Magma dynamics at the base of an evolving mafic magma chamber: Incompatible element evidence from the Partridge River intrusion, Duluth Complex, Minnesota, USA

Geochimica

Pergamon

et Cosmochimica

Acta, Vol. 60, No. 24, pp. 4997-501 I, 1996 Copyright 0 1996Elsevier Science Ltd Printed in the USA. All rights reserved 0016.7037196$15.00 + .OO

PI1 SOO16-7037(96)00294-3

Magma dynamics at the base of an evolving mafic magma chamber: Incompatible element evidence from the Partridge River intrusion, Duluth Complex, Minnesota, USA CHRISTOPHERI. CHALOKWU, ’* ALEXH A. ARISKIN,* and EVGENY V. KOFTEV -DVORNIKOV’ ‘Geology Department, Auburn University, Auburn, Alabama 36849, USA 2Vemadsky Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences, Kosygin 19, Moscow 117975, Russia 3Geological Department, Moscow State University, Moscow 119899, Russia (Received Junuary 10, 1996; accepted in

revisedform Augusr 19, 1996)

Abstract-A characteristic feature of the Partridge River intrusion of the Keweenawan Duluth Complex is the approximately fivefold to ninefold increase in the concentrations of incompatible elements in the lower zone compared with cumulates stratigraphically higher. The concentrations of incompatible elements decrease from the lower zone upward to steady state values, which is ascribed to variations in the proportions of trapped liquid rather than variable degrees of fractional crystallization of a single parental magma. The calculated average composition of trapped liquid using our algorithm is similar to typical Keweenawan low-alumina, high Ti-P basalts associated with the Duluth Complex but is different from the leading edge ferrodioritic liquid quenched in the chilled margin of the intrusion. This difference suggests that the chilled margin does not represent the original (parental) magma composition from which the whole intrusion solidified, and that the enrichment of incompatible elements may be related to the local flotation of magmatic suspensions. To test the latter hypothesis numerically, we have used heat-mass transfer models, assuming a sheet-like magma chamber, to calculate the parameters of the model that best reproduce the observed distribution of incompatible elements in a mush zone at the base of the Partridge River intrusion. The results indicate that a mush zone enriched in the incompatible elements is produced if the velocity of movement of the lower solidification front into the magma body was less than the floating velocity of the bulk crystal mush. The dynamic parameters that best reproduce the observed distribution of incompatible elements include a magma emplacement pressure of 2 kbar, critical crystallinities of SO-68% in the mush zone from which the liquid is being expelled, and an emplacement temperature of - 1160°C for the initial magma. 1. INTRODUCTION

upon this idea, Henderson ( 1975) described an efficiency factor for fractional crystallization and its effect on the rate of change of trace-element abundances during Rayleigh crystallization. Henderson ( 1975 ) showed that the distribution of an incompatible element between adjacent cumulate samples in a stratigraphic section of an intrusion reflects both the relative proportion and composition of trapped liquid. Consequently, on two-element variation diagrams, the incompatible elements can be expected to range from zero concentration (i.e., no trapped liquid) to concentrations reflecting the maximum amount of trapped liquid. Troctolitic and gabbroic rocks from the Partridge River intrusion of the Keweenawan Duluth Complex show these features very well (Chalokwu and Grant, 1990; Chalokwu et al., 1993). However, the rate of increase in the abundances of the incompatible elements with depth in the intrusion exceeds the rate of increase predicted on theoretical grounds for an intrusion formed by fractional crystallization of a single parental magma. In this paper, we use computer simulations to describe the composition of trapped liquid, crystallization temperatures, and the crystallinity of the initial (parental) magma to rocks from drill core BA-4 through the Partridge River intrusion. These data are then adjusted iteratively, using heat-mass transfer equations, to simulate the distribution of incompatible elements in core BA-4. The results enable us to constrain the dynamic parameters of the process responsible for the

The major-element composition of a cumulate is not the same as that of the initial (parental) magma because cumulate plutonic rocks do not represent original liquid compositions but instead are mechanical mixtures of fractionated liquidus crystals plus solidified interstitial liquid. Although severely criticized in recent years as being too restrictive and ineffective (e.g., McBimey and Hunter, 1994)) the cumulate paradigm as expounded by Wager and coworkers (e.g., Wager et al., 1960; Wager and Brown, 1968) provides a theoretical basis for using excluded (incompatible) elements to deduce magmatic parentage for layered igneous complexes (e.g., Cawthom, 1983; Grant and Chalokwu, 1992). A principal failing of models that are based on the inversion of cumulate trace element compositions to liquids is that the Rayleigh fractionation law (Greenland, 1970)) which governs trace-element behavior during closed-system magma crystallization, does not always apply. In their classic studies of the Skaergaard intrusion, Wager and Deer ( 1939) and Wager and Brown (1968) showed that P in the Skaergaard cumulates resides mostly in the interstitial liquid, and that the concentration of this element increases with increasing degree of fractionation. Building

+ Presenr uddresst School of Arts and Sciences, Benedict College, Columbia, SC 29204, USA. 4997

4998

C. I. Chalokwu et al.

enrichment of incompatible elements in the lowermost 200 m zone of the Partridge River intrusion.

This study is based on an 8 IO-m-long drill core (BA-4) from the Dunka Road deposit of the Duluth Complex (Fig. 1) The core intersected gabbros, troctolites, anorthosite, and rare peridotite before passing into the footwall Virginia Formation metasediments (Fiebor, 1994; Chalokwu et al., 1995 ) The igneous rocks in core BA-4 are composed of cumulus plagioclase and olivine, which form a framework for the intercumulus components now crystallized as plagioclase, olivine, pyroxene, and Fe-Ti oxides. The plagioclase is both normally and reversely zoned, with cores of An49 to AnT4 that are mantled by rims of And8 to Ane9. The olivine is unzoned, with compositions ranging from FOBSto Fo6*. The sulfide textures vary considerably and include: ( 1) eutectic-like intergrowths between sulfides, silicates, and Fe-Ti oxides suggesting coprecipitation; and (2) globular sulfides adjacent to Fe-Ti oxides suggesting sulfide-Fe-Ti oxide immiscibility (Pasteris, 1985; Fiebor, 1994). The abundances of incompatible elements (e.g., Zr and

2. PETROLOGIC AND GEOCHEMICAL SUMMARY OF THE PARTRIDGE RIVER INTRUSION The Partridge River intrusion (e.g., Chalokwu and Grant, 1990) is one of several troctolitic and gabbroic intrusions on the northwestern margin of the Duluth Complex that contains sub-economic Cu-Fe-Ni sulfides and noneconomic platinumgroup element mineralization (e.g., Ripley, 1990; Mogessie et al., 199 1). Accounts of the petrology of the Partridge River intrusion have been presented by Chalokwu and Grant ( 1990) and Grant and Chalokwu ( 1992) and references therein. Boundary conditions for the intrusion include emplacement of a low-alumina olivine tholeiite magma at pressures of -23 kbar (Simmons et al., 1974)) and oxygen fugacities varying between the quartz-fayalite-magnetite (QFM) and wiistitemagnetite (WM) buffers (Pasteris, 1985).

