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.     

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).     

Modeling of in-situ crystallization processes in the Permian mafic layered intrusion of Mont Collon (Dent Blanche nappe, western Alps)

The Mont Collon mafic complex is one of the best preserved examples of the Early Permian magmatism in the Central Alps, related to the intra-continental collapse of the Variscan belt. It mostly consists (> 95 vol.%) of ol + hy-normative plagioclase-wehrlites, olivine- and cpx-gabbros with cumulitic structures, crosscut by acid dikes. Pegmatitic gabbros, troctolites and anorthosites outcrop locally. A well-preserved cumulative sequence is exposed in the Dents de Bertol area (center of intrusion). P–T calculations indicate that this layered magma chamber emplaced at mid-crustal levels at about 0.5 GPa and 1100 °C. The Mont Collon cumulitic rocks record little magmatic differentiation, as illustrated by the restricted range of clinopyroxene mg-number (Mg#_cpx = 83–89). Whole-rock incompatible trace-element contents (e.g. Nb, Zr, Ba) vary largely and without correlation with major-element composition. These features are characteristic of an in-situ crystallization process with variable amounts of interstitial liquid L trapped between the cumulus mineral phases. LA-ICPMS measurements show that trace-element distribution in the latter is homogeneous, pointing to subsolidus re-equilibration between crystals and interstitial melts. A quantitative modeling based on Langmuir's in-situ crystallization equation successfully duplicated the REE concentrations in cumulitic minerals of all rock facies of the intrusion. The calculated amounts of interstitial liquid L vary between 0 and 35% for degrees of differentiation F of 0 to 20%, relative to the least evolved facies of the intrusion. L values are well correlated with the modal proportions of interstitial amphibole and whole-rock incompatible trace-element concentrations (e.g. Zr, Nb) of the tested samples. However, the in-situ crystallization model reaches its limitations with rock containing high modal content of REE-bearing minerals (i.e. zircon), such as pegmatitic gabbros. Dikes of anorthositic composition, locally crosscutting the layered lithologies, evidence that the Mont Collon rocks evolved in open system with mixing of intercumulus liquids of different origins and possibly contrasting compositions. The proposed model is not able to resolve these complex open systems, but migrating liquids could be partly responsible for the observed dispersion of points in some correlation diagrams. Absence of significant differentiation with recurrent lithologies in the cumulitic pile of Dents de Bertol points to an efficiently convective magma chamber, with possible periodic replenishment.     

Lateglacial palaeoenvironments and palaeoclimates from Conty and Houdancourt, northern France, reconstructed from Beetle remains

Two Lateglacial insect sequences are described (a) from Conty, in the Selle valley and (b) from Houdancourt in the Oise valley, both in northern France. These investigations are part of a multidisciplinary investigation involving archaeology, sedimentology, geomorphology, geochronology and palaeontology (pollen, macroscopic plant remains, vertebrates, molluscs and insect fossils). The sequences of insect assemblages date from the latter part of the Bølling to the end of the Allerød periods. Environmental analysis of these faunas shows that rivers with riffles and pools meandered across flood plains. The river was extensively fringed with reedy vegetation. The only trees growing close to the river were of Salix and/or Populus. All the insect assemblages indicate that the thermal climates during the Bølling and Allerød periods were similar to one another and during both periods were very nearly as warm as that of the present day. No insect fossils were recovered from the sediments attributed to the Older Dryas interval though other evidence from these sites suggests that this event was decidedly colder than those immediately preceding and succeeding it. Comparisons are made between Lateglacial climatic patterns in northern France with those elsewhere in Europe.     

Détermination expérimentale des paramètres équivalents d'un milieu poreux hétérogène en écoulements uniforme ou radial

Tracer tests are carried out in a heterogeneous porous medium that has a 3D correlated random distribution of the permeabilities. The fitting of numerical models provides the values of equivalent permeability and macrodispersivity characterizing a 2D homogeneous horizontal medium. Different flow configurations are studied: uniform, radial and pump and treat (doublet). The fitted parameter sets are independent of the flow type, except for the doublet. They are greater than the values predicted by stochastic theories, due to the small number of correlation lengths explored by the tracer and the limited extension of the experimental set-up. To cite this article: C. Danquigny, P. Ackerer, C. R. Geoscience 337 (2005).     

Profondeur d'extraction racinaire et signature isotopique de l'eau prélevée par les racines des couverts végétaux

We seek to identify the depth to which water is extracted by the roots in the soil. Indeed, in an isotopic steady-state condition of leaf water, transpiration introduces into the atmosphere a vapour whose isotopic signature is identical to that of root water. In the isotopic models of atmospheric general circulation, it is classically allowed that the signature of transpiration belongs to the meteoric water line. This supposes that the water taken by the roots has escaped with the evaporation of the soil and comes thus from the deep layers of the soil. At the time of experimentation carried out on maize plants (Nemours, Seine-et-Marne, France), this extraction depth was inferred from the comparison between the signature of the water measured on the level of the first internode of the stems of the plants and the isotopic profile of water in the soil. When the flow of transpiration reaches a maximum value, the plant uptakes water resulting from precipitations and which preserves its non-evaporating character after having quickly infiltrated in the deep layers of the soil. This relates to only 55% of the flux transpired by the canopy, the remainder presenting an evaporating character more or less marked according to ambient conditions. This experiment invalidates the classical hypothesis used in isotopic models of general atmospheric circulation in temperate regions. In fact, only half the amount of water vapour transpired by the canopy during the day presents a signature similar to that of the rainwater sampled in deep soil layers. To cite this article: Z. Boujamlaoui et al., C. R. Geoscience 337 (2005).