Shear viscosity of rhyolite-vapor emulsions at magmatic temperatures by concentric cylinder rheometry

The viscosity of natural rhyolitic melt from Lipari, Aeolian Islands and melt-bubble emulsions (30–50 vol% porosity) generated from Lipari rhyolite have been measured in a concentric cylinder rheometer at temperatures and shear rates in the range 925–1150°C and 10⁻³–10^−1.2 s⁻¹, respectively, in order to better understand the dependence of emulsion shear viscosity on temperature and shear rate in natural systems. Bubble-free melt exhibits Newtonian–Arrhenian behavior in the temperature range 950–1150°C with an activation energy of 395±30 kJ/mol; the shear viscosity is given by log η_m=−8.320+20624/T. Suspensions were prepared from natural rhyolite glass to which small amounts of Na₂SO₄ were added as a ‘foaming agent’. Reasonably homogeneous magmatic mixtures with an approximate log-normal distribution of bubbles were generated by this technique. Suspension viscosity varied from 10^6.1 to 10^8.37 Pa s and systematically correlates with temperature and porosity in the shear stress range (10^4.26–10^5.46 Pa) of the experiments. The viscosity of melt-bubble emulsions is described in terms of the relative viscosity, η_r=η_e/η_m where η_e is the emulsion viscosity and η_m is the viscosity of melt of the same composition and temperature. The dependence of relative viscosity on porosity for magmatic emulsions depends on the magnitude of the capillary number Ca≡G/(σr_b⁻¹η_m⁻¹), the ratio of viscous forces acting to deform bubbles to interfacial forces resisting bubble deformation. For inviscid bubbles in magmatic flows three regimes may be identified. For Ca<0.1, bubbles are nearly spherical and relative viscosity is an increasing function of porosity. For dilute systems, η_r=1+φ given by the classical result of Taylor [Proc. R. Soc. London A 138 (1932) 41–48]. For Ca in the range 0.1<Ca<10, emulsions behave as power law fluids and the relative viscosity depends on shear rate (or Ca) as well as porosity. At high Ca (Ca>10) an asymptotic regime is reached in which relative viscosity decreases with increasing porosity and is independent of Ca. Our experiments were carried out for 30<Ca<925 in order to quantify the maximal effect of bubbles in reducing the viscosity of magmatic emulsions relative to single-phase melt at identical conditions of shear rate and temperature. The viscosity of a 50 vol% emulsion is a factor of five smaller than that of melt alone. Rheometric measurements obtained in this study are useful in constraining models of magma transport and volcanic eruption mechanics relevant to transport of volatile-saturated magma in the crust and upper mantle.     

Pore-fluid pressures and frictional heating on a fault surface

This study considers the effects of heat transfer and fluid flow on the thernal, hydrologic, and mechanical response of a fault surface during seismic failure. Numerical modeling techniques are used to account for the coupling of the thermal, fluid-pressure, and stress fields. Results indicate that during an earthquake the failure surface is heated to a tempeature required for the thermal expansion of pore fluids to balance the rate of fluid loss due to flow and the fluid-volume changes due to pore dilatation. Once this condition is established, the pore fluids pressurize and the shear strength decreases rapidly to a value sufficient to maintain the thermal pressurization of pore fluids at near-lithostatic values. If the initial fluid pressure is hydrostatic, the final temperature attained on the failure surface will increase with depth, because a greater pressure increase can occur before a near-lithostatic pressure is reached. The rate at which thermal pressurization proceeds depends primarily on the hydraulic characteristics of the surrounding porous medium, the coefficient of friction on the fault surface, and the slip velocity. If either the permeability exceeds 10^–15 m² or the porous medium compressibility exceeds 10^–8 Pa^–1, then frictional melting may occur on the fault surface before thermal pressurization becomes significant. If the coefficient of friction is less than 10^–1 and if the slip velocity is less than 10^–2 msec^–1, then it is doubtful that either thermal pressurization or frictional melting on the fault surface could cause a reduction in the dynamic shear strength of a fault during an earthquake event.     

