On the Likelihood and Fluctuations of Gaussian Realizations

The likelihood of Gaussian realizations, as generated by the Cholesky simulation method, is analyzed in terms of Mahalanobis distances and fluctuations in the variogram reproduction. For random sampling, the probability to observe a Gaussian realization vector can be expressed as a function of its Mahalanobis distance, and the maximum likelihood depends only on the vector size. The Mahalanobis distances are themselves distributed as a Chi-square distribution and they can be used to describe the likelihood of Gaussian realizations. Their expected value and variance are only determined by the size of the vector of independent random normal scores used to generate the realizations. When the vector size is small, the distribution of Mahalanobis distances is highly skewed and most realizations are close to the vector mean in agreement with the multi-Gaussian density model. As the vector size increases, the realizations sample a region increasingly far out on the tail of the multi-Gaussian distribution, due to the large increase in the size of the uncertainty space largely compensating for the low probability density. For a large vector size, realizations close to the vector mean are not observed anymore. Instead, Gaussian vectors with Mahalanobis distance in the neighborhood of the expected Mahalanobis distance have the maximum probability to be observed. The distribution of Mahalanobis distances becomes Gaussian shaped and the bulk of realizations appear more equiprobable. However, the ratio of their probabilities indicates that they still remain far from being equiprobable. On the other hand, it is observed that equiprobable realizations still display important fluctuations in their variogram reproduction. The variance level that is expected in the variogram reproduction, as well as the variance of the variogram fluctuations, is dependent on the Mahalanobis distance. Realizations with smaller Mahalanobis distances are, on average, smoother than realizations with larger Mahalanobis distances. Poor ergodic conditions tend to generate higher proportions of flatter variograms relative to the variogram model. Only equiprobable realizations with a Mahalanobis distance equal to the expected Mahalanobis distance have an expected variogram matching the variogram model. For large vector sizes, Cholesky simulated Gaussian vectors cannot be used to explore uncertainty in the neighborhood of the vector mean. Instead uncertainty is explored around the n-dimensional elliptical envelop corresponding to the expected Mahalanobis distance.     

The Harvard-Smithsonian reference atmosphere

We present a model of the solar atmosphere in the optical depth range from ₅₀₀₀ = 10^–8 to 25. It combines an improved model of the photosphere that incorporates recent EUV observations with a new model of the quiet lower chromosphere. The latter is based on OSO 4 observations of the Lyman continuum, on infrared observations, and on eclipse electron densities.Our model differs from the Bilderberg Continuum Atmosphere (BCA) in the low chromosphere (₅₀₀₀ < 10^–4), where deviations from local thermodynamic equilibrium in hydrogen and carbon have been taken into account. It also differs in the transition region between the chromosphere and the photosphere (10^–4 < ₅₀₀₀ < 10^–2), where the temperature is lower than in the BCA, and in the convective region (₅₀₀₀ 2), where the temperature is higher than in the BCA.     

Two cation exchange models for direct and inverse modelling of solution major cation composition in equilibrium with illite surfaces

Na/K, Na/Ca and Na/Mg exchange isotherms were performed on the fine fraction (<2 μm) of Imt-2 illite samples at a total normality of about 0.005 mol/L in anionic chloride medium. The derived selectivity coefficients for Na/K, Na/Ca and Na/Mg were found to vary as a function of the exchanger composition and compared well with the data collected in the literature for similar experimental conditions. Two models were built to reproduce the data: the first was a multi(2)-site model with constant Gaines and Thomas selectivity coefficients; the second was a one-site model taking into account surface species activity coefficients. The results of the models were in rather good agreement with both our data and literature data. The multi-site model proved to be efficient in predicting the exchanger composition as a function of the Na/Ca/Mg/K concentrations in solution, whereas the one-site model proved to be a better approach to derive the Na/Ca/Mg/K concentrations in solution based on the knowledge of the exchanger composition and the total normality of the solution. The interest of this approach is illustrated by the need for major cation solute concentration predictions in compacted clay for the characterization of nuclear deep disposal host rock repositories.     

