In geostatistical studies, the fitting of the linear model of coregionalization (LMC) to direct and cross experimental semivariograms is usually performed with a weighted least-squares (WLS) procedure based on the number of pairs of observations at each lag. So far, no study has investigated the efficiency of other least-squares procedures, such as ordinary least squares (OLS), generalized least squares (GLS), and WLS with other weighing functions, in the context of the LMC. In this article, we compare the statistical properties of the sill estimators obtained with eight least-squares procedures for fitting the LMC: OLS, four WLS, and three GLS. The WLS procedures are based on approximations of the variance of semivariogram estimates at each distance lag. The GLS procedures use a variance–covariance matrix of semivariogram estimates that is (i) estimated using the fourth-order moments with sill estimates (GLS1), (ii) calculated using the fourth-order moments with the theoretical sills (GLS2), and (iii) based on an approximation using the correlation between semivariogram estimates in the case of spatial independence of the observations (GLS3). The current algorithm for fitting the LMC by WLS while ensuring the positive semidefiniteness of sill matrix estimates is modified to include any least-squares procedure. A Monte Carlo study is performed for 16 scenarios corresponding to different combinations of the number of variables, number of spatial structures, values of ranges, and scale dependence of the correlations among variables. Simulation results show that the mean square error is accounted for mostly by the variance of the sill estimators instead of their squared bias. Overall, the estimated GLS1 and theoretical GLS2 are the most efficient, followed by the WLS procedure that is based on the number of pairs of observations and the average distance at each lag. On that basis, GLS1 can be recommended for future studies using the LMC. 相似文献
The structural organization of a giant mafic dyke swarm, the Okavango complex, in the northern Karoo Large Igneous Province (LIP) of NE Botswana is detailed. This N110°E-oriented dyke swarm extends for 1500 km with a maximum width of 100 km through Archaean basement terranes and Permo-Jurassic sedimentary sequences. The cornerstone of the study is the quantitative analysis of N>170 (exposed) and N>420 (detected by ground magnetics) dykes evidenced on a ca. 80-km-long section lying in crystalline host-rocks, at high-angle to the densest zone of the swarm (Shashe area). Individual dykes are generally sub-vertical and parallel to the entire swarm. Statistical analysis of width data indicates anomalous dyke frequency (few data <5.0 m) and mean dyke thickness (high value of 17 m) with respect to values classically obtained from other giant swarms. Variations of mean dyke thicknesses from 17 (N110°E swarm) to 27 m (adjoining and coeval N70°E giant swarm) are assigned to the conditions hosting fracture networks dilated as either shear or pure extensional structures, respectively, in response to an inferred NNW–SSE extension. Both fracture patterns are regarded as inherited brittle basement fabrics associated with a previous (Proterozoic) dyking event. The Okavango N110°E dyke swarm is thus a polyphase intrusive system in which total dilation caused by Karoo dykes (estimated frequency of 87%) is 12.2% (6315 m of cumulative dyke width) throughout the 52-km-long projected Shashe section. Assuming that Karoo mafic dyke swarms in NE Botswana follow inherited Proterozoic fractures, as similarly applied for most of the nearly synchronous giant dyke complexes converging towards the Nuanetsi area, leads us to consider that the resulting triple junction-like dyke/fracture pattern is not a definitive proof for a deep mantle plume in the Karoo LIP. 相似文献
Wallace (in Thermodynamics of crystals, 1972) developed a theorem, rooted in rigid lattice dynamics, which incorporates intrinsic anharmonic effects in solids. The practical
application of this theorem in mineral physics is computationally involved and this is the main reason for the theorem not
getting the attention it deserves. Because intrinsic anharmonicity is an important issue at the extreme conditions in planetary
