Quasi-Symmetry and Reversible Markov Sequences in Sedimentary Sections     

W. E. Sharp  Thomas Markham 《Mathematical Geology》2000,32(5):561-579

Quasi-symmetry can be defined as a purely mathematical property of a matrix—that is, any matrix whose entries are strictly positive possesses quasi-symmetry if it can be written as a product of a diagonal and a symmetric matrix. A unique inverse solution for a quasi-symmetric matrix is readily obtained when the nondiagonal elements of the symmetric and quasi-symmetric matrix are set equal. Then it is shown that a Markov sequence is reversible if and only if it has a quasi-symmetric tally matrix. Because a properly counted Markov sequence must have marginal homogeneity, a simple chi-square test for symmetry on the tally matrix is sufficient to determine if an observed matrix is symmetrical and hence whether the Markov chain is reversible. Applications to sedimentary sequences are illustrated by the use of classical examples and with cyclothem data to determine if the sequence conforms to a reversible or nonreversible Markov process. Should the tally matrix lack marginal homogeneity, it is likely that a sampling bias was introduced by the counting procedure. However, a chi-square test for symmetry on a direct inverse of the tally matrix can be used to determine if the sedimentary sequence conforms to a reversible or a non-reversible Markov process.  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   

Tests for quasi-independence of embedded markov chains     

Jinsheng Yu 《Mathematical Geology》1984,16(3):267-282

This paper introduces the concept of quasi-independence into embedded Markov chains and identifies the maximum likelihood frequency estimates to be used with ² tests of the null hypothesis of quasi-independence within an embedded Markov chain.  相似文献   

Chi-square tests for markov chain analysis   总被引：1，自引：0，他引：1  

Richard N. Hiscott 《Mathematical Geology》1981,13(1):69-80

Markov chain analysis has become a popular and useful technique for the evaluation of stratigraphic information. Field data on frequencies of facies transitions are first assembled in a transition count matrix. Observed frequencies can be compared statistically with frequencies expected if no order, or memory, exists in the stratigraphic sequence. Two chi-square (²) tests have been proposed for this purpose. One of the previously proposed ² tests was observed to give anomalously large values of the test statistic during another study. This unsatisfactory behavior is verified here. Limiting values of the two ² tests (from tables) are compared with the distribution of values for both test statistics obtained by analyzing many random matrices generated by a simple computer program. In all cases, the logarithmic ² test, suggested by several previous authors, fails to provide any meaningful assessment of the presence or absence of order in stratigraphic sequences evaluated. Further use of this test should therefore be avoided.  相似文献   

Oxidation and Origin of Organic Matter in Surficial Eastern Mediterranean Hemipelagic Sediments     

P. J. M. Van Santvoort  G. J. De Lange  J. Thomson  S. Colley  F. J. R. Meysman  C. P. Slomp 《Aquatic Geochemistry》2002,8(3):153-175

