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.     

Fitting the Linear Model of Coregionalization by Generalized Least Squares

In geostatistical studies, the fitting of the linear model of coregionalization (LMC) to direct and cross experimental semivariograms is usually performed with a weighted least-squares (WLS) procedure based on the number of pairs of observations at each lag. So far, no study has investigated the efficiency of other least-squares procedures, such as ordinary least squares (OLS), generalized least squares (GLS), and WLS with other weighing functions, in the context of the LMC. In this article, we compare the statistical properties of the sill estimators obtained with eight least-squares procedures for fitting the LMC: OLS, four WLS, and three GLS. The WLS procedures are based on approximations of the variance of semivariogram estimates at each distance lag. The GLS procedures use a variance–covariance matrix of semivariogram estimates that is (i) estimated using the fourth-order moments with sill estimates (GLS₁), (ii) calculated using the fourth-order moments with the theoretical sills (GLS₂), and (iii) based on an approximation using the correlation between semivariogram estimates in the case of spatial independence of the observations (GLS₃). The current algorithm for fitting the LMC by WLS while ensuring the positive semidefiniteness of sill matrix estimates is modified to include any least-squares procedure. A Monte Carlo study is performed for 16 scenarios corresponding to different combinations of the number of variables, number of spatial structures, values of ranges, and scale dependence of the correlations among variables. Simulation results show that the mean square error is accounted for mostly by the variance of the sill estimators instead of their squared bias. Overall, the estimated GLS₁ and theoretical GLS₂ are the most efficient, followed by the WLS procedure that is based on the number of pairs of observations and the average distance at each lag. On that basis, GLS₁ can be recommended for future studies using the LMC.     

Petrology and geochemistry of a diamondiferous lherzolite from the Premier diamond mine, South Africa

This paper reports on the petrology and geochemistry of a diamondiferous peridotite xenolith from the Premier diamond mine in South Africa.

The xenolith is altered with pervasive serpentinisation of olivine and orthopyroxene. Garnets are in an advanced state of kelyphitisation but partly fresh. Electron microprobe analyses of the garnets are consistent with a lherzolitic paragenesis (8.5 wt.% Cr₂O₃ and 6.6 wt.% CaO). The garnets show limited variation in trace element composition, with generally low concentrations of most trace elements, e.g. Y (<11 ppm), Zr (<18 ppm) and Sr (<0.5 ppm). Garnet rare earth element concentrations, when normalised against the C1 chondrite of McDonough and Sun (Chem. Geol. 120 (1995) 223), are characterised by a rare earth element pattern similar to garnet from fertile lherzolite.

All diamonds recovered are colourless. Most crystals are sharp-edged octahedra, some with minor development of the dodecahedral form. A number of crystals are twinned octahedral macles, while aggregates of two or more octahedra are also common. Mineral inclusions are rare. Where present they are predominantly small black rosettes believed to consist of sulfide. In one instance a polymineralic (presumably lherzolitic) assemblage of reddish garnet, green clinopyroxene and a colourless mineral is recognised.

Infrared analysis of the xenolith diamonds show nitrogen contents generally lower than 500 ppm and variable nitrogen aggregation state, from 20% to 80% of the ‘B’ form. When plotted on a nitrogen aggregation diagram a well defined trend of increasing nitrogen aggregation state with increasing nitrogen content is observed. Carbon isotopic compositions range from −3.6 ‰ to −1.3 ‰. These are broadly correlated with diamond nitrogen content as determined by infrared spectroscopy, with the most negative C-isotopic compositions correlating with the lowest nitrogen contents.

Xenolith mantle equilibration temperatures, calculated from nitrogen aggregation systematics as well as the Ni in garnet thermometer are on the order of 1100 to 1200 °C.

It is concluded that the xenolith is a fertile lherzolite, and that the lherzolitic character may have resulted from the total metasomatic overprinting of pre-existing harzburgite. Metasomatism occurred prior to, or accompanied, diamond growth.     

Modélisation morphodynamique cross-shore d'un estran vaseux

Numerical experiments were performed to simulate the profile evolution of an intertidal mudflat with a 1D cross-shore morphodynamical model. First, the hydrodynamical forcing is a cross-shore tidal current due to semi-diurnal variations of the free surface elevation at the open boundary. Further, considering the conservation of the action density of surface gravity waves, a wave height (and resulting bottom shear stress) calculation is added to the morphodynamical model. Results of the numerical experiments show that the shape of the profile reaches equilibrium. The mudflat progrades continually when the forcing is tide only, whereas it can be steady under the simultaneous action of tide and waves. To cite this article: B. Waeles et al., 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).     

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.