Two-layer Ekman model for wind-induced shear flow near the sea surface

A simple two-layered model for steady wind-induced shear flow near the sea surface has been formulated. Basic assumptions of Ekman's theory are retained, including horizontal uniformity, infinite depth and constant (but differing) vertical eddy viscosities in the respective layers. Employing information coming from observational data, the parameters of the model (depth of the surface layer and the two eddy viscosities) are evaluated and optimized. The results thereby obtained favour the presence of a high shear layer, about 1 m thick, immediately below the sea surface. The eddy viscosity in that layer increases approximately linearly with wind speed but remains comparatively small, being generally less than 20 cm² s⁻¹ for wind speeds less than 20 m s⁻¹. In contrast, the eddy viscosity directly below the layer is two orders of magnitude larger and increases more steeply with wind speed.     

VELOCITY AND SUSPENSION CONCENTRATION IN SEDIMENT-MIXED FLUID

1 INTRODUCTION AND REVIEW Numerous investigations related to vertical velocity and suspension concentration distributions have been undertaken to the steady, uniform, open channel turbulent flow. The problems of sediment mixed water flows are of direct interest to the practical situations in the field of river sedimentation, coastalsediment transport and in the field of two-phase flow in particular. In hydraulic open channel flow, the vertical velocity profile is usually described by…     

Analytical models for bubble growth during decompression of high viscosity magmas

Analytical models for decompressional bubble growth in a viscous magma are developed to establish the influence of high magma viscosity on vesiculation and to assess the time-scales on which bubbles respond to decompression. Instantaneous decompression of individual bubbles, analogous to a sudden release of pressure (e.g. sector collapse), is considered for two end-member cases. The infinite melt model considers the growth of an isolated bubble before significant bubble interaction occurs. The shell model considers the growth of a bubble surrounded by a thin shell and is analogous to bubble growth in a highly vesicular magmatic foam. Results from the shell model show that magmas less viscous than 10⁹ Pa s can freely expand without developing strong overpressures. The timescales for pressure re-equilibration are shortened by increased ratios of bubble radius to shell thickness and by larger decompression. Time-scales for isolated bubbles in rhyolitic melts (infinite melt model) are significantly longer, implying that such bubbles could experience internal pressures greater than the ambient pressure for at least a few hours following a sudden release of pressure. The shell model is developed to assess bubble growth during the linear decompression of a magma body of constant viscosity. For the range of decompression rates and viscosities associated with actual volcanic eruptions, bubble growth continues at approximately the equilibrium rate, with no attendant excess of internal pressure. The results imply that viscosity does not have any significant role in preventing the explosive expansion of high viscosity foams. However, for viscosities of >10⁹ Pa s there is the potential for a viscosity quench under the extreme decompression rates of an explosive eruption. It is proposed that the typical vesicularities of pumice of 0.7–0.8 are a consequence of the viscosity of the degassing magmas becoming sufficiently high to inhibit bubble expansion over the characteristic time-scale of eruption. For fully degassed silicic lavas with viscosities in the range 10¹⁰ to 10¹² Pa s time-scales for decompression of isolated bubbles can be hours to many months.     

Carbonatitic volcanism in the Kaiserstuhl alkaline complex: Evidence for highly fluid carbonatitic melts at the earth's surface

Extrusive carbonatites are described from the Miocene alkaline complex of the Kaiserstuhl, Rhinegraben, Western Germany. Agglutinated carbonatitic lapilli form pyroclastic rocks in which all components show forms acquired when a highly fluid melt was sprayed into the air by an explosive eruption: droplets, spherical and elliptical lapilli, rods, dumbbell and pear-shaped forms.Complete morphological analogies suggest a mechanism similar to the formation of “Pele's tears”, basaltic droplets formed by the eruption of the most fluid Hawaiian basaltic magmas. Evidence is provided by this example that CaCO₃-carbonatitic magmas can exist in nature under surface conditions displaying extremely low viscosity.     

