Frank J. Spera

Carbon dioxide in petrogenesis III: role of volatiles in the ascent of alkaline magma with special reference to xenolith-bearing mafic lavas

Kinetic and fluid dynamic constraints on deep-seated magma migration rates suggest ascent velocities in the range 10 to 30 m/s, 10−1 to 10 m/s and 10−2 to 5 m/s for kimberlitic, garnet peridotite-bearing and spinel peridotite-bearing alkalic magmas. These rates virtually demand translithospheric magma transport by a fracture as opposed to diapiric mechanism. The hypothesis that volatile exsolution accelerates magma through the deep lithosphere is tested by solution of the appropriate set of conservation, mass balance and volatile component solubility equations governing the steady ascent (decompression) of compressible, two-phase magma (melt+H2O+CO2) in which irreversible phenomena (friction, heat transfer) are accounted for. The results of the numerical experiments were designed to test the importance of melt bulk composition (kimberlite, nephelinite, alkali basalt), initial conditions (mass flux (M), heat transfer coefficient (B), lumped friction factor (Cf)), conduit width (D), initial magma volatile content and geothermal gradients. The fractional increase in ascent rate (Δu/ui) is rarely greater than approximately 2 during translithospheric migration. The propellant hypothesis is rejected as a first-order mechanism driving magma acceleration during ascent. The most influential parameters governing ascent dynamics are M, Cf, D, B and the geotherm. Because of the relatively incompressible nature of the magmatic volatile phase at P>100 MPa, the initial magma volatile content plays a secondary (although demonstrable) role. The main role of volatiles is in controlling the initial magma flux (M) and the magma pressure during ascent. In adiabatic (B=0) simulations, magma ascends nearly isothermally. Generally, however, the assumption of adiabaticity is a poor one especially for flow through narrow (0.5 to 2 m) conduits in old (cold) lithosphere at rates ∼10−1 m/s. The proposed fluid dynamic model is consistent with and complementary to the magma-driven crack propagation models. The generation of mantle metasomatic fluid is a corollary of the non-adiabatic ascent of volatile-bearing magma through the lithosphere. Magma heat death is an important process for the creation of mantle heterogeneity.

High-temperature properties of silicate liquids: applications to the equilibration and ascent of basic magma

High-temperature heat content measurements have been made on a series of silicate liquids, which in conjunction with published data, are used to derive partial molar heat capacities of SiO2, TiO2, Al2O3, Fe2O3, FeO, MgO, CaO, Na2O and K2O in the temperature range 1200-1650 K. Only Fe2O3 appears to be compositionally dependent, and the best evidence suggests that there is no excess heat capacity (CPi i = C°). In combination with calorimetric data and the effect of pressure on the fusion temperature of solid compounds, a consistent set of enthalpy, entropy and volume data have been derived for the liquid compounds CaMgSi2O6, NaAlSi3O8, KAlSi3O8, Fe2SiO4 and TiO2. By using activities (relative to a liquid standard state) calculated at 1 bar for a range of lavas, the equilibration pressures and temperatures of lavas with a lherzolitic source material are calculated, and for basanites indicate 22-26 kbar and 1310-1360 °G. The regular solution formulation used in these calculations gives an estimated error of 40 °G and 5.7 kbar when compared to experimental equilibria. It is suggested that one of the thermal responses of ascending alkali basalt magma to engulfing cooler lherzolitic nodules could be the precipitation of megacrysts, and the calculated equilibration pressures and temperatures of the megacryst assemblage (16-20 kbar, 1220-1240 °G) is in accord with this. The importance of viewing volcanic eruptions as the last stage in a sequence of chemical and thermomechanical instabilities is pointed out. Equations expressing the conservation of energy, mass and momentum on a macroscopic scale are given. The high Rayleigh numbers appropriate for even the relatively small magma volumes of erupted alkali basalts indicate turbulent flow-regimes with characteristic thermal convection velocities of the same order as nodule settling velocities. There is a significant partial melting effect in the mantle surrounding an ascending diapir if buoyancy is a significant force acting to drive the magma upwards. The effect of latent heat and convective heat losses on the thermal budget of a rising diapir has been calculated and shows the assumption of adiabaticity is often unwarranted - even for rapidly ascending magma. Finally, mass transfer rates due to convective diffusion have been calculated for all the major components in a basic silicate liquid. Integral mass exchange depends inversely on the ascent rate and is quite small for the rapidly ascending alkalic basalts.

