Lithos, 30 (1993) 93-107
Elsevier Science Publishers B.V., Amsterdam
93
Crustal anatexis during the influx of mantle volatiles
B.A. L i t v i n o v s k y a a n d Y u . Y u . P o d l a d c h i k o v b
"Geological Institute of the Academy of Sciences Sakhyanova 6, 670042 ~Tan-Ude, Russia
blnstitute of Experimental Mineralogy qf the Academy of Sciences, 142432 Chernogolovka, Moscow district, Russia
(Received February 4, 1991; revised and accepted January 21, 1993 )
LITHOS
ABSTRACT
Many data show that large masses of silicic magma can be formed by crustal anatexis under the influence of volatiles, possibly enriched in primary water derived from a mantle source. In the present paper,
a model of crustal anatexis, accompanied by a limited influx of volatiles is suggested. The water influx is
not excessive, no independent fluid water phase appearing in the magma. Convective diffusion is assumed
to be the dominant mechanism of volatile transport within the silicic melt. This mechanism increases the
volatile flux by several orders of magnitude compared with the diffusion flux in a non-convectingsystem.
A high convective flux may be generated only at specific stages of magma-chamber formation. In this
paper, a mathematical formulation of the conditions favouring this type of anatexis is given.
The most plausible source of deep-seated, water-bearing volatiles beneath large, silicic, crust-derived
magma masses are mantle-derived magmas which maintain vigorous convection. It is shown that convective-diffusion influx of volatiles from a lower layer of mafic magma into an upper layer of silicic magma
leads to a quasi-equilibrium situation ("transient two-liquid eguilibrium"; Watson, 1976). In this situation, the distribution coefficient of water between adjacent silicic and mafic magmas is proportional to
the ratio of water solubilities in these magmas and amounts to about 1.4 by mass. The silicic magma
overlying the mafic magma can contain up to 6 wt.% water, which is particularly true of the latest stages
of cryatallization of the mafic magma, when its water content rises and diffusion of water across the
mafic/silicic melt boundary becomes more efficient. On the basis of our results, the different stages of
formation of a silicic magma are discussed, the geological consequences are analyzed and some new regularities in the interpretation of geological and petrological data relevant to granitoid petrogenesis are
proposed.
Introduction
A key question in the p r o b l e m of silicic m a g m a
genesis concerns the existence of an influx of volatiles a n d other c o m p o n e n t s into the zones of anatectic melting. Crustal granites are very variable,
both in regard to the c o m p o s i t i o n s of the source
rocks a n d the t h e r m o d y n a m i c c o n d i t i o n s of melting (Chappell a n d White, 1974; W h i t e a n d Chappell, 1977; C l e m e n s a n d Wall, 1981; Pitcher, 1987;
Wyllie, 1984; W h i t e et al., 1986). In this paper, we
discuss only the f o r m a t i o n of large silicic m a g m a s
that are generated by the m e l t i n g of m e t a s e d i m e n -
tary a n d metaigneous protoliths a n d form both Stype a n d I-type granites.
For m a n y years, most authors have t e n d e d to presume that silicic magmas are generated in closed
systems (Winkler, 1967; Mehnert, 1968; Brown and
Fife, 1970; Wyllie et al., 1976; H u p p e r t a n d Sparks,
1988; V i e l z e u f a n d Holloway, 1988 ). In the former
USSR, however, an alternative viewpoint has long
been popular. It involves the influx of a b u n d a n t
water-bearing volatiles a n d other c o m p o n e n t s into
the zones of melting ( K o r z h i n s k y , 1967; Marakushev a n d Perchuk, 1974, etc.). Recently, this discussion has been r e s u m e d a n d the problems of the
0024-4937/93/$06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved.
94
source and nature of the volatiles has been considered ( Holloway, 1976: Dobretsov, 1980; Kadik and
Frenkel, 1982; Litvinovsky, 1983, 1985; Wyllie,
1984, 1988; Pitcher, 1987; Wickham, 1987; MeMillan and Dungan, 1988; Whitney, 1988).
Wickham (1987) has shown that closed-system
melting can account for the petrological features of
migmatite terrains and can explain the generation
of large silicic magma masses if the temperature of
melting is high ( T > 900°C). The main difficulties
are the restriction of the amount of melt by the low
( 1-2 wt.%) water contents of typical source rocks
and the absence of an effective mechanism of melt
separation from the solid restite at these low degrees of melting. Such difficulties cannot be overcome even if one reckons with decompression melting accompanying an uplift of the melting regions
(Shkodzinsky, 1981 : Kadik and Frenkel, 1982). The
experimental data on closed-system melting of pelitic gneiss at 10 kbar showed that 50%-melting was
attained only at a temperature of 870°C (Vielzeuf
and Holloway, 1988). In our opinion, however,
these data cannot be extrapolated to large, crustal
silicic magmas. The reason is that Vielzeuf and
Holloway used gneisses with anomalously high mica
contents as compared with average crustal rocks.
The homogenization temperatures of crystallized
melt in microinclusions in quartz and apatite from
many crustally derived granites show that magma
formation temperatures did not exceed 800 to
850 ° C (Chupin et al., 1988 ). An increase of magma
temperatures is unlikely in the situation discussed
since the formation of a huge mass of silicic magma
would buffer the temperature at the site of magma
generation (Vielzeufand Holloway, 1988).
Thus the formation of large silicic magma masses
by the melting of crustal materials may be difficult
if additional water and, possibly, also other components are not introduced into the source region
of the melt. Water will promote a high degree of
melting also at temperatures below 850 ° C.