Diapirism in the earth's mantle: Experiments on the motion of a hot sphere in a fluid with temperature-dependent viscosity

The ascent of magma diapirs through the earth's mantle is modelled experimentally by the motion of a hot metal sphere through a fluid whose viscosity varies strongly with temperature. The dimensionless drag on the sphere (drag number D) and the heat transfer from it (Nusselt number Nu) are found as functions of the dimensionless velocity of the sphere (Peclet number Pe) and the viscosity contrast μ_∞/μ₀ = 10^γ, where μ_∞ and μ₀ are the viscosities of the fluid far from the sphere and at its surface. The drag D = D(Pe, γ) has two limits. For large Pe and small γ (“Stokes” limit), the drag approaches the Stokes' Law result. For small Pe and large γ (“lubrication” limit), the drag is orders of magnitude less than that predicted by Stokes' Law. Nu is a function of Pe alone. For reasonable values of the diapir radius and the viscosity contrast, the dimensionless scale height Pe/3 Nu may exceed a critical value, resulting in progressive melting during ascent. This suggests that diapirs may ascend great distances through the mantle while remaining largely molten. Lamont-Doherty Geological Observatory Contribution No. 3414.     

Viscosity measurements of subliquidus magmas: Alkali olivine basalt from the Higashi-Matsuura district, Southwest Japan

We carried out viscosity measurements and sampling of a crystal suspension derived from alkali olivine basalt from the Matsuura district, SW Japan, at subliquidus temperatures from 1230 °C to 1140 °C under 1 atm with NNO oxygen buffered conditions. Viscosity increased from 31 to 1235 Pa s with a decrease in temperature from 1230 to 1140 °C. On cooling, olivine first appeared at 1210 °C, followed by plagioclase at 1170 °C. The crystal content of the sample attained 31 vol.% at 1140 °C (plagioclase 22%, olivine 9%). Non-Newtonian behaviors, including thixotropy and shear thinning, were pronounced in the presence of tabular plagioclase crystals. The cause of such behavior is discussed in relation to shear-induced changes in melt–crystal textures. Relative viscosities, η_r (= η_s / η_m, where η_s and η_m are the viscosities of the suspension and the melt, respectively), were obtained by calculating melt viscosities from the melt composition and temperature at 1 atm using the equation proposed by Giordano and Dingwell [Giordano, D., Dingwell, D.B., 2003. Non-Arrhenian multicomponent melt viscosity: a model. Earth and Planetary Science Letters, 208, 337–349.]. The obtained relative viscosities are generally consistent with the Einstein–Roscoe relation, which represents η_r for suspensions that contain equant and equigranular crystals, even though the crystal suspension analyzed in the present experiments contained tabular plagioclase and granular olivine of various grain sizes. This consistency is attributed to the fact that the effect of crystal shape was counterbalanced by the effect of the dispersion of crystal size. The applicability of the Einstein–Roscoe equation with respect to crystal shape is discussed on the basis of the present experimental results. Our experiments and those of Sato [Sato, H., 2005. Viscosity measurement of subliquidus magmas: 1707 basalt of Fuji volcano. Journal of Mineralogical and Petrological Sciences, 100, 133–142.] show that the relationship between relative viscosity and crystal fraction is consistent with the Einstein–Roscoe relationship for axial ratios that are smaller than the critical value of 4–6.5, but discrepancies occur for higher ratios.     

Chemical and isotopic investigation of warm springs associated with normal faults in Utah

