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1.
Chang-Jo F. Chung 《Mathematical Geology》1993,25(7):851-865
Multivariate statistical analyses have been extensively applied to geochemical measurements to analyze and aid interpretation of the data. Estimation of the covariance matrix of multivariate observations is the first task in multivariate analysis. However, geochemical data for the rare elements, especially Ag, Au, and platinum-group elements, usually contain observations the below detection limits. In particular, Instrumental Neutron Activation Analysis (INAA) for the rare elements produces multilevel and possibly extremely high detection limits depending on the sample weight. Traditionally, in applying multivariate analysis to such incomplete data, the observations below detection limits are first substituted, for example, each observation below the detection limit is replaced by a certain percentage of that limit, and then the standard statistical computer packages or techniques are used to obtain the analysis of the data. If a number of samples with observations below detection limits is small, or the detection limits are relatively near zero, the results may be reasonable and most geological interpretations or conclusions are probably valid. In this paper, a new method is proposed to estimate the covariance matrix from a dataset containing observations below multilevel detection limits by using the marginal maximum likelihood estimation (MMLE) method. For each pair of variables, sayY andZ whose observations containing below detection limits, the proposed method consists of three steps: (i) for each variable separately obtaining the marginal MLE for the means and the variances,
,
,
, and
forY andZ: (ii) defining new variables by
and
and lettingA=C+D andB=C–D, and obtaining MLE for variances,
and
forA andB; (iii) estimating the correlation coefficient YZ by
and the covariance
YZ
by
. The procedure is illustrated by using a precious metal geochemical data set from the Fox River Sill, Manitoba, Canada. 相似文献
2.
Fractionation of yttrium (Y) and the rare earth elements (REEs) begins in riverine systems and continues in estuaries and the ocean. Models of yttrium and rare earth (YREE) distributions in seawater must therefore consider the fractionation of these elements in both marine and riverine systems. In this work we develop a coupled riverine/marine fractionation model for dissolved rare earths and yttrium, and apply this model to calculations of marine YREE fractionation for a simple two-box (riverine/marine) geochemical system. Shale-normalized YREE concentrations in seawater can be expressed in terms of fractionation factors (
ij
) appropriate to riverine environments (
) and seawater (
):
where
and
are input-normalized total metal concentrations in seawater and
is the ratio of total dissolved Y in riverwater before
and after
commencement of riverine metal scavenging processes. The fractionation factors (
ij
) are calculated relative to the reference element, yttrium, and reflect a balance between solution and surface complexation of the rare earths and yttrium. 相似文献
3.
Tore P?sse 《Mathematical Geology》1990,22(7):803-824
A nonuniform glacio-isostatic uplift results in differential uplift for different parts of a lake. If the lake outlet is situated in the area with the greatest rate of uplift, then the lake will be continuously transgressed. Ancient lake levels can be estimated by dating transgressed peat at different depths in such a lake. Two lakes in southwestern Sweden have been investigated by this method and the course of glacio-isostatic uplift has been determined empirically. The uplift can be expressed by an exponential function through the following formula
相似文献
4.
Prof. L. Fanfani Prof. P. F. Zanazzi Dr. Anna Rosa Zanzari 《Mineralogy and Petrology》1977,24(3):169-178
Summary The crystallography of roscherite is more complicated than previously thought. Single crystal X-ray work on material from Foote Mine (California) gave triclinic symmetry. The unit cell corresponding to the one adopted for monoclinic roscherite hasa=15.921,b=11.965,c=6.741 Å, =91°04, =94°21, =89°59 1/2, space group
. The least-squares refinement of the structure using 2380 non zero reflections with anisotropic temperature factors resulted in a conventional reliability factorR=0.060.The X-ray study indicates the formula
while that proposed for monoclinic roscherite is
The atomic arrangements of both varieties of roscherite are very similar. The lowering of symmetry is caused by the segregation of the trivalent cations into only half of the sites of a monoclinic point position. Crystallochemical considerations suggest that the symmetry of roscherite does not depend on the kind of trivalent cations occupying the 6-coordinated position, but rather by the ratio between trivalent and divalent metal ions.