B.A. L1TVINOVSKY AND YU.YU. PODLADCHIKOV
uation can arise under various conditions ranging
from very small influxes of volatiles (semi-closed
system behaviour) to very large influxes where water
and other components are present in excess. In the
following, we refer to this process as open-system
melting.
Open-system melting has been discussed and
studied for a long time (Mehnert, 1968; Dobretsov,
1980; Kadik and Frenkel, 1982: Kalinin and Reverdatto, 1984; Wickham, 1987). However, it is necessary to emphasize that despite the diversity of
these approaches, two questions still remaim unanswered. One of these concerns the problem of the
mechanism that ensures an effective transfer of
water from the bottom of a magma chamber to its
upper levels under conditions such that the magmas
are undersaturated in water. The other concerns the
nature of the volatile source.
The flotation of bubbles and drops of fluids in silicate liquid is ruled out because a free water phase
cannot exist under conditions of undersaturation in
water. The situation is not significantly different if
poorly soluble component, for example C02, is
present in volatile phase. In this case, the fluid in
equilibrium with the melt will only contain a few
percent of water (Portnyagin et al., 1987). This
mechanism of water transportation is thus irrelevant of fluid contents below 3 % by weight (Holloway, 1976). Diffusion of water in the melt can also
be excluded on account of it is very low effectivity
( D < 10-6cm2/s).
In the first part of this paper, we analyze the dynamics of the evolution o f a silicic magma chamber
that is increasing in size by the melting of its roof,
the roof melting being due to the influx of heat energy and volatiles through the floor of the magma
chamber.
The nature of the source of the volatiles is discussed later.
Transportation of water by convectively intensified
diffusion
The model of open-system melting
Attention has already been drawn to the hypothesis that melting may occur under conditions in
which access water and other components is so limited that an independent water phase does not appear in the magma (Litvinovsky, 1985). Such a sit-
In a previous publication, attention was drawn to
the circumstance that the development of convection in a melt may promote the transport of waterbearing volatiles to the upper levels of the magma
chamber (Litvinovsky, 1985). The appearance of
convection is favoured by a large, steadily increas-
CRUSTAL ANATEXIS DURING INFLUX OF MANTLE VOLATILES
95
TABLE 1
Symbols and abbreviations used
b
C
c¢, c,
Co
Cb,o,
Cbmo~,
C~
D
f
g
h
hb
h., h~
,4H
JD
= effective coefficient of thermal expansion
= water concentration
= average water concentration in m a g m a chamber far from a hot surface
= water concentration at the magma-solid rock contact and in solid rock
=concentration set on the hot surface ( Z = 0 , cf. Fig. 1 )
=total water concentration in basalt m a g m a
= w a t e r concentration in remaining basalt melt during gradual crystallization
= water concentration in basalt melt near the contact with adjacent silicic m a g m a
= mass diffusivity
= melt fraction in a partially crystallized m a g m a
= acceleration due to gravity
~ O. 1 (gbAT/Ku) =coefficient of heat exchange
= coefficient of heat exchange in the basaltic layer
= coefficients of heat exchange for the upper and lower boundaries of the convecting layer
= latent heat of melting
= I ~ z ~ 3( K/ D )h ( Co - ( ; ) ~ ( KD ) h ( Co - C') =diffusive flux at a horizontal surface
JT
OT
= 1 ~ ~ Ih,JT= heat flux at a horizontal surface
K
l
L
M
Nu ~ 0.1Ra °.3
NUD
Ra
t
7"
T
= t h e r m a l diffusivity
= coefficient of heal conductivity
= thickness of the convecting layer
= total mass of dissolved water
= Nusselt number
= Nusselt n u m b e r for diffusion
= (gb,JTL 3)/Ku = dimensionless parameter characterizing the intensity of convective movements
=time
= temperature of m a g m a
= average temperature of m a g m a far from a hot surface
= t e m p e r a t u r e of basalt m a g m a (b) and solid rock (s)
= t e m p e r a t u r e set on the hot surface ( Z = 0 , cf. Fig. 1 ) and the magma-solid rock contact
= temperature of begining convection in the partially melted layer ~ 30-40 vol.% of melt, C = Cs)
=liquidus and solidus temperature
= velocity of the melt front propagation
= vector of velosity of melting front propagation
= distance of melting front propagation
=distance to the hot surface (cf. Fig. 1 )
= parameters in equations in Appendix A:
T-7 ~
('-C
T~, Y~
To, T~
T¢on
U
X
z
~,q,F,A
v=[ 0
0
0 \
0
0
0~' or a-2);~ J = ~ + ~ ÷
2
P
P
Pb, Pl
=
=
=
=
=
0
oz 2
critical thickness of partially melted layer for the onset of convective motion
coefficient of heat conductivity
melt density
kinematic viscosity
kinematic viscosity in the upper and lower boundaries of the convecting layer
ing size of the magma body and also by the maintenance of gradients of temperature, density and volatile content between its bottom and top parts (e.g.
Kadik et al., 1971; Wickham, 1987). The convective melting of crustal materials with various water
contents (0 to 6 wt.%) has been investigated by
Huppert and Sparks (1988). These authors discovered several new and interesting relationships; however, their model is based upon melting in a closed
system and does not relate to the mass transfer
problem.
