Quantitative P-T paths from zoned minerals: Theory and tectonic applications

An analytical approach to the analysis of zoning profiles in minerals is presented that simultaneously accounts for all of the possible continuous reactions that may be operative in a given assemblage. The method involves deriving a system of simultaneous linear differential equations consisting of a Gibbs-Duhem equation for each phase, a set of linearly independent stoichiometric relations among the chemical potentials of phase components in the assemblage, and a set of equations describing the total differential of the slope of the tangent plane to the Gibbs free energy surface of solid solution phases. The variables are the differentials of T, P, chemical potentials of all phase components, and independent compositional terms of solid solution phases. The required input data are entropies, volumes, the compositions of coexisting phases at a reference P and T, and an expression for the curvature of the Gibbs functions for solid solution phases. Results derived are slopes of isopleths (dP/dT, dX/dT or dX/dP) which can be used to contour P-T diagrams with mineral composition.To interpret mineral zoning, T and P can be expressed as functions of n independent composition parameters, where n is the variance of the mineral assemblage. The total differentials of P and T are differential equations that can be solved by finite difference techniques using the derivatives obtained from the analytical formulation of phase equilibria.Results calculated from Zone I and Zone IV garnets of Tracy et al. (1976) indicate that Zone I garnets grew while T increased (T+72° C) and P decreased sharply (P–3 kb). Zone IV garnets zoned in response to decreasing T (T–17° C) and P (P–1 kb). A P-T path calculated for a zoned garnet from the Greinerschiefer series, western Tauern Window, Austria, also indicates growth during decompression (–3kb) and heating (T+15° C). A P-T path calculated for the Wissahickon schist (Crawford and Mark 1982) indicates growth during cooling and compression (T–25 C, P+2.2 kb). The calculated P-T paths differ according to structural environment and can be used to relate mineral growth to tectonic processes.     

Capillary Pressure Curves from Centrifuge Data: A Semi-Iterative Approach

The problem of determining capillary pressure functions from centrifuge data leads to an integral equation of the form _a ^x K(x,t)f(t)dt=g(x),x[a,b],(1)where the kernel K is known exactly and given by the underlying mathematical model. g is only known with a limited degree of accuracy in a finite and discrete set of points x ₁,...,x _M . However, the sought function f(t) is continuous. By the nature of the right-hand side, g(x), equation (1) is a discrete inverse problem which is ill-posed in the sense of Hadamard [9]. By a parameterization of the sought function, equation (1) reduces to a system of linear equations of the form Ac=b+ ,where b is the observation vector and A arises from discretization of the forward problem. is the error vector associated with b, and c contains the model parameters. The matrix A is usually ill-conditioned. The ill-conditioning is closely connected to the parameterization of the problem [23].In this paper a semi-iterative regularization method for solving the Volterra integral equation in the ₂-norm, namely, Brakhage's -method [2], is investigated. The iterative method is tested on synthetically generated, and on experimental data.     

On the derivation of the Buckley—Leverett model from the two fluid Navier—Stokes equations in a thin domain

We consider a two-phase incompressible immiscible flow, with neglected surface tension, in a thin domain. Using the method of asymptotic expansions with respect to the thickness of the domain, effective 1D equations are derived. Supposing that the fluids are strictly separated at t=0, we show that the derived equations equal the Buckley–Leverett equation for the saturation, in conjunction with the Reynolds law for each of the flowing phases. The fractional flow curve and corresponding relative permeabilities are determined explicitly and their heuristically observed properties verified.     

Compressional behaviour of CaNiSi2O6 clinopyroxene: bulk modulus systematic and cation type in clinopyroxenes

A single-crystal of composition CaNiSi₂O₆ (space group C2/c) was investigated at high pressure up to about 7.8 GPa by X-ray diffraction. The unit-cell parameters were measured at 18 different pressures. The P-V data were fitted by a third-order Birch-Murnaghan equation of state V₀=435.21(1) ų, K ₀=117.6(3) GPa and K^=6.4(1). The linear axial compressibilities _a, _b, _c and a sin are 2.14(1), 3.00(1), 2.43(1) and 1.63(1) × 10–3 GPa^–1. Comparing the compressibility data with other CaM1Si₂O₆ pyroxenes we suggest that the empirical K × V = constant relationships are followed in C2/c pyroxenes only if the same valence electron character is shared.     