r

Depth (m)

Zone IV

0 1 2 3

Anorthosite

Gabbronorite

6 7

ZokieIII

1:;;;

a 9 10

;I

Olivine Gabbro Troctolite

11 12 13 14 15 16

Peridotite Virginia Formation

17

ia 19

f-33

Zone I

FIG. 1. Summary megascopic log of drill core BA-4 based on changes in grain size and rock density, and do 1994). Zones I-IV are not laterally continuous through Consequently, we use the terms upper zone and lower m, respectively.

showing rock types and positions of samples. Zones I-IV are. not represent compositionally distinct magma batches (Fiebor, the Partridge River Intrusion and are of only local significance. zone to describe rocks from -0 to 400 m and -404 to 800

4999

Petrogenesis of the Duluth Complex, Minnesota, USA A

1.0-

A

A

0.8-

c

5

A

0.6-

A

m

A

A A

0.8-

A

0.6-

ap

0.4

-

Lower Zone MhM Upper Zone @***a

8 . .

P 3 0’.

0.2-

’ ??*

2

?? r

0

-

+

0.0

0.4

50

.

:. .

0.2-

Lower Zone Upper Zone

**a** aMM

: ’ 0’.

m

A

A : . .

hr,=770

A

A A

A

Thickness

A

A

AA

‘6 rc

2

ho=770

A

0 <

1.0-

Thickness

. ??

:t .

?? .

‘. .

1

I 150

l@Zl Zr,

ppm

0.0

I 0.0

1.0

ma

I

r 2.0

. r

I

.

I

3.0

TiOz,

, 4.0

wt.%

FIG. 2. Variations of Zr and Ti in whole-rocks with dimensionless height in core BA-4.

Ti) in core BA-4 are highest at the base of the core and decrease upward to steady state values in the upper zone (Fig. 2). This behavior corresponds to a gradation from a chill zone through an orthocumulate to a mesocumulate region, as has also been recognized from drill core DDH-221 from the Babbitt area where the chilled margin of the intrusion is preserved (Chalokwu and Grant, 1987, 1990; Grant and Chalokwu, 1992). The incompatible elements in core BA-4 correlate positively with each other (Fig. 3), with intercepts that are either indistinguishable from zero or only slightly different from zero (Fiebor, 1994). In the case of the Ti-Ba correlation (Fig. 3), the positive intercept for Ba indicates departure from ideal incompatible behavior, implying that minor amount of Ba is present in the cumulus crystals, most likely in the cumulus plagioclase. The most striking feature of the incompatible elements is the near uniformity of their ratios in light of large variations in absolute abundances (Fiebor, 1994), as also recognized by Grant and Chalokwu (1992) for core DDH-22 1, -30 km from core BA-4. This characteristic indicates that the incompatible elements (e.g., Zr, P, Y) are present in fixed ratios in the trapped liquid, and that the cumulates have been produced from a single-source magma pulse instead of multiple batches from different sources. The uniformity of incompatible element ratios with depth is closely matched by FeONgO and CaO/A1203 ratios (Fig. 4). This led us to conclude that large scale chemical fractionation did not occur during crystallization of the Partridge River intrusion magma, and that in situ crystallization of the magma followed by minor sorting and redistribution of intratelluric (suspended) crystals were the major processes responsible for the observed major- and trace-element variations (Chalokwu et al., 1993). 3. GEOCHEMICAL THERMOMETRY OF THE PARTRIDGE RIVER INTRUSION MODEL MAGMA AND MOLTEN ROCKS

The technique of geochemical thermometry is applied to inverse problems for the purpose of extracting thermodynamic information recorded in whole-rock chemical compo-

sitions, such as the formation conditions of igneous rock (Frenkel et al., 1988a, 1989). The technique involves computer modeling of the course of equilibrium (closed-system) crystallization of numerically molten rocks, which probably passed through a stage in their cooling history when the primary cumulative mineral assemblages were in equilibrium with a magmatic liquid. Given that assumption, a comparison of the calculated liquid lines of descent should enable one to define T-X cotectic lines that are maximally close to the primary equilibrium, and thereby specify the thermodynamic parameters attendant during magma crystallization. This approach has been successfully tested and applied to differentiated dolerite sills from the Siberian Platform (Barmina et al., 1989a), and to hypabyssal rocks from Eastern Kamchatka (Barrnina et al., 1989b). The Partridge River intrusion is an ideal natural object to apply the geochemical thermometry technique because of the intrusion’s cumulate nature, widely varying amounts of trapped liquid, and the absence of any clear record of in situ magma fractionation (Chalokwu and Grant, 1990), which allows us to assume the same emplacement temperature and equilibrium trapped liquid composition for all of the rocks. To estimate the most probable crystallization temperatures and magma composition at the initial stage of solidification of the Partridge River intrusion, we used the geochemical thermometry technique to simulate the equilibrium crystallization of melts corresponding to the Partridge River intrusive rocks and model parental magma using the COMAGMAT petrological program package developed at the Vemadsky Institute, Moscow, Russia (Ariskin et al., 1993). The COMAGMAT software is a series of linked programs designed to simulate phase equilibria in mafic magmas, including calculation of the effects of equilibrium and fractional crystallization at a given pressure and oxygen fugacity. The programs are based on a set of empirically calibrated expressions that describe mineral-melt equilibria for twelve major- and twenty trace-elements. They can also be used to calculate high-pressure (up to 12-15 kbar) isobaric and dry to water undersaturated decompression crystallization liquid lines of descent, or model in situ differentiation for layered intru-

C. I. Chalokwu et al. 160

0.3 -

125 1

3

-I

2

0.2-

0.1 -

: A

-a

0.0 0.0

?? ??

&A

I 1.0

I 2.0

I 3.0

1 4.0

TiOz, wt.%

250 1 ??

200 3

0

1

E

i

E 150 -

0 “. 0

s

l00-

!

0

0 ??

2; A0 ?A

50-

0

.@ #A

I

0.0

FIG. 3.

1

1.0

I

2.0

1

1

3.0

4.0

Ti02,

wt.%

Variations of Zr, Ba, PZ05, and

V

01

0.0

1

1.0

I

2.0

1

Ti&, .

