturesproppedopenby fragmental juvenile and accessory material (Heiken et al., 1988; Kendricketal.,2016; Kolzenburgetal., 2012; Saubin etal., 2016; Stasiuketal.,1996; Tuffenetal.,2003).

Mostintermediate to silicic volcanoes that produceVulcanian toPlinianeruptionsmaintainpost-eruptivepermeability.Evidence for efficient, long lived permeable networks includes: 1) perva-sive, long lived and large volume fumarole outgassing from ex-plosive volcanoes (Edmonds et al., 2003; Holland et al., 2011; Taran et al., 2002), 2) chemical variations within clasts in tuff-isite veins that document active outgassing on the timescale of hours to days (Berlo et al., 2013; Castro et al., 2012; Paisley et al., 2019), 3) changes in fumarole composition and volcanic

geothermal spring water chemistry reflecting changes in magma

outgassing patterns(Taran etal., 2002), and 4) constant or peri-odicoutgassingthroughwellestablishedandlonglivedlavadomes withoutanassociatedlargerexplosiveevent(Hollandetal., 2011; Lavalléeetal.,2012).

Incontrast,experimentsandmodels(Farquharsonetal.,2017b; GrunderandRussell,2005; Kolzenburg andRussell, 2014; Russell and Quane, 2005; Wadsworth et al., 2014) suggest the porosity andpermeabilityofvolcanicmaterialstobeephemeralwhenheld abovetheirglasstransitiontemperatures(Tg).Thislossof

perme-abilityathightemperatureshasalsobeenobservedinsomesilicic vents(Schipperetal.,2013).AttemperaturesinexcessofTg,

den-sificationprocesses,involvingreductionofporespaceand perme-abilityloss,canoperateontimescalesofminutestohoursvia vis-cousannealingandcompaction(i.e.sinteringorwelding(Grunder and Russell, 2005; Wadsworth et al., 2014)). Rapid densification andloss of permeabilityhas the inevitable consequence of lead-ingtorisinggasoverpressures andrenewedexplosivity(Edmonds etal.,2003; Farquharsonetal., 2017b; JaupartandAllègre,1991; KolzenburgandRussell,2014; MassolandJaupart,1999).

Onewaytoreconcileobservationsofnaturalsystems(sustained volcanic outgassing) andexperimental results (rapid loss of per-meability) is to consider the thermal histories of the pyroclastic depositsthatmakeup thevolcanicedifice. Here,weexplorehow geometryandsizeaffecttheextentandtimescaleofwelding dur-ingcoolingofhotpyroclasticdeposits,including:i)conduitfilling deposits and ii) networks of tuffisite veins within the host vol-canic edifice (i.e. emplaced within cool country rockrather than withinthemagmacolumn).Specifically,wehavecoupledamodel

for viscous compaction to conductive cooling models for these

twogeometries. Ourresultselucidate thetimescalesforheatloss vs.viscouscompactionandexploretheimplications for annihilat-ingorpreservingpermeabilityand,therewith,controllingeruption style.

2. Methods:aseriesofmodels 2.1. Modeloverview

Ouranalysisofweldingandcompactionprocessescouplesfour separate typesofmodels, Fig.1; modelparameters areshown in Table1.Weinclude:i)thermalmodelsforcoolingofconduitsand tuffisite sheets at their respective relevant dimension, Tables A1

andA2 (e.g.,Carslaw and Jaeger,1959; Crank,1979, ii)chemical modelsforthe melt properties(e.g.,H2Osolubility,viscosity, Tg;

Fig. 1. Flow chart showing the architecture of the numerical model. (Giordano etal., 2008; Liu etal., 2005), iii) models for porosity-permeabilityrelationships (WrightandCashman,2014),andiv) a viscous compactionmodel (Russelland Quane, 2005). Combined, thesecoupledmodels provideasystematicdescriptionofthe pa-rameters guidingthechange inpermeabilityofconduitinfill and tuffisite veinsduringweldingandcompaction.Wehaveorganized thesemodelsinseriessotheypredictweldingprogressasa func-tionoftimeiniterativeintervalsof1Hz.

Fig.1showsaschematicrepresentationofthemodel organiza-tion: for each time step themodel updatesthe temperatureand porosity, and calculates the temperature-dependent solubility of waterinthemelt(Liuetal.,2005).Solubilityresultsareforwarded to the melt viscosity modelof Giordano et al. (2008) torecover thetemperature- andH2O-dependentmeltviscosityandTg.Ifthe

time step inmodel temperature remains above Tg, the viscosity

valueisfedintotheweldingandcompactionmodelofRusselland Quane (2005) andthechangeinporosityoverthistimeintervalis calculatedandusedinthenext iteration(i.e.



t)ofthemodel.If themodeltimesteptemperatureisbelowTg thecurrentporosity

value isacceptedasthefinal porosityandmarksthecessationof weldingandcompaction(i.e.the“frozenin”porosity).Thedeposit permeabilityis thencalculated afterWrightandCashman (2014) to retrieve the “frozen in” permeability. These iterations are re-peated until either T

<

Tg or

Φ

=

0. While magmas commonly

retain small amountsof residualporosity when reaching the im-permeablestate,weuse0asanumericalstoppingcriterionforthe compactionmodelanddonotdefineanarbitraryfinalporosityas astoppingcriterion.Variationsinthisparameterhavenoeffecton

theimplications outlined in thediscussion since the permeabili-tiesexpectedattheselowporositiesarewellbelowthoserelevant for the discussion (

<

10−16 m2). Note that this model assumes that ifmaterialis emplaced at T

<

Tg porosity and permeability

are preservedsince compactionandporosity reduction are mod-eledasaviscous process.Thismodeldoesnot considertheeffect ofmineralprecipitation orsolid state diffusionsince they act on muchlongertimescales;forexamples seeTaranetal. (2002) and Ryanetal. (2018), respectively.Further, thismodeldescribesone emplacementeventanddoesnotconsiderrepeatedfragmentation andhealingofeitherdeposit.

2.2.Thermalmodeling

2.2.1. Constraintsonmodelgeometryanddimension

Ratesof heat dissipation are dependent on the geometry(i.e. surfacetovolumeratio)anddimensionsofthecoolingbody.Here, we have compiled the available literature to constrain the di-mensions ofvolcanic conduits (Table A1) andtuffisite veins (Ta-ble A2) associated with explosive volcanism. Constraints of con-duit diameters during active explosive eruptions are inherently difficultasthey eitherrelyonposteruptivemeasurements or in-ferences fromthe eruption column height andwidth (see refer-encelist in Table A1). The largest conduits reach 100–200 min diameter(Sigurdsson etal., 2015), however,the majority are re-ported at less than 40–60 m in diameter (Holland et al., 2011; Lavallée et al., 2012; Rutherford et al., 1985; Sigurdsson et al.,

2015). Conduit diameters supporting Vulcanian to Plinian

erup-tions, which are most relevant to the welding, compaction and

pressurizationprocesses,are generally narrower,andlie between 10–20 m(Sigurdssonetal., 2015). Wehaveadopted10 masthe conduitdiameterforourcoolingandwelding/compaction model-ing to maximize the potential for preserving permeabilityin the conduitduringcooling.

Estimates of characteristic tuffisite vein thickness are primar-ilybased on measurements of vein material preserved in blocks ejectedfrom andesiticto rhyolitic volcanoes during Vulcanian to Plinian eruptions (Table A2). Reported thicknesses vary between

0.001 m and 0.2 m (Berlo et al., 2013; Castro et al., 2012;

Farquharson et al., 2015; Kendrick et al., 2016; Kolzenburg et al., 2012; Saubin etal., 2016).Where tuffisite veinsare observed withindissectedextinct volcanicconduitsandtheir margins(e.g., Torfajökull,Tuffenetal.,2003andMuleCreek,Stasiuketal.,1996), measurementsbroadlyagreewiththerangeofvaluesreportedfor tuffisite preserved in ejected blocks. Only in rare cases do vein

thicknesses exceed 0.2 m: in a drill hole into the Inyo Domes

(Heiken et al., 1988) vein thicknesses up to 0.4 m are reported, andinthewallrocksoftheSchwäbischeAlpvolcanoes,Germany (Cloos,1941) veinthicknessesreach0.7m.Basedontheavailable dataweassign0.1 masanaveragetuffisitethicknessforour cool-ingandwelding/compactionmodeling.

2.2.2. Coolingmodel

Weemploytwoseparate,geometry-dependentmodelsto simu-latecoolinghistories:oneforcylinders(i.e.conduits),andonefor sheets(i.e. tuffisites).Weassumecooling oftheconduitand tuff-isiteveinsisdominatedby conductionandtheeffectsof convec-tivecoolingoradvectiveheatlossarenotconsidered.Any contri-butionoflatentheatofcrystallizationisassumedtobenegligible becausetheweldingandcompactionprocessesinsilicicmelts op-erateon muchfastertimescalesthan crystallization(Vetereetal.,

2015). We also assume thethermal diffusivities (

κ

) ofeach rock type(i.e.fragmental materialandcountryrock)do notchangein spaceorwithtime;thusweassignanaveragevalueforeachrock type (Table 1).We employ a 1D transient modelfor thethermal

Table 1

Modelparameters.

