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.     

Magnetic fabrics and rock magnetism of Proterozoic dike swarm from the southern São Francisco Craton, Minas Gerais State, Brazil

Magnetic fabric and rock magnetism studies were performed on 32 mafic dikes of a Proterozoic dike swarm from the southern São Francisco Craton (SFC; Minas Gerais State, SE Brazil). Magnetic anisotropies were determined by applying anisotropy of low-field magnetic susceptibility (AMS) and anisotropy of remanent magnetization (ARM). The latter was performed imposing both anhysteretic (total (AAR) and partial pAAR)) and isothermal remanence magnetizations (AIRM). Partial anhysteretic remanence anisotropy was performed based on remanent coercivity spectra from a pilot specimen of each site. In most sites, AMS is dominantly carried by ferromagnetic minerals, however, in some sites, the paramagnetic contribution exceeds 70% of bulk susceptibility. Rock magnetism and thin section analysis allow classifying the dikes as non-hydrothermalized and hydrothermalized. Magnetic measurement shows that the mean magnetic susceptibility is usually lower than 5×10⁻³ (SI). Ti-poor titanomagnetites up to pure magnetite pseudo-single-domain (PSD) grain sizes carry the majority of magnetic fabrics for non-hydrothermalized dikes whereas coarse to fine grained Ti-poor titanomagnetites carry the majority of magnetic fabrics for hydrothermalized dikes.Three primary AMS fabrics are recognized which are coaxial with ARM fabric, except for two dikes, from both non-hydrothermalized and hydrothermalized dikes. Normal AMS fabric surprisingly is not dominant (31%). The parallelism between AMS, pAAR_0–30, pAAR_30–60 and pAAR_60–90 fabrics in the hydrothermalized dikes indicates that magnetic grains formed due to late-stage crystallization or to remobilization of iron oxides due to hydrothermal alteration after dike emplacement have acquired a mimetic fabric coaxial with the primary fabric given by coarse-grained early crystallized Ti-poor titanomagnetites. This fabric is interpreted as magma flow in which the analysis of K_max inclination permitted the inference that the dikes were fed by horizontal or subhorizontal fluxes (K_max<30°). Intermediate AMS fabric is the most important (41%) in the investigated swarm. It is interpreted as due to vertical compaction of a static magma column with the minimum stress along the dike strike. ARM determinations for these sites also remained intermediate except for two dikes. In one of them, AIRM fabric resulted in normal AMS fabric while for the other AAR fabric resulted in inverse AMS fabric. A combination of AMS and ARM fabrics suggest that magmatic fabric for both dikes were overprinted by some late local event, probably related to Brasiliano orogenic processes after dike emplacement. InverseInverse AMS fabric is a minority (four dikes). ARM determinations also remained inverse suggesting a primary origin for inverse AMS fabric.     

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.     

Bismuth‐melt trails trapped in cassiterite–quartz veins

Native bismuth in the form of metallic melt has been considered instrumental to the formation of some metallic ore deposits via a mechanism dubbed the “Liquid Bismuth Collector Model.” Here, we provide petrographical documentation of trail‐forming, μm‐sized blebs of native bismuth in cassiterite–quartz veins from the Santa Bárbara greisen Sn deposit in the Rondônia tin province of northern Brazil. These inclusions suggest the trapping of a Bi melt that took place during vein formation, in a mechanism similar to the entrapment of fluid inclusions.     

Lake sedimentary processes and vegetation changes over the last 45k cal a bp in the uplands of south-eastern Amazonia

This study addresses paleoclimate influences in a southern Amazonia ecotone based on multiproxy records from lakes of the Carajás region during the last 45k cal a bp. Wet and cool environmental conditions marked the initial deposition in shallow depressions with detrital sediments and high weathering rates until 40k cal a bp. Concomitantly, forest and C3 canga plants, along with cool-adapted taxa, developed; however, short drier episodes enabled expansion of C4 plants and diagenetic formation of siderite. A massive event of siderite formation occurred approximately 30k cal a bp under strong drier conditions. Afterwards, wet and cool environmental conditions returned and persisted until the Last Glacial Maximum (LGM). The LGM was marked by lake-level lowstands and subaerial exposure. The transition from the LGM to the Holocene is marked by the onset of oscillations in temperature and humidity, with an expansion of forest and canga plants. Cool taxa were present for the last time in the Carajás region ~ 9.5–9k cal a bp. After 10k cal a bp , shallow lakes became upland swamps due to natural infilling processes, but the current vegetation types and structures of the plateaus were acquired only after 3k cal a bp under wetter climatic conditions.     

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.