Abstracts

Pre-eruptive Composition and Volatiles

Alfred Anderson

The pre-eruptive composition of a magma includes the composition of the melt, the bulk composition of the crystals, and the amount and composition of exsolved as well as dissolved volatiles.  For the purposes of eruptive modeling, the most important compositional attribute is the total crystal content and the size distribution of crystals.  This is because crystal surfaces may provide important sites for bubble nucleation during decompression.  The pre-eruptive size distribution of phenocrysts is an area of ignorance, and indeed the distinction between phenocryst and microphenocryst is obscure and mineral specific - compare a 20 micron long crystal of zircon with one of feldspar.  Cashman, Sparks and others have documented the sizes of crystals in some dacites, and there appears to be an important feedback between bubble nucleation and crystallization.

Melt (glass) inclusions in phenocrysts may constrain the composition of the pre-eruptive melt.  However, post-entrapment crystallization of host and daughter crystals can be significant, and the composition of the glass that is eventually preserved in the cold rock may differ significantly from the original composition of the hot molten precursor.  Indeed, for most magmas, even the volatile-free melt composition will change significantly as phenocrysts grow.  Rhyolitic and many dacitic magmas, however, contain a silica-rich rhyolitic residual melt whose non-volatile composition remains roughly constant with crystallization.  This is termed the eutectic condition.

There are important constraints on the compositional changes that occur in rhyolitic (near-eutectic) melt inclusions.  If only host mineral crystallizes from the trapped melt, then the melt composition will move away from the eutectic and become undersaturated with respect to host mineral.  The host mineral would tend to redissolve and restore the original melt composition.  If daughter, as well as host, minerals crystallized, again they would tend to do so in the eutectic proportions and the non-volatile composition of the trapped melt would still remain constant.  Certain trace elements would behave differently, because their concentrations would not necessarily be at saturation with some mineral.  For modeling, it might be useful in the beginning to consider a eutectic magma, because of the simplifying controls imposed by the eutectic condition.

Volatiles, especially H₂O, change the picture, because even a eutectic system will in general change with decompression and exsolution of H₂O.  The composition of the rhyolite eutectic shifts to become more SiO₂ rich with decompression, as emphasized recently by Blundy and Cashman.  This means that a decompressing magma would crystallize increasing proportions of feldspars relative to quartz, assuming equilibrium.

Behavior in melt inclusions may differ from the eutectic effect.  The H₂O dissolved in melt inclusions will tend to remain constant unless a bubble forms, and bubble nucleation may not occur.  The pressure in a bubble-free melt inclusion will diminish rapidly with only a little H₂O loss, and the inclusion will tend to dissolve host mineral.  Kinetics may not allow much of this, but there could be a feedback between H₂O loss and resorption of host mineral to restore the pressure and prevent bubble formation.  The point is that the composition of melt inclusions may differ significantly from that of the melt in the magma outside the host crystal.

Some phenocrysts may have formed in a magma other than the one in which they erupt.  The compositions of melt inclusions in such phenocrysts are irrelevant to the composition of the erupting melt.  Other phenocrysts may have formed long before eruption and their inclusions may reflect conditions that no longer existed when eruption began.

Phenocrysts in rhyolites commonly contain reentrants of unvesiculated glass.  Some volatile loss may have occurred by diffusive transport to the nearest bubble, and this can be checked by analyzing reentrants with narrow necks, called hourglass inclusions.  Hourglass inclusions may best reflect the volatile composition of the pre-eruptive melt.

Pre-eruptive magmas may contain bubbles of exsolved gas.  In some cases the amount of pre-eruptive gas can be estimated.  The total volatile inventory of a pre-eruptive magma may significantly exceed what is dissolved in the melt.  This may be significant in modeling eruption processes, because pre-eruptive bubbles can expand without requiring slow diffusive migration of volatiles from the melt to the bubble.

Evidently, many factors may influence eruptions.  This seems consistent with the wide array of eruption styles and eruptive products.  Hopefully, modeling will reveal conceptually useful relations between pre-eruptive conditions, eruptions and their products.

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Pre-eruption Magma Conditions and Timing of Pre-eruption Events in Intermediate Composition Arc Volcanoes

Malcolm J Rutherford

Estimates of pre-eruption conditions in arc volcanic systems are typically based on the compositions of phenocryst and melt (glass) phases in the eruption products combined with experimental and theoretical data for gas solubility in the melt phase.  Recent study of 1991 Pinatubo dacite, and 1995-2000 Montserrat andesite indicates that short tem processes occurring in the pre-eruption magma storage zone change the conditions from those recorded in many of the phenocrysts.  The late stage re-equilibration of the matrix glass in the explosively erupted Pinatubo dacite indicates a pre-eruption pressure of 155 MPa significantly lower than the 220 MPa indicated by glass inclusions in Qtz and plagioclase phenocryst.  This confirms a long standing concern about melt inclusions since the inclusions had to be trapped at some time before the eruption was triggered, a point particularly true for the plagioclase in this and similar magmas.  The andesite erupting at Montserrat also contains significant evidence of changes in the storage zone just prior to the eruption, as well as back through time. Cores of Fe-Ti oxide phenocrysts indicate at temperature of 830 ±10⁰C for the magma, but a diffusion profile of Ti-enrichment on the margins of many magnetite phenocrysts indicates that much of this magma was heated 2-30 days prior to being erupted. The maximum temperature increase in this heating is limited to about 30 ^oC by hornblende stability data. Variations in the composition of hornblende confirm the T increase, and have internal zoning that indicates similar heating events in the past were at the same constant total pressure of 130 MPa.  These zones illustrate seven repeated heating (and mingling of mafic magma) events in the magma now being erupted. This occurred in a time of more than 4 years.  The heating was apparently produced by an injection of basaltic andesite magma into the storage zone, and evidence of mingling of the two magma is present in almost all magma samples erupted.  Once again, the composition of the matrix glass quenched in rapidly ascended batches of the magma (no rims on hornblende) is more revealing about conditions in the erupting magma than melt inclusions. Both quartz and plagioclase melt inclusions contain 4.7 wt % H₂O and CO₂ below detection, indicating a P(fluid) of 130 MPa, but the composition of the included melt in plagioclase indicates entrapment at 850 ±15 ⁰C, while the quartz melt inclusions require a lower T (820 ±10 ⁰C) both at 130 MPa.  Together this evidence shows that the Montserrat magma was water saturated early in the crystallization sequence (i.e., during plag crystallization) at a depth where the total pressure was 130 MPa.  The variations observed in eruption style at Montserrat must be the result of variations in magma ascent rate and gas loss during ascent.

