Isotope transport and exchange within metamorphic core complexes

transcript

American Journal of ScienceMARCH 2007

ISOTOPE TRANSPORT AND EXCHANGE WITHIN METAMORPHICCORE COMPLEXES

MARK PERSON*†, ANDREAS MULCH**,‡, CHRISTIAN TEYSSIER**§§, andYONGLI GAO§

ABSTRACT. Field observations from the Shuswap metamorphic core complex inBritish Columbia indicate that meteoric fluids were focused along a sub-horizontalshear zone at a depth of at least 7 km. Fluid-rock interactions associated with this flowsystem resulted in oxygen isotope depletion of mylonitic rocks up to 4 permil in aregion less than 900m wide. Dating of the recrystallized shear zone fabric anddeformation-assisted fluid flow indicates that this paleo-fluid flow system was relativelyshort lived, (<1 Ma). Here we present idealized numerical representations of ametamorphic core complex system to assess the hydrologic and thermal controls onfluid-rock isotopic exchange. Our analysis focuses on understanding the relativeimportance of fault versus matrix controlled fluid flow, reactive-surface area, crustalpermeability structure, and isotopic composition of the recharging fluids. The analysispermits us to bracket the possible permeability and surface area conditions that areconsistent with field observations. We conclude that downward fluid flow along brittlefault systems and isotope exchange patterns could only be produced by a fracture flowdominated system. We found the fault permeability had to be greater than 10-16 m2 butless than or equal to 10-15 m2. Upper plate crystalline rocks adjacent to the fault zonehad to have a permeability less than 10-17 m2. The above findings are valid assuming alateral water table gradient of 5 percent, a shear zone surface area of 3.0x10-4

m2/mole, crustal rock surface area of 1.0x10�5 m2/mole, total duration of flow of200,000 years, and a basal heat flux of 90 mW/m2. Fault zone surface areas are muchtoo small to be consistent with pervasive grain boundary fluid-rock isotope interac-tions. Rather, the best fit surface areas were consistent with a fracture spacing of0.25 m for the shear/fault zones and a 5 m spacing for surrounding upper and lowerplate rocks. We found that fracture aperture widths of about 0.02 mm for thefault/shear zone units and 0.002 mm for the surrounding upper and lower plate rockswere consistent with the permeability values obtained from our generic modelingexercise. Imposing a more strongly 18O-depleted oxygen isotope composition for themeteoric recharge was directly reflected in lower computed �18O rocks. However,the effects were non-unique and to some degree, masked by the large oxygenreservoir within the crustal rocks. Computed rock isotopic values consistent with fieldobservations could have been produced with either heavier �18O fluids in the rechargearea over a longer period of infiltration or lighter �18O fluid compositions in therecharge region over shorter periods of time.

*Indiana University, Department of Geological Sciences, 1001 East 10th Street, Bloomington, Indiana47405

**University of Minnesota, Department of Geology and Geophysics, 301 Pillsbury Drive, SE, Minneapo-lis, Minnesota 55455

‡Stanford University, Geological and Environmental Sciences, 450 Serra Mall, Stanford, California94305; Present address: Institut fur Geologie, Leibniz Universität Hannover, Callinstrasse 30, 30167Hannover, Germany

§East Tennessee State University, Department of Physics, Astronomy and Geology, Box 70652, JohnsonCity, Tennessee 37614

§§Present address: Géologie et Paléontologie, UNIL, CH-1015 Lausanne, Switzerland†Corresponding Author: maperson@indiana.edu

[American Journal of Science, Vol. 307, March, 2007, P. 555–589, DOI 10.2475/03.2007.01]

introduction

There is a great deal of interest in understanding the permeability structure ofcrustal rocks as well as the fault zones that cut them, especially in tectonically activeregions of the Earth’s crust (Magee and Zoback, 1993; Zoback and Beroza, 1993;Moore and others, 1995). Faults that form in crystalline rocks can serve as conduits forgroundwater, heat, and ore forming fluids (see, for example Sibson and others, 1988;Lopez and Smith, 1995; Sibson and Scott, 1998). In crystalline rocks, fault zonepermeability is influenced by a number of factors including the development of alow-permeability core zone comprised of fault gouge (Morrow and others, 1984), ahigher permeability outer damage zone (Cain and others, 1996), syndeformationalmineralization, and the regional stress fields (Hobbs and others, 2004). While acomprehensive understanding of the hydraulic behavior of fault zones is still a longway off, there is growing consensus that faults should be represented as hydrologicunits (Haneberg, 1995; Bense and Person, 2006). One hurdle associated with determin-ing the permeability of fault zones on geologic time scales is the availability andinterpretation of paleohydrologic tracers that can accurately record the time-integrated fluid flow history along a fault zone. The focus of this paper is ondemonstrating the utility of fluid-rock isotope exchange patterns in combination withmathematical modeling as a means of constraining the permeability structure and flowpatterns within metamorphic core complex systems.

Isotopic exchange patterns in crustal rocks have been used for several decades todocument the rates, temperatures, and volumes of fluid migration within the uppercrust (for example, Valley and others, 1986). During the past decade, quantitativemodels of fluid-rock isotope exchange and transport have been used to quantify fluidflow rates associated with contact metamorphism (Bowman and Willett, 1991; Bowmanand others, 1994; Gerdes and others, 1995; Cook and others, 1997) and ore mineraliza-tion (Cathles and Smith, 1983). However, few quantitative studies of fluid-rock isotopeexchange exist for fault-controlled systems associated with uplift and exhumation ofmetamorphic rocks. Here, we present idealized models of advective-dispersive isotopetransport and fluid-rock interaction within an extensional detachment system bound-ing high-grade metamorphic core rocks. The models are intended to approximatehydrologic conditions within the Shuswap metamorphic core complex located inBritish Columbia, Canada (Vanderhaeghe and others, 2003); a site which providescompelling evidence of fault controlled fluid-rock isotope exchange down to the depthof the brittle-ductile transition zone. A sensitivity study is presented in which weaddress the paleohydrology of brittle-ductile detachment systems bounding metamor-phic core complexes and constrain the permeability structure of the detachmentsystem. A unique feature of this analysis is that our model simulations provide insightsinto the duration of the flow and range of permeabilities of crustal rocks/fault systemsthat access mid-crustal depths. We argue below that the permeability structure of theupper crustal normal fault and fracture system that facilitated downward transport ofD- and 18O-depleted meteoric fluid was sufficiently low to prevent significant convec-tive cooling in the vicinity of the localized fluid pathways yet high enough to permitadvective transport and fluid-rock oxygen isotope exchange within the brittle andductile segments of the detachment. Surface areas based on mineral grain sizesproduce rock 18O depletion patterns far too large to be consistent with field observa-tions. Effective surface areas for the shear/fault zone were consistent with a bulkmatrix block size of 0.25 m. Outside of the shear zone surface areas were much lowerand consistent with matrix block size of 5.0 m. Higher reaction rates and effectivesurface areas may have occurred within some regions of the mylonitic part of the shearzone but these could not be represented by our continuum based model. The

556 M. Person, A. Mulch, C. Teyssier, and Y. Gao—Isotope transport

alteration patterns produced by using a depth-dependent permeability structure forthe crust presented by Manning and Ingebritsen (1999) could not be easily distin-guished from simpler constant valued permeability models.

