Element partitioning in calcite as a function of solution flow rate: a study on vein calcites from the Harz Mountains     

P. Möller  V. Lüders  J. Schröder  J. Luck 《Mineralium Deposita》1991,26(3):175-179

A semi-empirical treatment of isothermal element partitioning caused by flow rate-dependent calcite growth from hydrothermal solutions yields element/Ca ratios that are qualitatively similar to those observed in calcite bands of the Pb-Zn banded ores from the Harz Mountains, Germany. The comparison of the calculations with the analytical results suggests that flow rates varied between episodes of calcite precipitation as well as during formation of individual bands. Based on a flow rate-dependent element partition coefficient, changing element/Ca ratios in precipitates from a hydrotherm are therefore not necessarily indicative of changing compositions of the fluid. The variations in element/Ca ratios to be envisaged could be as much as a factor of three.Notation A defined by Eq. 8 - a, b individual values of any element in Eq. 1 - c concentration in moles/m³ - C ₀ initial concentration moles/m³ - i running parameter - F area of precipitation in m² - k _p rate constant of pth order reaction in s · m³/moles^p - R linear (one-dimensional) growth rate in moles/m² · s - p order of growth reaction - s distance from entry of solution in m - s ₀ vertical extension of a vein in m - t time in s - v flow rate of hydrothermal solution in m/s - v₀ standard flow rate in m/s - _r relative flow rate in multiple of v₀ - fraction of total precipitation - ₀ fraction of precipitation under reference conditions when the hydrothermal solution leaves the vein - defining the sign in Eq. 1 for elements that are en riched (= +1) or impoverished (= -1) - logarithmic partition coefficient in Eq. 10 - (R) logarithmic partition coefficient as a function of variable growth rate - [ ], { } concentration ratios of fluids and solids, respectively - EL/Ca calculated ratio of El/Ca in the calcite surface zone after Eq. 11  相似文献   

Transport of stable isotopes: I: Development of a kinetic continuum theory for stable isotope transport     

L. P. Baumgartner  D. Rumble III 《Contributions to Mineralogy and Petrology》1988,98(4):417-430

Equations are developed describing migration of stable isotopes via a fluid phase infiltrating porous media. The formalism of continuum fluid mechanics is used to deal with the problem of microscopic inhomogeneity. Provision is made explicitly for local equilibrium exchange of isotopes between minerals and fluids as well as for kinetic control of isotopic exchange. Changing characteristic parameters of transport systems such as porosity, permeability, and changes in modal proportions of minerals due to precipitation or dissolution are taken into account.The kinetic continuum theory (KCIT) is used to show how to deduce the dominant mechanism of mass transport in metasomatic rocks. Determination of the transport mechanism requires data on the spatial distribution of the reaction progress of exchange reactions between minerals and fluids involving at least two stable isotope systems such as ¹³C-¹²C and ¹⁸O-¹⁶O, for example. It is concluded that a combination of field and laboratory measurements of two or more stable isotope systems can be used to place constraints not only on the mechanism of transport but also on the magnitude of fluid fluxes, the identity of fluid sources, and the molecular species composition of fluids.Variables used C number of chemical components - D _i,j hydrodynamic dispersion tensor [m²/s] - D _i ^j diffusion coefficient matrix [m²/s] - D ^* apparent diffusion coefficient, includes sorption, dispersion, porosity and tortuosity [m²/s] - F number of degrees of freedom (variance) - f _i ^j mass or number of isotope j in fluid species i - g acceleration due to gravity [m/s²] - flow [m³/m² s] - j isotope species - j chemical element - k coefficient defined in Eq. 17 - K permeability of porous media [m²], [darcy] - L _ij phenomenological diffusion coefficient matrix [mol²/j m s] - m number of fluid species - n number of isotope exchange vectors - p number of phases - P pressure [Pa] - P ^* hydrological pressure potential [Pa] - R ^j ratio of concentration of rare to common isotope of element j - r number of restrictions imposed on system - s _i ^j mass or number of isotope j in one mole of mineral phase i - t time [s] - V volume [m³] - X _i number of moles of fluid species i in unit fluid volume - X _l number of moles of mineral l in unit volume - X _l ^j mole fraction of isotope j in one mole mineral l - X ^* mole fraction with respect to the whole system - z space coordinate [m] - z transformed space coordinate - z ^* location of an infiltration front [m] - _x–y ^j fractionation factor between two phases, x, y, for isotope j - porosity - fluid viscosity [Ns/m²] - fraction of porosity accessible to a specific mass transport mechanism - chemical potential [j/mole] - stoichiometric reaction coefficient - normalized reaction progress variable - mass, specific mass [gr/cm] - tortuosity - fluid velocity [m/s] - c common isotope - init initial - j isotope species - r rare isotope - tot sum of common and rare isotope - dif diffusive - disp dispersive - eq mineral composition in equilibrium with initial infiltration concentration of the fluid - f fluid - inf infiltrative - r rock, without fluid phase - samp sample - std standard - sys system - tot fluid and rock  相似文献   