The Internal Energy of a PV = RT Gas: A Univariable or Multivariable Function

Historically, the characterization of the internal energy of a simple gas is based on free expansion experiments and imprecise use of the word function, which is rigorously defined in mathematics. Univariable equations of state show that the internal energy of simple monatomic, diatomic, and polyatomic gases can be expressed as a function of temperature only. However, multivariable equations of state derived from composite functions confirm that the internal energy of these gases can in each situation also be expressed as a function of pressure and volume only. It is essential that the mathematical definition of the word function be adhered to in science because it is fundamental for the formulation of the calculus, a mathematical tool essential for solving a variety of thermodynamics problems.     

Dependency of unit shaft resistance on in-situ stress: Observations derived from collected field data

In this study, a database comprised of 30 pullout pile load tests was collected from geotechnical literature and analyzed to investigate the dependency of unit shaft resistance on effective vertical stress. The collected database consists of steel pipe, timber, and concrete piles, with varying normalized penetration depth with respect to pile diameter, driven into loose to very dense sand. Different correlations for the uplift lateral earth pressure coefficient K, Bjerrum-Burland ratio , and the average unit shaft resistance f _ave were derived using different assumptions. A comparison between measured and predicted capacities of the collected piles using the developed correlations indicated that the assumption of values of K and that were constant with depth did not provide a reasonable fit for the measured capacities of the collected piles and thus this assumption is inappropriate. The best correlations for K and that yield a reasonable fit to the measured capacities of the collected piles were found to be functions of sand relative density, pile diameter, and level of effective vertical stress. This indicates that average unit shaft resistance does not reach a limiting value, but rather continues to increase with depth. Moreover, the correlations for K and in terms of effective stress revealed that average unit shaft resistance increases as pile diameter decreases and this increase depends on initial sand relative density. Comparisons of measured and predicted pullout capacities of the collected piles using the best-obtained correlations for K and were made and compared to predictionsobtained from other methods. On the basis of these comparisons, it is concluded that the correlations for K and in terms of effective stress give results comparable to those obtained from other methods, without stipulating limiting values for the average unit shaft resistance.     

Possible non-equilibrium oxygen isotope effects in mantle nodules,an alternative to the Kyser-O'Neil-Carmichael18O/16O geothermometer

Kyser, O'Neil, and Carmichael (1981, 1982) measured the ¹⁸O values of coexisting minerals from peridotite nodules in alkali basalts and kimberlites, interpreting the nodules as equilibrium assemblages. Using Ca-Mg-Fe element-partition geothermometric data, they proposed an empirical¹⁸O/¹⁶O geothermometer: T(°C)=1,151–173–68 ², where is the per mil pyroxene-olivine fractionation. However, this geothermometer has an unusual crossover at 1,150 °C, and in contrast to what might be expected during closed-system equilibrium exchange, the most abundant mineral in the nodules (olivine) shows a much greater range in ¹⁸O (+4.4 to +7.5) than the much less abundant pyroxene (all 50 pyroxene analyses from spinel peridotites lie within the interval +5.3 to +6.5). On ¹⁸O-olivinevs. ¹⁸O-pyroxene diagrams, the mantle nodules exhibit data arrays that cut across the ¹⁸O=zero line. These arrays strongly resemble the non-equilibrium quartzfeldspar and feldspar-pyroxene ¹⁸O arrays that we now know are diagnostic of hydrothermally altered plutonic igneous rocks. Thus, we have re-interpreted the Kyser et al. data as non-equilibrium phenomena, casting doubt on their empirical geothermometer. The peridotite nodules appear to have been open systems that underwent metasomatic exchange with an external, oxygen-bearing fluid (CO₂, magma, H₂O, etc.); during this event, the relatively inert pyroxenes exchanged at a much slower rate than did the coexisting olivines and spinels, in agreement with available exchange-rate and diffusion measurements on these minerals. This accounts for the correlation between ¹⁸O pyroxene-olivine and the whole-rock ¹⁸O of the peridotites, which is a major difficulty with the equilibrium interpretation.Contribution No. 3978, Publications of the Division of Geological and Planetary Sciences, California Institute of Technology     