The key mechanism which provides a solution to
the mass transfer problem may be the combination
of diffusion and convective movement of the liquid. It is known that diffusive fluxes increase when
convective movements occur together with thermal
flux. Whereas the result of diffusion may be disregarded in the absence of convection, this mecha-
96
B.A. LITVINOVSKY AND YU.YU. PODLADCHIKOV
nism o f mass transport may play an important role
when convection occurs.
In terms o f convection, the process o f silicic
m a g m a generation and intrusion can be considered
in three successive stages (Christensen, 1984; Galaktionov and Yezersky, 1985 ). These stages are:
( 1 ) conductive heating,
(2) the development o f convection in a heated,
partially melted layer,
(3) diapiric uplift o f the whole partially melted
still convecting layer (Fig. 1 ).
Alter uplift o f the diapir, relatively cold crustal
material subsides towards the heated surface ( Z = 0 )
and the cycle is repeated. Alternatively, the process
may stop at stage ( 1 ). which corresponds to partial
melting without mechanical m o v e m e n t s (migmatization ), or at stage (2), which corresponds to the
formation o f m a g m a chambers with relatively homogeneous, well mixed silicic magmas.
c
~l
,
x N
~.x,\\%.~\\',\~
X~V,N
Conuec t i ng
~ltt
t
cr~j~tal$
4I..i;
rocks
~ dia]p|r~
%.'~\\%\N%%
+,'~,*,\-~\\\\,
i
),',',',',',','2
"~._. ,j)
~.~,\\\\\\'
H trI~TED
SURTRCE
Fig. 1. The processes of granite magma generation within the
Earth's crust in terms of convective movements. As temperature increases, bedinning melting leads to a sharp decrease
of density and viscosity. Subsequently, convective movements are manifested in the formation of diapirs and in the
separation of these diapirs from the heated surface. Each of
the thermics undergoes several successive stages of evolution
(Christensen, 1984; Galaktionov and Yezersky, 1985): (a)
conductive heating, (b) emergence of convective movements in a thin heated layer and (c) uplifting of the whole
mass of heated liquid (the thermic) due to a Raleigh-Taylor
instability. After the uplifting of the thermic, relatively cold
lower crust is moved onto the heated surface and the cycle is
repeated.
The crilical thickness o f a melted layer capable of
convection is:
~1
/g
b(T~-T~)
Kv
when Ra =
103
( 1)
(Christensen, 1984; Galactionov and Yezersky,
1985; for symbols and abbreviations see Table 1 ).
According to W i c k h a m ' s (1987) calculations,
(~~ 100 m when v = 10 s cm2/s and b = 0 . 0 0 0 0 5 ° C -1.
If we take into account that during convection a
partially melted substance participates and the proportion of partial melt increases with temperature,
then b ~ 0 . 0 5 ° C -j and hence (5~ 10 m.
Heat and mass transfer increase in the liquid
phase when convection occurs. For example, for
vigorous convection the heat irradiation from a
horizontal surface ( Z = 0, Fig. 1 ) is characterized by
a Nusselt n u m b e r N u ~ 0 . 1 Ra (Galaktionov and
Yezersky, 1985; Huppert and Sparks, 1989) which
is the mean ratio o f the actual thermal flux to the
one which would exist in the absence o f convection.
In Appendix A we have evaluated the diffusive
mass flux of a "passive" mixture (for example water
in m a g m a ) from the same horizontal surface
( Z = 0 ) . The Nusselt n u m b e r for diffusion is:
NUD~
Nu~ 100Nu
(2)
and while a well-developed convection with Ra ~ 106
increases the heat flux by the factor of ten, the diffusive mass flux is increased by a factor o f 1000 as
c o m p a r e d with that which would occur without
convective movement. This result is consistent with
estimates o f the ratio o f heat to mass flux across the
separation surface in a layered system with double
diffusive and m u l t i c o m p o n e n t convection, obtainable from experimental data and model approximations (Turner, 1979, 1985 ). The same result can
be derived for the relationship between heat and
mass transfer from an ascending m a g m a sphere
(Marsh and Kantha, 1978). It follows from the
proposed analysis that
20T
JT = - ~ =2h( To- T)
JD=
(3)
DOC ~/~
OZ ~-D
h(Co-C)
=,,/k-D h( Co-C)
97
CRUSTAL ANATEXIS DURING INFLUX OF MANTLE VOLATILES
where art and JD are the heat and diffusive fluxes at
a horizontal surface and h is the coefficient of heat
exchange.
These relationships allow an assessment of the
propagation velocity of the melting front driven by
the subjacent convecting melt. An analysis of equations and boundary conditions (Appendix B) shows
that in the quasi-static approximation there are two
different melt regimes, depending on the temperature at the contact of the heat source:
Regime 1. The heat-source contact temperature
T exceeds the temperature required to provide 3040 vol.% melting necessary for beginning of convection ( T~o, ), the water content in the solid layer being
G:
Tc > ']con a t (7,
L~tt ~-huK( Cs - C) + DKh~(Cc - C)
for regime 1
(6)
and
L~tt~ ~
(huCs+hlCc-2Cfi)
forregime 2
The system Eq. (6) has static solutions:
L
C ~ Cs at t >> - -
huK
for regime 1
(7)
and
(4)
Here the solid layer melts at its own water contents
C~ at temperature T~on, which promotes high temperature contrasts (Tc-T~on) in the convecting
magma and high velocities of melting-front propagation U~hK (U~ 10 c m / y r when v = 1012 poise,
U= 1 c m / y r when v = 10 Is poise).
Regime 2.