Pore-pressure response due to penetration through layered media     

Derek Elsworth 《国际地质力学数值与分析法杂志》1992,16(1):45-64

A solution is developed for a point dislocation traversing a slab of saturated porous material under prescribed upper and lower hydraulic boundary conditions as an analogue to penetration in a layer of finite thickness. Pressure response is conditioned by geometrical parameters and those of dimensionless penetration rate U_D, dimensionless time following penetration initiation t_D, and dimensionless time following penetration arrest t′_D. The extended set of dimensionless parameters controlling the response makes parameter determination problematic and questionably non-unique. Pressure response in the proximity of a lower permeable or impermeable boundary is indistinguishable from the homogeneous case for coefficients of consolidation c in excess of 2 cm²/s. Below this threshold, penetration-generated pore pressures are visibly modified in the presence of a discrete boundary. In situ parameters inferred directly from pressure magnitudes, without due consideration for the influence of layering, may therefore be in considerable error. In the hydraulically visible range, the influence of layering on the generated tip pressures is apparent at a separation of the order of 1·5 cm for standard penetration. Although absolute pressure magnitudes are strongly modified in the presence of boundaries, dissipation rates remain relatively unaffected and are consistent with those recorded in the absence of boundaries. The monitoring of dissipation rates, post-arrest, is suggested as the most reliable and accurate method of extricating parameters, in situ.  相似文献   

Numerical modeling of three-dimensional contaminant migration from dissolution of multicomponent NAPL pools in saturated porous media     

K. Y. Lee  C. V. Chrysikopoulos 《Environmental Geology》1995,26(3):157-165

A three-dimensional model for contaminant transport resulting from the dissolution of multicomponent nonaqueous phase liquid (NAPL) pools in three-dimensional saturated subsurface formations is developed. The solution is obtained numerically by a finite-difference scheme, and it is suitable for homogeneous porous media with unidirectional interstitial velocity. Each dissolved component may undergo first-order decay and may sorb under local equilibrium conditions. It is also assumed that the dissolution process is mass transfer limited. The nonaqueous phase activity coefficients of the NAPL pool components are evaluated at each time step. The model behavior is illustrated through a synthetic example with a NAPL pool consisting of a mixture of TCA (1,1,2-trichloroethane) and TCE (trichloroethylene). The numerical solution presented in this work is in good agreement with a recently developed analytical solution for the special case of a single component NAPL pool. The results indicate the importance of accounting for the necessary changes in the organic phase activity which significantly affects the equilibrium aqueous solubility.Notation C liquid phase solute concentration (solute mass/liquid volume) (M L^–3) - C _s single component aqueous saturation concentration (solubility) (M L^–3) - C ^w equilibrium aqueous solubility (M L^–3) - D molecular diffusion coefficient (L² t ^–1) - D _e effective molecular diffusion coefficient (L² t ^–1) - D _x longitudinal hydrodynamic dispersion coefficient (L² t ^–1) - D _y lateral hydrodynamic dispersion coefficient (L² t ^–1) - D _z hydrodynamic dispersion coefficient in the vertical direction (L² t ^–1) - I() integer mode arithmetic operator - k local mass transfer coefficient (Lt ^–1) - k ^* average mass transfer coefficient (Lt ^–1) - L length - l _x ,l _y pool dimensions inx andy directions (L) - ll _x ,l _y x andy Cartesian coordinates of the pool origin (L) - M number of moles remaining in a pool (moles) - M initial number of moles (moles) - n finite-difference scheme time level - R retardation factor (dimensionless) - t time (t) - U _x average interstitial velocity (Lt ^–1) - x, y, z spatial Cartesian coordinates (L) - X dimensionless mole fraction - dimensionless activity coefficient - _w viscosity of water (=0.8904 cp at 25°C) - decay coefficient (t ^–1) - ^* tortuosity ( 1) - i,j, k finite-difference scheme grid indicators - p component number indicator - P total number of components - s pure single component - o nonaqueous phase - w aqueous phase  相似文献   