Aerobic mineralisation of C_org in surface sedimentsof the deep (>2000 m water depth) eastern Mediterranean Sea has been quantified by analysis of detailedbox core C_org concentration versus depth profiles and the modelling environment for early diageneticproblems MEDIA. The reactive fraction comprises 60–80% of the total C_org reachingthe sediments and is largely oxidised within the surficial 10 cm. A non-reactive C _orgfraction (G_NR) dominates at depths >10 cm, and makes up20–40% of the total C _org flux to the sediments. First-order rateconstants for decomposition of the reactive fraction calculated from theC _org profiles range from 5.4 × 10^-3 to8.0 × 10^-3 y^-1 to 8.0 × 10^-3 y^-1. Total mineralization rates in thesurface sediment are between 1.7 and 2.6 mol C cm^-2 y^-1 and thus are typical for oligotrophic, deep-seaenvironments. The low fluxes and rapid remineralisation of C _org are accompanied by²¹⁰Pb_excess surface mixed layers which are only 2 cm deep, among the thinnest reported for oxygenated marine sediments.Model results indicate a mismatch between the C _org profiles and O₂ microprofileswhich were measured onboard ship. This can be attributed to a combination of decompression artefactsaffecting onboard measurement of the O₂ profiles or the leakage ofoxygen into the core during handling on deck. Furthermore, the used D_b values, based on ²¹⁰Pb, may not befully appropriate; calculations with higher D_b values improve the O₂ fits. The surficial sediment¹³C _org values of -22 become less negative with increasing depth and decreasing C _orgconcentrations. The major ¹³C change occurs in the top 3 to 4 cm and coincides with the interval weremost of the organic carbon oxidation takes place. This indicates that the reactive fractionof organic matter, commonly assumed to be marine, has a more negative ¹³C _orgthan the refractory fraction, usually held to be terrestrial. Palaeoproductivity estimates calculated from thesediment data by means of literature algorithms yield low surface productivities(12–88 gC m^-2 y^-1), which are in good agreement with field measurements of primary productivity in otherstudies. Such values are, however, significantly lower than those indicated by recent productivitymaps of the area derived from satellite imagery (>100 gC m^-2 y^-1).  相似文献   

原子折射度与电子构型的关系          下载免费PDF全文

艾德生  曾荣树 《地质科学》1999,34(1):123-128

原子折射度与其电子构型密切相关。元素在周期表中按最外层电子数可分为s、p、sd、df4个区,原子折射度的变化在各个区内是不同的。原子折射度可表示为主量子数及最外层电子数的函数,根据这个函数计算出来的值与文献给出的值十分吻合。  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   

Reversible Markov grain sequences in granite     

W. E. Sharp  Kevin Severance 《Mathematical Geology》1991,23(3):305-324

A key feature of an ideal granite is the occurrence of grain sequences which are reversible Markov chains. This property was tested using a ² test on a 2 × 6 contingency table consisting of reversible grain pairs for microcline, plagioclase, quartz, and biotite, and on a 2 × 12 contingency table consisting of reversible grain triads. All 28 samples examined from the Pacolet Mills pluton, South Carolina, passed the ² test for grain pairs, and all but three of these passed the ² test for grain triads. The coefficients of the reversibility matrix were examined for statistical significance after normalization, using a logarithmic transformation. For all three phases of the Pacolet Mills pluton, the average coefficients were in the range 1.08–0.89. Elevated and depressed values of these coefficients suggested possible differences among the three phases of the granite in their crystallization paths.  相似文献   

Geological similarity byQ analysis     

John C. Griffiths 《Mathematical Geosciences》1983,15(1):85-108

Mineral resource assessment using areal, or unit regional, value approach estimates the variety of commodities likely to occur in a region by comparing its geology with that of regions already well developed and known to produce a variety of commodities. It is, therefore, essential to be able to discern regions which are similar in geology. The data used for this purpose are derived by point-counting geological maps of the regions to be evaluated; one aspect of this data is the presence-absence (i.e., 0–1 data)of 65 standardized rocktypes. It is then necessary to compare geological data from both the developed and undeveloped regions to determine which of the regions are geologically similar. The initial data consists of a matrix (A)of Cregions by Rrock types and all relations (λ)among Cand Rmay be expressed as λ ? C × R.We may then use Atkin's Qanalysis to determine the structure of these relations. Postmultiplying Aby its transpose and subtracting a suitably dimensioned unit matrix yields an output matrix K_C (R; λ)which expresses the relations among regions in terms of their rock types. This output matrix comprises qconnectivities among regions; its diagonal elements (denoted \(\hat q\) )are the number of rock types, minus one, in each region. The offdiagonal elements ( \(\check{q} \) )are the number of rock types (minus one)which are common to each pair. Similarities of regions in terms of their rock types are then found by using tables of equivalences in which the values of \(\hat q\) are the dimensions of simplicies representing each region; the rock types are the apicies of the simplicies and similarities are the shared edges and faces of the simplicies. The largest number of shared apicies equals \(\check{q} \) .Examples of the application of Qanalysis to a comparison of the geology of the 10 counties in New Hampshire and the 50 states of the U.S.A. and Puerto Rico illustrate the procedure. Qanalysis supplies an algebraic language and an equivalent geometry to express the relations among regions in terms of their rock types.  相似文献   