In the remainder of this paper, we briefly describe the field evidence for fluid-rockisotope exchange encountered in the Shuswap metamorphic core complex. We thendescribe the numerical model used in our sensitivity study in which the permeability,surface area, and isotopic composition of meteoric recharge were systematically varied.The transport equations used in this model are described in the Appendix.

study area

Geologic SettingThe Shuswap Metamorphic Core Complex (MCC), the largest in North America

(fig. 1), was exhumed in early Cenozoic time, following protracted compressionaltectonism that included accretion and crustal thickening during the Mesozoic (Arm-strong, 1982; Coney and Harms, 1984; Brown and others, 1986; Vanderhaeghe andTeyssier, 1997; Crowley and others, 2001). At the latitude of the Thor-Odin dome, twodetachment systems bound the metamorphic core complex, the Okanagan detach-ment to the west (Templeman-Kluit and Parkinson, 1986) and the Columbia Riverdetachment to the east (Read and Brown, 1981; Vanderhaeghe and Teyssier, 1997;Teyssier and others, 2005). The isotopic study reported here is focused on a portion ofthe Columbia River detachment, an approximately 1 km thick mylonite zone locatedin the footwall of the Columbia River fault (Read and Brown, 1981) and capped themigmatitic gneisses of the Thor-Odin dome. Isotopic dating using the U-Pb method onzircon and monazite (Vanderhaeghe and others, 1999; Teyssier and others, 2005), the40Ar/39Ar method on biotite and white mica (Vanderhaeghe and others, 2003; Mulchand others, 2004, 2006), and the fission-track technique on apatite and zircon(Lorencak and others, 2001) have shown that the migmatites of Thor-Odin crystallizedat �55 Ma, cooled through �400 to 300 °C at � 49 to 48 Ma, and were locally alreadynear the Earth’s surface at �45 Ma. This fast cooling was achieved by a combination ofdetachment-related denudation and diapiric emplacement of the Thor-Odin dome(Teyssier and others, 2005).

Temperature and Timing of Detachment ShearingThe stable isotopic data reported here focuses on the mylonitic zone that defines

the Columbia River detachment in the vicinity of Blanket Creek (fig. 2), where theshear zone cuts a thick micaceous quartzite unit. Samples were collected on a traversealong Rd 23, over approximately 900 m of structural section from high-grade quartziteat the base to the Columbia River fault (contact with hanging wall) at the top. Usinglaser-based extraction techniques, we determined temperatures of ductile deformationfrom oxygen isotope fractionations measured between muscovite fish and deformed/recrystallized quartz in the Columbia River detachment. A total of 19 samples werecollected and analyzed at an oblique angle to the detachment (fig. 2) to determinespatial variations in rock isotopic composition across the mylonitic detachment. Basedon the oxygen isotope data collected, calculated temperatures (Chacko and others,1996) fall within a range of 420 � 40°C. We interpret this temperature to reflectconditions of synkinematic fluid-rock interaction and oxygen isotopic exchange.

The white mica fish deformed in the quartzite mylonite were also dated using40Ar/39Ar geochronology. Five samples of mylonitic quartzite from within 150 m of thecontact with the hanging wall yield well-defined 40Ar/39Ar plateau ages ranging from49.0 � 0.2 Ma to 47.9 � 0.1 Ma (Mulch and others, 2004, 2006). Given the rapidcooling rates (for example, Vanderhaeghe and others, 2003) and the initial deforma-

557and exchange within metamorphic core complexes

tion and isotopic exchange temperatures of 420 � 40°C, these ages were interpreted asdeformation ages (Mulch and others, 2004), limiting the timing of ductile deforma-tion and syn-kinematic oxygen isotope water-rock exchange to a duration of about1.1 � 0.3 m.y. Deformation in the mylonitic segment of the detachment was strongly

Fig. 1. Simplified map and cross-sections of the Thor-Odin dome region of the Shuswap metamorphiccore complex (British Columbia) (after Vanderhaeghe and others, 2003).

localized and migrated towards deeper levels of the exhuming footwall over time(Mulch and others, 2006) such that deformation increments recorded at individuallevels of the shear zone are likely to be on the order of 100,000 to 200,000 years.

Fig. 2. Sampling locations and cross section of mylonitic quartzite across � 800 m of Columbia Riverdetachment; Sm and Ls indicate mylonitic foliation and mineral stretching lineations. Stars indicate positionof sampling traverse. (After Mulch, ms, 2004).

Oxygen and Hydrogen Patterns in the Mylonitic Shear ZoneThe �18O and �D patterns (fig. 3) across the mylonitic quartzite of the Columbia

River detachment have been described in Mulch and others (2004) and Mulch andothers (2006). Mylonitic quartzite in the detachment has �18O values ranging between10.0 and 11.9 permil only about 2.5 to 0.6 permil lower than quartzite found in thedeeper levels of the exhumed footwall of the core complex (�18O � 12.5 ‰) (Holk, ms,1997; Holk and Taylor, 2000). While too few samples were analyzed to establish theexact nature of the oxygen isotope depletion trend, a best-fit line through the datasuggests that the extent of alteration fell off rapidly over 200 to 400 m from the uppermargin of the lower plate. Because of lateral extensional movement of the upper platerocks, isotope alteration profiles along the subvertical feeder faults are not preserved.However, we observe strongly deuterium-depleted hydrogen isotope compositions indetachment muscovite with values as low as �D � -160 permil when compared tomuscovite from non-mylonitic quartzite (�D � -80 ‰) (Mulch and others, 2004).

These very low �D values are best explained by interaction with surface-derivedmeteoric waters (Mulch and others, 2004). Under equilibrium conditions these dataindicate that water percolating in the detachment at temperatures of 420 � 40°C had�D values of lower than -135 � 3 permil (Suzuoki and Epstein, 1976) or even less ifhydrogen isotopic water-rock exchange had already occurred prior to muscoviterecrystallization in the ductile detachment. We assume that the fluids in the deformingdetachment were of meteoric origin and had a �18O water value of � -18 permil, whichis used as a starting value for water entering the recharge fault in our sensitivity study.

Fig. 3. Conceptual model of fluid flow and summary of oxygen isotope data in the different modeldomains. Low �18O meteoric fluids percolate in normal fault systems that are kinematically and hydraulicallylinked to mylonitic shear zone at depth. Synkinematic fluids are involved in recrystallization of the myloniteaffecting �18O/�D in quartz and muscovite, respectively. (Data from Nesbitt and Muehlenbachs, 1995; Holk,ms, 1997; Holk and Taylor, 2000; Mulch, ms, 2004; Mulch and others, 2004).

mathematical modelThe sensitivity study is believed to be generally representative of the hydrologic,

isotopic, and thermal conditions present during deformation along the Early EoceneColumbia River Detachment. The geometry of sedimentary basins and near-surfacefaults in the upper crust that lied above the detachment is poorly known. However,remnants of upper crustal slices preserved above the detachment indicate that crustalblocks likely were on the order of 10 km in width. In addition, basins that developed bydomino-style extension, such as the Trinity Hills and Endery basins (fig. 1) containsedimentary detritus capped by volcanic ashes and flows that have been dated at about48 to 50 Ma (Matthews, 1981). Therefore, basins developed in close association withnormal faults during detachment activity. The model geometry used in figure 4 ishighly schematic but takes into account the likely presence of sedimentary basinsassociated with 10 km-wide tilted blocks. This geometry also corresponds to the generalcase of domino-style faulting of upper crust, a common model of detachment tectonics(Lister and Davis, 1989). However, because the precise geometry of the sub-verticalfault zones represented in figures 3 and 4 is poorly known, these models are idealizedand the results must be viewed in a generic fashion. The paleohydrologic system isrepresented using 5 lithologic units (fig. 4). These include a 7 km thick upper plate ofcrystalline rocks, a 2 km thick sedimentary basin fill in the hanging wall of a rechargenormal fault, two 100 m wide high-angle faults (one for recharge, one for discharge)that link to a 1 km thick shear zone separating the upper plate from a model domain of7 km of lower plate crystalline rocks. We assume that only a portion (100 m) of theshear zone is permeable at any one time. We further assume that high permeabilityconditions can only be maintained for a limited amount of time (�100,000 to 200,000years) due to the progressive downward migration of the mylonitic front and becausetemperatures in excess of 350°C should result in ductile flow of crustal rocks. In a firstattempt, a number of thermal and hydrologic parameters as well as boundary condi-tions were held constant in the sensitivity study (table 1). This was done either because

Fig. 4. Lithologic units and fault zones represented in sensitivity study. The position of vertical/lateralmonitoring points and profiles of computed temperature and rock isotopic composition are also indicated.

they were thought to not significantly influence model results or because these valueswere so poorly constrained that varying them did not seem appropriate. One exampleis the geometry of the water table. There is a 2 km change in elevation over the 40 kmwide solution domain. While this geometry produces a steep hydrologic gradient(5%), such gradients are not uncommon for mountainous terrains (Woodbury andSmith, 1988). The permeability conditions that were found to be largely consistentwith observed rock isotope conditions (referred to herein as the base conditions orbase model run) are presented below in table 2. These values were varied sequentiallyin a sensitivity study described in the SENSITIVITY STUDY section.