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Experiments in the Service of Volcanology

D. B. Dingwell (for the Munich Magma Group)

Interest in rising amongst volcanologists in the contribution that experimental work has to provide for volcanological research. Two major developments of the past decade have accelerated the growth of experimental studies which provide parameterisation of magmatic behavior, namely volcanic monitoring and volcanic simulation.

The experimental contributions to the improved understanding required to move forward in volcanology include 1) parameterisation of magma properties relevant to eruptions, 2) experimental evaluation of the feasibility of mechanisms theoretically proposed for magmatic behavior, 3) the observation, and description of unexpected phenomena encountered in experiments and evaluation of their significance for natural processes.

The major thrust of this meeting is the parameterisation and modelling of eruptions. Over the past decade we have been involved in the experimental determination of almost all magma properties of relevance to volcanic eruptions (Heat capacities, thermal history, volumes, rheology, surface tension, volatile solubilities, fragmentation and strength, etc.) Perhaps the most significant contributions of the Munich group in the past 3 years, however,  have been in the areas of rheology, volume and fragmentation. New devices and techniques, experimental strategies, compositional data bases, and modelling/parameterisation efforts have been and are being made.  Some of the most recent results include parameterisation of non-Arrhenian viscosity of multicomponent melts, temperature dependence of  melt volumes, and dynamic tensile strength as a function of vesicularity.

I will review the state of the art from our experimentalist perspective as of November 2002.

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Parameters critical to the modeling of volcanic processes

Youxue Zhang

Our work on volcanic eruptions covers magma fragmentation, bubble growth, experimental simulations of gas-driven eruptions using CO₂-water system, energetics and dynamics of lake eruptions, and experimental and theoretical investigations of some parameters used in modeling volcanic processes: water diffusivity and solubility in the melt, and viscosity of the magma.  My presentation will focus on parameters critical to the modeling of volcanic processes.

Although there are general viscosity models covering a wide range of melt compositions (Bottinga and Weill, 1972; Shaw, 1972), they have large uncertainties (e.g., two orders of magnitude) and are not good enough for modeling volcanic processes.  Currently, the best model for the viscosity of hydrous rhyolitic melt, in my opinion, is the non-Arrhenian model of Hess and Dingwell (1996).  However, there are some problems with the model, one of which is still the relatively large uncertainty in predicting viscosities (2 sigma uncertainty is 0.92 log units).  Liu and Zhang (2000) showed that the viscosity of Hess and Dingwell (1996) must be adjusted down by a factor of 1.3 to 4 (within the uncertainty of the model) so as to match calculated bubble growth curve with experimental data.  We are making an effort to improve the viscosity model (Zhang et al., in prep.).  We propose a new relation (or mixing law) for the dependence of hydrous rhyolitic melt viscosity on dissolved H₂O content.  Using the new relation, we develop a new model for the viscosity of hydrous rhyolitic melts as a function of temperature and H₂O content.  The new model is able to reproduce experimental data to within 0.38 log units (2 sigma) and accounts for the viscosity of dry melt (Zhang et al., in prep.).  The presence of crystals and bubbles affect the magma viscosity, which will not be discussed here.

H2O diffusion in rhyolitic melt has been investigated extensively (Shaw, 1974; Friedman and Long, 1976; Jambon, 1979; Delaney and Karsten, 1981; Karsten et al., 1982; Lapham et al., 1984; Zhang et al., 1991; Nowak and Behrens, 1997; Zhang and Behrens, 2000), culminating in both a diffusion model and a diffusivity formula applicable to a large temperature, pressure and H₂O content range (Zhang and Behrens, 2000).  However, H₂O diffusion behavior in other melts (basaltic, andesitic, and dacitic) is not well quantified (there is one study on diffusion in basaltic melt by Zhang and Stolper, 1991).  The absence of H₂O diffusion data in dacitic melt is unfortunate because many explosive volcanic eruptions are dacitic.  We recently begin to work on H₂O diffusion in dacitic melt.

H₂O solubility in natural silicate melts has been studied extensively.  From experimental data, numerous models have been developed, some cover a wide range of melt compositions, and some are for specific melts.  All models work well at the intermediate pressures (5 to 400 MPa), but few work well at both low and high pressures.  For example, H₂O solubility in rhyolitic melt at 1 bar and 850 °C is about 0.1 wt%.  The predicted solubility ranges from 0.012 wt % (Papale, 1997), 0.071 wt % (Moore et al., 1998), 0.074 wt% (Yamashita, 1999), 0.099 wt % (Zhang, 1999a), and to 0.104 wt % (Burnham, 1975).  Solubilities at low pressures are important for modeling volcanic eruptions because most of the expansion occurs at low pressures (see also Blower et al., 2001).  Hence it is important to choose a solubility model that is accurate to both high and low pressures.  For rhyolitic melt, such a model is available if there are no other gases (Zhang, 1999).  For melts of other compositions, more work must be done to assess the various models.

On magma fragmentation, Zhang (1999b) proposed a new model based on stress on bubble walls.  To apply the model, it is critical to determine the tensile strength of magma as a function of temperature, pressure, H₂O content, crystal content, as well as possible weaknesses in the lava.  Some data are available (e.g., Romano et al., 1996), but many more data are needed to gain a systematic understanding.

In summary, the best understood system is the high-SiO₂ rhyolitic melt.  For other melts that may produce explosive eruptions, much more work is necessary to understand the critical parameters of other melts and to produce general models for wide range of natural magma compositions.

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Bubble Nucleation in Magmas

Jim Gardner and Jessica Larsen

Rising magma supersaturates with water, because of lower pressure, and thus bubbles nucleate.  Growth of those bubbles can drive volcanic eruptions.  Stagnant magma may also nucleate bubbles, because it supersaturates with water as it crystallizes.  Creating a gas phase in magmas may trigger volcanic eruptions.  Knowing when and how fast bubbles nucleate is critical in understanding volcanic eruptions.  Bubbles may nucleate homogeneously, when enough water molecules cluster together to form bubbles without aid of foreign surfaces. If melts are heterogeneous, however, bubbles may nucleate much more easily, because of the reduced surface tension resisting nucleation.  Several experimental studies have established the profound difference between those two mechanisms.  Homogeneous nucleation requires supersaturations of =120 MPa, and bubbles nucleate at rates of 1-10⁶ cm^-3 s^-1, depending on the level of supersaturation.  Heterogeneous nucleation can occur at supersaturations as low as ~1 MPa, and at 10⁶-10⁸ cm^-3 s^-1.  One of the interesting results about experimentally induced nucleation is that nucleation almost always occurs as a single event.  Only fluctuations in experimental conditions seem to induce secondary nucleation events.  An important question becomes, do size distributions in pumices reflect a single nucleation event or multiple events?  If they record a single event, then their bubble number densities of 10^8-9 cm^-3 are more similar to those produced by heterogeneous nucleation.  If they record multiple events, what are the pathways that magmas follow during volcanic eruptions?