Vibrational spectroscopy of beta-eucryptite (LiAlSiO<Subscript>4</Subscript>): optical phonons and phase transition(s)     

M.?ZhangEmail author  H.?Xu  E. K. H.?Salje  P. J.?Heaney 《Physics and Chemistry of Minerals》2003,30(8):457-462

The structural behavior of -eucryptite (LiAlSiO₄) has been investigated using infrared (IR) spectroscopy over a temperature range of 20 to 900 K and FT-Raman spectroscopy at room temperature. IR reflectance measurements show that -eucryptite possesses high reflectivity in the far-IR region, as is consistent with its reported superionic conductivity along the c-axis. On heating, the Li-related IR bands near 246 and 300 cm^–1 (with A₂ symmetry) broadened and weakened dramatically, presumably as a result of Li⁺ positional disordering along the structural channels parallel to c. The disordering process appears to induce a framework distortion, as is evidenced by the broadening of some vibrations of Si(Al)–O with increasing temperature. A change in slope in the temperature dependence of the phonon frequency near 300 cm^–1 and the linewidth of the 760 cm^–1 band at 715 K indicates that Li becomes completely disordered above this temperature. In addition, the temperature dependence of the linewidth for the 760 cm^–1 band exhibits an additional change in slope at 780 K, implying the existence of an intermediate state within this temperature range. The detailed structure of this intermediate phase, however, needs further study. Our IR data provide no indication of structural changes between room temperature and 20 K.  相似文献   

Decline curve analyses revisited     

Walter Rose 《Mathematical Geology》1990,22(8):1051-1061

Empiricaldecline curve forecasts of future production rates and cumulative production to be expected from certain classes of petroleum reservoirs has been a methodology practiced and relied on by petroleum geologists for many years. New ways to consider the subject are described in this paper. Thereby it is seen that these forecasts sometimes can be made even when some of the record of the past performance history is sparse (say, because it has been lost, or never recorded).SI Units D, D _i initial reference production rate,s ^–1 - n dimensionless constant [cf. Eq. (1)] - N cumulative production, m³ - Q, Q _i production rate att and initially, m³/s - R dimensionless time variable [cf. Eq. (9)] - t time, s  相似文献   

Graphical estimations of magma densities and compositional expansion coefficients     

Takehiro Koyaguchi 《Contributions to Mineralogy and Petrology》1990,105(2):173-176

Assuming that the partial molar volume of each chemical component in a magma is constant, the magma density, _m , is expressed as 1/ _m =C _i / _fi , whereC _i is the weight fraction, and _fi is the fractionation density of thei ^th component. Using this linear relationship between 1/ and weight fraction, the density change due to addition or subtraction of any component can be graphically estimated on 1/ vs oxide wt% diagrams. The compositional expansion coefficient of thei ^th component, _fi , is expressed as _i = _m / _fi –1. The compositional expansion coefficient of H₂O has a much larger absolute value than those of any other oxide or mineral components, showing that addition of a small amount of H₂O can significantly decrease magma density. These simple expressions facilitate the estimation of magma densities during fractionation.  相似文献   

Study on the compositional dependence of the apparent partition coefficient of iron and magnesium between coexisting garnet and clinopyroxene solid solution     

Yasutami Oka  Takashi Matsumoto 《Contributions to Mineralogy and Petrology》1974,48(2):115-121