Symbol Description Values in model

Φcr Crystal fraction 0

Φp Porosity fraction 0.4

K Thermal diffusivity (m2_{/s) 10}−6

a Conduit radius (m) 5±2.5

b Vein halfwidth (m) 0.05±0.025

Tcr Country rock temperature (C) 150

T i Emplacement temperature (C) 750–800

P Bulk density (kg/m3_{) 2500}

P Pore pressure (MPa) 1

o Load stress (MPa) depth dependent

At Cooling interval (s) 1

evolutionofconduitmargins(seeHeapetal.,2017andSchauroth etal.,2016fordetailsandthereasoningthereof).

We model the cooling of conduit-filling pyroclastic materials, approximatedasacylinder,usinganequationforaninfinite cylin-dricalbody(equation3.11;Crank,1979):

T

(

t

)

= (

Ti

−

Tcr

)



1

−

exp



−

a2 4

κ

t



+

Tcr (1)

where T isthetransienttemperatureatthecenter ofthecylinder, Ti is the emplacement temperatureofthe conduit fill, Tcr is the

ambient temperatureofthe country rock(i.e. volcanic edifice),a iscylinderradius(5m),

κ

isthethermaldiffusivity,andt istime (seeTable1forunits).

Wemodelcoolingofthetuffisiteveinusingacoolingmodelfor aninfinitesheet,followingtheequationsforaninfiniteregionwith two boundary condition temperatures (equation (3), section 2.2, CarslawandJaeger,1959):

T

(

t

)

= (

Ti

−

Tcr

)



erf



b 2

√

(

4

κ

t

)



+

Tcr (2)

where T isthetransienttemperatureatthecenter ofthesheet,Ti

istheemplacementtemperatureofthevein fill,andb isthehalf widthofthetuffisitevein(0.05 m);allotherparametersasdefined above.

2.2.3. Inputtemperatures

Densification ofpyroclastic deposits by viscous compaction is limited to temperatures above the glass transition temperature (Tg) (Grunder and Russell, 2005). The time interval for reaching Tgispredictedbyourtwothermalmodels(i.e.cylindricalconduit vs. narrow sheet) anddepends on the initial temperature of the volcanicmaterial,thetemperatureoftheenclosingvolcanicedifice andthematerial’sthermaldiffusivity.

The temperatures of volcanic edifices reported in the

litera-ture span from ambient near the surface to

∼

350◦C in large

geothermalsystems(e.g.Eldersetal.,2014andreferencestherein).

We choose 150◦C as the edifice temperature for the purposes

of modeling. Eruptive temperatures ofpyroclastic materials span

∼

700–1000◦C,asinferredbyphaseequilibriaexperiments,drilling, thermoremanent magnetization, and analyses of textures in ign-imbrites (see e.g. Lesti et al., 2011; Rutherford et al., 1985 and references therein). For modeling purposes we assign 775◦C as the emplacementtemperature ofthepyroclastic material both in theconduitandthetuffisite veins.Higher initialtemperaturesfor each environment result in longer cooling time to Tg, whereas

cooler initial temperatures wouldresult in shorter cooling times (seeAppendixA3fordetails).

2.3. Compactionmodeling 2.3.1. Meltviscosity

Melt viscosity has been shown to exert the strongest

con-trolon the rate of porosity loss during welding and compaction (Farquharson et al., 2017b; Heap et al., 2014; Kolzenburg and Russell, 2014; Quane and Russell, 2005; Vasseur et al., 2013; Wadsworthetal., 2014).Inour modeling,we adoptthehigh Fe-rhyolitic (i.e. tholeiitic)composition of Hrafntinnuhryggur, Krafla, Iceland,reportedinTableA3(Ryanetal.,2015; Tuffenetal.,2008). We allow for melt viscosity to vary as a function of both

tem-perature and H2O content. We assume that upon fragmentation

thepore spaceinthe pyroclastic conduit infilland tuffisiteveins communicateswith the atmosphere (i.e. they participate in out-gassing).Basedonthisassumptionweascribeaconservativevapor overpressure of1MPa inthe pyroclastic material.We modelthe temperature-dependentdissolvedH2Ocontentusingthesolubility model ofLiu et al. (2005). As H2O solubilityis inversely related totemperature (Liuetal., 2005; Ryanetal., 2015), thedissolved watercontentwillincreaseduring cooling,thereby reducingboth themeltviscosityandTg (Giordanoetal.,2008).Thisexpandsand

expandingthe“welding window”–the temperaturerangewhere

pyroclastic material densifies by viscous processes. We then use themodelofGiordanoetal. (2008) toquantifythetransientmelt viscosity and Tg as a function of temperature and the modeled

transient H2Ocontent.Thecalculated melt viscosityisforwarded tothewelding/compactionmodel.

2.3.2. Welding

Werearrangedtheweldingequation developedbyRussell and Quane (2005) toexpressexplicitlythechanges inporosity asthe deposits cooland compact. Thismodel is frequently used to

ex-amine the welding and compaction of viscous materials (Heap

et al., 2015; Heap et al., 2014; Kolzenburg and Russell, 2014; Vasseuretal.,2013; Wadsworthetal.,2014).

Sinceweldingandcompactionoccurinaconfinedenvironment, thevolumetricstrain(

ε

v)canbeattributedcompletelytotheloss ofporosity:

ε

v

=



Φ

0

− Φ

1

− Φ



(3)

where

Φ

0 is the initial porosity and

Φ

is the evolving porosity duringcompaction.Quaneetal. (2009) modeled volumetricstrain inthedepositasdependentontime,stressandmeltviscositywith therelationship:

ε

v

=



1

− Φ

0

α



ln



ασ



t

η

0

(

1

− Φ

0

)

+

e −αΦ₀ 1−Φ0



+ Φ

0 (4)

where

η

0 is the melt viscosity(Pa s),



t the time difference be-tweenemplacementandthetimeofinterest(s),

σ

theloadstress in the deposit (Pa) and

α

is a dimensionless fitting parameter accounting for the textural heterogeneity of the compacting de-posit.Forweldingofcrystal-freeglassfragments,

α

is0.78

±

0.15 (Quaneetal.,2009).Forcrystal-bearingglassfragmentsthisvalue ishigher (

α

=

2

.

0 Heapet al., 2014). Giventhat the crystal con-tentsintuffisiteveinsandpumicesaregenerallylow(Castroetal.,

2012; Tuffenetal.,2003),weuse0.78for

α

.

Wesetaninitialporosityof40%(i.e.aporosityfractionof0.4) forour modeling, assuming that the particles are looselypacked duringemplacement (RussellandQuane, 2005; Wright and Cash-man,2014) andassumean averagedenserockequivalent density

of 2500 kg/m3. We model depths from10 to 500 m. These are

consistentwiththeshallowdegassingregimewheretuffisiteveins areexpectedtobefound(Heikenetal.,1988; Saubinetal., 2016;

Stasiuketal.,1996).Thestressactingduringcompactionis calcu-latedasafunctionofdepthusingthefollowingformula:

σ

=

ρ

gh (5)

where

σ

is the load stress (Pa),

ρ

the deposit density (kg/m3_), g the gravitationalaccelerationandh thedepth(m).Fortuffisite veinsweassumetheoverburden(i.e.thevolcanicedifice)tohave aconstantbulkdensityof2500kg/m3_.

Whilepurecompactionofconduitinfilldepositswouldnot in-crease the load at any given initial location in the deposit but merely reduce the height of the compacting deposit, it is com-monly observed that volcanicdomes forminthe crater after ex-plosive eruptions.Examples include the 1980 eruption of M. St. Helens(Swanson andHolcomb,1990) or the2300BPeruptionof Mt Meager (Hickson et al., 1999). The porosity loss is therefore compensated by risingmaterial through the conduit,resulting in densification andan increase inloadat afixed depth. Thestress acting on the conduit-filling deposits is therefore modeled as a functionofdepthanddensityoftheoverlyingdeposits,which in-creases during compaction asa function ofthe densification (i.e. porosityloss)oftheoverburden.Wedonotaccountforporefluid pressure whichmay reduce theeffectiveloadon thecompacting deposit. Therefore the resulting compaction timescales represent

minimumvalues.

2.3.3. Permeability

The development of empirical models spanning a large range

in permeability was initially hindered by the lower

measure-ment limit of commercial permeameters, a limitation that has

been addressed via custom built devices that enable

measure-ments down to

∼

10−23 m2 see Farquharson et al. (2015) and Kolzenburg et al. (2012) and references in both. A number of models describe the porosity-dependent permeability of volcanic fragmentalmaterials (Heapetal.,2015; KlugandCashman,1996; Wadsworthetal.,2016; WrightandCashman,2014).These mod-elsareprimarilyempirical,andbasedonporosityandpermeability measurementsofnaturalmaterialsorexperimentalproducts.

