Numerical modeling of fluid flow and oxygen isotope exchange in the Notch Peak contact-metamorphic aureole, Utah
Xiaojun Cui* Peter I. Nabelek Mian Liu Department of Geological Sciences, University of Missouri, Columbia, Missouri 65211, USA
ABSTRACT We investigated the macroscale fluid flow and oxygen isotope exchange in contact-metamorphic aureoles by using two-dimensional finite-element modeling. The model parameters are assigned according to geologic observations in the Notch Peak metamorphic aureole, Utah. The results show that fluid flow in contact aureoles depends strongly on time and space, unlike the commonly assumed uniform and unidirectional fluid flow in previous studies. In an aureole with homogeneous permeability, a simple convection cell develops in the inner aureole, causing d18O values to decrease in the inner aureole and increase in the upper outer aureole. However, when the horizontally layered permeability structure of the Notch Peak aureole is represented in the model, the resulting fluid flow is concentrated within high-permeability aquifers, and local convection cells develop near the contact within each aquifer. Subhorizontal down-temperature flow and up-temperature flow can coexist in the same aquifer. The up-temperature flow in the lower part of each aquifer mainly causes depletion of 18O in the inner aureole. Release of magmatic fluid significantly enhances the depletion of 18O in the inner aureole at early stages, although subhorizontal up-temperature flow at later stages tends to reduce the effects of the early-stage exchange. The isotopic features of the Notch Peak aureole are best explained by (1) infiltration of magmatic fluid having a d18O value of 8‰, (2) ;10% of the wall rocks involved in the oxygen isotope exchange with fluids, (3) no isotope exchange below 250 8C and during retrograde cooling, and (4) enhanced permeability in the inner aureole in addition to the lithologically layered permeability structure. Keywords: fluid-rock interactions, metamorphic aureoles, Notch Peak, numerical models, oxygen isotopes. INTRODUCTION Stable isotopes are useful tracers of fluid flow through rocks. Previous studies of reactive fluid flow during contact metamorphism were mostly based on one-dimensional (1D) continuum models of oxygen isotope transport in homogeneous porous rocks (e.g., Bickle and McKenzie, 1987; Baumgartner and Rumble, 1988; Lassey and Blattner, 1988; Bowman and Willett, 1991; Ferry and Dipple, 1992; Bowman *E-mail:
[email protected].
et al., 1994). These models provided basic understanding of fluid-rock interactions and mechanisms of oxygen isotope exchange. However, increasing geochemical and petrologic evidence shows that fluid flow and oxygen isotope exchange during metamorphic events are commonly heterogeneous (i.e., nonuniform) and controlled by kilometerto millimeter-scale permeability variations in crustal rocks (e.g., Nabelek et al., 1984; Heinrich et al., 1995; Valley and Graham, 1996; Satish et al., 1998; Nabelek, 2002). Such processes cannot be adequately represented by 1D models. Furthermore, 1D models or inverse geologic approaches sometimes lead to contradictory interpretations of the same metamorphic-hydrothermal systems (cf. Labotka et al., 1988; Ferry and Dipple, 1992; Nabelek et al., 1992). Two-dimensional (2D) fluid flow and transport models are better suited for simulating the complex temporal evolution of hydrothermal systems and geochemical properties of contact aureoles. Following the pioneering work of Norton and Taylor (1979), 2D reactive-flow models have successfully reproduced aspects of heterogeneous fluid flow and characteristic d18O patterns on the outcrop scale (e.g., Gerdes et al., 1995b; Cartwright and Weaver, 1997). However, only Cook and Bowman (1997) have developed a 2D reactive-transport model for aureolescale oxygen isotope exchange, although physical aspects of heterogeneous fluid flow in contact aureoles have been investigated in several studies (e.g., Baumgartner and Rumble, 1988; Hanson, 1995; Hayba and Ingebritsen, 1997; Gerdes et al., 1998; Cui et al., 2001). Gerdes et al. (1998) and Cui et al. (2001) demonstrated the dependence of geometries of fluid and heat flow on the permeability structures of aureoles. Lithologically layered permeability, as observed in many aureoles, focuses fluids into aquifers. Transient increase of permeability owing to metamorphic devolatilization reactions promotes strongly localized circulation of fluids in inner aureoles (Cui et al., 2001). Such flow patterns may have an important impact on the isotope-exchange pattern in an aureole. In this study, we investigated the coupling of oxygen isotope exchange with fluid and heat flow during contact metamorphism by using 2D numerical simulations of observed d18O values in the Notch Peak metamorphic aureole, Utah. The simulations were conducted to systematically investigate the effects of different permeability structures, fluid sources, and different oxygen isotope exchange mechanisms on the time-integrated oxygen isotope pattern. The results provide useful insights into fluid pathways, fluid sources, and kinetics of oxygen isotope exchange in contact aureoles with heterogeneous permeability.
GSA Bulletin; July 2002; v. 114; no. 7; p. 869–882; 16 figures; 2 tables.
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[email protected] q 2002 Geological Society of America
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CUI et al.
underscoring the low permeability of the marbles during the metamorphic event (Hover-Granath et al., 1983; Nabelek et al., 1984). In contrast, metamorphic reactions in all calcareous argillite units occurred in the presence of progressively more H2O-rich fluid as metamorphic grade increased (Hover-Granath et al., 1983; Labotka et al., 1988; Nabelek et al., 1992). The unmetamorphosed argillites consist of calcite, dolomite, quartz, and muscovite. The lowest metamorphic grade is defined by the phlogopite isograd. Rocks in the incipient phlogopite zone contain phlogopite, plagioclase, calcite, quartz, and minor K-feldspar. The assemblages suggest a continuous set of reactions leading to the overall reaction (Nabelek, 2002) Ms 1 Dol 1 Qtz → Phl 1 Kfs 1 An 1 Cc 1 CO2 1 H2O. Unchanged d18O values (;18‰; Fig. 3) of the phlogopite-grade rocks and the wide range of X(CO2)fluid for the continuous reactions support the presence of internally buffered fluid with a high CO2/H2O ratio. Diopside probably was formed by the reaction Phl 1 Qtz 1 Cc → Di 1 Kfs 1 CO2 1 H2O.