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Experimental results on bubble coalescence in rhyolite and phonolite melts

Jessica F. Larsen  and James E. Gardner

Magmatic degassing is a fundamental process recognized for many years to be of critical importance in the understanding of volcanic eruptions. Gas bubbles nucleate and grow in silicate magmas due to exsolution of H₂O CO₂, Cl, and S on decompression, and their sizes and number densities are modified during magmatic ascent. The results after the magma has fragmented and left the conduit are polymodal vesicle size distributions, and vesicularities that can vary even within a single stratigraphic unit. We are currently studying the coalescence process experimentally in rhyolitic and phonolitic melts with crystallinities between 0 and 44 vol. % and melt viscosities varying between 10³ and ~5x10⁵ Pas (rhyolite). Our experiments consist of both powders and solid chips of rhyolite and phonolite. From our decompression experiments, we have derived rates of coarsening of the bubble size distributions well as timescales for binary coalescence from our data, as a function of ending pressure at a constant decompression rate, and of time in experiments held at a given final pressure after decompression. Crystal-bearing experiments with bubble number densities on order of 10⁸ cm^-3 experience efficient coalescence, resulting from the smaller average separation between bubbles at high bubble number densities. However, the timescales for binary coalescence (t^1/2) are measurably slower in crystal bearing experiments (t^1/2=80 to 850 minutes) than they are for crystal-poor rhyolite and low viscosity phonolite melts (t^1/2 =22 to 25 minutes). During decompression of solid chips of rhyolite at a constant rate of 0.5 MPa/s, we see significant degrees of coalescence in crystal-poor rhyolite. This indicates that significant coalescence does occur at decompression rates equivalent to explosive ascent rates of ~20 m/s, at pressures relevant to crustal magmatic systems.

Application of our results to simple models of magmatic ascent from a crustal chamber residing at 5 km depth yields interesting insights into the timescales of coalescence prior to eruptions. At effusive ascent rates of ~0.001 to 0.01 m/s, we expect that significant bubble coalescence will occur in all compositions of magma at crystallinities up to ~25 vol.%. Thus, slowly ascending, crystal-poor magmas of all compositions are expected to achieve high bubble connectivity and lose gas easily as a result. This may lead to relief of pressure in the conduit, and effusive eruption, especially in the presence of permeable conduit walls that would allow gases to escape.  As ascent rates increase to 0.1 to 10 m/s, significant coalescence is impeded to varying degrees in magmas with high viscosities and/or crystal contents greater than a few vol. %.  At extreme ascent rates of ~100 m/s, bubble coalescence is not possible in any magma composition, regardless of crystallinity, during the very short (~10 s) timescale it would take the magma to ascend from a crustal magma chamber. At these rates, which are typical of explosive eruptions, incomplete coalescence and inhibition of bubble connectivity leads to inhibition of gas separation, and may lead to explosive pressure build-up in a conduit with impermeable walls.  It is important to note that bubble coalescence is only one of several important physical processes that are likely to influence the style of a volcanic eruption.  A combination of conduit processes, such as bubble nucleation and growth rates and mechanisms, coalescence rate, shear rate in the magma, and degree of permeability of the conduit walls may be the best way to explain the differences in style of all volcanic eruptions.

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Experimental Work on Bubble Nucleation, Number Density, and Size Distribution

Margaret Mangan and Thomas Sisson

Results from a series of recently-published experiments examining decompression of water-saturated rhyolite collectively suggest that the mechanism of gas bubble nucleation is a significant factor affecting the pressure-depth interval over which initiation of eruptive degassing occurs and the ensuing evolution of gas in the conduit during magma ascent.  The phenomenon of nucleation is essentially an energy exchange process.  The activation energy required to create a stable bubble nucleus is supplied by vaporization energy of the volatile species (e.g., water) in a supersaturated silicate melt.  Quantitatively, this is described by (Hirth et al., 1970; Landau and Lifshitz, 1980; Hurwitz and Navon, 1994)

            DF= 16ps³/3DP²

in which DF, the energy sink, is the Helmholtz free energy required for the formation of the curved bubble interface separating gas from melt; the energy source, DP, is the difference between the ambient pressure and the equilibrium vapor pressure of the melt, or overpressure; and s is the surface free energy of the interface.  The surfaces of any heterogeneity in the melt, e.g., crystal faces and corners, can induce bubble nucleation if the s of the crystal-gas interface is less than that of the melt-gas interface.  If that case, the DP required to trigger nucleation is reduced so that bubble nucleation is substantially enhanced.  Bubble nucleation occurring spontaneously at high DP in a uniform, crystal-free melt is known as homogeneous nucleation while heterogenous nucleation occurs more readily at lower DP in a melt with crystals.

            In natural systems it is unlikely that nucleation will take place strictly by one or the other mechanism.  Crystals are inevitably present in magma chambers and heterogeneous bubble nucleation will undoubtedly occur.  However, if the crystal content is low, ≤10³/cm³, volatile diffusion into these isolated, heterogeneously-nucleated bubbles may not be able to keep pace with decompression, and degassing of the bulk melt between crystals falls to the work of homogeneous bubble nucleation at high DP.  The dominant nucleation mechanism, which depends on magma crystallinity and decompression rate, controls whether the eruptive degassing occurs early and deep under quasi-equilibrium conditions or late and shallow at extreme supersaturation.

            Synthesis of the published experimental data for water-saturated rhyolite (~75 wt% SiO₂) shows that heterogeneous nucleation is triggered at ∆P < 5-20 MPa and leads to equilibrium degassing (at dP/dt ≤ 1MPa/s) through a single nucleation event (Hurwitz and Navon, O., 1994; Gardner et al, 1999).  Typically  number densities (N_T) of 10⁵-10⁶ bubbbles/cm³ are produced which evolve Gaussian size distributions.  Homogeneous nucleation, in contrast, requires a significantly larger ∆P of >120-150 MPa (at dP/dt ≤ 1MPa/s)  and leads to disequilibrium degassing (Mourtada-Bonnefoi and Laporte, 1999; Mangan and Sisson, 2000).  In this instance, nucleation is an ongoing process controlled  by changing supersaturation conditions via N_T = 6.15 x10³ e^2.677(SSr) where SSr is the supersaturation ratio (actual/equilibrium  wt% H₂O) and N_T is units of bubbles/cm^-3.  Exponential or power law size distributions are produced with number densities of  10⁶-10⁹ bubbles/cm³. 

