Sediment suspension dynamics and a new criterion for the maintenance of turbulent suspensions

The vertical component of the turbulent flow acceleration term, , is used to determine the net positive vertical force that may support a suspended sediment load. A dimensionless criterion, Λ, is proposed for the maintenance of suspension, defined as the ratio of the maximum vertical turbulent stress to immersed weight of the suspended load above a unit bed area. In order that a suspension be maintained: where v ′ is instantaneous vertical turbulent velocity, σ and ρ are solid and fluid densities, respectively and m is the suspended load dry mass. The Λ criterion is dynamic, being a ratio of stresses and is analogous in this respect to Shields dimensionless stress criterion, θ, for the initiation of bedload motion. The new criterion is successful in predicting the maintenance of steady-state suspended sediment transport in open channel shear flow and deposition from non-uniform particulate density flows of wall jet type.     

Giant calcite-cemented concretions, Dakota Formation, central Kansas, USA

Giant spheroidal concretions (cannonball concretions; some nearly 6 m in diameter) in fluvial channel‐fill sandstones at two localities of the Dakota Sandstone formed by import of cement constituents at a burial depth of <1 km. During cannonball concretion growth a self‐organizational process restricted concretions to a relatively few but widely spaced, and locally, evenly spaced, sites. Other forms of calcite cements at these localities are cement patches in the form of intergrown grape‐size concretions (grapestone), and, locally, pervasive cement. An early episode of invasion by thermogenically generated H₂S, which reacted with iron oxides on detrital grains, generated scattered pyrite crystals and decimetre‐scale spheroidal pyrite concretions. Intergranular volumes (IGV) in the concretions range from 36% to 27%. The absence of a trend in IGV and of carbon and oxygen‐isotope ratios from cannonball centres to margins indicates that these concretions did not cement progressively outwards from the centre. Rather, the modern spheres represent the spatial extent of nucleation sites that were not otherwise organized within that volume. Carbon and oxygen‐isotope values for concretion calcites plot along a swath between depleted values of δ18C of ?36‰ and δ18O of ?13‰ and enriched values of ?4‰ and ?6‰, respectively. Four groups of calcites are evident on the basis of trace‐element content and suggest that the calcite precipitated across a range of oxidation conditions that do not correlate strongly with the isotopic compositions. Although fluvial overbank sandstones have some pedogenic calcite, the channel sandstones have at most a trace of pedogenic calcite and carbonate rock fragments, so that the bulk of cement components were imported to the sandstones. Carbon and calcium sources for calcite cement include marine limestone, carbonate shells, and anhydrite in addition to HCO derived from oxidized methane, most likely derived from beds underlying or laterally in communication with Dakota sandstones. HCO in ascending formation waters, released during compaction, mixed with meteoric water whose temperature and composition varied with time, to generate the 7‰ range in δ18O_calcite values measured.     

Surface settlement of a finite elastic layer whose modulus increases linearly with depth

An examination has been made of the behaviour of a finite layer of elastic material of constant Poisson's ratio, whose Young's modulus increases linearly with depth, and which rests on a rough rigid base. Values of surface settlement at the corner of a rectangular area of uniform loading are presented for values of Poisson's ratio of \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{1}{2} $\end{document}, \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{1}{3} $\end{document} and 0, and for wide ranges of degree of inhomogeneity and loading breadth to depth ratio.     

DIE LITHOGENESE DER STEINMÜHL-KALKE DES ARRACHER STEINBRUCHES (JURA, ÖSTERREICH)

Lithogenesis of the Steinmiihl Limestone of the Arrach Quarry (Jurassic, Austria) The Upper Jurassic Steinmuhl Limestone Group on its type section (Arrach Quarry, Lower Austria) is subdivided into the following four members: These various sedimentary units represent a gradual change in the environments during sedimentation. The sequence sets in with the Filament Limestone. It possibly represents a sublittoral Lamellibranchiata debris and is of Callovian (?)age. Though the marine deposition continued without interruption to the Upper Jurassic, the environment changed markedly. The sea became deeper and the Filament Limestones were followed by pelagic-bathyal Radiolaria Siliceous Limestones. A distinct difference in the degree of subsidence within the Upper Jurassic geosyncline led to the formation of bathyal furrows and swells. Over the latter the calcilutite Saccocoma and Calpionella Limestones with mainly pelagic fossils were deposited in Kimmeridgian and Port- landian. Their thickness is small, for currents swept much sediment into the deeper furrows, in which the Oberalm stratas arose in great thickness at this time.     