Thermal springs associated with normal faults in Utah have been analyzed for major cations and anions, and oxygen and hydrogen isotopes. Springs with measured temperatures averaging greater than 40°C are characterized by Na + K- and SO₄ + Cl-rich waters containing 10³ to 10⁴ mg/l of dissolved solids. Lower temperature springs, averaging less than 40°C, are more enriched in Ca + Mg relative to Na + K. Chemical variations monitored through time in selected thermal springs are probably produced by mixing with non-thermal waters. During the summer months at times of maximum flow, selected hot springs exhibit their highest temperatures and maximum enrichments in most chemical constituents.Cation ratios and silica concentrations remain relatively constant through time for selected Utah thermal springs assuring the applicability of the geothermometer calculations regardless of the time of year. Geothermometer calculations utilizing either the quartz (no steam loss), chalcedony or Mg-corrected Na/K/Ca methods indicate that most thermal springs in Utah associated with normal faults have subsurface temperatures in the range of 25 to less than 120°C. This temperature range suggests fluid circulation is restricted to depths less than about three kilometers assuming an average thermal gradient of about 40°C/km.Thermodynamic calculations suggest that most thermal springs are oversaturated with respect to calcite, quartz, pyrophyllite, (Fe, Mg)-montmorillonite, microcline and hematite, and undersaturated with respect to anhydrite, gypsum, fluorite and anorthite. Chalcedony and cristobalite appear to be the only phases consistently at or near saturation in most waters. Theoretical evaluation of mixing on mineral saturation trends indicates that anhydrite and calcite become increasingly more undersaturated as cold, dilute groundwater mixes with a hot (150°C), NaCl-rich fluid. The evolution of these thermal waters issuing from faults appears to be one involving the dissolution of silicates such as feldspars and micas by CO₂-enriched groundwaters that become more reactive with increasing temperature and/or time. Solution compositions plotted on mineral equilibrium diagrams trend from product phases such as kaolinite or montmorillonite toward reactant phases dominated by alkali feldspars.Isotopic compositions indicate that these springs are of local surface origin, either meteoric (low TDS, < 5000 mg/l) or connate ground water (high TDS, > 5000 mg/l). Deviations from the meteoric water line are the result of rock-water isotopic exchange, mixing or evaporation. Fluid source regions and residence times of selected thermal spring systems (Red Hill, Thermo) have been evaluated through the use of a σ D-contour map of central and western Utah. Ages for waters in these areas range from about 13 years to over 500 years. These estimates are comparable to those made for low-temperature hydrothermal systems in Iceland.     

Shear and tension hydraulic fractures in low permeability rocks

Laboratory hydrofracture experiments were performed on triaxially stressed specimens of oil shale and low-permeability granite. The results show that either shear or tension fractures could develop depending on the level of differentials stress, even in specimens containing preexisting fractures. With 1 kb of confining pressure and differential stress greater than 2kb, hydraulic fluid diffusion into the specimens reduced the effective confining pressure until failure occurred by shear fracture. Below 2kb of differential stress, tension fractures occurred. These results suggest that hydraulic fracturing in regions of significant tectonic stress may produce shear rather than tension fractures. In this casein situ stress determinations based on presumed tension fractures would lead to erroneous results.     

Density and viscosity gradients in zoned magma chambers, and their influence withdrawal dynamics

The liquid being sampled from a draining reservoir of density-stratified fluid, such as an erupting zoned magma chamber, is derived from a relatively thin withdrawal layer adjacent to the level of the chamber outlet. This is a consequence of the buoyancy force associated with the density gradient inhibiting vertical motion so that the opportunity for widely separated density levels (compositions) to be tapped and mingled syneruptively is suppressed.Density gradients in zoned chambers of 0.02 – 10 kgm⁻³/m are suggested by data from caldera-forming eruptions. Viscosity gradients can be specified for a given density gradient using calculated relationships between viscosity and density. Published compositional and geothermometric data are used to show that zoned high-silica rhyolites decrease in viscosity upward because of the roofward concentration of dissolved volatiles. Other zoned calc-alkaline magmas increase in viscosity upward because of decreasing temperature and concentration of network modifying cations.A method is developed of calculating the scale of the withdrawal layer thickness, δ, for given kinematic viscosity, eruption rate, and density and viscosity gradients. The method is systematized by the identification of specific flow regimes describing the action of either viscous or inertial forces in balancing the buoyancy force. Thin withdrawal layers are favoured by small eruption rates, small viscosity, and by large density gradients. For particularly steep density gradients, however, the consequently large viscosity gradient plays a role in determining the withdrawal layer thickness. Withdrawal layer thicknesses of the order of 100 m are calculated for typical pyroclastic eruptions of zoned acid magma, and are mostly independent of the viscosity gradient.The vertical scale at which a zoned chamber is instantaneously being tapped during an eruption is equal to the scale of the withdrawal layer thickness. Thus, an eruption that causes collapse of a caldera block through a height that is less than that of the withdrawal layer scale will produce magmas from deeper levels than that to which the chamber roof sinks. In this case the eruption is said to oversample the chamber with respect to the amount of caldera collapse and will produce an essentially constant range of compositions throughout. Alternatively, if the caldera collapse distance is much greater than δ then the selective withdrawal process leads to successive levels of the chamber being “skimmed off” (on a scale δ). This allows the compositional stratigraphy of the chamber to be inverted by the eruptive process, with little opportunity for syneruptive mixing between diverse magma compositions. The geological record shows that most calderas associated with zoned magmas collapsed through vertical distances in excess of 100 m (the characteristic estimate for δ) and, in agreement with our modelling of selective withdrawal, show smooth correlations between composition, or temperature, and the order of eruption.     