WehavesummarizedthesemodelsinFig.A1.Allmodelshave broadlythesameshape,savethetwo-stepevolutionpredictedby Heapetal. (2015). Becauseofthe similarities intheway perme-ability decayswithdecreasing porosity,choosing onemodel over anotherchanges theabsolutepermeability(Fig. A1A),butnot the magnitudeofpermeabilitychange(Fig.A1B).Here,weusethe per-meability(k)modelpresentedbyWrightandCashman (2014) (red lineinFig.A1A):

k

=

1

.

3

×

10−21

Φ

5.2 (6)

asitwasfittomeasurementsfromsixnaturally-occurringwelded tuff deposits. Their model accounts for the change in porosity-dependentpermeabilityasmeasuredparalleltothe welding/com-paction fabric. This model has the advantage that it is simple, anddoes notinclude agrain size parameter. However, grain size can play andimportant role and varies drasticallydepending on the nature of and energy involved in the fragmentation process (Kolzenburg et al., 2013). Thus, ifone were toknow or assign a mono- or poly-dispersegrain size distributionto a welding/com-pacting deposit, the modelof Wadsworthet al. (2016) would be moresuitable.

3. Results

3.1. Thermalevolutionofvolcanicoutgassingsystems

Figs. 2A and 2B summarizethe thermal evolution of thetwo geometries: volcanic conduit and tuffisite vein, respectively. The

Fig. 2. Thermalevolutionwithinthecoolingdeposits,plottedashalfwidths.SubplotsAandBshowthedeposittemperatureasafunctionofdistancefromthewallrockat timeintervalsbetween1 min and1 h.SubplotCshowsazoominoftheresultsofthethermalmodelastemperaturevs.distancefromthewallrockforthetuffisitevein (solidlines)andtheconduitdeposit(dottedlines)fortimesasinAandB.

modelresultsdemonstrate howthe geometryandlarger scaleof theconduit,andtheassociatedsmallsurface tovolumeratio, in-ducesalarge thermalinertia–mostofthe depositremainsnear the emplacement temperature (Ti) over long timescales. Narrow

tuffisite veins, on the other hand,have a greater surface to vol-umeratio.Therefore,theentiretuffisiteveinvolumecoolsrapidly,

quenching to temperatures below Tg within minutes after

em-placement.

When plotted at the same horizontal scale (Fig. 2C) it be-comes apparent that, atthe cooling interface, both models show a similar thermal evolution during the initial few minutes and onlydivergewithincreasingtime(t

>

15 min).Thisisduetothe large volume of conduit material, which increases thermal iner-tiaandslowsdown coolingneartheconduitwall.Overthesame timescale,thintuffisiteveinscoolquickly,quenchingtobelowTg

int

<

30 min.

3.2.Porosity/permeabilityevolutionduringweldingandcompaction

Our model predicts porosity (subplots A and C) and

perme-ability (subplots B and D) during compaction until T

=

Tg or

Φ

=

0 as a function of normalizedlocation (i.e.margin vs. inte-rior)withinthedeposit.The modelresults(Fig.3)fortuffisitesof 10cmthicknessandconduitsof10m diametershow loadstress (i.e.depth)tohaveafirstordereffectonthecompactionefficiency incoolingdeposits.Increasingloadstressresultsinmoreefficient compaction– this effectis observed for both outgassing litholo-gies. However,asshownschematically inFig.3, whilethecenter oftuffisiteveinsdecreasesinporositywithincreasingdepth, tuff-isitemarginsalwayscoolsufficientlyfasttoretainhighporosities andpermeabilities.

Acomparisonofthe twooutgassingdeposittypesshowsthat, forexample,at100 m burial depth

∼

90% ofa 10cm wide tuff-isite vein remains at a permeability

>

10−14 _m2_{. In contrast, at} thesamedepth lessthan 1% ofthecross section ofa conduitof 10 mdiameter remains above 10−14 _m2_{.This demonstrates that} inconduitdeposits onlythezone indirect contactwiththe wall rockcoolssufficiently fasttoretain highporosity and permeabil-ityandthat,oncequenched,asingle10cmwidetuffisiteveinhas thesameoutgassingcapacityastheoutermost5–10cmofa10 m wideconduit.

3.3.Varyingemplacementparameters

The thermal model (Fig. 2) shows that the cooling history is

fundamentally dependenton thegeometry anddimension ofthe

deposit. Slow cooling in wide, cylindrical conduits supports in-tenseweldingandcompactionwhilstfastcoolingofnarrow,sheet like,veinssuppressesweldingandcompactionintensity. Emplace-ment temperaturealsoaffects the rateandefficiencyofthe pro-cess, wherea larger temperaturedifferential between Ti and Tg

createsalargerweldingwindowandmoreintensewelding.A de-tailed investigation of these parameters is presented in Figs. A2

and A3. The results show that increasing conduit diameter and tuffisite width, or emplacement temperature, decreases the frac-tion of the deposit that remains permeable, affecting the abso-lutecross-sectionalareaavailable tosupportoutgassing.However, while changes in Ti and length scale(radius a or vein thickness b inequations(1) and(2),respectively) affecttheabsolutevalues of porosity andpermeability for both deposittypes, the relative changes andthe resultingimplicationsforthegas flow partition-ingfollowthesameglobalpattern(see alsoAppendixA4). 4. Discussion

Results from our model simulations delineate the conditions wherebyconduitmarginsandtuffisiteveinsareabletoretainhigh porosity andpermeabilityduetoquenching. Yet,ourresults sug-gest that tuffisites hosted within the cool edifice retain higher porosities and permeabilities than measured for tuffisiteshosted in the magma (Kendrick et al., 2016; Kolzenburg et al., 2012; Saubin etal., 2016; Tuffen etal.,2003). Inthefollowing sections

we show how seemingly contradictory observations on 1) long

timescales of tuffisites as active gas pathways recorded in geo-chemicalsignatures(Berloetal.,2013; Paisleyetal.,2019; Saubin etal.,2016) and2)shorttimescalesofpermeabilityannihilationin tuffisitesproposedbyexperimentalandmodelingefforts,fitintoa unifiedconceptualmodelbyaccountingforitsnon-isothermal na-ture. Finally, we outline the potential use of these insights asa newmonitoring approachfor active volcanoesthat typically pro-duceVulcaniantoSub-Plinianeruptions.

Forthe purposeofthismodelwe assume cylindricalconduits andsheet-liketuffisiteveins(Seesection2.2.1).Assuch,themodel resultsrepresentlocalcrosssectionsthrough thedepositandthe modelresultsremainvalidalsoforfunnelshapedconduits(atthe locationwheretherespectivemodeled diameterispresent). How-ever,sincethequencheffectisrestrictedtotheoutermostportion oftheconduitincontactwiththecountryrock(

∼

10–60cm,

de-pendingon emplacementtemperature, depth anddeposit

dimen-sion;seealsoAppendixA3),theabsolutediameteroftheconduit has littleinfluence on compaction efficiencyof the remainder of

Fig. 3. Summaryofthemodelresultsshowingthequenched-inphysicalpropertiesofthedeposituponcessationofweldingandcompaction,contouredforvarying emplace-mentdepths(contours).SubplotsAandBshowtheporosityandpermeabilityofcompactingtuffisiteveinsof10cmwidth,asafunctionofdistancefromthewallrock(0 beingthecontacttothewallrockand1beingthecenterofthecoolingdeposit).SubplotsCandDshowtheporosityandpermeabilityofcompactingconduitdepositsof 10 mdiameter.Notethenarrownormalizeddistances(0to0.05;i.e.theouter25cmoftheconduitinfillclosesttothewallrockinterface)forsubplotsCandD.Insets showstheareaenlargedinsubplotsCandD.Thecartoonshowsmapsoftheresultsforconduitpermeabilityoverdepthanddistancefromthewallrockcontact.For bet-terreadability,resultsareplottedfortheouter15%oftheconduitonly.Tuffisitepermeabilitymapsareshownschematically.Independentoftheemplacementdepth,ahigh permeabilityquenchmarginremainsatthecontactbetweentheveinandthehostrock,whereasthecenteroftheveinreacheslowerpermeabilitieswithincreasingdepth. (Forinterpretationofthecolorsinthefigure(s),thereaderisreferredtothewebversionofthisarticle.)

thedeposit. Thesameapplies fornon-horizontaltuffisite veins.If oneweretotrytounderstandthedegassingbehavior ofanentire tuffisiteveinfromdepthtosurface,thecriticalparameterwouldbe thedepthatwhichittapsagasreservoir,ratherthanits orienta-tion.Thisisbecausetheoutgassingcapacityofaveinislimitedby themaximumdepthatwhichitintersectsthereservoir,since com-pactionefficiencyispositivelycorrelatedwithdepth(i.e.atdepth, porosity andpermeabilitywill belower than ifthevein tapsthe gasreservoiratashallowerlevels).

