Stability functions based upon shear functions

The stability functions for momentum and heat under a Richardson number formulation are derived from the nondimensional shear functions under a Monin-Obukhov formulation. The Prandtl number is also derived as a function of the Richardson number. Previously, this has been done only in a limited sense. Because the Richardson number formulation is expressed in closed form, iterative techniques are no longer needed in numerical models that use Monin-Obukhov similarity theory. This time-saving approach is made possible by deriving expressions for the friction velocity and temperature in terms of the Richardson-number-dependent stability functions. In addition, the Richardson number approximation in the lowest layer is made to depend explicitly upon the surface roughness.     

Slab weakening: Mechanical and thermal-mechanical consequences for slab detachment

Abstract Slab detachment is a geophysical instability whose manifestation can be revealed by seismic tomography. Evidence of this phenomenon is in the Dinarides/Hellenic and the New Hebrides subduction zones. Subducted slabs in these regions are torn horizontally at depths ranging from 100 to 300 km. We constructed a viscoelastic three-dimensional finite element model and investigated the state of stress. We found that an area with high stress concentration of the order of several hundred MPa is formed near the tip of the tear inside the slab, which can cause lateral migration of the tear. Favorable conditions for slab detachment are characterized by large interplate frictional force at a subduction zone and small slab resistance force deeper down. Stress concentration increases with the down-dip tension inside the slab. The phenomenon of slab weakening has also been studied from a thermal-mechanical standpoint, using a two-dimensional convection model with non-Newtonian, temperature-dependent rheology. The stress-dependent rheology plays an important role in causing local weakening of the descending slab. In strongly time-dependent situations the fast descending slab is not strong everywhere but has a weak region in the middle, making it vulnerable to slab detachment. The presence of viscous heating will enhance slab detachment tendency by further weakening the interior by the frictional heating. Besides these effects, there are other mechanisms which can also weaken the slab interior and help to make slabs more pliable and susceptible to detachment.     

A Sophisticated Ground Water Analytical Tool

Stiff diagrams arc a multivariate method of analysis used to describe the chemical state of ground water. The use of Stiff diagrams to describe multiconstituent contamination sites, such as landfills, has distinct advantages over single constituent analyses. Problems associated with traditional Stiff diagram analyses, such as diagram attentuation, can be addressed by allowing the scale of the diagram to vary with the ionic strength of the analyzed sample. The use of these sliding scale Stiff diagrams reveals the chemical slate of the ground water over wide ranges of constituent concentrations and thus allows for sensitive and sophisticated depictions of complicated contamination sites in a fashion that is extremely difficult to replicate with single constituent analyses. This approach has possible applications for understanding and tracing the mixing and chemical changes in uncontaminated settings.     

Experimental petrology of alkalic lavas: constraints on cotectics of multiple saturation in natural basic liquids

Experimental study of natural alkalic lava compositions at low pressures (pO₂QFM) reveals that crystallization of primitive lavas often occurs in the sequence olivine, plagioclase, clinopyroxene, nepheline without obvious reaction relation. Pseudoternary liquidus projections of multiply saturated liquids coexisting with plagioclase (±olivine±clinopyroxene±nepheline) have been prepared to facilitate graphical analysis of the evolution of lava compositions during hypabyssal cooling. Use of (TiAl₂)(MgSi₂)_–1 and Fe³⁺ (Al)_–1 exchange components is a key aspect of the projection procedure which is succesful in reducing a wide range of compositions to a systematic graphical representation. These projections, and the experiments on which they are based, show that low pressure fractionation plays a significant role in the petrogenesis of many alkalic lava suites from both continental and oceanic settings. However, the role of polybaric fractionation is more evident in the major element chemistry of these lava suites than in many tholeiitic suites of comparable extent. For example, the lavas of Karisimbi, East Africa, show a range of compositions reflecting a polybaric petrogenesis from primitive picrites at 1360° C/18 kb and leading to advanced low pressure differentiates. Evolved leucite-bearing potassic members of this and other suites may be treated in a nepheline-diopside-kspar (+olivine+leucite) projection. Compositional curvature on the plagioclase+clinopyroxene+olivine+leucite cotectic offers a mechanism to explain resorption of plagioclase in alkalic groundmass assemblages and the incompatibility of albite and leucite. This projection is useful for evaluating the extent of assimilation of the alkalic portions of crustal granulites. Assimilation appears to have played some role in the advanced differentiates from Karisimbi.     

Creep parameters of rocks on an engineering scale

Vertical shafts of 137 cm diameter were excavated to measure creep deformations of carbonate shale, weathered limestone and tuff. Changes of diameter at successive time intervals were recorded under constant, radial pressure. Three typical models were chosen for a regression analysis of the experimental data and their fitness were compared to one another in a statistical approach.The introduction of a steady state flow term improves the data fit considerably, and the power law was found to yield an even better result. It was also determined that rock masses in the field contain numerous discontinuities which increase the plasticity of the three types of rock tested. The viscosities determined in-situ were found to be much lower than those derived from small intact specimens by up to several orders of magnitude.     

