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.     

Simulations of a coupled hydro-chemo-mechanical system in rocks

A coupled hydro-chemo-mechanical numerical model is developed for these coupled phenomena in many engineering fields. The model has been applied to predicting the response of a stressed rockmass column to an injected reactive fluid (reagent) flow. The response includes evolutions of porosity, permeability, reagent and mineral concentrations during dissolution. In the model, the progress of dissolution is defined by the change in porosity ratio and the porosity increases with dissolution assuming there is no precipitation. The numerical evolutions of porosity, permeability, reagent and mineral concentrations during dissolution are validated against steady state solutions. The model results show that these evolutions are regulated to a certain extent by the applied external loadings: an applied extensional stress enhances the progress of the dissolution process while an applied compression stress slows the progress of the dissolution process. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

A modelling framework for evaluation of the hydrological impacts of nature‐based approaches to flood risk management,with application to in‐channel interventions across a 29‐km2 scale catchment in the United Kingdom

Nature‐based approaches to flood risk management are increasing in popularity. Evidence for the effectiveness at the catchment scale of such spatially distributed upstream measures is inconclusive. However, it also remains an open question whether, under certain conditions, the individual impacts of a collection of flood mitigation interventions could combine to produce a detrimental effect on runoff response. A modelling framework is presented for evaluation of the impacts of hillslope and in‐channel natural flood management interventions. It couples an existing semidistributed hydrological model with a new, spatially explicit, hydraulic channel network routing model. The model is applied to assess a potential flood mitigation scheme in an agricultural catchment in North Yorkshire, United Kingdom, comprising various configurations of a single variety of in‐channel feature. The hydrological model is used to generate subsurface and surface fluxes for a flood event in 2012. The network routing model is then applied to evaluate the response to the addition of up to 59 features. Additional channel and floodplain storage of approximately 70,000 m³ is seen with a reduction of around 11% in peak discharge. Although this might be sufficient to reduce flooding in moderate events, it is inadequate to prevent flooding in the double‐peaked storm of the magnitude that caused damage within the catchment in 2012. Some strategies using features specific to this catchment are suggested in order to improve the attenuation that could be achieved by applying a nature‐based approach.     

Influence of a coarse interlayer on seawater intrusion and contaminant migration in coastal aquifers

Vertical 2D slice laboratory experiments were carried out in homogenous and layered sand tanks to elucidate the effects of a highly permeable (coarse‐grained sand) interlayer on seawater intrusion and transport of contaminants to a coastal sea. Tidal fluctuations produced oscillations in the seawater–freshwater transition zone, fluctuations of the contaminant infiltration rate and a zigzag contaminant plume outline. The seawater wedge became discontinuous at the (vertical) edges of the interlayer because of increased lateral movement of the seawater–freshwater interface within the interlayer. The contaminant plume formed a tail within the interlayer depending on the tidal stage, and similar to the wedge, its movement was accentuated. A simple analytical model that neglected vertical flow reliably predicted steady‐state seawater intrusion into the coastal aquifer. Numerical modeling was used to gain insight into the groundwater hydrodynamics and contaminant migration. The numerical results confirmed the experimental findings, i.e. that a highly permeable interlayer can provide a rapid transit path for contaminants to reach the seaward boundary and that the interlayer amplifies the effects of tidal fluctuations, resulting in wider transition zones for the seawater wedge and contaminant plume. Numerical simulations further showed that, with increasing interlayer hydraulic conductivity, the maximum seawater intrusion distance inside the interlayer increases approximately linearly. For the fixed‐head contaminant injection condition used, the model showed that contaminant infiltration increases approximately logarithmically with increasing interlayer hydraulic conductivity (other factors held fixed). Copyright © 2013 John Wiley & Sons, Ltd.     

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.