4.1. Outgassinglithologiesintheirnaturalhabitat

Theextrememarginsofconduitsareinfrequentlyexposedbut, where available, field observations, includingoutgassing patterns (Hollandetal., 2011; Lavalléeetal., 2012) and porosity and per-meabilityvaluesaswellasalterationsinthemarginsofdissected conduits or boreholes (Cloos, 1941; Heiken etal., 1988; Stasiuk etal.,1996),showthe marginsofvolcanicconduits tooperateas long-livedoutgassing pathways.Similarly, where exposed in situ,

tuffisites are commonly poorly welded and display high

porosi-ties and high permeabilities (Cloos, 1941; Heiken et al., 1988; Stasiuketal.,1996).

Theseobservationsare ingoodagreementwithourmodel re-sults,whichpredicttuffisiteveinstohavehighporositiesand per-meabilities.However, theyareatoddswiththenumerousstudies thatdescribedenselywelded(Berloetal.,2013; Castroetal.,2012; Heap et al., 2015; Kendrick et al., 2016; Saubin et al., 2016; Tuffenetal.,2003) orotherwiselithified(Farquharsonetal.,2015; Kolzenburg et al., 2012) low porosity/permeability tuffisites

re-covered from deposits of explosive eruptions. These dense

ma-terials have been interpreted as representative of the charac-ter of tuffisite veins in the subsurface. As a result, experimen-tal studies (Heap et al., 2015, 2014; Kolzenburg and Russell,

2014; Vasseur et al., 2013; Wadsworth et al., 2014, 2016), em-pirical studies on natural materials ((Farquharson et al., 2015;

Gardneretal.,2018; Kendricketal.,2016; Kolzenburgetal.,2012; Quane andRussell,2003),2005; RustandCashman,2004; Wright andCashman,2014)andnumericalmodels(Chevalieretal.,2017; Farquharson et al., 2017b) have sought to understand the condi-tions that generate their microstructures andlow final porosities andpermeabilities.

We can resolve the apparent discrepancy betweenthe higher porosityoftuffisitesfoundinsituandsuggestedbyourmodel,and theobservationoflowporositytuffisitesinpyroclasticdepositsby considering their respective strengths: an increase in porosity is accompaniedbyamarkeddecreaseincoherenceandrockstrength (see for example Quane and Russell (2003), Kolzenburg et al. (2012) andHeapetal. (2015)).Thelowcoherenceofhighlyporous materialssuggestsalowerlikelihoodthatthematerialwillremain intactduringaneruption,andthusalowerpotentialforbeing pre-served inejectedblocks.Thus, theapparentdiscrepancybetween ourmodelresultsandtuffisiteveinsreportedintheliteraturemay reflect a samplingbias where only the strongesttuffisite blocks, havinglowerporosity andpermeabilityvalues,arepreserved dur-ing eruption. Many tuffisites described in the current literature arethereforelikelynotrepresentativeofpathwayscontributingto magmaoutgassingbutrepresentthemostevolved/completed

end-members ofthe welding andcompactionprocess that are strong

enoughtosurviveaneruptioni.e.“theoneswhogotaway”. 4.2. Tuffisitelongevity

Our model results show that both tuffisite veins and conduit margins are likely to “freeze in” high porosity and permeability, and to act as long-lived outgassing pathways. These compaction timescales appearat odds withthecurrent understandingof the lifespanoftuffisitesaspermeablepathways(Chevalieretal.,2017; Farquharson et al., 2017b; Gardner et al., 2018; Kendrick et al.,

2016; Kolzenburg et al., 2012; Rust and Cashman, 2004). How-ever, previous studies (Table A2 and section 4.1) have focused

on tuffisite veins that intrude the hot conduit-infilling deposits (lavaorpyroclastic deposits)where temperaturesaremaintained, compaction is rapid, and permeability networks are short lived (Heapet al., 2015; Quane andRussell, 2005; Quane etal., 2009; Vasseur et al., 2013; Wadsworth et al., 2016). As an example, Chevalier etal. (2017) and Farquharson etal. (2017b) model the decrease of porosity and permeable gas loss at the conduit-wall

rock interface during dome growth and loading of the edifice,

andreport significant permeability loss on the timescale of tens of minutes to hours. Similarly, Quane and Russell (2005) and Wadsworth et al. (2014) present experimental data on the den-sificationofanalogueandnaturalmaterialsandgivedensification timescalesoftensofminutestohourswhenthematerialviscosity issufficientlylowbothunderanormalloadandwhencompacting bysurface tensionalone.Thisis echoedalsoinarecentstudyby Gardneretal. (2018) thatexpandedtheexperimentalconditionsto elevatedhydrostaticpressureandhydrousconditions,resultingin adecreaseinmeltviscosityandevenfasterdensification(

<<

1 h). Thesetimescaleswoulddecreaseevenfurtherunderaloadstress.

However, we show here that the compaction history of hot

(

>

Tg) tuffisiteveinsinjected intothecooler edificeorwall rocks

(25–350◦C)isvery differentfromthe conditionsassumed inthe

aforementioned studies. Modeling the permeability loss due to

compactionastuffisiteveinscoolagainstcoolhostrocks(i.e.

<<<

Tg) allows to explain the preservation of long-lived outgassing

structuresresulting from“freezing in” porosity andpermeability. Ourresultsshow that for anyreasonable assumption of environ-mentalconditions,thisquencheffectoccursontimescalesshorter than the welding andcompaction timescale, allowing for poros-ityandpermeabilityretention.Thissuggeststhat tuffisitesinthe subsurfacearesignificantlymoreporousandpermeableand there-withremain active outgassingfeaturesforlonger timescalesthan previouslythought.

4.3.Implicationsfortheobservedgasflowbudgetatexplosive volcanoes

Ourresultsshow thatbothtuffisite veinsandconduitmargins can “freezein” high values ofporosity andpermeability thereby preserving long-lived outgassing pathways. Fig. 3 highlights that tuffisiteveinspossessquenchedmarginsevenatdeeplevelsinthe volcano. Theseintersect, andtherewith tap, thecompacting con-duitinfillaswell aspotentiallyexistingdeeperpocketsof perme-able,foamedmagmaandmaythusrepresenteffectiveoutgassing pathways.Inorder to assessthe balancebetweenthe outgassing capacitiesofthetwolithologies,wecalculatetheareawithineach depositthatremainsabovetheaverageedificepermeability.Asan

example we compare the permeability evolution of a 10 m

di-ameter conduit and a 10 cm thick tuffisite for an emplacement

temperatureof775◦C.Sinceweldingisdependentontheload act-ing during compaction, we evaluate the outgassing capacityat a fixeddepthof100 mforthisexample.

Estimationoftuffisite frequencyandproportioninthe subsur-face are tricky and literature values that are based on fracture densitydistributions and/or drill corefracture spacingvary dras-tically. They range from25% in Farquharson et al. (2017b), over 10–15%inHeikenetal. (1988),downto0.2%inGotoetal.(2008). Herewetake aconservativeapproachandassume thatduring an eruption

∼

5%oftheconduitvolumeisconvertedtotuffisiteveins withinthe surroundingwallrocks.Initially, therefore,the perme-able,highporosityhorizontalcross sectionof the10 mdiameter conduitequals78.54m2 _{andthat ofthetuffisite veinequals3.93} m2. For a tuffisite vein of 10 cm thickness, this translates to a

widthof

∼

40 m. These dimensions are in agreement with

esti-matesandtexturalworkontuffisiteveinsoriginatingfromshallow (10–300 mdepth) dome forming eruptions (Stasiuket al., 1996;

Fig. 4. Summaryofthemodelresultsshowingtheevolutionoftheoutgassing capac-ity(i.e.theratioofpermeableareas(k>10−16_m2_{))asafunctionofdimensionless} time(i.e.absolutetimenormalizedtothetimerequiredtoquenchtoTg).Theplot showstheresultsfora10 mconduitdiameteranda10cmtuffisitevein,bothat 100 mdepth.

Tuffenetal.,2003) aswellastuffisitesassociatedwithbasaltic di-atremes(Cloos,1941).

Inorderforgasescape tobe controlledby theconduit orthe tuffisite network,the permeabilityoftherespective depositmust

be higherthanboth thehostwall rocks andthe magmacolumn,

which are generally below 10−16 to 10−17 m2 (see Farquharson et al. (2015) and references therein). To assess the relative im-portance ofthe two outgassinglithologies we assign a threshold of 10−16 _m2 _{–for permeabilities above this value, gas escape is} concentrated withinthe respectivedeposit;forlower permeabili-ties, outgassing hasno preferredpathwayandoccurs pervasively throughthevolcanicedifice.Thisthresholdvalueissupportedthe workofCollinsonandNeuberg (2012) whomodeltimedependent variations inpressurebasedonDarcy’slawandfindthatsystems below 10−16 m2 behave as effectively sealed systems. Based on theirmodeltheyassignthisvalueasthethresholdbetween“open” and“closed”systemoutgassing.

