Modelling the dynamics and thermodynamics of volcanic degassing

 The rates of passive degassing from volcanoes are investigated by modelling the convective overturn of dense degassed and less dense gas-rich magmas in a vertical conduit linking a shallow degassing zone with a deep magma chamber. Laboratory experiments are used to constrain our theoretical model of the overturn rate and to elaborate on the model of this process presented by Kazahaya et al. (1994). We also introduce the effects of a CO₂–saturated deep chamber and adiabatic cooling of ascending magma. We find that overturn occurs by concentric flow of the magmas along the conduit, although the details of the flow depend on the magmas' viscosity ratio. Where convective overturn limits the supply of gas-rich magma, then the gas emission rate is proportional to the flow rate of the overturning magmas (proportional to the density difference driving convection, the conduit radius to the fourth power, and inversely proportional to the degassed magma viscosity) and the mass fraction of water that is degassed. Efficient degassing enhances the density difference but increases the magma viscosity, and this dampens convection. Two degassing volcanoes were modelled. At Stromboli, assuming a 2 km deep, 30% crystalline basaltic chamber, containing 0.5 wt.% dissolved water, the ∼700 kg s^–1 magmatic water flux can be modelled with a 4–10 m radius conduit, degassing 20–100% of the available water and all of the 1 to 4 vol.% CO₂ chamber gas. At Mount St. Helens in June 1980, assuming a 7 km deep, 39% crystalline dacitic chamber, containing 4.6 wt.% dissolved water, the ∼500 kg s^–1 magmatic water flux can be modelled with a 22–60 m radius conduit, degassing ∼2–90% of the available water and all of the 0.1 to 3 vol.% CO₂ chamber gas. The range of these results is consistent with previous models and observations. Convection driven by degassing provides a plausible mechanism for transferring volatiles from deep magma chambers to the atmosphere, and it can explain the gas fluxes measured at many persistently active volcanoes. Received: 26 September 1997 / Accepted: 11 July 1998     

The dynamics of xenolith assimilation

Xenolith assimilation has been simulated with experiments involving melting wax spheres into hot water and aqueous solutions and characterised by a theoretical analysis. Both the cases of neutrally buoyant stationary spheres and spheres sinking through the hot host fluid are examined. Melt generated on a sphere's surface flows (compositional convection) in two regimes; as a sheet over one hemisphere and then detaching as finger plumes from the other. Positional variations in the melting rate are dominantly controlled by differences in the melt layer thickness which influence the thermal gradient and heat flux across the layer. The theoretical model predicts melt layer thicknesses and the heat flux from the surrounding fluid. Calculated melting rates agree well with experimental measurements. Partial melting of non-eutectic compositions produces a layer of crystal-melt mush at the xenolith's surface. The theoretical analysis is extended to account for variation in rheological properties across the mush layer. When stoped into typical magmas, xenoliths of common continental crust lithologies are predicted to melt at rates in the order of 2 mm/hour. Thicknesses of the mobile mush layer around xenoliths are predicted to be typically a few centimetres. Relatively mafic lithologies can melt quicker than silicic compositions because, although they are typically more refractory, their lower melt viscosities result in thinner mush layers and so higher heat fluxes. Especially quick melting of water-saturated lithologies occurs as a consequence of both the reduction in melting temperatures and melt viscosities. Due to hot ambient conditions in the lower continental crust the assimilation of xenoliths into underplated basaltic magma can be very rapid. For granulites and mafic-granulites the predicted melting rates are up to 17 mm/hour. Fast rates of melting and efficient mixing of melt into the host magma indicate that assimilation of xenoliths will have a significant influence on the compositional and thermal evolution of magmas. Received: 7 November 1996 / Accepted: 5 January 1998     

Fracture initiation, growth and effect on stress field: a numerical investigation

A numerical investigation was made of the relationships between fracture initiation, growth, stress field and boundary conditions. Two-dimensional plane strain continuum models were used in which fractures appeared as zones of strain localization developed through application of a strain softening Mohr–Coulomb constitutive model. R and R′ fractures developed first, followed by Y fractures at larger strains. The models showed that equal development of conjugate R and R′ fractures is easily changed to favor one or the other set by minor variations in model initial conditions. Strength loss in fractures caused stress field rotations in regions bounded by fractures, altering the orientation of subsequent fractures. The amount and sense of stress field rotation is dependent on the strength loss during displacement on the fractures, the orientation of fractures, and on the boundary conditions. Y oriented fractures could be explained on the basis of a Mohr–Coulomb failure criterion provided that stress field rotation is accounted for. Monitoring of fracture slip activity showed that, under conditions of constant boundary velocity, slip was discontinuous in time, alternating on fractures throughout the model.     

Origin of granitic magma by crustal remobilisation: Rb-Sr and Pb/Pb geochronology and isotope geochemistry of the late Archaean Qôrqut Granite Complex of southern West Greenland

Rb-Sr and Pb/Pb whole rock isochrons on the Qôrqut Granite Complex yield ages of $\text{2530 ± 30}\text{Myr}\text{(}\text{initial}{}^{87}\text{Sr}{}^{86}\text{Sr}\text{= 0.7081 ± 0.0008)}$ and 2580 ± 80 Myr respectively. A model relating initial Sr and Pb isotopic compositions of the Qôrqut granites to the Sr and Pb isotopic compositions of the Amîtsoq gneisses (ca. 3700 Myr) and Nûk gneisses (ca. 2900 Myr) at 2550 Myr ago, as well as Sr and Pb contents of the gneiss units, suggests that between 40 and 50% of the Qôrqut granite magma was generated by partial melting of Amîtsoq gneisses, and the remainder by partial melting of Nûk gneisses.     