mantles, we derived a method which removes the computational obstacles in applying this theorem. We extended the theorem to
incorporate details of the phonon spectrum and tested our algorithm on forsterite (Mg2SiO4). Using a least squares inversion technique applied to all available experimental data, we show that it results in an accurate
representation of thermodynamic properties and sound wave velocities of Mg2SiO4 in its complete pressure–temperature stability range. We also show that the accuracy of our results is not significantly
affected by the use of a different equation of state. 相似文献
Noble gases trapped in meteorites are tightly bound in a carbonaceous carrier labeled “phase Q.” Mechanisms having led to their retention in this phase or in its precursors are poorly understood. To test physical adsorption as a way of retaining noble gases into precursors of meteoritic materials, we have performed adsorption experiments for Ar, Kr, and Xe at low pressures (10−4 mbar to 500 mbar) encompassing pressures proposed for the evolving solar nebula. Low-pressure adsorption isotherms were obtained for ferrihydrite and montmorillonite, both phases being present in Orgueil (CI), for terrestrial type III kerogen, the best chemical analog of phase Q studied so far, and for carbon blacks, which are present in phase Q and can be considered as possible precursors.Based on adsorption data obtained at low pressures relevant to the protosolar nebula, we propose that the amount of noble gases that can be adsorbed onto primitive materials is much higher than previously inferred from experiments carried out at higher pressures. The adsorption capacity increases from kerogen, carbon blacks, montmorillonite to ferrihydrite. Because of its low specific surface area, kerogen can hardly account for the noble gas inventory of Q. Carbon blacks in the temperature range 75 K-100 K can adsorb up to two orders of magnitude more noble gases than those found in Q. Irreversible trapping of a few percent of noble gases adsorbed on such materials could represent a viable process for incorporating noble gases in phase Q precursors. This temperature range cannot be ruled out for the zone of accretion of the meteorite precursors according to recent astrophysical models and observations, although it is near the lower end of the temperatures proposed for the evolving solar nebula. 相似文献
Garnet–melt trace element partitioning experiments were performed in the system FeO–CaO–MgO–Al2O3–SiO2 (FCMAS) at 3 GPa and 1540°C, aimed specifically at studying the effect of garnet Fe2+ content on partition coefficients (DGrt/Melt). DGrt/Melt, measured by SIMS, for trivalent elements entering the garnet X-site show a small but significant dependence on garnet almandine content. This dependence is rationalised using the lattice strain model of Blundy and Wood [Blundy, J.D., Wood, B.J., 1994. Prediction of crystal–melt partition coefficients from elastic moduli. Nature 372, 452–454], which describes partitioning of an element i with radius ri and valency Z in terms of three parameters: the effective radius of the site r0(Z), the strain-free partition coefficient D0(Z) for a cation with radius r0(Z), and the apparent compressibility of the garnet X-site given by its Young's modulus EX(Z). Combination of these results with data in Fe-free systems [Van Westrenen, W., Blundy, J.D., Wood, B.J., 1999. Crystal-chemical controls on trace element partitioning between garnet and anhydrous silicate melt. Am. Mineral. 84, 838–847] and crystal structure data for spessartine, andradite, and uvarovite, leads to the following equations for r0(3+) and EX(3+) as a function of garnet composition (X) and pressure (P):
Accuracy of these equations is shown by application to the existing garnet–melt partitioning database, covering a wide range of P and T conditions (1.8 GPa<P<5.0 GPa; 975°C<T<1640°C). DGrt/Melt for all 3+ elements entering the X-site (REE, Sc and Y) are predicted to within 10–40% at given P, T, and X, when DGrt/Melt for just one of these elements is known. In the absence of such knowledge, relative element fractionation (e.g. DSmGrt/Melt/DNdGrt/Melt) can be predicted. As an example, we predict that during partial melting of garnet peridotite, group A eclogite, and garnet pyroxenite, r0(3+) for garnets ranges from 0.939±0.005 to 0.953±0.009 Å. These values are consistently smaller than the ionic radius of the heaviest REE, Lu. The above equations quantify the crystal-chemical controls on garnet–melt partitioning for the REE, Y and Sc. As such, they represent a major advance en route to predicting DGrt/Melt for these elements as a function of P, T and X. 相似文献