L<Lo..
nism; C is the average water content of the melt and
M is the total mass of dissolved water. Substituting
into the balance relationship the expressions for the
diffusive flux and front velocity obtained above
yields:
(5)
Here To is governed by T~ and may be lowered to
T~on, this being the temperature of melting when the
water content at the contact of the heat source equals
Co > C~ and is defined not by C~ only but, possibly,
by additional access of water. This situation is characterized by a relatively low temperature contrast
(D/K) °5 (T~-T,) in the convecting magma (no
more than 10°C) and by a slower propagation of
the melting front U~ (DK) °5 h, i.e. by two orders
of magnitude slower than under regime 1.
To assess the effectiveness of convective diffusion in these two cases, the mass balance relationship of the dissolved volatile component in the
whole melt must be considered:
dM d(CpL)
.
dt ~=']D + LTCs,
where JD is the diffusive influx from the lower levels of the melt where an elevated water concentration Cc is maintained by some unspecified mecha-
C Cshu+Cch,
L
at t > > - hu + hj
[[x~
for regime 2,
where hu and h~ are the heat exchange coefficients
for the upper and the lower boundaries of the convecting layer, respectively. Thus h=(hu+ht)/2.
Taking into account that the proportion of crystals
and the viscosity increase with decreasing temperature, we may assume that hi< hu or even hi << h~
depending on the value of the temperature contrast
7~-To.
From the correlations obtained, the conclusion
follows that for melting regime 2 the mechanism of
convective diffusion is able to provide an elevated
water content in the forming melts. Under melting
regime 1, the influx of volatiles from the lower levels is insignificant.
From the geological viewpoint, melting regime 2
corresponds to the model of open-system melting,
which is being discussed here. Regime 1 essentially
characterizes conditions of quasi-isochemical anatexis (closed-system m e l t i n g ) u n d e r which a high
degree of melting is caused mainly by an increase of
the temperature in the system. Under these conditions, the increase of the height and volume of the
melt greatly outstrips the influx ofvolatiles into the
system, so that the average water concentration in
the melt layer will always be very close to the water
concentration in the solid source layer. This is true
even if a considerable quantity of water-containing
volatiles enters the bottom of the melt layer.
98
The nature of the source of the volatiles
There has been much discussion of the transportation of aqueous volatiles within the upper mantle
(Korzhinsky, 1972; guts, 1975; Dobretsov, 1980;
Wyllie, 1984, 1988; Ryabchikov, 1988). Two main
sources of water have been proposed. These are the
degassing of the mantle and the degassing of subducted oceanic crust (Green and Ringwood, 1968;
Brown and Fife, 1972; Maaloe and Petersen, 1981;
Wyllie, 1984, 1988; Whitney, 1988). There are at
present good reasons to question the existence of free
aqueous fluids in the mantle at pressures less than
25-30 kbar. Indeed, about the solidus of basic melts
( T> Tsoj), water-bearing fluids will be dissolved in
partial melts (Wyllie, 1977, 1988; Kadik and Frenkel, 1982 ). If T < Tso~,water will be used up to form
phlogopite and amphibole (Wyllie, 1977).
The low water contents of the overwhelming majority of basaltic magmas and the extreme scarcity
of mantle xenoliths entirely consisting of mica and
amphibole, show that water-saturation is not usually attained in the upper mantle either in the system "melt-H20" or in the system "rock-H20". It is
likely that the mantle is an efficient geochemical
barrier which prevents the influx of water to higher
levels in the form of aqueous fluids.
Mantle volatiles can be transported through the
upper mantle only by mechanical transfer in some
other agent, the most plausible one being magmas
(Dobretsov, 1980; McKenzie and Bickle, 1988; Ryabchikov, 1988) such as those in ascending mantle
diapirs which contain basaltic melts in their upper
parts. If these diapirs reach the base of the crust,
melting of crustal rocks will invariably occur. Extensive melting is due to the high temperatures of
basaltic melts and convection inside the basaltic
layer. This ensures efficient transfer of energy and,
possibly, also some chemical components to the
sialic rocks. The conditions of open-system melting
could be attained in such situations.
It still remains uncertain what mechanism determines the transfer of H20 from water-undersaturated mafic magmas to the layers of silicic magma
forming atop. Moreover, the transfer of water appears to occur in such quantities that the water contents of silicic melts becomes higher than those in
the mafic ones. Mafic melts usually contain 1-2
wt.% water (Ringwood, 1975), whereas the water
B.A.
LITVlNOVSKYANDYU.YU.PODLADCHIKOV
contents reach 4-5 wt.% in crust-derived magmas
( R e y f a n d Bazheev, 1982; Holloway et al., 1986).
Transient two-liquid equilibrium at the contacts
between mafic and silicic magmas
It is known that the flux of some melt components by diffusion leads to the establishment of
"transient two-liquid equilibria" (Watson, 1976,
1982 ) with some components showing strong preference for one liguid over the other. Such situations
persist only as long as the structure-controlling species of each liquid do not mix completely.
The ratios of transient equilibrium concentrations of water in silicic and mafic melts (the distribution coefficients) are approximately equal to the
water solubility ratios in these melts. Data on the
solubility of water in silicic and mafic magmas are
listed by Kadik et al. (1971), Huang and Wyllie
(1975), Kadik (1975), Eggler and Burnham
(1984) and Silver and Stolper (1985). It appears
probable from these data that the numerical value
of the water-solubility ratios varies from 1.2 to 1.5.
Similar results can be obtained from the water solubility model in aluminosilicate melts as proposed
by Burnham ( 1967, 1975). Equal water activities
in silicic and mafic melts are reached when the
products of molar water concentrations and activity coefficients are equal. In terms of mass contents,
this indicates distribution coefficients of 1.4-1.5.