Figure 1. Simplified geologic map of the Notch Peak contact-metamorphic aureole, Utah (after Hintze, 1974, and Nabelek and Labotka, 1993). Heavy solid lines show metamorphic isograds as defined by assemblages in calcareous argillites. The heavy dashed line marks the position of a preintrusion fault. The solid square shows the location of the outcrop shown in Figure 5. GEOLOGY OF THE NOTCH PEAK CONTACT AUREOLE The Notch Peak contact-metamorphic aureole in the House Range, west-central Utah, resulted from intrusion of the Jurassic granitic Notch Peak stock into Cambrian sedimentary formations (Fig. 1). The intrusion depth is estimated to be ;4–5 km, and the stock has a laccolithic shape with an estimated radius of at least 4 km (Nabelek et al., 1986). The roof of the intrusion consists of the Orr Formation, a sequence of interbedded nearly pure limestones and calcareous argillites (Fig. 2). Below the Orr Formation is the 360-m-thick Weeks Formation, which is a relatively thinly bedded silicic limestone with abundant graphite. The underlying Marjum Formation is similar to the Weeks Formation but has thicker bedding. Below the Marjum Formation is a sequence of interbedded Middle to Lower Cambrian massive limestones and shales. The unexposed lowest part of the aureole probably is the .1500-m-thick Prospect Mountain Quartzite (Hintze, 1974). Previous studies of the aureole concentrated on the two upper limestone units, the 220-m-thick Big Horse Member of the Orr Formation and the underlying Weeks Formation (Hover-Granath et al., 1983; Nabelek et al., 1984, 1986, 1992; Labotka et al., 1988; Novick and Labotka, 1990). Metamorphic reactions in the marble layers of the Big Horse Member occurred in equilibrium with a CO2-rich fluid phase at all grades, resulting in assemblages of forsterite 1 tremolite 1 dolomite 1 calcite at the highest grade (Hover-Granath et al., 1983). Because the assemblages within the marbles are mostly univariant, HoverGranath et al. (1983) argued that fluids within the marbles were internally buffered and, therefore, the layers were closed to influx of external fluids. The marble layers have uniform sedimentary d18O and d13C values of ;20.5‰ and 0.5‰, respectively, at all grades (Fig. 3),
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Because the diopside-forming reaction spans a wide fluid composition range, it does not define X(CO2)fluid. However, rocks in the diopside zone also have unchanged d18O values (Fig. 3), which indicates little flux of externally derived water-rich fluid at this metamorphic grade. The presence of scapolite, restricted to the upper diopside zone, indicates some infiltration of aqueous fluids. The highest metamorphic grade is defined by the wollastonite-forming reaction Cc 1 Qtz → Wo 1 CO2. Many wollastonite-grade rocks also include vesuvianite and have d18O values down to ;9.5‰, approximately the value of the stock. Because reactions that formed the highest-grade rocks were mostly decarbonation reactions, the presence of vesuvianite and the low d18O values imply infiltration of externally derived water into the wollastonite zone. The estimated radial distances of the isograds from the shallowly dipping contacts of the intrusion are ;1300 m for the phlogopite isograd, ;700 m for the diopside isograd, and ;350 m for the wollastonite isograd (Fig. 1; Nabelek and Labotka, 1993). The calc-silicate forming reactions caused up to 30% volume loss in the rock (Labotka et al., 1988; Nabelek and Labotka, 1993). Unlike rocks at lower grades, rocks within the wollastonite zone were highly fractured. Meter-scale fractures parallel to bedding commonly occur in silicate-rich laminae. They appear to have relatively dense distribution. Few larger discrete fractures cutting perpendicularly mostly through pure limestone beds were sealed with calcite, garnet, and diopside. In the wollastonite zone, graphite in the Weeks Formation has extensively reacted away, particularly near the silicate-rich laminae and near the fractures, providing good evidence for the local and nonpervasive flow of fluids in the inner aureole (Nabelek and Labotka, 1993). THE HYDRODYNAMIC MODEL Governing Equations Following previous hydrodynamic models (e.g., Norton and Taylor, 1979; Hanson, 1995; Cook and Bowman, 1997; Gerdes et al., 1998; Cui et al., 2001), fluid flow in contact aureoles is assumed to follow
Geological Society of America Bulletin, July 2002
MODELING OF FLUID FLOW AND OXYGEN ISOTOPE EXCHANGE IN A CONTACT-METAMORPHIC AUREOLE
Figure 2. Stratigraphy of the Notch Peak aureole (after Hintze, 1974).
Darcy’s law (all symbols in the following equations are defined in Table 1):
1fm2 · (¹P 2 r g).
y52
k
(1)
f
The fluid-mass conservation equation, coupled with Darcy’s law (equation 1) and expressed in terms of primary variables pressure (P) and temperature (T), is
1f ]P 2 ]t 1 1f ] T 2 ] t 5 2 ¹ · (fr y) 1 Q . ]r f ]P
]r f ] T
f
Figure 3. Profiles of whole-rock d18O values through the Notch Peak aureole (after Nabelek and Labotka, 1993). Data are for limestone/marble samples of the Big Horse Member of the Orr Formation and for samples of calcareous argillites in the Big Horse Member and the Weeks Formation. Values for different metamorphic zones as defined by assemblages in the calcareous argillites are shown.
f
(2)
Here, fluid density (rf) is assumed to be independent of concentration of solutes because we only consider the transport of oxygen isotopes. For simplicity, deformation of the solid matrix is neglected as only local meter-scale ductile deformation was observed near to the pluton. The amount of energy or solute per unit of combined matrix-fluid volume may change owing to modification in the total fluid mass by pressure or porosity, while the temperature and solute concentrations in the fluid and rock remain constant. Such a change in energy or solute concentration is implicitly accounted for in the fluid-mass balance (equation 2; see Voss, 1984). Thus, if it is assumed that the velocity of the solid matrix is negligible, energy transport is expressed by
Geological Society of America Bulletin, July 2002
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CUI et al. TABLE 1. SYMBOLS USED IN TEXT Symbols
cs cf g r t v A0 A, B Cf Cqf Cs Df D Ea F H I P Qf Qx R S0 T Tq Xf, Xs a aL aT k lf, ls m rf, rs f
Units* 21
21
Definition and values used in the study
J·kg ·K J·kg21·K21 m·s22 mol·m23·s21 s m·s21 mol·m22·s21 N.U. N.U. N.U. N.U. m2·s21 m2·s21 J·mol21 mol·m23·s21 J·m3·s21 N.U. kg·m21·s22 kg·m23·s21 mol·m23·s21 J·mol21·K21 m2·m23 8C 8C mol·m23 N.U. m m m2 J·m21·K21·s21 Pa·s kg·m23 N.U.