Geochemistry,geochronology, and petrogenesis of a Late Precambrian (∼ 590 Ma) composite dike from the North Eastern Desert of Egypt

Late Precambrian (575–600 Ma) igneous activity in the North Eastern Desert of Egypt produced large volumes of compositionally bimodal magmas. A single composite dike was studied to further examine petrogenetic relationships between andesitic and rhyolitic melts. The dike consists of 1.5–2 m of andesite on either side of a 5–6 m wide rhyolite core. Contact relations indicate that the andesite and rhyolite simultaneously existed as porphyritic liquids. Wholerock Rb-Sr dating indicates an age of 591 Ma, but with considerable scatter. Andesite and rhyolite had similar initial⁸⁷Sr/⁸⁶Sr of 0.7032±2, indicating derivation from a low Rb/Sr source, either the upper mantle, very young upper crust, or depleted lower crust. The composition of the andesites on either margin cannot be distinguished; these are very similar to andesites of the Dokhan Volcanics of similar age. Correspondingly, the rhyolite is compositionally similar to the epizonal Pink Granites. This dike and others like it represent hypabyssal feeders for the extrusive and shallow intrusive members of the North Eastern Desert bimodal suite.Major and trace element studies of the dike rocks show no evidence of mixing. With the exception of the alkaline earths, there is no evidence of diffusional transport across the rhyolite-andesite contacts. REE patterns indicate that petrogenesis of the andesite must have left a garnetiferous residue: either 10% melting of LREE-enriched garnet lherzolite or 25% melting of eclogite, followed by a small amount of shallow fractionation. Petrogenesis of the rhyolites remains enigmatic. Partitioning of trace elements and different plagioclase compositions in andesite and rhyolite argue against an origin by liquid immiscibility. Major and trace element models indicate that the rhyolite formed by fractional crystallization of the andesite or by anatexis of young amphibolite-facies crust.

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Zusammenfassung SpÄtprÄkambrische (575–600 Ma) magmatische AktivitÄt in der »North Eastern Desert« Ägyptens förderte gro\e Mengen bimodaler Magmen. Um die petrogenetischen Beziehungen zwischen andesitischen und rhyolitischen Schmelzen zu studieren, wurde ein einzelner, »bimodaler« Gang (composite dyke) untersucht.Der Gang besteht aus einem Rand von 1,5–2 m mÄchtigem Andesit auf beiden Seiten eines 5–6 m mÄchtigen Kernbereiches von Rhyolit. Die Kontaktbeziehungen zeigen, da\ Andesite und Rhyolite gleichzeitig als porphyritische Schmelzen existierten. »Whole-Rock« Rb-Sr Datierung ergab ein Alter von 591 Ma, jedoch mit einem erheblichen Fehler. Andesit und Rhyolith hatten Ähnliche initiale⁸⁷Sr/⁸⁶Sr VerhÄltnisse von 0.7032±2, die eine Herkunft aus Bereichen mit niedrigen Rb/Sr VerhÄltnissen erkennen lassen: Oberer Mantel, sehr junge obere Kruste, oder verarmte untere Kruste. Die Zusammensetzung der Andesite von den verschiedenen Seiten des Ganges ist nicht zu unterscheiden. Sie sind den Andesiten der Dokhan Vulkanite Ähnlich und etwa gleich alt. Entsprechend sind die Rhyolite den epizonalen rosa Graniten (»pink granite«) in der Zusammensetzung Ähnlich. Dieser Gang und andere gleich ihm stellen die Zufuhrspalten für die extrusiven und seichtintrusiven Magmatite der »North Eastern Desert« bimodalen Folge dar.Haupt- und Spurenelemente der Ganggesteine zeigen keine Anzeichen einer Mischung. Mit Ausnahme der Erdalkalien gibt es keinen Hinweis auf eine Diffusion der Elemente über den Rhyolit-Andesit Kontakt. Die Verteilung der Seltenen Erden deutet auf ein granatführendes Residuum bei der Petrogenese der Andesite: entweder10% Aufschmelzen von Granat-Lherzolit, angereichert an leichten Seltenen Erden, oder 25% Aufschmelzen von Eklogit, gefolgt von geringer Fraktionierung unter niedrigem Druck.Die Petrogenese der Rhyolite bleibt unklar. Die Verteilung der Spurenelemente und die unterschiedliche Plagioklas-Zusammensetzung in Andesit und Rhyolith sprechen gegen eine Entstehung aus unvermischbaren Schmelzen. Modelle basierend auf Haupt- und Spurenelementen deuten darauf hin, da\ der Rhyolit entweder durch fraktionierte Kristallisation des Andesits entstand oder durch Anatexis junger Kruste im Bereich der Amphibolit-Fazies.