Groundwater FlowIn orogenic belts, groundwater flow can be induced primarily by either tectonic

compression (Oliver, 1986; Ge and Garven, 1994; McPherson and Garven, 1999) ortopographic gradients in the water table due to rock and surface uplift (Garven andFreeze, 1984b; Woodbury and Smith, 1988). Because fluid circulation to mid-crustaldepths occurs under non-isothermal conditions, density-driven flow due to buoyancycontrasts (Raffensperger and Garven, 1995a, 1995b) is also possible. We did not considerupward migration of crustal fluids produced by prograde metamorphic reactions(Hanson, 1997; Smith and Yardley, 1999) because the isotopic composition of suchfluids would be incompatible with the measured oxygen and hydrogen isotopic

Table 1

Rock properties fixed in sensitivity study

Table 2

Rock properties assumed for base conditions

composition of syndeformational fluids. A review of fluid flow impelling mechanismscan be found in Person and others (1996) and Ingebritsen and others (2006).Relatively high permeability conditions are required for fluid-rock isotopic interac-tions at mid crustal depths. Because tectonically induced flow is only important in lowpermeability environments, it is neglected in this study. In relatively permeable rocks(that is, � 10-16 m2), topography- and density-driven flow are thought to be the mostimportant mechanisms to transport significant quantities of strongly isotopicallydepleted in D or 18O meteoric fluids to mid-crustal depths. Both of these mechanismsare accounted for in the groundwater flow equation used in this study and presented inthe Appendix (equations 9 and 10). The groundwater flux is calculated using avariable-density formulation of Darcy’s Law (Appendix, equation 13). Because fluiddensity varies with temperature, the direction of groundwater flow cannot be directlyinferred from the hydraulic head gradients. The effect of salinity on haline convection(Duffy and Al Hassan, 1988; Leising and others, 1995) was not considered in this study.Equations (9) and (10) represent quasi-steady-state, variable-density groundwater flowin heterogeneous and anisotropic porous media in which the principal directions ofthe permeability ellipse need not be aligned with the lithologic units. Boundaryconditions for the groundwater flow equation include a specified head (water table)condition at the Earth’s surface and no flow boundary conditions along the sides andbottom of the solution domain. The hydraulic-head boundary condition was assumedto be a replica of paleotopography (Toth, 1962). Because the time scale of fluid flowand fluid-rock isotopic exchange are relatively short lived (200,000 years), a static gridwas used in this study. Hydrostatic heads were assigned as an initial condition.

Heat TransferConductive/convective heat transfer associated with fault-controlled fluid flow

along the Columbia River Detachment is represented using equation (12) of theAppendix. The solid phase is implicitly assumed to be in thermal equilibrium with thefluid phase and the thermal dispersivity tensor is treated in an analogous manner tosolute dispersivity (see equation 14 in the Appendix; see also de Marsily, 1986).Boundary conditions for the heat transport equations include a constant temperatureboundary of 10 °C at the Earth’s surface. The side and bottom boundaries are specifiedheat flux boundaries. This does not take into account changes in surface temperaturedue to climate change over the time scales considered in the model or changes intemperature with elevation. A specified basal heat flow of 90 mW/m2 is assumed in thisstudy. Further, the thermal conductivity is fixed at 2.5 W/m-°C for all lithological unitsand we assume a conductive geothermal gradient (about 45oC/km) as an initialcondition for the temperature distribution in the crust. Such steep geothermalgradients are not uncommon in areas undergoing rapid extension and are thought tobe representative for footwall environments in rapidly evolving extensional shear zonesystems.

We use a thermal Peclet number (PeT) to characterize the relative importance ofconvection and conduction as agents in heat transport. The thermal Peclet number isdefined in two ways depending on whether flow was confined to a fault zone or morediffusive flow occurs throughout the Earth’s crust (fig. 5):

PeT �5�fcfqzb2

�Lzfault (1a)

PeT ��fcfqzLz

�matrix (1b)

where �f � fluid density (kg/m3)cf � specific heat capacity of the fluid (J/kg-oC)qz � Vertical Darcy Flux in sub-vertical fault zone (m/s)� � bulk thermal conductivity of crustal rocks (W/m oC)b � characteristic width of the fault zone (100 m)

Lz � characteristic length in z-direction over which convective heat transferoccurs (9 km)

PeT � thermal Peclet Number

Details of how we derived equation (1a) are presented in the Appendix (seeequations 4-8, Appendix). For fault-controlled groundwater flow (equation 1a), weassumed that the dominant conductive heat transfer losses occurred laterally (x-direction) and thus two characteristic length scales (Lz for convection and b for lateralconduction) need to be represented. For diffuse groundwater flow through the uppercrust, the more conventional thermal Peclet number (equation 1b) can be used(Phillips, 1991; Ingebritsen and others, 2006). Here, the vertical velocity within therecharge area is used. For tectonically active, permeable portions of the Earth’s crust,thermal Peclet numbers are generally less than 1 but typically greater than 0.01. APeclet number of 0.1 can result in significant (� 30°) cooling or heating in the upper10 km of the Earth’s crust (see for example, Person and others, 1995).

Fig. 5. Isotope breakthrough curves for different solute Peclet numbers (from Bowman and others,1994). Schematic diagram illustrating characteristic length scales used to calculate one- and two-dimensionalthermal Peclet Numbers (PeT) found in equations 1a (matrix dominated flow) and 1b (fracture dominatedflow).

Isotope TransportWe represent advective–dispersive isotope transport and fluid-rock isotope ex-

change (equation 15, Appendix) using the approach outlined in Bowman and Willett(1991). Given the broad temperature ranges measured within the shear zone underdifferent permeability conditions, we adopt a kinetic formulation for fluid-rock isotopeexchange (equation 17, Appendix). In order to solve for fluid rock isotope exchangeat depth, the temperature dependent equilibrium isotope fractionation factors need tobe calculated for each mineral phase (m; equation 18, Appendix). The polynomialcoefficients cm - fm (table 3; equation 20, Appendix) for all of the mineral phases usedin this study were derived from laboratory experiments of fluid-rock isotope exchangesummarized by Cole and Ohmoto (1986). The kinetic parameters including thepre-exponential factor (Ao) and the activation energy (Ea) as well as the initial isotopiccomposition of each mineral (�o) are also specified for each mineral phase (table 3;equation 23, Appendix).

The isotope exchange reactions are driven by the degree of isotopic disequilib-rium between fluid and rock. For matters of simplification the five lithologic units usedin our model are assumed to be composed of seven different minerals. Their fractionalabundances within each lithologic unit are listed in table 4 and are derived from Holk(2000) and Mulch and others (2004). Averaged quantities for the fractionation factor,the reaction rate, and fractional mass ratio of oxygen in the solid phase weredetermined for each lithologic unit using the averaging rules presented in equations19, 21, and 22 in the Appendix.

