Émergence de la complexité dans un modèle simple de comportement mécanique des roches

We propose a mechanical model for the behaviour of rocks based on progressive damage at the elementary scale and elastic interaction. It allows us to simulate several experimental observations: mechanical behaviour ranging from brittle to ductile, fractal structure of the damage, power-law distribution of the damage avalanches. These macroscopic properties are not incorporated at the elementary scale, but are the results of the interaction between elements. This emerging complexity permits us to consider the strain rock process as a complex system characterized by non-linear dynamics. To cite this article: D. Amitrano, C. R. Geoscience 336 (2004).     

Uncertainty,entropy, scaling and hydrological stochastics. 1. Marginal distributional properties of hydrological processes and state scaling / Incertitude,entropie, effet d'échelle et propriétés stochastiques hydrologiques. 1. Propriétés distributionnelles marginales des processus hydrologiques et échelle d'état

Abstract

The well-established physical and mathematical principle of maximum entropy (ME), is used to explain the distributional and autocorrelation properties of hydrological processes, including the scaling behaviour both in state and in time. In this context, maximum entropy is interpreted as maximum uncertainty. The conditions used for the maximization of entropy are as simple as possible, i.e. that hydrological processes are non-negative with specified coefficients of variation (CV) and lag one autocorrelation. In this first part of the study, the marginal distributional properties of hydrological variables and the state scaling behaviour are investigated. Application of the ME principle under these very simple conditions results in the truncated normal distribution for small values of CV and in a nonexponential type (Pareto) distribution for high values of CV. In addition, the normal and the exponential distributions appear as limiting cases of these two distributions. Testing of these theoretical results with numerous hydrological data sets on several scales validates the applicability of the ME principle, thus emphasizing the dominance of uncertainty in hydrological processes. Both theoretical and empirical results show that the state scaling is only an approximation for the high return periods, which is merely valid when processes have high variation on small time scales. In other cases the normal distributional behaviour, which does not have state scaling properties, is a more appropriate approximation. Interestingly however, as discussed in the second part of the study, the normal distribution combined with positive autocorrelation of a process, results in time scaling behaviour due to the ME principle.     

Analyses multifractales et spatio-temporelles des précipitations du modèle Méso-NH et des données radar

Résumé

Dans le cadre des multifractals universels, il est possible de caractériser la variabilité spatio-temporelle de la pluie sur une grande gamme d’échelle à l'aide de trois paramètres invariants d’échelles. Dans cette étude, nous avons estimé ces paramètres multifractals sur des simulations numériques effectuées avec le modèle méso-échelle Méso-NH, développé par Météo-France et le Laboratoire d'Aérologie (Univ. P. Sabatier, Toulouse, France), et des images radar composites, couvrant le même événement pluvieux, à savoir un orage particulièrement violent, dit de type Cévenol, ayant eu lieu sur la partie sud de la France du 5 au 9 Septembre 2005. La comparaison des résultats montre que les deux types de données présentent des domaines d'invariance d’échelle relativement similaires, et dont les propriétés sont en accord avec les modèles de précipitation spatio-temporels unifiés et scalants les plus simples. Néanmoins l’évaluation de leurs exposants conduit à des valeurs parfois fortement différentes.

Citation Gires, A., Tchiguirinskaia, I., Schertzer, D. & Lovejoy, S. (2011) Analyses multifractales et spatio-temporelles des précipitations du modèle Méso-NH et des données radar. Hydrol. Sci. J. 56(3), 380–396.     

Temporal scaling in river flow: can it be chaotic? / L’invariance d’échelle de l’écoulement fluvial peut-elle être chaotique?

Abstract

Abstract Identification of the presence of scaling in the river flow process has been a challenging problem in hydrology. Studies conducted thus far have viewed this problem essentially from a stochastic perspective, because the river flow process has traditionally been assumed to be a result of a very large number of variables. However, recent studies employing nonlinear deterministic and chaotic dynamic concepts have reported that the river flow process could also be the outcome of a deterministic system with only a few dominant variables. In the wake of such reports, a preliminary attempt is made in this study to investigate the type of scaling behaviour in the river flow process (i.e. chaotic or stochastic). The investigation is limited only to temporal scaling. Flow data of three different scales (daily, 5-day and 7-day) observed in each of three rivers in the USA: the Kentucky River in Kentucky, the Merced River in California and the Stillaguamish River in Washington, are analysed. It is assumed that the dynamic behaviour of the river flow process at these individual scales provides clues about the scaling behaviour between these scales. The correlation dimension is used as an indicator to distinguish between chaotic and stochastic behaviours. The results are mixed with regard to the type of flow behaviour at individual scales and, hence, to the type of scaling behaviour, as some data sets show chaotic behaviour while others show stochastic behaviour. They suggest that characterization (chaotic or stochastic) of river flow should be a necessary first step in any scaling study, as it could provide important information on the appropriate approach for data transformation purposes.     

Analyse multi-échelle par ondelettes des contacts géologiques : application à la carte gravimétrique du Maroc nord-oriental

The multiscale wavelet analysis has been applied to the gravity data from northeastern Morocco to map the major geological contacts, such us faults. Hence, the faults affecting the survey area were outlined with their importance level and dip direction. Seismic data confirm these results and testify the efficiency of this method, particularly in studying structure of plains. The structural map established is a very useful document in the planning of natural resources investigations (i.e. water, mines) to be undertaken in the area of study. To cite this article: D. Khattach et al., C. R. Geoscience 338 (2006).     

