珪長質マグマ溜まりの固化前線における沈降結晶の
捕獲
著者
雑誌名
号
ページ
発行年
URL
西村 光史
東洋大学紀要. 自然科学篇 = Journal of Toyo
University. 東洋大学自然科学研究室 編
59
35-46
2015-03
http://id.nii.ac.jp/1060/00007018/
Creative Commons : 表示 - 非営利 - 改変禁止
http://creativecommons.org/licenses/by-nc-nd/3.0/deed.ja
Crystal Capture and Settling in Sheet-like Silicic Magma
Chambers Consisting of Eutectic Melt and Pre-existing Crystals
Koshi NISHIMURA
東洋大学紀要 自然科学篇 第 59 号 抜刷
Reprinted from
Journal of Toyo University, Natural Science
No. 59, pp.35 ∼ 46, March, 2015
Tokyo, Japan
東洋大学紀要　自然科学篇　第 59 号：35-46（2015）
35
Crystal Capture and Settling in Sheet-like Silicic Magma
Chambers Consisting of Eutectic Melt and Pre-existing Crystals
Koshi NISHIMURA *
Abstract
In a solidifying magma chamber, settling crystals are captured by an advancing
solidification front. The effects of the crystal capture process on the compositional
structure of a silicic magma chamber are investigated based on a theoretical model.
Previous studies have shown that the capture process causes an S-shaped vertical
distribution of captured crystals especially in mafic intrusive bodies. However, the
present results show that for a high-silica magma body, consisting of eutectic melt and
pre-existing crystals, the vertical concentration of captured crystals changes linearly
and a clear compositional gap exists at certain depths.
Keywords: crystal capture, solidification front, magma chamber, high-silica magma
1. Introduction
Crystal settling plays a fundamental role in controlling the compositional evolution
of a magma chamber regardless of the presence or absence of convection. Geological,
experimental, and theoretical studies have revealed how petrological and geochemical
features of intrusive suites are controlled by crystal settling (Gray and Crain, 1969;
Fujii, 1974; Marsh, 1988; Martin and Nokes, 1988; Koyaguchi et al., 1990; Mangan
and Marsh, 1992; Sparks et al., 1993; Nishimura, 2006, 2009). Convection impedes
the settling process because the settling velocity is greatly exceeded by the convective
velocity throughout most of the depth of the magma chamber (e.g., Martin and Nokes,
1988; Koyaguchi et al., 1990; Sparks et al., 1993). In general, the thermal Rayleigh
number (Ra) for a silicic magma chamber is thought to be extremely large and thermal
convection must therefore be highly vigorous (Martin et al., 1987). However, where
a melt in a cooling magma chamber has a water-saturated eutectic composition,
thermal convection does not occur because there is no temperature gradient within the
chamber (i.e., Ra is equal to zero). Moreover, there is no compositional convection
* Natural Science Laboratory, 5-28-20 Hakusan, Bunkyo-ku, Tokyo 112-8606
36
Koshi NISHIMURA
in the chamber due to the homogeneous composition of the eutectic melt (i.e., the
compositional Rayleigh number (Rs) is equal to zero). Hence, crystal settling occurs in
a static magma chamber. As the compositions of many silicic magmas are close to the
water-saturated eutectic (or minimum) composition (Luth et al., 1964), it is important
to consider silicic magma chambers consisting of a eutectic melt and pre-existing
crystals, which can be composed of early formed phenocrysts or source rock residues
(i.e., restite crystals) (White and Chappell, 1977; Wyborn and Chappell, 1986; Chappell
et al, 1987).
Marsh (1988) studied the thermal and compositional evolution of a static magma
in a sheet-like chamber, and proposed the following scenarios: (1) a downwardsolidifying crust of magma might overtake slowly settling crystals, capture them, and
incorporate them into the crust itself when the growth rate of the leading edge of the
capturing crust (i.e., the capture front) is higher than the rate of crystal settling; (2) the
crust grows systematically slower with time, capturing fewer and fewer crystals; (3)
the concentration of preexisting crystals decreases downward and then increases due to
basal accumulation. This capturing process has been widely used to explain the modal
and chemical variations observed in many sheet-like mafic bodies (Gray and Crain,
1969; Fujii, 1974; Marsh, 1988, 1989, 1996; Mangan and Marsh, 1992).