I

w;.;

against TiOz for the upper and lower zone rocks from core BA-4.

sions. Recent comparisons of the COMAGMAT model with other petrological modeling packages (e.g., the MELTS program of Ghiorso and Sack, 1995) and experimental data obtained at 1 atmosphere and 4 kbar by Yang et al, (1996), indicate that the COMAGMAT program best reproduces plagioclase-olivine and plagioclase-olivine-augite crystallization proportions in modeled basaltic systems. The mechanism by which the COMAGMAT program can be used to calculate a parental magma for a group of cumulates is based on the premise that a cumulate consists of cumulus crystals plus trapped parent magma. If a cumulate is treated as a liquid, COMAGMAT will first crystallize all of the cumulus crystals before crystallizing the trapped melt, and the point where the cumulus crystals have been removed and the trapped melt begins to crystallize is not known. However, if a number of rocks representing different amounts and ratios of cumulus crystals with the same trapped melt are used, the various crystallization curves should intersect or converge at the temperature and composition of

trapped melt. A detailed description of the theoretical and thermodynamic basis for the COMAGMAT-based computer simulations was presented by Frenkel et al. ( 1988a, 1989). The results of extensive tests, applying COMAGMAT to basaltic liquids, was reported by Ariskin and Barmina (1990) and Ariskin et al. (1987, 1988, 1990). Below we present the results of computer simulations for a model parental magma to gabbroic and troctolitic rocks in core BA4. The model parental magma (Table 1) was estimated by geochemical summation of fifty bulk cumulate compositions weighted according to the average density of the four zones into which the drill core has been subdivided (Fiebor, 1994). Results of the simulations show that at 2 kbar pressure and an fo, slightly more reducing than the iron-wiistite buffer, the model parental magma for core BA-4 crystallized plagioclase first at -1253°C and was followed almost immediately by olivine at 1247”C, with orthopyroxene and magnetite appearing simultaneously at -1160°C. This is consistent with petrographic observations, which indicate that plagioclase and

5001

Petrogenesis of the Duluth Complex, Minnesota, USA Sample

5l

-

0.6

r.8

0.4

0.6

.&

32

38

40

44

40

4

52

8

12

16

20

24

Wt.%

A FeO/MgO f 0.6

0.6

Wt.%

Wt.

ratios

FIG. 4. Variations in selected major-element concentrations and ratios as a function of relative height in core BA4 through the Partridge River intrusion. Tick marks and numbers to the right indicate relative stratigraphic position of samples used in numerical simulation described below.

olivine are the cumulus minerals in the intrusion (Chalokwu and Grant, 1990; Fiebor, 1994). The trajectories of equilibrium crystallization for the model magma and those for melts corresponding to selected cumulates are shown in Fig. 5. The liquid lines of descent (e.g., T-Na*O) converge at two temperatures, one at 1240 2 10°C and the other at 1160 2 10°C. Chalokwu et al. ( 1993) obtained an upper intersection temperature of 1260 t 10°C and a lower intersection temperature of 1150 +- 10°C for drill core DDH-221 model magma and cumulate melts and interpreted the lower value as the temperature of emplacement of the Partridge River intrusion. The crystallization trajectories for core BA-4 are similar to those described by Chalokwu et al. ( 1993 ) for core DDH221 except for TiO*. The lines of descent for TiOz (Fig. 5) do not form a tight cluster similar to that calculated for core DDH-221, suggesting different arrival times on the liquidus for titanomagnetite and the influence of sulfides (Chalokwu et al., 1993). Based on the temperatures of convergence of the major- and trace-element liquid lines of descent for the putative parent magma and cumulate melts for core BA-4, we have estimated the average composition of the trapped

liquid in equilibrium with the cumulus crystals using the low intersection temperature of 1160 -C 10°C (Table 2). The calculated average trapped liquid for core BA-4 (Table 3) is similar to the trapped liquid for core DDH-221 (Chalokwu et al., 1993), even though both drill cores are from different parts of the intrusion. The estimated trapped liquid composition resembles typical Keweenawan low-alumina, high-TiP basalts from the North Shore Volcanic Group (see Table 3)) as also observed by Chalokwu et al. ( 1993). The average proportion of cumulus phases and trapped liquid (i.e., critical crystallinity) can be estimated based on the assumption that every calculated equilibrium temperature has a corresponding weight proportion of trapped liquid to cumulus crystals during in situ magma crystallization (Frenkel et al., 1989). Using the calculated average emplacement temperature of 116O”C, the average proportion of cumulus crystals to trapped liquid for the initial magma was estimated to be 70-30, with uncertainties of 3-6 wt% based on the precision of t 10°C for mineral-melt geothermometers used in the COMAGMAT programs (Ariskin et al., 1987, 1993). The exceptions are samples from the basal chill zone of

5002

C. I. Chalokwu et al. Table 1. Camposftions of selected cumulates from core EA-4 and model initii magma used in computer simulation

8

21

29

34

Depth (m)

243.8

566.1

870.6

715.3

751.94

SiO2

45.94

48.52

45.85

46.69

46.48

47.03

TiO,

0.57

0.79

1.37

0.74

1.70

1.07

AP,

17.76

10.89

18.98

19.91

18.23

19.49

Fe0

11.72

9.78

11.45

9.99

11.08

10.46

MnO

0.16

0.14

0.16

0.12

0.15

0.14

MgC

10.95

7.47

10.55

8.03

8.29

9.19

CaO

8.67

9.93

8.82

9.32

9.58

9.51

NG’

2.46

2.66

2.47

2.20

2.53

2.52

KC

0.22

0.28

0.36

0.84

0.52

0.34

p*4

0.03

0.06

0.12

0.09

0.23

0.11

FeOiMgO

1.07

1.31

1.09

1.24

1.34

1.14

CaO/A~O~

0.49

0.52

0.52

0.47

0.52

0.49

Be

36

97

144

147

197

106

Cr

129

229

269

98

308

227

Ni

332

149

336

1383

912

335

Rb

7

10

10

18

a

11

Sr

285

340

238

300

86

313

V

77

117

130

78

314

99

Zr

29

47

89

52

75

49

Sample No.