绿洲防护林系统的最优控制模式及其应用研究   总被引：3，自引：0，他引：3  

李自珍  程国栋  惠苍 《地球科学进展》2002,17(1):27-32

以河西地区绿洲防护林系统为研究对象，分析了防护林资源分布的时空特征及建群种的增长动态，运用生物控制理论，构建了防护林区生物资源管理的最大持续产量模型、生态经济意义下的最优控制模型及多资源种群控制模型。根据有关模型和试验观测结果，确定了防护林建群种的资源保护指标、生态经济意义下的最优种群水平和人工调控措施。该防护林主要建群种二白杨胸径的保护指标为 k/2＝18．22cm，在不同成本与价格比下计算了主要建群种二白杨胸径指标的个最优控制量。估算了防护林系统的生态需水量，其中农田生态需水量为 1 796 m³/hm²，固沙林和阻沙防护林生态需水量为57 100m³/hm²，并提出了相应的持续发展对策。  相似文献   

A distribution-free alternative to least-squares regression and its application to Rb/Sr isochron calculations     

Raymond G. Vugrinovich 《Mathematical Geology》1981,13(5):443-454

A distribution-free estimator of the slope of a regression line is introduced. This estimator is designated S_m and is given by the median of the set of n(n – 1)/2 slope estimators, which may be calculated by inserting pairs of points (X _i, Y_i)and (X _j, Y_j)into the slope formula S _i = (Y _i – Y_j)/(X _i – X_j),1 i < j n Once S _m is determined, outliers may be detected by calculating the residuals given by R_i = Y_i – S_mX_i where 1 i n, and chosing the median R_m. Outliers are defined as points for which |R_i – R_m| > k (median {|R _i – R_m|}). If no outliers are found, the Y-intercept is given by R_m. Confidence limits on R_m and S_m can be found from the sets of R_i and S_i, respectively. The distribution-free estimators are compared with the least-squares estimators now in use by utilizing published data. Differences between the least-squares and distribution-free estimates are discussed, as are the drawbacks of the distribution-free techniques.  相似文献   

The relation between c dimension and exchange components in micas     

Embaie Asmerom Ferrow 《Mineralogy and Petrology》1990,43(1):23-35

Summary A number of micas of varying compositions and polytypism have been selected from the literature for multiple linear regression analysis. The c dimension in micas is found to depend on the sizes of the interlayer cation, d_i, and tetrahedral cation, d_t, as well as on the hydroxyl content, [OH]. The regression equation obtained: c_r = 5.415 + 0.071[OH] + 2.098d_i + 2.335d_t with R² = 90.5%, shows that the three variables affect the c-axis dimension in the order d_t > d_i [OH]. Addition of 2- and 3-layer polytypes to the regression analysis reduces R² to 87.2%. Application of the regression analysis to synthetic Al-rich biotites from the literature shows that the amount of [A1^IVA1^VI]_1Y[Fe²⁺, MgSi]_–1y in solid solution is limited and always less than [A1^VIO]_1z[Fe²⁺, MgOH]_–1z (i.e. 0.35 > y z). The maximum value of the vector y in solution is slightly higher than that reported for natural Al-rich biotites.

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Die Beziehung zwischen der Gitterkonstante c und den Austauschkomponenten in Glimmern

Zusammenfassung Eine Anzahl von Glimmern unterschiedlicher Zusammensetzung und Polytypie wurde aus der Literatur für eine multiple lineare Regressionsanalyse ausgewählt. Es stellte sich heraus, dass in Glimmern die Gitterkonstante c von den Grössen des Zwischenschicht-Kations d_i und des tetraedrischen Kations d_t abhängt, ferner vorn Hydroxylgehalt, [OH]. Die erhaltene Regressionsgleichung c_r = 5,415 + 0,071 [OH] + 2,098d_i + 2,335d_t mit R² = 90,5% zeigt, dass die drei Variablen die Grösse der c-Achse in der Reihenfolge d_t > d_i [OH] beeinflussen. Der Einschluss von 2- und 3-Schicht Polytypen in die Regressionsanalysen verkleinert R² auf 87,2%. Die Anwendung der Regressionsanalysen auf synthetische Al-reiche Biotite aus der Literatur zeigt, der Betrag von [A1^IVA1^VI]_1y[Fe²⁺, MgSi]_–1y beschränkt und immer kleiner als [A1^VIO]_1z[Fe²⁺, MgOH]_–1z (mit 0,35 < y z) ist. Der Maximalwert des Vektors y in Lösung ist etwas grösser als jener, der für natürliche Al-reiche Biotite angegeben wurde.