Thecontributionoftherespectivedeposittosystem-wide out-gassing is evaluated by calculating the area of the tuffisite and conduitdepositsthatremains abovethepermeabilitythresholdof 10−16 _m2 _{as a function of time. Then we calculate the ratio of} theseareas:aratioof

<

1indicatesalargergasflowcapacity(i.e. crosssectional area available foroutgassing) inthe conduitinfill, whereasaratioof

>

1indicatesthatthereishighergasflow capac-ityinthetuffisite.Usingthisratiowecanreconstructtherelative contributiontooutgassingofthesetwotypesofdeposit through-out theweldingandcompactionprocesses,untilthepoint where finalporositiesandpermeabilitiesare“frozenin”(Fig.4).

Secondsafteremplacementboththeconduitandtuffisiteveins have permeabilities

>>

10−16 m2. Because of the greater area availableforoutgassingintheconduit,theratiobetweenthe tuff-isite to conduit permeable area is very small, and gas flow will

dominantly be focused within the conduit. However, due to the

high thermal inertia of the conduit geometry, the central parts of the conduit remain hot and quasi-isothermal (see Fig. 2). As aresult,compactionwithintheconduitinfillisveryefficient,and permeabilityrapidlydecreasesbelow10−16_m2_{forthelargestpart} of the conduit, leaving only a narrow permeable annulus at the contact with the host rock. This rapidpermeability reduction in theconduit isnot mirroredin thetuffisite veinsbecauseoftheir fastcoolingrate(Figs.2and3).Therefore,ascompactionproceeds, thesystem-widepermeableoutgassingarearatiobecomes

>

1;i.e.

outgassingis focused within thetuffisite vein system. Thisis ex-pressedinthemodelresults asanalmostinstantaneouschangein theoutgassingarea ratio(Fig.4). Afterthispoint,the majorityof theconduitiseffectivelyre-sealedandquenchedtuffisiteveinsact astheprimaryoutgassingpathways.Insummary,Fig.4showsthat theoutgassingpotentialofeachdepositwillundergoa character-isticevolutionthatisdictatedbythegeometryanddimension de-pendentvariationincoolinghistoryofthetuffisiteveinsand con-duit.Ananalysisofvariationsinveingeometryonthisoutgassing budgetispresentedinAppendixA4andshowsthatthisoutgassing patternremainsunchangedforanyreasonableveinsize.

Smallchangesinthecapacityofavolcanicsystemtodissipate overpressure via outgassing can bring forth dramatic changes in eruptionstyle(explosivevs.effusive)anddriveinstabilitiesinthe eruption regime e.g. Jaupart andAllègre (1991). Thus our model foranevolving outgassingbudgetmayyieldinformationon criti-calchangesinthephysicalstate ofavolcanicsystemthatarenot detectableviacurrentlyavailablemonitoringapproaches.

5. Potential useasalowcostmonitoringtool

Ourresultsshowthattuffisiteveinsinthevolcanicedificemay retainhighpermeabilitiesoverlongtimescalesrelativetothe com-pactingconduit,andthatthey canbecomethedominant contrib-utortomagmaoutgassingatrelativelyshorttimesaftereruption. Thistemporalevolutioninoutgassingbehavior (shiftfrom

conduit-to tuffisite-dominated outgassing) has been suggested by field

measurements, for example during SO2 outgassing at Soufrière

Hillsvolcano(Edmondsetal.,2003):theauthorsobservedecreases inSO2fluxoverthreeordersofmagnitude,whichtheylinkto per-meability changes on two different timescales 1) slow and long termpermeabilitydecreasefromJuly1998toNovember1999that they attribute to precipitation of hydrothermal minerals, as also suggestedbyforexampleTaranetal. (2001) and2)rapidincrease ofpermeabilityduringtheproductionofpyroclasticflowsfollowed byfast(timescalesofminutestohours)permeabilityreduction in the upper conduit anddome dueto cooling and“sealing”. Seal-ingoftheupperconduitanddomeresultsingasgettingtrapped withinclosedfractures,primingthenextpyroclasticevent.This in-dicatesthat outgassingpatterns mayinformondensification and permeability-reductionoccurringwithin volcanicedifices.On this basis we see the potential for a new monitoring strategy to as-sessthe development ofgasoverpressures andpotentialonset of explosiveactivity.

Asshownabove,theredistributionofgasflowbetweenconduit andtuffisitesisaresultoftheir geometry-dependentquench effi-ciency.Thistimedependencyintheoutgassingcapacityofthetwo depositsuggeststhatchangesintheactivityandtotalfluxratesof distal fumaroles may inform on the pressure-state of a volcano. Immediatelyafter an eruption, the high gasflow capacity ofthe conduit will result in little to no gas flow through the tuffisite-linkedfumarolenetwork. Withtimethough theconduitinfill de-posits will densify, and the outgassing capacity of tuffisites will rapidlyexceedthatoftheconduit(Fig.4).Atthispoint,fumaroles linkedtothesetuffisitestheywillresumetheiractivity.Anychange inthepressurestateofthevolcanowillthenbedirectlyreflected inthevolumeofgasfluxfromthesefumaroles(i.e.anincreasein gaspressurewithintheconduitwillresultinhigherflux,andvice versa)makingthetotalgasvolumeexpelledviathesefumarolesa directindicatorofthepressureevolutionwithintheedifice.

Wesuggestthishypothesis couldbetestedinthefield, where recordsoffumaroleactivityanderuptiveactivitycanbelinked.We proposeseverallocationswherethisworkmaybeinformative:

•

Santiaguito, Guatemala, where small explosive eruptions are frequent andcan be readilymonitored andcorrelated to the temporalevolutionofflowratesoffumaroles.

•

Colima, Mexico,whereVulcanianstyleeruptionsarefrequent andawealthofmonitoringproceduresisinplacethatinclude dataonthedome/crateractivityandfumaroleactivity.

•

Tungurahua,Equador,wheregas-particleintrusionsinthe ed-ificehavebeenidentifiedpreviously(Molinaetal.,2004) and gasmonitoringequipmentcouldbeaddedwithreasonable ef-fort.

•

Turrialba, Costa Rica, where automated video monitoring for crateroutgassingisinplaceandmonitoringsitesforfumaroles couldbeaddedwithlimitedeffort.

•

Sabancaya,Peru,wheresmallexplosiveeruptionsoccurevery fewhoursandautomatedvideomonitoringoftheedificeisin place.

•

Mount Agung, Indonesia, where Vulcanian style eruptions

startedrecentlyandmonitoringsitesatadvantageousvantage pointscouldbeaddedwithreasonableeffort.

Thisstrategy(monitoringtheactivityofor,ideally,totalfluxof fumaroles) could potentially be employed as a low cost pressure monitoring tool,whichwouldbe ofgreatbenefitto communities wherethefinancialcapacityforsophisticatedinstrumentationsuch asseismometers,tilt-metersorinfrasoundrecordersislimited. 6. Conclusions

Resultsfromourmodeling suggestthefollowingconclusions:

1. The differences in geometry and dimensions between the

two dominant outgassing pathways (conduit infill vs.

tuff-isiteveins) resultindrasticallydifferentposteruptivecooling paths, creatingcharacteristicpatternsofcompactionand per-meabilityloss.

2. Thethermalevolutionoftheoutgassingsystemduring

weld-ing andcompactionis ofparamount importance forthe

effi-ciencyofpermeabilityretention.

3. Thetimescalesforporositylossinbothoutgassingsystemsare highlydependentontheevolutionofthebulkrheologyofthe deposit(governedbymeltcompositionandcoolinghistory).

4. The switch from conduit-dominated outgassing to

tuffisite-dominated outgassing occurs abruptly once the bulk of the

conduit fillingdeposithasreachedpermeabilityvaluesbelow theedificeformingrocks(commonly

<

10−16_m2_),andwillbe reflectedintheactivity/totalfluxfromtuffisite-fumaroles. 5. Thischaracteristicevolutionofposteruptivegasflowhasthe

potential to be used forlow cost monitoring ofpermeability shut-offandtheonsetofpressurizationofexplosivevolcanoes. Acknowledgements

S. Kolzenburg acknowledges the support of a H2020 Marie

Skłodowska-Curie Actions fellowship DYNAVOLC – No. 795044.

J.K. Russell acknowledges an Natural Sciences and Engineering

Research Council of Canada Discovery grant number:

RGPIN-2018-03841.TheconstructivecommentsofHeatherWright,Hugh

Tuffen andTamsin Mather helpedusimprove the quality ofthis manuscript.

