Simulation of normal distributed smooth fields by Karhunen-Loéve expansion in combination with kriging

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.     

Influence of the zone of weakness on dip angle and shear heating of subducted slabs

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.     

Tetrahedral Plots of the Phase Relations for Basalts

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.     

Gas mixing with aqueous solution in the ore-forming hydrothermal process: an example of gold

The mixing of gas and aqueous fluid in hydrothermal ore-forming processes is discussed with reference to gold deposits to demonstrate that this phenomenon may affect ore deposition. Data on fluid inclusions in samples from the Sukhoi Log and Olimpiadinskoe deposits in Russia are utilized to demonstrate possible implications of gas mixing with hydrothermal solution when gold ores are formed. A simplified thermodynamic model is suggested to show how interaction between aqueous saline solutions with pure carbon dioxide or carbon dioxide—methane mixture may affect gold solubility. Further studying such processes may provide interesting information for understanding the genesis of ore mineralization.     

Spatially controlled Fe and Si isotope variations: an alternative view on the formation of the Torres del Paine pluton

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.     

Provenance analysis for Middle Eocene sediments in the West Kamchatka sedimentary basin (Tigil area)

The paper presents the results of reconstruction of Middle Eocene provenances for the West Kamchatka sedimentary basin (WKSB) corresponding to the Tigil area. It has been established that the early (Eocene) evolution stage of WKSB was marked by the deposition of terrigenous sediments in intermontane depressions followed by the accumulation of shallow-marine sediments after transgression. In terms of the composition, sandstones of the Middle Eocene Snatol Formation correspond to graywackes. With respect to the geochemistry of sandstones, their provenances were confined to an active continental margin and island arc. The mineral composition of the heavy fraction suggests an alternating dominance of felsic and mafic rocks in the provenances. Dating of the clastic zircon from sandstones of the Snatol Formation by the LA-ICP-MS method revealed a wide variation range of their age. The most significant peak is close to the age of calc-alkaline magmatism in the Okhotsk–Chukotka volcanic belt. This fact provides insight into the Eocene paleogeography: the major rock provenances were located in the Okhotsk–Chukotka volcanic belt and the eastern Achaivayam–Valagin island arc. Local sources of clastic material were represented by the Utkholok and Kinkil volcanic belts.     

Some general relations of the development of complex molecular objects at early stages of biosphere formation as a consequence of the physical properties of condensed medium

We analyzed the character of molecular transformations under conditions of condensed media, in which intermolecular interactions always occur. It was shown that, instead of discrete transfer of external energy into the molecule, the energy characteristics of the condensed medium (appearance of zones) could result in gradual accumulation of internal energy in reaction centers owing to sequential thermal collisions with particles of the medium initiating the chemical reaction. This does not require high temperatures. The established physical properties related to the energy characteristics of condensed media could play an important role in molecular transformations and, consequently, formation of complex molecular objects at early stages of biosphere formation.