We also use a Peclet number to characterize the relative importance of lateraladvective to diffusive isotope (PeI) transport along the horizontal portion of the faultzone:

Pe1 �Lx

qxD(2)

where D � is the solute diffusivity � porosity

qx � horizontal groundwater flux in sub-horizontal faultLx � characteristic lateral length scale of the sub-horizontal fault system in the

shear zone (12.5 km)PeI � isotope Peclet Number

Table 3

Temperature dependent coefficients used in the determination of mineral equilibriumisotopic exchange

Ao—moles/m2-s; Es—kcal/mole

We neglect vertical isotope transport within the sub-vertical fault zone in ourisotope Peclet number calculations because most fluid-rock isotope interactions arelikely to occur at high temperatures (� 250 °C) within the sub-horizontal shear zone.High Peclet numbers (fig. 6C) produce relatively sharp compositional fronts forisotope transport and would produce sharp isotope gradients within the detachmentshear zone if reaction rates were high. Solute diffusivity generally varies between 10-10

to 10-11 m2/s. For crustal rocks, porosity varies between 0.01 and 0.05. Using represen-tative estimates of fluid velocities (0.01 to 10 m/yr) indicates that isotope transportshould be dominated by advection for all but the least permeable crustal rocks (that isPeI � 1) in our sensitivity study.

The Damkohler number characterizes the relative importance of fluid-rockisotope exchange reactions to advective transport:

ND �rrkLx

ReactiveAdvective

where rrk � fluid-rock isotope exchange rate between the fluid and rock phases � porosity

qx � horizontal groundwater flux in sub-horizontal faultLx � characteristic lateral length scale of the sub-horizontal fault system (fig.

6H) in the shear zone (12.5 km)

For low Damkohler numbers, isotopes behave more or less like a conservativesolute (figs. 6A and 6C). The combination of a high Peclet number and low Damkohlernumber (ND � 0.1; figs. 6D and 6E) produces little exchange between the fluid androck phases. The exchange that does occur is spread out over a large area. HigherDamkohler numbers (ND � 1.0; figs. 6F and 6G) also produce a relatively diffusiveisotopic front in the rock phase. This is similar to what we observed in our sensitivitystudy discussed below.

Numerical Methods and Finite Element MeshThe fluid flow and heat transport equations were solved using the finite element

method. The solute transport equation was solved using a finite element formulationof the modified method of characteristics algorithm (Zheng and Bennet, 1995).Three-node triangular elements are used to discretize the solution domain. For allthree transport equations, the resulting set of algebraic equations was solved usingiterative techniques (Bramley and Wang, 1996). The finite element mesh used torepresent fault-controlled fluid flow, heat, and isotope transport is shown in figure 7.The solution domain was discretized using 26807 Delanay triangular elements com-posed of 13558 nodes. The elements varied in size from about 1000 m in the low

Table 4

Fractional mineral abundances (Fm) for lithologic units

permeability crustal rocks to 40 m in the fault zone. While further mesh refinementwithin the fault zone would have been desirable, the processing time required for thesesimulations was on the order of several days per run and additional mesh refinementmay not have been computationally feasible without implementing parallel computingtechniques (Person and others, 2006).

sensitivity studyWe hypothesize that variations in permeability of the different lithologic units,

surface area, and isotopic composition on rock-water oxygen and hydrogen isotopeexchange all have important effects on the change in isotopic composition of shearzone rocks and hence permeability was varied as part of a sensitivity study. There is asignificant range of uncertainties with respect to these variables and our sensitivitystudy helps to elucidate the effects these have on rock isotopic composition. Thesensitivity study also helps us determine whether or not the observed isotopic exchangeshown in figure 3 is unique or could be produced by a wide range of conditions.

Fig. 7. Numerical grid Shuswap metamorphic core complex hydrothermal model composed of 26807triangular finite elements 13558 nodes. Yellow and dark blue represent upper and lower plat rocks,respectively. Green and light blue shown in the inset represent the shear zone and sub-horizontal fault zone,respectively. The grid was refined along the fault zones. The characteristic element lengths varied fromabout 1000 to 100 meters.

��

,Lz�

Effect of PermeabilityThe permeability of the shear zone, high-angle faults, and upper plate lithologic

units were varied as part of a sensitivity study to assess its effect on temperatureredistribution and fluid-rock isotope exchange (table 5). We used published permeabil-ity data sets for crustal rocks as a guide in selecting these values (Freeze and Cherry,1972; Brace, 1984; Clauser, 1992). The sedimentary basin unit was assigned permeabil-ity in the x direction of 10-14 m2 with an anisotropy of 10. We varied the permeability ofcrustal rocks between 10-17 to 10-19 m2 outside the fault zone. We also allow permeabil-ity of crustal rocks above the shear zone to decrease exponentially over 6 orders ofmagnitude with depth using the exponential relation proposed by Manning andIngebritsen (1999). We assumed that crystalline crustal rocks were isotropic withrespect to permeability. Several studies have compiled data on the permeability ofcrustal rocks (Brace, 1984; Clauser, 1992; Manning and Ingebritsen, 1999). We variedthe fault zone permeability over three orders of magnitude (10-14 to 10-17 m2). Faultpermeability depends on aperture width and fracture spacing. For example, using thecubic permeability law presented by Brace (1980) (k � Nb3/12; b is fracture aperturewidth, N is the number of fractures per unit width, and k is rock permeability) factureshaving an aperture width of 0.031 mm spaced 25 cm apart would have a bulkpermeability of about 10-14m2. A 0.002 mm wide fracture spaced 5 m apart would havea permeability of about 10-19 m2.

Stream functions.—Computed stream functions are depicted in figure 8. The rechargeand discharge areas are indicated using “R” and “D”, respectively. For the base model run(fig. 8A), there is a large contrast between the high-angle faults and upper plate permeabil-ity (Kfault/Kupper plate � 104) and shear zone (Kfault/Kshear zone � 103) rocks. As a result,vigorous fluid flow is isolated to the high-angle faults as represented using computedstream functions (presented in m2/yr). Fluids access the high-angle faults through thesedimentary basin sediments with inflow occurring in the high topography basin anddischarge occurring into the lower elevation basin. Where the shear zone merges into thehigh-angle faults, fluid flow is not isolated to the fault zones. Velocities in the high-anglefaults are about 1.2 m/yr while the flow rates in the upper plate rocks are about 0.0001m/yr after 200,000 years. Decreasing the permeability contrast between the shear zone andthe high-angle faults to only one order of magnitude (fig. 8B) allowed leakage of fluids outof the fault into the shear zone. Lateral flow rates in the shear zone are about 0.2 m/yr.Raising the permeability of the upper plate crystalline rocks (10-17 m2) so that there is onlytwo orders of magnitude variation in rock permeability between the fault and the upperplate rocks results in a marked change in flow (fig. 8C). Now fluids sweep through theupper plate rocks and are no longer focused into the high-angle faults, as was the case infigures 8A or 8B. Meteoric fluids penetrate the upper plate and surface-derived fluids flowlaterally into the recharge high-angle fault at mid crustal depths. Discharge still occurs intothe lower elevation basin, but flow exits the fault zone below the basin at a depth of about 5km. In addition, fluids now leak out of the shear zone over a wide area into the fault zone.Flow rates in the upper plate rocks increase to 0.03 m/yr. The flow rates in the fault zoneare not markedly different from the base model run (fig. 8A). When the permeability ofthe fault zone is increased by one order of magnitude (from 10-15 to10-14 m2; fig. 8D)relative to the base model run (fig. 8A), flow patterns are again isolated to the fault zone.The main difference from the base model run is that the fluid velocities in the fault zoneare now �11 m/yr. Under these conditions, a convection cell forms deep within the lowersedimentary basin. Scenario E represents the most permeable conditions with both upperplate and shear zone rocks permeability set at 10-17 m2 and the permeability of thehigh-angle faults fixed at 10-14 m2. Despite the higher permeability conditions outside thehigh-angle faults, the three order of magnitude contrast in permeability between the faultsand the surrounding rocks focuses most of the flow within the faults (fig. 8E). Allowing

permeability to decrease with depth within the upper plate and lower plate rocks using theempirical model of Manning and Ingebritsen (1999) induces shallow flow of meteoricfluids within the upper 3 km (fig. 8F). Flow rates in the upper plate rocks increase to about6 m/yr. Maximum flow rates in the fault zone increase modestly to 1.3 m/yr and fluids areonly focused in the fault zone below a depth of about 3 km. The last two scenarios are thesame as the base model run (scenario A) except that the fault zone permeability isdecreased to 10-16 m2 (fig. 8G) and 10-17 m2 (fig. 8H). As one might expect, decreasing thepermeability of the fault zone so that there is only a three order of magnitude contrastbetween the fault zone and upper plate rocks (fig. 8G) results in substantially less focusingof flow into the high-angle fault. The maximum velocity within the fault is 0.1 m/yr.Further decreasing fault permeability to 10-17 m2 results in much less integrated flowthrough the high-angle fault, reducing maximum velocity within the fault zone to 0.01m/yr. There is virtually no focusing of fluids into the high-angle fault. The dominant flownow occurs in the shallow crust adjacent to large gradients in topography (fig. 6H).