            New experiments  (Mangan and Sisson, 2001; Mangan and Sisson, in preparation) suggest that the extreme supersaturation seen in homogeneously-nucleating  rhyolite may not be characteristic  of less silicic compositions.  In water-saturated, crystal-free dacite melt (65 wt% SiO₂) nucleation is triggered at DP = 50-80 MPa.  Number densities are lower than in crystal-free rhyolite experiments, ranging from 10⁴-10⁶ bubbles/cm³ with N_T = 3.34 x10⁴ (SSr)^2.0557, and the size distributions are Gaussian.   The relative ease of homogeneous nucleation in dacite appears to be a consequence of lowered surface tension. Nucleation theory shows that a small decrease in surface tension dramatically  decreases the DP required to trigger homogeneous nucleation. A fit of empirical data to theoretical predictions  suggest an effective surface tension for dacite melt at 1000 °C and 5.2 wt% H₂O of 0.05-0.06 N/m.  Similar calculations give 0.10-0.11 N/m for rhyolite at 900°C and 5.2 wt% H₂O.

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Radar Doppler velocimitry of volcanic eruptions:  Theoretical considerations and quantitative documentation of changes in eruptive behavior at Stromboli volcano, Italy

M. Hort, R. Seyfried, and M. Vöge

The use of radar Doppler velocimitry for the observation of volcanic activity is new.  We used this method to continuously observe the activity of one vent of Stromboli volcano, Italy, from the end of April 2000 till early May 2000.  During this period we recorded 702 eruptions, 132 of which occurred before a strong rains storm passed over the island on April 29th.  In order to interpret the recorded Doppler data we developed a program that simulates different strombolian eruption scenarios, for which we then calculate the theoretical Doppler spectra.  Comparing our theoretical data to the observed ones we are able to show that most of the eruptions are nearly vertical, although we did observe only one component of the eruption vector with our Doppler radar.  One of the most interesting features of the data set is a significant change in eruptive behavior that correlates with the occurrence of the rain storm:  We find that on average the eruption duration increased by a factor of 2, eruptive velocities were much higher and indirect evidence indicates that the average particle diameter of the erupted material decreased.  This change may have several causes, but the coincidence with the rain storm is taken as evidence of magma/water interaction and feedback onto volcanic activity.  Because the fluid source (rain) changing the eruptive style is at the surface and in near surface layers we infer that the main control on final eruption dynamics at Stromboli volcano must also be in rather shallow regions.

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Bubble growth in silicic magmas

Oded Navon

A precise description of bubble growth in magmas is needed for calculations of the bulk magma flow conditions and the modeling of volcanic eruptions.  Three major processes control the dynamics of bubble growth during decompression of magmas: the rate of decompression of the magma, the diffusion of volatiles into the bubbles, and the viscous deformation of the surrounding melt. Model of bubble growth during decompression must accounts for the interplay of these three dynamic processes and must be solved numerically.  Analytical solutions were developed under simplifying assumptions for cases where growth is controlled by one of these processes, and the others are less important.  It was also possible to constrain the transition between the different growth regimes using the analytical solutions.  Two governing dimensionless parameters, the ratios of either the diffusive or viscous time scales over the decompression time scale are used to describe the system.  By specifying these parameters and using a “map” of analytical solutions of the different growth regimes, one may estimate the state of erupting magma in terms of gas overpressure, supersaturation and gas volume fraction.  The analytical calculations are in agreement with numerical simulations and measurements from bubble growth experiments.  They also agree with the conditions of both explosive and effusive eruption styles in silicic volcanoes.

The analytical solutions use a uniform effective viscosity and diffusivity. As bubbles grow the melt dehydrate and a radial profile of volatile content develops in the melt shell, leading to a large variation in viscosity and diffusivity in the shell. We show analytically that during decompression, the effective melt viscosity resisting gas overpressure is close to the viscosity at the dehydrated rind, even when the rind is very narrow compared with the shell width.  The effective viscosity may be higher than that of the surrounding melt by more than an order of magnitude and may lead to buildup gas overpressure, delayed degassing, and eventually to magma fragmentation.  If diffusion occurs under steady state conditions, it too may be described by a uniform coefficient that is close to the faster diffusion away from the bubble.

The bulk viscosity of expanding magma, the differential relation between driving pressure and the resulted expansion strain-rate, is an important property needed to model the bulk compressible flow.  When the diffusive volatile flux is taken into account in the expression of bulk viscosity of the bubble-bearing melt the resulting bulk viscosity is highly non-linear.  Following decompression, at the beginning of the expansion process, when gas exsolution is efficient, the expansion rate grows exponentially while the driving pressure decreases, which means that bulk viscosity is formally negative.  This negative value reflects the release of the energy stored in the supersaturated liquid and its transfer to mechanical work during exsolution. Under conditions of negative viscosity, rarefaction waves traveling through the magma may be amplified.

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"Bubbledrive" numerical model

Alex Proussevitch and Dork Sahagian

Numerical models provide powerful tools for the investigation of volcanic eruption processes. A number of models have emerged in recent years and steps are being taken to compare and assess performance of the models to shed light on the contrasting results of different analytical and numerical formulations. In addition, models can be used to test the sensitivity of eruption processes to variations or uncertainties in the values of the relevant volcanic parameters such as diffusivity, rheology, composition, geometry, etc. One such model is "Bubbledrive", based on interactive diffusive and decompressive bubble growth in the context of magma hydrodynamics within a volcanic conduit. We have developed and now apply this model to case of a rhyolitic system and explore the sensitivity of eruption style to conduit geometry. We hold other factors (e.g. composition, external conditions, rheology, etc.) the same between model runs so as to isolate the role of geometry. Two basic geometries are explored. The first is a simple cylinder, testing sensitivity to width and length. The second is more complex and includes a cylindrical magma chamber at specific depths in the cylindrical conduit. The position and size of the chamber are variable. In all cases, there is no recharge of fresh magma from below. Also, the triggering mechanism is instantaneous decompression at the top of the conduit (as from a landslide). These results, in concert with the large number of additional emerging sensitivity studies may provide insights regarding the most critical observational parameters on which to focus in the field and in the lab.