Die Kristallstruktur eines triklinen Roscherites Zusammenfassung Die Kristallographie des Roscherites ist komplizierter als man bisher annahm. Einkristall-Röntgenuntersuchungen an Material von Foote Mine (Kalifornien) ergaben trikline Symmetrie. Die Elementarzelle, welche der für monoklinen Roscherit angenommenen entspricht, hata=15,921,b=11,965,c=6,741 Å, =91°04, =94°21, =89°59 1/2, Raumgruppe . Die Verfeinerung der Struktur mit der Methode der kleinsten Quadrate ergab unter Verwendung anisotroper Temperaturfaktoren für 2380 beobachtete Reflexe einen konventionellen ZuverlässigkeitsindexR=0,060.Die Röntgenuntersuchung weist auf die Formel , während für monoklinen Roscherit vorgeschlagen wurde. Die Atomanordnungen beider Abarten des Roscherites sind sehr ähnlich. die Symmetrieerniedrigung wird dadurch hervorgerufen, daß die dreiwertigen Kationen nur die Hälfte der Positionen einer monoklinen Punktlage besetzen. Kristallchemische Überlegungen weisen darauf hin, daß die Symmetrie nicht von der Art der dreiwertigen Kationen, welche eine 6-koordinierte Punktlage besetzen, abhängt, sondern vielmehr von dem Mengenverhältnis zwischen 3-wertigen und 2-wertigen Metallionen. With 1 Figure 相似文献 5.
To investigate the point defect chemistry and the kinetic properties of manganese olivine Mn2SiO4, electrical conductivity () of single crystals was measured along either the [100] or the [010] direction. The experiments were carried out at temperatures T=850–1200 °C and oxygen fugacities
atm under both Mn oxide (MO) buffered and MnSiO3 (MS) buffered conditions. Under the same thermodynamic conditions, charge transport along [100] is 2.5–3.0 times faster than along [010]. At high oxygen fugacities, the electrical conductivity of samples buffered against MS is 1.6 times larger than that of samples buffered against MO; while at low oxygen fugacities, the electrical conductivity is nearly identical for the two buffer cases. The dependencies of electrical conductivity on oxygen fugacity and temperature are essentially the same for conduction along the [100] and [010] directions, as well as for samples coexisting with a solid-state buffer of either MO or MS. Hence, it is proposed that the same conduction mechanisms operate for samples of either orientation in contact with either solid-state buffer.The electrical conductivity data lie on concave upward curves on a log-log plot of vs
, giving rise to two
regimes with different oxygen fugacity exponents. In the low-
regime
, the
exponent, m, is 0, the MnSiO3-activity exponent, q, is 0, and the activation energy, Q, is 45 kJ/mol. In the high
regime
10^{ - 7} {\text{atm}}} \right)$$
" align="middle" border="0">
, m=1/6, q=1/4–1/3, and Q=45 and 200 kJ/mol for T<1100 °c=" and=">1100>T>1100 °C, respectively. 相似文献
6.
An experimental study of the diffusion of oxygen in quartz and albite using an overgrowth technique 总被引:1,自引:0,他引:1
S. C. Elphick P. F. Dennis C. M. Graham 《Contributions to Mineralogy and Petrology》1986,92(3):322-330
Diffusion rates of18O tracer in quartz ( c, 1 Kb H2O) and Amelia albite ( 001, 2 Kb H2O) have been measured, using Secondary Ion Mass Spectrometry (SIMS). A new technique involving hydrothermal deposition of labelled materials has removed the possibility of pressure solution-reprecipitation processes adversely affecting the experiments. Reported diffusion constants are:-quartz ( c),
,Q=98±7 KJ mol–1 (600–825° C, 1 Kb); Amelia albite ( 001),
,Q=85±7 KJ mol–1, (400–600° C, 2 Kb). Measured quartz18O diffusivities decrease discontinuously at the- transition, reflecting strong structural influences. The reported albite data agree with previously recorded studies, but-quartz data indicate significantly lower activation energies. Possible causes of this discrepancy, and some geological consequences, are noted. 相似文献
7.
