Numerical Scheme for Treatment of Uehling–Uhlenbeck Equation for Binary and Triple Interactions in Relativistic Plasma

We present a new efficient method to compute Uehling–Uhlenbeck collision integral for any two-particle and three-particle interactions in relativistic plasma with drastic improvement in computation time with respect to existingmethods. Reaction rates are compared, where possible, with the corresponding analytical expressions and another numerical results.     

Relativistic Reductions in High-Precision Measurements of the Earth’s Global Gravity Field Using a Multipair Constellation

Astronomy Reports - The theory of relativistic reductions for future challenges of space gravimetry with target accuracy of up to 1 picometer is developed in this paper.     

The Quantitative Models of Trace Elements for Different Genetic Types of Enclaves in Granites

An attempt has been made to give an insight into the genesis of enclaves in granites by mathematically quantitative methods.After some deduction,the quantitative models of trace elements for the genetically different enclaves have been established,including those for restites,segregation schlierens,enclaves formed out of solidified margins ,and enclaves derived from the mixing of different magmas.These models have been tested and proven to be valid and reliable.The conclusions inferred from these quantitative models are consistent with field observations and petrological ,mineralogical and geochemical evidence.     

Arsenocolusite in Pyrite Ores of the Saum Copper–Zinc Massive Sulfide Deposit,North Urals

Geology of Ore Deposits - Pyrite ores on the flanks of the Saum copper–zinc massive sulfide deposit are clastic sediments intensely transformed under conditions of acid diagenesis. Colusite...     

REE Geochemistry and Mineralogy in Ores of the Talgan Cu–Zn Massive Sulfide Deposit,Southern Urals

Doklady Earth Sciences - The high REE concentrations (57.23–561.2 ppm) in thin-layered sulfide ores of the Talgan Cu–Zn massive sulfide deposit (Southern Urals) are related to the...     

Identifying the Representative Elementary Volume for Permeability in Heterolithic Deposits Using Numerical Rock Models

Using a range of realistic 3D numerical lithofacies (dm-scale) models of ripple laminated sandstone intercalated with mudstone we evaluate how single-phase permeability varies as a function of sample support. The models represent a range of mudstone content which is typical for tidal deposits. Furthermore, the spatial distribution of flow barriers (i.e. mudstone) is not random, but governed by sedimentological rules giving a variable anisotropy ratio as a function of mudstone content. Both vertical and horizontal permeability are found to vary at small sample volumes, but these fluctuations reduce as the sample volume increases. The vertical permeability increases while the horizontal permeability is nearly constant as a function of sample support for small mudstone contents. For higher mudstone content, the horizontal permeability decreases while the vertical permeability is nearly constant as a function of sample support. We propose a criterion, based on a normalised standard deviation, to determine the Representative Elementary Volume (REV). The size of the REV is dependent on both the property measured (vertical and horizontal permeability) and the correlation lengths of the lithological elements (i.e. lithofacies). Based on this we identify three flow upscaling regimes that each require a different method for upscaling: (1) layered systems where the arithmetic and harmonic averages are appropriate, (2) systems close to the percolation threshold where a percolation model should be used, and (3) discontinuous systems where an effective medium method provides the best estimate of permeability. The work gives, by using numerical experiments on a range of heterogeneous systems, a new insight in determination of the REV for permeability at the lithofacies scale and its relation to sedimentological parameters.     

Gravity anomalies,flexure, and deformation of the converging Indian lithosphere in Nepal and Sikkim–Darjeeling Himalayas