Fig. 8. Computed stream functions (m2/year) for different representations of fault zone, upper plate,and shear zone permeability within a metamorphic core flow system complex after 200,000 years. Thepermeabilities used for figures 9A-H are listed in table 5. The recharge and discharge areas are indicatedusing “R” and “D”, respectively.

Temperatures.—Computed temperatures for the base model run (fig. 9A) indicatemodest convective effects in and adjacent to the sub-vertical segments of the faultzones with a disturbance in the geothermal field of about 25 °C. The thermal Pecletnumber computed on the downwelling limb of the subvertical fault (equation 1a; table5) is about 0.16. Descending fluid flow along the high-angle fault zone draws coolfluids downward which are warmed primarily by lateral conductive heat transfer.Conductive heat transfer clearly dominates. Decreasing the permeability contrastbetween the high-angle fault and shear zone (fig. 9B) to one order of magnitude (10-15

/10-16; fig. 9B) did little to the computed temperatures or Peclet number (PeT � 0.14).Increasing the permeability of the upper plate rocks (10-17; fig. 9C) does result inmodest convective thermal effects in both recharge and discharge areas. We usedequation 1b to compute the Peclet number for this simulation (PeT � 0.12) as verticalflow was not confined to the fault zone and does not noticeably change the thermalstructure of the basin. Increasing the permeability of the fault zone by one order of

Fig. 9. Computed temperature for different representations of upper plate, fault, shear zone permeabil-ity after 200,000 years. Initial conductive thermal conditions were imposed at the simulations. Thepermeabilities used in figures 9A-H are listed in table 5 along with computed thermal Peclet numbers (PeT)for the fault zone and matrix.

magnitude (from 10-15 m2 to 10-14 m2) has a profound effect on the thermal structureof the basin (fig. 9D) and the faulted upper plate. Temperatures decrease by 200°Calong the down flow limb of the high-angle fault zone relative to conductive conditions(fig. 9H). The thermal Peclet number for scenario D is about 1.19. Within 300 m of theEarth’s surface, temperatures exceed 250oC along the upflow high-angle fault. Decreas-ing the permeability contrast between the shear zone and fault zone by one order ofmagnitude did little to change the computed temperature anomalies (fig. 9E).Allowing permeability to decay with depth in an exponential manner (Manning andIngebritsen, 1999; fig. 6F) produced pronounced and pervasive cooling in the upperplate rocks over most of the domain with a positive thermal anomaly occurring inisolated areas of the sedimentary basin. The thermal Peclet number for this simulationis quite high (3.0; equation 1b; Lz � 3 km) in the shallow crust where it was calculated.The locations of the positive thermal anomalies are controlled by water table topogra-phy. After 200,000 years, low geothermal gradient (11oC/km) conditions exist in theupper plate down to a depth of �3 km. If the simulation was extended for longer (106

years), these shallow cooler conditions would propagate down to the shear zone. Lowpermeability fault zone scenarios represented by model runs G and H both result inconductive thermal conditions with Peclet numbers (1a) between 0.013 and 0.001.

Lateral temperature variations across the shear zone are presented in figure 10 fortwo of the scenarios (A and D; table 5); in which the high-angle fault permeability wasincreased from 10-15 (A) to 10-14 (D). The location of the lateral temperature profile isshown in figure 4. A modest cooling trend is observed when the high-angle faults havea permeability of 10-15 m2 (fig. 10A). This modest lateral cooling trend across the shearzone results from both changes in depth to the Earth’s surface under conduction

Fig. 10. Lateral, transient variations in temperature variations across the shear zone. The location ofthis profile with the sub-horizontal fault zone is shown in figure 4. The numbers indicate time in thousandsof years. The computed temperatures correspond to model simulations A and D shown in figures 9A and 9D.The permeabilities used for these two simulations are listed in table 5.

dominated conditions. After 200,000 years, convective anomalies occur in figure 10Awith modest cooling and heating occurring near the down flow (� -5oC) and up flow(� �10oC) sides of the sub-horizontal fault. The maximum temperature change acrossthe shear-zone is about 15oC. The lateral thermal conditions illustrated in figure 10Aare similar to all of the scenarios, which included a relatively low permeability faultzone (scenarios B-C, F-H in table 5). Increasing the permeability to 10-14 m2 results in alateral cooling trend of over 100°C (fig. 10D). After 200,000 years, the down flow sideof the sub-horizontal fault zone dropped in temperature from 430oC to about 200oC,and the upflow portion of the sub-horizontal fault zone dropped to 340°C.

Transient temperature changes at different points along the sub-vertical fault andsub-horizontal fault zone (see fig. 4 for location of monitoring points) suggests that thesystem has approached, but not reached, equilibrium conditions after 200,000 yearsfor scenarios A and D (fig. 11). For the base model run, temperatures within thesub-horizontal fault zone gradually increase while temperatures decrease and increasealong the down flow and up flow high-angle faults, respectively (fig. 11A). Increasingthe permeability by one order of magnitude causes the discharge area along thehigh-angle fault to first heat up to a maximum temperature of 400oC after about 50,000years before beginning to cool (fig. 11D). The recharge fault region cooled exponen-tially from 320oC down to less than 100oC.

Fluid isotopic composition.—Infiltration of meteoric water from the high elevationcatchment areas into the normal fault system commonly resulted in interaction of low�18O and low �D meteoric water with rocks in the high-angle faults and shear zone thatare undergoing dynamic recrystallization. For the base model run, anomalously low

Fig. 11. Transient changes in temperature at observations points in fault and shear zones. The locationof these points along the fault zone are shown in figure 4. The computed temperatures correspond to modelsimulations A and D shown in figures 9A and 9D. The permeabilities used for these two simulations are listedin table 5.

�18O fluid compositions at depths are restricted to the high-angle faults. Meteoricfluids with �18O values as low as –13 permil enter the shear zone from the down flowhigh-angle fault (fig. 12A). Fluids become enriched as they move across the shear zone.Fluid-rock isotope exchange drives fluid oxygen isotopic composition up to -6 permil.Isotope transport in the fault zone is dominated by advection with the isotope Pecletnumbers on the order of 106 (table 5). Relatively high temperatures associated withthis conduction dominated system lead to relatively high fluid-rock isotope exchangereaction rates. The Damkohler number for this system is on the order of 1.0 (table 5).Decreasing the contrast in high-angle faults /shear zone permeability results insignificant leakage into the shear zone (fig. 12B), especially where the sub-vertical faultintersects the shear zone on the right side of the solution domain. The Damkohler andPeclet numbers are similar to table 5A for this scenario. Increasing the permeability ofthe upper plate crystalline rocks causes low �18O meteoric fluids to leak out of the

Fig. 12. Computed fluid oxygen isotope composition ‰ after 200,000 years. The permeability of thefault zone, shear zone, and upper plate rocks used in these simulations are listed in table 5 along with theisotopic Peclet and Damkohler numbers.

high-angle fault and move laterally across the upper 5 km of the upper plate rocks (fig.12C). As a result, the lowest �18O fluid compositions in the shear zone were only -5permil. Increasing the permeability of the fault zone by one order of magnitude (fig.12D) results in focused flow in the high-angle faults similar to the situation shown infigure 12A. Under these conditions, �18O of fluids in the shear zone are as low as -15permil (fig. 12D). This is due, in part, to reduction in the temperature dependentreactions rates (fig. 13). Cooler temperatures induced by higher permeability condi-tions for scenarios C and D results in low Damkohler number (about 10-3; table 5).Increasing the permeability of the shear zone by one order of magnitude causesdepleted �18O fluids to migrate laterally across the shear zone (fig. 12E). Using anexponential permeability model for crustal rocks in the upper plate results in pervasivemigration of meteoric fluids in the upper 3 km of the crust (fig. 12F) similar to figure12C, but fluid penetration is not as deep in this case. Much of the meteoric fluidsremain in the upper plate although some are not focused into the fault system.Meteoric fluid composition in the shear zone never is less than -6.5 permil. Therelatively low flow rates (Peclet Numbers decreased to 104 to 105) and high reactionrates (Damkohler numbers on the order of 101 to 102) associated with low permeabilityfault zones of scenarios G and H results in relatively small shifts in fluid isotopiccomposition within the fault zone. This is because fluids quickly equilibrate to localrock isotopic composition.