Specific heat of minerals Specific heat of fluids Gravitational acceleration vector (9.8 m·s22) Exchange-rate constant for minerals Time Average linear velocity or seepage velocity of fluid flow Preexponential factor for reacting minerals (4.72 3 1024 mol·m22·s21)† Constants of calcite-fluid oxygen isotope fractionation (A 5 2.78 and B 5 22.89)§ Oxygen isotope ratio, 18O/(18O 1 16O), in fluid Oxygen isotope ratio, 18O/(18O 1 16O), in fluid sources or sinks Oxygen isotope ratio, 18O/(18O 1 16O), in rocks Apparent diffusivity of solute in fluids (5.0 3 1028 m2·s21) Dispersion tensor# Activation energy for oxygen diffusion into calcite (43.472 kj·mol21)† Net volumetric 18O transfer rate from fluid to solid minerals Latent heat of sources or sinks Identity tensor (2 3 2) Fluid pressure (Pa) Fluid-mass sources or sinks Oxygen mass of fluid source Universal gas constant (8.3144 J·mol21·K21) Surface area of minerals for isotope exchange per unit volume (1.0 3 103 m2·m23 for 100% mineral exchanging oxygen with fluids) Temperature Temperature of fluid sources or sinks Moles of oxygen (18O 1 16O) in fluid and rocks (Xs 5 82 500 mol·m23) Oxygen isotope fractionation factor between minerals and fluid Longitudinal dispersion coefficient, 100 m Transverse dispersion coefficient, 10 m Permeability tensor Thermal conductivities of fluid (0.6) and solid matrix (2.25) Fluid viscosity Density of fluid and solid grains, 2750 kg·m23 for solid minerals Effective porosity
*N.U. 5no unit or dimensionless. † From Cole and Ohmoto (1986). § From O’Neil et al. (1969). # The dispersion tensor is determined by fluid velocity and longitudinal (aL) and transverse (aT) dispersion coefficients (cf. Voss, 1984).
[fr f c f 1 (1 2 f) r scs ]
]T 5 2frf c f y · ¹T ]t
solid mineral phase and the fluid. The coefficient depends on temperature according to
1 ¹ · 5{[flf 1 (1 2 f) ls] I 1 fr f c f D} · ¹T6 1 Qf cf (T 2 T) 1 H.
(3)
q
]C f Xf f 5 2F 2 f Xf y · ¹Cf 1 ¹ ]t
(5)
where QX is the oxygen source contributed by the fluid source (Qf in equation 2) and F is the net rate at which 18O is transferred from the fluid to the minerals. When the oxygen isotope exchange between the fluid and the rock is fast compared to the fluid flow, local equilibrium can be assumed. In this case, F is ] (a Cf ) F 5 (1 2 f) X S ]t
(6b)
(4) F 5 r (a C f 2 C S )
]C (1 2 f )X S S 5 1F ]t
(6c)
where r is the rate constant for oxygen isotope exchange in minerals. For a surface-controlled reaction, the rate constant is given by (Cole et al., 1983; Cole and Ohmoto, 1986)
1 2
E r 5 S 0 A 0 exp 2 a RT
(6d)
Numerical Implementation (6a)
where a is the oxygen isotope fractionation coefficient between the
872
10 6 A 1B T2
where A and B are constants (Table 1). When the rate of oxygen exchange is slow compared to the rate of fluid flow, then kinetic retardation of isotopic exchange has to be considered. If first-order kinetic exchange is assumed, the rate is given by (Cole et al., 1983; Criss et al., 1987)
The reactive oxygen isotope transport is expressed by
· [f Xf (Df I 1 D) · ¹Cf ] 1 QX (Cfq 2 Cf )
103 ln (a) 5
To investigate fluid flow and oxygen isotope exchange in contact aureoles, equations 2–5 needed to be solved simultaneously with the oxygen isotope exchange rate equation 6a or 6c. When instantaneous
Geological Society of America Bulletin, July 2002
MODELING OF FLUID FLOW AND OXYGEN ISOTOPE EXCHANGE IN A CONTACT-METAMORPHIC AUREOLE
oxygen isotope exchange was assumed, equations 5 and 6a were combined into equation 4. Then, equations 2–4 were solved in terms of the principal unknowns—pressure (P), temperature (T), and oxygen isotope ratio in the fluid (Cf), by using the finite-element method. We used the publicly available 2D SUTRA code (Voss, 1984) to build our numerical model, and we modified the code to simulate simultaneously the heat and solute transport. When kinetic retardation was considered, the sequential noniterative approach was applied to solve the reactive-transport equations for oxygen isotope. This approach is also called ‘‘operator splitting’’ or ‘‘time splitting’’ (Valocchi and Malmstead, 1992; Steefel and MacQuarrie, 1996). In this approach, a single time step consists of a transport step that is followed by a reaction step. They were implemented by first solving equations 1, 2, and 3 and the oxygen isotope transport equation
fXf
]C f 5 2 f X fy · ¹Cf 1 ¹ ]t · [f X f (Df I 1 D) · ¹Cf ] 1 QX (C fq 2 C f )
(7a)
Then, by using the newly obtained Cf, the following coupled, nonlinear reaction equations
f Xf
]Cf 5 2F 5 2r ( a Cf 2 CS) ]t
(1 2 f )XS
]CS 5 r ( a Cf 2 CS) ]t
(7b)
(7c)
were solved in the reaction step. The unknowns Cs and Cf were obtained by using the trapezoidal algorithm with Newton iteration (Burden and Douglas, 1997). The new concentration Cf was then applied to solve equation 7a in next time step. We tested the numerical codes by successfully reproducing the results of the analytical solutions of selected 1D and 2D problems and the hydrodynamic model results of Hanson (1995) as modified by Cui et al. (2001). PROPERTIES OF THE PHYSICAL MODEL Physical properties of the model were described by Cui et al. (2001). The shape of the model pluton (Fig. 4) reflects the estimated dimensions of the laccolithic Notch Peak intrusion. Only half of the pluton is shown because of the symmetry. Both homogeneous and layered permeability structures of the wall rocks were considered. Previous studies (e.g., Hover-Granath et al., 1983; Nabelek et al., 1984, 1992; Labotka et al., 1988; Nabelek and Labotka, 1993) indicated that a large amount of CO2-poor magmatic fluids flowed through the calc-silicate rocks of the Big Horse Member and the Weeks Formation, whereas virtually no fluids infiltrated pure limestone beds of the Big Horse Member. This difference in fluid flux resulted in extensive 18O exchange in calc-silicate layers, whereas the protolith d18O values in pure limestone/marble layers were preserved (Fig. 3). In a similar study, Hoernes and Voll (1991) have shown no fluid infiltration into quartzite in the Ballachulish aureole, Scotland. Therefore, in our models with layered permeability structures, calc-silicate layers were considered as aquifers, and pure limestone layers and quartzite as aquitards. However, for the purpose of modeling isotopic exchange, all wall rocks were assumed to consist of calcite as calcite is a dominant mineral even in the calc-silicate layers (.70 wt%) and it is among the most responsive
Figure 4. Geometry of the model domain. The layered permeability structure used in cases 4–9 is based on the stratigraphy of the Notch Peak aureole (Fig. 2). Sedimentary units that are mainly limestones and quartzite are assumed to be aquitards, and those that are dominantly calcareous argillites are assumed to be aquifers. The Big Horse Member, which consists of interbedded pure limestones and calcareous argillites, was considered as an aquitard in the grid scale used in simulations. The dashed box shows the part of the model domain that is highlighted in figures that show results for cases with layered permeability structure.