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Silicic conduit flow

Hélène Massol

Eruption style often varies in course of a single eruption alternating episodes of explosive eruptions and dome growth. To forecast these changes, we need to couple field data and geophysics measurements with theoretical models of magma ascent. Explosive eruptions involve the fragmentation of magma; however, physics of this process is still poorly understood.  The understanding of these two processes, (1) alternation in eruptive style and (2) fragmentation of magma requires the detailed knowledge of the geometry of the gas phase and of the pressure inside the bubbles. In order to predict the distribution of gas content and bubble pressure in an eruption conduit, we develop two different numerical models.

One is a two-dimensional finite element numerical code which solve for three different pressures: those of the gas and magma phases, and that of the exterior. Indeed, magma behaves as a compressible viscous liquid and one must account for expansion in all directions. Even with small dissolved water concentrations, gas overpressures may reach values larger than 1 MPa at a volcanic vent. For constant viscosity the magnitude of gas overpressure does not depend on magma viscosity and increases with the conduit radius and magma chamber pressure. In the conduit and at the vent, there are large horizontal variations of gas pressure and hence of exsolved water content. Such variations depend on decompression rate and are sensitive to the ``exit'' boundary conditions for the flow. For zero horizontal shear stress at the vent, relevant to lava flows spreading horizontally at the surface, the largest gas overpressures, and hence the smallest exsolved gas contents, are achieved at the conduit walls. For zero horizontal velocity at the vent, relevant to lava flows spreading horizontally at the surface, the largest gas overpressures, and hence the smallest exsolved gas contents, are achieved at the conduit walls. For zero horizontal velocity at the vent, corresponding to a plug-like eruption through a preexisting lava dome or to spine growth, gas overpressures are largest at the center of the vent. The magnitude of gas overpressure is sensitive to changes of magma viscosity induced by degassing and to shallow expansion conditions in conduits with depth-dependent radii.

The second 1-D finite difference model intents to couple macroscopic parameters such as ascent velocity or mass flux with microscopic processes such as nucleation and growth of individual bubbles. It allows us to predict bubble sizes and number density under realistic conditions. As magma rises toward the surface the pressure decreases and eventually becomes less than the solubility pressure. When the difference between the concentration of volatiles in the melt and the concentration at equilibrium is high enough, nucleation of bubbles occurs.  Nucleation will stop as the concentration of volatiles in the melt decreases due to growth of existing bubbles. Hence the degree of supersaturation decreases. We show that a second nucleation event can occur just below the fragmentation level as the magma rapidly decompresses. At this level, the degree of supersaturation continuously increases with decreasing pressure.  In that case, nucleation will not stop until fragmentation occurs. This late nucleation event may explain the pore size distribution measurements made in true pumices that often shows a fine bubble size population. We also show that this late stage nucleated population of bubbles has high internal gas pressure of order of 2 MPa greater than the liquid pressure. This may cause the fragmentation of the magma.

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Kamchatka-steady model

Oleg Melnik and Alexey Barmin

This model applies to steady state magma flow with fragmentation (explosive eruption). Magma consists of the melt, crystals and gas (H2O). It flows in the conduit from magma chamber to atmosphere. Flow is separated into several zones with different magma states: homogenous liquid, bubbly liquid, fragmentation zone, and gas-particle dispersion.

Temperature and pressure are fixed in the magma chamber. As magma ascends from the magma chamber it includes crystals, melt and dissolved gas. Crystal content is constant. Nucleation assumed to be immediate when pressure drops down to saturation level. After that gas starts to exsolve from the melt to the bubbles.

Bubbly liquid viscosity depends on gas concentration in the melt, temperature and crystal content. Bubbly liquid is assumed to be permeable to gas. Permeability grows with bubbles volume. The pressure disequilibria in melt and bubbles is accounted.

Fragmentation zone is modeled with discontinuity surface. According to a proposed fragmentation criterion, the overpressure in the bubbles leads to fragmentation. Bubbly liquid turns to gas-particle dispersion that consists of three interacting phases: gas, small particles moving with gas, big particles containing gas. At the outlet gas velocity is sonic or pressure is equal to atmospheric.

Model reveals two regimes of flow with same parameters in the magma chamber but essentially different discharges.

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Kamchatka-transient model

Oleg Melnik, Rob Mason, Alexey Barmin, and Alexander Starostin

This model applies to transient magma flow with fragmentation (vulcanian explosive eruption generated by lava dome collapse). Magma consists of the melt and gas (H2O). It flows in the conduit from magma chamber to atmosphere. Flow is separated into several zones with different magma states: bubbly liquid, fragmentation zone and gas-particle dispersion.

There are fixed temperature and pressure in the magma chamber. As magma ascends from the magma chamber it consists of melt and gas dissolved in it. Gas exsolves from the melt to the bubbles. Bubbles have the same velocity as melt has. Bubbly liquid viscosity depends on gas concentration in the melt and temperature. The pressure disequilibria in melt and bubbles is accounted.

Fragmentation zone is modeled with discontinuity surface. Accordingly to a proposed fragmentation criterion the overpressure in the bubbles leads to fragmentation. Bubbly liquid turns to gas-particle dispersion. It consists of gas and grain particles moving together. At the outlet gas velocity is sonic or supersonic or pressure is equal to atmospheric.

Initially the parameters distribution in the conduit corresponds to situation with plug at the end of the conduit. The magma chamber parameters remain constant.

Model describes dynamics of explosive eruption. It reveals the pulsation of fragmentation front position and discharge. It was applied to Sufrier Hills eruptions 1996,1997.

The modification of the model for phreatomagmatic eruption considers the flow in the system conduit—porous layer. The influx of water from the layer changes the dynamic of explosive eruption. It can lead to an additional maximum of discharge due to influx from the layer.

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MFIX model

George Bergantz

This report describes the MFIX (Multiphase Flow with Interphase eXchanges) com-puter model. MFIX is a general-purpose hydrodynamic model that describes chemical reac-tions and heat transfer in dense or dilute fluid-solids flows, flows typically occurring in energy conversion and chemical processing reactors. MFIX calculations give detailed infor-mation on pressure, temperature, composition, and velocity distributions in the reactors. With such information, the engineer can visualize the conditions in the reactor, conduct parametric studies and what-if experiments, and, thereby, assist in the design process.

The MFIX model, developed at the Morgantown Energy Technology Center (METC), has the following capabilities: mass and momentum balance equations for gas and multiple solids phases; a gas phase and two solids phase energy equations; an arbitrary number of species balance equations for each of the phases; granular stress equations based on kinetic theory and frictional flow theory; a user-defined chemistry subroutine; three-dimensional Cartesian or cylindrical coordinate systems; nonuniform mesh size; impermeable and semi-permeable internal surfaces; user-friendly input data file; multiple, single-precision, binary, direct-access, output files that minimize disk storage and accelerate data retrieval; and extensive error reporting.