Appendix A1. Overviewofavailablepermeabilitymodels

There are a number of models that describe the

porosity-dependent permeabilityofvolcanicfragmental materials(Heapet al.,2015; KlugandCashman,1996; Sparksetal.,1999; Wadsworth et al., 2016; Wright and Cashman, 2014; Burgisser et al., 2017;

Fig. A1. Availablepermeabilitymodels.(A)Modelsvaryinthepredictedabsolutepermeabilityvaluesbyseveralordersofmagnitude,butshowabroadlysimilarshape. Thetwo-stepevolutionofthemodelpresentedin(Heapetal.,2014) isaresultoftheidentificationofachangepointinthisrelationship.(B)Thedependenceofrelative permeability(ratioofmodeled permeabilityatagivenporositytothemodeled permeabilityat0.40porosity)toporositydoesnotchangesignificantlybetweenindividual models.

Farquharson etal., 2017a). Thesemodels are primarily empirical,

and based on the measured porosity and permeability of

natu-ral materials or experimental products; they are summarized in Fig.A1.Allmodelshavebroadlythesameshape,savethetwo-step evolution presented by Heap et al. (2015). Because of the simi-laritiesin the way permeabilitydecays with decreasingporosity,

choosing one model over another changes the absolute

perme-ability (Fig. A1A), but does not significantly change the relative

permeability (permeability at a modeled porosity ratioed to the permeability atthe initial porosity)(Fig. A1B). For ourmodeling

purposes we have therefore selected the model of Wright and

Cashman (2014) –equation (6) inthismanuscript,that describes the porosity-permeability relationship for gas flow along the fo-liation of porous volcanic rocks. This model represents the best approximation of the average relative permeabilityof all models (redlineinFig.A1).

Table A1

Compilationofexistingconduit diametermeasurements.

Volcano Diameter

(m)

Lithology Reference

Chaitén, Chile 20–50 Rhyolite Browne and Szramek,2015

Chaitén, Chile 10–100 Rhyolite Castro and Dingwell,2009

Colima, Mexico 50 Andesite Lavallée et al.,2012

Cordon Caulle, Chile 50 Rhyolite Schipper et al.,2013

Etna, Italy 25 Trachybasalt Rymer et al.,1993

Mt. Meager, Canada 40–45 Dacite Campbell et al.,2013

Mt. St. Helens, USA 20±5 Dacite Barmin et al.,2002; Rutherford and Hill,1993; Swanson and Holcomb,1990

Mt. St. Helens, USA 40 Dacite Chadwick et al.,1988

Mt. St. Helens, USA 150–200 Dacite Vallance et al.,2008; Schneider et al.,2012

NW Rota-1 Mariana Arc <15 Basaltic-Andesite Embley et al.,2006; Walker et al.,2008; Butterfield et al.,2011; Deardorff et al.,2011

Paracutin, Mexico 10 Basalt Vespermann and Schmincke,2000

Santiaguito, Guatemala 150 Dacite Head et al.,2003

Santiaguito, Guatemala 36 Dacite Holland et al.,2011

Santiaguito, Guatemala 50 Dacite Bluth and Rose,2004

Soufrière Hills, Montserrat 30 Andesite Browne and Szramek,2015

Soufrière Hills, Montserrat 50–60 Andesite Watts et al.,2002

Soufrière Hills, Montserrat 30–50 Andesite Sparks et al.,2000

Tavurcur, New Guinea 100 Dacite McNutt et al.,2015

Vesuvius, Italy 65 Tephrite Shea et al.,2011

Vesuvius, Italy 80–90 Tephrite Macedonio et al.,2008

Mule Creek, USA 50 Rhyolite Stasiuk et al.,1996

Shiotani, Japan >1 km Rhyolite Kano et al.,1997

Generic Explosive 20 N/A Neuberg,2000

Generic Vulkanian 30 N/A Melnik and Sparks,1999; Costa et al.,2007; Delany and Pollard,1981; Clarke et al.,2015

Generic Explosive 50 N/A Mangan et al.,2004; Caricchi et al.,2007

Generic Explosive 100 N/A Neri and Dobran,1994

Generic Explosive 127 N/A Papale,1999

Generic Explosive 10–50 N/A Bonaccorso and Davis,1999; De Michieli Vitturi et al.,2008

Generic Explosive 50–90 N/A Jellineck and Bercovici,2011

Generic Explosive 20–40 N/A Gonnermann and Manga,2003

Generic Explosive 20–100 N/A Wilson et al.,1980

Fig. A2. Examplesofthetemporalevolutionofthemodelparameters.SubplotsA,B,C,D,EandFshowthetemporalevolutionoftemperature,dissolvedwatercontent,

Tg,viscosity,porosityfractionandpermeability,respectively.Resultsareplottedfortuffisitethicknessesof5,10and10cmwidthassolid,dashdottedanddashedlines, respectively.Notethatthe15 cmveiniscompactionlimited(i.e.completeporositylosspriortoreachingTg)whereasthe10and5cmveinsarecoolinglimited(i.e.Tgis reachedbeforecompleteporosityloss,quenchinginapermeabletexture).

Appendix A2. Temporalevolutionofallmodelparametersduring compaction

A2.1. Conduitgeometry

Dueto thelarge thermalbufferingcapacityof thematerial in theinteriorofaconduit (seethermalevolution ofacooling con-duitinFig.A2inthemaintext),thenon-isothermalarea,relevant forpermeabilityretention,is anarrowregion ofthedepositnear theconduitwall.Sinceanythingbeyondthisnon-isothermalzone cools so slowly that porosity is annihilated before reaching Tg,

variations in the conduit diameter do not affect the model re-sults of porosity and permeability evolution across this contact zone significantly. Therefore, an increase in conduit diameter re-sultsinan overall increase inthe area ofthepermeableannulus incontactwiththeconduitwallbutnottheevolutionofits physi-calproperties.Sinceweassumethatinanymodeledscenarios,the cross sectional area of tuffisitescreated during eruption is5% of thecross sectional area oftheconduit, thearea ratio (Fig.4 and Fig.A5)remainsunaffectedbyconduitgeometry.

A2.2. Tuffisitegeometry

Contrary to theconduit infill deposit, dimension plays an im-portantroleintheevolutionofthephysicalpropertiesoftuffisites. In ordertoevaluatethe significanceofthechangeincompaction efficiency,weranourmodelusingvaryingtuffisitewidths(within the range expected in nature) and assess how this controls the modelresults:InFig.A2weploteachofthemodelparameters(i.e. thermal, transportandphysicalproperties)againsttime. Thedata

showthecontemporaneousmodelparameterevolutionthroughout

the compaction process in three tuffisite veins from initial em-placement to the point where the process stalls (i.e. T

≤

Tg or

Φ

=

0). Results are plotted for the following model parameters: thickness: 5, 10 and 15 cm; Ti

=

775◦C; pore pressure 1 MPa;

Φ

0

=

0

.

4;depth

=

150m;location:centerofthecompactingvein (i.e.2.5,5and7.5cmfromthewallrockcontact).

This analysis demonstrates the interdependence of model pa-rameters.Compactioninthecenterofboththe5and10cmthick veins is cooling limited (i.e. the process reaches Tg), quenching

ina porosityof35% and7%,andapermeabilityof8

×

10−14 _m2 Table A2

Compilationofexistingtuffisitethicknessmeasurementsandlocations.

Volcano Thickness

(m)