The ability of crystals to settle through silicic melt is strongly dependent on the
melt viscosity. Until the 1990s, silicic melt was commonly thought to have a viscosity
close to that of solid rock (e.g., Pitcher, 1993). However, recent experimental studies
have established that silicic melts generated over a wide range of crustal pressure–
temperature conditions have viscosities in the range of 108–103 Pa s (e.g., Clemens and
Petford, 1999; Petford et al., 2000). Therefore, the amount of crystal settling should be
estimated for different melt viscosities.
I propose a simple theoretical model that demonstrates how the degree of crystal
settling affects temporal and spatial variations in the distribution of preexisting crystals
in silicic magma chambers. This study shows that silicic magma chambers form various
compositional structures depending on the viscosity of the melt. The implications of
this model for compositional structures of granitic suites and rhyolitic magma chambers
are discussed.
2. Model
Although multi-component melts generally solidify over a temperature range
(typically 100–300°C), melts with a water-saturated eutectic (or minimum) composition
solidify at a constant temperature. Emplacement of a silicic magma consisting of a
eutectic (or minimum) melt and pre-existing crystals (i.e., restites or early formed
volume) liquids rather than largely crystalline magmas. In a eutectic magma chamber,
4
crystallization is confined to the solid–magma boundary analogous to the ice–water
Crystal capture in silicic magma chambers
37
transition (Nishimura, 2006). The boundary conditions are T  T∞ at z ∞ and T = TE at
phenocrysts) is often observed within the continental crust (White and Chappell, 1977).
z = E(t)
(Fig. 1); the initial
condition
is T and
T∞compositional)
for z > 0 and E = 0.the
At magma
time t = 0, the 4
Due
to a homogeneous
liquid
volume)
liquids rather
thandensity
largely(thermal
crystalline
magmas. In awithin
eutectic magma
chamber,
chamber, the convective motion is suppressed. The compositional evolution of such a
magma begins to solidify from the initial solid–magma boundary (z = 0) in the negative
crystallization
is confined
to the
boundary
to the ice–water
solidified
silicic magma
chamber
(i.e.,solid–magma
granite) is governed
solelyanalogous
by the interaction
of
the
solidifyingIn
and
crust, and
of pre-existing
z direction.
themigrating
surrounding
rocktheorsettling
the solidified
part ofcrystals.
the magma chamber, the
transition (Nishimura, 2006). The boundary conditions are T  T∞ at z ∞ and T = TE at
Considerliquids
a sheet-like
chamber
consisting
of a water-saturated
volume)
rather magma
than largely
crystalline
magmas.
In a eutectic eutectic
magma chamber,
heatand
conduction
equation
can be expressed
as(volume fraction φ ) at the time of
melt
spherical
crystals
distributed
uniformly
z = E(t) (Fig. 1); the initial condition is T  T∞ for z > 0 and E0= 0. At time t = 0, the
crystallization
confined
tofraction
the solid–magma
analogous
to the ice–water
consistent with
the predictions
of
emplacement.
Theisinitial
crystal
φ 0 should be boundary
magma
begins
to solidify
from theand
initial
solid–magma
boundary
(z = 0)
in the negative
2
recent
experimental
studies (Clemens
Petford,
1999; Petford
et al., 2000),
which
T
T
transition (Nishimura,
2006). The boundary conditions are T  T at z ∞ and T = T at
= that most granite plutons were initiated as crystal-poor (<30%∞ crystals by (1) E
showed
ztdirection.
2 the surrounding rock or the solidified part of the magma chamber, the
 z In
volume)
rather
largely
crystalline
z = E(t)liquids
(Fig.
1);
thethan
initial
condition
is Tmagmas.