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With 1 Figure  相似文献   

The stability of sublittoral, fine-grained sediments in a subarctic estuary   总被引：1，自引：0，他引：1  

CARL L. AMOS  T. F. SUTHERLAND†  J. ZEVENHUIZEN‡ 《Sedimentology》1996,43(1):1-19

The erodibility of natural estuarine sediments was measured in sit along a longitudinal transect of Manitounuk Sound, Hudson Bay, using the benthic flume Sea Carousel. Sedimentation processes along the transect varied from continuous, rapid, post-glacial sedimentation in the inner Sound, to glacial outcrops and seabed reworking of the outer Sound. The grain size and physical bulk properties reflect changes in depositional environment and correlate with sediment erosion threshold stress (τ_c), erosion rate (E), erosion type and still-water mass settling rate. There was a steady increase in τ_c (0·8–2·0 Pa) with distance down the Sound in parallel with the decreasing sedimentation rate (0·003–0·001 m yr^?1) and increasing sediment bulk density (1650–2010 kg m^?3). The near-surface friction coefficient varied up to 68° in proportion to the clay content of post-glacial material. Glacial sediments were characterized by variable results and generally higher friction coefficients. Seabed erosion in Sea Carousel began with surface creep of loose aggregates, pellets and organic debris. This was followed by Type I bed erosion at rates that varied between 0·0002 and 0·0032 kg m^?2 s^?1 (mean 0·0015). Type I peak erosion rate was inversely related to applied bed shear stress (τ_o). Type II erosion succeeded Type I, often after a broad transitional period. Simulations of suspended sediment concentration in Sea Carousel were made using four commonly used erosion (E) algorithms. The best results were obtained using Krone's dimensionless ratio relationship: E=M(τ_o/τ_c-1). Simulations were highly sensitive to the definition of erosion threshold with sediment depth [τ_c(z)]. Small errors in definition of τ_c(z) caused large errors in the prediction of suspended sediment concentration which far exceeded differences between the methods tested.  相似文献   

Validation and implications of an energy‐based bedload transport equation     

PENG GAO 《Sedimentology》2012,59(6):1926-1935

A recently developed bedload equation (Abrahams & Gao, 2006) has the form i_b = ωG^3˙4, where i_b is the immersed bedload transport rate, ω is the stream power per unit area, G = 1?θ_c/θ, θ is the dimensionless shear stress and θ_c is the associated threshold value for the incipient motion of bed grains. This equation has a parsimonious form and provides good predictions of transport rate in both the saltation and sheetflow regimes (i.e. flows with low and high θ values, respectively). In this study, the equation was validated using data independent of those used for developing it. The data represent bedload of identical sizes transported in various steady, uniform, fully rough and turbulent flows over plane, mobile beds. The equation predicted i_b quite well over five orders of magnitude. This equation was further compared with six classic bedload equations and showed the best performance. Its theoretical significance was subsequently examined in two ways. First, based on collision theory, the parameter G was related to the ratio of grain‐to‐grain collisions to the total collisions including both grain‐to‐grain and grain‐to‐bed collisions, P_g by P_g = G², suggesting that G characterizes the dynamic processes of bedload transport from the perspective of granular flow, which partly accounts for the good performance of the equation. Moreover, examining the ability of two common equations to predict bedload in gravel‐bed rivers revealed that G can also be used to simplify equations for predicting transport capacities in such rivers. Second, a simple dimensionless form of the equation was created by introducing B = i_b/ω. The theoretical nature of the term B was subsequently revealed by comparing this equation with both the Bagnold model and two commonly used parameters representing dimensionless bedload transport rates.  相似文献   

Ri-μi/μm-Ci dependent oblateness of deformed pebbles in the Baraitha conglomerate,Central India and tectonic implications     