Model

39

Magma -

Model magma is summed bulk compositionof 50 samples weighted according to the volume of the four zones in core BA-4; all compositbns are water free, wt. %. Trace element concentratii are h ppm.

the intrusion for which the geochemical thermometry results indicate -80% melt and -20% crystals, with the latter interpreted as the amount of intratelluric crystals captured by the lower crystallization front. Note that from simple mass balance, one can expect only a fourfold increase in incompatible elements (D = 0) across the basal zone if the mode of identical trapped liquid varied from 80-20% instead of the approximately fivefold to ninefold increase observed. We consider this an indication that the basal rocks of the Partridge River intrusion are mixtures of an initial magmatic melt plus intratelluric crystals, and that rocks higher up in the intrusion are composed of cumulus crystals plus relatively low amounts (-lo-30%) of trapped liquid of uniform composition. Below we test this hypothesis using the INTRUSION subroutine of COMAGMAT, which was developed to simulate in situ differentiation processes in sheet-like magma bodies (Frenkel et al., 1989; Ariskin et al., 1993). 4. DYNAMICS OF IN SITU MAGMA CRYSTALLIZATION Perhaps the most important contribution to the understanding of magma chamber processes in recent years was the

recognition of the importance of convective styles which are responsible for in situ magma differentiation, and which ultimately determine both the textural and geochemical features of intrusive rocks. Since the pioneering work by Bartlett ( 1969), petrologists have focused largely on the Rayleigh number as the main determinant of the efficiency of thermal convection in homogeneous magmas. Within the last decade, it has been realized that crystal nucleation and temperature distribution within a mush zone close to the upper solidification front can play a significant role in driving convection (Frenkel et al., 1988b; Morse, 1988; Marsh, 1988, 1989, 1996; Worster et al., 1990; Mangan and Marsh, 1992; Simakin et al., 1994; Frenkel, 1995; Jaupart and Tait, 1995; Spera et al., 1995). However, petrologic interpretations resulting from these studies differ considerably. For example, Marsh (1988, 1989) concluded that in magma chambers cooled predominantly from above, crystallization near the roof will prevent the destabilization of the magma body from driving vigorous convection. This conclusion was based on the assumption that the fluid part of the magma (isolated from the roof by a transient layer) is always isothermal at the temperature of the liquidus, which makes the effective temperature difference too small to drive convec-

5003

Petrogenesis of the Duluth Complex, Minnesota, USA

1100

’

L 2

0

1100

I

’

4

NaaO

TiOa

1400

I

1350 u 0

EY

1300

1250

1250

1200

1200

1150

1150

8

-

1100 4

12

6

CaO

u 0

?

&To

1400

1400

1350

1350

1300

1300

1250

1250

1200

1200

1150

1160

2

1100

1100 6

12

16

20

AW3 FIG.

4

8

16

20

&

5. Major-element liquid lines of descent during equilibrium crystallization simulated for core BA-4 molten

rocks and model parental magma using the COMAGMAT program (Ariskin et al., 1993).

tion in the magma chamber as a whole. Marsh ( 1988,1989) also pointed out that such a dynamic style does not allow crystals to reach the floor of the magma chamber (i.e., the crystals cannot escape capture) so that differentiation cannot occur in the interior. The opposite conclusion was arrived at by Worster et al. (1990) who concluded that vigorous convection, significant internal cooling, and differentiation can take place in a magma chamber which is cooled by losing heat by conduction to the overlying country rocks even if there is no initial superheat. 4.1. The Sedimentation

Model

Frenkel and coworkers presented the first attempt to solve the above problem quantitatively (Frenkel and Yaroshevsky, 1976, 1978; Koptev-Dvomikov et al., 1979). They devel-

oped a model integrating phase equilibria calculations with heat-mass balance within sublayers of a tabular magma body into a single program unit that allowed them to numerically model the effect of crystal settling on the thermal history and differentiation of mafic magmas. The most important variables in the simulation include bulk magma composition, crystal settling velocities, and the percent of intratelluric phases with thermophysical parameters taken from the literature. The above authors used a simplified phase diagram similar to the Fo-An-Di system to calculate the dynamical parameters. It was shown that crystal settling is a much more powerful mechanism of heat transport than conduction, because by crystal settling temperature is equalized faster in the interior of the chamber than at the roof. The final distribution of minerals in an intrusion depends largely upon the crystalliza-

C. I. Chalokwu et al.

5004

Table2. Caqxxbns

of trepped liquiddefined near 1160% for core BA4 rocks and model magma by means of Geochemical Thermornetry

Sample

Model

Average

Magma

(SD.)

1160

1159.80 (0.30)

48.83

47.60

47.74 (1.26)

21

29

34

39

T”C

1160

1160

1160

1160

SiO*

47.57

46.98

50.20

NO.

TiO,

2.69

2.36

3.90

1.97

3.78

3.52

2.94 (0.77)

ALO,

13.46

13.49

13.95

16.22

14.29

14.54

14.29 (1 .Ol)

Fe0

16.47

16.49

14.75

14.01

15.12

15.11

15.37 (0.98)

MnO

0.24

0.24

0.22

0.18

0.21

0.22

0.22 (0.02)

5.67

5.82

8.03

5.37

5.95

5.77

5.81 (0.23)

10.67

10.52

10.16

7.72

9.67

9.21

9.75 (1.07)

Na&’

2.43

2.65

2.38

2.48

2.55

2.45 (0.12)

W

0.89

I .03

1.70

1.16

1.12

1.16 (0.28)

P*D5

0.19

0.34

0.24

0.51

0.36

0.26 (0.13)

CaO

Cr

261.5

312.8

456.9

172.3

503.3

442.6

341.36 (122.78)

Ni

59.38

87.63

362.8

258.6’

76.08

65.1 (6.5)

Sr

197.2

183.7

178.3 (14.8)

308.1

314.4 (36.1)

286.7

54.66’ 672.2’

Standard deviation in parentheses (I u). = Not involved in calculating average. ??

tion sequence and the Stokesian settling velocity used for each crystallizing phase (Frenkel and Yaroshevsky, 1978). This also was the first model to reproduce the progressive enrichment of intratelluric mineral grains from the bottom to the top of intrusions (i.e., the well-known S-shaped modal profiles widely observed in nature; e.g., see Fig. 1 of Mangan and Marsh, 1992). A detailed analysis of the petrological consequences of the crystal sedimentation model was made by Koptev-Dvornikov et al. (1979) who compared the structure of the modeled and naturally observed differentiated sills from the Siberian Platform. Many features of the modeled objects were found to correspond to the natural observations, e.g., the predominance of the cumulative phases, the order of appearance of cumulative phases, and the structure of the basal zone. However, the extent of differentiation of the modeled bodies was much higher (even at low crystal settling velocities) than that observed in the Siberian sills. In addition, the crystal sedimentation model implies that the boundaries

between cumulative crystal assemblages are sharp compared to the gradual transition that is typical of natural objects. The latter observation led petrologists to invoke a mechanism which destabilizes the interior of magma chambers by destroying the whole or part of the thermal boundary layer and thus provide a smooth cumulative mineral distribution curves in the accumulation zone (e.g., Worster et al., 1990). A vigorous convection was logically assumed to be the major process responsible for the destabilization. 4.2. The Convective-Cumulative

Model

As a consequence of the crystal sedimentation model, Frenkel et al. ( 1989) proposed the convective-cumulative model based on the same heat-mass transfer algorithm but including efficient mixing within the whole magma body. Although the physical reasons driving vigorous convection in magma chambers (Frenkel et al., 1988b) were described 10 years after the convective-cumulative model was initially