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Effusive/explosive transition model

T. Koyaguchi

Water rich silicic magmas may erupt explosively giving rise to massive columns of fragmented ash, or effusively as viscous bubbly lavas to form lava domes. The models WK-1 (Woods and Koyaguchi, 1994) and YK-1 (Yoshida and Koyaguchi, 1999) are designed to investigate transition between explosive and effusive silicic magmas.

In WK-1, we modeled the ascent of magma along a permeable conduit. In this model magma ascends through a conduit, while exsolved gas is allowed to escape from the conduit as a permeable flow. The model predicts two extreme flows with distinct flow rates are possible under the same boundary condition (i.e. the presence of multiple steady solutions). The steady solution at high flow rate is characterized by eruption as gas-pyroclastic dispersion at sound velocity, which corresponds to an explosive eruption. The solution at low flow rate, on the other hand, is characterized by a bubbly flow with a low gas content, which corresponds to effusive eruption.

In YK-1 we introduced a new flow regime, "fractured-turbulent flow regime", between bubbly flow and gas-pyroclasts dispersion. The effects of relative velocity between gas and liquid phase are also taken into account in this model. In the fractured-turbulent flow regime, both liquid magma and gas are assumed to be continuous phases. It is shown that this flow regime greatly enhances the relative motion of gas and liquid and modifies behavior of the two-phase flow. This effect can also result in the presence of multiple steady solutions with distinct flow rates.

The presence of multiple steady solutions in these models may explain complex feature of transition between explosive and effusive silicic magmas.

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Conflow: a user-friendly model for flow of magma-gas mixtures through volcanic conduits

Larry G. Mastin

Numerical models that calculate the fluid dynamics of explosive volcanic eruptions have been used with increasing frequency to understand volcanic processes and evaluate volcanic hazards.  In this workshop I present a visual, interactive, open-source numerical model that calculates steady-state flow of magma and gas in vertical eruptive conduits, and contains user-friendly utilities for determining physical, thermodynamic, and transport properties of silicate melts, H₂O gases, and melt-gas-crystal mixtures.  The conduit model (available at http://vulcan.wr.usgs.gov/Projects/Mastin) assumes homogeneous flow of gas and melt and, in its publicly posted version, equilibrium degassing.  It incorporates a non-Arrhenian viscosity relation for hydrous silicate melts, a relation between viscosity and volume-fraction of gas that depends on Capillary number, and adiabatic temperature changes in the mixture.  Gas properties are calculated using the full equation of state for H₂O gas, and melt properties (including gas solubility) using the full thermodynamic MELTS relations of Ghiorso and Sack (1995; Contrib. Min. Petrol. 119:197-212).  The strength of the model is its visual interface, which has made it a useful teaching tool in volcanology classes, and which allows non-modelers to quickly and easily calculate material properties, and test hypotheses regarding conduit flow.  As a research tool, the model has been used to evaluate conditions under which groundwater could enter eruptive conduits; and to study effects of non-equilibrium degassing and adiabatic temperature changes on eruptive dynamics.

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Constraints on cooling and degassing of pumice during Plinian volcanic eruptions based on model calculations

M. Hort and J. Gardner

During explosive volcanic eruptions, pumice clasts are transported into the atmosphere, and their thermal and degassing histories determine how much volatiles are lost syneruptively.  This process is studied by combining a steady state eruption column model with a model for the cooling and degassing of pumice.  In the model we investigate the impact of various parameters (e.g., mass eruption rate, Biot number, eruption temperature, and geometry) on the cooling and degassing of pumice and find that the Biot number and the eruption temperature are the most influential.  During typical risetimes of pumices inside eruption columns (200-300 s), those smaller than 0.5 cm in diameter are found to lose little of their volatiles syneruptively and remain in thermal equilibrium with the plume.  In the case of larger pumices the ratio of the cooling timescale to the degassing controls degassing.  If this ratio is larger than 50, degassing of the pumice will be nearly complete with a few percent of the original volatiles left in the outer rind of the pumice.  For a ratio of less than 0.1 no volatiles escape the pumice.  Typical values for thermal and species diffusivity as well as vesicle wall thickness indicate that in the case of degassing Cl and H₂O the transition from 0.1 to 50 will be in the pumice size range of 1-10 cm.  Here volatile concentration is a strong function of position inside the pumice, suggesting that values for volatile contents measured on picked matrix glass from crushed samples may not be the best way to estimate the volatile content of matrix glass, a number which is frequently used to estimate the total volatile input of volcanic eruptions.  This effect is even more pronounced when looking at hydrogen isotopic fractionation with larger pumices tending toward DD < -120 and small samples giving DD > -80.

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The rheology of bubble-bearing magmas: theory and experiments

Ed Llewelin

The addition of bubbles to a Newtonian liquid introduces viscoelastic effects such as shear thinning (the viscosity can change by more than an order of magnitude depending on conditions of shear) and non-zero normal-stress differences (radial stress in conduit flow can exceed shear stress). A fully-general, semi-empirical constitutive equation for the viscoelastic rheology of bubble suspensions with gas volume-fractions <0.5 is presented. The model relates the rheological behaviour of a bubble suspension to observable material parameters: the viscosity of the continuous phase, gas volume-fraction, the relaxation time and bubble size-distribution. The model is underpinned by data from experiments on aerated golden syrup, collected using the rheometric technique of forced oscillations.

Two flow regimes are identified: in one, the viscosity of the suspension increases as  increases (regime 1); in the other, the viscosity decreases as  increases (regime 2). The flow regime depends upon two dimensionless quantities: the capillary number Ca (the ratio of viscous to surface tension forces in steady flow) and the dynamic capillary number Cd (which describes the steadiness of the flow). Ca << 1 and Cd << 1denotes regime 1, Ca >> 1 or Cd >> 1 denotes regime 2. Significant elastic behaviour is predicted (and observed) at intermediate Cd.

The general semi-empirical model is solved for the case of steady, conduit-flow of a bubbly magma and the velocity profile across the conduit and the volume flow-rate are calculated from material parameters, conduit radius and driving pressure-gradient. Two flow regimes are identified which depend upon a dimensionless number, the conduit capillary number Cc. At Cc << 5 a bubbly magma behaves as a Newtonian fluid with a viscosity greater than the viscosity of the bubble-free magma; at Cc >> 5 a bubbly magma behaves as a Newtonian fluid with a viscosity lower than the viscosity of the bubble-free magma. At intermediate Cc the velocity profile indicates plug flow and significant normal-forces are predicted.

