The Genesis of Intermediate and Silicic Magmas in Deep Crust(5)

In summary,the available petrological and experi-mental data are consistent with the derivation

of

Fig.4.Schematic representation of the evolution of the modelled hot zone.Basalt sills are emplaced at a fixed depth (a,b)or at random throughout the lower crust (c,d).The system is shown at the onset of intrusion (a,c)and after the emplacement of a series of sills (b,d).Each new sill volume is accommodated by downward displacement of the crust,previous sills and mantle below the injection level.Temperature is represented by the dashed line.The initial temperature is determined by a geothermal gradient of 20 C/km.The temperature of inpidual sills evolves with time and with their evolving position along the geotherm.The temperatures at the Earth’s surface and at 60km depth are fixed.

514JOURNAL OF PETROLOGY VOLUME 47NUMBER 3MARCH 2006

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H 2O-rich andesites

by crystallization of hydrous,mantle wedge-derived basalt in a lower crustal hot zone.MODELLING DEEP CRUSTAL HOT ZONES I—METHODS We address the thermal development of a crustal hot zone with specific attention paid to all potential sites of melt generation,including partially crystallized basalt and partially melted crust.In our model a hot zone develops by injection of numerous discrete basaltic sills at the Moho or within the crust (Fig.4).The thermal evolution of the hot zone,as a result of heat transfer between successive basaltic intrusions and country rock,is computed using the heat balance equation r C p @T @t t@X @t r L ?k @2T

@x 2e1Twhere r is density,C p is specific heat capacity,T is temperature,t is time,X is melt fraction,L is latent heat of fusion,k is thermal conductivity and x is (vertical)distance.The system is discretized into a one-dimensional array of cells,and equation (1)is solved by forward finite difference and iterative methods.The code was written with Delphi 4óin Object Pascal language.The resolution of the finite difference cells is 25m.Between the liquidus and solidus the finite differ-ence equivalent to equation (1)is solved by iterative approximation:

r c T p t1i àT P

i D t tL X p t1i àX p

i

D t

?k T p i à1àT p i D x 2tk T p i t1àT P

i D x 2

e2T

where D t is the time step between the time p and the time

p t1.Cells i –1and i t1are below and above cell i ,

respectively.D t is limited by the cell dimension,D x ,and

rock diffusivity to <8á5years.Above the liquidus or

below the solidus,the latent heat is zero and the

temperature of cell i at time p t1is

T p t1i ?

D t r c k T p i à1àT p i D x tk T p i t

1àT P

i D x !

tT P i e3T

The values of the parameters used in the model are given in Table 1.For sills with a horizontal dimension of 20km or more,the neglected lateral heat loss at the boundary

of the system does not significantly affect the outcome for

timescales of <4Myr (Annen &Sparks,2002).The

basalt emplacement rate,the fertility of the crust,the

temperature of the injected basalt,and the sill injection

level all control the thermal evolution of the system,and the amount and composition of the melt generated

(Annen &Sparks,2002).The model is entirely conduct-

ive and static.The issue of melt segregation process is discussed below,but it is instructive to consider the static

case first.

Temperature and melt fraction

Application of equation (2)requires knowledge of the variation of melt fraction X with temperature T .The liquidus temperature (T L ;X ?1)of a basalt varies with dissolved H 2O and MgO contents (Ulmer,2001;Wood,2004).The relationship between X and T was paramet-erized using experimental data.There is no single set of experiments on a primitive basalt with fixed H 2O content against which to calibrate X –T relationships from solidus

to liquidus.Instead we have spliced together two datasets,

one at low temperature and one at high temperature,for two different basalt compositions obtained at slightly dif-

ferent pressures (Fig.5).For high temperatures (X >0á5)

we have used the 1á2GPa experimental data of Mu ¨ntener et al .(2001)for a Cascades basaltic andesite (sample 85-44;10á8wt %MgO,mg-number 0á71)with initial H 2O contents of 5,3á8and 2á5wt %(Fig.5a),run at f O 2close to QFM (the quartz–fayalite–magnetite buffer).For lower temperatures (X <0á4)we used the 0á7GPa experi-ments of Sisson et al .(2005)on Cascades basalt (87S35A;6á5wt %MgO,mg-number 0á54)with 2á3wt %H 2O (Fig.5b).To match the f O 2of the two datasets we have only used those experiments of Sisson et al .(2005)that are within 0á5log units of QFM.

