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.     

Effective resource estimates for primary diamond deposits from the EKATI Diamond Mine™, Canada

Primary economic diamond deposit modelling has rarely been documented in the public domain. This paper presents information collected from significantly diamondiferous kimberlite pipes located near Lac de Gras in the Arctic region of Canada's Northwest Territories. The resource estimation process is widely accepted as a cyclical iteration of data collection and evaluation processes. A resource database is typically assembled from a large inventory of exploration data. These data must be methodically quality checked before accepting the information for interpretive analysis. The foundation of a mineral resource model is based on clear understanding of the geology model along with subsidiary grade, volume, and density models. Defining these models is an iterative process of statistical analyses and interpretation. As a deposit progresses along a path towards development, reducing risk to acceptable levels is critical for identifying and realizing its maximum value.     

Spatial and Temporal Cusp Structures Observed by Multiple Spacecraft and Ground Based Observations

Downward precipitating ions in the cusp regularly exhibit sudden changes in ion energy distributions, forming distinctive structures that can be used to study the temporal/spatial nature of reconnection at the magnetopause. When observed simultaneously with the Polar, FAST, and Interball satellites, such cusp structures revealed remarkably similar features. These similar features could be observed for up to several hours during stable solar wind conditions. Their similarities led to the conclusion that large-scale cusp structures are spatial structures related to global ionospheric convection patterns created by magnetic merging and not the result of temporal variations in reconnection parameters. The launch of the Cluster fleet allows cusp structures to be studied in great detail and during changing solar wind conditions using three spacecraft with identical plasma and field instrumentation. In addition, Cluster cusp measurements are linked with ionospheric convection cells by combining the satellite observations with SuperDARN radar observations that are used to derive the convection patterns in the ionosphere. The combination of satellite observations with ground-based observations during variable solar wind conditions shows that large-scale cusp structures can be either spatial or temporal. Cusp structures can be described as spatial features observed by satellites crossing into spatially separated flux tubes. Cusp structures can also be observed as poleward-traveling (temporal) features within the same convection cell, most probably caused by variations in the reconnection rate at the magnetopause.     

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.     

华南地区栖霞组“菊花石”假象与海泡石矿成因关系探讨

根据对华南地区二叠系栖霞组内菊花石假象的成因研究,结合对该组内燧石结核,菊花石内正延性玉髓和海泡石形成时代关系的现状关系的观察,认为华南地区栖霞组内的海泡石形成于早期成岩作用过程中,与该组内燧石结核和菊花石假象内的正延性玉髓同期形成,其成因既与高盐度的沉积环境或高盐度的成岩环境条件无关,也与热液活动无关。     

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.     

Isotopic constraints on Columbia River flood basalt genesis and the nature of the subcontinental mantle

Pb, O, Nd, and Sr isotopic data for the Columbia River basalts paint a complex picture for the origin of this flood basalt province. At least 3 distinct mantle sources appear to have been involved, superimposed upon which are the effects of crystal fractionation and mass exchange with evolved crustal wallrocks. To a large degree, the initiation of Columbia River volcanism and the geochemical characteristics of the basalts appear to have been influenced by subduction of the Juan de Fuca plate beneath the North American plate in a manner analogous to the origin of back-arc basins. The physical structure of the crust appears to have influenced the late stage evolution of the magmas by directing the locus of eruption to the border between the ancient continental interior and much younger crust to the south and west. This proximity to the continental interior also allowed old enriched subcontinental mantle to become involved in the very late stages of Columbia River volcanism. An important consequence of the existence of enriched mantle regions beneath continents is that the combination, crust plus enriched mantle, requires more incompatible elements to have been extracted from the remainder of the mantle than would be the case if no enriched mantle existed.