Oleg E. Melnik

Nonlinear dynamics of lava dome extrusion

During the eruption of the Soufrière Hills volcano, Montserrat (1995–99), and several other dome eruptions, shallow seismicity, short-lived explosive eruptions and ground deformation patterns indicating large overpressures (of several megapascals) in the uppermost few hundred metres of the volcanic conduit have been observed. These phenomena can be explained by the nonlinear effects of crystallization and gas loss by permeable flow, which are here incorporated into a numerical model of conduit flow and lava dome extrusion. Crystallization can introduce strong feedback mechanisms which greatly amplify the effect on extrusion rates of small changes of chamber pressure, conduit dimensions or magma viscosity. When timescales for magma ascent are comparable to timescales for crystallization, there can be multiple steady solutions for fixed conditions. Such nonlinear dynamics can cause large changes in dome extrusion rate and pulsatory patterns of dome growth.

Periodic behavior in lava dome eruptions

Lava dome eruptions commonly display fairly regular alternations between periods of high activity and periods of low or no activity. The time scale for these alternations is typically months to several years. Here we develop a generic model of magma discharge through a conduit from an open-system magma chamber with continuous replenishment. The model takes account of the principal controls on flow, namely the replenishment rate, magma chamber size, elastic deformation of the chamber walls, conduit resistance, and variations of magma viscosity, which are controlled by degassing during ascent and kinetics of crystallization. The analysis indicates a rich diversity of behavior with periodic patterns similar to those observed. Magma chamber size can be estimated from the period with longer periods implying larger chambers. Many features observed in volcanic eruptions such as alternations between periodic behaviors and continuous discharge, sharp changes in discharge rate, and transitions from effusive to catastrophic explosive eruption can be understood in terms of the non-linear dynamics of conduit flows from open-system magma chambers. The dynamics of lava dome growth at Mount St. Helens (1980–1987) and Santiaguito (1922–2000) was analyzed with the help of the model. The best-fit models give magma chamber volumes of ∼0.6 km3 for Mount St. Helens and ∼65 km3 for Santiaguito. The larger magma chamber volume is the major factor in explaining why Santiaguito is a long-lived eruption with a longer periodicity of pulsations in comparison with Mount St. Helens.

Control of magma flow in dykes on cyclic lava dome extrusion

(1) Lava dome eruptions are commonly characterized by large fluctuations in discharge rate with cyclic behaviour on time-scalesranging from hours to decades. Examples include Bezymianny volcano (Russia), Merapi (Java), Santiaguito (Guatemala), Mt St Helens (USA), Mt Unzen (Japan), and Soufriere Hills volcano (Montserrat). Previous models have assumed simple cylindrical conduits for magma transport, but extrusions are mainly fed by dykes, with cylindrical geometries developing only at shallow levels. The widths of dykes embedded in an elastic medium are influenced by local magma pressure, affecting flow rates and system dynamics strongly. We develop a model for magma flow in dykes, which predicts intense pulsations of magma extrusion for the case of a constant source pressure. The period time scale is determined by the elastic deformation of the dyke walls and the length-to-width ratio of the dyke. The dyke acts like a volumetric capacitor, storing magma as pressure increases and then releasing magma in a pulse of extrusion. For the Soufriere Hills volcano, cyclic extrusions with time-scales of a few weeks are predicted for dykes 300-500 m long and 3-6 m wide, matching observations. The model explains the sharp onset of tilt pulsations and seismic swarms. Citation: Costa, A., O. Melnik, R. S. J. Sparks, and B. Voight (2007), Control of magma flow in dykes on cyclic lava dome extrusion, Geophys. Res. Lett., 34, L02303, doi:10.1029/ 2006GL027466.

Depressurization of fine powders in a shock tube and dynamics of fragmented magma in volcanic conduits

Abstract Samples of fine glass beads (mean grain size equal to 38 and 95 μm) have been depressurized within a vertical shock tube. These short-lived, rapid decompressions resemble discrete, cannon-like vulcanian explosions and produce two-phase flows that are inhomogeneous in density in both vertical and horizontal directions because of the presence of bubble-like heterogeneities. We suggest that also volcanic flows may present similar inhomogeneities in density. In the experimental apparatus the flow velocities increase from approximately 1 to 13 m/s when the pressure drop increases from approximately 200 to 900 mbar. A physical model of the initial velocities of expansions in the shock tube has been applied to a range of volcanic overpressures between 0.1 and 20 MPa, suggesting initial velocities of volcanic flows caused by the removal of a rock plug in volcanic conduits between 25 and 400 m/s. During the experiments at large pressure drops, as the mixture expands and moves up the tube, the flow front becomes highly irregular and bubble-like heterogeneities form. The shape of these bubbles becomes distorted and stretched in the turbulent flow. During the experiments at relatively small pressure drops, the sample oscillates when the particles, after the expansion, flow back and bounce upward again. Jets with diameter smaller than that of the tube are ejected from the oscillating samples generating independent pulses. Large bubble-like heterogeneities whose diameter is a significant fraction of the tube diameter can also discretize the flows. Similar mechanisms in real volcanoes may produce pulse-like ejections of gas–particle mixtures out of the vent.

Eruption dynamics of high-viscosity gas-saturated magmas

A model of eruption, which is a variant of that described in [4] and takes into account the disequilibrium of the pressure in the bubble and in the liquid in the absence of total solidification is proposed. The fragmentation zone is simulated by a disintegration wave with allowance for the velocity and temperature nonequilibrium of the particles of the gas suspension formed and its polydispersity. On the basis of the model constructed steady-state magma flow calculations are made for a given pressure difference and channel length. The results of the calculations show that taking pressure nonequilibrium into account leads to a qualitatively new dependence of the flow rate on the governing parameters and makes it possible to propose a catastrophic eruption intensification mechanism different from that proposed in [3].