 T∞ forInz a> eutectic
0 and Emagma
= 0. Atchamber,
time t = 0, the
crystallization
is
confined
to
the
solid–magma
boundary
analogous
to
the
ice–water
heat conduction equation can be expressed as
magma begins
to solidify
fromboundary
the initial
solid–magma
= 0)
and
T =inTEthe negative
transition
(Nishimura,
2006). The
conditions
are T = boundary
T∞ at z = ∞(z
T is
temperature,
time, and
for z > 0diffusivity.
and E = 0. AtConservation
time t = 0, theof energy at
atwhere
z = E(t)
(Fig.
1); the initialt is
condition
is T is
T∞thermal
2 In the surrounding rock or =
zTdirection.
the
solidified
part
of
the
magma
chamber, the
 T to solidify from the initial solid–magma boundary (z = 0) in the negative
magma begins
(1) away
= 
the solid–magma
boundary requires that released crystallization heat is conducted
zheat
direction.
rock
the solidified
conduction
equation can
beorexpressed
as part of the magma chamber, the
t
 In
z 2the surrounding
heat
conduction
equation
can bethe
expressed
as process, conservation of energy at the boundary
from
the boundary.
During
capture
2
z = E(t) indicates
that
T
T
where
 is temperature, t is time, and  is thermal diffusivity. Conservation
(1) at
= T
(1) of energy
t
z2
the solid–magma boundary requires that released crystallization heat is conducted away
T
where
temperature,
L(1-T0is)dE
+L0VS t=isktime, and κ is thermal diffusivity. Conservation of energy at
(2)
from the dt
boundary. Duringzthe capture process, conservation of energy at the boundary
the
solid–magma
boundary
requires
that
released
crystallization
heat
is
conducted
away
z
=E
where T is temperature, t is time, and  is thermal diffusivity. Conservation of energy at
from
the boundary.
z = E(t)
indicatesDuring
that the capture process, conservation of energy at the boundary
solid–magma
zthe
= E(t)
indicates thatboundary requires that released crystallization heat is conducted away
where  is density, L is the latent heat of solidification, k is thermal conductivity and VS
from the boundary. DuringTthe capture process, conservation of energy at the boundary
dE +
(2)solidification

L0VS =velocity,
k
(2)
isL(1the crystal
settling
which is negative in the case of downward
0)
dt
z = E(t) indicates
that
z z =E
(Fig. 1 a) and vice versa (Fig. 1b). The second term on the left represents the effect of
where ρ is density, L is the latent heat of solidification, k is thermal conductivity and VS
varying
liquid
proportions
due toiscrystal
which
is negligible
when the VS is
iswhere
the crystal
settling
velocity, T
which
negativesettling,
in the case
of downward
solidification
is density,
L(1-0)dE
+L0VSL=is kthe latent heat of solidification, k is thermal conductivity and
(2)VS
(Fig. 1 a) and
dt vice versa (Fig.z1b). The second term on the left represents the effect
z =E here for simplification and equation (2) can be
small. Hence, this term is omitted
is varying
the crystal
settling
velocity,
which
is settling,
negativewhich
in theis case
of downward
of
liquid
proportions
due to
crystal
negligible
when the solidification
VS
isrewritten
small. Hence,
as this term is omitted here for simplification and equation (2) can be
(Fig. 1 a) and vice versa (Fig. 1b). The second term on the left represents the effect of
rewritten
where asis density, L is the latent heat of solidification, k is thermal conductivity and V
S
varying liquid proportions due to crystal settling, which is negligible when the VS is
T velocity, which is negative in the case of downward solidification
is the crystal settling
(3)
L(1-0 )dE = k
(3)
small. Hence,
this
term is omitted here for simplification and equation (2) can be
dt
z
z
=E
(Fig. 1 a) and vice versa (Fig. 1b). The second term on the left represents the effect of
rewritten as
varying liquid proportions due to crystal settling, which is negligible when the VS is
small. Hence, thisTterm is omitted here for simplification and equation (2) can be
L(1-0 )dE = k
rewritten dt
as
z
(3)
38
Koshi NISHIMURA
a
z
Co untry rock
Surrounding rock
z=0
T∞
T
TE
T
Solidifie d
mag ma
z = E(t)
Mag ma
(crystal
fraction φ 0)
b
b
Mag ma
(crystal
fraction φ 0)
z = E(t)
z=0
T∞
Solidifie d
mag maT
TE
T
Surrounding
rock
Co untry rock
b
z
Figure. 1 Boundary conditions of cooling of a sheet-like magma chamber consisting of a eutectic melt and
pre-existing crystals (crystal fraction φ 0). a: downward solidification. b: upward solidification.