Prakash P. Roday  Gopal Maheshwari  Narendra H. Vaghmarey 《Journal of Earth System Science》1990,99(2):321-338

Strain analysis of the Baraitha conglomerate is attempted by direct measurements on extracted pebbles and by micrometric analysis. The overall deformation is of flattening type, with thek value lower by more than half in the matrix than in the pebbles. The viscosity contrast between pebbles and matrix (μ _i/μ_m) is in the ratio of 2:1 and the bulk deformation appears to be strongly controlled by C_i (concentration of pebbles expressed as percentage). The total shortening (≃35%) in the Baraitha conglomerate is comparable with the shortening accomplished in the folding of the overlying Bijawar Group volcanosedimentary sequence. The bulk strain axesX _t, Y_t andZ _t, as determined from the analysis of the deformed conglomerate, are unsymmetrically oriented with reference to folds formed by oblique flexural-slip with neitherX _t norY _tcoincident with the fold hinges. The lack of transection of folds by cleavage again suggests flattening deformation. The extension in theY _tdirection is greater in the matrix than in the pebbles.  相似文献   

U–Pb zircon,geochemical and Sr–Nd–Hf isotopic constraints on age and origin of the intrusions from Wunugetushan porphyry deposit,Northeast China: implication for Triassic–Jurassic Cu–Mo mineralization in Mongolia–Erguna metallogenic belt     

Kui-Feng Mi  Rui-Bin Liu  Chun-Feng Li  Jian-Ping Wang  Run-Min Peng 《International Geology Review》2018,60(4):496-512

The Wunugetushan porphyry Cu–Mo deposit is located in northeastern China. The deposit lies within the Mongolia–Erguna metallogenic belt, which is associated with the evolution of the Mongol–Okhotsk Ocean. The multiple episodes of magmatism in the ore district, occurred from 206 to 173 Ma, can be divided into pre-mineralization stage (biotite granite), mineralization stage (monzogranitic porphyry and rhyolitic porphyry), and post-mineralization stage (andesitic porphyry). The biotite granite has (⁸⁷Sr/⁸⁶Sr)_i values of 0.704105–0.704706, ε_Nd(t) values of ?0.67 to ?0.07, and ε_Hf(t) values of ?0.4 to 2.8, yielding Hf two-stage model ages (T_DM2) 1250–1067 Ma, and Nd model ages of 1.04–0.96 Ga, indicating that the pre-mineralization magmas were generated by the remelting of Neoproterozoic juvenile crustal material. The monzogranitic porphyry has (⁸⁷Sr/⁸⁶Sr)_i values of 0.704707–0.706134, ε_Nd(t) values of 0.29–1.33, and ε_Hf(t) values of 1.0–2.9, yielding T_DM2 model ages of 1173–1047 Ma. The rhyolitic porphyry has (⁸⁷Sr/⁸⁶Sr)_i ratio of 0.702129, ε_Nd(t) value of ?0.21, and ε_Hf(t) values of ?0.5 to 7.1, T_DM2 model ages from 1269 to 782 Ma. These results show that the magmas of mineralization stage were generated by the partial melting of juvenile crust mixed with mantle-derived components. The andesitic porphyry has (⁸⁷Sr/⁸⁶Sr)_i ratio of 0.705284, ε_Nd(t) value of 0.82, and ε_Hf(t) values from 4.1 to 7.4, indicating that the post-mineralization magma source contained more mantle-derived material. The Mesozoic Cu–Mo deposits which genetically related to Mongol–Okhotsk Ocean were temporally distributed in Middle to Late Triassic (240–230 Ma), Early Jurassic (200–180 Ma), and Later Jurassic (160–150 Ma) period. The Middle Triassic to Early Jurassic Cu–Mo mineralization was dominated by Mongol–Okhotsk oceanic plate southeast-directed subducted beneath the Erguna massif. The Later Jurassic Cu–Mo mineralization was controlled by the continent–continent collision between Siberia plate and Erguna massif.  相似文献   

Cation diffusion in aluminosilicate garnets: experimental determination in spessartine-almandine diffusion couples,evaluation of effective binary diffusion coefficients,and applications   总被引：9，自引：1，他引：8  

Sumit Chakraborty  Jibamitra Ganguly 《Contributions to Mineralogy and Petrology》1992,111(1):74-86