Researchers ubiquitously noted that the common processes of partitioning oblique convergence in response to drag from the trench-hanging plate simultaneously produce radial slips, along-strike translation, and extension parallel to the deformation front. Here, we focus on the area between Nepal and Sikkim–Darjeeling Himalayas, and carry out gravity and finite-element stress modeling of the strike-orthogonal converging Indian lithosphere. We delineate the geometries of different layers and their interfaces through gravity modeling. The optimum model parameters along with rheological parameters of different layers are used for finite-element modeling. Finite-element modeling is done with boundary conditions of keeping the upper surface free and rigidly fixing the section of the northern boundary below the Main Himalayan Thrust. We impart on its frontal section an amount of 6 × 10¹² N/m force, equivalent to resistive force of the Himalayan–Tibet system, and analyze the maximum and minimum compressive stress fields evolved in the lithosphere. We testify our observations with earthquake database and other geophysical and geological studies. We note that an increasing flexing of the Indian lithosphere beyond the Main Boundary Thrust becomes maxima between the Main Central Thrust and South Tibetan Detachment in both the areas; however, more steepening of the Moho boundary is identified in the Sikkim–Darjeeling Himalaya. This abrupt change in lithospheric geometry beneath the Greater Himalaya is likely correlated with the sharp elevation changes in the topography. Although the highest seismicity concentration is dominant in this zone, the Lesser and the Tethys Himalayas in Sikkim–Darjeeling area also record relatively fair seismic activity. More compressive stress field in different layers right within the sharp bending zone supports this observation. We thus propose that the sharp bending zone beneath the Greater Himalaya is suffering maximum deformation, and the deformation is continued in the mantle too. We also identify both right-lateral shear and radial vergence slip, which are presumably associated with the general dynamics and kinematics of the Himalaya.     

Statistical Models of Temperature in the Sacramento–San Joaquin Delta Under Climate-Change Scenarios and Ecological Implications

Changes in water temperatures caused by climate change in California’s Sacramento–San Joaquin Delta will affect the ecosystem through physiological rates of fishes and invertebrates. This study presents statistical models that can be used to forecast water temperature within the Delta as a response to atmospheric conditions. The daily average model performed well (R ² values greater than 0.93 during verification periods) for all stations within the Delta and San Francisco Bay provided there was at least 1 year of calibration data. To provide long-term projections of Delta water temperature, we forced the model with downscaled data from climate scenarios. Based on these projections, the ecological implications for the delta smelt, a key species, were assessed based on temperature thresholds. The model forecasts increases in the number of days above temperatures causing high mortality (especially along the Sacramento River) and a shift in thermal conditions for spawning to earlier in the year.     

A Hamilton–Jacobi Framework for Modeling Folds in Structural Geology

A novel mathematical framework for modeling folds in structural geology is presented. All the main fold classes from the classical literature: parallel folds, similar folds, and other fold types with convergent and divergent dip isogons are modeled in 3D space by linear and non-linear first-order partial differential equations. The equations are derived from a static Hamilton–Jacobi equation in the context of isotropic and anisotropic front propagation. The proposed Hamilton–Jacobi framework represents folded geological volumes in an Eulerian context as a time of arrival field relative to a reference layer. Metric properties such as distances, gradients (dip and strike), curvature, and their spatial variations can then be easily derived and represented as three-dimensional continua covering the whole geological volume. The model also serves as a basis for distributing properties in folded geological volumes.     

Comparison of Static,Kinematic and Dynamic Geodetic Deformation Models for Kutlugün Landslide in Northeastern Turkey

Being the cause of the loss of life and damaging property, landslide is an important natural hazard. Therefore, landslides have to be monitored and preventive measures taken accordingly. In Geodesy, landslides can be determined with static, kinematic and dynamic geodetic models. The aim of this study is to develop a dynamic geodetic model for landslides and compare it with static and kinematic geodetic models. A study area was selected in the Northeastern Black Sea Region of Turkey where landslides are the most effective natural hazard. Movements were determined with static, kinematic and dynamic geodetic models using geodetic, geologic and geophysical measurements made in the study area. Groundwater levels changes were regarded as causative forces in the formulation of the dynamic model. The dynamic model delivered more detailed information (direction, values, velocity, acceleration of movements) about landslide movements. It is possible to formulate more realistic strategies about prevention of landslides by using this information. As a result, it can be suggested that dynamic geodetic models are more useful in landslide studies.     