minerals to isotopic exchange. Only the quartzite at the bottom of the aureole was assumed to be inert to oxygen exchange. The upper boundary of the model domain represents the water table, with constant fluid pressure (1.0 bar), temperature (0 8C), and rock d18O value (18‰). The bottom boundary is impermeable, and a conductive heat flux is applied there. The conductive heat flux (qc) is given by the formula qc 5 ls(T0–T)/Dd, where T0 is the initial temperature of the pluton (900 8C), T is transient node temperature at the bottom boundary, and Dd is a distance of 28 km. Thus, there is a row of auxiliary nodes at a depth of 36 km with a fixed temperature of 900 8C. Such a boundary condition assumes a conductive heat flux into the bottom of the model domain with a normal value of 56.25 mW·m–2 or less when the aureole is heated up. It also prevents downward heat flow through the bottom boundary because temperature there cannot be .900 8C. The left side of the model domain is a symmetrical boundary, i.e., no heat or mass flux crosses it. The right side is assumed to be permeable with a hydrostatic pressure gradient, a vertical thermal gradient of 25 8C·km–1, and a constant rock d18O value of 18‰. The granitic pluton was assumed to have been emplaced instantaneously at a depth of 4.8 km with a uniform temperature of 900 8C. Initially, the wall rocks and the pore fluid within the whole model domain have the same properties as those described at the right boundary. The d18O value of the pore fluid, assumed to be in equilibrium with calcite, was determined according to equation 6c, with F 5 0. The granitic magma, with constant d18O value of 8‰, was assumed to be inert to oxygen isotope exchange because no oxygen isotope alteration is indicated by the uniform ;9.4‰ d18O value of the pluton (Nabelek et al., 1984). When magmatic fluid infiltration was considered, we assumed that the
Geological Society of America Bulletin, July 2002
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CUI et al. TABLE 2. DESCRIPTIONS OF CASES Cases
Mechanism of 18 O exchange
Wall-rock permeability* (10216 m2)
Magmatic fluid (wt%)
Fraction of rock oxygen mass(%)
Surface area (m2·m23)
Case Case Case Case Case Case Case Case Case
Equilibrium Kinetic Kinetic Kinetic Kinetic Kinetic Kinetic Kinetic Kinetic#
Homogeneous (1.0) Homogeneous (1.0) Homogeneous (0.1) Layered (1.0–0.01) Layered (1.0–0.01) Layered (0.1–0.01) Layered (1.0–0.01) Laterally variable§ (0.1–0.01) Laterally variable§ (0.1–0.01)
0.0 0.0 0.0 0.0 3.0 3.0 3.0 3.0 3.0
10.0 10.0 10.0 10.0 10.0 10.0 50.0 10.0 10.0
N.A.† 100 100 100 100 100 500 100 100
1 2 3 4 5 6 7 8 9
*Single value is for homogeneous permeability of the wall rock. For layered-permeability structures, the first value is applied to aquifers, and the second value is applied to aquitards. In all cases, the pluton has permeability of 1.0 310218 m2. The permeability magnitude is within the range of measured values in the Notch Peak aureole and predicted values in other studies (Cui et al., 2001). † N.A. 5 not applicable. § In the models, a vertical, 200-m-wide zone along the side margin of the pluton and a 4.2 3 0.8 km zone along the top of the pluton have high permeability of 1.0 3 216 10 m2. The rest of the model domain has a layered permeability structure (aquitards: 1.0 3 10218 m2; aquifers: 1.0 3 10217 m2). # More constraints on reaction-controlled oxygen isotope exchange such that when the temperature is ,250 8C or during cooling, no exchange occurs.
magma contained 3 wt% of H2O with d18O value of 8‰, which exsolved as a linear function of temperature during crystallization. The latent heat generated by the crystallization of magma and consumed by the metamorphic reactions was accounted for by adjustment of the specific heats of the pluton and the wall rocks (Cui et al., 2001). The effective porosity was determined from the specified permeability by a cubic law relationship (e.g., Walsh and Brace, 1984; Cui et al., 2001). The fluid was assumed to be pure H2O, and multiphase flow was not considered. The fluid density and heat capacity were calculated by interpolation of steam tables (Burnham et al., 1969), and fluid viscosity was calculated from the density and temperature (Haar et al., 1984). Node spacing in the simulations was uniformly 200 m in cases 1–3 with homogeneous wall-rock permeabilities. In cases 4–9 with layered permeability structures, the node spacing was 100 m in interior regions and 200 m in the outer regions of the model domain (Table 2). Field observations and geochemical studies have shown that d18O values in many contact aureoles are highly heterogeneous. Commonly, isotope exchange was confined only to formations where calc-silicate reactions occurred. For example, even in the inner Notch Peak aureole, oxygen isotope exchange was concentrated within discrete calc-silicate beds and fracture zones (Nabelek, 2002). Typical is an outcrop in the wollastonite zone in which calc-silicate bands have d18O values of 12.0‰–15.3‰, whereas marble layers have essentially constant d18O value of 18‰–20‰, the same as the protolith, except along their margins where the values are somewhat lower (Fig. 5). Thus, overall only a fraction of the rock volume underwent oxygen exchange with external fluids. The grid-size of our model domain precludes examination of fluid-flow structures on the scale shown in Figure 5. Therefore, in all model cases (Table 2), we assumed that only a fraction of the wall rock underwent oxygen isotope exchange. This was implemented by reducing the total rock oxygen mass (Xs) in equation 7c to the fraction of exchangeable oxygen (Table 2). The predicted model values only represent oxygen isotope exchange in the discrete calc-silicate layers, which dominate the calc-silicate data in Figure 3. Volume diffusion of oxygen through calcite is very slow compared to the time scales of transient heat and fluid flow in contact aureoles. Moreover, the diffusion has a high closure temperature of 500–600 8C (Labotka et al., 2000). Oxygen isotope exchange is facilitated, however, by the surface-reaction mechanism during mineral reactions (Cole et al., 1983), as demonstrated by the correlation of decrease in the d18O values of Weeks Formation samples with the amount of reaction progress (Nabelek et al., 1992). For surface-reaction exchange, a controlling
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Figure 5. Outcrop sketch of interlayered calc-silicates and pure marbles in the wollastonite zone of the Weeks Formation (Fig. 1). Note the scale bar of the outcrop. The calc-silicates (light gray), consisting of wollastonite, diopside, vesuvianite, and scapolite, were strongly depleted of 18O, whereas the marbles (black) preserve the original protolith values, except for isotopically altered margins (medium gray). Bar on the right highlights isotopic variation across the layers.