Compositional dependence of apparent partition coefficient of iron and magnesium between coexisting garnet and clinopyroxene from Mt. Higasiakaisi is studied by means of a multicomponent regular solution model. It is shown that garnet and clinopyroxene solid solutions are positively non-ideal, and the non-ideal parameters according to the symmetric regular solution model are 2.58 kcal and 2.39 kcal, respectively, assuming the equilibration temperature of the mass to be 550° C.Notations a _i ^h activity of component i in phase h - _ij interaction parameter of component i and j in a solid solution - _i activity coefficient of component i - X _i mole fraction of component i - K partition coefficient of Fe and Mg between coexisting garnet and clinopyroxene - K apparent partition coefficient of Fe and Mg between coexisting garnet and clinopyroxene - G ⁰ difference in free energy of the partition reaction - H ⁰ difference in enthalpy of the partition reaction - S ⁰ difference in entropy of the partition reaction - R gas constant - G garnet - Alm almandine component - Py pyrope component - Gr grossular component - Sp spessartine component - CPx clinopyroxene - Hd hedenbergite component - Di diopside component - Jd jadeite component - Ts Tschermac's molecule component Deceased on April 17, 1974.  相似文献   

Identifying sources of groundwater in the lower Colorado River valley, USA, with δ18O, δD, and 3H: implications for river water accounting     

Bradley E. Guay  Christopher J. Eastoe  R. Bassett  Austin Long 《Hydrogeology Journal》2006,14(1-2):146-158

Isotope measurements (¹⁸O, D, ³H) indicate groundwater origin in the Lower Colorado River Valley (LCRV) and provide an alternative, or supplement, to the US Bureau of Reclamations proposed accounting surface method. The accounting surface method uses a hydraulic criterion to identify certain wells away from the flood plain that will eventually yield mainstream Colorado River water. New isotope data for 5 surface-water and 18 groundwater sites around Topock Marsh, Arizona, are compared with river-water data (1974–2002) from 11 sites between Utah and Mexico and with groundwater data from previous LCRV studies. Three groundwater sources are repeatedly identified in the LCRV: (1) local recharge derived from precipitation, usually winter rain, plots slightly below the global meteoric water line (GMWL) and has D values that are 20 greater than those of recent river water; (2) older (pre-1950) upper basin river-water plots on or near the GMWL, distinct from local rainfall and recent river water; and (3) recent (post-1950) Colorado River water, including Topock Marsh samples, plots below the GMWL along an evaporation trend. Large floods, as in 1983, complicate interpretation by routing less evaporated upper basin water into the LCRV; however, tritium content can indicate the age of a water. River-water tritium has declined steadily from its peak of 716 TU in 1967 to about 11 TU in 2002. Mixtures of all three groundwater sources are common.

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Resumen Mediciones isotópicas (¹⁸O, D, ³H) indican cual es el origen del agua subterránea en el Valle Bajo del Río Colorado (LCRV) y aportan una alternativa, o complemento, para el método superficie de conteo propuesto por el Buró de Reclamación de Estados Unidos. El método superficie de conteo utiliza un criterio hidráulico para identificar ciertos pozos alejados de la planicie de inundación que eventualmente producirán agua a partir de la corriente principal del Río Colorado. Los nuevos datos isotópicos para 18 sitios de agua subterránea y 5 sitios de agua superficial cerca de los Pantanos Topock, Arizona, se comparan con datos de agua de río (1974–2002) provenientes de 11 sitios localizados entre Utah y México, y con datos de aguas subterráneas de estudios previos realizados en el LCRV. Se identifican reiteradamente tres fuentes de aguas subterráneas en el LCRV: (1) recarga local derivada de precipitación, generalmente lluvia de invierno, cuya composición cae ligeramente por debajo de la línea de agua meteórica global (GMWL) y tiene valores D que son 20 mayores que los reportados para agua de río reciente; (2) el agua de río más vieja (pre-1950) de la cuenca alta cuya composición cae sobre o cerca de la GMWL, diferente de la lluvia local y del agua de río reciente; (3) agua reciente (post-1950) del Río Colorado, incluyendo muestras de los Pantanos Topock, con composición por debajo de la GMWL a lo largo de una tendencia a la evaporación. Inundaciones grandes, como en 1983, complican la interpretación al transmitir menos agua evaporada de la cuenca alta hacia el LCRV; sin embargo, el contenido de tritio puede indicar la edad del agua. El contenido de tritio en agua de río ha disminuido constantemente desde la concentración pico de 716 TU en 1967 a cerca de 11 TU en 2002. Es común que exista mezclas de las tres fuentes de agua subterránea.