We have studied the influence of Ca-Tschermaks (Calcium Tschermaks or CaTs) content of clinopyroxene on the partitioning of trace elements between this phase and silicate melt at fixed temperature and pressure. Ion probe analyses of experiments carried out in the system Na2O–CaO–MgO–Al2O3–SiO2, at 0.1 MPa and 1218°C, produced crystal-melt partition coefficients (D) of 36 trace elements (Li, Cl, Sc, Ti, V, Cr, Fe, Co, Ge, Sr, Y, Zr, Nb, Mo, Ru, Rh, In, Sn, Sb, Ba, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Hf, Ta and W), for clinopyroxene compositions between 10 and 32 mol% CaTs. Partition coefficients for 2+ to 5+ cations show, for each charge, a near parabolic dependence of log D on ionic radius of the substituting cation, for partitioning into both the M1 and M2 sites of clinopyroxene. Fitting the results to the elastic strain model of Blundy and Wood [Blundy, J.D., Wood, B.J., 1994. Prediction of crystal-melt partition coefficients from elastic moduli. Nature 372, 452–454] we obtain results for the strain-free partition coefficients of theoretical cations (D0), with site radius r0, and for the site's Young's Modulus (E).
In agreement with earlier data our results show that increasing ivAl concentration in cpx is matched by increasing D, EM1, EM2 and D0 for tri-, tetra- and pentavalent cations. The degree of fractionation between chemically similar elements (i.e. Ta/Nb, Zr/Hf) also increases. In contrast, D values for mono-, di- and hexavalent cations decrease with increasing ivAl in the cpx. The large suite of trace elements used has allowed us to study the effects of cation charge on D0, r0 and E. We have found that D0 and r0 decrease with increasing cation charge, e.g. r0=0.66 Å for 4+ cations and 0.59 Å for 5+ cations substituting into M1. Values of EM1 and EM2 increase with cation charge as well as with increasing ivAl content. The increase in EM2 is linear and close to the trend set by Hazen and Finger [Hazen, R.M., Finger, L.W., 1979. Bulk modulus-volume relationship for cation–anion polyhedra. J. Geophys. Res. 84 (10) 6723–6728] for oxides. EM1 values are much higher and do not fit the trend predicted by the Hazen and Finger relationship. 相似文献
Understanding the mobility of chemical elements during fluid–rock interactions is critical to assess the geochemical evolution of a rock undergoing burial and metamorphism and, more generally, to constrain the geochemical budget of the subduction factory. In particular, determining the behavior and mobility of Ti in aqueous fluids constitutes a great challenge that is still under scrutiny. Here, we study plant fossils preserved in blueschist metasedimentary rocks from the Marybank Formation (New Zealand). Using scanning and transmission electron microscopies (SEM and TEM), we show that the carbonaceous material (CM) composing the fossils contains abundant nano-inclusions of Ti- and Fe-oxides. These nanocrystals are mainly anatase, rutile, and Fe–Ti oxides. The mineral composition observed within the fossils is significantly different from that detected in the surrounding rock matrix. We propose that Ti and Fe might have been mobilized by the alteration of a detrital Ti–Fe-rich protolith during an early diagenetic event under acidic and reducing conditions. Aqueous fluids rich in organic ligands released by the degradation of organic matter may have been involved. Moreover, using mass balance and petrological observations, we show that the contrasted mineralogy between the rock matrix and the fossil CM might be the consequence of the chemical isolation of fossil CM during the prograde path of the rock. Such an isolation results from the early formation of quartz and Fe-rich phyllosilicate layers enclosing the fossil as characterized by SEM and TEM investigations. Overall, this study shows that investigating minerals associated with CM down to the nanometer scale in metamorphic rocks can provide a precious record of early prograde geochemical conditions. 相似文献