An unusual modern silica–carbonate sinter from Pavlova spring, Ngatamariki, New Zealand

ABSTRACT A silica–carbonate deposit is forming from the dilute alkali chloride waters of Pavlova spring, a small thermal pool and outflow channel (85 to <40 °C), situated at the northern extent of the South Orakonui area of the Ngatamariki geothermal field, Taupo Volcanic Zone (TVZ), New Zealand. It is one of a small but growing number of thermal spring features known to yield deposits of mixed mineralogy. At Pavlova, a distinctive, crustose, chalk‐white, meringue‐like sinter, comprising non‐crystalline opal‐A silica with subordinate calcite, is actively precipitating both around the margins of and as small islets within the spring, with an average accumulation rate of ≈ 2 mm year^?1. Both emergent and partly submerged substrates host the sinter, including fallen pine branches, twigs, needles and cones, gum leaves, grass blades, bracken fronds, pumice, sediment and microbial mats. The sinter is thin (25–35 mm thickness), finely laminated and contains three distinct types of stacked horizons. Submerged basal layers constitute stratiform to undulatory microstromatolites with pseudocolumns, which grew outwards and upwards on narrow twig nuclei. Emergent middle layers comprise discontinuous, spicular microstromatolites (to 10 mm height), with prostrate and erect microbial filaments, silica spheres and silicified mucus, overlain by silicified structures of probable fungal origin. In places, lower and middle sinter layers are capped by white, smooth, convex surfaces that coalesce into subdued, curved ridges, resembling laterally continuous peaks of egg‐white meringue. The meringue is internally laminated, with fossilized microbes preserved in thin horizons. Small lensoid masses of calcite crystals nestle between silica laminae throughout the sinter. The near‐neutral (pH ≈ 7·2) spring water is a dilute chloride‐carbonate type (HCO≈ 470 µg g^?1, Cl^–≈ 600 µg g^?1) with low (≈ 50 µg g^?1), typical of TVZ thermal fields where deep chloride fluid mixes with CO₂‐rich, steam‐heated shallow waters before discharge. The hot water changed little in composition from 1993 to 1999 and, despite dilution by meteoric waters, contains sufficient SiO₂ (≈ 220 µg g^?1) for opal‐A to deposit at the surface upon cooling. However, the concentration of Ca²⁺ (≈ 6 µg g^?1) is such that the precipitation of calcite is not expected without modification of spring waters. Precipitation occurs by evaporation of thin water films at exposed substrate surfaces, via meniscoid as well as capillary creep (wicking), through porous sinter horizons and across emergent vegetative surfaces in contact with spring water or steam. The height of the deposit above the water surface is restricted by the upper limit of moisture bathing these substrates. Splash and spray are not involved in the formation of Pavlova spicular microstromatolites, as is the case for other texturally similar deposits from hotsprings elsewhere. This young (< 15 years), mineralogically and morphologically complex hot‐spring deposit exhibits > 10 times lower accumulation rates than typical siliceous sinters in the TVZ, and deposition of both silica and calcite is controlled by microchemical conditions and local temperature gradients, rather than by bulk spring water chemistry.     

Note on boundary effects on stream meandering

This paper provides some additional evidence supporting the necessary (but insufficient) condition for the formation of stream meandering proposed by Nakagawa: where M_e is a non-dimensional parameter, τ_s, and τ_b are the average bank and bed shear stress respectively, p_s and p_b are the average bank and bed wetted perimeter of a half-channel respectively, and K?0.2 is the critical value of the parameter estimated from experimental data. Provided the criterion is satisfied, the main thread of the stream meanders in the non-erodible channel, and the maximum amplitude a_max, the angle a between the channel central axis and oblique crest line of the surface wave, and the mean wavelength L of the main thread decrease as the non-dimensional parameter Me increases.     