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Résumé Les mesures isotopiques (d18O, dD, 3H) indiquent les origine de leaux souterraines dans la Vallée de la Rivière du Bas Colorado (LCRV) et sont une alternative, ou un supplément, à la méthode des bilans hydrologiques proposée par du «US Bureau of Reclamation». Cette méthode de bilan hydrologique utilise un critère hydraulique permettant didentifier certains puits hors de la plaine dinondation qui pomperaient une part non négligeable de leur eau dans la rivière Colorado. De nouvelles données isotopiques provenant de 5 sites deau de surface et 18 deaux souterraines autour de Topock Marsh en Arizona, sont comparées avec les données (1974–2000) de 11 sites localisés entre Utah et Mexico, ainsi que des données dautres études sur la LCRV. Ces sources deaux souterraines sont identifiées à plusieurs reprises dans la LCRV: (1) la recharge locale dérivant des précipitations, généralement les pluies hivernales, se retrouvent légèrement sous la ligne deau météoritique globale (GMWL) et possède des valeurs de dD 20% supérieures aux valeurs des eaux récentes de la rivière; (2) les eaux vieilles (pre-1950) du bassin supérieur de la rivière possèdent une valeurs très proches de la GMWL, distinctes des valeurs de la pluie locale et des eaux récentes de la rivière; et (3) les eaux récentes (post-1950) de la Rivière Colorado, incluant les échantillons de Topock Marsh, se positionnent à côté de la GMWL sur une droite dévaporation. Les grandes inondations, par exemple celle de 1983, compliquent linterprétation en reprenant dans la LCRV moins deaux marquées comme évaporées et provenant du bassin supérieur; par ailleurs le pic de tritium est descendu de 716 TU en 1967 à 11 TU en 2002. Les mélanges de ces trois sources sont assez fréquentes.

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Space group and hydrogen sites of δ-AlOOH and implications for a hypothetical high-pressure form of Mg(OH)<Subscript>2</Subscript>     

Y. ?KudohEmail author  T. ?Kuribayashi  A. ?Suzuki  E. ?Ohtani  T. ?Kamada 《Physics and Chemistry of Minerals》2004,31(6):360-364

The space group and hydrogen positions of -(Al_0.84Mg_0.07Si_0.09)OOH are investigated using a single crystal synthesized using a multi-anvil apparatus under conditions of 1000 °C and 21 GPa. The space group determined by single-crystal X-ray diffraction is to Pnn2, with unit-cell parameters of a=4.6975(8) Å, b= 4.2060(6) Å, c=2.8327(4) Å, and V=55.97(1) ų. Partial occupancy of the Al site by Mg and Si suggests the possibility of a limited solid solution between -AlOOH, stishovite, and a hypothetical CaCl₂-type Mg(OH)₂ that is 16% denser than brucite. Difference-Fourier maps reveal two small but significant Fourier peaks attributable to hydrogen atoms. Atomic distances and angles around the first peak indicate a hydrogen bond with O···O distances of 2.511 Å, while those around the second peak are suggestive of a bifurcated hydrogen bond with O···O distances of 2.743 and 2.743 Å.  相似文献   