Co-mingling of acid and basic magma with implications for the origin of mafic I-type xenoliths: Field and petrochemical relations of an unusual dike complex at eagle lake, Sequoia National Park, California, U.S.A.

Open-system magmatic processes result in a continuum of disequilibrium features, from hybrid magmas to lamprophyre dikes. Through application of recent theoretical work on magma chamber convection we quantify thermal and mechanical parameters for a single, somewhat unique, plutonic system and propose a general scheme for interpreting magma mixing based on petrographic, dynamical and heat-transfer considerations. At Eagle Lake, intrusion of nearly aphyric basaltic melt into mostly crystallized acidic host has created a 2–4-m-wide dike-like train of ellipsoidal mafic inclusions set in a matrix of unfoliated leucocratic material. The host magma (∼65% SiO2) is estimated to have been 70–90% crystallized at the time of mafic melt injection; mafic magma (∼51% SiO2) was intruded near its liquidus, at 1050–1150°C. Formation of a hybrid compositional product is not observed. Upon intrusion, the mafic magma formed ellipsoidal pillows of average areal size 50 cm2, many are encased by fine-grained margins interpreted as remnant quench rims. The host acted initially as a brittle solid; the absence of evidence for creep or brittle-ductile transitional flow implies strain rates around 10−2 s−1 within the zone of mafic melt injection. A thermal model predicts that the heat released during thermal equilibration was sufficient to raise the temperature of the host to above its rheological locking point in the region adjacent to the mafic conduit; lack of foliation in the leuco-cratic material in this region supports the model. Schlieren zones developed along dike complex margins, where strain gradients were maximized. The schlieren are chemically linked to the mafic melt; mineral deformation features indicate strain rates ∼10−5 s−1 at 700–1000°C. A general model of mixing is proposed in which the relative volumes, temperatures and viscosities of the distinct magmas play a pivotal role in determining the spatial scale of the resultant compositional heterogeneity. For example, evidence for intrusion of mafic melt 103 years after silicic pluton emplacement will not be visible on outcrop scale; vigorous convection will have eradicated all but xenolithic and xenocrystic traces. We believe that many I-type mafic “xenoliths” in Sierran plutons are the result of this style of magma mixing. Alternatively, if intrusion occurs 106 years following pluton emplacement, map-scale features such as lamprophyre dikes and large inclusion swarms are evident. In the context of a general model, the Eagle Lake quartz monzodiorite pluton preserves the earliest stages of formation of individual mafic inclusions.

Rheology and microstructure of magmatic emulsions - Theory and experiments

Abstract The rheological properties of viscous emulsions composed of melt plus vapor bubbles constitute a critical but largely uninvestigated aspect of magmatic transport phenomena. In this study, the rheological behavior of dilute emulsions of GeO2 containing from 0.8 to 5.5 vol.% air bubbles has been measured experimentally between 1100 and 1175°C at 100 kPa in a rotating rod rheometer at shear rates between 0.05 and 7 s−1. At constant bubble volume fraction, when the range of shear rates examined is greater than a factor of twenty, the rheological behavior of the emulsions can be modeled by a power-law constitutive relation. The power-law emulsions are pseudoplastic (shear-thinning), having a flow index of 0.87–0.93. A tentative correlation between relative viscosity and bubble volume fraction is given as ηr = 1 + 13.1 φ, with ηr = ηe/ηm (ηe is the emulsion viscosity at constant shear stress and ηm is the viscosity of the pure Newtonian melt phase.) The strong variation of relative viscosity with volume fraction of bubbles is placed in the context of current theoretical and experimental understanding of the effects of shear on viscous emulsions, and is attributed to the deformation and eventual disruption of bubbles by shear forces. Bubble deformation is promoted by shear and opposed by surface tension. Two dimensionless parameters governing bubble deformation are the capillary number Ca≡ γ η m r b /σ and viscosity ratio λ ≡ ηv/ηm determined from melt viscosity ηm, vapor viscosity ηv bubble radius rb, shear rate γ, and vapor-melt interfacial tension σ. The capillary number is a measure of the relative importance of shear and interfacial stresses. Low-λ bubbles may attain very elongate stable shapes, and high shear rates are required before fragmentation occurs at a critical capillary number Cacrit,f. The number of daughter bubbles formed during disruption is known to depend on Ca/Cacrit,f and to rise steeply as this ratio increases from 1 to 20. Bubbles are deformed into prolate ellipsoids with deformation parameter D = (l − b) (l + b) where l and b represent the long and short axes of the ellipsoidal bubble; for small non-dimensional shear rate (Ca The deformation of bubbles produces viscoelastic behavior in viscous emulsions. Normal stress differences amounting to several per cent of the total shear stress can be produced at shear rates of less than 10 s−1. In rotating rod rheometry, this leads to rod-climbing behavior (Weissenberg effect) which permits the measurement of the normal stress differences by climbing rod viscometry. A preliminary assessment of the first normal stress difference (defined N1 = τθθ − τrr) is made in one of our experiments, and is estimated to be about 2% of the total shear stress. Inferences drawn regarding the viscosity and discharge of lava flows may be misleading if allowance is not made for the effects of vapor bubbles on magma rheology.