Uncertainty,entropy, scaling and hydrological stochastics. 2. Time dependence of hydrological processes and time scaling / Incertitude,entropie, effet d'échelle et propriétés stochastiques hydrologiques. 2. Dépendance temporelle des processus hydrologiques et échelle temporelle

Abstract

The well-established physical and mathematical principle of maximum entropy (ME), is used to explain the distributional and autocorrelation properties of hydrological processes, including the scaling behaviour both in state and in time. In this context, maximum entropy is interpreted as maximum uncertainty. The conditions used for the maximization of entropy are as simple as possible, i.e. that hydrological processes are non-negative with specified coefficients of variation and lag-one autocorrelation. In the first part of the study, the marginal distributional properties of hydrological processes and the state scaling behaviour were investigated. This second part of the study is devoted to joint distributional properties of hydrological processes. Specifically, it investigates the time dependence structure that may result from the ME principle and shows that the time scaling behaviour (or the Hurst phenomenon) may be obtained by this principle under the additional general condition that all time scales are of equal importance for the application of the ME principle. The omnipresence of the time scaling behaviour in numerous long hydrological time series examined in the literature (one of which is used here as an example), validates the applicability of the ME principle, thus emphasizing the dominance of uncertainty in hydrological processes.     

The Hercules Échelle Spectrograph at Mt. John

The High Efficiency and Resolution Canterbury University Large échelle Spectrograph (HERCULES) a fibre-fed échelle spectrograph that was designed and built at the University of Canterbury and has been in operation at Mt. John University Observatory since April 2001.HERCULES receives light from the f/13.5 Cassegrain focus of the 1 m McLellan telescope. Resolving powers of R = 41 000, 70 000 and 82 000 are available. An R2 200 × 400 mm échelle grating provides dispersion and cross-dispersion uses a large BK7 prism in double pass. The wavelength coverage is designed to be 380–880 nm in a single exposure. The maximum detective quantum efficiency of the fibre, spectrograph and detector system is about 18% in 2 arc second seeing. High wavelength stability (to better than 10 ms^-1 in radial velocity) is achieved by installing the whole instrument in a large vacuum tank at 2–4 torr and by there being no moving parts. The tank is in a thermally isolated and insulated environment. The paper describes the design philosophy of HERCULES and its performance during the first year of operation. Now deceased; formerly at This revised version was published online in July 2006 with corrections to the Cover Date.     

Evaluation of In Situ Heterogeneity of Elements in Solids: Implications for Analytical Geochemistry

A general method for the evaluation of in situ heterogeneity of geochemical materials is described and the significance of the results discussed, by using three case studies and earlier data sets. The heterogeneity of Pb in soil (expressed as RSD due to sampling, RSD_samp) varies from < 5 to > 100% between different sites, in a way that relates to the mode of deposition of the element. The heterogeneity of an element also varies systematically as a function of the distance scale at some sites. This variation can be modelled using linear regression, accounting for over 90% of the experimental variance, at seven scales over three orders of magnitude. Variation in heterogeneity between elements at the same site, seems to be somewhat diagnostic of the origin of the element, lithogenic being less than anthropogenic, although the later is also being modified by the mode of deposition. Where the heterogeneity is large (RSD > 30%), it is proposed that it can be expressed more accurately as a heterogeneity factor (10^GSDsamp), to reflect its frequency distribution, which is positively skewed towards higher concentration values.     

Volcanic passive margins

Compared to non-volcanic ones, volcanic passive margins mark continental break-up over a hotter mantle, probably subject to small-scale convection. They present distinctive genetic and structural features. High-rate extension of the lithosphere is associated with catastrophic mantle melting responsible for the accretion of a thick igneous crust. Distinctive structural features of volcanic margins are syn-magmatic and continentward-dipping crustal faults accommodating the seaward flexure of the igneous crust. Volcanic margins present along-axis a magmatic and tectonic segmentation with wavelength similar to adjacent slow-spreading ridges. Their 3D organisation suggests a connection between loci of mantle melting at depths and zones of strain concentration within the lithosphere. Break-up would start and propagate from localized thermally-softened lithospheric zones. These ‘soft points’ could be localized over small-scale convection cells found at the bottom of the lithosphere, where adiabatic mantle melting would specifically occur. The particular structure of the brittle crust at volcanic passive margins could be interpreted by active and sudden oceanward flow of both the unstable hot mantle and the ductile part of the lithosphere during the break-up stage. To cite this article: L. Geoffroy, C. R. Geoscience 337 (2005).     

Satellite-Derived ERS scatterometer sea-surface wind-stress curl in the southwestern Indian Ocean

Surface marine wind data base from ERS-1 scatterometer has been processed to define the characteristic seasonal distribution of wind-stress curl throughout the southwestern Indian Ocean between January and December 1994. A compact model to obtain satellite-derived wind-stress curl fields on smaller scales than previously available is proposed and evaluated. The results indicate the strong capability of the ERS-1 scatterometer to monitor wind-driven variations in the mesoscale ocean patterns. To cite this article: M. Petit et al., C. R. Geoscience 338 (2006).