5005

Petrogenesis of the Duluth Complex, Minnesota, USA Table 3. wn T-P compositions

of cakulatsd trapped liquidconpositionfor core EA.4 with Kswsenawan low-alumina,high

1 SiO,

47.74(1.26)

2 48.26(0.43)

3

4

5

6

49.44

50.68

47.34

47.70

TiO,

2.94(0.77)

2.94(0.23)

2.21

3.29

2.31

2.66

AR

14.29(1 .Ol)

15.01(0.34)

15.08

15.62

15.55

16.08

Fe0

15.37(0.96)

15.84(0.53)

12.53

13.72

14.96

13.70

Ml0

0.22(0.02)

0.20(0.20)

0.18

0.19

0.21

0.22

MgO

5.81(0.23)

5.19(0.09)

5.99

4.37

6.85

6.18

CaO

9.75(1.07)

8.21(0.40)

9.01

6.36

7.59

6.87

N+=’

2.45(0.12)

2.63(0.24)

3.83

4.18

3.17

3.10

K@

1.16(0.28)

1.32(0.20)

1.39

1.16

1.64

1.28

0.34

0.41

0.18

0.24

P*C,

0.28(0.13)

0.40(0.07)

Notes: Major elements in wt.% anhydrous basis. 1, Average trapped liquidfor core BA-4 given by the mean of all model liquids(Table 2) at - 1160 “C; 2, Average trapped liquidfor core DDH-221 at - 1150 OC(CHALOKWU et al., 1993). Values in parentheses are standard errors (1 a); 3,4, basal& from the North Shore Volcanic Group (GREEN, 1972; samples LW-10 and GP44, respectively); 5.6. Keweenawan Pottage Lake lava (WILBAND and WASUWANICH. 1980; samples WOT87 and WC39C, respectively).

proposed (Frenkel and Yaroshevsky, 1978), we emphasize that the model was based on over 20 years of field, petrographic, geochemical, and computer modeling studies of differentiated dolerite sills from Siberia. Consequently, the convective-cumulative model is different from other models which are based solely on theoretical analytical solutions. The convective-cumulative model is based on the assumption that the major force driving vigorous convection is density difference between the more crystallized upper mush zone and the main magma body. This difference results in the dropping of dense crystals from the roof and a complimentary rise of magma toward the roof (Frenkel et al., 198813). This implies an efficient convective process, which is assumed not to prevent eventual settling of suspended crystals. Thus, the solid phases formed near the upper boundary of the chamber are postulated to drop with entrained liquid as plumes through the convecting magma body to form a series of cumulates at the base, with the dynamics of movement of the accumulation and solidification fronts shown in Fig. 6. A rigorous analysis of convection processes requires two dimensional models linking convection with crystallization. Only recently has there been attempts to simulate sidewall convection with crystallization in a simple binary system (Spera et al., 1995 ) . In our computer models, we have greatly simplified the simulation of vigorous convection by replacing the sequence of sublayers between the upper crystallization and accumulation fronts with a single layer which is assumed to be uniform in temperature and composition (as a function of time) up to the point where the magma chamber becomes filled with cumulates (Fig. 6). From the generalized scheme in Fig. 6, the upper crystallization front does not advance into the magma during the main stage of differentiation. Interestingly, this is not a feature of the convective-cumulative pro-

cess but a numerically obtained response of the crystallizing system to crystal settling. In other words, crystal settling competes with capture by the upper solidification front due to a decoupling of crystallization from the dynamics of the front (Frenkel et al., 1989; Frenkel, 1995). It is also important to note that asymmetry of magma chamber (and the linked temperature field) is the principal difference between magma chamber dynamics assuming the convective-cumulative process and models which do not take into account the importance of crystal settling in heat-mass transport (e.g., Marsh, 1988, 1989; Worster et al., 1990; Mangan and Marsh, 1992). This observation is also true for recent attempts to link the crystal sedimentation process with the kinetics of nucleation in the upper boundary layer (e.g., Simakin et al., 1994). The convective-cumulative model involves a set of simplifications that ignore the structure of vigorous convection and implies an infinite mixing velocity for crystals formed near the roof with magma (suspended crystals + melt) in the interior of the chamber. Although considered a first approximation, the convective-cumulative model nonetheless reproduced the principal mineralogical and chemical features (e.g., S-shaped chemical profiles) of differentiated Siberian sills compared to results based on the crystal sedimentation model without convection ( Koptev-Dvomikov et al., 1979).

5. INTRUSION

(DYNAMIC) SUBROUTINE OF COMAGMAT

Perhaps the strongest indication of the potential of the convective-cumulative style of in situ magma differentiation is whether the observed major- and trace-element distributions in tabular intrusions can be quantitatively reproduced. For this purpose, a subroutine of COMAGMAT program

5006

C. I. Chalokwu et al.

Dynamics

of In

Situ

Magma

Differentiation

chamber

Front solidificr

t t+At 1

-Ol+Liq,

2 -Ol+Pl+Liq,

Tii

SeCtiOII

at

of

tion

t+At

3 -Ol+Pl+Px+Liq

FIG. 6. Dynamics of in situ magma crystallization based on the convective-cumulative model of Frenkel et al. ( 1989). High efficiency of convection is assumed to maintain uniform temperature and composition in the magma body up to the point where the chamber is choked with crystals and differentiation stops.

(called INTRUSION or DYNAM) was developed (Ariskin et al., 1993). The interaction between the INTRUSION sub-

routine and the phase equilibria model is based on the relationship between an increment of crystallization and the time needed to cool and crystallize the melt to a specific crystallinity. This link includes the values of heat flows through the upper and lower contacts of the intrusion chamber, the amounts of suspended crystals in the magma, the specific heat of the melt, the latent heat of melting for endmember components, crystal settling velocities for olivine, plagioclase, pyroxenes, and magnetite, and other thermophysical parameters. A detailed description of the semi-empirical constraints approximating the convective-cumulative process was presented by Frenkel et al. (1988b) and Ariskin et al. (1993). Numerical simulation using the INTRUSION subroutine is an example of forward modeling in which the response of a modeled system to a set of assumed or measured initial parameters is calculated and the results compared with the natural data. Such a model may be used in an iterative way by modifying the input parameters until a satisfactory fit to the natural data is obtained. The INTRUSION subroutine of COMAGMAT has been applied to the major- and traceelement geochemistry of three differentiated dolerite sills from the Siberian Platform (Frenkel et al., 1988b, 1989) in order to find values of the dynamic parameters, such as crystal settling velocities and the porosity of crystal-bonded (cumulus) and crystal-nonbonded (porphyritic) aggregates, that best reproduce the geochemical features observed. As a result of forty to fifty calculations, the INTRUSION subroutine successfully reproduced the observed petrochemical, geochemical, and mineralogical characteristics of the Kuzmovka (thickness h = 85 m), Vavukan (h = 100 m), and Vilyui (h = 160 m) intrusions from Siberia (Frenkel et al., 1989). Given the large number of natural observations (particularly major- and trace-element compositions), and the relatively small number of variable parameters, the solution that best explains all the data is by no means over-

determined. The similarity of calculated data to the natural suites led Frenkel et al. ( 1989) to conclude that the convective-cumulative model represents a plausible physical mechanism that is responsible for the differentiation of sheet-like magma bodies - lOO- 1000 m thick. 6. FORWARD MODELING OF IN SITU DIFFERENTIATION IN THE PARTRIDGE RIVER INTRUSION