parameter is the surface area of the reacting minerals, which likely changes during an ongoing metamorphic reaction. As a first-order approximation, we assumed a constant surface area (S0 in equation 6d) of 1000 m2·m–3 throughout the simulations, which corresponds to a grain size of ;1 mm for rhombohedral calcite (Cole et al., 1983). However, because only a fraction of the rocks was considered to have exchanged oxygen with fluids, the surface area (S0) was reduced by an amount corresponding to the reduction of the exchangeable oxygen in the calcite (Xs; Table 2). FLUID FLOW AND OXYGEN ISOTOPE EXCHANGE We conducted a series of simulations of fluid and heat flow to determine how various hydrodynamic parameters affect oxygen isotope exchange in contact-metamorphic aureoles (Table 2). Cases 1 and 2 with homogeneous permeability compare the effects of different mechanisms of oxygen isotope exchange. They also serve as reference models for more complex subsequent cases. Cases 3 and 4 demonstrate contrasting fluid flow and patterns of oxygen isotope exchange caused by variable permeability structures. The influence of a magmatic fluid
Geological Society of America Bulletin, July 2002
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source is illustrated in cases 5 and 6. The assumption that only a fraction of the rock volume underwent oxygen exchange in the Notch Peak aureole is tested in case 7. Case 8 shows the influence of reactionenhanced permeability on thermal and fluid-flow fields and the consequent isotopic shifts. Finally, a mineral reaction-controlled, kinetic, isotope-exchange model was evaluated in case 9. Salient results are compared with the observed d18O data for the Big Horse Member and the Weeks Formation. In all cases, the initial d18O value of the wall rocks was assumed to be 18‰. Effects of Kinetic Retardation Cases 1 and 2 illustrate the effects of kinetic retardation on patterns of oxygen isotope exchange. Equilibrium exchange of oxygen between wall rocks and fluid is assumed in case 1, whereas temperature-dependent kinetic retardation of oxygen exchange is considered in case 2. Other parameters in the two cases are the same (Table 2). Only the flow of primary pore fluid is considered, and only 10% of the wall rock undergoes oxygen isotope exchange. Fluid circulation driven by thermal buoyancy develops along the side edge of the pluton at early stages in case 1 (Fig. 6A). With increasing time, the high-flux region expands above the top margin of the pluton (Fig. 6B). The thermal field is dominated by conduction. At ;10 000 yr after the pluton’s intrusion, the inner aureole reaches peak temperatures, and temperatures remain elevated up to ;20 000 yr. By 50 000 yr, the inner aureole has already substantially cooled while the outer aureole still undergoes heating (Fig. 6B). By 10 000 yr, an 18O-depleted zone develops near the contact owing to isothermal and/or up-temperature flow, whereas an 18O-enriched zone develops above the upper corner of the pluton (Fig. 6A). By 50 000 yr, both the 18O-enriched and -depleted zones expand into the wall rocks (Fig. 6B). The 18O-enriched zone extends from the depth of 3.5 km to the surface with a peak value of ;32‰ at the depth of ;2.5 km. An ;500-m-wide zone near the right upper corner of the pluton has a low d18O value of ;11‰. This remarkable redistribution of oxygen isotopes is controlled by the geometry of fluid flow relative to the thermal field. In an up-temperature flow regime, flow of low-d18O fluids that equilibrated with calcite at low temperatures will cause decrease of d18O values of hightemperature rocks as the fractionation factor between calcite and water decreases with increasing temperature (equation 6b). In contrast, downtemperature flow of fluids that equilibrated with rocks at high temperatures will cause 18O enrichment in cooler rocks as the calcite-water fractionation factor increases. Decrease of d18O values occurs primarily in the lower part of the model domain where up-temperature flow is dominant. Increase of d18O values mainly occurs in the region above the pluton where down-temperature flow is dominant. 18 O depletions occur in most inner contact aureoles, but the predicted 18 O enrichment in the outer aureole is generally not observed. A probable explanation is that the assumed local fluid-rock equilibrium may hold at high temperatures but is invalid at low temperatures at which the oxygen exchange rate is very slow. The effect of kinetic retardation of oxygen isotope exchange between water and rocks is illustrated in case 2 (Fig. 7). The temperature dependence of the reaction-controlled exchange-rate constant for oxygen (r) is given by equation 6d. The results for kinetically controlled exchange are similar to those in case 1 at early stages (,;10 000 yr; cf. Figs. 6A and 7A). However, at 50 000 yr, the 18O-enriched zone remains confined to depths of .2 km (Fig. 7B) whereas the 18O-depleted zones in the inner aureole are similar to case 1.
Figure 6. Snapshots of predicted temperature and fluid-flow fields and d18O pattern for case 1. Gray lines are isotherms (8C). Arrows represent scaled vectors of fluid flux. The maximum flux value and the associated flow vector are shown on the top of each snapshot for scale. The gray-scaled background image is the wall-rock d18O pattern; white indicates most 18O enriched, and darker shades indicate progressively less 18O enriched or 18O depleted. (A) A narrow convection cell develops near the contact at 10 000 yr after the pluton’s intrusion, resulting in 18O depletion along the contact and enrichment around the upper corner of the pluton. (B) A broad convection cell that develops next to the pluton by 50 000 yr after its intrusion broadens the 18O-depletion zone near the pluton and causes a large, 18O-enriched region above the pluton.
