The Genesis of Intermediate and Silicic Magmas in Deep Crust(6)

X ?1T >T L e6a T

X ?6á36·10à3T à5á17T L T 900 C e6b TX ?1á75·10à3T à1á017900 C T T s e6c T

X ?0T

The solidus temperature,T s ,is taken to be 812 C.The model lower crust is an amphibolite for which we have adopted the experimentally constrained T –X rela-tionship of Petford &Gallagher (2001).It should be noted that their model amphibolite has a more fertile bulk composition than the amphibolite modelled by Annen &Sparks (2002).Consequently,at a given temperature the amphibolite generates more melt than the hydrous man-tle basalt,except close to the solidus where basalt melt

fractions are higher (Fig.5b).Melt generated by dehyd-ration melting of pelite or greywacke is peraluminous in composition (Montel &Vielzeuf,1997)and differs signi-ficantly from that generated by basalt crystallization or by

amphibolite dehydration melting.

Basalt emplacement rate We use an emplacement rate of 5mm/year,correspond-ing to an addition rate of one 50m basalt sill every 104years.This value is representative of typical estimates of magma productivity in arcs (Crisp,1984).We also tested intrusion rates of one 50m basalt sill every 5·103and every 25·103years,corresponding to average intrusion rate of 10and 2mm/year,respectively.High intrusion rates result in fast rates of melt accumulation and high melt fractions,whereas low intrusion rates reduce or inhibit melt production.For a given emplace-ment rate,if the sill thickness is small compared with the total thickness of intruded basalt,the exact dimensions of sills only modify the details of the temperature and melt fraction on short timescales.As long as the repose period between sill intrusions (104years)is much shorter than the total duration of basalt emplacement (106years),the long-term evolution of the system is controlled by the average emplacement rate and is not affected by the details of sill thickness and injection frequency (Annen &Sparks,2002).An intrusion rate of 5mm/year is equival-ent to 5km of new crust per million years.Over several million years crustal thicknesses of tens of kilometres could be generated.However,our model does not con-sider the counteracting thinning processes such as spread-ing of hot thickened crust and delamination of dense lower

crust.

Fig.6.Modelled melt fraction (X)–T curves for greywacke and pelite under upper crustal conditions.The greywacke curve is based on experimental data of Patin ?o-Douce &Beard (1996)and Montel &Vielzeuf (1997).The pelite curve is based on the model of Clemens &Vielzeuf (1987).517ANNEN et al.DEEP CRUSTAL HOT ZONES

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Boundary and initial conditions The boundary conditions are constant temperatures at the surface (T ?0 C)and at 60km depth (T ?1200 C).The initial temperature variation with depth is determ-ined by the geothermal gradient.Here we chose an ini-tially linear geothermal gradient of 20 C/km.The upper crust,which is greywacke or pelite,is taken to be that part of the crust initially situated above 20km depth;the amphibolite lower crust is initially situated between the Conrad Discontinuity at 20km and the Moho at 30km (Fig.4).We have investigated intruding basalt magmas with 1á5and 2á5wt %H 2O.Emplacement depth Because the temperature through the hot zone varies with depth according to the geotherm,the basalt emplacement depth controls the temperature of equilib-ration of the intrusions and the consequent melt genera-tion.We present results for two fixed emplacement levels,30km and 20km (Fig.4a and b),which model the Moho and Conrad discontinuities,respectively.We also tested a model where basalt sills are randomly emplaced in the lower crust (Fig.4c and d).In all models,the thickness of each intruded sill is accommodated by downward dis-placement of the sequence below the sill resulting in a thickening of the crust and a downward displacement of the Moho.This type of accommodation is an approxima-tion of isostatic equilibration.MODELLING DEEP CRUSTAL HOT ZONES II—RESULTS Sills are emplaced at the basalt liquidus temperature (T L )appropriate for the chosen H 2O content.Each sill trans-fers its heat to the country rocks and equilibrates with the surrounding temperature,which depends on em-placement depth and the geotherm.With successive in-trusions the temperature of the system progressively increases,the hot zone develops and the geotherm slowly evolves.Eventually new sills equilibrate above their sol-idus temperature and start to retain residual melt.Figures 7and 8show the evolution of temperature and melt fraction over time for a selection of 50m sills em-placed every 10kyr (Fig.7)and every 25kyr (Fig.8)at 30km depth (Figs 7a and 8a)and at 20km depth (Figs 7b and 8b).Figures 7and 8depict the first sill (emplaced at time 0),the 50th sill (emplaced at time 500kyr),the 100th sill (emplaced at time 1Myr),and so on.The temperature and melt fraction of each sill evolve with its position on the geotherm,which changes shape with time as heat is supplied by successive sills (Fig.4b and d).When the solidus of the surrounding crust is reached it begins to undergo partial melting.Thus,melt in the hot zone ultimately comes from two distinct sources:from crystallization of basalt,which we refer to as residual melt ;and from partial melting of crust,which we refer to as crustal melt .The crustal melt may derive from upper crust (greywacke or pelite)or lower crust (amphibolite).The relative contribution from each source depends on the thermal profile of the hot zone and the depth of basalt sill injection.In some cases the earliest intruded basalt sills will cool below their solidus,only to be heated above their solidus by subsequent basalt sills (Figs 7and 8).In this case previously solidified basalt sills can be remelted.In detail these remelts may differ in composition from residual melts because of loss of volatiles on complete