Threshold of sediment motion under unidirectional currents

Carefully selected data for the threshold of sediment movement under unidirectional flow conditions have been utilized to re-examine the various empirical curves that are commonly employed to predict this threshold. After a review of the existing data, we employed only that data obtained from open channel flumes with parallel sidewalls where flows were uniform and steady over flattened beds of unigranular, rounded sediments. Without these restrictions, an unmanageable amount of scatter is introduced. This selected data is used to develop a modified Shields-type threshold diagram that extends the limits of the original diagram by three orders of magnitude in the grain-Reynolds number. The equally general but more easily employed Yalin diagram for sediment threshold is also examined. Although the Shields and Yalin diagrams are general in that they apply to a wide range of different liquids, in both cases somewhat different curves are obtained for threshold under air than for the liquids. The often used empirical curves of the friction velocity u_*, the velocity 100 cm above the bed u₁₀₀, the bottom stress θ_t, and Shields’ relative stress θ_t, all versus the grain diameter D, are limited in their ranges of application to certain combinations of grain density, fluid density, fluid viscosity and gravity. These conditions must be selected before the curves are generated from either the more general Shields or Yalin curves. For example, on the basis of the data selected for use in this paper, empirical threshold relationships for quartz density material in water are where the velocity u₁₀₀ measured 100 cm above the sediment bed is given in cm/sec and the grain diameter D is in cm. The limitations on any of the threshold relationships are severe. These limitations should be properly understood so that the empirical curves and relationships are not improperly employed.     

Palaeoproterozoic evaporites in Fennoscandia: implications for seawater sulphate, the rise of atmospheric oxygen and local amplification of the δ13C excursion

This paper addresses global oxygenation and establishment of a marine sulphate reservoir in the Palaeoproterozoic. We report syn-depositional, marine, anhydrite-containing pseudomorphs after Ca-sulphates as widespread throughout the Tulomozero Formation in the SE Fennoscandian Shield, implying that surface waters were oxidized and a large SO marine reservoir was developed as early as 2100 Ma. The Ca-sulphates and associated magnesite and halite precipitated syn-depositionally from oxidized, evolved and modified seawater in coastal playa, sabkha and intertidal flat settings. ⁸⁷Sr/⁸⁶Sr and δ¹³C of associated ¹³C-rich stromatolitic dolostones were environmentally controlled with the highest ratios occurring in playa and sabkha carbonates. The results imply that the Palaeoproterozoic δ¹³C_carb excursion was amplified by 8‰ by local environmental factors and calls into question many observations of putative δ¹³C global signals reported previously from similar Palaeoproterozoic, evaporitic, dolostones. The local environmental amplification can explain a large regional and intercontinental δ¹³C discrepancy observed in synchronous carbonates.     

Microscopic calcite dendrites in cold-water tufa: implications for nucleation of micrite and cement

Dendritic calcite forms in an active cold-water tufa system in association with extracellular polymeric substances (EPS) that discontinuously coat bryophytes and cyanobacteria. Dendrites consist of 100–200 nm thick calcite fibres that form 3D lattice-like domains. In each dendrite domain, fibres have three structurally equal orientations, which correspond in disposition to radii from the centre of a calcite unit cell to the convex triple face junctions on its surface. Fibres do not form in the orientation of the c-axis. The external form of each dendrite has the shape of half of a shortened octahedron, with an upper triangular surface parallel to the substrate. Dendrite nucleation takes place on or in microbial EPS, whether microbial cells are present or not, and is probably effected by attraction of Ca²⁺ cations to negatively charged EPS, together with CO₂-degassing and concomitant pH increase of supersaturated spring water in stream splash zones. Ensuing dendrite growth is abiogenic and controlled by diffusion. Dendrite c-axes are perpendicular to the substrate, probably because the negative charge of EPS forces the orientation of Ca²⁺ and CO planes within the developing dendrite crystal to be parallel to the EPS film surface. Dendrites are eventually filled and overgrown by solid, syntaxial calcite, which gradually and completely obliterates the dendrites as more familiar calcite crystal forms develop. No trace of the dendritic nucleus remains in the rock record. Calcite crystal nucleation may take place by this mechanism in many marine and meteoric settings, given that microbial EPS is now assumed to be virtually ubiquitous in these environments. This phenomenon could contribute to the development of familiar fabrics such as marine micrite cement and fibrous calcite cement, radial ooids, peloids, ‘abiogenic’ stromatolites, sea floor precipitates, microbialites, tufa, travertine, speleothems, and some meteoric cements. It may also contribute to the substrate-normal orientation of c-axes of common cement fabrics.     