Valent state and coordination of cobalt Ions in beryl and chrysoberyl crystals     

V. P.?Solntsev  E. G.?Tsvetkov  A. I.?Alimpiev  R. I.?MashkovtsevEmail author 《Physics and Chemistry of Minerals》2004,31(1):1-11

We have studied the polarized optical absorption and EPR spectra of Co-doped beryls grown by hydrothermal, flux, and gas-transport methods, and chrysoberyl grown by the Czochralski method. In beryls three groups of bands, belonging to three various Co centers, were distinguished by analysis of the absorption band intensities. The first group, bands with maxima at 22 220 (E c), 17 730 (E c), and 9090 (E c), 7520 (E c) cm^–1 are due to Co²⁺ in octahedral site of Al³⁺. The second group is bands at 18 940, 18 250, 17 700 (E c), 18 300, 17 700, 17 000 (E c) and 8830 (E c), 7350 (E c) cm^–1 and 5320 (E c), 3880 (E c) cm^–1, which are caused by Co²⁺ in tetrahedral site of Be²⁺. A weak wide band in flux and gas-transport beryl in the region of 12 500–8300 cm^–1 (E , c) is related to Co³⁺ in octahedral Al³⁺ site. In hydrothermal beryl, bands 13 200 (E c), 10 900 (E c), and 8500 (E c) cm^–1 are caused by an uncontrolled impurity of Cu²⁺ ions. For Co-doped chrysoberyl one type of center of Co has been established: Co²⁺ in the octahedral site of Al³⁺. In the approximation of the trigonal field with regard to Trees correction, the energy levels of Co²⁺ have been calculated in octahedral and tetrahedral coordination. There is good agreement between the obtained experimental and calculated data. The polarization dependence of the optical absorption bands is explained well in terms of the spin-orbit interaction.  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   

High-resolution210Pb dating of Lake Constance sediments: Stable lead in Lake Constance     

A. Bollhöfer  A. Mangini  A. Lenhard  M. Wessels  F. Giovanoli  B. Schwarz 《Environmental Geology》1994,24(4):267-274

Two sediment cores (BO90/13b and BO90/17b) from Lake Constance were investigated by-spectrometry for²¹⁰Pb,¹³⁴Cs,¹³⁷Cs,²⁴¹Am,²³⁴Th, and other members of the²³⁸U decay chain. The sediments were dated using the constant-flux model for²¹⁰Pb, and accumulation rates were determined. These range from 0.04 to 0.65g/cm ²/yr (BO90/13b) and 0.04 to 0.8g/cm ²/yr (BO90/17b), respectively. The mean accumulation rate amounts to 0.16g/cm ²/yr for both cores. The cores had already been dated by lamination counting and reconstruction of high-water events at the Limnological Institute at Constance, so that a very precise time scale was available. Both ages derived are in agreement within statistical error up to 1900, which means dating with the constant-flux model for²¹⁰Pb was confirmed up to that age. The position of the maxima of bomb cesium and americium confirm the stratigraphic and²¹⁰Pb datings. With²⁴¹Am a further radioactive isotope is available, which can, due to the half-life of²⁴¹Pu (t _1/2=14.4yr) be detected now by-spectrometry and can serve as an additional time indicator, the maximum being dated at 1963. By applying the various time scales, the depth profiles of stable lead and zinc of core BO90/13b were dated. Both heavy metals show a very significant maximum located beneath the layer of the maxima of bomb cesium and americium, showing that these maxima are older than those of the bomb isotopes. It is remarkable in this context that the maximum of zinc concentration occurs a little later than that of stable lead. Similar concentration profiles are observable in core BO90/17b and other, older sediment cores (CS6-CS10) on a transect across the lake. In contrast to a former assumption, the depth profile of stable lead in Lake Constance sediments does not reflect the anthropogenic gasoline lead emissions into the atmosphere for Germany, their maximum being dated at 1971.  相似文献   

The relationship between collision-related calcalkaline, and within-plate alkaline volcanism in the Karacadağ Area (Konya-Türkiye, Central Anatolia)     

