Stochastic modelling of groundwater flow and solute transport in aquifers

This paper presents an introductory overview of recently developed stochastic theories for tackling spatial variability problems in predicting groundwater flow and solute transport. Advantages and limitations of the theories are discussed. Lastly, strategies based on the stochastic approaches to predict solute transport in aquifers are recommended.     

Three dimensional simulation of fluid flow in X‐ray CT images of porous media

A numerical scheme is developed in order to simulate fluid flow in three dimensional (3‐D) microstructures. The governing equations for steady incompressible flow are solved using the semi‐implicit method for pressure‐linked equations (SIMPLE) finite difference scheme within a non‐staggered grid system that represents the 3‐D microstructure. This system allows solving the governing equations using only one computational cell. The numerical scheme is verified through simulating fluid flow in idealized 3‐D microstructures with known closed form solutions for permeability. The numerical factors affecting the solution in terms of convergence and accuracy are also discussed. These factors include the resolution of the analysed microstructure and the truncation criterion. Fluid flow in 2‐D X‐ray computed tomography (CT) images of real porous media microstructure is also simulated using this numerical model. These real microstructures include field cores of asphalt mixes, laboratory linear kneading compactor (LKC) specimens, and laboratory Superpave gyratory compactor (SGC) specimens. The numerical results for the permeability of the real microstructures are compared with the results from closed form solutions. Copyright © 2004 John Wiley & Sons, Ltd.     

Pressure-induced incipient amorphization of α-quartz and transition to coesite in an eclogite from Antarctica: a first record and some consequences

Monocrystalline quartz inclusions in garnet and omphacite from various eclogite samples from the Lanterman Range (Northern Victoria Land, Antarctica) have been investigated by cathodoluminescence (CL), Raman spectroscopy and imaging, and in situ X‐ray (XR) microdiffraction using the synchrotron. A few inclusions, with a clear‐to‐opalescent lustre, show ‘anomalous’ Raman spectra characterized by weak α‐quartz modes, the broadening of the main α‐quartz peak at 465 cm^?1, and additional vibrations at 480–485, 520–523 and 608 cm^?1. CL and Raman imaging indicate that this ‘anomalous’α‐quartz occurs as relicts within ordinary α‐quartz, and that it was preserved in the internal parts of small quartz inclusions. XR diffraction circular patterns display irregular and broad α‐quartz spots, some of which show an anomalous d‐spacing tightening of ～2%. They also show some very weak, hazy clouds that have d‐spacing compatible with coesite but not with α‐quartz. Raman spectrometry and XR microdiffraction characterize the anomalies with respect to α‐quartz as (i) a pressure‐induced disordering and incipient amorphization, mainly revealed by the 480–485 and 608‐cm^?1 Raman bands, together with (ii) a lattice densification, evidenced by d‐spacing tightening; (iii) the cryptic development of coesite, 520–523 cm^?1 being the main Raman peak of coesite and (iv) Brazil micro‐twinning. This ‘anomalous’α‐quartz represents the first example of pressure‐induced incipient amorphization of a metastable phase in a crustal rock. This issue is really surprising because pressure‐induced amorphization of metastable α‐quartz, observed in impactites and known to occur between 15 and 32 GPa during ultrahigh‐pressure (UHP) experiments at room temperature, is in principle irrelevant under normal geological P–T conditions. A shock (due to a seism?) or a local overpressure at the inclusion scale (due to expansion mismatch between quartz and its host mineral) seem the only geological mechanisms that can produce such incipient amorphization in crustal rocks. This discovery throws new light on the modality of the quartz‐coesite transition and on the pressure regimes (non‐lithostatic v. lithostatic) during high‐pressure/UHP metamorphism. In particular, incipient amorphization of quartz could favour the quartz‐coesite transition, or allow the growth of metastable coesite, as already experimentally observed.     

P‐wave transmission across fractures with nonlinear deformational behaviour

Stress wave attenuation across fractured rock masses is a great concern of underground structure safety. When the wave amplitude is large, fractures experience nonlinear deformation during the wave propagation. This paper presents a study on normal transmission of P‐wave across parallel fractures with nonlinear deformational behaviour (static Barton–Bandis model). The results show that the magnitude of transmission coefficient is a function of incident wave amplitude, nondimensional fracture spacing and number of fractures. Two important indices of nondimensional fracture spacing are identified, and they divide the area of nondimensional fracture spacing into three parts (individual fracture area, transition area and small spacing area). In the different areas, the magnitude of transmission coefficient has different trends with nondimensional fracture spacing and number of fractures. In addition, the study reveals that under some circumstances, the magnitude of transmission coefficient increases with increasing number of fractures, and is larger than 1. Copyright © 2006 John Wiley & Sons, Ltd.     