Tracing effects of decalcification on solute sources in a shallow groundwater aquifer, NW Germany

δ⁸⁷Sr values and Ca/Sr ratios were employed to quantify solute inputs from atmospheric and lithogenic sources to a catchment in NW Germany. The aquifer consists primarily of unconsolidated Pleistocene eolian and fluviatile deposits predominated by >90% quartz sand. Accessory minerals include feldspar, glauconite, and mica, as well as disperse calcium carbonate in deeper levels. Decalcification of near-surface sediment induces groundwater pH values up to 4.4 that lead to enhanced silicate weathering. Consequently, low mineralized Ca–Na–Cl- and Ca–Cl-groundwater types are common in shallow depths, while in deeper located calcareous sediment Ca–HCO₃-type groundwater prevails. δ⁸⁷Sr values and Ca/Sr ratios of the dissolved pool range from 7.3 to −2.6 and 88 to 493, respectively. Positive δ⁸⁷Sr values and low Ca/Sr ratios indicate enhanced feldspar dissolution in shallow depths of less than 20 m below soil surface (BSS), while equilibrium with calcite governs negative δ⁸⁷Sr values and elevated Ca/Sr ratios in deep groundwater (>30 m BSS). Both positive and negative δ⁸⁷Sr values are evolved in intermediate depths (20–30 m BSS). For groundwater that is undersaturated with respect to calcite, atmospheric supplies range from 4% to 20%, while feldspar-weathering accounts for 8–26% and calcium carbonate for 62–90% of dissolved Sr²⁺. In contrast, more than 95% of Sr²⁺ is derived by calcium carbonate and less than 5% by feldspar dissolution in Ca–HCO₃-type groundwater. The surprisingly high content of carbonate-derived Sr²⁺ in groundwater of the decalcified portion of the aquifer may account for considerable contributions from Ca-containing fertilizers. Complementary tritium analyses show that equilibrium with calcite is restricted to old groundwater sources.     

Circulation of bubbly magma and gas segregation within tunnels of the potential Yucca Mountain repository

Following an intersection of rising magma with drifts of the potential Yucca Mountain nuclear waste repository, a pathway is likely to be established to the surface with magma flowing for days to weeks and affecting the performance of engineered structures located along or near the flow path. In particular, convective circulation could occur within magma-filled drifts due to the exsolution and segregation of magmatic gas. We investigate gas segregation in a magma-filled drift intersected by a vertical dyke by means of analogue experiments, focusing on the conditions of sustained magma flow. Degassing is simulated by electrolysis, producing micrometric bubbles in viscous mixtures of water and golden syrup, or by aerating golden syrup, producing polydisperse bubbly mixtures with 40% of gas by volume. The presence of exsolved bubbles induces a buoyancy-driven exchange flow between the dyke and the drift that leads to gas segregation. Bubbles segregate from the magma by rising and accumulating as a foam at the top of the drift, coupled with the accumulation of denser degassed magma at the base of the drift. Steady-state influx of bubbly magma from the dyke into the drift is balanced by outward flux of lighter foam and denser degassed magma. The length and time scales of this gas segregation are controlled by the rise of bubbles in the horizontal drift. Steady-state gas segregation would be accomplished within hours to hundreds of years depending on the viscosity of the degassed magma and the average size of exsolved gas bubbles, and the resulting foam would only be a few cm thick. The exchange flux of bubbly magma between the dyke and the drift that is induced by gas segregation ranges from 1 m³ s⁻¹, for the less viscous magmas, to 10⁻⁸ m³ s⁻¹, for the most viscous degassed magmas, with associated velocities ranging from 10⁻¹ to 10⁻⁹ m s⁻¹ for the same viscosity range. This model of gas segregation also predicts that the relative proportion of erupted degassed magma, that could potentially carry and entrain nuclear waste material towards the surface, would depend on the value of the dyke magma supply rate relative to the value of the gas segregation flux, with violent eruption of gassy as well as degassed magmas at relatively high magma supply rates, and eruption of mainly degassed magma by milder episodic Strombolian explosions at relatively lower supply rates.     