Lithology Reference

Chaiten, Chile <0.1 ObsidianΦ <0.1 Saubin et al.,2016

Chaiten, Chile <0.03 ObsidianΦ <0.1 Castro et al.,2012

Colima, Mexico 0.003–0.05 AndesiteΦ >0.8 Kolzenburg et al.,2012

Colima, Mexico 0.02 AndesiteΦ >0.8 Heap et al.,2015

Colima, Mexico 0.001–0.01 AndesiteΦ >0.8 Farquharson et al.,2016

Colima, Mexico 0.001–0.03 AndesiteΦ >0.8 Kendrick et al.,2016

Cordon Caulle, Chile <0.5 ObsidianΦ <0.1 Schipper et al.,2013

Inyo Domes, USA 0.07–0.4 RhyodaciteΦ <0.78 Heiken et al.,1988

Mono Craters, USA 0.001–0.02 ObsidianΦ <0.1 Rust and Cashman,2004

Mule Creek, USA 0.001–0.05 RhyoliteΦ <0.1 Stasiuk et al.,1996

Rocche Rosse, Italy 0.001–0.5 ObsidianΦ <0.1 Cabrera et al.,2015

Rocche Rosse, Italy 0.03–0.1 ObsidianΦ <0.1 Cabrera et al.,2011

Schwaebische Alp, Germany <0.7 BasaltΦ <0.9 Cloos,1941

Torfajokull, Iceland 0.001–0.01 ObsidianΦ <0.1 Tuffen et al.,2003

Torfajokull, Iceland 0.001–0.05 ObsidianΦ <0.1 Tuffen and Dingwell,2004

Torfajokull, Iceland 0.013–0.05 ObsidianΦ <0.1 Berlo et al.,2013

Torfajokull, Iceland 0.001–0.02 ObsidianΦ <0.1 McGowan et al.,2016

Unzen, Japan 0.035 DaciteΦ >0.6 Farquharson et al.,2017b

Unzen, Japan <0.25 DaciteΦ >0.6 Goto et al.,2008

Fig. A3. Summaryofthemodelresultsshowingthequenchedinphysicalstateofthedeposituponcessationofweldingandcompactionforvaryingdepositgeometries(line style)andemplacementdepth(labels).SubplotsAandBshowtheporosityandpermeabilityofcompactingtuffisiteveinsof5(solidlines),10(dashedlines),and15(dash dottedlines)cmwidth,asafunctionofdistancefromthewallrock,respectively.SubplotsCandDshowtheporosityandpermeabilityofcompactingconduitdepositsof5 (solidlines),10(dashedlines),and15(dashdottedlines) mdiameter,asafunctionofdistancefromthewallrock,respectively.Shadedareashighlightthefieldsforeach geometryat100 mburialdepth.NotethatduetotherelativelysmallvolumeofmaterialthatisabletoretainporosityandpermeabilityaftercompactiontheX-axisforthe modelresultsofcompactingconduitsisonlyshownfornormalizeddistancesof0to0.08.ThesmallinsertinsubplotCshowstheareaenlargedinsubplotsCandD. and3

×

10−17 _m2 _{forthe 5and 10cmvein center, respectively.}

Compaction in the center of the 15 cm thick vein is complete

(i.e.

Φ

reaches 0), rendering the center of the vein

imperme-able,before significantcooling occurs. However, the outer 10cm

of the 15 cm vein that are in contact with the wall rock are

cooling limited and retain permeability. In the following section we present the model results at the point of cessation of com-paction(i.e.thefinal

Φ

andk thatarequenchedinuponreaching Tg).

Appendix A3. Theeffectofchangingprocessparameters

Due to the large parameter variation we present the model

results incrementally in the following sub sections, investigating theeffectofeach parameterontheefficiencyofcoolingand per-meability retentionseparately. We start by showingthe effectof depositgeometry,varying withdepth,andproceedtodiscussthe effectofvaryingemplacementtemperatures.

A3.1. Theeffectcoolinggeometryanddimension

Fig.A3showsthemodeled porosity(subplotsAandC)and per-meability(subplotsBandD)attheendofcompaction(i.e.where T

=

Tg or

Φ

=

0) asafunction oflocationwithinthe depositfor

tuffisitesof5,10and15cmthicknessandconduits of5,10and 15 mdiameter.Resultsare reportedasabsolutevaluesfor poros-ityandpermeability,whereasthelocationinthedepositisplotted asnormalizeddistancebetweenthecenteroftheveinorconduit

Table A3

Majorelement(anhydrous)compositionofobsidianfrom Hrafntinnuhryggur, Krafla, Iceland from Tuffen et al. (2008). Oxide Wt% oxide SiO2 75.23 TiO2 0.23 Al2O3 12.00 FeO(t) 3.28 MnO 0.11 MgO 0.10 CaO 1.66 Na2O 4.15 K2O 2.75 P2O5 0.00 Analytical total 99.51

andthecontacttothewallrock,0beingthecontact,and1being thecenteroftherespectivedeposit.

The modelresults show that both depth (controllingthe load stress) and deposit geometry (controlling the cooling efficiency) havefirstordereffectsonthecompactionefficiencyincooling de-posits. Increasingloadstress resultsinmore efficientcompaction – this effect is observed for both geometries. For tuffisite veins, an increase in vein width results in slower cooling and, there-with, more efficient compaction, resulting in decreasing porosity andpermeabilitywithincreasing distancefromthewall rock(i.e. the cooling surface). For conduit deposits, only the zone in di-rect contact with the wall rock is cooling sufficiently rapidly to

Fig. A4. Summaryofthemodelresultsshowingthequenchedinphysicalpropertiesofthedeposituponcessationofweldingandcompactionfora10cmtuffisitewidth (subplotsAandB)anda10 mconduitdiameter(subplotsCandD)asafunctionofdistancefromthewallrock.Solid,dashedanddot-dashedlinesrepresentthemodel resultsfor750,775and800◦C,respectively.Dataareplottedfor25,100,200and500 mdepthforallthreeemplacementtemperatures.Smallnumberslabeldepthcontours foremplacementat775◦C.Light,mediumanddarkgreyfieldshighlightthequenchedinstateat200 mdepthforemplacementtemperaturesof750,775and800◦C, respectively.

quenchinporosityandpermeability.Incontrasttotuffisiteweins, thelargestpart ofthedepositremains attemperaturesabove Tg

for sufficient time to result in complete compaction and

poros-ity/permeabilityloss.Albeitincreasinginconduitdiameterresults inadecrease inthefractionofthe conduitcrosssection that re-mainspermeable,theabsoluteoutgassingareaincreases.At100 m

burial depth, for example,

∼

90% of a 10 cm wide tuffisite vein

(mediumgreyshadedareasinAandB)remain ata permeability above10−14m2,whereasforaconduitof10 mdiameter(medium greyshadedareasinCandD)lessthan1%ofthecrosssection re-mainabove10−14m2.

A3.2. Theeffectofemplacementtemperature

To investigate the effect of emplacement temperature on the quenchefficiencyandporosityandpermeabilityretentionwe plot themodelresultsuponcessationofcompactionfor10cmtuffisite

widthand 10 mconduit diameter atemplacement temperatures

of750, 775and800◦C forshallow (25 m), intermediate (100 m

and200 m) anddeep (500 m)emplacement scenarios (Fig. A4).

The results show that for both tuffisite veins and conduit walls, emplacementtemperaturehasafirstordereffectontheefficiency ofporosity andpermeabilityloss, whereincreasing emplacement temperaturesresultsinmoreefficientcompactionand,therewith, decreasingporosityandpermeabilityforanygivenlocationwithin thedeposit.

Themodelresultshighlightthat,incrosssection,asingle tuff-isitevein of10cmwidthretainsthesameoutgassingcapacityas

the margin (outermost 5–10 cm)of a conduit of 10 mdiameter

upon quenching. The data show that the absolute differences in permeabilityandporosityquenchedindirectlyattheconduit mar-gin and acrossthe tuffisite vein are relativelysmall. The conduit wall coolssomewhat slowerandtherefore,compactionisslightly moreefficiently,especiallyinlocationsdeeperintheconduit.This resultsinaslightlynarrowerzoneofhighporosityand permeabil-ity atthe conduit wall than atthe contactbetweentuffisite and host rock.Thedata show furtherthat the absolutedifferencesin permeabilityandporosityquenchedindirectlyattheconduit mar-ginandacrossthetuffisiteveinarerelativelysmall.

Appendix A4. Theeffectoftuffisitewidthonthegasflowbudget duringoutgassing

As outlinedinAppendixA2,thearea relevantforpermeability retention in conduit infill encompassesonly the outermost frac-tions ofthe deposit nearthe conduit wall, and variations in the conduit diameterdo notaffect themodel resultsofporosity and permeabilityevolutionacrossthiscontactzonesignificantly.An in-creaseinconduitdiameterresultsinanincreaseintheareaofthis permeableannulusandcould,withthat, influencetheoutgassing budget.However,sinceweassumethatthecrosssectionalareaof tuffisitesis5% ofthe crosssectionalareaoftheconduit,thearea ratioremainsunaffectedbyconduitgeometry.

Fig. A5. Summaryofthe modelresultsshowing theevolutionoftheoutgassing capacity(i.e.the ratioofpermeableareas)as afunctionofdimensionlesstime. Theplotshowstheresultsfora10 mconduitdiameterandtuffisitesofvarying thicknesses.Smallnumbersindicatethefractionofpermeablearearetainedinthe tuffisiteuponcompletionofcompactionrelativetotheinitialarea.

Tuffisite geometry,on theother handdoesaffectthe area ra-tio,sincetheabsolutearea available foroutgassingisaffected by theevolution ofcompactionacrossthe vein.As long asavein is

narrow enough to quench in permeability values above the

edi-ficepermeabilitythresholdacrossitsentirecrosssection,thearea availableforoutgassingremainsattheassigned5% oftheconduit area. If, however, the vein issufficiently wide to allow for com-paction to proceed beyond the threshold permeability, the area availableforoutgassing willreduce. The effectofthisprocess on theoveralloutgassingbudgetofavolcanoisreportedinFig.A5.

