Constraint energy minimizing generalized multiscale finite element method in the mixed formulation

This paper presents a novel mass-conservative mixed multiscale method for solving flow equations in heterogeneous porous media. The media properties (the permeability) contain multiple scales and high contrast. The proposed method solves the flow equation in a mixed formulation on a coarse grid by constructing multiscale basis functions. The resulting velocity field is mass-conservative on the fine grid. Our main goal is to obtain first-order convergence in terms of the mesh size which is independent of local contrast. This is achieved, first, by constructing some auxiliary spaces, which contain global information that cannot be localized, in general. This is built on our previous work on the generalized multiscale finite element method (GMsFEM). In the auxiliary space, multiscale basis functions corresponding to small (contrast-dependent) eigenvalues are selected. These basis functions represent the high-conductivity channels (which connect the boundaries of a coarse block). Next, we solve local problems to construct multiscale basis functions for the velocity field. These local problems are formulated in the oversampled domain, taking into account some constraints with respect to auxiliary spaces. The latter allows fast spatial decay of local solutions and, thus, allows taking smaller oversampled regions. The number of basis functions depends on small eigenvalues of the local spectral problems. Moreover, multiscale pressure basis functions are needed in constructing the velocity space. Our multiscale spaces have a minimal dimension, which is needed to avoid contrast dependence in the convergence. The method’s convergence requires an oversampling of several layers. We present an analysis of our approach. Our numerical results confirm that the convergence rate is first order with respect to the mesh size and independent of the contrast.     

Hydro-thermal coupled analysis for health monitoring of embankment dams

Measuring and analyzing internal dam temperature may provide insight into evaluating the integrity of earthen dams. Temperature in a dam, with the advent of modern distributed temperature sensing (DTS) technique, is conveniently measured. The analysis of the temperature is conducted based on a hydro-thermal coupled analysis technique. In this study, DTS-based temperature data and VS2DHI (a finite difference code for analyzing two-dimensional heat transport in porous media) were used to analyze the hydro-thermal coupled behavior in a dam. The results of this analysis show that the temperature variation in an earthen dam is closely related to seepage conditions. Additionally, a localized high-temperature (26 °C) zone found in the measured data of the dam, which raised concern to engineers on site, is explained through either hot water infiltration into the foundation layer or lower permeability of the foundation layer than the magnitude that appeared in the design document. These findings demonstrate that hydro-thermal coupled analysis has the potential for evaluating the integrity of earthen dams.     

Formation by silicate–fluoride + phosphate melt immiscibility of REE-rich globular segregations within aplite dikes

Aplite dikes intruding the Proterozoic 1.42(±?3) Ga Longs Peak-St. Vrain Silver Plume-type peraluminous granite near Jamestown, Colorado, contain F, P, and rare earth element (REE)-rich globular segregations, with 40–46% REE, 3.7–4.8 wt% P₂O₅, and 5–8 wt% F. A combination of textural features and geochemical data suggest that the aplite and REE-rich globular segregations co-existed as two co-genetic liquids prior to their crystallization, and we propose that they are formed by silicate–fluoride?+?phosphate (+?S?+?CO₂) melt immiscibility following ascent, cooling, and decompression of what was initially a single homogeneous magma that intruded the granite. The REE distribution coefficients between the silica-rich aplites and REE-rich segregations are in good agreement with experimentally determined distribution coefficients for immiscible silicate–fluoride?+?phosphate melts. Although monazite-(Ce) and uraninite U–Th–Pb microprobe ages for the segregations yield 1.420(±?25) and 1.442(±?8) Ga, respectively, thus suggesting a co-genetic relationship with their host granite, ε_Nd1.42Ga values for the granites and related granitic pegmatites range from ??3.3 to ??4.7 (average ??3.9), and differ from the values for both the aplites and REE-rich segregations, which range from ??1.0 to ??2.2 (average ??1.6). Furthermore, the granites and pegmatites have (La/Yb)_N <50 with significant negative Eu anomalies, which contrast with higher (La/Yb)_N >100 and absence of an Eu anomaly in both the aplites and segregations. These data are consistent with the aplite dikes and the REE-rich segregations they contain being co-genetic, but derived from a source different from that of the granite. The higher ε_Nd1.42Ga values for the aplites and REE-rich segregations suggest that the magma from which they separated had a more mafic and deeper, dryer and hotter source in the lower crust or upper mantle compared to the quartzo-feldspathic upper crustal source proposed for the Longs Peak-St. Vrain granite.     

