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Simulation of multigaussian stochastic fields can be made after a Karhunen-Loéve expansion of a given covariance function. This method is also called simulation by Empirical Orthogonal Functions. The simulations are made by drawing stochastic coefficients from a random generator. These numbers are multiplied with eigenfunctions and eigenvalues derived from the predefined covariance model. The number of eigenfunctions necessary to reproduce the stochastic process within a predefined variance error, turns out to be a cardinal question. Some ordinary analytical covariance functions are used to evaluate how quickly the series of eigenfunctions can be truncated. This analysis demonstrates extremely quick convergence to 99.5% of total variance for the 2nd order exponential (‘gaussian’) covariance function, while the opposite is true for the 1st order exponential covariance function. Due to these convergence characteristics, the Karhunen-Loéve method is most suitable for simulating smooth fields with ‘gaussian’ shaped covariance functions. Practical applications of Karhunen-Loéve simulations can be improved by spatial interpolation of the eigenfunctions. In this paper, we suggest interpolation by kriging and limits for reproduction of the predefined covariance functions are evaluated.  相似文献   
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We study the importance of the zones of weakness and the pattern of downgoing flow in steady-state models of subducting lithosphere, which interacts mechanically and thermally with the ambient mantle. The non-linear system of governing equations consists of (i) the momentum equation in stream function formulation and (ii) the steady-state heat transfer equation including conduction and advection of heat and dissipation. A finite element method has been applied to this system. We consider the viscosity to be a non-linear function of both the temperature and the stream function. In steady-state two-dimensional (2D) flow, the stream function isolines follow material trajectories. They are used to follow the top of the subducting slab, which because of its possible increase in water content, is assumed to have a lower viscosity. The zone of weakness has been thus obtained in the self-consistent fashion since the stream function as well as the temperature are the output from our modeling and no a priori assumptions about the shape of the bending lithosphere are taken into account. It was shown that several orders decrease of viscosity in the zone of weakness is required to obtain the dip angle of about 45°. If the decrease of viscosity is not sufficient enough, the subducted slab either sinks almost vertically or does not exhibit a plate-like behavior. We have also demonstrated that shear heating can unrealistically increase at the zone of weakness for fast subductions if decrease of viscosity is underestimated.  相似文献   
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The effect of anomalous snow cover over the Tibetan Plateau upon the South Asian summer monsoon is investigated by numerical simulations using the NCAR regional climate model (RegCM2) into which gravity wave drag has been introduced. The simulations adopt relatively realistic snow mass forcings based on Scanning Multi-channel Microwave Radiometer (SNINIR) pentad snow depth data. The physical mechanism and spatial structure of the sensitivity of the South Asian early summer monsoon to snow cover anomaly over the Tibetan Plateau are revealed. The main results are summarized as follows. The heavier than normal snow cover over the Plateau can obviously reduce the shortwave radiation absorbed by surface through the albedo effect, which is compensated by weaker upward sensible heat flux associated with colder surface temperature, whereas the effects of snow melting and evaporation are relatively smaller.The anomalies of surface heat fluxes can last until June and become unobvious in July. The decrease of the Plateau surface temperature caused by heavier snow cover reaches its maximum value from late April to early May. The atmospheric cooling in the mid-upper troposphere over the Plateau and its surrounding areas is most obvious in May and can keep a fairly strong intensity in June. In contrast, there is warming to the south of the Plateau in the mid-lower troposphere from April to June with a maximum value in May.The heavier snow cover over the Plateau can reduce the intensity of the South Asian summer monsoon and rainfall to some extent, but this influence is only obvious in early summer and almost disappears in later stages.  相似文献   