Table 1:Parameters used in the model r Density (kg/m 3)Injected basalt 2830Lower crust 3050Upper crust 2650C p Specific heat capacity (J/kg)Injected basalt 1480Lower crust 1390

Upper crust 1370L Specific latent heat (J/kg per K)Injected basalt 4.0·105Lower crust 3.5·105Upper crust 2.7·105k 0Thermal conductivity at surface Injected basalt 2.6temperature and pressure Lower crust 2.6(J/s per m per K)Upper crust 3.0

k Thermal conductivity (J/s per m per K)k ?k 0(1t1.5·10à3z )/(1t1.0·10à4T )Sources:r ,Holbrook et al .(1992)and Kay et al .(1992);C p

and L ,Bohrson &Spera (2001);k 0

and k ,

Chapman &

Furlong (1992).In the expression for thermal conductivity,z is the depth in kilometres,and T is the temperature in Kelvin.515ANNEN et al.DEEP CRUSTAL HOT ZONES

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For the modelled basalt we assumed linear X –T rela-

tionships between T L and the onset of amphibole crystal-lization,T a ,and between T a and the solidus,T s :

X ?1T >T L e4a T

X ?3á25·10à3eT àT L Tt1T L T T a e4b T

X ?X a

T a àT s eT àT s TT a T T s

e4c TX ?0T

T L was extrapolated from the 3á8wt %H 2O experiment of Mu ¨ntener et al .(2001)to 1261 C (Fig.5a).Following Wood (2004)T L varies with H 2O according to the relationship

D T L ?80ewt %H 2O T0á4e5T

where D T L is the liquidus depression relative to an anhydrous basalt of the same composition.T L was calculated with equation (5)to be 1225,1285and 1302 C for total H 2O contents of 5,2á5and 1á5wt %,respectively (Fig.5a)in good agreement with the variation in T L of the experiments of Mu ¨ntener et al .(2001).The solidus temperature (T s ;X ?0)of basalt also depends on H 2O content.However,for any basalt that contains more H 2O than can be accommodated in sub-solidus hydrous phases,principally amphibole for arc basalts,the appropriate solidus is that for H 2O saturation.Amphibole contains $2wt %H 2O and 40wt %amphibole is an approximate upper limit for a basaltic composition amphibolite.Thus,for basalts with !0á8wt %we have adopted the experimentally determ-ined H 2O-saturated solidus of 720 C (Liu et al .,1996).The change of slope in the linear function at temper-atures below the appearance of amphibole T a [Fig.5b;equation (4c)]is consistent with experimental data (e.g.

Foden &Green,1992;Kawamoto,1999;Sisson et al .,2005).In equation (4c),X a is the melt fraction at T a ,calculated using equation (4b).We chose T a ?1075 C based on the data of Mu ¨ntener et al .(2001)data—the 1GPa data of Foden &Green (1992)on a slightly more evolved arc basalt indicate a similar T a of 1040 C.The values of T L and T a are for a pressure of 1á2GPa

and are modified by 90and 120 C/GPa,respectively (Foden &Green,1992).We have not included here the effect of f O 2on melt fractions and compositions,al-

though we recognize that f O 2can play a key role in controlling the stability of an oxide phase and the con-sequent SiO 2enrichment at a given X (Osborn,1957;Sisson et al .,2005).Of course,at other subduction

zones,

(b)

Fig.5.Modelled melt fraction (X )vs temperature (T )curves for basalts.(a)At 1á2GPa with,from left to right,initial H 2O contents of 5,3á8,2á5and 1á5%.Symbols show experimental data from Mu ¨ntener et al .(2001).The liquidus temperature (T L )of basalt with 3á8wt %initial H 2O is estimated by extrapolation.T

L for basalts with 1á5,2á5and

5wt %initial H 2O is calculated with equation (5).The curves have a slope of 0á325 C à1between T L and T a .They kink at T a to fall linearly to T s ,the H 2O-saturated basalt solidus.(b)At 1GPa,the modelled basalt curve with 2á5wt %initial H 2O shows a good fit to the experi-

mental data points of Sisson et al .(2005).The dashed curve is the X –T variation for amphibolite lower crust (after Petford &Gallagher,2001).At low temperature the basalt produces more melt than the amphibol-ite because H 2O concentrates in the residual melt.At higher temper-atures the higher fertility of the amphibolite is attributed to its slightly more differentiated composition (see Petford &Gallagher,2001).Dashed lines in (a)pide fields in which the residual melt composition is,broadly speaking,basaltic andesite,andesite and dacite.516JOURNAL OF PETROLOGY VOLUME 47NUMBER 3MARCH 2006

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with different primary magma compositions,a different X –T parameterization may be more useful.However,at present there are insufficient experimental data available to make this worth while.As X decreases so the SiO 2content of the residual melts increases and MgO content decreases.An accurate para-meterization of SiO 2content would require additional experimental data as well as consideration of f O 2and is beyond the scope of this paper.None the less we are able to sketch indicative contours of melt composition onto Fig.5a as an approximate guide to how melt composition varies during basalt crystallization.Andesitic residual melts are generated at 0á35