Contribution to a geodynamic reconstruction of the Anti-Atlas (Morocco) during Pan-African times with the emphasis on inversion tectonics and metallogenic activity at the Precambrian–Cambrian transition

New geochronological analyses (U–Pb SIMS zircon ages) have yielded ages of 552 ± 5 Ma for the Bou Madine rhyolitic dome (Ougnat, eastern Anti-Atlas), 543 ± 9 Ma for the Tachkakacht rhyolitic dyke (Saghro–Imiter, eastern Anti-Atlas), and 531 ± 5 Ma for the Aghbar trachytic sill (Bou Azzer, central Anti-Atlas). Inherited zircon cores from the Aghbar trachytic sill and from the Bou Madine rhyolitic dome have been shown to be of Statherian age (ca. 1600–1800 Ma) and Palæoproterozoic (>2100 Ma) age, respectively, suggesting that a significantly older protolith underlies the Pan-African rocks in the Central and Eastern Anti-Atlas. Granodiorites and rhyolites from the Saghro–Imiter area have similar low ⁸⁷Sr/⁸⁶Sr (0.702–0.706) and ¹⁴³Nd/¹⁴⁴Nd (0.5116–0.5119) initial ratios, suggesting a mixture of mantle and lower crust sources. This can also be inferred from the low ¹⁸⁷Os/¹⁸⁸Os ratios obtained on pyrite crystals from the rhyolites.A recently published lithostratigraphic framework has been combined with these new geochemical and geochronological data, and those from the literature to produce a new reconstruction of the complex orogenic front that developed at the northern edge of the Eburnian West African craton during Pan-African times. Three Neoproterozoic magmatic series can be distinguished in the Anti-Atlas belt, i.e., high-K calc-alkaline granites, high-K calc-alkaline to shoshonitic rhyolites and andesites, and alkaline-shoshonitic trachytes and syenites, which have been dated at 595–570, 570–545 and 530 Ma, respectively.The accretion of the Pan-African Anti-Atlas belt to the West African super continent (WAC) was a four-stage event, involving extension, subduction, moderate collision and extension. The calc-alkaline magmatism of the subduction stage was associated with large-scale base metal and gold mineralisation. Metallogenic activity was greatest during the final extensional stage, at the Precambrian–Cambrian boundary. It is characterised by world-class precious metal deposits, base–metal porphyry and SEDEX-type occurrences.     

Does sediment resuspension by storms affect the fate of polychlorobiphenyls (PCBs) in the benthic food chain? Interactions between changes in POM characteristics, adsorption and absorption by the mussel Mytilus galloprovincialis

Environmental parameters and gross sedimentation rates (GSR) were monitored at a fixed site located in the Bay of Banyuls-sur-Mer (NW Mediterranean), between March 1997 and April 1998, together with the main biochemical characteristics of both sedimenting and sedimented particulate organic matter (POM). Three storms which occurred during this time period resulted in natural sediment resuspension. This is indicated by the corresponding increase in GSR and a decrease in the enzymatically hydrolysable amino acids/totally hydrolysable amino acids ratio (EHAA/THAA), within the sedimenting POM. Only the strongest storm resulted in (1) a transitory increase in fine-grained particles, (2) concomitant increases in organic carbon, carbohydrates, lipids and THAA, and (3) a decrease in the EHAA/THAA ratio in surficial sediments. For most of the assayed parameters, the values recorded after the December 1997 storm corresponded to extremes for the whole period under study. This emphasises the role of storms in controlling the characteristics of sedimented and sedimenting POM.Ten sediment types, with contrasting biochemical characteristics, were selected for experiments; these were based on the results of the monitoring survey and were used during adsorption and absorption experiments involving ¹⁴C tetrachlorobiphenyl (TCB). Adsorption rates differed significantly between the sediment types, but did not correlate with any of the assayed biochemical parameters. Absorption efficiency by the mussel Mytilus galloprovincialis also differed between the sediment types; it correlated positively with all the assayed biochemical parameters, except lipids. Comparison between the magnitudes of the increase in GSR, together with the decrease in absorption efficiency during resuspension events, suggests that resuspension tends to enhance the transfer of organic pollutants in the benthic food chain.     

Early and late Holocene water-level fluctuations of Lake Annecy, France: sediment and pollen evidence and climatic implications

Early and late Holocene water-level changes in Lake Annecy, France, were reconstructed from a sediment sequence from Annecy. Two early Holocene successive rises in lake level at ca. 8900-8700 BP are recorded. Another increase in lake level, beginning at ca. 780 BP, is documented. The higher lake-level conditions in Lake Annecy during the 9th millennium BP, i.e. between the Preboreal oscillation and the 8200 yr event, appear to coincide with a more widespread cooling period which has been recorded in western Europe, in the Greenland ice-sheet and the North Atlantic ocean. The rise in lake level at ca. 780 BP can be related to the early Little Ice Age.