Experimental investigation on fluid characteristics of medium dense saturated fine sand in pre- and post-liquefaction

Liquefaction of saturated loose sand is a major cause of extensive damage to buildings and infrastructures during large earthquakes. A better understanding of the behaviour of liquefied soil is becoming increasingly necessary to mitigate earthquake damage, and the fluid method has become an increasingly popular means to study the behaviour of liquefied soils. The purpose of this study is to determine the fluid characteristics of liquefied fine sand. In this paper, the apparent viscosity was measured as an index of fluid characteristics using the shaking table tests of pre-liquefaction behaviour of saturated fine sand at approximately 45 % relative density; the relationship of apparent viscosity and shear strain rate on liquefying fine sand was indicated as a power-law shear-thinning non-Newtonian fluid; and liquefying fine sand has the alternating behaviour of shear dilatancy and compressibility during cyclic loading. Additionally, a series of a monotonic axial compression loading tests in an undrained manner were performed to measure the shear stress and excess pore pressure ratio relationship on the post-liquefaction saturated fine sand at approximately 50 % relative density. The fluid characteristics of post-liquefaction fine sand exhibits rate dependence and can be described by a combined fluid model of time-independent and time-dependent power-law functions; the time-independent viscous resistance is not relevant to the excess pore pressure ratio; but the time-dependent frictional resistance is closely related to the excess pore pressure ratio. Furthermore, the results of the verification tests demonstrate that the proposed fluid model has good applicability for the fluid behaviour of the post-liquefaction fine sand.     

Comparison of methods for modelling the behaviour of bubbles produced by marine seismic airguns

Three models for the dynamics of seismic airgun‐generated bubbles and their associated far‐field signals are developed and compared with geophysical data. The first model of an airgun‐generated bubble uses a spherical approximation, the second is an approximate Lagrangian model which allows for small deformations from a spherical shape, whilst the final model is an axisymmetric boundary‐integral method which permits the bubble to evolve into highly non‐spherical geometries. The boundary‐integral method also allows both geometric interference and strong dynamic interactions in multi‐bubble studies. When comparing the spherical model to experimental data there are three apparent, significant differences: the magnitude of the primary pressure peak, which is greater in the model; the subsequent decay of the pressure peaks and motion – the experimental data demonstrating greater decay and a slower rise rate; and the frequency of oscillation, which is slower in the experimental data. It is believed that the first discrepancy is due to the initial stages of expansion where the compressed air is forced to sparge through the airgun ports. The other differences indicate that there is some other energy‐loss mechanism which is not accounted for in the spherical bubble model. Non‐spherical bubble behaviour is investigated through the use of two different deformable many‐bubble codes and their predictions are compared with the spherical model and experimental data. The Lagrangian model predicts the formation of a buoyancy‐driven liquid jet on the first collapse of a typical airgun bubble; however, the model breaks down when the bubble becomes significantly deformed, due to a low‐order spherical‐harmonic approximation for the potential. The axisymmetric boundary‐integral code models the jet shape accurately and it is found that these bubbles evolve to toroidal geometries when the jet impacts on the opposite surface of the bubble. This highly non‐spherical behaviour is readily observed on high‐speed films of airgun bubbles, and is one key source of energy loss; it damps the pulsations of the bubble and slows its rise speed. Inter‐bubble interactions are investigated using the two deformable bubble models, and the predictions are compared to field data. It was found that as the bubbles approach each other, their periods of oscillation increase in accordance with observations, and jets are formed in the direction of motion upon collapse.     

