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.     

Organic matter in small mesopores in sediments and soils

The three-way correlation among organic matter concentrations, specific surface area and small mesopores observed for many soils and sediments led to the hypothesis that enclosure within the pores might explain the apparent protection of organic matter by minerals. We test this hypothesis by examining whether the bulk of organic matter resides within small mesopores. Pore volumes as a function of pore width were measured before and after organic matter removal, and the volume differences ascribed to organic matter filling of pores. Minor changes in small mesopore size distributions upon treatments such as centrifugation and muffling indicate the robustness of the mineral matrices that form these pores. We developed an additional method to assess organic matter densities using high-resolution pycnometry, and used these densities to convert pore volumes to organic matter contents. Although smaller mesopores are shown to have sufficient volumes to contain significant fractions of the total organic matter, only small fractions of total organic matter were found to reside in them. These results are consistent with preferential association between organic matter and aluminous clay particle edges, rather than the largely siliceous clay faces that contribute most surface area and form pore walls. While simple enclosure within smaller mesopores cannot, therefore, explain protection, network effects working at larger size scales may account for exclusion of digestive agents and hence organic matter protection.     

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.     

Pumpellyite in Low-grade Metamorphism

The regional metamorphism of the Kant? Mountains in Japan producedrocks of the following facies, with rising temperature: chloritefacies, pumpellyite-chlorite facies, glauco-phane-schist facies,and greenschist facies. This relationship is compared with theprogressive metamorphic zones in other regions where pumpellyitehas been found. Almost similar relations appear to hold in manymetamorphic terrains. Pumpellyites in glaucophanitic metamorphicterrains have, generally, low Fe'/R'R ratios. Physical andchemical conditions responsible for the formation of pumpellyiteare also discussed.     

High- and low-Cr chromitite and dunite in a Tibetan ophiolite: evolution from mature subduction system to incipient forearc in the Neo-Tethyan Ocean

The microstructures, major- and trace-element compositions of minerals and electron backscattered diffraction (EBSD) maps of high- and low-Cr# [spinel Cr# = Cr³⁺/(Cr³⁺ + Al³⁺)] chromitites and dunites from the Zedang ophiolite in the Yarlung Zangbo Suture (South Tibet) have been used to reveal their genesis and the related geodynamic processes in the Neo-Tethyan Ocean. The high-Cr# (0.77–0.80) chromitites (with or without diopside exsolution) have chromite compositions consistent with initial crystallization by interaction between boninitic magmas, harzburgite and reaction-produced magmas in a shallow, mature mantle wedge. Some high-Cr# chromitites show crystal-plastic deformation and grain growth on previous chromite relics that have exsolved needles of diopside. These features are similar to those of the Luobusa high-Cr# chromitites, possibly recycled from the deep upper mantle in a mature subduction system. In contrast, mineralogical, chemical and EBSD features of the Zedang low-Cr# (0.49–0.67) chromitites and dunites and the silicate inclusions in chromite indicate that they formed by rapid interaction between forearc basaltic magmas (MORB-like but with rare subduction input) and the Zedang harzburgites in a dynamically extended, incipient forearc lithosphere. The evidence implies that the high-Cr# chromitites were produced or emplaced in an earlier mature arc (possibly Jurassic), while the low-Cr# associations formed in an incipient forearc during the initiation of a new episode of Neo-Tethyan subduction at ~130–120 Ma. This two-episode subduction model can provide a new explanation for the coexistence of high- and low-Cr# chromitites in the same volume of ophiolitic mantle.