A potential problem in applying the convective-cumulative algorithm to the lower zone of the Partridge River intrusion is the high primary crystallinity (65-70%) obtained using the geochemical thermometry technique (see also Chalokwu et al., 1993, who obtained a critical crystallinity of 68%). Jones (1984) described the Logan quartz tholeiite sills in Minnesota as sub-volcanic examples of Keweenawan magmas emplaced with 50-60% of entrained plagioclase. The calculated crystallinities seem at odds with conventional wisdom which suggests that crystal bridging in natural magmas begins at -5O-55% crystals (e.g., Marsh, 1981, 1988; Bergantz, 1990). Consequently, one would expect that high crystallinity would result in a high dynamical viscosity of the magma system, thereby precluding vigorous convection in the chamber. Note that for the Siberian sills described above, Frenkel et al. ( 1989) calculated primary magma crystallinities of 2.1% for Vavukan and 7.8% for Vilyui intrusions. However, there is a feature of the convective-cumulative model (described below) which allows us to apply the model to the formation of the lower parts of intrusions, even if there was no vigorous convection. If we assume a small increment of crystallization and efficient mixing of newly formed crystals with the main body of magma with -65% crystallinity, a suitably short time scale would exist over which temperature, trapped liquid, and cumulative crystal compositions will not change drastically (Frenkel et al., 1989; Frenkel, 1995). This feature allows us to study numerically the processes of crystal settling, sorting, and capture which occurred at the lower solidi-

Petrogenesis of the Duluth Complex, Minnesota, USA fication front. To elaborate upon this idea, we considered the following mass balance equations, which are a critical part of the INTRUSION subroutine of the COMAGMAT (Ariskin et al., 1993). 6.1. Mass Balance Constraints for Incompatible Element Distribution in the Partridge River Intrusion Based on simple mass balance, and assuming that the concentrations of incompatible elements in cumulate crystal assemblage is zero, the concentration of an incompatible element in a cumulate (R) can be described by the equation CR = f “CF,

(1)

where i is a major (Ti, K, P) or trace element, m is melt trapped in the cumulate, f ” is the mass fraction of trapped melt, and CF is the concentration of the element i in the trapped melt. The value off ” is defined by fm = 1 - xfcfm,

(2)

where f I”“”is the mass fraction of crystals of the mineral j in a mixture of cumulate minerals with trapped melt. According to the convective-cumulative model, the steady state fraction of the cumulate crystals may be calculated as f$”

=fl””

[l - (VjSIVSF)],

(3)

where f ;,, is the fraction of crystals of mineral j suspended (circulating) in the convecting magma body, VT is the absolute velocity (e.g., m/yr) of crystal settling or flotation, and VsF is the absolute rate of movement of the lower solidification front into the magma body (see Fig. 6). In accordance with the vertical coordinates for Figs. 2 and 6, the sign of the crystal settling velocity in Eqn. 3 must be negative, whereas the crystal flotation and V,, velocities are always >O. Therefore, when V,S < 0 (settling) and fy > 0, the fraction of cumulate crystals f f”” > fy > 0. At VJ > 0 (flotation), the use of Eqn. 3 has a physical restriction (i.e., f 7”’= 0 if Vj 2 VSF, in which case floating crystals would escape capture by the solidification front). From Eqns. l3 one can calculate the concentrations of incompatible elements in rocks as cp = (1 - Cf1”“[1 - (V;I/VSF)] ) cy.

(4)

Based on a quantitative solution of the mass balance, in which Ti is used as a proxy for the other incompatible elements, it appears that the increase in the abundance of incompatible elements near the base of the Partridge River intrusion (Fig. 2) may be due to a decrease in the total fraction of accumulated plagioclase and olivine crystals (Cf 7”‘) followed by their increase in the advancing solidification front. A comparison of the estimated average Ti02 content of trapped liquid (2.94 ? 0.77 wt%; Table 2) with TiO, concentrations in the lower zone rocks (maximum = 3.2 wt%; Fig. 1) suggests that the lowermost rocks represent mixtures of crystals plus magma. This interpretation is consistent with the absence of large scale magma fractionation within the intrusion chamber (e.g., the uniform incompatible trace-element ratios), which allows us to assume that Cr = constant, particularly in the lower zone.

5007

This also is consistent with the amounts (-65-70 wt%) of intratelluric phases in the initial magma of the Partridge River intrusion (Chalokwu et al., 1993). Assuming a closed-system magma chamber and singlestage emplacement for the Partridge River intrusion, we consider two mechanisms which could be responsible for the decrease of suspended crystals and the enrichment of incompatible elements in the lower zone. The first involves the pressing out of crystals from the lower zone during flow differentiation of a crystal-ladden magma (e.g., Bhattacharji, 1967; Barriere, 1976). This mechanism causes suspended crystals in a moving liquid to migrate to regions of minimum shear stress due to the Bagnold effect (Barriere, 1976). Flow differentiation of the lower zone of the Partridge River intrusion is supported by the chilled margin of the intrusion being an evolved ferrodioritic liquid (Chalokwu et al., 1993) from which crystals have been stripped to create a transition from essentially pure liquid to the crystal-liquid mixtures. The other mechanism for the enrichment of incompatible elements involves the flotation of plagioclase + olivine crystal assemblage from the bottom of the intrusion accompanied by compaction in the upper part of the chamber. Both mechanisms would result in an increase in the amount of trapped liquid in the lower horizon and a related increase in incompatible element contents in rocks near the bottom contact (see Fig. 6). However, the fluid dynamics and crystal flotation mechanisms are critically dependent upon the densities of suspended crystals and magmatic melt. In order to calculate densities, we assumed that the parental magma with an average composition given in Table 2 was emplaced at a temperature of 1160°C and a pressure of 2 kbar, and that the average compositions of suspended crystals of plagioclase and olivine were An, and Fo,, , respectively (Chalokwu and Grant, 1987, 1990). Liquid density at the above emplacement conditions was calculated using the method of Lange ( 1994), whereas the densities of plagioclase and olivine were calculated using parameters in the thermoseism geophysical database (Kuskov, 1995). The results indicate a magma density of 2.793 g/cm3 and densities of plagioclase and olivine of 2.651 and 3.452 g/cm3, respectively. Consequently, the density contrast between melt and plagioclase (0.142 g/cm3) supports the hypothesis for the flotation of crystals of plagioclase from the bottom of the magma chamber. Based on simple mass balance, we also calculated the mass proportion of plagioclase and olivine required for plagioclase + olivine glomerocrysts to float as a single phase with respect to the magmatic melt; the results indicate that for this to occur the mass fraction of plagioclase should be greater than 78%. However, the bulk density for plagioclase + olivine assemblage in a 2 to 1 cotectic proportion (2.871 g/cm3) is higher than the density of the coexisting melt (2.793 g/cm3), implying that plagioclase + olivine aggregates would not float if plagioclase is -70% of the mixture. The modeled percent plagioclase for the cotectic aggregate is similar to the value obtained by Chalokwu and Grant ( 1990) for trapped liquidfree rocks in drill core DDH-221. 6.2. Results of Forward Modeling Within the framework of the mass balance constraints (i.e., without consideration for other physical mechanisms