Use of Pitzer Equations to Examine the Formation of Mercury(II) Hydroxide and Chloride Complexes in NaClO<Subscript>4</Subscript> Media

The thermodynamic stability constants for the hydrolysis and formation of mercury (Hg²⁺) chloride complexes

Heat capacity of minerals in the system Na2O-K2O-CaO-MgO-FeO-Fe2O3-Al2O3-SiO2-TiO2-H2O-CO2: representation,estimation, and high temperature extrapolation

A revised equation is proposed to represent and extrapolate the heat capacity of minerals as a function of temperature: C _P=k₀+k₁ T ^–0.5+k₂ T ^–2+k₃ T ^–3 (where k₁, k₂0).This equation reproduces calorimetric data within the estimated precision of the measurements, and results in residuals for most minerals that are randomly distributed as a function of temperature. Regression residuals are generally slightly greater than those calculated with the five parameter equation proposed by Haas and Fisher (1976), but are significantly lower than those calculated with the three parameter equation of Maier and Kelley (1932).The revised equation ensures that heat capacity approaches the high temperature limit predicted by lattice vibrational theory (C _P=3R+²VT/). For 16 minerals for which and have been measured, the average C _Pat 3,000 K calculated with the theoretically derived equation ranges from 26.8±0.8 to 29.3±1.9 J/(afu·K) (afu = atoms per formula unit), depending on the assumed temperature dependence of . For 91 minerals for which calorimetric data above 400 K are available, the average C _Pat 3,000 K calculated with our equation is 28.3±2.0 J/(afu·K). This agreement suggests that heat capacity extrapolations should be reliable to considerably higher temperatures than those at which calorimetric data are available, so that thermodynamic calculations can be applied with confidence to a variety of high temperature petrologic problems.Available calorimetric data above 250 K are fit with the revised equation, and derived coefficients are presented for 99 minerals of geologic interest. The heat capacity of other minerals can be estimated (generally within 2%) by summation of tabulated oxide component C _Pcoefficients which were obtained by least squares regression of this data base.     

Non-riemannian and fractal geometries of fracturing in geomaterials

The mechanism of earthquakes is presented by use of the elastic dislocation theory. With consideration of the continuous dislocation field, the general problem of medium deformation requires analysis based on non-Riemannian geometry with the concept of the continuum with a discontinuity (no-more continuum). Here we derive the equilibrium equation (Navier equation) for the continuous dislocation field by introducing the relation between the concepts of the continuous dislocation theory and non-Riemannian geometry. This equation is a generalization of the Laplace equation, which can describe fractal processes like diffusion limited aggregation (DLA) and dielectric breakdown (1313). Moreover, the kinematic compatibility equations derived from Navier equation are the Laplace equations and the solution of Navier equation can be put in terms of functions which satisfy the biharmonic equation, suggesting a close formal connection with fractal processes. Therefore, the relationship between the non-Riemannian geometry and the fractal geometry of fracturing (damage) in geomaterials as earthquakes can be understood by using the Navier equation. Moreover, the continuous dislocation theory can be applied to the problem of the earthquake formation with active folding related with faulting (active flexural-slip folding related to the continuous dislocation field).     