Transient creep and semibrittle behavior of crystalline rocks

We review transient creep and semibrittle behavior of crystalline solids. The results are expected to be pertinent to crystalline rocks undergoing deformation in the depth range 5 to 20 km, corresponding to depths of focus of many major earthquakes. Transient creep data for crystalline rocks at elevated temperatures are analyzed but are poorly understood because of lack of information on the deformation processes which, at low to moderate pressure, are likely to be semibrittle in nature. Activation energies for transient creep at high effective confining pressure are much higher than those found for atmospheric pressure tests in which thermally-activated microfracturing probably dominates the creep rate. Empirical transient creep equations are extrapolated at 200° to 600°C, stresses from 0.1 to 1.0 kbar, to times ranging from 3.17×10² to 3.17×10⁸ years. At the higher temperatures, appreciable transient creep strains may take place but the physical significance of the results is in question because the flow mechanisms have not been determined. The purpose of this paper is to stimulate careful research on this important topic.     

Amphibole zonation in metabasites as a guide to the evolution of metamorphic conditions

In low grade metabasites the amphibole components tremolite, glaucophane, edenite and tschermakite have their activities controlled by interactions with the excess components albite, clinozoisite, chlorite, quartz and H₂O vapor. Three types of reaction are involved, (i) Those in which only components of condensed phases take part: isopleths of equilibrium constant are straight lines in the P-T plane. (ii) Dehydration reactions in which entropy change due to change in Al coordination is of the same sign as that due to dehydration: isopleths of constant K are positive at low pressure and negative at high pressure. (iii) Dehydration reactions in which entropy change due to Al coordination change is opposite in sign to that of dehydration: isopleths of constant K loop in the P-T plane with positive slopes at low and at high pressure. Zonation in naturally occurring amphiboles records the evolution of metamorphic conditions in particular rocks. In an example from the eastern Alps (Austria) early conditions calculated as 15 kb, 200 ° C evolve upgrade to 6 kb, 525 ° C implying concurrent heating and erosion. The record of evolving conditions may span some 30 Ma of geological history.     

A geochemical study of magmatism associated with the initial stages of back-arc spreading

Bransfield Strait is a narrow basin separating the South Shetland Islands from the Antarctic Peninsula and is attributed to recent back-arc extension behind the South Shetland volcanic arc. The volcanic islands of Deception and Bridgeman are situated close to the axis of spreading, whereas Penguin Island lies slightly to the north of this axis. The mineralogy, petrology and geochemistry of the lavas of the three volcanoes have been studied in order to provide information on the nature of magmatism associated with the initial stages of back-arc spreading.Deception Island lavas range from olivine basalt to dacite, and all are highly sodic, with high Na/K, K/Rb, Ba/Rb and Zr/Nb ratios and with Ce_N/Yb_N = 2. Incompatible elements increase systematically between basalt and rhyodacite, while Sr decreases, suggesting that fractional crystallisation is the dominant process relating lava compositions. The rhyodacites have high concentrations of Zr, Y and the REE and negative Eu anomalies and are compositionally similar to oceanic plagiogranite. Bridgeman Island lavas are mostly basaltic andesites, but the levels of many incompatible elements, including REE, are significantly lower than those of Deception lavas, although Ce_N/Yb_N ratios and ⁸⁷Sr/⁸⁶Sr ratios (0.7035) are the same. Penguin Island lavas are magnesian, mildly alkaline olivine basalts with a small range of composition that can be accommodated by fractional crystallisation of olivine, clinopyroxene and/or chromite. Penguin lavas have higher ⁸⁷Sr/⁸⁶Sr (0.7039) and Ce_N/ Yb_N (4) ratios than Deception and Bridgeman lavas. The Rb/Sr ratios of Deception and Penguin basalts (ca. 0.01) are much too low to account for their present ⁸⁷Sr/⁸⁶Sr ratios.Modelling suggests that the source regions of the lavas of the three volcanoes share many geochemical features, but there are also some significant differences, which probably reflects the complex nature of the mantle under an active island arc combined with complex melting relationships attending the initial stages of back-arc spreading. Favoured models suggest that Bridgeman lavas represent 10–20% melting and the more primitive Deception lavas 5–10% melting of spinel-peridotite, whereas Penguin lavas represent less then 5% melting of a garnet-peridotite source. The mantle source for Bridgeman lavas seems to have undergone short-term enrichment in K, Rb and Ba, possibly resulting from dewatering of the subducted slab. Hydrous melting conditions may also account for the more siliceous, high-alumina nature and low trace element contents of Bridgeman lavas.     

Effect of freeze—thaw cycles on resilient properties of fine-grained soils

Stress-deformation data for silt and clay subgrade soils were obtained from in-situ tests and laboratory tests, for use in mechanistic models for design of pavements that will experience freezing and thawing. Plate-bearing tests were run on in-service allbituminous-concrete (ABC) pavements constructed directly on silt subgrade, and on an experimental ABC pavement constructed on clay subgrade, applying repeated loads to the pavement surfaces while the subgrade was frozen, thawing, thawed, and fully recovered. The in-service pavement had experienced several seasons of natural cyclic freezing and thawing, while the experimental pavement was artificially frozen and thawed twice. Repeated-load laboratory triaxial compression tests were performed on the same soils in the frozen and thawed states.

Analysis of deflection data from the in-situ tests showed resilient moduli of the subgrade soils up to more than 10 GPa when frozen, as low as 2 MPa during the thawing period, and up to more than 100 MPa when fully recovered. Analysis of the laboratory tests, which gave moduli comparable to the latter values, showed that resilient modulus and Poisson's ratio in the thawed and recovering conditions can be expressed as a function of the stress state, the moisture content, and the dry density.