Which effective viscosity?

Magmas undergoing shear are prime examples of flows that involve the transport of solids and gases by a separate (silicate melt) carrier phase. Such flows are called multiphase, and have attracted much attention due to their important range of engineering applications. Where the volume fraction of the dispersed phase (crystals) is large, the influence of particles on the fluid motion becomes significant and must be taken into account in any explanation of the bulk behaviour of the mixture. For congested magma deforming well in excess of the dilute limit (particle concentrations >40% by volume), sudden changes in the effective or relative viscosity can be expected. The picture is complicated further by the fact that the melt phase is temperature- and shear-rate-dependent. In the absence of a constitutive law for the flow of congested magma under an applied force, it is far from clear which of the many hundreds of empirical formulae devised to predict the rheology of suspensions as the particle fraction increases with time are best suited. Some of the more commonly used expressions in geology and engineering are reviewed with an aim to home in on those variables key to an improved understanding of magma rheology. These include a temperature, compositional and shear-rate dependency of viscosity of the melt phase with the shear-rate dependency of the crystal (particle) packing arrangement. Building on previous formulations, a new expression for the effective (relative) viscosity of magma is proposed that gives users the option to define a packing fraction range as a function of shear stress. Comparison is drawn between processes (segregation, clustering, jamming), common in industrial slurries, and structures seen preserved in igneous rocks. An equivalence is made such that congested magma, viewed in purely mechanical terms as a high-temperature slurry, is an inherently non-equilibrium material where flow at large Péclet numbers may result in shear thinning and spontaneous development of layering

Shear-induced pressure changes and seepage phenomena in a deforming porous layer-I

We present a model for flow and seepage in a deforming, shear-dilatant sensitive porous layer that enables estimates of the excess pore fluid pressures and flow rates in both the melt and solid phase to be captured simultaneously as a function of stress rate. Calculations are relevant to crystallizing magma in the solidosity range 0.5–0.8 (50–20 per cent melt), corresponding to a dense region within the solidification front of a crystallizing magma chamber. Composition is expressed only through the viscosity of the fluid phase, making the model generally applicable to a wide range of magma types. A natural scaling emerges that allows results to be presented in non-dimensional form. We show that all length-scales can be expressed as fractions of the layer height H, timescales as fractions of H2(nβ'θ+ 1)/(θk) and pressures as fractions of . Taking as an example the permeability k in the mush of the order of magnitude 1015 m2 Pa1 s1, a layer thickness of tens of metres and a mush strength (θ) in the range 108–1012 Pa, an estimate of the consolidation time for near-incompressible fluids is of the order of 105–109 s. Using mush permeability as a proxy, we show that the greatest maximum excess pore pressures develop consistently in rhyolitic (high-viscosity) magmas at high rates of shear ( , implying that during deformation, the mechanical behaviour of basaltic and rhyolitic magmas will differ. Transport parameters of the granular framework including tortuosity and the ratio of grain size to layer thickness (a/H) will also exert a strong effect on the mechanical behaviour of the layer at a given rate of strain. For dilatant materials under shear, flow of melt into the granular layer is implied. Reduction in excess pore pressure sucks melt into the solidification front at a velocity proportional to the strain rate. For tectonic rates (generally 1014 s1), melt upwelling (or downwelling, if the layer is on the floor of the chamber) is of the order of cm yr1. At higher rates of loading comparable with emplacement of some magmatic intrusions (1010 s1), melt velocities may exceed effects due to instabilities resulting from local changes in density and composition. Such a flow carries particulates with it, and we speculate that these may become trapped in the granular layer depending on their sizes. If on further solidification the segregated grain size distribution of the particulates is frozen in the granular layer, structure formation including layering and grading may result. Finally, as the process settles down to a steady state, the pressure does not continue to decrease. We find no evidence for critical rheological thresholds, and the process is stable until so much shear has been applied that the granular medium fails, but there is no hydraulic failure

Petrogenesis of rhyolite-trachyte-basalt composite ignimbrite P1, Gran Canaria, Canary Islands