A method for estimating earthquake occurrence probability using first- and multiple-order Markov chain models

It is valuable in earthquake prediction to determine the occurrence probability of major earthquakes by making use of data obtained from precursory phenomena up to the time of the evaluation. In this study, the time evolution of the state determined by earthquakes and precursory phenomena was modelled using Markov chains. Various probabilities suitable for earthquake prediction were derived from the transition probability of the Markov chain with a chosen length of memory time. As an example, earthquake sequence records for northern China, which covered a period of about two thousand years, were examined and the results were also obtained from modern scientific observations of the radon anomaly which covered a period of about 10 years.Assuming moderate-sized earthquakes of two magnitude ranges 4 3/4 M 5 3/4, 6 M 6 3/4 as precursors to large earthquakes of a magnitude range, 7 M 8 1/2, transition probabilities were calculated for a time interval from 2 to 40 yr. The results showed that the precursory time of moderate-sized earthquakes is mainly distributed in a time span of around several years and that the earthquake occurrence probability is considerably large when the precursory earthquakes occur successively. Furthermore, it was shown that a larger moderate-sized earthquake (4 3/4 M 5 3/4) is a more effective precursor than an entire moderate-sized earthquake (4 3/4 M 6 3/4).Second, a multiple precursor case was tried by means of simulation based on the radon anomaly data obtained during a limited observation period. Simultaneous occurrence of two precursors makes the earthquake occurrence probability increase by 1.5–2.0 for a reasonable choice of a mean recurrence interval of the radon anomaly compared with the case where only a moderate-sized earthquake was treated as the precursor. However, the probability is much the same if the average recurrence interval of the radon anomaly is the same through time, including the preparatory period before the earthquake.     

Kinetics and mechanisms of the reaction of zoisite to anorthite under hydrothermal conditions: reaction phenomenology away from the equilibrium region

The kinetics and mechanisms of the dehydration reactions of zoisite have been studied at 635°–792° C, 1–2 kbar. The equilibrium reaction does not occur and is replaced by metastable reactions involving the formation of gehlenite and a calcium tri-octahedral mica, instead of corundum: zoisite anorthite+grossular+gehlenite +calcium 3T mica+H₂O.The experimental data can be interpreted by zero-order equations dX _An/dt=k (X _An=fractional extent of reaction, t=time, k=zero-order rate constant). These relations hold for variations in P, T, A _initial(the initial surface area of zoisite) and also in the presence of seed crystals, which enhance the reaction rate. No induction period is evident and only at advanced stages of reaction are sharp decreases observed in the rate, which are attributed to physical affects (shrinking particles, armouring). SEM studies show that dissolution of zoisite is anisotropic, occurring preferentially parallel to the crystallographic b-axis, with the result that a characteristic sawtooth etch structure develops. Garnet grows as euhedral crystals located in cavities or on teeth of dissolving zoisite, whereas anorthite forms as clusters of coalescing grains which spread over and enclose the zoisite. In seeded runs, garnet growth initiates on both seeds and on zoisite surfaces whereas anorthite growth is more closely tied to the seeds, resulting in the development of clusters of smaller grains.The experimental evidence favours dissolution and nucleation-controlled growth as rate-determining processes. The preservation of zero-order kinetics in the face of shrinking particles is attributed to the anisotropic dissolution mechanism, which effectively preserves a constant reaction interface. The rate effects of nucleation appear to accord with the classic model in which growth of crystal layers is initiated by the formation of coherent nuclei.The temperature dependence of rate constants reflects both thermally activated Arrhenius-type behaviour and the rate-depressing influences of approach to equilibrium. Similarly pressure affects on reaction rate can be interpreted in terms of competition between rate enhancement due to pressure increase and rate-depression accompanying the approach to equilibrium. Although the equilibrium-approach effects accord with current treatments of reaction kinetics, a problem exists in deriving an exact relation coupling dissolution and nucleation rate control. Consequently an overall-reaction rate equation, such as that of Fisher and Lasaga (1981), is only partially successful in interpreting the temperature dependence of rates. The data suggest that the surface reaction equation of Wood and Walther (1983) only applies when nuclei are present.     

