Fuzzy factorial analysis of snow avalanches

The mutual influence of 21 factors pertaining to terrain, weather, forest and snowpack have been discussed by 10 experts. The semantic (nil, weak, medium, high) evaluations are translated as membership degrees of fuzzy sets, and averaged between the experts by taking their fuzzy expectation value, yielding a 21 × 21 fuzzy matrix for direct interactions. Fuzzy successive multiplications and additions of the matrix give the indirect interactions. The activity and the passivity of the factors with respect to avalanches is represented by directed weighted graphs, and the average semantic values by a 4 × 4 matrix: the activity (passivity) is weak (strong) for tree damage; medium (nil) for altitude; medium (weak) for ground shape; medium (medium) for vegetation, soil, wind, microclimate, tree type, vertical distribution and mechanics of trees, snowpack distribution and snow gliding; strong (nil) for ground inclination and exposition, weather; strong (medium) for heat, precipitation, horizontal distribution of trees, snowpack constitution and stability.     

Convective instabilities in a variable viscosity fluid cooled from above

Whether in the mantle or in magma chambers, convective flows are characterized by large variations of viscosity. We study the influence of the viscosity structure on the development of convective instabilities in a viscous fluid which is cooled from above. The upper and lower boundaries of the fluid are stress-free. A viscosity dependence with depth of the form ν₀ + ν₁ exp(?γ.z) is assumed. After the temperature of the top boundary is lowered, velocity and temperature perturbations are followed numerically until convective breakdown occurs. Viscosity contrasts of up to 10⁷ and Rayleigh numbers of up to 10⁸ are studied.For intermediate viscosity contrasts (around 10³), convective breakdown is characterized by the almost simultaneous appearance of two modes of instability. One involves the whole fluid layer, has a large horizontal wavelength (several times the layer depth) and exhibits plate-like behaviour. The other mode has a much smaller wavelength and develops below a rigid lid. The “whole layer” mode dominates for small viscosity contrasts but is suppressed by viscous dissipation at large viscosity contrasts.For the “rigid lid” mode, we emphasize that it is the form of the viscosity variation which determines the instability. For steep viscosity profiles, convective flow does not penetrate deeply in the viscous region and only weak convection develops. We propose a simple method to define the rigid lid thickness. We are thus able to compute the true depth extent and the effective driving temperature difference of convective flow. Because viscosity contrasts in the convecting region do not exceed 100, simple scaling arguments are sufficient to describe the instability. The critical wavelength is proportional to the thickness of the thermal boundary layer below the rigid lid. Convection occurs when a Rayleigh number defined locally exceeds a critical value of 160–200. Finally, we show that a local Rayleigh number can be computed at any depth in the fluid and that convection develops below depth z_r (the rigid lid thickness) such that this number is maximum.The simple similarity laws are applied to the upper mantle beneath oceans and yield estimates of 5 × 10¹⁵?5 × 10¹⁶ m² s^?1 for viscosity in the thermal boundary layer below the plate.     

Petrology of the mafic rocks of the Xigaze ophiolite,Tibet

The Xigaze ophiolite (Yarlung-Zangbo suture zone, Southern Tibet, China) shows an unusual crustal sequence characterized by a lack of large masses of cumulate gabbros, by dolerites intrusive throughout the whole ophiolite sequence, and by the injection of dolerites in already serpentinized peridotites. The abyssal tholeiitic nature of all the mafic rocks indicates that they have been generated at an oceanic ridge. All the geological arguments and petrological and textural data on the mafic rocks point to very low heat production and large heat losses through widespread intensive sea-water circulation, for the spreading centre in which they have been formed, in good agreement with a slow-spreading ridge origin.     

The mechanical state of the lithosphere in the Altiplano-Puna segment of the Andes

Information about topography, the shape of the geoid, seismicity, Neogene deformation and volcanism in the region of Altiplano-Puna of western South America is used to analyse the state of stress across the convergent plate margin in terms of the effects of topography and simple models of its compensation. An average elevation near 4 km is consistent with compensation by a yet unresolved combination of crustal root and hot uppermost mantle producing a geoid high of 22–27 meters, average horizontal compressive stress (in excess of a reference sea level lithostatic value) of 390 bars in a 150 km thick lithosphere, and an average shear stress of 170 bars along a 30° dipping interplate boundary. The basis for these estimates is evidence for a neutral to extensional stress regime within the high plateau contrasted with a compressional regime on the eastern slopes and along the interplate boundary itself. Comparison with other plateaus in a convergent plate tectonic setting suggests an evolutionary sequence from compressional to extensional tectonics as elevation of the plateau increases.     

Statistical analysis of isotopic ratios in MORB: the mantle blob cluster model and the convective regime of the mantle

A statistical examination of isotopic distributions for MORB from various ocean ridges leads to the “blob cluster model”, in which the oceanic crust accreting at ridges results from the mixing of two components within the ascending mantle. These are (1) upper mantle material and (2) discrete rising blobs of more radiogenic material. The blobs are fractionated to a variable degree and are distributed in the upper mantle circulation in a manner that is related to the spreading rate.(1) Themean values of the isotopic distributions allow us to calculate the probabilities of the two types of material within the mantle. The results show that theproportion of asthenospheric material in the mixtureincreases with the spreading rate, in agreement with the hypothesis of blob dilution within the upper mantle convection.Mass fluxes can be estimated for the rising blobs from these probabilities, which depend on the respective concentrations in the sources of the two types of material. If the blobs originate in the lower mantle, this flux estimation would suggest that a significant part of the lower mantle has been injected into the upper mantle during earth history.(2) Thestandard deviations of the distributions depend on the “efficiency” of the mixing process:the more imbricated are the asthenospheric and blob materials in the mixture,the smaller is theisotopic spread. This efficiency parameter is shown to increase with the spreading rate, as already suggested by previous comparisons between the East Pacific Rise and the Mid-Atlantic Ridge. Moreover, this feature may also be correlated with other data such as ridge bathymetric variations.     