The magma solidifies at z = E(t) and at eutectic temperature TE. The surrounding rock near the
magma is heated above T∞ by the release of latent crystallization heat, but T→ T∞ at greater
distances from the magma z→∞.
E = -2   t
(4)5
The position of the boundary between solid and magma, E(t), is negative (Fig. 1) and
can be expressed using the thermal diffusion length (t)1/2 as
where  is a constant.
Crystal
capture in
silicic magma
chambers
39
Combining
equation
and the
solution
of equation
The position of the boundary
between
solid(3),
and(4),
magma,
E(t),
is negative
(Fig. 1)(1)
and
gives
a transcendental
(Turcotte
Schubert,
1982)
determining
The
position
of the boundary
solid
andand
magma,
E(t),
negative
1) and :
can
usingequation
thebetween
thermal
diffusion
length
(t)is1/2
as for(Fig.
E = be
-2expressed
 t
1/2
can be expressed using the thermal diffusion length (κ t) as
(4)
2
L(1 )
e -
(4)
E = -20  t =
(5) (4)
c (T e -T
 (1+erf
) equation (3), (4), and the solution of equation (1)
where
 is)a constant.
Combining
gives λa transcendental
equationequation
(Turcotte
1982) of
forequation
determining
is a constant. Combining
(3),and
(4),Schubert,
and the solution
(1) :
where
gives
equation
(Turcotte
and Schubert,
1982)
determining
λ : equation (1)
wherea transcendental
 is a constant.
Combining
equation
(3), (4),
andforthe
solution of
where c is the specific heat.
2
givesa 0transcendental
(Turcotte and Schubert, 1982) for determining :
L(1)

e -equation
(5)
==
(5)
c (T e -TThe
 (1+erf
) a spherical crystal in a concentrated suspension is
velocityof
) settling
2
generally
less
than the
velocity mainly because of the equal volumetric flow
L(1c 0is)the
 specific

where
heat.
e -Stokes’
=
(5)
The
settling
velocity
of
a
spherical
crystal
in
a
concentrated
suspension
is
generally
c
(T
-T
)

(1+erf

)
e cthe
where
is the
specific
heat.
rate
of
displaced
fluid
relative to which the crystals must move. For uniform crystals,
less than the Stokes’ velocity mainly because of the equal volumetric flow rate of
the
displaced and
fluidZaki
relative
to which
the crystals
must settle
move.asFor
uniform crystals,
Richardson
(1979)
established
that they
follows:
Richardson
and
Zaki
(1979)
established
that
they
settle
as
follows:
The settling velocity of a spherical crystal in a concentrated suspension is
where c is the specific heat.
generallya2less
g than the NStokes’ velocity mainly because of the equal volumetric flow
(6)
VS =
1 - 0
(6)
18settling velocity
The
of
a
spherical
crystal
in
a
concentrated
suspension
rate of the displaced fluid relative to which the crystals must move. For uniformiscrystals,
generally
than
the(1979)
Stokes’
velocity
mainly
because
of follows:
the
flow
is thevolumetric
density
where
a is less
crystal
diameter,
g is
the
acceleration
due
to gravity,
∆ρequal
Richardson
and
Zaki
established
that they
settle
as
of the
contrast
between
the diameter,
crystal andgthe
liquid,
η is the shear
0 is
where
is displaced
crystal
is the
dueviscosity
to gravity,
liquid,
isFor
theφuniform
density
rate of athe
fluid relative
toacceleration
which
the crystals
must move.
crystals,
the modal fraction of the crystals in suspension, and the constant (N) is empirically
2g 
abetween
N 4.6 and
contrast
thefrom
crystal
theand
liquid,
is thesettle
shearas
of the and
liquid, 0 is
determined
varies
(Mirza
Richardson,
1979)
toviscosity
6.55 (Al-Naafa
Richardson
and
established
thatthey
follows:
V S = and
1Zaki
- 0 (1979)
(6)
18
Selim, 1992).