ZEOLITES IN SEDIMENTARY ROCKS, WITH REFERENCE TO THE DEPOSITIONAL ENVIRONMENTS AND ZONAL DISTRIBUTION

The authors have studied alterations of Cenozoic and Mesozoic pyroclastic rocks of Japan, which contain several kinds of zeolites in abundance. This paper summarizes zeolites in sedimentary rocks, with reference to the depositional environments and zonal distribution, by a survey of the literature in addition to the authors’ data. The zonal distribution of zeolites is recognized in buried sedimentary rocks as follows: The zeolites in syngenetic or early diagenetic origin depend strongly upon a specific sedimentary environment. Phillipsite occurs largely in pelagic sediments of the younger geologic age. Analcime is found in saline-lake and terrestrial sediments in a warm, rather arid region, frequently associated with phillipsite, chabazite and natrolite. The zeolites are not influenced by the sedimentary environments but depend upon the depth of burial, i.e., increasing temperature and pressure. Most of clinop- tilolite, mordenite and erionite, forming at a relatively shallow depth, occur only as an alteration product of acidic to intermediate volcanic glass and cement of the post- Jurassic pyroclastic rocks. Laumontite, forming at a greater depth, on the other hand, is widely distributed in the pre-Pliocene various sedimentary rocks.     

Strain rates from snowball garnet

Spiral inclusion trails in garnet porphyroblasts are likely to have formed due to simultaneous growth and rotation of the crystals, during syn‐metamorphic deformation. Thus, they contain information on the strain rate of the rock. Strain rates may be interpreted from such inclusion trails if two functions are known: (1) The relationship between rotation rate and shear strain rate; (2) the growth rate of the crystal. We have investigated details of both functions using a garnetiferous mica schist from the eastern European Alps as an example. The rotation rate of garnet porphyroblasts was determined using finite element modelling of the geometrical arrangement of the crystals in the rock. The growth rate of the porphyroblasts was determined by using the major and trace element distributions in garnet crystals, thermodynamic pseudosections and information on the grain size distribution. For the largest porphyroblast size fraction (size L=12 mm) we constrain a growth interval between 540 and 590 °C during the prograde evolution of the rock. Assuming a reasonable heating rate and using the angular geometry of the spiral inclusion trails we are able to suggest that the mean strain rate during crystal growth was of the order of =6.6 × 10^?14 s^?1. These estimates are consistent with independent estimates for the strain rates during the evolution of this part of the Alpine orogen.     

Mineralogical and Chemical Composition of International Carbon and Oxygen Isotope Calibration Material NBS 19, and Reference Materials NBS 18, IAEA-CO-1 and IAEA-CO-8

International carbon and oxygen isotope calibration material NBS 19 and reference materials NBS 18, International Atomic Energy Agency (IAEA)-CO-1 and IAEA-CO-8 are prepared from naturally occurring rock specimens of marble and carbonatite. Mineralogical and chemical analysis showed that only NBS 19 and IAEA-CO-1 represent essentially pure samples of calcite containing < and minimal (< 1%) quantities of quartz. In contrast, both NBS 18 and IAEA-CO-8, although primarily composed of calcite, are contaminated by a range of additional phases. NBS 18 was estimated to contain 1% Fe-dolomite and trace (< 1%) quantities of apatite and quartz. IAEA-CO-8 was estimated to contain at least 4% non-carbonate material (including apatite, barite, biotite and magnetite). NBS 18 and IAEA-CO-8 are both derived from samples of carbonatite and the calcite component of each material is characterised by appreciable substitution of Mg + Mn + Sr ± Fe ± Ba (Σ ≈ 14000–15000 μg g^-1) for Ca. The observations reported in this study complement data in the literature detailing significant grain-scale isotopic heterogeneity in NBS 18 and IAEA-CO-8. Both data sets highlight the need for careful characterisation of calibration materials prior to distribution.     