Photo-interprétation à différentes échelles et relevés de terrain: exemples de corrélations structurales dans le Bassin Méditerranéen et sur le socle Ouest africain

Résumé L'interprétation structurale des linéaments, décelés sur clichés photographiques pris par satellite, est discutée sur les bases suivantes: d'une part en pratiquant au minimum un changement d'échelle (plus grande); d'autre part en utilisant les relevés de terrain. Des exemples pris dans le Bassin Méditerranéen sédimentaire et sur le socle cristallophyllien de l'Afrique de l'Ouest permettent de définir une méthodologie commune. Ainsi en région sédimentaire, partant de prises de vue par exemple au 1/2 500 000, les échelles au 1/15 000 et au 1/50 000 se révèlent être des compléments précieux en photo-interprétation. De la même façon en zone de socle, les échelles au 1/20 000 et au 1/50 000 sont complémentaires du 1/200 000. De plus grâce aux donnés de terrain, il est possible de qualifier l'information photogéologique et d'en exprimer sa nature. Enfin les problèmes de corrélations entre rhegmatisme de socle et fracturation de couverture sont abordés de façon préliminaire: la similitude directionnelle observée devrait orienter les futures recherches en ce domaine.

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The structural interpretation of disclosed lineaments on satellite's pictures ist discused on the following basis: first, with a minimum scale change (making it bigger); on the other hand using field plotting. The examples took from the Mediterranean sedimentary basin and from the western Africa crystalographic shield allow us to define a common methodology. Thus, in sedimentary area, through 1/2 500 000 scale aerial photographys, the 1/15 000 and 1/50 000 scales would be real valuable complements in photo-interpretation. Same way as, in shield zone, the 1/20 000 and 1/50 000 scales would be complements of the 1/200 000 one. More than that, because of field plotting utilisation is possible to quality photogeological information and even to explain its nature. In short correlation problems are exposed in a preliminary approach; the observed directional similitude could orientate the future research.

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Zusammenfassung Die strukturelle Deutung von Lineamenten, die aus Satellitenphotos abzulesen sind, wird nach folgenden Voraussetzungen erörtert: zum einen wird zumindest eine Vergrößerung des Maßstabes vorgenommen, zum anderen werden Geländebefunde herangezogen. An Hand von Beispielen aus dem sedimentären Mittelmeerbecken sowie dem Kristallo-phyllitischen Sockel Westafrikas ist es möglich, eine gemeinsame Methodik zu definieren. So erweisen sich im sedimentären Gebiet die Maßstäbe 115 000 und 150 000 als wertvolle Ergänzungen zur Photointerpretation zum Beispiel einer Aufnahme von 12 500 000. Entsprechend ergänzen im Bereich des Sockels die Maßstäbe 120 000 und 150 000 die Aufnahme von 1200 000. Darüber hinaus ist es mit Hilfe von Geländedaten möglich, die photogeologische Information zu qualifizieren und zu beinhalten. Schließlich werden die Probleme der Korrelation zwischen Bruchbildung im Sockel und Brücken im Deckgebirge angesprochen: Die beobachtete Annäherung in der Ausrichtung soll zukünftige Untersuchungen auf diesem Gebiet orientieren.

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A new parameterization of eddy diffusivities for nocturnal boundary-layer modeling

Exchange coefficients and mixing lengths under stable stratification have been studied through measurements of mean wind velocity and temperature in the nocturnal boundary layer. For values of the gradient Richardson number lower than 0.15, our measurements fit well the relation of Delage (1974). Beyond Ri = 0.15, the decrease of mixing length is much slower. So a new parameterization of turbulent exchanges is suggested. When introduced in a model of the nocturnal boundary layer, it results in a thickening of the turbulent and inversion layers.     

Textural, isotopic and REE variations in spinel peridotite xenoliths, Massif Central, France

Sr and Nd isotope analyses and REE patterns are presented for a suite of well-documented mantle-derived xenoliths from the French Massif Central. The xenoliths include spinel harzburgites, spinel lherzolites and some pyroxenites. They show a wide range of textures from undeformed protogranular material through porphyroclastic to equigranular and recrystallised secondary types. Textural differences are strongly linked to trace element geochemistry and variations in radiogenic isotope ratios. Many undeformed protogranular xenoliths are Type IA LREE-depleted with MORB-type ε_Sr values between − 30.7 and − 23.6, and ε_Nd values + 13.9 to + 9.4. A second group of undeformed xenoliths are Type IB LREE-enriched with higher ε_Sr values (− 22.7 to − 10.6) and lower ε_Nd values (+ 11.9 to + 5.6). Deformed xenoliths with porphyroclastic, equigranular and secondary recrystallised textures are all Type IB (LREE-enriched, ε_Nd < 6.4, ε_Sr > 11.8). It is proposed that two separate events have given rise to the observed mixing arrays: (1) MORB-source depleted mantle was enriched by a component derived from an enriched mantle. Deformation and recrystallisation accompanied this event. (2) Subsequently, unenriched MORB-source mantle interacted with magmas chemically akin to the host basalts, and enrichment occurred with little deformation. Hypotheses of Tertiary mantle diapirism resulting in isochemical deformation and refinement of protogranular mantle to equigranular mantle are untenable because of differences in REE patterns and isotopic ratios between different textural groups.