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Figure 7. Snapshots of predicted thermal and fluid-flow fields and d18O pattern for case 2 (full explanation in Fig. 6). (A) Small 18Odepleted and -enriched zones develop along the boundary of the pluton at 10 000 yr. (B) The enrichment of 18O is limited to depths of .2 km. As with the d18O values of minerals in the high-temperatures zones (.250 8C), d18O values of pore fluid are also similar in the two cases (Fig. 8, A and B). However, below 250 8C, the difference is significant. This is because at high temperatures, the rate of oxygen isotope exchange is fast compared to the fluid-flow rate and approaches equilibrium exchange. At low temperatures, the exchange rate is slow relative to the fluid-flow rate. Thus, because the 18O/16O ratio in water cannot be buffered by minerals, the 18O-enriched fluids are convected toward the surface in a plume (Fig. 8B). In case 1, where water is isotopically buffered by minerals in the whole model domain, such an 18O-enriched plume does not exist (Fig. 8A). These results show that the common assumption of local equilibrium
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Figure 8. Comparison of the predicted d18O values (in per mil) of pore fluid at 50 000 yr for cases 1 and 2 (Table 2). (A) The concentration of 18O in the fluids is mainly controlled by equilibrium with the rocks. (B) An 18O-enriched plume of unbuffered fluids develops in the upper part of the model domain.
for oxygen isotope exchange may be inappropriate, especially when the temperature is below ;250 8C. Therefore, temperature-dependent kinetic retardation of oxygen exchange is incorporated into all subsequent models. Effects of Permeability Previous studies (e.g., Gerdes et al., 1998; Cui et al., 2001) showed that the permeability structure of a contact aureole exerts a major control on the flow pattern and the consequent time-integrated fluid-flux
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Figure 9. Snapshots of the predicted fluid and heat flow and d18O pattern for case 3 at (A) 10 000 yr and (B) 50 000 yr (full explanation in Fig. 6).
distribution in the aureole. In this section we discuss the effects of variable permeability structures on oxygen isotope exchange. Figure 9 shows the results for case 3 (Table 2) in which 10% of the wall rock undergoes oxygen isotope exchange and no magmatic fluids are included. The wall rocks have a homogeneous permeability of 1.0 3 10–17 m2, which is one order of magnitude lower than that in case 2, resulting in smaller instantaneous fluid flux (cf. Figs. 7 and 9). A smaller difference of permeability between the pluton and the wall rocks causes more pervasive fluid flow in the aureole (Fig. 9A), relatively more fluid infiltration through the pluton at ;50 000 yr (Fig. 9B), and a thermal field that is dominated entirely by conduction. Because of the smaller fluid flux in case 3, little isotopic exchange occurs at 10 000 yr (Fig. 9A). At 50 000 yr, the isotope-exchange pattern is
Figure 10. Snapshots of the predicted temperature and fluid-flux fields and d18O pattern in an aureole with layered permeability (case 4; Table 2). Only the region defined by the dashed rectangle in Figure 4 is shown. The dashed dark line is the boundary of the pluton (full explanation in Fig. 6). (A) Up-temperature flows in the convection cells reduce the d18O values near the pluton, and the down-temperature flow in the outer aureole increases d18O values. (B) Unidirectional up-temperature flow dominates in the aureole, resulting in horizontal, finger-shaped, .1.3-km-long 18O-depleted zones (darker shading) within the aquifers. similar to that in case 2 (cf. Figs. 7B and 9B) but with smaller shifts in isotopic ratios (,;4‰). Case 4 (Table 2) shows the effects of layered permeability (Fig. 10). The aureole consists of interlayered aquifers with permeability of 1.0 3 10–16 m2 and aquitards with permeability of 1.0 3 10–18 m2 (Fig. 4). Both are assumed to behave like calcite with respect to oxygen exchange. No magmatic fluid is involved, and only 10% of the wall rocks is assumed to undergo isotopic exchange. The layered permeability structure causes subhorizontal focusing of fluid flow within the aquifers (Fig. 10), in contrast to simple convection cells in an aureole with homogeneous permeability (Figs. 7 and 9). Small convection cells de-
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result suggests that an external fluid source with a lower d18O value may have been involved. Effects of Fluid Sources
Figure 11. Comparison of the model d18O profile for cases 2 and 4 with the observed profile in the Notch Peak aureole. The areas bounded by curves represents the range of calculated d18O values for the model Big Horse Member and the top 300 m of Weeks Formation in case 2. The gray zone represents the predicted d18O profile in case 4. The symbols represent measured d18O values in the two stratigraphic units (Fig. 4).
velop within the aquifers at the early stage (,5000 yr; Fig. 10A) but are gradually replaced by unidirectional up-temperature fluid flow at later stages (Fig. 10B). A characteristic isotope-exchange pattern evolves accordingly. At ;5000 yr, reduced d18O values of ;16‰ occur in the aquifers within ;200 m of the contact (Fig. 10A). By 50 000 yr, the 18O-depleted zones in the aquifers of the lower aureole extend outward to ;1.5 km from the contact (Fig. 10B). A notable feature is that up- and down-temperature flow regimes coexist within the aquifers. The up-temperature flow causes depletion of 18O along the bottom of each aquifer, whereas the down-temperature flow results in enrichment of 18O along the top of each aquifer (Fig. 10, A and B). The predicted d18O values across the wall rock in cases 2 and 4 are compared to the observed d18O values in the Notch Peak aureole (Fig. 11). Model results in case 2 with a homogeneous permeability do not match very well the observed pattern at either 10 000 yr (Fig. 11A) or 50 000 yr (Fig. 11B). In case 4 with a layered permeability, the strongly depleted 18O isotope signature in the Big Horse Member and the Weeks Formation within ;400 m of the contact are not reproduced. This