Isotope hydrological study of mean transit time in the granitic Strengbach catchment (Vosges massif,France): application of the FlowPC model with modified input function

Measurements of ¹⁸O concentrations in precipitation, soil solution, spring and runoff are used to determine water transit time in the small granitic Strengbach catchment (0·8 km²; 883–1146 m above sea level) located in the Vosges Mountains of northeastern France. Water transit times were calculated by applying the exponential, exponential piston and dispersion models of the FlowPC program to isotopic input (rainfall) and output (spring and stream water) data sets during the period 1989–95. The input function of the model was modified compared with the former version of the model and estimated by a deterministic approach based on a simplified hydrological balance. The fit between observed and calculated output data showed marked improvements compared with results obtained using the initial version of the model. An exponential piston version of the model applied to spring water indicates a 38·5 month mean transit time, which suggests that the volume in the aquifer, expressed in water depth, is 2·4 m. A considerable thickness (>45 m) of fractured bedrock may be involved for such a volume of water to be stored in the aquifer. Copyright © 2005 John Wiley & Sons, Ltd.     

Nutrient transports in a Swedish estuary

Himmerfjärd is a Swedish estuary bordering on the Baltic. The estuary lacks astronomical tides and its circulation is driven by winds and freshwater runoff. Because of a tertiary sewage treatment plant located at its inner end, the estuary is becoming increasingly eutrophic. A field study was carried out for a 78-day period in late summer and early fall of 1977 to determine rates of nutrient transport and to construct nutrient budgets. Since physical parameters (current velocity, temperature, salinity, winds and water level changes) were measured more frequently than nutrients (phosphate, nitrate, nitrite and ammonium) it was necessary to develop a suitable method to calculate nutrient flux time series and net nutrient fluxes. Over the study period, Himmerfjärd imported phosphorus and exported nitrogen. Direction of nutrient fluxes and changes in flux direction were consistent with the structure of the baroclinic currents.     

Porphyroblast inclusion-trail orientation data: eppure non son girate*!

Extensive examination of large numbers of spatially orientated thin sections of orientated samples from orogens of all ages around the world has demonstrated that porphyroblasts do not rotate relative to geographical coordinates during highly non-coaxial ductile deformation of the matrix subsequent to their growth. This has been demonstrated for all tectonic environments so far investigated. The work also has provided new insights and data on metamorphic, structural and tectonic processes including: (1) the intimate control of deformation partitioning on metamorphic reactions; (2) solutions to the lack of correlation between lineations that indicate the direction of movement within thrusts and shear zones, and relative plate motion; and (3) a possible technique for determining the direction of relative plate motion that caused orogenesis in ancient orogens.     

Finite element formulation and algorithms for unsaturated soils. Part II: Verification and application

The finite‐element formulation and integration algorithms developed in Part I are used to analyse a number of practical problems involving unsaturated and saturated soils. The formulation and algorithms perform well for all the cases analysed, with the robustness of the latter being largely insensitive to user‐defined parameters such as the number of coarse time steps and error control tolerances. The efficiency of the algorithms, as measured by the CPU time consumed, does not depend on the number of coarse time steps, but may be influenced by the error control tolerances. Based on the analyses presented here, typical values for the error control tolerances are suggested. It is also shown that the constitutive modelling framework presented in Part I can, by adjusting one constitutive equation and one or two material parameters, be used to simulate soils that expand or collapse upon wetting. Treating the suction as a strain variable instead of a stress variable proves to be an efficient and robust way of solving suction‐dependent plastic yielding. Moreover, the concept of the constitutive stress is a particularly convenient way of handling the transition between saturation and unsaturation. Copyright © 2003 John Wiley & Sons, Ltd.     

Chemical alteration of tephra in the depositional environment: theoretical stability modelling

The study of the chemical stability of vitreous material in aqueous media is well‐established. There has to date been little consideration of the implications of variations in the chemical durability of tephra in Quaternary tephrochronology. Chemical alteration can take the form of cationic leaching from the matrix, or complete destruction of the silica network, either of which could constrain the ability to chemically identify distal tephra. Here we apply established models of vitreous durability to the published chemical analyses of a large number of Icelandic tephras in order to predict their relative durabilities under equivalent conditions. This suggests that some important tephras have relatively poor chemical stability, and that rhyolitic tephras are, in general, more stable than basaltic. We conclude that tephras should be expected to show predictable differential chemical stability in the post‐depositional environment. Copyright © 2003 John Wiley & Sons, Ltd.     

On cross-correlating weak lensing surveys

The present generation of weak lensing surveys will be superseded by surveys run from space with much better sky coverage and high level of signal-to-noise ratio, such as the Supernova/Acceleration Probe ( SNAP ). However, removal of any systematics or noise will remain a major cause of concern for any weak lensing survey. One of the best ways of spotting any undetected source of systematic noise is to compare surveys that probe the same part of the sky. In this paper we study various measures that are useful in cross-correlating weak lensing surveys with diverse survey strategies. Using two different statistics – the shear components and the aperture mass – we construct a class of estimators which encode such cross-correlations. These techniques will also be useful in studies where the entire source population from a specific survey can be divided into various redshift bins to study cross-correlations among them. We perform a detailed study of the angular size dependence and redshift dependence of these observables and of their sensitivity to the background cosmology. We find that one-point and two-point statistics provide complementary tools which allow one to constrain cosmological parameters and to obtain a simple estimate of the noise of the survey.