J. W. Jones 《Contributions to Mineralogy and Petrology》1972,37(4):291-306
In the Rogers Pass area of British Columbia the almandine garnet isograd results from a reaction of the form: 5.31 ferroan-dolomite+8.75 paragonite+4.80 pyrrhotite+3.57 albite+16.83 quartz+1.97 O2=1.00 garnet+16.44 andesine+1.53 chlorite+2.40 S2+1.90 H2O+10.62 CO2. The coefficients of this reaction are quite sensitive to the Mn content of ferroan-dolomite.Experimental data applied to mineral compositions present at the isograd, permits calculation of two intersecting P, T equilibrium curves. P=29088–39.583 T is obtained for the sub-system paragonite-margarite (solid-solution), plagioclase, quartz, ferroan-dolomite, and P=28.247 T–14126 is obtained for the sub-system epidote, quartz, garnet, plagioclase. These equations yield P=3898 bars and T=638° K (365° C). These values are consistent with the FeS content of sphalerite in the assemblage pyrite, pyrrhotite, sphalerite and with other estimates for the area.At these values of P and T the composition of the fluid phase in equilibrium with graphite in the system C-O-H-S during the formation of garnet is estimated as:
bars,
bars,
bars,
bars,
bars,
bars,
bars,
bars,
, bars,
bars. 相似文献
8.
Volker von Seckendorff Hugh St. C. O'Neill 《Contributions to Mineralogy and Petrology》1993,113(2):196-207
The partitioning of Mg and Fe2+ between coexisting olivines and orthopyroxenes in the system MgO-FeO-SiO2 has been investigated experimentally at 1173, 1273, 1423 K and 1.6 GPa over the whole range of Mg/Fe ratios. The use of barium borosilicate as a flux to promote grain growth, and the identification by back-scattered electron imaging of resulting growth rims suitable for analysis by electron microprobe, results in coexisting olivine and orthopyroxenene compositions determined to a precision of±0.003 to 0.004 in molar Fe/(Mg+Fe). Quasi-reversal experiments were performed starting with Mg-rich olivine and Fe-rich orthopyroxene (low KD) and vice versa (high KD), which produced indistinguishable results. The distribution coefficient, KD, depends on composition and on temperature, but near Fe/(Mg+Fe)=0.1 (i.e. mantle compositions) these effects cancel out, and KD is insensitive to temperature. The results agree well with previous experimental investigations, and constrain the thermodynamic mixing properties of Mg-Fe olivine solid solutions to show small near-symmetric deviations from ideality, with
between 2000 and 8000 J/mol. Multiple non-linear least squares regression of all data gave a best fit with
(implying 5450 J/mol at 1 bar) and
, but the two W
G
parameters are so highly correlated with each other that our data are almost equally well fit with
, as obtained by Wiser and Wood. This value implies
, apparently independent of temperature. Our experimental results are not compatible with the assessment of olivine-orthopyroxene equilibria of Sack and Ghiorso. 相似文献
9.
10.
Peter Ulmer 《Contributions to Mineralogy and Petrology》1989,101(3):261-273
The equilibrium partitioning of Fe2+ and Mg between olivine and liquid along a liquid line of descent has been determined for a calc-alkaline system, ranging in composition from picritic to andesitic. Experiments were conducted between 1000–1450° C and 1 bar to 30 kbar. Within the compositional range investigated
and
, the compositional dependence of the Fe2+ and Mg partitioning is a function of the Mg-content of the liquid. The Mg-content of the liquid correlates strongly with temperature. The variation of the Fe2+ and Mg partitioning were therefore evaluated individualy as functions of composition and temperature alone. The composition dependence of the cation-partitioning coefficients (Kd) is given by the following two equations:
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