AsshowninAppendixA2,boththe5and10cmveinsare cool-ing limited and remain above the edificepermeability threshold (10−16_m2_{),thereforetheyplotonalongthesamelinethroughout} compaction. Thismeans that their entirearea remains above the permeability threshold. Their absolute permeability is, however,

higherin themore narrowvein due tomore efficientquenching

(seeFigs.A3,A4). Thickerveins(

>

10cm),ontheother hand, re-mainsufficientlyhotintheirinteriorssothatcompactionproceeds furtherandthecentralpartsoftheseveinsdropbelowtheedifice permeabilitythreshold, resulting in a decreased ratio of tuffisite outgassing area to conduit outgassing area (Fig. A5, y-axis). The smallinsetinFig.A5showsthatthetuffisitetoconduitoutgassing area ratiodecreases slightlyprior to permeabilityshut off across the largest part of the conduit. This is because at equal depth, compactionis slightlymoreefficientinthetuffisite veinsasthey experienceaconstantloadoftheoverlyingedificerocks,whereas

the load on the conduit deposit is porosity dependent and

in-creaseswithcompaction.

Insummary,themodelresultsplottedinFig.A5showthat(1) tuffisiteveinshavea higheroutgassingcapacitythan theconduit materialforanyreasonable tuffisite veinthickness, and(2)under

any reasonable geometric circumstances tuffisite outgassing may

yieldinsightsto thepressurestate ofa volcano.The evolutionof thegasescapebudget(i.e.thepartitioningofgasescapebetween the permeableconduit annulus and tuffisite linked fumaroles) is thenlargelycontrolledbythetuffisiteveingeometry.

References

Alidibirov,M.,Dingwell,D.B.,1996.Magmafragmentationbyrapiddecompression. Nature 380,146–148.

Barmin,A.,Melnik,O.,Sparks,R.S.J.,2002.Periodicbehaviorinlavadomeeruptions. EarthPlanet.Sci.Lett. 199(1),173–184.

Berlo,K.,Tuffen,H.,Smith,V.,Castro,J., Pyle,D.,Mather,T.,Geraki,K.,2013. El-ement variations inrhyolitic magmaresulting from gas transport. Geochim. Cosmochim.Acta 121,436–451.

Bluth,G.J.,Rose,W.I.,2004.ObservationsoferuptiveactivityatSantiaguitovolcano, Guatemala.J.Volcanol.Geotherm.Res. 136(3–4),297–302.

Bonaccorso,A.,Davis,P.M.,1999.Modelsofgrounddeformationfromvertical vol-canicconduitswithapplicationtoeruptionsofMountSt.HelensandMount Etna.J.Geophys.Res.,SolidEarth 104(B5),10531–10542.

Browne,B.,Szramek,L.,2015.Chapter9–RatesofmagmaascentandstorageA2. In:Sigurdsson,Haraldur(Ed.),TheEncyclopediaofVolcanoes,secondedition. AcademicPress,Amsterdam,pp. 203–214.

Burgisser,A.,Chevalier,L.,Gardner,J.E.,Castro,J.M.,2017.Thepercolationthreshold andpermeabilityevolutionofascendingmagmas.EarthPlanet.Sci.Lett. 470, 37–47.

Butterfield,D.A.,Nakamura,K.-i.,Takano,B.,Lilley, M.D.,Lupton,J.E.,Resing,J.A., Roe,K.K.,2011.HighSO2flux,sulfuraccumulation,andgasfractionationatan eruptingsubmarinevolcano.Geology 39(9),803–806.

Cabrera,A.,Weinberg,R.F.,Wright,H.M.,2015.Magmafracturinganddegassing as-sociatedwithobsidianformation:theexplosive–effusivetransition.J.Volcanol. Geotherm.Res. 298,71–84.

Cabrera,A.,Weinberg,R.F.,Wright,H.M.,Zlotnik,S.,Cas,R.A.,2011.Meltfracturing andhealing:amechanismfor degassingandoriginofsilicicobsidian. Geol-ogy 39(1),67–70.

Campbell,M.E.,Russell,J.K.,Porritt,L.A.,2013.Thermomechanicalmillingof acces-sorylithicsinvolcanicconduits.EarthPlanet.Sci.Lett. 377–378,276–286. Carey,S.,Sigurdsson,H.,1989.Theintensityofplinianeruptions.Bull.Volcanol. 51

(1),28–40.

Caricchi, L., Burlini, L., Ulmer, P., Gerya, T., Vassalli, M., Papale, P., 2007. Non-Newtonian rheologyofcrystal-bearing magmasand implications for magma ascentdynamics.EarthPlanet.Sci.Lett. 264(3–4),402–419.

Carslaw,H.,Jaeger,J.,1959.ConductionofHeatinSolids,vol.302.OxfordUniversity Press,NewYork,p. 302,340–341.

Castro,J.,Cordonnier,B.,Tuffen,H.,Tobin,M.J.,Puskar,L.,Martin,M.C.,Bechtel,H.A., 2012.Theroleofmelt-fracturedegassingindefusingexplosiverhyolite erup-tionsatvolcánChaitén.EarthPlanet.Sci.Lett. 333–334,63–69.

Castro,J.M.,Dingwell,D.B.,2009.RapidascentofrhyoliticmagmaatChaitén vol-cano,Chile.Nature 461(8Octobre),780–784.

Chadwick, W.W., Archuleta, R.J.,Swanson, D.A., 1988. The mechanics ofground deformation precursory to dome-building extrusions at Mount St. Helens 1981–1982.J.Geophys.Res.,SolidEarth. 93(B5),4351–4366.

Chevalier,L.,Collombet,M.,Pinel,V.,2017.Temporalevolutionofmagmaflowand degassingconditionsduringdomegrowth,insightsfrom2Dnumerical model-ing.J.Volcanol.Geotherm.Res. 333,116–133.

Clarke,A.B.,Esposti Ongaro,T., Belousov,A.,2015.Chapter 28–Vulcanian erup-tionsA2.In:Sigurdsson,Haraldur(Ed.),TheEncyclopediaofVolcanoes,second edition.AcademicPress,Amsterdam,pp. 505–518.

Cloos, H., 1941. Bau und Taetigkeit von Tuffschloten; Untersuchungen an dem schwaebischenVulkan.Trans.StephanKolzenburg.Geol.Rundsch. 32,709–800. Collinson,A.S.D.,Neuberg,J.W.,2012.Gasstorage,transportandpressurechanges inanevolvingpermeablevolcanicedifice.J.Volcanol.Geotherm.Res. 243,1–13. Costa,A.,Melnik,O.,Sparks,R.S.J.,2007.Controlsofconduitgeometryandwallrock

elasticityonlavadomeeruptions.EarthPlanet.Sci.Lett. 260(1),137–151. Crank,J.,1979.TheMathematicsofDiffusion.OxfordUniversityPress.

DeMichieliVitturi,M., Clarke,A.B.,Neri,A.,Voight,B., 2008.Effectsofconduit geometryonmagmaascentdynamicsindome-formingeruptions.EarthPlanet. Sci.Lett. 272(3),567–578.

Deardorff, N.D., Cashman, K.V., Chadwick, W.W., 2011. Observations oferuptive plumedynamicsandpyroclasticdepositsfromsubmarineexplosiveeruptions atNWRota-1,Marianaarc.J.Volcanol.Geotherm.Res. 202(1),47–59. Delaney,P.T.,Pollard,D.D.,1981.Deformationofhostrocksandflowofmagma

dur-inggrowthofminettedikesandbreccia-bearingintrusionsnearShipRock,New Mexico.USGSProf.Pap. 1202.

Edmonds, M., Oppenheimer,C., Pyle,D.M., Herd, R.A.,Thompson,G., 2003. SO2 emissionsfromSoufrièreHillsVolcanoandtheirrelationshiptoconduit perme-ability,hydrothermalinteractionanddegassingregime.J.Volcanol.Geotherm. Res. 124,23–43.

Eichelberger,J.,Carrigan,C.,Westrich,H.,Price,R.,1986.Non-explosivesilicic vol-canism.Nature 323,598–602.

Elders,W.A.,Friðleifsson,G.Ó.,Albertsson,A.,2014.Drillinginto magmaand the implicationsoftheIcelandDeepDrillingProject(IDDP)forhigh-temperature geothermalsystemsworldwide.Geothermics 49,111–118.

Embley,R.W.,Chadwick,W.W.,Baker,E.T.,Butterfield,D.A.,Resing,J.A.,DeRonde, C.E.,Tunnicliffe,V.,Lupton,J.E.,Juniper,S.K.,Rubin,K.H.,2006.Long-term erup-tiveactivityatasubmarinearcvolcano.Nature 441(7092),494–497. Farquharson,J.I.,Baud,P.,Heap,M.J.,2017a.Inelasticcompactionandpermeability

evolutioninvolcanicrock.SolidEarth 8(2),561.

Farquharson,J.I.,Heap,M.J.,Lavallée,Y.,Varley,N.R.,Baud,P.,2016.Evidenceforthe developmentofpermeabilityanisotropyinlavadomesandvolcanicconduits.J. Volcanol.Geotherm.Res. 323,163–185.