These relationships imply that at the contact with
low-water (1-2 wt.%) basaltic melts, convective
melting can lead to the formation of silicic magmas
with water contents of 1.5 to 3.0 wt.%
However, in crystallizing basalts, the water concentrations in the remaining melts (Cbme~,) may
considerably exceed the original total water concentration (Cbto~). Provided that the maximum possible solubility of water in basaltic melt is not exceeded, they will be inversely proportional to the size
of the remaining melt fraction:
Cbmelt ~- Cbto` / f
(8)
w h e r e f i s the remaining melt fraction in a partially
crystallized basaltic body.
Hence,
Cc ~ 1.5 Cb,ot/f
(9)
and when the basalt melt with 1-2 wt.% H20 is 50
99
CRUSTAL ANATEXIS DURING INFLUX OF MANTLE VOLAT1LES
% crystallized (Cb,o,= 1-2 %, f = 0 . 5 ) , the water
content in the equilibrium silicic melt will be C~ ~ 35 wt.%
Establishment of transient two-liquid equilibria in
convecting mafic and silicic melts by convectivelyintensified diffusion
The condition for realizing such a type of melting
is
Ub< 10Vl,
i.e. the viscosity of the convecting basaltic melt that
provides the water influx, must be at least 10 times
less than that of the silicic magma.
Case(2) when hb <<hi
The spreading of the transient equilibrium at the
contact throughout the entire mass of convecting
melt by convectively- intensified diffusion depends
on the intensity of the convective movements in
both melts. Thus, the distribution of water in the
lower and upper parts of the silicic magma reservoir
might deviate from transient equilibrium if insufficient convection occurs in the basaltic layer. In
such a case, the rapid increase of volume of the silicic melt would result in a decrease in its water contents. It is therefore necessary to evaluate the parameters which control the intensity of convection
in the basaltic layer.
C ~ (C~hu +Cchl)/(hu +h~)
(13)
(14)
This case describes the conditions for isochemical melting like that occurring during the formation
of migmatites. There is insufficient convective motion in the upper part of the basaltic layer and thus
the basaltic melt will not provide efficient volatile
delivery to the contact vith the forming silicic
magma. By analogy with the previous case we have:
Vb> 10V~.
(15)
In other words, if we assume that the viscosity of
the developing silicic melt together with the relic
unmelted crystals is 107-101° poise, viscosities exceeding 10 poise in the adjacent part of the mantle
diapir would not permit an efficient influx of water.
for regime 2 [from (7) ]
h,( Cc-C) =%( C'b,o,/f--Cbc)
(10)
and
Ra>> 103
C~l.5Cb~
(ll)
Here hb is the coefficient of heat exchange in the
basaltic layer, while the Eqs. (10), ( 11 ) describe the
mass balance and the "transient two-liquid equilibrium" of the water that has passed through the inter-melt contact surface. We shall discuss two cases
separately:
Case ( 1 ) where hb >> hi
( 12 )
In this case convection in the basaltic layer efficiently delivers water to the contact with the developing silicic melt. According to the model of opensystem melting, this condition will allow the influx
of water into the silisic magma chamber by convective diffusion. The precondition is that:
hb/ h, ~ aTb/ ( Tc
These relationships apply only if convection is
vigorous in both reservoirs, i.e.
-
To) (Vl/ lib) )> 1
and, given the above relationships and the previously defined parameters for melting by this model:
ATb/ ( T c - To) ~ ( K / D ) ° ~
100.
(16)
which depends on the thickness and viscosity of
the convecting layer.
Thus, the calculations above show that if two adjacent convecting magma systems, a basic and a silicic one have been established, a transfer of water
from the basaltic layer into the silicic one can be
effected by convective diffusion if the conditions
described by equation sets ( 1 ), (4) and (12), or
( 13 ) and ( 15 ) apply. The indicated mechanism of
volatile transfer allows considerable masses of silicic magma to be generated in the lower crust under
conditions of low water contents and relatively low
temperatures ( < 850 ° C).
It is probable that a similar redistribution mechanism may also apply to alkalis, which have similarly high diffusivities. For potassium, such redistribution has actually been proved by experiment in
the case of a adjacent acid and mafic melts (Watson, 1976, 1982; Johnston and Wyllie, 1988; Koyaguchi, 1989). Watson (1984) showed that the distribution coefficient of potassium between
100
coexisting granite and basaltic magma is higher than
2.
Geological interpretation
Interpreting the above results in geological terms,
we can distinguish several evolutionary stages of
granitoid magma chambers forming atop the basaltic parts of mantle diapirs (Fig. 2).
When convection is efficient in mantle diapirs,
their vertical temperature gradients will be gentle
and maximum melting will occur in the uppermost
parts where pressures are lowest. Also, convection
as such promotes enrichment of the upper diapir
levels in melt. As the mantle diapirs advance, crustal rocks will therefore be brought into contact with
mantle materials comprising sizable melt fractions
and presumably also containing pockets of segregated basaltic magma. Indirect evidence of the existence of segregated bodies of magma (cf. Dobretsov, 1980; McKenzie and Bickle, 1988) comes from
plutons of (alkali-basaltic) gabbro which occasionally reach large sizes and are direct precursors of
granitoid igneous activity.
During the initial phase of ensuing crustal melting, the mafic magmas are at temperatures close to
their liquidus and do not contain more than 1 or 2
wt.% water (Ringwood, 1975; Ryabchikov, 1988).
