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.     

Crystal morphologies in pillow basalts: implications for mid-ocean ridge processes

We present the results of a detailed petrological study of a sparsely phyric basalt (MAPCO CH98-DR11) dredged along the Mid-Atlantic Ridge (30°41′N). The sample contains microphenocrysts of olivine that display four different rapid-growth morphologies. Comparison of these morphologies with those obtained in dynamic crystallization experiments allows us to constrain the thermal history of the sample. The dendritic morphology (swallowtail, chain and lattice olivine) is directly related to the final quenching during magma–seawater interaction. In contrast, the three other morphologies, namely the complex polyhedral crystal, the closed hopper and the complex swallowtail morphology result from several cycles of cooling–heating (corresponding to a maximum degree of undercooling of 20–25°C) during crystal growth. These thermal variations occurred before eruption and are interpreted to be the result of turbulent convection in a small magmatic body beneath the ridge. The results suggest that the Mid-Atlantic Ridge is underlain by a mush zone that releases batches of liquid during tectonic segregation. Aphyric basalts are emitted during eruptions controlled by the tectonic activity, whereas phyric basalts correspond to small fractions of magma from the mush zone mobilized by reinjections of primitive magmas.     

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.     

Assessing land use/cover changes: a nationwide multidate spatial database for Mexico

A nationwide multidate GIS database was generated in order to carry out the quantification and spatial characterization of land use/cover changes (LUCC) in Mexico. Existing cartography on land use/cover at a 1:250,000 scale was revised to select compatible inputs regarding the scale, the classification scheme and the mapping method. Digital maps from three different dates (the late 1970s, 1993 and 2000) were revised, evaluated, corrected and integrated into a GIS database. In order to improve the reliability of the database, an attempt was made to assess the accuracy of the digitalisation procedure and to detect and correct unlikely changes due to thematic errors in the maps. Digital maps were overlaid in order to generate LUCC maps, transition matrices and to calculate rates of conversion. Based upon this database, rates of deforestation between 1976 and 2000 were evaluated as 0.25 and 0.76% per year for temperate and tropical forests, respectively.     

Experimental pressure solution compaction of synthetic halite/calcite aggregates

Experimental observations are reported of weakening of sediment-like aggregates by addition of hard particles. Sieved mixtures of calcite and halite grains are experimentally compacted in drained pressure cells in the presence of a saturated aqueous solution. The individual halite grains deform easily by pressure solution creep whereas calcite grains act as hard objects and resist compaction. The fastest rate of compaction of the mixed aggregate is not obtained for a 100% halite aggregate but for a content of halite grains between 45% and 75%. We propose that this unusual compaction behavior reflects the competition between two mechanisms at the grain scale: intergranular pressure solution at grain contacts and grain boundary healing between halite grains that prevent further compaction.     

Dérive à la surface de l'océan sous l'effet des vagues

We model the drift velocity near the ocean surface separating the motion induced by the local current, itself influenced by winds and waves, and the motion induced by the waves, which are generated by local and remote winds. Application to the drift of ‘tar balls’, following the sinking of the oil tanker Prestige-Nassau in November 2002, shows that waves contribute at least one third of the drift for pollutants floating 1 m below the surface, with a mean direction about 30° to the right of the wind-sea direction. Although not new, this result was previously obtained with specific models, whereas the formalism used here combines classical wave and circulation forecasting models. To cite this article: F. Ardhuin et al., C. R. Geoscience 336 (2004).     

Apports de la méthode sismique réflexion haute résolution à l'identification des structures profondes des formations tertiaires en Médoc (Gironde,France) : implications hydrogéologiques

Near Bordeaux (France), the Oligocene aquifer is a potential target for drinking water supply. A high-resolution seismic campaign and several exploration wells helped to clarify the geometry of this formation and, as a consequence, the Medoc Tertiary aquifers. The major information extracted from these new data is the existence of a soft deformation inducing two different deposit areas, showing different hydrogeological characteristics (thickness, type, hydraulic properties, etc.). The presence of an erosional gap area affecting the Oligocene formations lead us to propose a new image of groundwater flow in the area, in the context of a predicted intensive exploitation of this resource. To cite this article: F. Larroque, A. Dupuy, C. R. Geoscience 336 (2004).     

Variations of U and Sr isotope ratios in Alsace and Luxembourg rain waters: origin and hydrogeochemical implications

Major and trace element concentrations, as well as Sr and U isotope ratios, were measured in rainwater samples collected in three different locations in Alsace (East of France) and Luxembourg: a mid-altitude mountain site (Aubure Environment HydroGeochemical Observatory), an urban site (Strasbourg) and a peri-urban site located in an area of well developed industrial activity (Esch-sur-Alzette in Luxembourg). Results highlight the quite high spatial and temporal variability of the chemical and isotopic characteristics of rainwater at the regional scale. They also suggest a quite systematic contribution of a local component in the chemical composition of rainwater. In urban and peri-urban sites, the local component is certainly linked to human activities, as it is well illustrated in this study with the Esch-sur-Alzette samples. On the other hand, for the Aubure site, i.e. a small forested watershed of mid-altitude mountain, data presented in this study demonstrate the influence of the vegetation on the chemical composition of rainwater for alkali and calc-alkali elements, as well as for the Sr isotope ratios. Such a result questions the reliability of the method classically used to estimate the rainwater contribution on the river chemical budget. In addition, data of the present study confirm the very low content of uranium in rainwater and demonstrate, especially through the U isotope analysis of Aubure rainwater, the negligible effect of rainwater on U budget of river waters. This work thus outlines the property of U to be a geochemical tracer specific of weathering fluxes carried by rivers. To cite this article: F. Chabaux et al., C. R. Geoscience 337 (2005).