Carbon and nitrogen isotope,and mineral inclusion studies on the diamonds from the Pozanti–Karsanti chromitite,Turkey

The Pozanti–Karsanti ophiolite (PKO) is one of the largest oceanic remnants in the Tauride belt, Turkey. Micro-diamonds were recovered from the podiform chromitites, and these diamonds were investigated based on morphology, color, cathodoluminescence, nitrogen content, carbon and nitrogen isotopes, internal structure and inclusions. The diamonds recovered from the PKO are mainly mixed-habit diamonds with sectors of different brightness under the cathodoluminescence images. The total δ¹³C range of the PKO diamonds varies between ??18.8 and ??28.4‰, with a principle δ¹³C mode at ??25‰. Nitrogen contents of the diamonds range from 7 to 541 ppm with a mean value of 171 ppm, and the δ¹⁵N values range from ??19.1 to 16.6‰, with a δ¹⁵N mode of ??9‰. Stacking faults and partial dislocations are commonly observed in the Transmission Electron Microscopy foils whereas inclusions are rather rare. Combinations of (Ca_0.81Mn_0.19)SiO₃, NiMnCo-alloy and nano-sized, quenched fluid phases were observed as inclusions in the PKO diamonds. We believe that the ¹³C-depleted carbon signature of the PKO diamonds derived from previously subducted crustal matter. These diamonds may have crystallized from C-saturated fluids in the asthenospheric mantle at depth below 250 km which were subsequently carried rapidly upward by asthenospheric melts.     

Experimental study of quartz inclusions in garnet at pressures up to 3.0 GPa: evaluating validity of the quartz-in-garnet inclusion elastic thermobarometer

Garnet crystals with quartz inclusions were hydrothermally crystallized from oxide starting materials in piston–cylinder apparatuses at pressures from 0.5 to 3 GPa and temperatures ranging from 700 to 800 °C to study how entrapment conditions affect remnant pressures of quartz inclusions used for quartz-in-garnet (QuiG) elastic thermobarometry. Systematic changes of the 128, 206 and 464 cm^?1 Raman band frequencies of quartz were used to determine pressures of quartz inclusions in garnet using Raman spectroscopy calibrations that describe the P–T dependencies of Raman band shifts for quartz under hydrostatic pressure. Within analytical uncertainties, inclusion pressures calculated for each of the three Raman band frequencies are equivalent, which suggests that non-hydrostatic stress effects caused by elastic anisotropy in quartz are smaller than measurement errors. The experimental quartz inclusions have pressures ranging from ??0.351 to 1.247 GPa that span the range of values observed for quartz inclusions in garnets from natural rocks. Quartz inclusion pressures were used to model P–T conditions at which the inclusions could have been trapped. The accuracy of QuiG thermobarometry was evaluated by considering the differences between pressures measured during experiments and pressures calculated using published equation of state parameters for quartz and garnet. Our experimental results demonstrate that Raman measurements performed at room temperature can be used without corrections to estimate garnet crystallization pressures. Calculated entrapment pressures for quartz inclusions in garnet are less than ~?10% different from pressures measured during the experiments. Because the method is simple to apply with reasonable accuracy, we expect widespread usage of QuiG thermobarometry to estimate crystallization conditions for garnet-bearing silicic rocks.     

Electrical conductivity of the plagioclase–NaCl–water system and its implication for the high conductivity anomalies in the mid-lower crust of Tibet Plateau

In order to investigate the origin of the high conductivity anomalies geophysically observed in the mid-lower crust of Tibet Plateau, the electrical conductivity of plagioclase–NaCl–water system was measured at 1.2 GPa and 400–900 K. The relationship between electrical conductivity and temperature follows the Arrhenius law. The bulk conductivity increases with the fluid fraction and salinity, but is almost independent of temperature (activation enthalpy less than 0.1 eV). The conductivity of plagioclase–NaCl–water system is much lower than that of albite–NaCl–water system with similar fluid fraction and salinity, indicating a strong effect of the major mineral phase on the bulk conductivity of the brine-bearing system. The high conductivity anomalies of 10^?1 and 10⁰ S/m observed in the mid-lower crust of Tibet Plateau can be explained by the aqueous fluid with a volume fraction of 1 and 9%, respectively, if the fluid salinity is 25%. The anomaly value of 10^?1 S/m can be explained by the aqueous fluid with a volume fraction of 6% if the salinity is 10%. In case of Southern Tibet where the heat flow is high, the model of a thin layer of brine-bearing aqueous fluid with a high salinity overlying a thick layer of partial melt is most likely to prevail.     