Effect of grossular-content in garnet on the partitioning of Fe and Mg between garnet and biotite

In contrast to Ferry (1980) (X _Ca)-values in garnet even lower than 0.1 have a significant effect on the calculated equilibrium temperature using the experimental calibration of the Fe and Mg paritioning between garnet and biotite. Garnet compositions and Mg/Fe — distribution coefficients from samples of the Eoalpine staurolite — in zone in the southern Ötztal are related by the quadratic regression equation: InK _D= -1.7500 (±0.0226) + 2.978 (±0.5317)X _Ca ^Gt -5.906(±2.359)(X _Ca ^Gt )² Temperatures derived by the Ferry and Spear (1978) calibration using chemistry — correctedK _D values are petrologically realistic.Analysis of our data supports non ideal mixing of grossular with almandine — pyrope solid solution. The derived excess mixing energies are quite small for the almandine — pyrope solution (W _FeMg= –133 cal/mole) and about +2775 cal/mole for the difference between pyrope-grossular and almandine-grossular solutions (W _MgCa —W _FeCa) at metamorphic conditions of 570° C and 5,000 bar. The mixing parameters proposed by Ganguly and Saxena (1984) are not confirmed by our data as they would result in significantly lower temperatures.     

Unilateral ARMA processes on a square net by the herringbone method

Because multidimensional ARMA processes have great potential for the simulation of geological parameters such as aquifer permeability, it was important to resolve which of two proposed alternative methods should be used for determining the two-dimensional weighting parameter, , for a unilateral ARMA (1, 0) process on a square net. Practical simulations demonstrates that the correct formulation is: =₁₀/(1+ ₁₀ ² where _r,s is the correlation between lattice points at lagsr and s. When the simulations are performed with correlations of 0.8 or more a residual bias was detected which was found to be caused by a difference in the variance between the one- and two-dimensional models. This can be rectified by modifying the two- dimensional model as follows: z_ij=(z_{i–1, j} + z_{i, j–1}) + a_ij where ²=1/(1 + ₁₀ ² ).     

On the maximum width of oil stringers under hydrodynamic flow conditions

An analysis is presented of the maximum thickness of a stationary buoyant oil-mass, trapped under an angled incline, when subjected to hydrodynamic, surface tension and buoyancy forces. For high water-flow speeds down the aquifer, with upward buoyancy forces dominantly combating hydrodynamic pressure, it is shown that the maximum oil thickness occurs at about 60% of the length of the oil stringer measured from the upward end. The length of the oil stringer then is roughly proportional to the square root of the oil-mass contained, as is the maximum thickness. For low water-flow speeds, in which buoyancy and surface tension are dominantly balanced (with only lesser contributions from hydrodynamic pressure), the oil length is effectively constant, whereas the maximum thickness grows proportionately to the 3/4 power of the contained oil mass at low oil masses, and proportionately to the oil mass at high mass values. As the water-flow velocity increases, the shaping of the oil stringer shifts from the small bubble form to the long oil stringer form. Analytic formulae are given to provide approximate methods from which to estimate oil and gas accumulations under more complex conditions.     

Aluminous orthopyroxene: Order-disorder,thermodynamic properties,and petrologic implications

Orthopyroxene has two tetrahedral sites, designated A and B, and two octahedral sites, M1 and M2. Crystallographic studies of synthetic and natural orthopyroxenes (opx) suggest that the tetrahedral Al is ordered nearly completely in the B site, but the octahedral Al disorders between M1 and M2 sites with a preference for M1. If the aluminum avoidance principle is obeyed, then the tetrahedral Si-Al ordering limits the Al substitution in opx to 25 mol%, thus leading to an end-member stoichiometry of Mg₃Al₂Si₃O₁₂ instead of MgAl₂SiO₆.The enthalpy of formation of these two components has been deduced from the available phase equilibrium data. The thermodynamic properties of the opx solid solution approximates ideal solution behavior more closely when treated in terms of the components Mg₄Si₄O₁₂(QEn)-Mg₃Al₂Si₃O₁₂(Py) than when expressed in terms of the components Mg₂Si₂O₆-MgAl₂SiO₆. A model has been developed for the octahedral disordering of Al as function of temperature and composition. These data enable calculation of the configurational entropy and molar entropy of Al-opx; distinction has been made between the cases of completely random mixing of Al and Si in the tetrahedral B site, and of random mixing without violation of the aluminum avoidance principle. The second model yields entropy of the Mg₃Al₂Si₃O₁₂ end member which agrees almost exactly with the value derived from phase equilibrium data. The partial molal entropies of the Orthopyroxene components QEn and Py can be derived from these data; their implications with respect to the P-T slopes of Al₂O₃ isopleths for the equilibrium of Orthopyroxene with forsterite and spinel/garnet have been discussed.     