theThe
modal
fraction of the crystals in suspension, and the constant (N) is empirically
compositions of pre-existing crystals and eutectic melt correspond to the mafic
 varies
a2gand
N end-member, respectively. Therefore, the distribution of
end-member
silicic
determined
and the
VS =
1-
(6)and
0 from 4.6 (Mirza and Richardson, 1979) to 6.55 (Al-Naafa
18

pre-existing
crystals
can
be
regarded
as
a
compositional
structure.
When
the
growth
where a is crystal diameter, g is the acceleration due to gravity,  is the density
Selim,
rate
of a1992).
downward-solidifying crust (solid roof) is higher than the rate of crystal
contrastthe
between
the crystal
and the
liquid, crystals
 is the(Fig.
shear2a).
viscosity
of the rate
liquid, 0 is
settling,
crust might
incorporate
the settling
If the settling
becomes
higher
than diameter,
the migration
of the solid roof,
a clear
liquid phase
where
aThe
is fraction
crystal
israte
the
due
toeutectic
gravity,

isdevelops
density
the modal
of the crystals
in acceleration
suspension,
constant
(N)
isthe
empirically
compositions
of gpre-existing
crystalsand
andthe
melt
correspond
to the
under the roof of the chamber and consequently, the fraction of captured crystals, φ E,
contrast
between
the
crystal
and(Mirza
the
liquid,
is respectively.
the
viscosity
ofupwardthe
liquid,
and
at
the solid–magma
boundary
zero
(Fig.
2b).
On shear
the other
hand,
an
0 is
determined
and varies
from
4.6
and
Richardson,
1979)
to 6.55
(Al-Naafa
mafic
end-member
and
thebecomes
silicic
end-member,
Therefore,
the
distribution
solidifying crust (solid floor) can also capture the settling crystals. Unless φ E exceeds
the modal
fraction of the crystals in suspension, and the constant (N) is empirically
aSelim,
critical1992).
fraction, φ crit, which is needed for packing, crystal settling would not form a
settling
layer (i.e.,
cumulus
crystals
intercumulus
liquid) on the
solidto
floor
(Fig.
2c).
determined
and varies
from
4.6 +(Mirza
and Richardson,
1979)
6.55
(Al-Naafa
and
During the capture processes (Fig. 2a, c), φ E can be calculated by mass balance at the
The compositions of pre-existing crystals and eutectic melt correspond to the
Selim, 1992).
solid–magma
boundary as
mafic end-member and the silicic end-member, respectively. Therefore, the distribution
The compositions of pre-existing crystals and eutectic melt correspond to the
mafic end-member and the silicic end-member, respectively. Therefore, the distribution
critical fraction, crit, which is needed for packing, crystal settling would not form a
settling layer (i.e., cumulus crystals + intercumulus liquid) on the solid floor (Fig. 2c).
During the capture processes (Fig. 2a, c), E can be calculated by mass balance at the
40
solid–magma
boundary as
Koshi NISHIMURA
 E = (dE/dt - VS)  0
(7)
dE/dt
(7)
where VS becomes negative in the case of downward solidification (Fig. 2a) and vice
versa
(Fig.
The dE/dt
is obtained
differentiating
equation
(4) as follows:
where
VS 2c).
becomes
negative
in thebycase
of downward
solidification
(Fig. 2a) and vice
versa (Fig. 2c). The dE/dt is obtained by differentiating equation (4) as
b
a
follows:
a
b
dE = -   1/2
t
dt
(8)
Perfect solid
Perfect solid
φE
Clear liquid
φE
dE/dt
The time t required to move the solid–magma boundary from z = 0 to E can be obtained
Vs (4) as
directly from equation
(-)
φ0
dE/dt
Vs
(-)
φ0
2 Suspension
t= E
4 2
c
Suspension
(9)
d
c
d
Incorporating equations (8) and (9) into equation (7), E can be rewritten as
0 E
φE =  0 - VSSuspension
2
0
2 
φE
Vs
(+)
φ0
Vs
(+)
dE/dt
φcrit
Perfect solid
φE
(10)
Suspension
Settling layer
Vc
dE/dt
dE/dt
Perfect solid
Figure. 2 Schematic illustration of crystal capture processes. a: A downward-solidifying crust (solid roof)
captures settling crystals as long as the growth rate of the crust exceeds the crystal settling rate.