Eruption volume, periodicity, and caldera area: Relationships and inferences on development of compositional zonation in silicic magma chambers

Abstract In order to put constraints on the mechanisms of compositional zonation in magma chambers, data were collected on caldera areas, ash-flow volumes and repose times between zoned ash flows for a number of magmatic systems of different age, composition, size and tectonic environment. First-order correlations between volume, repose time and stratification rate are apparent. Chemical zonation is developed to partially compensate for the internal production of entropy due to heat conduction through magma chamber thermal boundary layers. Repose times are proportional to eruption volumes and are consistent with convection-aided diffusion processes such as Soret diffusion or double-diffusive convection. Volume and area relations suggest that small-volume systems tend to be more conical than cylindrical in shape. An important factor controlling magma chamber evolution appears to be the ratio of magma chamber surface area to magma chamber volume, other factors remaining the same. Small magma chambers appear to stratify in shorter periods of time and at faster rates than large-volume systems.

Lunar magma transport phenomena

Abstract An understanding of the most significant events during the first Ga or so of lunar history—global differentiation associated with a Lunar Magma Ocean (LMO) and the later generation of about 10 7 km 3 of mare basalts—depends profoundly on magma transport dynamics. LMO evolution is dominated by the characteristics of hard-turbulent convection of a fluid undergoing phase change. Quench protocrust, formed at the ocean surface in early times, is repeatedly disrupted by bolide impact, ocean body tides, and associated crustal foundering. During this epoch, the ocean temperature is set by the balance between convective heat brought to the surface and brown-body radiation from the surface. At later times, the convective flow is organized into a number of regimes. From top to bottom these include conductive crustal lid, a viscous sublayer, an inertial core, a lower viscous sublayer, and a mushy cumulate region. Crystal settling and flotation is restricted to the viscous sublayer regions. Dilatancy pumping may prevent the efficient expulsion of intercumulus melt during cumulate formation. Typical velocities within the inertial region are of order 10 m/s. Because late-stage Ti-rich cumulates are dense relative to the earlier Mg-rich cumulates, hyper-to-sub-solidus convection tends to mix LMO crystallization products. Numerical simulations that account simultaneously for compositional and thermal buoyancy effects indicate a characteristic mixing time ∼ 200 Ma. Statistical measures of mixing (variance and spatial correlation length) quantify the details of mixing. The Darcy percolative and vein-drain models of melt extraction are briefly discussed. Because compaction lengths are small, ~ 10 2 m, the rate of melt extraction is governed by the balance between melt buoyancy and Darcy friction. Differential (melt/matrix) velocities are of order 10 km/Ma for nominal values appropriate for mare basalt melt extraction from a heterogeneous (mixed) LMO source. Transport of magma through the lunar lithosphere via a connected crack network seems highly probable. For the range of inferred discharge rates applicable for Lunar Mare Volcanism (LMV; 10 3 to 10 7 m 3 /s) typical fracture widths and ascent speeds are 10 −1 to 50 m and 10 −1 to 10 m/s, respectively. A simple model is proposed to evaluate the extent of fractionation as magma traverses cold lunar lithosphere. If Apollo green glasses are primitive and have not undergone significant fractionation en route to the surface, then mean ascent rates of 10 m/s and cracks of widths > 40 m are indicated. Lunar tephra and vesiculated basalts suggest that a volatile component plays a role in eruption dynamics. The predominant vapor species appear to be CO, CO 2 , and COS. Near the lunar surface, the vapor fraction expands enormously and vapor internal energy is converted to mixture kinetic energy with the concomitant high-speed ejection of vapor and pyroclasts to form lunar fire fountain deposits such as the Apollo 17 orange and black glasses and Apollo 15 green glass.