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Thus far, our discussion was limited to the effects of pore-fluid flow. Various external fluids out of isotopic equilibrium with the wall rocks may also impact the isotope-exchange pattern. Meteoric water can penetrate into shallow contact aureoles, interact with pore fluids and alter the isotopic ratios in the aureoles (e.g., Norton and Taylor, 1979). However, the role of meteoric water is likely to be small when the pluton is capped by layers of aquitards (e.g., Cui et al., 2001). Although metamorphic fluids may change oxygen isotope ratios in aureoles, their influence is generally smaller than the influence of external fluids (Nabelek et al., 1984; Bebout and Carlson, 1986). Particularly, the effects of magmatic water can be significant. Here we present two cases showing the effects of infiltration of magmatic fluids from a magma that contained 3 wt% water with d18O of 8‰, analogous to exsolution of water from the Notch Peak magma (Nabelek et al., 1983). The water is assumed to exsolve linearly from the crystallizing magma as the temperature drops from 900 to 750 8C. In case 5 (Table 2), the wall rocks have the same layered permeability structure as in case 4, and only 10% of wall rock undergoes 18O exchange (Fig. 12). The release of magmatic fluid from the crystallizing magma causes radial, focused fluid flow into aquifers in the early stage, reducing d18O values in the inner aureole to ;8‰ (Fig. 12A). However, down-temperature flow also causes enrichment of 18O in the outer aureole because the calcite-water fractionation factor increases with decreasing temperature. The radial-flow regime switches to local convection cells within the aquifers in the inner aureole after ;10 000 yr (Fig. 12B). The down-temperature flow of the top wings of the aquifer-scale convection cells enhances the depletion of 18O in the inner aureole, whereas the up-temperature flow of the bottom wings of the convection cells tends to counteract the depletion (Fig. 12B). This flow regime lasts up to ;20 000 yr. Subsequently, flow gradually becomes unidirectional, mostly up-temperature, except near the contact where it is subvertical (Fig. 12C). This post–peak-metamorphic flow tends to moderate the extensive isotopic exchange that develops at early stages. The early reduction of d18O values in the inner aureole is caused mainly by the infiltrating magmatic fluids, in contrast with case 4 in which it was caused by up-temperature flow of pore fluids. The 18O depletion in the present case is much more extensive than in case 4 (8‰ vs. 14‰; cf. Figs. 10 and 12). The model d18O profile at 10 000 yr is comparable to the observed profile in the Notch Peak aureole, especially for the highest-grade rocks (Fig. 13A). However, after 50 000 yr, the model values are generally more 18O enriched than the observed ones in the outer aureole, and the depletion front of 18O in the inner aureole retreats toward the contact (Fig. 13B). Reduction of permeability of the aquifers to 1.0 3 10–17 m2 in case 6 (Table 2) does not significantly affect the pattern of oxygen isotope exchange, except that the exchange fronts are smoother because the early radial flow of magmatic fluids lasts up to ;10 000 yr and the fluid flux is less focused. The mismatch between the predicted and observed d18O values in the outer aureole is similar to that in case 5. Effects of Exchangeable Mass of Rock In the previous sections, to reflect the fact that fluid flow in contact aureoles is commonly confined to discrete beds and fractures, we assumed that only 10% of the minerals in the wall rocks exchanged
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Figure 13. Comparison of the predicted d18O values for case 5 with the observed data from the Notch Peak aureole (full explanation in Fig. 11). oxygen isotopes with fluids. Generally, a more pervasive fluid flow results in a larger mineral surface area across which isotopic exchange can occur. Consequently, a larger volume of minerals can exchange isotopes with fluids and enhance retardation of isotopic fronts if the global budget of fluids from different sources remains constant. In case 7 (Table 2), 50% of the rock was allowed to exchange oxygen (Fig. 14). The hydrodynamic parameters are the same as in case 5 (Fig. 12). Whereas the fluid-flow and thermal fields are the same in both cases, the reduction of d18O values is ,;4‰ in case 7 and is limited to zones within ,200 m of the pluton/wall-rock contact at both 10 000 and 50 000 yr (Fig. 14, A and B). Moreover, the resulting d18O values in both the inner and outer aureole are significantly higher compared to the observed ones. This result supports the observation that fluid flow was channeled by local bedding and fractures as modeled in case 5. Reaction-Enhanced Permeability
Figure 12. Snapshots of predicted temperature and fluid-flux fields and rock d18O values for case 5 (Table 2), which includes magmatic fluid production (full explanation in Fig. 10).
Rocks in the wollastonite zone of the Notch Peak aureole were highly fractured and have undergone significant volume reduction because of extensive devolatilization reactions (e.g., Nabelek et al., 1984, 1992). These two processes probably significantly enhanced the permeability in the inner aureole. The transient enhancement of permeability by metamorphic reactions can promote localization of fluid flow
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Figure 15. Effect of enhanced permeability in the inner Notch Peak aureole on isotopic exchange modeled in case 8 (Table 2; full explanation in Fig. 11).
Figure 14. Predicted fluid-flow and thermal fields and wall-rock d18O values for case 7, in which 50% of the wall-rock volume is allowed to exchange oxygen with fluids (Table 2; full explanation in Fig. 10).
in the inner aureole and diminish fluid flux in the outer aureole (Cui et al., 2001). When the effects of reaction-enhanced permeability are accounted for by assuming a laterally varying permeability structure (case 8; Table 2), the enhanced fluid flux in the inner aureole indeed promotes decrease of d18O values in the high-permeability zones and better fit to the observed data (Fig. 15). However, the predicted d18O values for the outer aureole are still too high. Changing the relative permeabilities of aquifers in the inner and outer aureole by one order of magnitude does not appreciably alter the result. Reaction-Controlled Isotopic Exchange We have seen thus far that the release of magmatic fluid tends to produce d18O values that are too high for the outer aureole, whereas assuming no magmatic fluid release or having more wall rocks in-
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volved in oxygen isotope exchange leads to a poor fit of the d18O values in the inner aureole. A plausible explanation for the high d18O values predicted in the outer aureole is overestimation of the exchange rate in the lower temperature range. Experiments of Labotka et al. (2000) suggest that the closure temperature for oxygen exchange in calcite in the rapidly evolving temperature gradients in contact aureoles may be .500 8C. Moreover, as already noted, isotopic exchange is strongly facilitated by recrystallization associated with metamorphic reactions. For example, mineral reactions in the outer Notch Peak aureole did not begin until .400 8C with the production of phlogopite. Unless retrograde mineral reactions are extensive, the observed isotopic exchange profile likely preserves the exchange that has occurred during prograde mineral reactions at high temperatures. To evaluate the effect of reaction-enhanced isotopic exchange, we conducted a simulation (case 9) in which isotopic exchange ceases after peak temperature is reached or when the temperature is below 250 8C. Except for this kinetic constraint, case 9 has the same parameters as case 8, including reactionenhanced permeability. Consequently, the predicted fluid-flow and thermal structure remain the same as in case 8. The results show that no enrichment of 18O occurs in the outer aureole and the exchange pattern that develops prior to ;10 000 yr during prograde heating is preserved at 50 000 yr (Fig. 16). This finding contrasts with the remarkable influence of retrograde fluid flow on d18O values in case 8 (Fig. 15B).
