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.     

Coastal neotectonics in Southern Central Andes: uplift and deformation of marine terraces in Northern Chile (27°S)

Neotectonic observations allow a new interpretation of the recent tectonic behaviour of the outer fore arc in the Caldera area, northern Chile (27°S). Two periods of deformation are distinguished, based on large-scale Neogene to Quaternary features of the westernmost part of the Coastal Cordillera: Late Miocene to Early Pliocene deformations, characterized by a weak NE–SW to E–W extension is followed by uppermost Pliocene NW–SE to E–W compression. The Middle Pleistocene to Recent time is characterized by vertical uplift and NW–SE extension. These deformations provide clear indications of the occurrence of moderate to large earthquakes. Microseismic observations, however, indicate a lack of shallow crustal seismicity in coastal zone. We propose that both long-term brittle deformation and uplift are linked to the subduction seismic cycle.     

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.     

Stormflow concentration–discharge dynamics of suspended sediment and dissolved phosphorus in an agricultural watershed

Concentration–discharge (C-Q) relationships are an effective tool for identifying watershed biogeochemical source and transport dynamics over short and long timescales. We examined stormflow C-Q, hysteresis, and flushing patterns of total suspended sediment (TSS) and soluble reactive phosphorus (SRP) in two stream reaches of a severely impaired agricultural watershed in northeastern Wisconsin, USA. The upper watershed reach—draining a relatively flat, row crop-dominated contributing area—showed predominantly anti-clockwise TSS hysteresis during storms, suggesting that particulate materials were mobilized more from distal upland sources than near- and in-channel areas. In contrast, the incised lower watershed reach produced strong TSS flushing responses on the rising limb of storm hydrographs and clockwise hysteresis, signalling rapid mobilization of near- and in-channel materials with increasing event flows. C-Q relationships for SRP showed complex patterns in both the upper and lower reaches, demonstrating largely non-linear chemodynamic C-Q behaviour during events. As with TSS, anti-clockwise SRP hysteresis in the upper reach suggested a delay in the hydrologic connectivity between SRP sources and the stream, with highly variable SRP concentrations during some events. A broad range of clockwise, anti-clockwise, and complex SRP hysteresis patterns occurred in the lower watershed, possibly influenced by in-channel legacy P stores and connection to tile drainage networks in the lower watershed area. Total suspended sediment and SRP responses were also strongly related to precipitation event characteristics including antecedent precipitation, recovery period, and precipitation intensity, highlighting the complexity of stormflow sediment and phosphorus responses in this severely impaired agricultural stream.     

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.