Rock isotopic composition.—The spatial distribution of rock isotopic exchange withinthe high-angle faults and shear zone is tied to temperature, fluid composition, andtime-integrated fluid flux. The kinetically controlled reaction rates decrease as the rateof convective transport increases the cooling effects of groundwater flow (fig. 13).Figure 14 presents computed oxygen isotopic composition of the rocks for all scenarios

Fig. 13. Relationship between reaction rate (kA� ) and temperature within the fault zone rocks. Thereaction rate is described in equations 17-23 in the Appendix.

that produced significant (� 2‰) fluid-rock isotope exchange. For the base modelrun (fig. 14A), the alteration in the high-angle faults began when fluid temperaturesreach 250oC. After 200,000 years, the sub-horizontal fault zone isotopic compositiondeclines from about 11 permil to -0.5 permil in the vicinity of the high-angle fault alongthe recharge side of the system. As the fluid evolves to higher �18O values along theflow path, the amount of fluid-rock isotopic exchange declines. At the discharge end ofthe sub-horizontal fault zone, the alteration is only 5.0 permil and �18O fluid attainsabout -4 permil. Alteration continues moving up the discharge high-angle fault untiltemperatures decline below 300oC and fluid isotopic composition is about -0.5 permil.If a -18 permil fluid was allowed to equilibrate with the fault zone mineral assemblageat 425oC, the rock would have an isotopic composition of about -15.8 permil. Thus,much more time is required for the fluid to completely alter the rock to an isotopiccomposition consistent with equilibrium values. Reducing the contrast in permeabilitybetween the high-angle faults and the shear zone to one order of magnitude (fig. 14B)enhances the amount of advection-controlled alteration in the shear zone and de-creases the alteration along the up flow side of the high-angle fault. Lower tempera-tures associated with relatively permeable upper plate rocks reduced the volume ofrock in the fault zone undergoing isotopic enrichment (fig. 14C). The Damkohler

Fig. 14. Computed rock isotopic compositions (‰) after 200,000 years for different representations offault zone, shear zone and upper plate rock permeability within the Shuswap metamorphic core complexflow system. The permeabilities used in these units is listed in table 5. Model runs D, G, and H in table 5 didnot produce significant (2 ‰ �) changes in rock isotopic composition and were not plotted here.

number did not change much from the previous two models, however. The coolingthat resulted from increasing the permeability of the fault zone by one order ofmagnitude had a profound effect on reaction rates. The Damkohler number is nowabout 4000 times less than the base model run (table 5). This is because rocktemperatures in the shear zone area have decreased to about 200 oC, which is too lowto sustain vigorous fluid-rock isotope interactions (fig. 13). The maximum alteration isonly 1.5 permil (from 11 to 9.5 ‰). Increasing the permeability of the shear zone andupper plate rocks to 10-17 m2 (fig. 14E) results in modest isotope exchange (from 11 to2 ‰) occurring near the down flow (left) side of the sub-horizontal fault zone. Theexchange begins to occur once temperatures reach 300 oC in the downflow high-anglefault and shear zone. Surprisingly, the Damkohler number is still low for this scenarioindicating significant introduction of fluids from outside the faults. An exponentialdecay of permeability with depth (fig. 14F) results in vigorous fluid-rock isotopeexchange patterns similar to the base case. The patterns of isotope exchange weresymmetrical in the fault zone with maximum amount of exchange occurring at thedownflow edge of the shear zone (fault rock isotopic composition of 5 ‰). This islargely due to the higher temperatures that occur within the shear zone rocks.Decreasing fault permeability below 10-15 m2 (table 5, G and H) results in highDamkohler numbers (between 101 and 102) but the time integrated fluid fluxes aretoo low to alter the rocks over a 200,000 year time frame. If simulation was run for alonger time (perhaps 2 million years) scenario G would have also produced morenoticeable alteration. However, this time frame is likely too long for an individualsegment of the shear zone to remain active in such a rapidly extending region as theShuswap core complex.

The complexity of interactions between flow rates, temperatures, and fluid-rockisotope exchange is further illustrated by considering lateral variations in computedrock isotopic composition for two scenarios (A and D) along the sub-horizontal faultzone (fig. 15). For the case of a relatively low permeability fault system (10-15 m2; fig.

Fig. 15. Lateral variations in rock oxygen isotope composition for simulations A and D of the sensitivitystudy. (‰). The numbers indicate time in thousands of years. The position of the lateral transect used infigure 15 is shown in figure 4. The permeability of the fault zone, shear zone, and upper plate rocks used inthese simulations are listed in table 5 along with the isotopic Peclet and Damkohler numbers.

15A), near isothermal conditions along the horizontal portion of the fault zone (fig.10A) resulted in lower rock isotopic composition along the recharge portion of thefault, where the rocks are exposed to isotopically light (-13 ‰) fluids. There is lessexchange down (hydraulic) gradient as the rocks see fluids sequentially enriched in18O. However, for the higher permeability case (10-14 m2; fig. 15D) fluids heat up asthey move laterally along the sub-horizontal fault (fig. 10D), resulting in higherreaction rates on the left side of the domain. Thus, maximum exchange rates, thoughmodest in absolute values, occur on the down gradient portion of the sub-horizontalfault zone. It is important to point out that the reaction fronts observed in one-dimensional studies of Bowman and Willett (1991) are not produced along thesub-horizontal zone shown in figure 15. This is due, in part, to the fact that the rates offluid-rock isotope exchange vary along the flow path and are slower or equal to the rateof advective transport. At 425 oC, the equilibration time would be on the order of about103 years. On this time scale, fluids migrate laterally over a large portion of the faultzone (about 1 km).

Effect of Surface AreaThe reactive surface area for fluid-rock isotope exchange can be calculated either

based on mineral grain diameter (Brantley and Mellott, 2000) or fracture density(Rimstidt and Barnes, 1980). For example, assuming a one meter fracture spacing, thereactive surface area is about 7.56E-5 m2/mole. For comparison, an aggregate ofanorthite grains with grain diameters of 0.35 mm result in an effective surface area ofabout 6.216 m2 /moles. (John Ferry, personal communication). The surface areas usedin our sensitivity study were varied for different lithologic units. We assumed arelatively close fracture spacing (25 cm; 0.0003 m2/mole) for the shear/fault zone and

Fig. 16. Effect of surface area on vertical profiles of rock oxygen isotope composition across shear zone.The permeabilties and surface areas used in these simulations are listed in table 6. All other parameters usedin these simulations are listed in tables 1-4. The location of the vertical profiles across the shear zonepresented are shown in figure 4. The shaded area denotes the location and width of the relatively highpermeability, sub-horizontal fault zone. The numbers denote time in thousands of years.

basin fill and a coarser spacing (5 m; 0.00001 m2/mole) for the upper plate, basement.In figure 16, we compare two additional simulations in which uniform surface areas of1.0E-5 (fig. 16I) and 0.2 (fig. 16J) m2/mole were compared in an attempt tounderstand how this poorly constrained parameter influences exchange patterns. Forthe simulations presented in figure 16, all other parameters are consistent with thebase run case (table 6). Assigning a relatively high sub-vertical surface area (fig. 16J)results in maximum rock isotopic exchange centered in the fault zone with values aslight as –10 permil. The vertical rock profile has a diffusional shape, which extendsoutside the higher permeability sub-horizontal fault zone (shade region in fig. 16J).Reducing the surface area to 0.00001 m2/mole resulted in lower absolute amounts ofexchange and also resulted in less symmetric exchange profiles (fig. 16I). The shape ofthe vertical rock oxygen isotope profile in figure 16I is more consistent with field datapresented in figure 3.