P–T–fluid evolution in the Mahalapye Complex, Limpopo high-grade terrane, eastern Botswana

Metapelites, migmatites and granites from the c. 2 Ga Mahalapye Complex have been studied for determining the P–T–fluid influence on mineral assemblages and local equilibrium compositions in the rocks from the extreme southwestern part of the Central Zone of the Limpopo high‐grade terrane in Botswana. It was found that fluid infiltration played a leading role in the formation of the rocks. This conclusion is based on both well‐developed textures inferred to record metasomatic reactions, such as Bt ? And + Qtz + (K₂O) and Bt ± Qtz ? Sil + Kfs + Ms ± Pl, and zonation of Ms | Bt + Qtz | And + Qtz and Grt | Crd | Pl | Kfs + Qtz reflecting a perfect mobility (Korzhinskii terminology) of some chemical components. The conclusion is also supported by the results of a fluid inclusion study. CO₂ and H₂O ( = 0.6) are the major components of the fluid. The fluid has been trapped synchronously along the retrograde P–T path. The P–T path was derived using mineral thermobarometry and a combination of mineral thermometry and fluid inclusion density data. The Mahalapye Complex experienced low‐pressure granulite facies metamorphism with a retrograde evolution from 770 °C and 5.5 kbar to 560 °C and 2 kbar, presumably at c. 2 Ga.     

Global tectonics under g having a minute westward tilt

The convection seen to affect Moon's mantle takes place under gravity having a component of asymmetry, in the form of a minute westward slope or tilt constituting the external part of the field. Its effect is explored employing the equivalent potential, denominated . Its nature is to bias convection of internal origin, inducing east–west polarization of a type prominent in global tectonics. Separately, research at Harvard has shown that by causing advection of non‐hydrostatic masses within the heterogeneous mantle, deep‐seated convection inevitably displaces the axis of maximum moment, compelling polar wander. A reconstruction based on observed dissipation suggests that the combined effect of these factors is to contribute a not inconsiderable low‐latitude, surface‐west component to the structure of the convection. Cumulative alteration in the direction ‘west’ must eventually require global rearrangement of its cell structure, offering explanation of the abrupt Mesozoic–Tertiary transition and progressive net lithosphere rotation.     

Autogenic incision‐backfilling cycles and lobe formation during the growth of alluvial fans with supercritical distributaries

Autogenic cycles of channelization, terminal deposit formation, channel backfilling and channel abandonment have been observed in the formation of fans and deltas. In subcritical flow, these terminal deposits are characterized as mouth bars that lead to flow bifurcation, backwater and eventual channel backfilling. Similar, although less well characterized, cycles also take place on supercritical subaerial and submarine fans. This study investigates the hydraulics and morphodynamics of autogenic incision and backfilling cycles associated with supercritical distributive channel flow in alluvial fans. The research questions of the study are: (i) how are supercritical autogenic cycles on alluvial fans different from the subcritical cycles; (ii) what are the hydraulic and sediment transport characteristics at the various stages of autogenic feedback cycles; and (iii) what role do the cycles play in the overall fan evolution? These questions are investigated in the laboratory, and emphasis is placed on measuring the hydraulic and topographic evolution of the systems during the cycles. The cycles arise quasi‐periodically under constant water and sediment discharge. Periods of sheet‐like flow are competent to move sediment () but not competent enough to carry the full imposed load. The net result is preferential deposition near the inlet, resulting in fan steepening and an increase in flow competency with time. At a sediment supply to capacity ratio of , the sheet‐like flow is unstable to small erosional events near the inlet, resulting in the collapse of the distributed flow to a strong channelized state. During channelization, a graded () supercritical (Fr > 1) channel develops and transports eroded and fed sediment up to and through the fan front – extending the fan, initiating a lobe shaped deposit and reducing the local slope. The slopes defined by a sheet‐like flow with and channelized flow with set the maximum and minimum slopes on the fan, respectively. Once formed, graded channels act as bypass conduits linking the inlet with the terminal deposit. On average, deposits are up to six channel depths in thickness and have volumes approximately five times that of the excavated channel. The main distinctive characteristics of the supercritical cycles relate to how the flow interacts with the terminal deposit. At the channel to deposit transition, the flow undergoes a weak hydraulic jump, resulting in rapid sedimentation, dechannelization and lateral expansion of the flow, and deposition of any remaining sediment on top of the channel fill and floodplain. This process often caps the channel as the deposit propagates up channel erasing memory of the excavated channel.     