5008

C. I. Chalokwu et al.

which could be responsible for redistributing crystals), we test our hypothesis for the flotation of magmatic suspensions numerically using the INTRUSION subroutine of the COMAGMAT petrological programs (Ariskin et al., 1993). In general, upward compaction of magmatic suspensions can be simulated as a simple flotation of plagioclase + olivine crystal assemblage by setting the floating velocity for plagioclase equal to that of olivine. These calculations were performed assuming that the Partridge River intrusion is a sheetlike body -770 m-thick (with a bulk composition equivalent to the model magma in Table l), which was emplaced at 2 kbar pressure and oxygen fugacity conditions slightly more reducing than the iron-wttstite buffer. The latter assumption minimizes the probable effect of magnetite crystallization on the distribution of TiOz. The simulations begin with a preliminary calculation in which we assumed a system that is initially all liquid (degree of crystallization F = 0 at a temperature of 1253°C) followed by equilibrium crystallization with a crystal increment dF = 1%. The equilibrium crystallization proceeds up to a value of intratelluric phases Fin, = 65%. This restriction is based on the results of geochemical thermometry modeling (Chalokwu et al., 1993)) which indicate that plagioclase and olivine fractionated in a 2 to 1 proportion at this crystallinity. The dynamic part of the calculation starts with F = Fin, at an initial time t = 0, when all the equilibrium state information such as phase proportions and compositions are entered into the INTRUSION subroutine and repeated after each increment of crystallization. The thermophysical parameters for surrounding rocks used in the modeling include a density of 2.7 g/cm3, heat conduction of 0.006 Cal/cm* s * grad, and a heat capacity of 0.25 cal/g*grad. The thermophysical parameters for magma were calculated as a function of composition and temperature (Frenkel et al., 1988b, 1989). The assumed dynamic parameters include a temperature difference of 500°C between magma and surrounding rocks, a minimum cumulate porosity of 20 vol%, and duration of chilling t* = 24 h. Using the assumed duration of chilling, the model defines the thickness of the upper and lower chilled zones which results in a loss in the volume of the model magma system both in terms of the liquid and the solidified equilibrium phases. After correcting for the volume loss, the remaining melt is incrementally crystallized in terms of dF, and the phase equilibria at a new percent crystallinity are calculated. Each successive iteration through the INTRUSION subroutine begins with the determination of the heat and crystal mass fluxes as well as the time interval corresponding to the given dF. From this information, we can determine the phase compositions of the upper crystallization and lower accumulation zones and calculate their thicknesses (Ariskin et al., 1993 ) . If the bulk chemistry of the upper and lower zones are known, one can calculate the shift in the bulk model magma composition before the next increment of crystallization is calculated. The final results of the simulation (particularly the variations in the proportions of solid phases and trapped melt) are dependent upon the crystal settling velocities. The latter should be determined for each mineral and may be assumed to be constant or dependent upon the extent of crystallization (F) or time. In the calculations presented below, we simulated upward

compaction of crystals in the lower zone by setting the velocity of olivine equal to that of plagioclase. We also studied thirty combinations of VJ values for olivine and plagioclase, which resulted in changes in the ratio of VjlV,, in Eqn. 3 and variations in the values of CR (Eqn. 4). Figure 7 shows a comparison of the observed variations of TiOz in rocks from the lower 400 m of core BA-4 with variations calculated using the INTRUSION subroutine and assuming two different dynamic models (see below). In Model 1, we performed a series of calculations in which the flotation of suspended crystals with a constant velocity Vj > 0 was varied from 3-9 rn/yr. The calculated value of Vs, > 0 using the above thermophysical parameters is decreased from 22 to 4 mlyr during solidification. This leads to a moderate increase in the VslV,, ratio and a corresponding increase in f” and hence Ti02 in the solidified rocks (Fig. 7a). Note that the calculations for the lower half of the intrusion cover a small range of fractionation of the parental melt ( < 12%)) which results in a small increase in the TiOZ content of the liquid from 3.06-3.43 wt% (i.e., CF is approximately constant in Eqn. 4). The flotation process is quickly arrested due to the remaining magma layer, above the solidification front, achieving a prohibitively high critical crystallinity of 80% during the modeling. This increase in crystallinity is reflected in the abrupt decrease of TiOl from 4.0-1.5 wt% in the lower zone of the modeled section (Fig. 7a), owing to a decrease in trapped liquid abundance. We conclude that although the crystal flotation process can produce maximum enrichment of TiOz in rocks of the Partridge River intrusion, it is not able to reproduce the gradual upward decrease in TiO?, contents in the lower zone. Therefore, the upward decrease in TiOz contents is due to a decrease in the amount of liquid, which suggests that the value of Vf might be less than that of VsF (i.e., Vs could not be constant as assumed in Model 1). In Model 2, we assumed another dynamic situation involving the flotation of suspended crystals in which the floating velocity is slightly decreased during the modeling almost to the point where Vj = 0. We performed twenty calculations in which the floating velocity was varied. Figure 7b represents an optimal model which provides the best fit to the natural data. The results lead us to conclude that the redistribution of intratelluric phases can explain the observed variations in Ti02 and other incompatible elements. The assumed values of V,? for the plagioclase + olivine assemblage and the calculated values of Vs, are shown in Fig. 8 for the best fit model. We reiterate that V,, is strongly dependent upon the set of thermophysical parameters used, including the efficiency of heat loss from the magma body (Frenkel et al., 1988b; Ariskin et al., 1993). Therefore, the absolute values of the crystal settling velocities and the rate of movement of the lower solidification front are not so much important as the ratios of VjlV,, (see Eqns. 3 and 4). The calculated amount of trapped melt (f”) in the lowermost 20% of the intrusion vary from a value of 100-25 wt% for the best fit model (Fig. 8c), and, therefore, represents a normal gradation from a chill through an orthocumulate region to a mesocumulate. The dynamic simulation suggests that the cumulus/intercumulus structure of the lowermost zone of the Par-

Petrogenesis of the Duluth Complex, Minnesota, USA

. . . .