LB-Flow - LB-flow is being developed to model the flow of a bubble- and crystal-bearing magma through realistic conduit geometries. The model utilizes the Lattice-Boltzmann method, a powerful technique for the numerical modeling of fluid flow which allows multiphase flows (fluid-fluid, fluid-solid) to be modeled directly. Fluid flow is modeled by allowing populations of fluid and solid particles to move and collide on a two- or three-dimensional lattice. The discreet nature of the lattice allows highly efficient computation of flow through complex geometries whilst accurately reproducing the behaviour of real fluids. Three populations of particles with different “color” can exist on the same lattice and different viscosities and densities can be specified for each, allowing a liquid, solid and gas phase to be modeled. The model is intuitively physical and the mesoscopic behaviour of the bubbles - including bubble deformation and breakup - can be investigated. The proportions of the three phases and the viscosity of the two fluid phases and their interfacial tension can be specified so that a variety of magma types can be modeled.

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The Erupt Model

Karl L. Mitchell and Lionel Wilson

Erupt (Mitchell, 2002) is an axially-symmetric 1.5-dimensional quasi-static model for conduit flow in volcanic and analogous eruptions, based on previous work by Wilson (Wilson, 1980; Wilson et al., 1980). The computational implementation is written in the C programming language, incorporating a 4th order Runge-Kutta iterative simultaneous solution of conservation of mass, momentum and energy (isothermal or adiabatic). Its stability makes it suitable for the entire range of magma chemistries, including basalts, rhyolites and experimental systems. At present we are using erupt to explore three aspects of conduit dynamics:

Eruptions through inclined conduits. Erupt can be run assuming an inclined conduit (Mitchell, 2002; Mitchell et al., 2002). However, if eruption velocities are small, the basic assumption of homogenous flow is violated. We are using an iterative scheme of running erupt and a separate bubble migration and accumulation program to characterise when slug formation or complete phase separation occurs – in effect we are investigating the effect of conduit inclination on determining the transition between effusive, Hawaiian and strombolian styles of activity (Wilson and Head, 1988). At present we are applying our work to gain greater insights into eruptions at Pu’u ‘O’o (Hawai’i) and Stromboli (Italy), both of which exhibit inclined conduits. Results from our initial study are soon to be submitted for review. Later we shall be focussing on applications to experimental systems (below) and to eruptions on other planets, especially Mars.

Modelling volcano analogue systems. Erupt has been modified to allow simulation of analogue experimental systems (Lane and Chouet, 2001; Phillips et al., 1995). As well as being a useful exercise that allows for external validation of our model, this should also prove useful in assisting with scaling problems between analogue and real volcanic systems.

Supersonic compressible flow in volcanic conduits. Some modelers have used a pressure-balanced assumption (Wilson, 1980) in order to constrain their volcanic eruption models, allowing the choking point to descend deep into the conduit and eruption velocities to be significantly supersonic. However, this method breaks down shortly after Mach 1 as it allows lateral velocities to exceed Mach 1 which is impossible. A more realistic model in the supersonic compressible regime would use a Prandtl-Meyer expansion to control the flow behaviour, similar to models by Kieffer for the Mount St. Helens lateral blast, and for plumes on Io. We are working on a simplified implementation of such a scheme at present.

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Magma Interaction model

Edward S. Gaffney

One of the significant threats to the proposed Yucca Mountain nuclear waste repository has been identified as the possibility of intersection of the underground structure by a basaltic intrusion. Based on the geology of the region, it is assumed that such an intrusion would consist of an alkali basalt similar to the nearby Lathrop Wells cone, which has been dated at about 78 ka (Perry et al, 1998). The threat of radioactive release may be either from eruption through the surface above the repository of basalt that had been contaminated or from migration through ground water of radionucleides released as a result of damage to waste packages that interact with the magma. As part of our study of these threats, we are analyzing the phenomena associated with magma expansion into drifts in tuff. The early phenomena of the encounter of volatile-rich basaltic magma with a drift are discussed here.

CFDLIB is a code library for computational fluid dynamics developed by Los Alamos National Laboratory for simulation of multi-material, multi-phase fluid-structure interaction problems in two or three dimensions. We have modified this library to address some specific issues related to volcanic activity. Specifically, we have included the equation of state of mixed H₂O-CO₂ gas after the manner of Papale (1999), and a temperature- and volatile-dependent viscosity with Shaw's method. Simulations have been run of the expansion of magma with 0.5-4.0% by weight of water into empty circular drifts and into drifts with blockages representing waste canisters.

Typical results for the early expansion of magma into an empty drift indicate that the process is quite complicated. Using a four-material model with air in the drift and in the pore spaces of rhyolite tuff and magma consisting of basalt liquid and water vapor, we start with a wall of magma at one end of a 2-dimensional cylindrical drift. The magma expands into the drift with water vapor (2 percent by weight) separating from the basalt liquid. With this abrupt beginning, the expanding products drive a shock down the drift.

Our results agree with numerous field observations that the interaction between magma and air is a complicated multiphase problem. The model assumed that the total water content of the magma was vapor which is certainly not correct for the initial state of the magma since the solubility of water in basalt magma at our initial condition of 20 MPa is about 1 percent (Valentine, 2000). The effect of not including solubility of water in the basalt will be that our calculated phase separation and shock strengths will be too large. Likewise the length of the water vapor slug driving the air shock is also overestimated. We are currently preparing a model which will include the solubility of water in the magma. A related effect, which is certainly important but which is not included in our model nor in our near-term plans, is the kinetics of exsolution whereby the transformation of water to the vapor phase is retarded by the need for it to diffuse through the magma to a surface or to nucleate a new bubble. This has been addressed in some models of magma exsolution (Moore, 1998).

The calculation with the axis partially blocked by rigid cans illustrates some of the phenomena that are likely to complicate the flow in a real repository environment. Radial flow and mixing associated with formation of eddies between the cans reduce the efficiency with which energy is transferred down the drift to sustain shock waves. This is more than a simple change in cross-sectional area effect of the sort addressed in calculations by Woods et al. (Woods, 2002).

Based on a comparison of the results illustrated in Figures 1 and 3, it appears that use of more realistic models for the initial interaction between an intruding dike and a drift diminishes, if not eliminates, the threat of shock wave formation during the early parts of the dike-drift interaction. This also is consistent with observations of the early parts of the eruption of Pericutin (Luhr and Simkin, 1993).