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Figure 16. Results for case 9, which includes metamorphic, reaction-controlled isotope exchange (Table 2; full explanation in Fig. 11). Note the good fit between the predicted and the observed d18O values for the calc-silicates. The predicted d18O profile in case 9 matches well the observed profile in the Notch Peak aureole. DISCUSSION AND SUMMARY Fluid flow in metamorphic terranes influences the physical properties and chemical evolution of the Earth’s crust. Inverse geochemical and petrologic approaches are useful in evaluating fluid fluxes but sometimes lead to nonunique interpretations of data, which usually reflect the integrated metamorphic processes. The spatial limits of available petrologic and geochemical data also make it difficult to reconstruct a whole metamorphic system. Forward numerical models for fluid flow in contact aureoles, such as those presented in this paper, are useful because they show the temporal geochemical response of rocks to the evolving fluid-flow and thermal fields. Moreover, their multidimensional nature gives a broad perspective on fluid flow on the scale of a whole aureole, which is critical when the permeability structure is highly heterogeneous. Systematic examination of the critical flow and isotope-exchange parameters can help to elucidate the integrated nature of real petrologic and geochemical data. Heterogeneous fluid flow unavoidably causes heterogeneous exchange of 18O in contact aureoles. Spatial variability of oxygen isotope data even on the scale of outcrops has been attributed to the heterogeneous distribution of time-integrated fluid fluxes owing to large variations in permeability (e.g., Cartwright, 1994; Gerdes et al., 1995b; Cartwright and Weaver, 1997; Skelton et al., 2000; Nabelek, 2002). Our results demonstrate that formation-scale heterogeneous exchange patterns can also develop in contact aureoles. Gerdes et al. (1995a) and Marchildon and Dipple (1998) used stochastic heterogeneous twodimensional permeability simulations to reproduce the scatter of d18O values in the inner 500 m of the Alta aureole. Dipple (1998) suggested that the mismatch of the stochastic permeability models to the d18O values in siliceous dolomites outside of the depletion front at Alta can perhaps be attributed to kinetically dispersed stable isotope exchange. However, these models assumed essentially unidirectional fluid flow, which may not appropriately reflect the evolving flow regimes during metamorphism. Our model results indicate that fluid infiltration through any stratigraphic unit likely switches from one flow regime to another
during metamorphism. Variable d18O values in outer aureoles are best attributed to initially heterogeneous protoliths because (1) there is only limited fluid flux and little mineral reaction progress during which isotopic exchange is likely to occur and (2) by the time peak temperatures are reached in the outer aureole, the flow regime in the outer aureole has already become up-temperature, which invalidates the assumption that downstream kinetic dispersion may cause d18O variations in outer aureoles (cf. Dipple, 1998). Another essential feature of our results is that fluid flow in the inner aureole is mostly vertically upward and focused, consistent with geochemical field observations in several aureoles (e.g., Nabelek and Labotka, 1993; Roselle et al., 1999). With respect to the Notch Peak aureole, models that best reproduce the observed d18O variation in the Big Horse Member and the Weeks Formation include magmatic fluid release, a layered permeability structure, and only 10% of the wall rock exchanging oxygen isotopes with fluids. This result is consistent with the previous suggestion that the 18 O-depletion pattern in the inner Notch Peak aureole was caused by magmatic fluid infiltration from the crystallizing pluton (e.g., Labotka et al., 1988; Nabelek and Labotka, 1993). The model cases that assume reaction-controlled exchange give the best fit to the observed d18O profile. This result indicates that progress of metamorphic reactions and other mechanisms of recrystallization need to be considered when evaluating isotopic exchange. Although we assumed in the models that the fluid was pure H2O, the metamorphic fluid was likely CO2-rich owing to extensive decarbonation reactions. However, the release of aqueous magmatic fluids can significantly dilute the CO2 in the inner aureole, such that relatively CO2-rich fluids remain confined to the outer aureole (e.g., Labotka et al., 1988; Nabelek and Labotka, 1993; Cui et al., 2001; Nabelek, 2002). In contrast to H2O, CO2 is enriched in 18O relative to carbonate minerals. Flow of CO2-rich fluids will then tend to cause 18O depletion in down-temperature flow zones (Dipple and Ferry, 1992). In detail, the observed d18O data for calc-silicates in the outer Notch Peak aureole do show a slight depletion in 18O (Nabelek, 2002), which may indicate an early down-temperature flow of CO2-rich fluids in the outer aureole with limited flux, although the depletion could also reflect a change in the calcite/dolomite ratio. Enhancement of permeability in inner aureoles by fracturing and volume loss associated with progress of metamorphic reactions should facilitate infiltration of CO2-poor magmatic fluids (Cui et al., 2001). The resulting positive feedback between reaction-enhanced permeability and progress of devolatilization reactions will promote pervasive infiltration of fluids into the calc-silicate layers and the development of the characteristic d18O profile in these layers. In contrast, limited progress of calc-silicate devolatilization reactions in nearly pure limestone layers results in limited external fluid infiltration and unchanged d18O values even in the inner aureole. However, the similar magnitude of permeability (;10–17 m2) measured on the metamorphosed and unmetamorphosed samples from the Notch Peak aureole (Cui et al., 2001) suggests that reaction enhancement of permeability is indeed transient, consistent with the experimental study of Zhang et al. (2000). Such transient enhancement of permeability should cause even more transient and heterogeneous fluid flow than predicted by our models, which have steady permeability structures. However, to further define the permeability structure in the aureole during contact metamorphism, broader sampling of d18O data across the whole aureole would be necessary in future studies to test our modeled permeability distributions. Overall, our results show that the permeability structure of an aureole strongly influences the flow pattern and flux distribution and, therefore, the patterns of oxygen isotope exchange. However, the most
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significant isotopic exchange is attributed to the early infiltration of magmatic fluid from the crystallizing magma. ACKNOWLEDGMENTS We thank John Bartley and Mark Person for providing valuable and constructive reviews of the manuscript. This work was supported by National Science Foundation grant EAR-9805102. REFERENCES CITED Baumgartner, L.P., and Rumble, D., 1988, Transport of stable isotopes. 1. Development of a kinetic continuum theory for stable isotope transport: Contributions to Mineralogy and Petrology, v. 98, p. 417–430. Bebout, G.E., and Carlson, W.D., 1986, Fluid evolution and transport during metamorphism: Evidence from the Llano uplift, Texas: Contributions to Mineralogy and Petrology, v. 92, p. 518–529. Bickle, M.J., and McKenzie, D., 1987, The transport of heat and matter by fluid during metamorphism: Contributions to Mineralogy and Petrology, v. 95, p. 384–392. 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Hayba, D.O., and Ingebritsen, S.E., 1997, Multiphase groundwater flow near cooling plutons: Journal of Geophysical Research, v. 102, p. 12235–12253. Heinrich, W., Hoffbaur, R., and Hubberten, H.W., 1995, Contrasting fluid flow patterns at the Bufa del Diente contact metamorphic aureole, north-east Mexico; evidence from stable isotopes: Contributions to Mineralogy and Petrology, v. 119, p. 362–376. Hintze, L.F., 1974, Preliminary geologic map of the Notch Peak Quadrangle, Millard Coun-
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Geological Society of America Bulletin, July 2002