In these conditions, melting of crustal materials will
occur independently of the water contents of the
mafic sources. It is also worth noting that the low
water contents of the mafic magmas will prevent
water influx into the first melting crustal materials
which are made up of various high-grade gneisses
and crystalline schists with 1-1.5 wt.% of water.
The single important requirement of this initial
melting regime is thus strong heating of the crust
overlying the mantle diapir. This leads to the addition of refractory components to the first crustal
melts which become granodioritic or quartz-monzonitic in composition. As is well known, the magmatism of regional-scale composite intrusions usually begins with the emplacement of magmas of such
kind (Leontiev et al., 1981; Didier et al., 1985).
There also exists a large body of evidence of the coexistence of silicic and mafic melts in common
magma chambers (Litvinovsky and Letnikov, 1980;
McMillan and Dungan, 1988; Nixon, 1988a,b; Litvinovsky et al., 1992 and many others).
B.A. LITVINOVSKY AND YU.YU. PODLADCHIKOV
The following melting stage is connected with
further cooling of the diapir and its associated basalts. This has two important consequences:
-Firstly, dropping temperature in the heat source
(To) causes a change of the relationship between Tc
and T¢o, (the latter being the 30-40 % melting temperature of the sialic material under Cs cf.p. 95).
When T¢ ~< T~on,melting by regime 1 (p. 97) stops.
-Secondly, partial crystallization of the diapir
progressively causes increase of the water contents
in the residual basaltic liquid. In the presence of 50%
of crystals, water contents are doubled, etc. until
water saturation is eventually reached. When water
concentration in the mafic magma exceeds the critical value for diffusion into the silicic melt, melting
regime 2 (p. 97) the open-system melting, begins at
Tc < Tcon.
In the following, quantitative estimates of the
critical thickness of the convecting layer and of the
intensity of transfer by diffusion allow us to monitor various stages during the development of the
magma chamber by open-system melting of the
crustal lithologies (Fig. 2 ). The following stages can
be distinguished:
Stage ( 1)-Migmatization. This implies isochemical partial melting of various lithologies during
conductive heating. At this stage, the proportion of
melt does not exceed 20-30 % (Shkodzinsky, 1981;
Wickham, 1987).
Stage (2)-The beginning of complete melting.
During this stage, a suspension of crystals in melt
forms in the lower part of the migmatite zone,
mainly promoted by diffusion of water from the
diapir source. The thickness of this melt layer cannot exceed some tens of metres, inasmuch as any
further increase would trigger convection.
Stage (3)-Magma generation during convective
transfer of heat and material. The convection during this stage ensures effective transportation of
water from the bottom of the magma chamber to its
upper levels in a system which is far from being
water saturated. Convective motion also promotes
magma homogenization and removal of refractory
restite. The ultimate size of the silicic magma
chamber is nearly reached at this stage.
Stage (4)-Melting involving the separation of a
volatile H20 phase. This stage is reached only if and
when the water content of the melt becomes equal
to its saturation concentration. Our calculations in-
CRUSTAL ANATEXIS DURING INFLUX OF MANTLE VOLATILES
Stile I
//
Stale 2
Stalle 3
l0 |
Stage 4
giter iituritimn
. . . . . fi, h'( . . . . . . .
Zone of
con~tctil~J
transfer
olf v o l i t i l i t
IT
and v o l a t i l e s
F--~ Mi flt41~.t i tes
L~
~,~aso~t ic
"grin i f iiat ion"
wilk r l ~ t ~ f # !
~
Crostal
1it6olo9~ts
Fig. 2. Successive evolutionary stages o f a m a g m a - g e n e r a t i n g processes occurring u n d e r conditions o f a limited influx o f m a n t l e
volatiles. See the text for m o r e detailed c o m m e n t a r i e s .
dicate that there is a very low probability of ever
attaining stage 4 before the ultimate crystallization
of the contents of the magma chamber. The reason
is, among other things, that gravitational instability
will cause separation and ascent of silicic magma. A
detailed discussion of this aspect is the subject of a
special study and is reserved for a future publication.
Thus the evolution of a silicic magma chamber
from stage l to stage 3 (or 4) leads to the formation
of a magmatic system which comprises several successive zones as shown in Fig. 2. There is normally
a succession of various stages of magma generation
in the framework of a single, continuous process
featuring initial closed-system melting (stage 1 ) and
subsequent open-system melting without (stage 2)
or with (stage 3) melt convection, and with a limited volatile influx from a source which may be a
mantle diapir. Open-system melting likely plays the
main role in the generation of a large volume of silicic magma. It will continue until 60-70% of the basaltic diapir magma has crystallized. At that point,
the viscosity of the mafic melt will exceed 1012-1014
poise, and convection becomes too weak. Convection may also cease because the thickness of the
"layer" of basaltic melt decreases below a critical
value.
Melting of crustal materials by open-system processes may result in the formation of large volumes
of granitoid magma with water content reaching 6
wt.% Typical subliquidus temperatures of granitic
melts with such water contents are 800-900°C at
the 8 to 12 kbar pressures which characterize the
lower levels of the crust (Huang and Wyllie, 1975;
Wyllie, 1988).
Generally, the temperatures during open-system
melting will be lower than those during the initial
stages of interaction between the mantle diapir and
the crust with close-system melting, and open-system melt composition will be more silicic.
A persistent and voluminous influx of water thus
promotes the formation of crustally-derived igneous complexes made up mainly of granites rather
than granodiorites.