We present new experimental data on diffusion of divalent cations in almandine-spessartine diffusion couples in graphite capsules in the P-T range of 14–35 kb, 1100–1200° C. The tracer diffusion coefficients of the major divalent cations, viz. Fe, Mg and Mn, retrieved from the multicomponent diffusion profiles, have been combined with earlier data from our laboratory at 29–43 kb, 1300–1480° C (Loomis et al. 1985) to derive expressions of the P-T dependence of the diffusion coefficients at fO₂ approximately corresponding to that defined by equilibrium in the system graphite-O₂. We review the conditions, discussed earlier by Cooper, under which the flux of a component in a multicomponent system becomes proportional to its concentration gradient (Fickian diffusion), as if the entire solvent matrix behaves as a single component, and also suggest a method of incorporating the thermodynamic effect on diffusion in the same spirit. Regardless of the magnitude or sign of the off-diagonal terms of the D matrix, it is always possible to define an effective binary diffusion coefficient (EBDC) of a component in a semi-infinite multicomponent diffusion-couple experiment such that it has the property of the Fickian diffusion coefficient, provided that there is no inflection on the diffusion profiles. It is shown that the success of Elphick et al. in fitting the experimental diffusion profiles of all components over a limited concentration range by a single diffusion coefficient is due to fortuitous similarity of the EBDCs of the components (Fe, Mg, Mn and Ca) in their diffusion couple experiments. In common metapelitic garnets showing compositional zoning, the EBDCs of the divalent cations do not differ from each other by more than a factor of 2.5. However, the EBDC of a component changes from core to rim by a factor of 3 to 12, depending on the composition. We suggest a method of volume averaging of the EBDC which should prove useful in approximate calculations of diffusion flux during relaxation of compositional zoning. The EBDC of Mn is found to reduce essentially to D _MnMn, the main diagonal term of the D matrix, and consequently can be calculated quite easily. Evaluation of EBDC of Fe, Mg and Mn in garnets from a prograde Barrovian sequence did not reveal any significant dependence on the extent of relaxation of garnet. The diffusion data have been applied to calculate the cooling rate of natural biotite-garnet diffusion couple from eastern Finland and diffusional modification of growth zoning in garnet in early Proterozoic Wopmay orogen, Canada. The results are in good agreement with geochronological and other independent constraints.Symbols and abbreviations a Radius of a spherical garnet crystal - BSE Back-scattered electron imaging - C Column vector of (n-1) independent components - D Diffusion coefficient matrix - D _ij An element of the diffusion matrix on the i th row and j th column - D _* ⁱ Tracer diffusion coefficient of component i - D(i) Effective interdiffusion coefficient (EIC) of various components in a multicomponent solution rich in the component i - D(i-j) Interdiffusion coefficient of components i and j in a binary solution - D _i (EB) Effective binary diffusion coefficient of component i in a multicomponent solution - D _i (EB:Ideal) D _i (EB) under condition of ideal thermodynamic mixing of the diffusing species - D _i (EB:thermo) Thermodynamic component of D _i(EB) - D _O ^A Interdiffusion coefficient at peak temperature T ₀ in the phase A - D ₀ Pre-exponential factor in an Arrhenius relation - EBDC Effective binary diffusion coefficient between a solute and a multicomponent solvent matrix - FEC Fixed edge composition model - EIC Effective interdiffusion coefficient - f _i Fugacity of component i - HM Hematite-magnetite oxygen fugacity buffer - kb Kilobars - P Pressure - Q Activation energy (enthalpy) of diffusion - Extent of relaxation defined as the difference between core and rim compositions normalized to the same difference in the initial zoning profile - R Gas constant - s Cooling rate - T ₀, T _Ch Peak temperature and characteristic temperature, respectively - t Time - VEC Variable edge composition model - V ⁺ Activation volume - W _ij Simple mixture interaction parameter between i and j - W _i(EB) Effective simple mixture interaction parameter of a component i in a multicomponent solution - _ij Margules interaction parameter between i and j - X _i Mole fraction of component i - _i Activity coefficient of component i - A dimensionless variable =D t/a ² - _ij Kronecker delta (i=j, _ij =1; ij, _ij =0) - Z_i Charge on the ion i  相似文献   

Spatial and multivariate analysis of geochemical data from metavolcanic rocks in the Ben Nevis area, Ontario   总被引：4，自引：0，他引：4  