The genesis of emeralds and their host rocks from Swat,northwestern Pakistan: a stable-isotope investigation

Emerald deposits in Swat, northwestern Pakistan, occurring in talc-magnesite and quartz-magnesite assemblages, have been investigated through stable isotope studies. Isotopic analyses were performed on a total of seven emeralds, associated quartz (seven samples), fuchsite (three samples) and tourmaline (two samples) from the Mingora emerald mines. The oxygen isotopic composition ( ¹⁸O SMOW) of emeralds shows a strong enrichment in¹⁸O and is remarkably uniform at + 15.6 ± 0.4 (1,n = 7). Each of the two components of water in emerald (channel and inclusion) has a different range of hydrogen isotopic composition: the channel waters being distinctly isotopically heavier (D = –51 to –32 SMOW) than the other inclusion waters (D = –96 to –70 SMOW). Similarly the oxygen isotopic compositions of tourmaline and fuchsite are relatively constant ( ¹⁸O = + 13 to + 14 SMOW) and show enrichment in¹⁸O. The ¹⁸O values of quartz, ranging from + 15.1 to + 19.1 SMOW, are also high (+ 16.9 ± 1.4 1, n = 7). The meanD of channel waters measured from emerald (–42 ± 6.6 SMOW) and that of fluid calculated from hydrous mineralsD_calculated (–47 ± 7.1 SMOW) are consistent with both metamorphic and magmatic origin. However, the close similarity between the measuredD values of the hydroxyl hydrogen in fuchsite (–74 to –6 SMOW) and tourmaline (–84 and –69 SMOW) with pegmatitic muscovite and tourmaline suggests that the mineralization was probably caused by modified (¹⁸O-enriched) hydrothermal solutions derived from an S-type granitic magma. The variation in the carbon and oxygen isotopic composition of magnesite, locally associated with emerald mineralization, is also very restricted ( ¹³ –3.2 ± 0.7%, PDB; ¹⁸O + 17.9 ± 1.27 SMOW). On the basis of the isotopic composition of fluid ( ¹³C –1.8 ± 0.7 PDB; ¹⁸O + 13.6 ± 1.2 SMOW calculated for the 250-550 °C temperature), it is proposed that the Swat magnesites formed due to the carbonation of previously serpentinized ultramafic rocks by a CO₂-bearing fluid of metamorphic origin.     

Analysis of A New Model for Unsaturated Flow in Porous Media Including Hysteresis and Dynamic Effects

A new model for unsaturated flow in porous media, including capillary hysteresis and dynamic capillary effects, is analyzed. Existence and uniqueness of solutions are established and qualitative and quantitative properties of (particular) solutions are analyzed. Some results of numerical computations are given. The model under consideration incorporates simple play-type hysteresis and a dynamic term (time-derivative with respect to water content) in the capillary relation. Given an initial water content distribution, the model determines which parts of the flow domain are in drainage and which parts are in imbibition. The governing equations can be recast into an elliptic problem for fluid pressure and an evolution equation for water content. Standard methods are used to obtain numerical results. A comparison is given between J.R. Philip's semi-explicit similarity solution for horizontal redistribution in an infinite one-dimensional domain and solutions of the new model.     

Triangle based interpolation

Triangle based interpolation is introduced by an outline of two classical planar interpolation methods, viz. linear triangular facets and proximal polygons. These are shown to have opposite local bias. By applying cross products of triangles to obtain local gradients, a method designated slant-top proximal polygon interpolation is introduced that is intermediate between linear facets and polygonal interpolation in its local bias. This surface is not continuous, but, by extending and weighting the gradient planes, a C¹ surface can be obtained. The gradients also allow a roughness index to be calculated for each data point in the set. This index is used to control the shape of a blending function that provides a weighted combination of the gradient planes and linear interpolation. This results in a curvilinear, C¹,interpolation of the data set that is bounded by the linear interpolation and the weighted gradient planes and is tangent to the slant-top interpolation at the data points. These procedures may be applied to data with two, three, or four independent variables.     