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Compositional studies on different forms of magnetite, ulvospinel, ilmenite and hematite mineral phases occurring in 37 lava flows and 6 dykes of the Mandla lobe are presented in this paper. Ilmenite (0001) in equilibrium with titanomanetite show high values of temperature of equilibration, ranging from 1172–974°C, for high alumina quartz normative tholeiitic lava flows of Chemical Type - A; 1129–1229°C for low alumina quartz normative tholeiitic lava flows of Chemical Type - B; 1283–1124°C for tholeiitic lava flows of Chemical Type - F and 1243°C and 99O°C for two diopside olivine normative tholeiite flows of Chemical Type D. High olivine normative flows of Chemical Type - G and H show 1095°C and 1092°C respectively. Whereas, high hypersthene normative tholeiite flow of Chemical me C shows temperature of 1187°C. Data plots disposition over iron-titanium oxide equilibration temperature vs – logfo2, diagram for Mandla lava flows and other parts of the Deccan (Igatpuri, Mahabaleshwer, Nagpur and Sagar areas) revealed that tholeiitic (evolved) basalt of the eastern Deccan volcanic province formed at high temperatures whereas, picritic (primitive) lavas of Igatpuri and tholeiitic basalt of Mahabaleshwar areas were formed at low temperatures. Mahabaleshwer basalts follow FMQ (fayalite-magnetite-quartz) buffer curve but, plots of the Mandla basalts lie above this curve indicating higher temperatures of crystallisation of ilmenite-titanomagnetite than that of the lava flows from other parts of Deccan 'Raps. The eastern Deccan Traps are most evolved types of lava as characterised by its low Mg-number and Ni content whereas, Igatpuri lava flows are picritic (primitive), having high Mg-number and Ni contents. Temperature vs FeO + Fe2O3 / FeO + Fe2O3 + MgO ratio data plots for Mandla and other Deccan lava flows and liquidus data for Hawaiian tholeiites, indicated that Igatpuri basalts lie parallel to the liquidus line of Hawaiian tholeiite but at lower temperatures. Large data plots of Mandla lava flows lie along the liquidus line of the Hawaiian lava. The highly vesicular nature of compound lava flows having large amount of volatile is responsible for low temperature values whereas, lava flows represented by high temperatures show high modal values of glass and opaque minerals.  相似文献   
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The phase relations of quaternary systems are generally represented by projections onto ternary compositional planes. Such projections often obscure relationships that would only be evident in a three-dimensional tetrahedral plot. The tetrahedral plot requires that compositions of the minerals and melts be transformed into Cartesian coordinates. It is shown here how this transformation is carried out. The application is demonstrated by tetrahedral plots of experimental melt compositions of partially molten lherzolite. Furthermore, the plot can be used to evaluate whether or not a particular basaltic composition represents a primary melt. The methods are applicable to any four-component system.  相似文献   
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We present new Fe and Si isotope ratio data for the Torres del Paine igneous complex in southern Chile. The multi-composition pluton consists of an approximately 1 km vertical exposure of homogenous granite overlying a contemporaneous 250-m-thick mafic gabbro suite. This first-of-its-kind spatially dependent Fe and Si isotope investigation of a convergent margin-related pluton aims to understand the nature of granite and silicic igneous rock formation. Results collected by MC-ICP-MS show a trend of increasing δ56Fe and δ30Si with increasing silica content as well as a systematic increase in δ56Fe away from the mafic base of the pluton. The marginal Torres del Paine granites have heavier Fe isotope signatures (δ56Fe = +0.25 ± 0.02 2se) compared to granites found in the interior pluton (δ56Fe = +0.17 ± 0.02 2se). Cerro Toro country rock values are isotopically light in both Fe and Si isotopic systems (δ56Fe = +0.05 ± 0.02 ‰; δ30Si = ?0.38 ± 0.07 ‰). The variations in the Fe and Si isotopic data cannot be accounted for by local assimilation of the wall rocks, in situ fractional crystallization, late-stage fluid exsolution or some combination of these processes. Instead, we conclude that thermal diffusion or source magma variation is the most likely process producing Fe isotope ratio variations in the Torres del Paine pluton.  相似文献   
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