E. C. Grunsky  F. P. Agterberg 《Mathematical Geology》1988,20(7):825-861

A study of the lithogeochemistry of metavolcanics in the Ben Nevis area of Ontario, Canada has shown that factor analysis methods can distinguish lithogeochemical trends related to different geological processes, most notably, the principal compositional variation related to the volcanic stratigraphy and zones of carbonate alteration associated with the presence of sulphides and gold. Auto- and cross-correlation functions have been estimated for the two-dimensional distribution of various elements in the area. These functions allow computation of spatial factors in which patterns of multivariate relationships are dependent upon the spatial auto- and cross-correlation of the components. Because of the anisotropy of primary compositions of the volcanics, some spatial factor patterns are difficult to interpret. Isotropically distributed variables such as CO ₂ are delineated clearly in spatial factor maps. For anisotropically distributed variables (SiO ₂ ), as the neighborhood becomes smaller, the spacial factor maps becomes better. Interpretation of spatial factors requires computation of the corresponding amplitude vectors from the eigenvalue solution. This vector reflects relative amplitudes by which the variables follow the spatial factors. Instability of some eigenvalue solutions requires that caution be used in interpreting the resulting factor patterns. A measure of the predictive power of the spatial factors can be determined from autocorrelation coefficients and squared multiple correlation coefficients that indicate which variables are significant in any given factor. The spatial factor approach utilizes spatial relationships of variables in conjunction with systematic variation of variables representing geological processes. This approach can yield potential exploration targets based on the spatial continuity of alteration haloes that reflect mineralization.List of symbols c _i Scalar factor that minimizes the discrepancy between andU _i - D Radius of circular neighborhood used for estimating auto- and cross-correlation coefficients - d Distance for which transition matrixU is estimated - d _ij Distance between observed valuesi andj - E Expected value - E _i Row vector of residuals in the standardized model - F(d _ij) Quadratic function of distanced _ij F(d _ij)=a+bd _ij+cd _ij ² - L Diagonal matrix of the eigenvalues ofU - _i Eigenvalue of the matrixU;ith diagonal element ofL - N Number of observations - p Number of variables - Q Total predictive power ofU - R Correlation matrix of the variables - R _0j Variance-covariance signal matrix of the standardized variables at origin;j is the index related tod andD (e.g.,j=1 ford=500 m,D=1000 m) - R _1j Matrix of auto- and cross-correlation coefficients evaluated at a given distance within the neighborhood - R _m ² Multiple correlation coefficient squared for themth variable - S _i Column vectori of the signal values - s _k ² Residual variance for variablek - T _i Amplitude vector corresponding toV _i;ith row ofT=V ^–1 - T Total variation in the system - U Nonsymmetric transition matrix formed by post-multiplyingR ₀₁ ^–1 byR _ij - U _i Componenti of the matrixU, corresponding to theith eigenvectorV _i;U _i= _iV_iT_i - U* _i ComponentU _i multiplied byc _i - U _ij Sum of componentsU _i+U _j - V _i Eigenvector of the matrixU;ith column ofV withUV=VL - w Weighting factor; equal to the ratio of two eigenvalues - X _i Random variable at pointi - x _i Value of random variable at pointi - y _i Residual ofx _i - Z _i Row vectori for the standardized variables - z _i Standardized value of variable  相似文献   