0.5

5009

0.5

A < J!

. .

0.4

L +L---I$iy, , .

.

2 .rl

a0 .

,

0.3

0.2

!J .rl

% $ p:

R Mode *****Natural

I -2

a* . \. .

2

?? e

B

.I

0

,:k7,

0.1

(

,

,

0.0

0.0

0.0

1.0

2.0

3.0

4.0

5.0

Ti02,

wt.%

0.0

2.0

1.0

3.0

4.0

5.0

TiOz,

wt.%

FIG. 7. Comparison of the natural and modeled distributions of TiOz in the lower zone of core BA-4. Models 1 and 2 correspond to two different dynamic situations described in the text.

tridge River intrusion formed during the first 20-40 years of the crystal flotation-accumulation process. The modeling also suggest that crystal redistribution in the entire magma body should be completed approximately 120- 130 years after the magma has achieved crystallinities of 75-80%.

Partridge River intrusion in order to understand the distribution of incompatible elements resulting from a specific dynamics of in situ magma crystallization. The dynamics include the existence of a crystal-liquid mush prior to emplacement, the absence of large scale magma fractionation, and the redistribution of suspended crystals during flow differentiation at the bottom of the intrusion. This pressing out process has been simulated numerically as a continuous flotatipn of plagioclase + olivine suspensions soon after emplacement of the intrusion. It was found, however, that crystal flotation with a constant velocity cannot explain the observed distribution of incompatible elements. Instead, the incompatible elements can be accounted for by crystal flotation in which the velocity of movement of the lower solidification front into the magma chamber was less than the bulk crystal mush floating velocity, followed by crystal settling. The results of this study also have implication for the thermal history of the magma body. In order to simulate the details of the TiOZ distribution in core BA-4, we assumed a

Based on these results, we suggest that during further cooling of the 770 m-thick magma body only high density phases such as magnetite or sulfides could contribute to the primary geochemical structure formed in the early stages of crystallization of the parental magma. The movement of these phases to the basal zone soon after the primary porosity was established for the rocks could account for the observed increase in the bulk Fe0 and the related increases in Ni and other

siderophile elements (Fiebor, 1994). 7. SUMMARY

In this study we have illustrated how the convective-cumulative model can be applied to the lower zone of the

A 01 A Pl

-

0.0

4.0

6.0

12.0

VSP,mh

16.0

20.0

-4.0

-2.0

0.0

2.0

4.0

6.0

VW VPI, m/v

6.0

J

.

0.0

0.0

Model-2

0.0

0.2

Trapped

0.4

liquid,

0.6

0.6

1.0

vol. fraction

FIG. 8. Variations in the velocities of the lower solidification front, crystals of olivine (01) and plagioclase (Pl), and trapped liquid abundance with dimensionless height (h/b) for the best-fit model (Model 2).

5010

C. I. Chalokwu et al.

temperature difference of 500°C between the magma body and the surrounding rocks, which is twice the value assumed for differentiated sills from the Siberian Platform (Frenkel et al., 1989). This may indicate that, unlike the Siberian Plaform sills, the Partridge River intrusion magma was emplaced into rocks that were already heated by Keweenawan volcanism produced during lithospheric extension above an asthenospheric thermal anomaly termed the Keweenaw hotspot (Hutchinson et al., 1990). We consider the results of the modeling as another evidence that many of the observed chemical features of the Partridge River intrusion are due to variations in the proportions of cumulus crystals and intercumulus liquid. This implies that the magma chamber was closed with respect to other magma reservoirs, and that additional emplacements of compositionally diverse magmas (i.e., recharge) are not necessary to explain quantitatively the observed distribution of incompatible elements in the intrusion. Acknowledgments-Partly supported by NSF grant EAR-88 17074 to Chalokwu. Additional financial support was provided by grants from the International Science Foundation and the Russian Foundation for basic research to Ariskin (grant 96-05-6423 1) and Koptev-Dvornikov (grant 96-05-65483). Parts of this work were carried out while Ariskin was a research visitor at Auburn University. We thank Clive Neal, S. A. Morse, and Roger Nielsen for thoughtful reviews. However, the authors retain full responsibility for all calculations and interpretations. Editorial

handling:

C. R. Neal

REFERENCES Ariskin A. A. and Barmina

Cl. S. (1990) Equilibria thermometry between plagioclases and basalt or andesite magmas. Geochem. Id 27, 129-134. Ariskin A. A., Barmina G. S., and Frenkel M. Ya. (1987) Computer simulation of basalt magma crystallization at a fixed oxygen fugacity. Geochem. Intl. 24, 92-100. Ariskin A. A., Barmina G. S., Frenkel M. Ya., and Yaroshevsky A. A. (1988) Simulating low-pressure tholeiite-magma fractional crystallization. Geochem. Intl. 25, 21-37. Ariskin A. A., Frenkel M. Ya., and Tsekhonya T. I. ( 1990) Highpressure fractional crystallization of tholeiitic magmas. Geochem. Intl. 27, 10-20. Ariskin A. A., Frenkel M. Ya., Barmina G. S., and Nielsen R. L. (1993) COMAGMAT: A Fortran program to model magma differentiation processes. Computers Geosci. 19, 1155- 1170. Barriere M. (1976) Flowage differentiation: Limitation of the “Bagnold effect” to narrow intrusions. Contrib. Mineral. Petrol. 55, 139-145. Barmina G. S., Ariskin A. A., Koptev-Dvomikov E. V., and Frenkel M. Ya. (1989a) Estimates of the primary compositions of cumulate-minerals in differentiated traps. Geochem. Intl. 26, 32-42. Barmina G. S., Ariskin A. A., and Frenkel M. Ya. (1989b) Petrochemical types and crystallization conditions of the Kronotsky Peninsula plagiodolerite (Eastern Kamchatka). Geochem. Intl. 26, 24-37. Bartlett R. W. ( 1969) Magma convection, temperature distribution, and differentiation. Amer. J. Sci. 267, 1067- 1082. Bergantz G. W. (1990) Melt fraction diagrams: The link between chemical and transport models. Rev. Mineral. 24,239-257. Bhattacharji S. (1967) Mechanics of flow differentiation in ultramafic and mafic sills. J. Geol. 75, lOl- 112. Cawthorn R. G. ( 1983) Magma addition and possible decoupling of major- and trace-element behavior in the Bushveld Complex, South Africa. Chem. Geol. 39, 335-345. Chalokwu C. I. and Grant N. K. (1987) Reequilibration of olivine

with trapped

liquid in the Duluth Complex,

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