Characteristics and chronology of fracture — fluid infiltration in the Archean,Eye Dashwa Lakes pluton,Superior Province: evidence from H,C, O-isotopes and fluid inclusions

The Archean Eye Dashwa Lakes pluton (2672±24 Ma) has domains of mineralogically fresh isotropic granite, domains that have undergone bulk hydrothermal alteration, and at least eleven sets of sequential fracture arrays, each with distinctive mineral assemblages. Fresh granite is characterized by whole rock ¹⁸O=8.1 to 8.6 and primary magmatic quartz-feldspar (+1.3), quartz-biotite (5.2 to 5.4) and quartz-magnetite (+9.8) fractionations. Magmatic fluids had a calculated isotopic composition of ¹⁸O=7.9±0.5, and D=–80±5. These isotropic volumes of the granite have not experienced significant incursion of external thermal waters. Pegmatites, quartz-molybdenite veins, and phlogopite-muscovite coated fractures are sporadically distributed in the granite, and were precipitated from high-temperature magmatic fluids where ¹⁸O=8.0 to 10.3 and D=–80±5.The most abundant variety of fracture filling assemblage is epidote-quartz-chlorite±muscovite: fractures are bounded by domains of mineralogically similar bulk hydrothermal alteration of the granite. These minerals formed at 160 to 280° C, in the presence of NaCl, and NaCl-MgCl₂ brines (up to 25 wt% NaCl equivalent) of probable evolved marine water origin ( ¹⁸O=+0.4 to +3.8, D=–10 to –35) undergoing transient boiling. Upper plateau ⁴⁰Ar/³⁹Ar ages for the muscovite are 2650±15 Ma. Sequentially in the chronology of fracture-infiltration events, calcite-fluorite veins were deposited from boiling fluids at 340 to 390° C, isotopically characterized by ¹⁸O=4.7 and ¹³C=–5; and rare prehnite-chlorite lined fractures formed at 250 to 290° C. A generation of adularia-bearing veins precipitated at 140 to 230° C, from CaCl₂-NaCl brines, where ¹⁸O=0 to –6.5 and D=–10 to –30. Incremental ⁴⁰Ar/³⁹Ar age spectra on the K-feldspar yield an upper plateau of 1100 Ma. Subsequently, hematite developed during reactivation of earlier fractures, at 140 to 210° C in the presence of fluids characterized by ¹⁸O=–0.4 to –5.4 and D=–15 to –25. Arrays of open fractures partially occupied by gypsum and goethite reflect a fluid infiltration event at temperatures <50° C. Many of the earlier generations of fracture minerals have transgranular fracture infillings which record the presence of low temperature (88–190° C), hypersaline CaCl₂-NaCl brines. Narrow fractures lined with clays±calcite are sites for seepage of modern ground-waters. The isotopic signature of clay ( ¹⁸O=12 to 20, D=–80±5) plots near the line for modern kaolinites, confirming its formation in the presence of recent surface waters. Calcites coexisting with the clay minerals, and in fractured pegmatite show a common isotopic signature ( ¹⁸O=23±0.5, ¹³C=–13.6), indicating precipitation from modern groundwaters, where reactivated fractures have acted as conduits for infiltration of surface waters to depths of 200 m. Intermittent fracture-infiltration has occurred over 2.7 Ga. The early sequences of fracture-related fluid flow are interpreted in terms of devolatilization of the granite, followed by thermal contraction fracturing, incursion of marine water and convective cooling in the Archean. Hematite and adularia fracture fillings correspond to a stage when meteoric water infiltrated the volcanicplutonic terrain during Proterozoic and later times. Episodic fracture-fluid expulsion events may have been driven by seismic pumping, in response to magmatically and tectonically induced stresses within the Shield, with surface waters penetrating to depths of 15 km in the crust.