Chapter 3 Dual-chamber-conduit models of non-linear dynamics behaviour at Soufrière Hills Volcano, Montserrat

Abstract Modern geophysical data recorded during lava dome building eruptions indicate the presence of multiple connected magma storage regions. Most numerical models for lava dome eruptions assume a single magma chamber fed from below with a constant or prescribed time dependent influx rate and connected to the Earth surface through a conduit. Here we present a development of the model of extrusive eruptions considering a system made of two magma chambers located in elastic rocks and connected by a dyke between each other. We use locations and volumes of the magma chambers inferred for Soufrière Hills Volcano, Montserrat from ground deformation studies and seismic tomography. The model shows cyclic behaviour with a period that depends on the intensity of the influx rate, the volumes and shape of the two chambers and the degree of connectivity of the two reservoirs. For a weak connectivity the overpressure in the lower chamber stays nearly constant during the cycle and the influx of fresh magma into the shallow chamber is also nearly constant. For a strong connectivity between the chambers their overpressure increases or decreases during the cycle in a synchronous way.

Subvolcanic plumbing systems imaged through crystal size distributions

The configuration of subvolcanic magma storage regions exercises a fundamental control on eruptive style and hazard. Such regions can be imaged remotely, using seismic, geodetic, or magnetotelluric methods, although these are far from routine and rarely unambiguous. The textures of erupted volcanic rocks, as quantified through crystal size distributions (CSD), provide space- and time-integrated information on subvolcanic plumbing systems, although these data cannot be used readily for reconstruction of key parameters such as conduit geometry or magma chamber depth. Here we develop a numerical approach to interpretation of CSD in products of steady eruptions, based on crystallization kinetics and hydrodynamic flow simulation, to image subvolcanic plumbing systems. The method requires knowledge of magma properties, crystal growth kinetics (measured experimentally), and discharge rate (measured observationally). The method is applicable to steady-state eruptive regimes. Distributions of pressure, temperature, crystal content, and conduit cross-section area with depth are obtained from a CSD from a sample erupted from Mount St. Helens volcano, USA. Values of average conduit diameter (∼30 m) and magma chamber depth (∼14 km below the summit) are in good agreement with independent estimates.

Volcanology: Fragmenting magma

Explosive eruptions of volcanoes, such as that which destroyed Pompeii, are especially threatening to neighbouring human populations. Understanding of this type of eruption is still at an early stage, although it is clear that fragmentation of magma in the conduit inside the volcano is a key process. New models of magma fragmentation provide improved — but still imperfect — simulations of the behaviour of real volcanoes.

Modeling of the dynamics of diffusion crystal growth from a cooling magmatic melt

The process of diffusion growth of a single crystal of plagioclase (consisting of two components: albite and anorthite) from a cooling magma melt is considered. Crystallization starts when the temperature becomes lower than the melting (liquidus) temperature and occurs as a result of the diffusion of melt components to the boundary of the growing crystal. The crystallization process is simulated by solving a system of nonlinear, linked by cross terms, nonstationary diffusion equations for albite, anorthite, and residual melt in the coordinate system moving with the growing crystal boundary. The dependence of the crystal growth rate on undercooling and temperature and of its composition on temperature and pressure is taken into account. Both quantities substantially depend on the component concentration ratio in the melt on the crystal-melt interface. The competition between the diffusion and crystal growth processes and the complex dependence of these processes on the current melt and crystal compositions and the system temperature lead to a strong nonlinearity of the problem. As a result of numerical simulation, it is established that with a linear decrease in temperature the growing crystal composition changes nonmonotonically. This makes it possible to propose a novel interpretation of the crystal zoning typical of natural magmatic systems.

Modeling of trace elemental zoning patterns in accessory minerals with emphasis on the origin of micrometer-scale oscillatory zoning in zircon

Abstract We present a numerical model of trace-element oscillatory zoning patterns formed when zircon crystallizes from silicate melt, which is also appropriate for other accessory phases with known partition and diffusion coefficients and saturation conditions. The model accounts for diffusion-controlled accessory mineral growth and the equilibrium crystallization of major mineral phases. Consideration of recent, experimentally determined dependencies of partition coefficients on temperature, we find that thermal changes provide the simplest explanations of oscillatory zoning in accessory minerals. Numerical experiments with different cooling rates explore different crystallization scenarios with and without the precipitation of other phases and/or the interface reaction of phosphorus (P) and yttrium (Y) to form xenotime. However, these processes are monotonically related to growth rate and do not cause oscillations. Minor 3–10 °C variations in temperature do not result in zircon dissolution, but strongly influence zircon growth and lead to variations in coeval Y, Hf, and rare earth element (REE) concentrations of up to a factor of two, comparable to those observed in nature. Such temperature variations may be very common in any igneous body in response to external factors such as replenishment by hotter magmas or convection. More significant temperature fluctuations may result in initial minor dissolution at higher temperatures during a mafic recharge event but with continuous growth afterward. At high temperature (>~850 °C) the amplitude of oscillations is relatively small that confirms observations of both less common oscillatory zoning in hot and dry volcanic rhyolites and abundant oscillations in plutonic zircons and in zircons in cold and wet crystal-rich mushes. Additional oscillations in zircon are modeled in response to oscillations of pressure on the order of ±35–50 bars, causing water concentration fluctuations of ±0.1 wt% in water-saturated melt cells with a gas bubble. These variations cause variations of Zr diffusion and zircon growth rates. Such fluctuations could result from pressure oscillations due to recharge and convection in the magma chamber. All simulated runs generate smoothed oscillatory growth zoning; similar patterns found in nature may not necessarily require post-growth intracrystalline diffusion.