Nd–Sr–Hf–O isotope provinciality in the northernmost Arabian–Nubian Shield: implications for crustal evolution

Multi-isotope study including whole-rock Nd–Sr, single zircon Hf, and SIMS δ¹⁸O analyses of zircons sheds light on magma sources in the northernmost Arabian–Nubian Shield (ANS) during ~820–570 Ma. Reconnaissance initial Nd and Sr isotope data for the older rocks (~820–740 Ma) reaffirms previous estimates that early crustal evolution in this part of the shield involved some crustal contamination by pre-ANS material. Prominent isotope provinciality is displayed by post-collisional calc-alkaline and alkaline igneous rocks of ~635–570 Ma across a NW-SE transect across basement of the Sinai Peninsula (Egypt) and southern Israel. Silicic rocks of the NW-region are characterized by lower εNd(T)–εHf(T) and higher Sr_i and δ¹⁸O compared with rocks of the SE-region, and the transition between the regions is gradual. Within each region isotope ratios are independent of the extent of magma fractionation, and zircon cores and rims yield similar δ¹⁸O values. Comparison with southern segments of the ANS shows that the source for most ~635–570 Ma rocks can be modeled as the isotopically aged lower-intermediate crust in the ANS core (SE-region) and its northern, more contaminated ANS margins (NW-region). Nevertheless, Nd–Sr isotope enrichment of the lithospheric mantle is indicated by some basic magmas of the NW-region displaying the most enriched Nd–Sr isotope compositions. Comparison of Nd and Hf depleted mantle model ages for rocks of the SE-region may indicate that crustal formation events in the ANS geographical core took place at 1.1–1.2 Ga and were followed by crustal differentiation starting at ~0.9 Ga.     

Optimization of area–volume–elevation curve using GIS–SRTM method for rainwater harvesting in arid areas

The major limitation in planning water harvesting is the lack of knowledge in the estimation of surface area and storage volume at any depth of dam reservoir. The area–volume–elevation (AVE) curve of a reservoir plays a key role in estimating the most suitable depth, optimum surface area and highest capacity of reservoir storage. The existing methods to estimate the AVE curve are costly and time-consuming and require laborious work. This study attempts to develop a method to optimize the AVE curve for earth dams, using the digital elevation model generated by the Shuttle Radar Topography Mission (SRTM) data, and integrate it with the geographic information system (GIS), known as the GIS–SRTM. The proposed method was tested using field data in the Western Desert of Iraq, which is an arid environment. Three constructed small earth dams were selected for this study. The AVE curves were extracted for Horan 2 (H2), Al-gara 2 (G2) and Al-gara 4 (G4) earth dams. Comprehensive analyses have been carried out to evaluate the performance of the AVE curves using the proposed GIS–SRTM method and the field data. From the comparison, the proposed GIS–SRTM method was able to produce reliable AVE curves with a relative error less than 20%. Additionally, the proposed method was less time-consuming and the AVE curves can be visualized immediately. The proposed GIS–SRTM method is relatively supportive in analyzing spatial data to select the optimal site for rainwater harvesting and prevent excessive evaporation losses.     

Re–Os isotope evidence for mixed source components in carbonate-replacement Pb–Zn–Ag deposits in the Lavrion district,Attica, Greece