An experimental study of Fe–Ni exchange between sulfide melt and olivine at upper mantle conditions: implications for mantle sulfide compositions and phase equilibria

The behavior of nickel in the Earth’s mantle is controlled by sulfide melt–olivine reaction. Prior to this study, experiments were carried out at low pressures with narrow range of Ni/Fe in sulfide melt. As the mantle becomes more reduced with depth, experiments at comparable conditions provide an assessment of the effect of pressure at low-oxygen fugacity conditions. In this study, we constrain the Fe–Ni composition of molten sulfide in the Earth’s upper mantle via sulfide melt–olivine reaction experiments at 2 GPa, 1200 and 1400 °C, with sulfide melt \(X_{{{\text{Ni}}}}^{{{\text{Sulfide}}}}=\frac{{{\text{Ni}}}}{{{\text{Ni}}+{\text{Fe}}}}\) (atomic ratio) ranging from 0 to 0.94. To verify the approach to equilibrium and to explore the effect of \({f_{{{\text{O}}_{\text{2}}}}}\) on Fe–Ni exchange between phases, four different suites of experiments were conducted, varying in their experimental geometry and initial composition. Effects of Ni secondary fluorescence on olivine analyses were corrected using the PENELOPE algorithm (Baró et al., Nucl Instrum Methods Phys Res B 100:31–46, 1995), “zero time” experiments, and measurements before and after dissolution of surrounding sulfides. Oxygen fugacities in the experiments, estimated from the measured O contents of sulfide melts and from the compositions of coexisting olivines, were 3.0?±?1.0 log units more reduced than the fayalite–magnetite-quartz (FMQ) buffer (suite 1, 2 and 3), and FMQ ??1 or more oxidized (suite 4). For the reduced (suites 1–3) experiments, Fe–Ni distribution coefficients \(K_{{\text{D}}}^{{}}=\frac{{(X_{{{\text{Ni}}}}^{{{\text{sulfide}}}}/X_{{{\text{Fe}}}}^{{{\text{sulfide}}}})}}{{(X_{{{\text{Ni}}}}^{{{\text{olivine}}}}/X_{{{\text{Fe}}}}^{{{\text{olivine}}}})}}\) are small, averaging 10.0?±?5.7, with little variation as a function of total Ni content. More oxidized experiments (suite 4) give larger values of K_D (21.1–25.2). Compared to previous determinations at 100 kPa, values of K_D from this study are chiefly lower, in large part owing to the more reduced conditions of the experiments. The observed difference does not seem attributable to differences in temperature and pressure between experimental studies. It may be related in part to the effects of metal/sulfur ratio in sulfide melt. Application of these results to the composition of molten sulfide in peridotite indicates that compositions are intermediate in composition (\(X_{{{\text{Ni}}}}^{{{\text{sulfide}}}}\)?~?0.4–0.6) in the shallow mantle at 50 km, becomes more Ni rich with depth as the O content of the melt diminishes, reaching a maximum (0.6–0.7) at depths near 80–120 km, and then becomes more Fe rich in the deeper mantle where conditions are more reduced, approaching (\(X_{{{\text{Ni}}}}^{{{\text{sulfide}}}}\)?~?0.28)?>?140 km depth. Because Ni-rich sulfide in the shallow upper mantle melts at lower temperature than more Fe-rich compositions, mantle sulfide is likely molten in much of the deep continental lithosphere, including regions of diamond formation.     