Observations on the extended Matsuoka–Nakai failure criterion

The equivalent Mohr–Coulomb (M‐C) friction angle ? (J. Geotech. Eng. 1990; 116 (6):986–999) of the extended Matsuoka–Nakai (E‐M‐N) criterion has been examined under all possible stress paths. It is shown that ? depends only on the ratio of cohesion to confining stress c^′/σ and the frictional angle ?, where ? is the friction angle measured in triaxial compression (or extension) to which the E‐M‐N surface is fitted. It is also shown that ? is independent of c^′, when σ=0 and of σ when c^′=0, with the former representing an upper bound and the latter a lower bound of ? for any particular stress path. The closest point projection method has also been implemented successfully with the E‐M‐N criterion, and plane strain and axisymmetric element tests performed to verify some theoretical predictions relating to failure and post‐yielding behavior. Finally, a bearing capacity problem was analyzed using both E‐M‐N and M‐C, highlighting the conservative nature of M‐C for different friction angles. Copyright © 2009 John Wiley & Sons, Ltd.     

Dissolution and precipitation processes in deformed amphibolites: an example from the ductile shear zone of the Ryoke metamorphic belt, SW Japan

The granitic mylonite zone in the Cretaceous Ryoke metamorphic belt contains deformed amphibolites as thin layers. The amphibolite layers do not exhibit pinch‐and‐swell or boudinage structures, even when contained in a high‐strain granitic mylonite. This mode of occurrence suggests that they were deformed as much as the surrounding granite mylonite. In the highly deformed zone, strongly foliated amphibolites contain Ti‐rich brown amphibole porphyroclasts rimmed by Ti‐poor green amphibole, titanite and chlorite. These porphyroclasts are elongated, forming shear surfaces defined by preferential distribution of the chlorite and titanite. Porphyroclastic plagioclase in the strongly foliated amphibolites consists of two components: an anorthite‐rich core and an anorthite‐poor rim. Based on these observations, the mass‐balanced reaction occurring during deformation is defined as As the reaction products form a weak interconnected matrix, the strain rate of the amphibolites may be controlled by the rate of dissolution–precipitation through fluids. Weakly foliated amphibolites in the low‐strain zone exhibit cataclastic microstructures, whereas the strongly foliated amphibolites do not exhibit such features. These microstructural and chemical changes suggest that high‐strain amphibolites were initially deformed by cataclasis, followed by deformation through metamorphic reactions. During the metamorphism/deformation, old plagioclase grains with high X_an were not stable and dissolved, and new plagioclase grains with low X_an crystallized at the old plagioclase rim. Dissolution of old plagioclase and precipitation of new plagioclase occurred normal to and parallel to the foliation, respectively, reflecting incongruent pressure solution due to differential stress and changes in P–T–H₂O conditions. The development of incongruent pressure solution is attributed to increased fluid flux in the strongly foliated amphibolites, as evidenced by the greater abundance of hydration‐reaction products in the strongly foliated amphibolites than in the weakly foliated ones.     

Quartz‐in‐garnet and Ti‐in‐quartz thermobarometry: Methodology and first application to a quartzofeldspathic gneiss from eastern Papua New Guinea