The Lavrion ore district contains carbonate-replacement and vein-type Pb–Zn–Ag deposits as well as low-grade porphyry Mo, Cu–Fe skarn, and minor breccia-hosted Pb–Zn–Cu sulfide mineralization. These ore types are spatially related to a Late Miocene granodiorite intrusion (7 to 10 Ma), and various sills and dikes of mafic to felsic composition. Samples of sphalerite and pyrite from the Ilarion carbonate replacement deposit, and galena from Vein 80 (vein-type mineralization) in the Adami deposit show heterogeneous Re–Os values. These values were partially disturbed by hydrothermal activity associated with the formation of hydrothermal veins (e.g., Vein 80). A plot of initial ¹⁸⁷Os/¹⁸⁸Os versus 1/Os_common ratios for pyrite and sphalerite from the Ilarion deposit form a mixing line (r²?=?0.78) between high concentration crustal-like and low concentration mantle-like end-members, or two crustal end-members one of which was more radiogenic than the other. Based on the Re–Os systematics and previously published geological and geochemical evidence, the most plausible explanation for the Re–Os isotope data is that ore-forming components were derived from mixed sources, one of which was a radiogenic crustal source from schists and carbonates probably near intrusion centers and the other, intrusive rocks in the district that are less radiogenic. Although the Re and Os concentrations of galena from Vein 80 are above background values they cannot be used as a chronometer. However, the results of the current study suggest that although pyrite, sphalerite, and galena are poor geochronometers in this ore deposit, due to partial open-system behavior, they still yield valuable information on the origin of the source rocks in the formation of bedded replacement and vein mineralization in the Lavrion district.     

Crystallogenetic models for metasomatic replacement in zircons: implications for U–Pb geochronology of Precambrian rocks

Recrystallization of zircons under the influence of fluids was studied using examples from Precambrian rocks (microcline granites, metasedimentary, and mafic rocks) of the Kola Peninsula. All zircon crystals showed complex internal textures visible by cathodoluminescence and backscattered electron (BSE) imaging. Detailed mineralogical and geochemical studies with subsequent secondary ion mass spectrometer U–Pb dating of different zircon domains show that secondary texture formation can be interpreted in terms of metasomatic replacement of zircon crystals on the base of crystallogenetic experimental models. Mechanisms of zircon replacement and interpretation of U–Pb ages for secondary zircon domains are dependent on the degree of damage of the zircon structure and the fluid composition. The recrystallization of metamict zircon without additional supply of new zircon substance (Zr, SiO₂) goes with the dissolution of amorphous domains and precipitation of new polycrystalline zircon, which preserves the U–Pb initial age, but loses radiogenic lead, and the lower intercept of Discordia lines with the Concordia curve determines the time of fluid influence. The recrystallization of metamict zircon or crystalline zircon with high contents of impurities with additional supply of Si and Zr forms monocrystalline replacements. Dissolution of primary zircon is accompanied by growth of new zircon domains differing in the composition of isomorphic impurities and zones of transitional composition, whose ages have no geological sense. The study is of particular importance for zircons from Precambrian rocks with long and complex histories.     

Prospectivity for epithermal gold–silver deposits in the Deseado Massif,Argentina

Previous prospectivity modelling for epithermal Au–Ag deposits in the Deseado Massif, southern Argentina, provided regional-scale prospectivity maps that were of limited help in guiding exploration activities within districts or smaller areas, because of their low level of detail. Because several districts in the Deseado Massif still need to be explored, prospectivity maps produced with higher detail would be more helpful for exploration in this region.We mapped prospectivity for low- and intermediate-sulfidation epithermal deposits (LISEDs) in the Deseado Massif at both regional and district scales, producing two different prospectivity models, one at regional scale and the other at district-scale. The models were obtained from two datasets of geological evidence layers by the weights-of-evidence (WofE) method. We used more deposits than in previous studies, and we applied the leave-one-out cross validation (LOOCV) method, which allowed using all deposits for training and validating the models. To ensure statistical robustness, the regional and district-scale models were selected amongst six combinations of geological evidence layers based on results from conditional independence tests.The regional-scale model (1000 m spatial resolution), was generated with readily available data, including a lithological layer with limited detail and accuracy, a clay alteration layer derived from a Landsat 5/7 band ratio, and a map of proximity to regional-scale structures. The district-scale model (100 m spatial resolution) was generated from evidence layers that were more detailed, accurate and diverse than the regional-scale layers. They were also more cumbersome to process and combine to cover large areas. The evidence layers included clay alteration and silica abundance derived from ASTER data, and a map of lineament densities. The use of these evidence layers was restricted to areas of favourable lithologies, which were derived from a geological map of higher detail and accuracy than the one used for the regional-scale prospectivity mapping.The two prospectivity models were compared and their suitability for prediction of the prospectivity in the district-scale area was determined. During the modelling process, the spatial association of the different types of evidence and the mineral deposits were calculated. Based on these results the relative importance of the different evidence layers could be determined. It could be inferred which type of geological evidence could potentially improve the modelling results by additional investigation and better representation.We conclude that prospectivity mapping for LISEDs at regional and district-scales were successfully carried out by using WofE and LOOCV methods. Our regional-scale prospectivity model was better than previous prospectivity models of the Deseado Massif. Our district-scale prospectivity model showed to be more effective, reliable and useful than the regional-scale model for mapping at district level. This resulted from the use of higher resolution evidential layers, higher detail and accuracy of the geological maps, and the application of ASTER data instead of Landsat ETM + data. District-scale prospectivity mapping could be further improved by: a) a more accurate determination of the age of mineralization relative to that of lithological units in the districts; b) more accurate and detailed mapping of the favourable units than what is currently available; c) a better understanding of the relationships between LISEDs and the geological evidence used in this research, in particular the relationship with hydrothermal clay alteration, and the method of detection of the clay minerals; and d) inclusion of other data layers, such as geochemistry and geophysics, that have not been used in this study.     