Hüseyin Kurt  Kürad Asan  Gilles Ruffet 《Chemie der Erde / Geochemistry》2008,68(2):155-176

The Karacadağ (Kulu-Konya) area is one of the main volcanic provinces in Central Anatolia. The Karacadağ volcanites are composed of large volumes of andesitic-dacitic lavas associated with pyroclastics and small volumes of alkali basalt, trachybasalt and trachyandesite lavas. Two groups of volcanic rocks can be distinguished: (1) calcalkaline rocks including andesites and dacites, and (2) alkaline rocks including basalts, trachybasalts and trachyandesites. ⁴⁰Ar/³⁹Ar ages show that the Karacadağ volcanites were erupted during Early Miocene (ca.18–19 Ma) and suggest that alkaline volcanites succeed shortly afterwards calcalkaline volcanites. Major oxides and trace elements plotted versus SiO₂ suggest fractionation of hornblende, Fe–Ti oxide and apatite for calcalkaline volcanic rocks and olivine, clinopyroxene and Fe–Ti oxide for alkaline volcanic rocks in the magmatic evolution. The incompatible trace element patterns of the calcalkaline volcanites show enrichment of LILEs (Sr, K, Rb, Ba and Th) and negative HFSEs (Nb, Ta) anomalies suggesting an enriched lithospheric source by a subduction-related process. On the other hand, alkaline volcanites show enrichment of both LILEs and HFSEs suggesting an enriched lithospheric source by small volume melts from the asthenosphere. The rocks also have moderately fractionated REE patterns with (La/Lu)_N ratios of 7–24 for calcalkaline and 6–17 for alkaline volcanites. Moreover, the volcanites have relatively low ⁸⁷Sr/⁸⁶Sr(t) ratios for between 0.703782 and 0.705129, and high ε_Nd(t) values between +2.25 and +4.49. Generally, the Sr–Nd isotopic compositions of the rocks range from the mantle array to bulk earth. All of these observations and findings suggest that the calcalkaline volcanites were formed in a subduction modified orogenic setting, and the alkaline volcanites in a within-plate setting.  相似文献   

Groundwater chemistry within a plateau neighboring Matsumoto city,Japan     

H. Ii  S. Misawa 《Environmental Geology》1994,24(3):166-175

The change in groundwater chemistry along the groundwater flow path in the Matsumoto tunnel vicinity was studied, and the origin of the groundwater and dissoluted substances was determined. The relationship between the concentration of HCO₃ ^–, Ca²⁺, and Na⁺, and CO₂ gas pressure in the groundwater indicated that the HCO₃ ^–, Ca²⁺, and Na⁺ were produced by the reaction of the CO₂ gas in the groundwater and feldspar in the rocks. The relationship between the concentration of NO₃ ^– and the Eh and pH values in the groundwater indicated that in an oxidative condition, ammonia-oxidizing and nitriteoxidizing bacteria used NH₄ ⁺ and produced NO₃ ^– and H⁺, and in a reductive condition, denitrifying bacteria used NO₃ ^– and produced N₂ gas and OH^–. The stable hydrogen and oxygen isotopic ratio in the groundwater and precipitation indicated that the groundwater originated from precipitation that had fallen on the area. The concentration of³H and the stable hydrogen and oxygen isotopic ratios in the groundwater suggested that it has been getting warmer climatically for more than 60 years. The stable carbon isotopic ratio indicated that the HCO₃ ^– in the groundwater, excluding deep well water, originated from CO₂ gas produced by organic matter in the soil. The deep well water, which had a higher concentration of HCO₃ ^– than the other groundwater sampled, was thought to have acquired HCO₃ ^– though contact with rocks. The³⁶Cl/Cl ratio indicated the recharge age of the deep well water sampled at a depth of 760 m at the foot of the plateau was recent.  相似文献