b: A clear liquid phase develops under the roof when the crystal settling rate is higher than the
growth rate of the crust. c: An upward-solidifying crust (solid floor) captures settling crystals
unless the concentration of captured crystals, φ E, reaches a critical fraction, φ crit, which is needed
for packing. d: After φ E reaches φ crit, a settling layer (cumulus crystals + intercumulus liquid)
develops on the solid floor.
dE/dt
where VS becomes negative in the case of downward solidification (Fig. 2a) and vice
where VS becomes negative in the case of downward solidification (Fig. 2a) and vice
versa (Fig. 2c). The dE/dt is obtained by differentiating equation (4) as
versa (Fig.
2c). Thenegative
dE/dt is in
obtained
equation (4)(Fig.
as 2a) and vice
the casebyofdifferentiating
downward solidification
where
VS becomes
follows:
follows:
versa
(Fig. 2c). The dE/dt is obtained by differentiating equation (4) as
Crystal capture in silicic magma chambers
41
dE = -   1/2
(8)
1/2
follows:
dE
dt = -  t
(8)
t
dt
dE = -   1/2
(8) (8)
t
dt
The time t required to move the solid–magma boundary from z = 0 to E can be obtained
The time t required to move the solid–magma boundary from z = 0 to E can be obtained
The
time tfrom
required
to move(4)
theassolid–magma boundary from z = 0 to E can be obtained
directly
equation
directly
from
equation
(4) asthe solid–magma boundary from z = 0 to E can be obtained
directly
from
equation
(4)
as
The time
t required
to move
2
tdirectly
= E 2 from equation (4) as
(9)
7
t = 4E
(9)
(9)
 22
4 2
t= E
(9)
2
can
be
rewritten
as
Incorporating
equations
(8)
and
(9)
into
equation
(7),
φ

can
be
rewritten
as
Incorporating
equations
(8)
and
(9)
into
equation
(7),
E
E
4 
rewrittenlinearly
as
Incorporating
equations
(9) into
equation crystals,
(7), E can
This
equation shows
that(8)
theand
fraction
of captured
E,be
decreases
with
S 0 E
E = 0 - V
(10)
(10)
V
increasing
depth
boundary
negative)
and
increases
can
be rewritten
as
Incorporating
(8) and (9) into equation
(7),(VsE is
 E =  0 - 2S20equations
E at the downward-moving
(10)
2 2
linearly with
increasing
height at the upward-moving boundary (Vs is positive) (cf.,
0 E that the fraction of captured crystals, φ , decreases linearly
with
This
 E =equation
 0 - VSshows
(10)
E
2
2


is
negative)
and
increases
increasing
depth
at
the
downward-moving
boundary
(V
Nishimura, 2006). After E reaches crit at the upward-moving
boundary, a settling layer
s
linearly with increasing height at the upward-moving boundary (Vs is positive) (cf.,
develops on
the After
solidφfloor
of the chamber (Fig. 2d). The growth rate of the settling
Nishimura,
2006).
E reaches φ crit at the upward-moving boundary, a settling layer
develops on the solid floor of the chamber (Fig. 2d). The growth rate of the settling
layer VC (negative) is represented by a mass balance at the top of the layer (Koyaguchi
layer VC (negative) is represented by a mass balance at the top of the layer (Koyaguchi
and
2000)
as as
andKaneko,
Kaneko,
2000)
VC =
VS 0
 0 -  crit
(11) (11)
It should be noted that the rate VC has a constant value. The values for the relevant
2 -1a constant value.