Stability numbers for an unsupported vertical circular excavation in c–ϕ soil

By using an axisymmetric lower bound finite element limit analysis formulation, the stability numbers (γH/c) for an unsupported vertical circular excavation in a cohesive–frictional soil have been generated. The numerical results are obtained for values of normalized excavation height (H/b) and friction angle (ϕ) greater than those considered previously in the literature. The results compare well with those available in literature. The stability numbers presented in this note would be beneficial from a design point of view.     

Fe–Mg interdiffusion rates in clinopyroxene: experimental data and implications for Fe–Mg exchange geothermometers

Chemical interdiffusion of Fe–Mg along the c-axis [001] in natural diopside crystals (X _Di = 0.93) was experimentally studied at ambient pressure, at temperatures ranging from 800 to 1,200 °C and oxygen fugacities from 10^?11 to 10^?17 bar. Diffusion couples were prepared by ablating an olivine (X _Fo = 0.3) target to deposit a thin film (20–100 nm) onto a polished surface of a natural, oriented diopside crystal using the pulsed laser deposition technique. After diffusion anneals, compositional depth profiles at the near surface region (~400 nm) were measured using Rutherford backscattering spectroscopy. In the experimental temperature and compositional range, no strong dependence of D ^Fe–Mg on composition of clinopyroxene (Fe/Mg ratio between Di₉₃–Di₆₅) or oxygen fugacity could be detected within the resolution of the study. The lack of fO₂-dependence may be related to the relatively high Al content of the crystals used in this study. Diffusion coefficients, D ^Fe–Mg, can be described by a single Arrhenius relation with $$D^{{{\text{Fe}} - {\text{Mg}}}} = 2. 7 7\pm 4. 2 7\times 10^{ - 7} {\text{exp(}}-3 20. 7\pm 1 6.0{\text{ kJ}}/{\text{mol}}/{\text{RT)m}}^{ 2} /{\text{s}}.$$ D ^Fe–Mg in clinopyroxene appears to be faster than diffusion involving Ca-species (e.g., D ^Ca–Mg) while it is slower than D ^Fe–Mg in other common mafic minerals (spinel, olivine, garnet, and orthopyroxene). As a consequence, diffusion in clinopyroxene may be the rate-limiting process for the freezing of many geothermometers, and compositional zoning in clinopyroxene may preserve records of a higher (compared to that preserved in other coexisting mafic minerals) temperature segment of the thermal history of a rock. In the absence of pervasive recrystallization, clinopyroxene grains will retain compositions from peak temperatures at their cores in most geological and planetary settings where peak temperatures did not exceed ~1,100 °C (e.g., resetting may be expected in slowly cooled mantle rocks, many plutonic mafic rocks, or ultra-high temperature metamorphic rocks).