One-dimensional modelling of mantle flow

A one-dimensional model of flow between a fixed boundary at the bottom and a moving one on top with no net flow through vertical sections is tested for geophysically interesting mantle viscosity-depth functions. Such a model, although simplistic, may help in answering the question to what depth the return flow extends, at least in the case of moving plates measuring many thousand kilometers across, such as the Pacific plate.It the viscosity in the asthenosphere is less than three orders of magnitude smaller than that of the mantle below, the return flow extends to great depth and the asthenosphere is a zone of concentrated shear. If the viscosity contrast is greater, the return flow is concentrated in the asthenosphere. For a wide range of model parameters typical flow velocities below the asthenosphere are about one-tenth of the plate velocity. The pressure gradient required by the mantle flow may be manifest in gravity trends across moving plates, but no excessive gravity anomalies are required by the model if the absolute viscosity values conform to those inferred from post-glacial rebound data. A thinner and lower-viscosity layer is favored over a thicker and more viscous layer if both fit glacial rebound evidence. The present model may not be applicable if down to the core the viscosity is as low as about 10²¹ N s m^–2 with a free-slip bottom boundary.     

Fluid involvement in normal faulting

Evidence of fluid interaction with normal faults comes from their varied role as flow barriers or conduits in hydrocarbon basins and as hosting structures for hydrothermal mineralisation, and from fault-rock assemblages in exhumed footwalls of steep active normal faults and metamorphic core complexes. These last suggest involvement of predominantly aqueous fluids over a broad depth range, with implications for fault shear resistance and the mechanics of normal fault reactivation. A general downwards progression in fault rock assemblages (high-level breccia-gouge (often clay-rich) → cataclasites → phyllonites → mylonite → mylonitic gneiss with the onset of greenschist phyllonites occurring near the base of the seismogenic crust) is inferred for normal fault zones developed in quartzo-feldspathic continental crust. Fluid inclusion studies in hydrothermal veining from some footwall assemblages suggest a transition from hydrostatic to suprahydrostatic fluid pressures over the depth range 3–5 km, with some evidence for near-lithostatic to hydrostatic pressure cycling towards the base of the seismogenic zone in the phyllonitic assemblages. Development of fault-fracture meshes through mixed-mode brittle failure in rock-masses with strong competence layering is promoted by low effective stress in the absence of thoroughgoing cohesionless faults that are favourably oriented for reactivation. Meshes may develop around normal faults in the near-surface under hydrostatic fluid pressures to depths determined by rock tensile strength, and at greater depths in overpressured portions of normal fault zones and at stress heterogeneities, especially dilational jogs. Overpressures localised within developing normal fault zones also determine the extent to which they may reutilise existing discontinuities (for example, low-angle thrust faults). Brittle failure mode plots demonstrate that reactivation of existing low-angle faults under vertical σ₁ trajectories is only likely if fluid overpressures are localised within the fault zone and the surrounding rock retains significant tensile strength. Migrating pore fluids interact both statically and dynamically with normal faults. Static effects include consideration of the relative permeability of the faults with respect to the country rock, and juxtaposition effects which determine whether a fault is transmissive to flow or acts as an impermeable barrier. Strong directional permeability is expected in the subhorizontal σ₂ direction parallel to intersections between minor faults, extension fractures, and stylolites. Three dynamic mechanisms tied to the seismic stress cycle may contribute to fluid redistribution: (i) cycling of mean stress coupled to shear stress, sometimes leading to postfailure expulsion of fluid from vertical fractures; (ii) suction pump action at dilational fault jogs; and, (iii) fault-valve action when a normal fault transects a seal capping either uniformly overpressured crust or overpressures localised to the immediate vicinity of the fault zone at depth. The combination of σ₂ directional permeability with fluid redistribution from mean stress cycling may lead to hydraulic communication along strike, contributing to the protracted earthquake sequences that characterise normal fault systems.     