The 14 Ma caldera-forming composite ignimbrite P1 on Gran Canaria (Canary Islands) represents the first voluminous eruption of highly differentiated magmas on top of the basaltic Miocene shield volcano. Compositional zonation of the ignimbrite is the result of vertically changing proportions of four component magmas, which were intensely mixed during eruption: (1) Crystal-poor to highly phyric rhyolite (∼10 km3), (2) sodic trachyandesite through mafic to evolved trachyte (∼6 km3), (3) Na-poor trachyandesite (<1 km3), and (4) basalt zoned from 5.2 to 4.3 wt % MgO (∼26 km3). P1 basalt is composed of two compositionally zoned magma batches, B2 basalt and B3 basalt. B3 basalt is derived from a mantle source depleted in incompatible trace elements compared to the shield basalt source. Basaltic magmas were stored in a reservoir probably underplating the crust, in which zoned B2 basaltic magma formed by mixing of “enriched” (shield) and “depleted” (B3) mafic melts and subsequent crystal fractionation. Evolved magmas formed in a shallow crustal chamber, whereas intermediate magmas formed at both levels. Abundant pyroxenitic to gabbroid cumulates in P1 support crystal fractionation as the major differentiation process. On the basis of major and trace element modeling, we infer two contemporaneous fractional crystallization series: series I from “enriched” shield basalt through Na-poor trachyandesite to rhyolite, and series II from “depleted” P1 basalt through sodic trachyandesite to trachyte. Series II rocks were significantly modified by selective contamination involving feldspar (Na, K, Ba, Eu, Sr), zircon (Zr) and apatite (P, Y, rare earth elements) components; apatite contamination also affected series I Na-poor trachyandesite. Substantial sodium introduction into sodic trachyandesite is the main reason for the different major element evolution of the two series, whereas their different parentage is mainly reflected in the high field strength trace elements. Selective element contamination involved not only rapidly but also slowly diffusing elements as well as different saturation conditions. Contamination processes thus variably involved differential diffusion, partial dissolution of minerals, partial melt migration, and trace mineral incorporation. Magma mixing between trachyte and rhyolite during their simultaneous crystallization in the P1 magma chamber is documented by mutual mineral inclusions but had little effect on the compositional evolution of both magmas. Fe-Ti oxide thermometry yields magmatic temperatures of around 850°C for crystal-poor through crystal-rich rhyolite, ∼815°C for trachyte and ∼850°–900°C for the trachyandesitic magmas. High 1160°C for the basalt magma suggest its intrusion into the P1 magma chamber only shortly before eruption. The lower temperature for trachyte compared to rhyolite and the strong crustal contamination of trachyte and sodic trachyandesite support their residence along the walls of the vertically and laterally zoned P1 magma chamber. The complex magmatic evolution of P1 reflects the transient state of Gran Canaria's mantle source composition and magma plumbing system during the change from basaltic to silicic volcanism. Our results for P1 characterize processes operating during this important transition, which also occurs on other volcanic ocean islands

Mixing of rhyolite, trachyte and basalt magma erupted from a vertically and laterally zoned reservoir, composite flow P1, Gran Canaria

The 14.1 Ma composite welded ignimbrite P1 (45 km3 DRE) on Gran Canaria is compositionally zoned from a felsic lower part to a basaltic top. It is composed of four component magmas mixed in vertically varying proportions: (1) Na-rhyolite (10 km3) zoned from crystal-poor to highly phyric; (2) a continuously zoned, evolved trachyte to sodic trachyandesite magma group (6 km3); (3) a minor fraction of Na-poor trachyandesite (<1 km3); and (4) nearly aphyric basalt (26 km3) zoned from 4.3 to 5.2 wt% MgO. We distinguish three sites and phases of mixing: (a) Mutual mineral inclusions show that mixing between trachytic and rhyolitic magmas occurred during early stages of their intratelluric crystallization, providing evidence for long-term residence in a common reservoir prior to eruption. This first phase of mixing was retarded by increasing viscosity of the rhyolite magma upon massive anorthoclase precipitation and accumulation. (b) All component magmas probably erupted through a ring-fissure from a common upper-crustal reservoir into which the basalt intruded during eruption. The second phase of mixing occurred during simultaneous withdrawal of magmas from the chamber and ascent through the conduit. The overall withdrawal and mixing pattern evolved in response to pre-eruptive chamber zonation and density and viscosity relationships among the magmas. Minor sectorial variations around the caldera reflect both varying configurations at the conduit entrance and unsteady discharge. (c) During each eruptive pulse, fragmentation and particulate transport in the vent and as pyroclastic flows caused additional mixing by reducing the length scale of heterogeneities. Based on considerations of magma density changes during crystallization, magma temperature constraints, and the pattern of withdrawal during eruption, we propose that eruption tapped the P1 magma chamber during a transient state of concentric zonation, which had resulted from destruction of a formerly layered zonation in order to maintain gravitational equilibrium. Our model of magma chamber zonation at the time of eruption envisages a basal high-density Na-poor trachyandesite layer that was overlain by a central mass of highly phyric rhyolite magma mantled by a sheath of vertically zoned trachyte-trachyandesite magma along the chamber walls. A conventional model of vertically stacked horizontal layers cannot account for the deduced density relationships nor for the withdrawal pattern