Experimental calibration of vanadium partitioning and stable isotope fractionation between hydrous granitic melt and magnetite at 800 °C and 0.5 GPa

Vanadium has multiple oxidation states in silicate melts and minerals, a property that also promotes fractionation of its isotopes. As a result, vanadium isotopes vary during magmatic differentiation, and can be powerful indicators of redox processes at high temperatures if their partitioning behaviour can be determined. To quantify the partitioning and isotope fractionation factor of V between magnetite and melt, piston cylinder experiments were performed in which magnetite and a hydrous, haplogranitic melt were equilibrated at 800 °C and 0.5 GPa over a range of oxygen fugacities (\({f_{{{\text{O}}_{\text{2}}}}}\)), bracketing those of terrestrial magmas. Magnetite is isotopically light with respect to the coexisting melt, a tendency ascribed to the VI-fold V³⁺ and V⁴⁺ in magnetite, and a mixture of IV- and VI-fold V⁵⁺ and V⁴⁺ in the melt. The magnitude of the fractionation factor systematically increases with increasing log\({f_{{{\text{O}}_{\text{2}}}}}\) relative to the Fayalite–Magnetite–Quartz buffer (FMQ), from ?⁵¹V_mag-gl = ? 0.63?±?0.09‰ at FMQ ? 1 to ? 0.92?±?0.11‰ (SD) at ≈?FMQ?+?5, reflecting constant V³⁺/V⁴⁺ in magnetite but increasing V⁵⁺/V⁴⁺ in the melt with increasing log\({f_{{{\text{O}}_{\text{2}}}}}\). These first mineral-melt measurements of V isotope fractionation factors underline the importance of both oxidation state and co-ordination environment in controlling isotopic fractionation. The fractionation factors determined experimentally are in excellent agreement with those needed to explain natural isotope variations in magmatic suites. Furthermore, these experiments provide a useful framework in which to interpret vanadium isotope variations in natural rocks and magnetites, and may be used as a potential fingerprint the redox state of the magma from which they crystallise.     

Petrogenesis of low-δ<Superscript>18</Superscript>O quartz porphyry dykes,Koegel Fontein complex,South Africa

This paper investigates the origin of low-δ¹⁸O quartz porphyry dykes associated with the 144–133 Ma Koegel Fontein Igneous Complex, which was intruded during the initial phase of breakup of Africa and South America. The 25-km diameter Rietpoort Granite is the largest and youngest phase of activity, and is roofed by a 10-km diameter pendant of gneiss. Quartz porphyry (QP) dykes, up to 15 m in width, strike NW–SE across the complex. The QP dykes that intruded outside the granite have similar quartz phenocryst δ¹⁸O values (average 8.0‰, ± 0.7, n?=?33) to the granite (average 8.3?±?1.0, n?=?7). The QP dykes that intruded the roof pendant have quartz phenocrysts with more variable δ¹⁸O values (average 1.6‰, ± 2.1, n?=?55). In some cases quartz phenocrysts have δ¹⁸O values as low as ? 2.5‰. The variation in δ¹⁸O value within the quartz crystal population of individual dykes is small relative to the overall range, and core and rim material from individual quartz phenocrysts in three samples are identical within error. There is no evidence that quartz phenocryst δ¹⁸O values have been affected by fluid–rock interaction. Based on a ?_quartz?magma value of 0.6‰, magma δ¹⁸O values must have been as low as ? 3.1‰. Samples collected along the length of the two main QP dykes that traverse the roof pendant have quartz phenocryst δ¹⁸O values that range from +?1.1 to +?4.6‰, and ? 2.3 to +?5.6‰, respectively. These δ¹⁸O values correlate negatively (r = ? 0.96) with initial ⁸⁷Sr/⁸⁶Sr, which can be explained by the event that lowered δ¹⁸O values of the source being older than the dykes. We suggest that the QP dykes were fed by magma produced by partial melting of gneiss, which had been variably altered at high temperature by ¹⁸O-depleted meteoric water during global glaciation at ~?550 Ma. The early melts had variable δ¹⁸O value but as melt pockets interconnected during melting, the δ¹⁸O values approached that of average gneiss. Variable quartz phenocryst δ¹⁸O values in the same dyke can be explained by vertical emplacement, at variable rates of ascent along the dyke. The lateral variation in quartz, and hence magma δ¹⁸O value at a particular point along a single dyke would depend on the rate of ascent of magma at that point along the dyke, and the ‘age’ of the particular magma batch.