3-D spherical shell modeling of mantle flow and its implication for global tectogenesis

In order to study the relationship between mantle flow and global tectogenesis, we present a 3-D spherical shell model with incompressible Newtonian fluid medium to simulate mantle flow which fits the global tectogenesis quite well. The governing equations are derived in spherical coordinates. Both the thermal buoyancy force and the self-gravitation are taken into account. The velocity and pressure coupled with temperature are computed, using the finite-element method with a punitive factor. The results show that the lithosphere, as the boundary layer of the earth's thermodynamic system, moves with the entire mantle. Both its horizontal and vertical movements are the results of the earth's thermal motion. The orogenesis occurs not only in the collision zones at the plates' boundaries, but also occurs within the plates. If the core-mantle boundary is impermeable and the viscosity of the lower mantle is considerable, the vertical movement is mostly confined to the upper mantle. The directions of the asthenospheric movements are not fully consistent with those of the lithospheric movements. The depths of spreading movements beneath all ridges are less than 220 km. In some regions, the shear stresses, acting on the base of the lithosphere by the asthenosphere, are the main driving force; but in other regions, the shear stresses are the resisting force.     

Two-dimensional kinematic and rheological modeling of the 1912 pyroclastic flow,Katmai, Alaska

Pyroclastic flow emplacement is strongly influenced by eruption column height. A surface along which kinetic energy is zero theoretically connects the loci of eruption column collapse with all coeval ignimbrite termini. This surface is reconstructed as a two-dimensional energy line for the 1912 Katmai pyroclastic flow in the Valley of Ten Thousand Smokes from mapped flow termini and the runup of the ignimbrite onto obstructions and through passes. Extrapolation of the energy line to the vicinity of the source vent at Novarupta suggests the eruption column which generated the ignimbrite eruption was approximately 425 m high. The 1912 pyroclastic flow travelled about 25 km downvalley. Empirical velocity data calculated from runup elevations and surveyed centrifugal superelevations indicate initial velocities near Novarupta were greater than 79–88 m s^–1. The flow progressively decelerated and was travelling only 2–8 m s^–1 when it crossed a moraine 16 km downvalley. The constant slope of the energy line away from Novarupta suggests the flow was systematically slowed by internal and basal friction. Using a simple physical model to calculate flow velocities and a constant kinetic friction coefficient (Heim coefficient) of 0.04 derived from the reconstructed energy line, the flow is estimated to have decelerated at an average rate of –0.16 m s^–2 and to have taken approximately 9.5 minutes to travel 25 km down the Valley of Ten Thousand Smokes. The shear strength of the flowing ignimbrite at the moraine was approximately 0.5 kPa, and its Bingham viscosity when it crossed the moraine was 3.5 × 10³ P. If the flow was Newtonian, its viscosity was 4.2 × 10³ P. Reynolds and Froude numbers at the moraine were only 41–62 and 0.84–1.04, respectively, indicating laminar, subcritical flow.     

Characterization of a mud deposit offshore of the Patos Lagoon,southern Brazil

Rapid deposition of mud on the beach along the shoreface of Rio Grande do Sul, Brazil dramatically influences the normal operations in the littoral zone. In the surf zone, fluid and suspended mud opposes water-wave movement and dissipates water-wave energy; on the beach, mud limits trafficability. As part of a multinational, multidisciplinary program to evaluate the influence of mud strength, density and viscosity on water-wave attenuation, sediments were evaluated in situ or collected for evaluation from an area offshore of Cassino Beach, slightly south of the Patos Lagoon mouth. Shear strength of deposited sediments ranged from 0.6 kPa at the seafloor to 3.4 kPa at ∼1 m below the seafloor. Mud sediments were also collected to simulate the in situ response of fluid mud to shear stresses. For this determination, rheological evaluations were made using a strain-controlled Couette viscometer on numerous remixed samples that ranged in density from 1.05 to 1.30 g/cm³. It was determined that this mud is a non-ideal Bingham material in that it has a true initial yield stress as well as a upper Bingham yield stress. Initial yield stress ranged from 0.59 to 2.62 Pa, upper Bingham yield stress ranged from 1.05 to 7.6 Pa. Apparent viscosity ranged from 0.02 to 4.7 Pa s with the highest viscosities occurring between the two yield stresses. Sediment strength in the remixed samples is 2 to 3 orders of magnitude lower than the horizontal shear strength of the sediment bed as determined by shear vane or predicted from penetrometer measurements. This difference is partially due to the fact that rheological evaluations are made on fully remixed sediments, whereas horizontal shear strength is determined within relatively undisturbed sediments. Similar values of viscosity and shear strength are comparable to those determined for mud in other coastal areas where fluid mud deposits occur.