solidification.We have not,however,taken this subtle

effect into account because a further parameterization is required (dehydration melting of hydrous mantle basalt),which is not well constrained by experiments.In practice,relatively little melt in the hot zone derives from remelt-ing,and in the interests of simplicity we group all remelts with residual melts.Incubation times The incubation time is defined as the time between the emplacement of the first sill,which typically cools below its solidus,and the generation of the first silicic melt,whether as residual melt or crustal melt.The incubation time for residual and crustal melt strongly depends on basalt emplacement rate and emplacement depth

(Fig.9a).For a fixed emplacement depth at 30km,the incubation time for residual melt generation varies from

260kyr for an emplacement rate of 2mm/year to 20kyr for an emplacement rate of 10mm/year (Fig.9a).At

shallow level the ambient temperature is lower and the

incubation time for a given emplacement rate is signific-antly longer (Fig.9a).In the case of sills randomly emplaced in the lower crust between the Conrad and Moho discontinuities the heat advected by the basalts is distributed over the entire thickness of the lower crust,rather than being focused at one depth.Consequently,the incubation time is longer than in the case of fixed emplacement at 30km or 20km,except for a low emplacement rate of 2mm/year (Fig.9a).The incubation time for crustal melts depends on the depth of sill injection (Fig.9b),but is typically greater than the corresponding incubation time for residual melt generation.One exception is for basalt emplaced in dir-ect contact with fertile pelitic upper crust.Hot zone efficiency and melt productivity Figures 10and 11illustrate the efficiency of the system in generating melt for different emplacement levels and emplacement rates.Figure 10shows the productivity of accumulated melt,i.e.the total thickness of residual or crustal melt generated for each 1m of basalt injected in

518JOURNAL OF PETROLOGY VOLUME 47NUMBER 3MARCH 2006

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the system since the beginning of intrusions,whereas Fig.11shows the production rate,i.e.the amount of melt generated per unit of time.Figure 10a confirms that it is a lot more efficient to generate residual melt from the basalt at deep rather than at shallow level.For example,with an emplacement rate of 5mm/year,after 3á2Myr of basalt injection each 1m of intruded basalt has generated 0á35m of residual melt if emplaced at 30km depth,0á22m if emplaced at 20km depth,and only 0á14m if emplaced at 10km depth.If the sills are ran-domly emplaced in the lower crust,after 3á2Myr,each 1m of intruded basalt has,on average,generated 0á23m of residual melt.Thus,to generate a given quantity of melt less basalt needs to be intruded at deep level than at shallow level.The residual and crustal melt production rates strongly depend on the emplacement rate (Fig.11).The production of residual melt continuously increases with time after the initial incubation period because more residual melt is generated with each new crystallizing basalt injection (Figs 10a and 11a).In contrast,the pro-ductivity of crustal melt is limited by the thickness of crust that can be partially melted.For a fixed intrusion depth,crustal melt productivity and production rates reach a maximum and then decrease (Figs 10b–d and 12b).This is because within the crust heat from the underlying basalt is transferred by conduction whereas the crust is cooled from above (fixed temperature at the Earth’s surface).Thus the thickness of the partially melted crust is limited by heat diffusivity in the crust and cannot grow indefinitely.The situation is somewhat dif-ferent for randomly emplaced sills because screens of crust are sandwiched between hot sills,thereby providing heating from below and above.Consequently,although it requires the longest incubation time,random sill injection is the most efficient way to partially melt the lower crust on a long timescale (Fig.10b).Another effici-ent way to produce crustal melt is to inject basalt at 20km in contact with a fertile upper crust (Fig.10d).At still shallower depths the efficiency of this process

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