-3
-1
It shouldparameters
be notedare:
thatk the
rate
V-7C m
has
s , ρ = 2.4 × 103 kg mThe
, L values
= 2.5 × for
105 the
J kgrelevant
,
physical
= 7.7
× 10
-1
-1
3
-1
-1
°C, T = 150 °C, = 0.2,
= 0.6,
k = 2.4 W m K , c = 1.3 × 10 J kg K , T-7E = 700
physical parameters are: k = 7.7 10 m2 s-1,-3 =∞2.4  103 φkg0 -3m-3, Lφ crit
= 2.5 -2 105 J kg-1,
λ = 0.715 (calculated from equation (5)), a = 5 × 10 m, ∆ρ = 500 kg m , g = 9.8 m s ,
and
= 5.
k = N2.4
W m-1 K-1, c = 1.3  103 J kg-1 K-1, TE = 700 °C, T∞ = 150 °C, 0 = 0.2, crit = 0.6,
The settling of crystals in a silicic melt is strongly dependent
on the physical
-3
 = 0.715of(calculated
fromwhich
equation
(5)),isathe
= 5most
 10important
m,  (see
= 500
kg m-3(3)).
, g = 9.8 m s-2,
properties
the melt, among
viscosity
equation
Experimental studies have shown that the viscosity of natural silicic melts generated
and N = 5.
at a given crustal pressure is largely independent of temperature (Scaillet et al., 1998).
In paticular, the eutectic (or minimum) melt on the water-saturated solidus at a given
pressure The
must settling
have a constant
viscosity
becausemelt
majoris oxide
contents
(including
of crystals
in a silicic
strongly
dependent
on Hthe
2O)physical
and temperature are constant throughout the solidification history. The viscosities of the
properties of the
melt,(oramong
which
viscosity
is the most
important
(see
(3)).
water-saturated
eutectic
minimum)
melts
for haplogranite
are shown
in Fig.
3. equation
The
Experimental studies have shown that the viscosity of natural silicic melts generated at
a given crustal pressure is largely independent of temperature (Scaillet et al., 1998). In
paticular, the eutectic (or minimum) melt on the water-saturated solidus at a given
42
Koshi NISHIMURA
H2O content of a eutectic (or minimum) melt decreases and the melt viscosity increases
with decreasing pressure.
3. Results and discussion
The distribution of pre-existing crystals is calculated for constant melt viscosities in
the range 104–108 Pa s. Figure 4 shows the temporal evolution of the crystal distribution
within the initially 1000-m-high magma chamber (left panels) and the resulting
compositional structure within the solidified granite (right panels). In the magma
chamber with a melt viscosity greater than 107 Pa s, a homogeneous distribution of preexisting crystals is maintained throughout the cooling history (Fig. 4a,c). However,
the concentration of pre-existing crystals in the solidified granite decreases downward
and then suddenly increases near the center of the pluton (Fig. 4b,d). The gradient in
crystal concentration increases with decreasing melt viscosity. Previous studies of the
capture processes have shown that in many cases the pre-existing crystal concentration
gradually changes along an S-shaped curve (Gray and Crain, 1969; Fujii,1974; Marsh,
Melt viscosity (Pa s)
109
108
7
10
2.4 wt.% H2O
E
J
3.7
E
J
5.8
E
J
106
105
9.9
J
4
10
3
10
0
E
100
200
300
400
Pressure (MPa)
500
600
Figure. 3 Pressure dependence of the viscosity of water-saturated eutectic (or minimum) melt in the
haplogranite system Q–Ab–Or–H2O. The melt viscosities are calculated from temperature and
compositional data by Tuttle and Bowen (1958) and Holtz et al. (1992) using models by Shaw
(1972) and Giordano et al. (2008) (open and solid circles, respectively).