102
Discussion and conclusions: petrogenetic
consequences as seen against the background of
current opinion
The present analysis of open-system melting and
its causes and consequences leads to the following
petrogenetic conclusions and implications:
( 1 ) The mode of thermodynamic calculation of
the phase relationships in the open-system melting
of crustal rocks must be different from that used in
closed-system calculation (Korzhinsky, 1967, 1972;
Marakushev and Perchuk, 1974; Holloway, 1976).
The main difference is in the constant chemical potentials of water and others components with high
coefficients of diffusion. These potentials must equal
the chemical potentials of the relevant components
in the source, in the present case in a basaltic mantle-diapir melt. Closed-system melting, in contrast
is characterized by constant bulk contents of components termed "perfectly mobile" by Korzhinsky
(1967, 1972). The Korzhinsky approach is necessary for the thermodynamic description of opensystem melting involving "perfectly mobile" and
"inert" components (Korzhinsky, 1967, 1972;
Marakushev and Perchuk, 1974).
(2) Within the areas where gradational transition between successive zones (granites-migmarites-high grade metamorphic rocks), can be seen
in vertical cross-sections the evidence of closed-system formation of migmatites does not exclude subjacent granite magma generation in the open system (cf.stage 3, Fig. 2).
(3) The composition of migmatite leucosomes
formed during stages 2 and 3 above in-situ granitic
melting products (generated as a consequence of
mantle diapirism), is defined by the composition of
the local source material, whereas the composition
of granite melt in magma chambers depends on the
addition of volatiles and other components derived
from a deep source. This means that the plutonic
rocks and the migmatitic leucosomes may be compositionally heterogenous despite their almost simultaneous formation.
(4) Evidence of pre-melting metasomatic alteration of the source rocks adjoining in-situ granitoid
melting products, and of the xenoliths contained in
the granites, may be rare. The reason is that metasomatic alteration is most likely to occur only after
the formation of a free aqueous vapour phase, which
is umcommon during "open-system" melting.
B.A. LITVINOVSKY AND YU.YU. PODLADCHIKOV
( 5 ) The essential role of convective mixing in the
formation of most of the melt: in granite magma
chambers formed by open-system melting, granitoids may have a high degree of textural and compositional homogeneity. Well-known features of
some aqueous granitic bodies, such as conformable
xenoliths, inheritance of source-rock textures, ghost
stratigraphies, etc. are probably preserved only in
the peripheral parts ofin-situ magmatic bodies.
(6) In our model, the influx of water is continuously dissolved in newly formed melt and does not
proceed to the roof of the magma chamber as separate phase. Water-saturation occurs only during the
rare stage 4 of the development of the magma
chamber (cf. Fig. 3). This may explain the absence
of thick zones ofbasification (basic rims) above insitu granitic bodies.
Finally, we wish to emphasize the main differences of our complex melting model from the
models proposed by other writers. Models based on
anatectic melting, describe magma generation in
closed systems (Winkler, 1967; Mehnert, 1968;
Wells, 1980; Jaupart and Provost, 1985; Lux et al.,
1986; Huppert and Sparks, 1988; Zen, 1988 and
many others). Our model, in contrast, emphasizes
the influx of external water and some other components into the melting zone. However, this influx
occurs so that water saturation is normally not attained (cf. Wickham, 1987).
There are also some differences in the interpretation of the role of the thermal energy source. Even
in models assuming that the heat source are basalt
sills intruded into the crust (Kalinin and Reverdatto, 1984; Huppert and Sparks, 1988; Whitney,
1988), the role of the sills is initially reduced only
to conductive heating of the enclosing silicic rocks
with subsequent partial melting of the latter. In our
model, mafic magmas are the source both of the
thermal energy and the chemical components, at
least water. Their derivation from an ascending
mantle diapir ensures a protracted time period for
the formation of the silicic magma. The influx of
water allows and necessitates lower melting temperatures and higher degrees of melting than simple
contact heating.
To the best of the authors' knowledge, models assuming a regular influx of water and other components during melting, have been discussed mainly
by geologists from the former USSR. For instance,
the model of magmatic replacement elaborated by
103
CRUSTAL ANATEXIS D U R I N G I N F L U X OF MANTLE VOLATILES
,
t
In~ S
~ Lj t~ ~e 8
C ~
Fig. 3. Model of the generation of a granitic magma chamber above an ascending mantle diapir encountering continental crust.
Basic and silicic magma chambers form together two conjugated convecting systems. Interaction of these systems ensures the
transfer of heat energy as well as water and alkalis from mantle-derived magma chamber into producing crustal silicic melt; it
also promotes the formation of mixing zone between two convecting systems.
Korzhinsky (1967, 1972) and his followers (Marakushev and Perchuk, 1974) suggests that juvenile
volatiles were carried from mantle depths, and the
amount of volatiles transported into the melting
zone was so great that volatiles existed as a separate
water-vapour phase in equilibrium with the silicic
melt during all stages of its formation. The Kalinin
and Reverdatto model (Kalinin and Reverdatto,
1984; Reverdatto and Kalinin, 1989) is similar to
ours but has some differences. That model is based
on the assumption that the main thermal energy
source is a basalt sill that was emplaced into the
crust, and the main source of chemical components
is a flux of heated mantle fluids that were filtered
through a vertical permeable zone within the crust.
However, these authors do not address the problem
of how this water is extracted and transported from
the mantle, how the water and potassium are transferred to silicic melts and, lastly, how water is transported to the upper levels of an expending silicic
m a g m a chamber where the silicic magma is undersaturated in water.