Mineral inclusions are ubiquitous in metamorphic rocks and elastic models for host‐inclusion pairs have become frequently used tools for investigating pressure–temperature (P–T) conditions of mineral entrapment. Inclusions can retain remnant pressures () that are relatable to their entrapment P–T conditions using an isotropic elastic model and P–T–V equations of state for host and inclusion minerals. Elastic models are used to constrain P–T curves, known as isomekes, which represent the possible inclusion entrapment conditions. However, isomekes require a temperature estimate for use as a thermobarometer. Previous studies obtained temperature estimates from thermometric methods external of the host‐inclusion system. In this study, we present the first P–T estimates of quartz inclusion entrapment by integrating the quartz‐in‐garnet elastic model with titanium concentration measurements of inclusions and a Ti‐in‐quartz solubility model (QuiG‐TiQ). QuiG‐TiQ was used to determine entrapment P–T conditions of quartz inclusions in garnet from a quartzofeldspathic gneiss from Goodenough Island, part of the (ultra)high‐pressure terrane of Papua New Guinea. Raman spectroscopic measurements of the 128, 206, and 464 cm^?1 bands of quartz were used to calculate inclusion pressures using hydrostatic pressure calibrations (), a volume strain calculation (), and elastic tensor calculation (), that account for deviatoric stress. values calculated from the 128, 206, and 464 cm^?1 bands’ hydrostatic calibrations are significantly different from one another with values of 1.8 ± 0.1, 2.0 ± 0.1, and 2.5 ± 0.1 kbar, respectively. We quantified elastic anisotropy using the 128, 206 and 464 cm^?1 Raman band frequencies of quartz inclusions and stRAinMAN software (Angel, Murri, Mihailova, & Alvaro, 2019,  234 :129–140). The amount of elastic anisotropy in quartz inclusions varied by ~230%. A subset of inclusions with nearly isotropic strains gives an average and of 2.5 ± 0.2 and 2.6 ± 0.2 kbar, respectively. Depending on the sign and magnitude, inclusions with large anisotropic strains respectively overestimate or underestimate inclusion pressures and are significantly different (<3.8 kbar) from the inclusions that have nearly isotropic strains. Titanium concentrations were measured in quartz inclusions exposed at the surface of the garnet. The average Ti‐in‐quartz isopleth (19 ± 1 ppm [2σ]) intersects the average QuiG isomeke at 10.2 ± 0.3 kbar and 601 ± 6°C, which are interpreted as the P–T conditions of quartzofeldspathic gneiss garnet growth and entrapment of quartz inclusions. The P–T intersection point of QuiG and Ti‐in‐quartz univariant curves represents mechanical and chemical equilibrium during crystallization of garnet, quartz, and rutile. These three minerals are common in many bulk rock compositions that crystallize over a wide range of P–T conditions thus permitting application of QuiG‐TiQ to many metamorphic rocks.     

Stability properties of the Newmark,Houbolt and Wilson θ methods

This paper analysis the stability of several methods for obtaining numerical solutions of second-order ordinary differential equations. The methods are popular in structural and geotechnical engineering applications and are direct, that is they do not require the transformation of the second-order equation into a first-order system. They include Newmark's method in both implicit and explicit forms, Wilson's θ-method, Houbolt's method and some variants on this latter method. We shall examine the stability of the methods when applied to the second-order scalar test equation where a and c are real.     

Reverse flow in turbidity currents: the role of internal solitons

Pickering & Hiscott, (1985) have demonstrated amply the presence of reverse-flow units within the thick-bedded calcareous wacke (TCW) beds of the turbiditic Cloridorme Formation (Middle Ordovician, Gaspé Peninsula, Quebec, Canada). These reverse-flow units are underlain and overlain by units which reveal flow in the primary (obverse) direction. In this paper, a model is proposed for this reverse flow, based on the probable nature of the primary turbidity flow. It appears that the initial flow was highly elongated (thickness h? length L), with h～ 500 m, velocity U～ 2 m s^-1 and sediment concentration C～ 1·25%_o. The rate of momentum loss of the flow is estimated by means of a useful parameter which we call the ‘drag distance’, symbol d_D, defined by where h and L are the thickness and length of the flow, respectively; _cC_d is a combined drag coefficient representing friction on the bottom and at the upper interface; and _fC_d is a form-drag coefficient related to the shape and size of the head. d_D is the distance travelled by a current of constant h and L, flowing over a horizontal bottom and obeying a quadratic friction law, for an e-fold reduction in velocity. Simple considerations, confirmed by our own experiments (described in this paper), show that such an elongated turbidity current cannot be reflected as a whole from an adverse slope: when the nose of the current reaches the slope, it forms a hump, which surges backwards and sooner or later breaks up into a series of internal solitons. The latter, probably numbering 4–7, will cause reverse flow at a given point as they pass by, provided that the residual velocity in the tail is not too great. Flow in the original (obverse) direction will be re-established after the passage of the solitons. Quiescent periods in front of, between and behind the solitons, when soliton-associated currents cancelled out the residual obverse flow, would allow the deposition of thin mud-drapes. Additional flow reversals observed in a few of the TCW beds cannot be explained readily by the re-passage of solitons, since wave breaking at the ends of the basin would cause massive energy loss; internal seiches are the preferred explanation for these later reversals.