Effect of Isotopic Composition of Meteoric WaterWe also varied the oxygen isotopic composition of the infiltrating meteoric fluids

at the upper boundary between �18O -12 and -24 permil (table 6). All other parameterswere the same as those used in the base case (table 5). For the case of the moderately18O depleted meteoric recharge (fig. 17K, -12 ‰), the rock oxygen isotopic composi-tion declines to about -1.5 permil on the right side of the sub-horizontal fault zone. Onthe discharge-side of the sub-horizontal fault zone, the fluid isotopic compositionbecomes relatively enriched resulting in less depletion of the rock to about 3 permilafter 200,000 years. For the more depleted meteoric recharge (fig. 17L, -24 ‰), therock isotopic composition declines on the recharge side of the sub-horizontal faultzone to -4.0 permil and increases to �3 permil and the discharge and after 200,000years (about the same as in fig. 17K). In summary, the differences in compositionbetween the two simulations were less than a 1 permil for the left profile and less than 4permil for the right profile; much less than the differences in the initial isotopiccomposition of infiltration (12 ‰). This suggests that deuterium remains the mostreliable isotopic tracer for identifying the isotopic composition of meteoric recharge.

discussion and conclusionsDue to the abundance of oxygen isotope data, the Columbia River detachment

and neighboring crystalline rocks represents a well-characterized detachment systemwhere fluid flow models can be tested against measured isotopic compositions. Isotopeexchange patterns reflect the interplay among initial fluid composition of meteoricfluids and rock types, temperature, fluid flux, duration of exchange, permeability, andsurface area as well as scale and form of fluid pathways (surface area for isotopicexchange). The rock isotope profiles presented in figure 17 resemble the mainfeatures of observed conditions presented in figure 3. The computed and observed

Table 6

Summary of sensitivity study model results in which surface area and recharge isotopiccomposition were varied

profiles depict a core zone of isotopic depletion within the shear zone which extendsoutward on the order of hundreds of meters. Future collection of isotopic data wouldbenefit from more closely spaced samples oriented both parallel and perpendicular tothe shear zone plane. Results are non-unique; different combinations of permeabilityconfigurations, surface areas, and initial fluid isotopic composition produce similarpatterns and shifts in rock isotope composition. Nevertheless, the model results placeimportant bounds on the permeability of upper crustal fault zones (less than 10-14 m2;probably around 10-15 m2) and crustal rocks (less than 10-17 m2). The relatively lowsurface areas which had to be used to match the degree of fluid-rock isotope exchangesupports the notion of a fracture dominated fluid flow system with fracture spacing onthe order of 0.25 (fault zone) to 5 m (unaltered crustal rocks). Clearly, field observa-tions at the Shuswap Metamorphic Core Complex indicate that there must be someareas where fluid-rock alteration occurs at the grain scale. However, on average,grain-scale fluid-rock isotope interactions can’t be occurring pervasively throughoutthe crustal rocks in this metamorphic core complex.

One interesting finding from this study is that relatively low-permeability faultsystems produce a conduction-dominated thermal regime and a lateral trend ofincreasing rock isotopic composition along the shear zone. Convection-dominated,higher permeability fault systems produce a decreasing lateral trend in rock isotopiccomposition across the shear zone and relatively little isotope exchange. The widelycited permeability-depth relationship of Manning and Ingebritsen (1999) does notproduce unique rock isotopic exchange patterns that could be easily distinguishedwhen compared to more idealized (constant valued) crustal permeability models. Saarand Manga (2004) noted that Manning and Ingebritsen’s permeability depth modeldidn’t provide a good fit to shallow (0.8 – 2 km) hydrologic, thermal, and seismic datawithin the Cascade Mountains of Oregon, USA. The reaction rates are sufficiently slow

Fig. 17. Effect of oxygen isotope composition of meteoric fluid on vertical profiles of rock isotopiccomposition. The permeabilities and isotopic composition of the meteoric recharge used in these simula-tions are listed in table 6. All other parameters used in these simulations are listed in tables 1-4. The locationof the vertical profiles across the shear zone presented is shown in figure 4. The shaded area denotes thelocation and width of the relatively high permeability, sub-horizontal fault zone. The numbers denote timein thousands of years.

that sharp reaction fronts are not preserved in the rock record. The large amount ofexchange between the fluid and rock reservoirs suggests that oxygen isotopes are notparticularly useful in identifying the isotopic composition of the recharge. Fortunately,hydrogen isotopes remain a useful tracer for this purpose due to the low concentra-tions of hydrogen in crustal rocks. The lateral rock isotopic composition away from thefeeder fault could be used to test different fault permeability models if sufficient rockoutcrops were available in the field.

The main limitations of the current model include: 1) the inability to representmineralization reactions that would reduce fault zone permeability; 2) fracture perme-ability is represented using a continuum assumption; and 3) there is a dearth ofappropriately sampled spatial isotopic data collected in most studies today to provideground truth for studies like these.

acknowledgmentsWe acknowledge access to the stable isotope laboratories at Universite de Lau-

sanne (T. Vennemann) and Stanford University (C. P. Chamberlain). Researchsupported by NSF-EAR 0106953 (C. Teyssier and M. Person), NSF EAR-0412509 (C.Teyssier and A. Mulch). We thank Lukas Baumgartner for his stimulating discussionregarding the complexity of fluid rock isotope exchange and to John Ferry for histhorough review of this manuscript.

Appendix

A.1 Scaling Analysis

The two-dimensional Peclet number (equation 1a) we used in this study is based on an energy balancerelationship presented by Bethke and Marshak (1990). We consider the ratio of downward heating rate of aninitially cool fluid flowing through an aquifer of width “b” which is warmed by lateral heat conduction:

b�fcfqz

�T�z

� ��T�x

vertical convection � lateral conduction (4)

where cf � fluid heat capacity�f � fluid densityT � temperatureb � fault zone width

qz � vertical groundwater flux

This approach assumes that vertical heat conduction is much less significant than in the horizontal direction.Indeed, we were motivated to develop this two dimensional Peclet number when we realized that aconventional Peclet number (equation 1b) produced a value of 53 for the base run which is much too highgiven the conductive dominated numerical solution seen in figure 9A.

We normalized the spatial derivatives in the above expression as follows:

�zLz

; � �x

5b; � �

where Lz � vertical distance along the sub-vertical fault zonez � elevation � dimensionless elevationx � horizontal distance� � dimensionless horizontal distanceT � temperature

Tmax � maximum temperature� � dimensionless temperatureb � fault zone width

We choose a width of 5b to characterize the length scale over which lateral heat conduction occurs becauseconduction is not confined to the fault zone but extends out into the country rock. We assumed that thedistance of convective anomaly would extend outside the fault zone should be twice the fault zone width inboth lateral directions. Substituting these variables into equation (1) yields:

b�fcfqz

Lz� ��

� � � �Tmax

5b � ��

�� (6)

Moving the convective terms to the numerator and the conductive terms in the denominator yields anexpression for our two-dimensional Paclet number for fault controlled heat transfer:

Pe �

5b2�fcfqzTmax� ��

� ��LzTmax� ��

��(7)

Canceling like terms and assuming that the normalized spatial derivatives are of the same order ofmagnitude leaves us with our two-dimensional Peclet Number in equation la:

Pe �5b2�fcfqz

�Lz(8)

A.2 Fluid Flow

In this study, we follow the approach of Cathles and Smith (1983) and Garven and Freeze (1984a) forrepresenting groundwater flow on geologic time scales. We solve the quasi- steady-state, variable-densitygroundwater flow given by:

�x ��og�f

�kxx

�h�x

� kxz

�h�z��

�z ��og�f

�kzx

�h�x

� kzz

�h�z�� rkzz

�og�f

where kxx, kzz, kxz, kzx � components of the permeability tensor in the x- and z directionsg � gravity constant

�f � fluid viscosity (�r � �o/�f)h � hydraulic head

�o � reference fluid density�r � Relative density [�r � (�f-�o)/�o]�f � temperature dependent fluid density

x,z � spatial coordinates

This equation can represent flow induced by fluid-density gradients as well as imposed water-table gradientsalong the top boundary. The equation can represent changes in crustal flow patterns associated withtransient changes in temperature but not changing head patterns. This implies that the flow system adjustsitself quickly to changes in fluid pressures relative to thermal processes. This is supported by analysis ofhydraulic diffusivity which is typically much higher than the thermal dispersivity.