We wish to emphasize, however, that the proposed model of open-system melting in many ways
approaches Dobetsov's (1980) model of "fluid
syntexis". But, unlike Dobretsov's model, our model
involves open-system melting with volatiles being
separated from the mafic source during its crystallization in the temperature interval T~iq-Tso] rather
than by retrograde boiling. Water transfer into the
developing silicic magma chamber takes place directly from the basic into the silicic melt by diffusion intensified by convection. No fluid flows are
involved. More important is that in our model redistribution of water can occur before water-bearing minerals start to crystallize from the mafic melt.
In the actual geological situation, mixing of silicic
and basic magmas appears inevitable and this effect
must be considered in future modeling (Fig. 3 ). The
elaboration of this problem is the next stage of our
studies. The behaviour of the major rock-forming
elements, particularly the alkalies, during the opensystem melting in our model similarly remains an
urgent subject of study. It may be assumed that
physical-chemical analysis of the possible modes of
element migration during convective diffusion will
prove to be fruitful approach.
Appendix A
This appendix evaluates the diffusive mass flux
104
B.A. LITVINOVSKY AND YU.YU. PODLADCHIKOV
of a "passive" admixture (e.g. water in magma)
from a given horizontal surface ( Z = O, see Fig. 1 ).
"Passive" in this case means that the water has little
influence on the density of the magma. The equations of convective diffusion are:
~t + vVa = DAa, ~t + ~Vq=K3q
q= 1, o~= 1 at Z=O and q~O, a ~ O at Z - ~
Changing the coordinates and the corresponding
scaling of velocity yields:
In accordance with Galaktionov and Yezersky
(1985), and Huppert and Sparks (1989), the melting front for a sufficiently high supercritical convection can be considered to be a flat surface. It can
thus be calculated from one-dimensional models.
The temperature distribution in the solid layer
above the melting front conforms to the one-dimensional equation of heat conditions:
OT uOT 02T
0-7- -~x = K~x 2
The boundary conditions will be the temperature of
the onset of convection Tcon and the far-field temperature T~ which had characterized the solid phase
before the initial (conductive) stage of heating:
T= T~at x - ~ , T= T¢onat x=O
which converts the equation for concentration into
an equation for the distribution of temperature.
However, according to the approximation adopted,
the distribution of temperature does not depend on
the concentrations and, as stated above, the following ratios apply:
dT~ N u ( T ° - I P ) - ~ 0 . 1 gb
dZL
-Kv(_
- T~ - T ).
Here and below, the bar over a symbol means that
the corresponding value has been averaged over a
characteristic time interval. According to the above
analysis of the diffusion equations:
00/
OZ
-OZ'°r o-z-N/-D\T--~o--Tf~~
DNu
- C
L
Hence, the Nusselt number for diffusion is:
NUD ~
Nu ~ 100 Nu
Appendix B
To estimate the propagation velocity of the melting front driven by a subjacent convecting melt it is
necessary to use a coordinate system which moves
together with the melt front with a velocity U:
x=Z-Ut.
The front propagation velocity will be governed by
the Stephan condition:
p 3 H U = 2 ~ - 2 h ( Tco.- Ts)
We have assumed that convective heat exchange
with magma will occur, AH being the latent heat of
melting and p-the melt density. In agreement with
the phase diagram, it is necessary to choose the following dependence:
T = T¢o,.
Here it is assumed that Too. is the temperature of
beginning convection, i.e. the temperature at which
the degree of melting is about 30 to 40%. To calculate the water concentration at the melting front it
is necessary to assume the balance relation:
U( Co - Cs) = J D ~ -- ,,/KD h ( Co - C)
An analyses of these equation and boundary conditions shows that in the quasi-static approximation
there are two different melt regimes, depending on
the temperature at the contact of the heat source:
Regime 1. The heat-source contact temperature
Tc exceeds the temperature required to provide 3040% melting (Tcon), the water content in the solid
layer being Cs:
Tc>T~on, atC=Cs
Here, the solid layer melts at its own water content
Cs at temperature T¢o,, which promotes high temperature contrasts (To-Too,) in the convecting
magma and high velocities of melting front propa-
CRUSTALANATEXISDURINGINFLUXOF MANTLEVOLATILES
gation U~hK ( U ~ I 0 c m / y r when v - 1 0
U = 1 c m / y r when v = 10 poise).
poise,
Regime 2.
To<Too.
Here To is governed by 7~ a n d m a y be lowered to
T¢on at C~ , this being the t e m p e r a t u r e of melting
when the water c o n t e n t at the heat source contact
equals Co= C~. This situation is characterized by a
relatively
low
temperature
contrast
(D/
K ) ° 5 ( T ~ - T s ) in the c o n v e c t i n g m a g m a ( n o more
than 1 0 ° C ) a n d by slow propagation of the melting
front U~ (DK) °5 h, i.e. by two orders of m a g n i t u d e
slower than u n d e r regime 1.
Acknowledgements
The authors are deeply grateful to Profs. N.L.
Dobretsov, V.P. Myasnikov, A.A. Kadik, L.L. Perchuk a n d A.A. Saveliev for their useful discussions
of the m a i n aspects of this paper. We also wish to
t h a n k Prof. J.R. Holloway for his constructive critical c o m m e n t s a n d suggestions. We are especially
grateful to Profs. R. G o r b a t s c h e v a n d S.M. Wickham for their thoughtful a n d fruitful review of this
paper and the i m p r o v e m e n t of both the text a n d our
poor English.
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