Thermal evolution of plutons: a parameterized approach.

A conservation-of-energy equation has been derived for the spatially averaged magma temperature in a spherical pluton undergoing simultaneous crystallization and both internal (magma) and external (hydrothermal fluid) thermal convection. The model accounts for the dependence of magma viscosity on crystallinity, temperature, and bulk composition; it includes latent heat effects and the effects of different initial water concentrations in the melt and quantitatively considers the role that large volumes of circulatory hydrothermal fluids play in dissipating heat. The nonlinear ordinary differential equation describing these processes has been solved for a variety of magma compositions, initial termperatures, initial crystallinities, volume ratios of hydrothermal fluid to magma, and pluton sizes. These calculations are graphically summarized in plots of the average magma temperature versus time after emplacement. Solidification times, defined as the time necessary for magma to cool from the initial emplacement temperature to the solidus temperature vary as R1,3, where R is the pluton radius. The solidification time of a pluton with a radius of 1 kilometer is 5 x 104 years; for an otherwise identical pluton with a radius of 10 kilometers, the solidification time is ∼106 years. The water content has a marked effect on the solidification time. A granodiorite pluton with a radius of 5 kilometers and either 0.5 or 4 percent (by weight) water cools in 3.3 x 105 or 5 x 104 years, respectively. Convection solidification times are usually but not always less than conduction cooling times.

Dynamics of magma withdrawal from stratified magma chambers

The time history of magma withdrawal through a central vent from a flat-roofed chamber strongly stratified in density and viscosity has been numerically modeled. Important parameters include the geometry of the reservoir; the initial vertical compositional profile; the ratio of viscous, inertial, and gravitational forces; and the basal normal stress driving the eruption. Finite critical stresses in the range 102 to 106 Pa are required to initiate and maintain an eruption. The composition-time history of erupted magma depends strongly on the reservoir/conduit width ( A ) such that large A increases (1) the time interval during which mixed magma is erupted, (2) the steady-state time ( ts ), defined as the time at which the composition of erupted magma is within 1% of the initial basal composition, and (3) the fraction of silicic magma trapped within the chamber. Steady-state times increase by a factor of two as the viscosity contrast increases from 1 to 102, and they become independent of viscosity variations for contrasts > 104. It is possible to distinguish continuous from discontinuous (i.e., layered) pre-eruptive gradients within chambers by comparing synthesized and measured geochemical stratigraphic sections for particular pyroclastic flow deposits. A mechanism for the generation of compositional gaps in ignimbrites following either a short eruption hiatus or an abrupt increase or decrease of the discharge during an otherwise quasi-steady eruption is quantitatively predicted. Most important, a compositional gap or a series of gaps within a pyroclastic deposit does not necessarily mean that one existed within the chamber before the eruption. It is impossible to invert stratigraphically controlled geochemical data to obtain in situ chamber compositional structure if one does not have detailed information regarding the location of vents and the variation of magma discharge with time during a pyroclastic eruption.

Carbon Dioxide in igneous petrogenesis: I

AbstractA number of experimental CO2 solubility data for silicate and aluminosilicate melts at a variety of P- T conditions are consistent with solution of CO2 in the melt by polymer condensation reactions such as SiO4(m4−+CO2(v)+SinO3n+1(m)(2n+1)⇌Sin+1O3n+4(m)(2n+4)−+CO3(m)2−.For various metalsilicate systems the relative solubility of CO2 should depend markedly on the relative Gibbs free change of reaction. Experimental solubility data for the systems Li2O-SiO2, Na2O-SiO2, K2O-SiO2, CaO-SiO2, MgO-SiO2 and other aluminosilicate melts are in complete accord with predictions based on Gibbs Free energies of model polycondesation reactions.A rigorous thermodynamic treatment of published P- T-wt.% CO2 solubility data for a number of mineral and natural melts suggests that for the reaction CO2(m) ⇌ CO2(v)(1)CO2-melt mixing may be considered ideal (i.e., {