Subseabed disposal of radioactive waste: effects of consolidational fluid flow     

K. Bitzer 《Environmental Geology》1996,27(4):300-308

Subseabed disposal of radioactive waste applies a multiple-barrier concept with the sediment being the most important barrier for preventing a release of nuclides into the biosphere. While many investigations have been carried out to analyze the risk potential in this type of disposal, the effects of sediment consolidation and associated fluid flow have not fully been taken into consideration. Here, possible effects of consolidational fluid flow in the penetrator disposal option and possible consequences to the transport of nuclides in the sediment are analyzed. Results of numerical experiments demonstrate that consolidation contributes to the transport of radioactive nuclides released from containers buried in the sediment and to the release of nuclides at the sediment-water interface. Both depend on geological conditions and to a large extent on possible alterations of hydraulic conductivity i of the sediment in the vicinity of the entry path of a penetrator.Symbols c concentration ml m^–3 - c _a concentration of adsorbed solute mg kg^–1 (relative to dry weight of sorbing substance) - c _in solute concentration of source q mg m^–3 - c ₀ initial concentration mg m^–3 - ID dispersion tensorm ²s^–1 - ID ^* diffusion tensor m²s^–1 - D coefficient of dispersion m²s^–1 - d ₀ coefficient of molecular diffusion m²s^–1 - d coefficient of effective diffusion m²s^–1 - g gravity m²s^–1 - h piezometric pressure m - k hydraulic conductivity m²s^–1 - m mass kg - p pressure Pa - q source/sink m³s^–1 - S ₀ specific surface m²m^–3 - t time s - v velocity m s^–1 - x, z cartesian coordinates m - compressibiliy of sediment m²N^–1 - _L longitudinal dispersivity m - effective porosity (decimal fraction) - density kg m^–3 - _s density of sediment kg m^–3 - _w density of water kg m^–3 - decay constant per s - kinematic viscosity m²s^–1  相似文献   

Experimental determination of the diffusion coefficient for calcium in olivine between 900°C and 1500°C     

L.A. Coogan  A. Hain  S. Chakraborty 《Geochimica et cosmochimica acta》2005,69(14):3683-3694

Experiments have been carried out to determine the temperature, oxygen fugacity (fO₂) and compositional dependence of the tracer diffusion coefficient (D) of calcium in olivine. These data constrain the diffusion coefficient over the temperature range 900 to 1500°C for the three principal crystallographic axes. Well constrained linear relationships between the reciprocal of the absolute temperature and log(D) exist at any given oxygen fugacity. There is a strong dependence of the diffusion coefficient on oxygen fugacity with D ∝ fO₂^(1/3). This makes a knowledge of the T-fO₂ path followed by geological samples a prerequisite for modelling Ca diffusion in olivine. The best fitting preexponential factor (Do) and activation energy (E) to the Arrhenius equation log (D) = log [Do exp(−E/RT)] + 0.31Δ log fO₂ for Ca diffusion in olivine at a given oxygen fugacity (fO₂*) are given by:diffusion along [100]: log [Do (m²/s)] = −10.78 ± 0.43; E = 193 ± 11 kJ/moldiffusion along [010]: log [Do (m²/s)] = −10.46 ± 0.37; E = 201 ± 10 kJ/moldiffusion along [001]: log [Do (m²/s)] = −10.02 ± 0.29; E = 207 ± 8 kJ/molwhere Δ log fO₂ = log[fO₂*] − log[10⁻¹²] with fO₂* in units of bars. There is no measurable compositional dependence of the diffusion coefficient between Fo₈₃ and Fo₉₂. Diffusion in Fo₁₀₀ has a much higher activation energy than in Fe-bearing olivine and has a weaker fO₂ dependence.  相似文献   

Water speciation and diffusion in haploandesitic melts at 743-873 K and 100 MPa     

Huaiwei Ni  Yang Liu  Lijin Wang  Youxue Zhang 《Geochimica et cosmochimica acta》2009,73(12):3630-124

Water is an important volatile component in andesitic eruptions and deep-seated andesitic magma chambers. We report an investigation of H₂O speciation and diffusion by dehydrating haploandesitic melts containing ?2.5 wt.% water at 743-873 K and 100 MPa in cold-seal pressure vessels. FTIR microspectroscopy was utilized to measure species [molecular H₂O (H₂O_m) and hydroxyl group (OH)] and total H₂O (H₂O_t) concentration profiles on the quenched glasses from the dehydration experiments. The equilibrium constant of the H₂O speciation reaction H₂O_m+O?2OH, K = (X_OH)²/(X_H2OmX_O) where X means mole fraction on a single oxygen basis, in this Fe-free andesite varies with temperature as ln K = 1.547-2453/T where T is in K. Comparison with previous speciation data on rhyolitic and dacitic melts indicates that, for a given water concentration, Fe-free andesitic melt contains more hydroxyl groups. Water diffusivity at the experimental conditions increases rapidly with H₂O concentration, contrary to previous H₂O diffusion data in an andesitic melt at 1608-1848 K. The diffusion profiles are consistent with the model that molecular H₂O is the diffusion species. Based on the above speciation model, H₂O_m and H₂O_t diffusivity (in m²/s) in haploandesite at 743-873 K, 100 MPa, and H₂O_t ? 2.5 wt.% can be formulated as