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Résumé L'activité magmatique au Précambrien supérieur (575–600 Ma) dans le »North Eastern Desert« d'Egypte a engendré de grandes quantités de magmas bimodaux. De manière à préciser les relations entre fusions andésitiques et rhyolitiques, un dyke composite a été étudié.Ce dyke est constitué d'un coeur rhyolitique de 5 à 6 m, encadré de deux bordures andésitiques de 1,5 à 2 m. Les contacts indiquent que ces deux roches ont coexisté sous la forme de liquides porphyriques. Une datation Rb-Sr sur roche totale donne un âge de 591 Ma, mais avec une approximation importante. L'andésite et la rhyolite ont un mÊme rapport initial de 0,7032±2, indiquant une source à faible rapport Rb/Sr: manteau supérieur, croûte supérieure jeune ou croûte inférieure appauvrie. Les compositions des deux bordures andésitiques sont identiques et très semblables à celle des andésites de mÊme âge du complexe volcanique du Dokhan. De mÊme, la rhyolite a une composition semblable à celle des granites roses épizonaux. Ce dyke et d'autres du mÊme type représentent les voies d'alimentation des termes extrusifs et intrusifs superficiels de la série bimodale du »North Eastern Desert«.L'étude des éléments majeurs et en traces ne montre aucun mélange entre les roches du dyke. A l'exception des alcalino-terreux, il n'existe aucune indication de diffusion des éléments à travers le contact rhyolite — andésite. La distribution des terres rares montre que la genèse de l'andésite doit avoir laissé un résidu grenatifère: soit une lherzolite à grenat enrichie en terres rares légères et représentant moins de 10% de taux de fusion, soit une éclogite (jusqu'à 25% de taux de fusion) suivie d'un léger fractionnement à basse pression.La pétrogenèse de la rhyolite reste obscure. La répartition des éléments en traces et la différence de composition du plagioclase entre l'andésite et la rhyolite plaident contre une origine par immiscibilité. Les modèles tirés des éléments majeurs et en traces indiquent comme origine pour la rhyolite soit la cristallisation fractionnée de l'andésite, soit l'anatexie de matériaux crustaux jeunes dans les conditions du facies des amphibolites.

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Possible effects of pre-existing basement topography on thrust fault ramping

Finite-element models show that one way in which thrust ramps may arise is through the mechanical interaction between basement and overlying sediments. In the simplest case, shear coupling between a planar basement—sediment contact causes the differential stresses in the sediments to die out with depth and distance from the applied load. For such cases, curved thrust faults may result if the strength of the rock is exceeded. Basement topography may also affect the location and shape of ramps by acting as a stress concentrator, by producing a stress shadow and by changing principal stress orientations. Modeling suggests that whether or not these basement topographic features cause ramping will depend on the height and angularity of the feature as well as the rock types that overlie it.Under the assumption of linear elasticity and for given boundary conditions, the Poisson's ratio plays an important role in determining the orientation and magnitude of the principal stresses. Calculations using experimentally measured Poisson's ratios predict that the earliest maximum compressive stress directions should be nearly vertical in the more cratonward portions of thrust belts. However, the stress directions which are inferred to have occurred earliest in this part of thrust belts are nearly horizontal. This suggests that non-elastic or ductile processes have an effect on the propagation of thrust faults.     

Petrographic constraints on models of intergranular pressure solution in quartzose sandstones

Petrographic and SEM observations on 478 samples of six quartzose sandstones provide a data base that can be used to evaluate the role of intergranular pressure solution (IPS) in sandstone diagenesis and to constrain predictive models of the pressure solution process. SEM examination of grain contacts that have experienced pressure solution suggests that IPS occurs at the interior portions of contacts where the greatest stress is concentrated and that granulation of quartz grains at points of contact may contribute to the process. The chemical compaction fabrics that result from IPS suggest that the process is most commonly induced by effective lithostatic stress and that the resulting strain is uniaxial.Numerous geological variables influence IPS. Grain size exerts a fundamental influence, with finer grained samples experiencing more IPS than coarser grained samples. On both local and regional scales, IPS is inhibited by poor sorting, an abundance of ductile grains, the presence of “shallow” cement, slow rates of shallow burial, and overpressured conditions. In contrast, IPS is enhanced by the presence of illite grain coatings, increased maximum burial depth, rapid rates of shallow burial, longer times spent at great depths, higher temperatures, and high volumes and rates of fluid flow.Silica budgets indicate that some of the analyzed sandstones approximate mass balance whereas others have exported silica. Calculations of fluid flow requirements indicate that advanced stages of IPS are favored by high volume, high velocity fluid flow. Such flow can occur as a result of uplift of basin margins, which is typical of foreland and intractonic basins.