Submarine Fernandina : magmatism at the leading edge of the Galapagos hot spot

Author Posting. © American Geophysical Union, 2006. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geochemistry Geophysics Geosystems 7 (2006): Q12007, doi:10.1029/2006GC001290.New multibeam and side-scan sonar surveys of Fernandina volcano and the geochemistry of lavas provide clues to the structural and magmatic development of Galápagos volcanoes. Submarine Fernandina has three well-developed rift zones, whereas the subaerial edifice has circumferential fissures associated with a large summit caldera and diffuse radial fissures on the lower slopes. Rift zone development is controlled by changes in deviatoric stresses with increasing distance from the caldera. Large lava flows are present on the gently sloping and deep seafloor west of Fernandina. Fernandina's submarine lavas are petrographically more diverse than the subaerial suite and include picrites. Most submarine glasses are similar in composition to aphyric subaerially erupted lavas, however. These rocks are termed the “normal” series and are believed to result from cooling and crystallization in the subcaldera magma system, which buffers the magmas both thermally and chemically. These normal-series magmas are extruded laterally through the flanks of the volcano, where they scavenge and disaggregate olivine-gabbro mush to produce picritic lavas. A suite of lavas recovered from the terminus of the SW submarine rift and terraces to the south comprises evolved basalts and icelandites with MgO = 3.1 to 5.0 wt.%. This “evolved series” is believed to form by fractional crystallization at 3 to 5 kb, involving extensive crystallization of clinopyroxene and titanomagnetite in addition to plagioclase. “High-K” lavas were recovered from the southwest rift and are attributed to hybridization between normal-series basalt and evolved-series magma. The geochemical and structural findings are used to develop an evolutionary model for the construction of the Galápagos Platform and better understand the petrogenesis of the erupted lavas. The earliest stage is represented by the deep-water lava flows, which over time construct a broad submarine platform. The deep-water lavas originate from the subcaldera plumbing system of the adjacent volcano. After construction of the platform, eruptions focus to a point source, building an island with rift zones extending away from the adjacent, buttressing volcanoes. Most rift zone magmas intrude laterally from the subcaldera magma chamber, although a few evolve by crystallization in the upper mantle and deep crust.This work was supported by the National Science Foundation grants OCE0002818 and EAR0207605 (D.G.), OCE0002461 (D.J.F. and M.K.), OCE9811504 (D.J.F. and M.R.P.), and EAR0207425 (K.H.) and WHOI postdoctoral support for Soule

Modeling volcanic deformation in a regional stress field: Implications for the formation of graben structures on Alba Patera, Mars

Abundant grabens transect the volcano Alba Patera. Their complex geometry and formation mechanisms are still poorly understood. Tectonic processes and magmatic intrusions are responsible for these long surface features. Cross-cutting relationships of the grabens show radial fractures that were formed during early stages and were progressively overprinted by concentric fractures on the mid and upper flanks of the volcano. Two modeling methods are used to understand the formation of the observed structures and to evaluate their implications for hidden subvolcanic processes. Surface deformation and fault arrangements predicted in finite element models are compared to the graben systems observed in Viking images. The orientation and position of the concentric grabens are found to be best reproduced by local crustal subsidence, superimposed on a regional NW-SE oriented extension with decreasing magnitude from south to north. In analogue sandbox models we also simulate surface structures of arrangements that almost perfectly mimic the observed lineaments on Alba Patera. Formation of the grabens spans a period on the order of a billion years, suggesting long-term geodynamic processes to be responsible for the subsidence of the central Alba Patera area. The progressive change toward higher concentricity is likely resultant from an increase in density in the crust by accumulation of intrusive material and cooling, thus causing subsidence of the region above this volcanic root