Thermodynamic equations of state are required to compute the density and viscosity of ground water atelevated temperature, pressure, and salinity conditions. We used the equations of state of Haar and others(1984) that are capable of representing fluid density and viscosity up to 900 oC and 150 MPa for pure watersystems. For visualization purposes, we also solved a variable-density form of the stream function equation(Garven and others, 1993):

�x ��f�kxx

�k��

�x�

�k��

�z ��

�z ��f�kzx

�k��

�x�

�k��

�z �� g��r

�x(10)

where � � stream functionkxx, kzz, kxz, kzx � components of the permeability tensor in the x- and z directions

�k� � kxxkzz � kzxkzz

g � gravity constant�f � fluid viscosity�r � Relative viscosity [�r � (�f-�o)/�o]

x,z � spatial coordinates

For anisotripic porous media who’s principal directions are not aligned with the coordinate system, thecomponents of the permeability tensor are given by:

kxx � kmaxcos2� � kminsin2�

kzz � kmincos2� � kmaxsin2�

kzx � kxz � �kmax � kmax�cos � sin � (11)

where � � angle between the horizontal and the fault planekmax � maximum permeability in the direction of the fault plane (or bedding for sedimentary units)kmin � minimum permeability perpendicular to the fault plane (or bedding for a sedimentary unit).

A.3 Heat Transfer

Transient, conductive/convective heat transfer is represented in this study using the following tempera-ture based equation:

�x ��xx

�T�x

� �xz

�T�z��

�z ��zx

�T�z

� �zz

�T�z�� qx�fcf

�T�x

� qz�fcf

�T�z

� ��fcf � �1 � ��scs��T�t

where T � temperatureqx, qz � components of Darcy flux in x- and z-directions

cf � specific heat capacity of the fluidcs � specific heat capacity of the solid � porosity

�xx, �zx �xz �zz � are the components of the thermal conductivity-dispersion tensor of the porous medium

The Darcy flux used in the heat equation is computed using a variable density form of

qx � ��og�f�kxx

�h�x

� kxz

�h�z�

qz � ��og�f�kzx

�h�x

� kzz

�h�z�� kzz

�og�f

�r (13)

The components of the conduction-dispersion tensor are given by:

�xx � �fcfL

�q� � �fcfT

�q� � �f � �1 � ��s

�zz � �fcfT

�q� � �fcfL

�q� � �f � �1 � ��s

�zx � �xz � �L � T�qxqz

�q� (14)

where 1 � longitudinal dispersivityt � transverse dispersivity�q� � �qx

2 � qz2

�s, �f � thermal conductivity of the fluid (f subscript) and solid (s subscript) phases, respectively.

The heat and flow equations are formally coupled through the equations of state for fluid density andviscosity. However, the non-linearity is relatively weak and the two equations can be solved separately andsequentially while marching through time.

A.4 Isotope Fluid-Rock Exchange and Transport

Quantitative models of fluid rock isotopic exchange have been developed by a number of authorsincluding Bowman and Willett (1991), Bowman and others (1994), and Gerdes and others (1998). Here, weadopt a kinetic approach given by Bowman and others (1994):

�x �Dxx

�x� Dxz

�z ��

�z �Dzx

�z� Dzz

�z �� vx

�x� vz

�z�

�t�

Xf(15)

where Rf � fluid 18O/16O ratioRrk � bulk rock 18O/16O ratiox,z � spatial coordinates

t � timeXrk � fractional abundance of oxygen in the bulk rock phaseXf � fractional abundance of oxygen in watervx � qx/, groundwater velocity in the x-directionvz � qz/, groundwater velocity in the z-direction

The hydrodynamic dispersion tensor is given by:

Dxx �vx

�v� L �vz

�v� T � Dd

Dzz �vx

�v� T �vz

�v� L � Dd

Dxz � Dzx � �L � T�vxvz

�v� (16)

where Dxx, Dxz, Dzx, Dzz � components of dispersion-diffusion tensor,vx and vz � components of seepage velocity in the x- and z-directions (qx/ and qz/)

Dd � diffusion coefficient, is porosity�v � � absolute value of the groundwater velocity defined by �v � � �vx

2 � vz2.

Fluid-rock isotope exchange is described in our model using the following first order rate law:

dt� A� rrk�rkRf � Rrk� (17)

where �A � bulk rock surface area (m2/mole)rrk � bulk rock reaction rate (moles/m2-s) for the fluid-rock system.

Note that at equilibrium, dRrk/dt � 0 and we have:

rkRf � Rrk (18)

where rk � bulk fluid-rock equilibrium isotope exchange factor.

The bulk equilibrium fluid-rock isotope exchange factor is an averaged quantity and depends on thefractional abundance (fm) of the mth oxygen bearing mineral phases:

rk � �m�1

fmm (19)

where fm � fractional abundance of mth oxygen bearing mineral phasem � temperature dependent fluid-rock isotope exchange factor for the mth mineral phaseM � total number of oxygen bearing mineral phases for a given rock

Note that fm must sum to 1. An empirical expression has been developed from experimental data relatingthe fractionation factor for a given mineral phase to temperature. These take the general form (Cole andOhmoto, 1986):

103ln�m� �109cm

�T � 273.15�3 �106dm

�T � 273.15�2 �103em

�T � 273.15�� fm (20)

The fractional abundance of oxygen for rock (Xrk) and water (Xf) per unit volume is calculated from theindividual fractional abundances of oxygen in a given mineral phase:

Xrk ��1 � �

M �m�1

fm�m

vmGAWmO

GFWm(21)

Xf � GAWH2O

GFWH2O�f (22)

where GFWm � gram formula weight of the mth mineral phaseGFWH2

OO � gram formula weight of waterGAWO � gram atomic weight of oxygen

fm � fractional abundance of mth mineral phase�m � density of the mth mineral phase�m � stochometric coefficient of oxygen of the mth mineral phaseXf � mass fraction of oxygen in the water phase

Xrk � mass fraction of oxygen in the bulk solid phase � porosity

The isotope exchange rate (rk) between the bulk rock and fluid is a function of temperature:

rrk �1M �

Aomexp�� Eo

RT� (23)

where Aom � the preexponenital factor of the mth mineral phase (moles/m2-s)

Ema � the activation energy for the exchange reaction (kcal/mole)

R � the ideal law constant (kcal/mole-oK)T � temperature (oK)M � number of oxygen bearing mineral phases

In order to compute the initial fluid composition in equilibrium with subsurface mineral assemblages atelevated temperatures, the following relation is used:

�18Of � �18Ork � 1000�rk

18O� 1

18O � (24)

Where �18Ork is the isotopic composition of the rock in permil notation, and rk

18Ois the fractionation factor

for rock and fluid.The oxygen isotope composition of the fluid is then converted into the isotopic ratio using the definition ofthe permil notation:

18O� ��18Of

1000� 1�R

18O(25)

The value of the isotopic standard for oxygen (Rstd) is based on mean sea water composition (SMOW) andhas a value of 0.0020052.

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Isotope transport and exchange within metamorphic core complexes

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