Crystal capture in silicic magma chambers
1,000
a
900
Height (m)
700
600
b
108 Pa s
800
43
108 Pa s
Suspension
Suspension
(20 vol.% crystals)
500
400
300
200
Solidified magma
100
0
1,000
900
c
Height (m)
800
d
107 Pa s
107 Pa s
700
600
500
400
300
200
100
0
1,000
900
e
Height (m)
700
f
10 6 Pa s
800
106 Pa s
Clear liquid
600
500
400
300
200
100
0
1,000
g
Height (m)
900
105 Pa s
600
500
400
300
Cumulus
Settling layer
200
100
0
1,000
i
900
800
Height (m)
h
10 5 Pa s
800
700
j
10 4 Pa s
104 Pa s
700
600
500
400
300
200
100
0
0
0
1,000 2,000 3,000 4,000 5,000 6,000
Time (years)
0.2
0.4
0.6
0.8
Fraction of pre-existing
crystals
Figure. 4 Temporal evolution of the crystal distribution within magma chambers with different melt
Nishimura_Figure
4
viscosities (a, c, e, g, i) and resulting
compositional structures
(distribution of pre-existing
crystals) of the resulting granite plutons (b, d, f, h, j). A compositional structure is formed
within a granite pluton even if a uniform crystal distribution is maintained in the magma
throughout its cooling history (a–d). A settling layer develops on the floor of the chamber if the
melt viscosity is less than 105 Pa s (g, i).
44
Koshi NISHIMURA
1988; Mangan and Marsh, 1992). However, the present results show that for highsilica magma bodies, the captured crystal concentration changes linearly, and a clear
compositional gap exists at certain depths.
In the magma chamber with a melt viscosity of 106 Pa s, a uniform distribution
of pre-existing crystals is maintained for a long time (~3,000 years) and a clear
liquid phase is formed at the last stage of crystallization (Fig. 4e). In this case, the
compositional gap near the center of the pluton reaches ~50 vol.% (Fig. 4f). In the
magma chamber with a melt viscosity lower than 105 Pa s (Fig. 4g, i), a clear liquid
phase and a settling layer (cumulus crystal + inter-cumulus liquid) develop in a
short time span (10 –102 years), forming a vertically zoned magma chamber. The
concentration of pre-existing crystals in the granite pluton becomes zero in the upper
part of the pluton and a settling layer (φ crit = 0.6) develops on the pluton floor (Fig. 4h,
j). Even if the eutectic (or minimum) melt is water-undersaturated, its melt viscosity is
almost equal to that of a water saturated eutectic (or minimum) melt at a given pressure
(Hess and Dingwell, 1996; Scaillet et al., 1996, Holtz et al., 2001, Nishimura, 2006).
Therefore, the calculated results (Fig. 4) represent a good approximation for waterundersaturated high-silica magmas. Petrological studies suggest that some rhyolitic
volcanic rocks are erupted from the upper part of a magma chamber that successively
crystallizes to form a granitic pluton (e.g., Bachmann et al., 2007). For a 1000-m-thick
sheet-like magma chamber with a melt viscosity greater than 107 Pa s (shallower level),
the rhyolite (area labeled ‘20 vol. % crystal’ in Fig. 4a, c) and the granite (Fig. 4b, d)
have almost the same composition. Conversely, crystal-poor rhyolite and crystal-rich
cumulative granite are formed at melt viscosities lower than 105 Pa s (deeper level).
The calculated time period required for settling layer formation (Fig. 4g, i) is not
significantly different from that estimated for a vigorously convecting magma chamber
(Martin and Nokes, 1988). Although there are many factors that affect the evolution
of magma chambers (e.g., magma recharge, wall-rock assimilation, magma mixing),
crystal capture would inevitably occur and an idealized model of this process may help
to provide new explanations for the compositional evolution of magmas.
Acknowledgements
The author would like to acknowledge T. Kawamoto, T. Shibata, M. Yoshikawa and
K. Takemura for valuable discussions.
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要　旨
珪長質マグマ溜まりの固化前線における沈降結晶の捕獲
西 村 光 史
共融点メルトと浮遊結晶からなる珪長質マグマ溜まりを仮定し、固化前線による沈降結
晶の捕獲が組成の空間構造にもたらす影響について計算を行った。これまでの研究では主
に苦鉄質貫入岩体中に見られる結晶捕獲プロセスが調べられ、沈降結晶が S 字型のモード
分布を形成することが示されてきた。しかし今回の計算の結果、共融点メルトと浮遊結晶
からなる珪長質マグマ溜まりでは沈降結晶のモードは直線的に変化し、ある深さにおいて
急激な組成ギャップを形成することが明らかとなった。