Download Gaffney.doc (MS Word abstract file with images)

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CONDUIT4 – a computer code for the simulation of magma ascent through volcanic conduits and fissures

P. Papale and M. Polacci

The computer code CONDUIT4 has been developed during last ten years, starting from the initial DUCT code by F. Dobran ( JVGR1992) which solved the steady, isothermal, two-phase non-equilibrium flow of a liquid-gas mixture in the bubbly flow and gas-particle/droplet flow regimes for a volcanic conduit or fissure. That code assumed constant and assigned liquid density and used simple semi-empirical relationships for water solubility and water-dependent magma viscosity. Other input data were constituted by constant magma temperature, stagnation (magma chamber) pressure, conduit length, conduit geometry (cylindrical conduit with constant diameter, or long fissure with constant width), mass flow-rate, total amount of water, and anhydrous magma viscosity. Subsequent implementations (Papale and Dobran, JVGR 1993, JGR 1994; Papale, Nature 1999; JGR 2001; Papale and Polacci, BV 1999) include the following: introduction of a homogeneous liquid-crystal dense phase with assigned crystal density and water-free crystal volume distribution; inclusion of composition-dependent models from the literature for liquid density and viscosity; inclusion of a separately-developed (Papale, CMP 1997, AM 1999) non-ideal, non-Henrian compositional-dependent model for H₂O, CO₂, and H₂O+CO₂ saturation in silicate melts; real equation of state for H₂O-CO₂ gas mixture; inclusion of dynamic fragmentation modeling based on the occurrence of rate-induced visco-to-elastic transition of magma, or on gas bubble overpressure; inclusion of pseudo-plastic liquid magma rheology; generation of a spectrum of magmatic particles at fragmentation including vesicular crystal-bearing pumice, free crystals, and liquid drops or glassy shards (volcanic ash), with variable extent of equilibrium to non-equilibrium degassing from pumice; inclusion of sets of constitutive equations for mechanical gas-particle and particle-particle interactions covering conditions from dense to dilute gas-particle mixtures. To-date, the input data to run the code include the followings: magma temperature; stagnation pressure; conduit or fissure length; anhydrous magma composition in terms of 10 major oxides; total H₂O and total CO₂ in the magma; crystal volume and density distributions; fragmentation efficiency, or the relative amount of non-vesicular ash to pumice generated at fragmentation; representative diameters of pumice, free crystals, and drops/shards in the gas-particle/droplet flow region above magma fragmentation; extent of non-equilibrium degassing from pumice; and one among conduit diameter (or fissure width) and mass flow-rate. Down-flow boundary conditions are represented by either choking of the magmatic mixture or atmospheric pressure at the exit. Collaboration with experimentalists has led to the inclusion in the modelling of non-Harrenian constitutive equations for the liquid viscosity as a function of temperature and dissolved water content for a variety of natural compositions including rhyolites, trachytes, phonolites, and basalt. Parameters used by the code include bubble number density (common values adopted in the range 10¹¹-10¹⁵ m^-3), and bulk modulus of magma (25 GPa). The model restitutes the distribution along the volcanic conduit and across magma fragmentation, of magma pressure, gas velocity, dense phase (liquid+crystals, or particles) velocity, total and continuous gas weight and volume fractions, and one among conduit diameter (fissure width) and mass flow-rate, as well as the vertical distribution of liquid and magma viscosity, dissolved amount of each volatile component, density of all phases, and any other dynamic and thermodynamic quantity derived from the above or determined for the above calculations. Extensive use of the code has been done in the years for i) investigating the general characteristics of magma ascent dynamics, mostly during large explosive eruptions; ii) performing parametric studies aimed at extracting the net roles, that often revealed to be complex and non-intuitive, of several quantities among those in the input data; iii) simulating real eruption cases; iv) forecasting the hazard at active volcanoes. In many of the above applications, the CONDUIT4 code has been used in conjunction with the PDAC-2D code (Neri et al., JGR submitted) for calculating the entire large-scale explosive eruption dynamics from the conduit base to within the atmosphere and along pyroclastic flows (e.g., Papale et al., JVGR 1998; Neri et al., JVGR 1998, JVGR in press; Todesco et al., BV 2002).

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The PDAC-2D (Pyroclastic Dispersal Analysis Code, 2D) model

A. Neri, T. Esposti Ongaro, G. Macedonio, D. Gidaspow, A.B. Clarke, and B.Voight

The PDAC-2D code was developed to simulate the transient, 2D, multiphase dynamics of gas-pyroclast mixtures produced by explosive eruptions (Neri et al., JGR submitted). The code has been applied mainly to the simulation of collapsing columns and associated pyroclastic flows in spite it is able to describe the dynamics of any gas-particle flow generated by the fragmentation of magma (e.g. conduit flow above the fragmentation level). The dynamics of the processes are simulated by adopting a Large Eddy Simulation (LES) approach able to resolve the large-scale features of the flow and parametrizing the sub-grid scale turbulence. The model accounts for full mechanical and thermal non-equilibrium conditions between the continuous gas phase and n different particulate solid phases through the solution of the fundamental conservation equations for each phase. Solid phases are characterized by specific physical parameters and properties such as diameter, density, specific heat, thermal conductivity, and viscosity. Viscous and interphase effects are expressed in terms of Newtonian stress tensors, and gas-particle and particle-particle interactions, respectively. The particulate phases are typically representative of pyroclasts ranging from a few tens of micron up to several millimeters in diameter, whereas the gas phase can consist of water vapor and carbon dioxide leaving the vent and atmospheric air. Atmospheric dispersal dynamics typically describe the timewise formation of the vertical jet, the generation of radially spreading density currents, and the development of thermal convective instabilities from the fountain and the flow. Simulation results highlight the importance of the multiparticle flow formulation of the model. Finer particles tend to follow the hot ascending gas, mainly in the phoenix column and, secondarily, in the convective plume above the fountain. Coarser particles tend to segregate and sediment along the ground.

The PDAC-2D code has been applied also to the simulation of Vulcanian explosion dynamics (Clarke et al., Nature 2002). In this case, the code was used to link the unsteady conduit dynamics of Vulcanian explosions to the resulting dispersal of volcanic ejecta. Observational data from well documented explosions at the Soufriere Hills volcano, Montserrat, were used to constrain pre-eruptive conduit conditions and to compare with simulation results. The resulting simulations duplicate many features of the observed explosions and reveal internal dynamics and particle-size segregation mechanisms that may occur in such explosions. The PDAC-2D code has been also used in combination with the conduit model CONDUIT4 (Papale, JGR 2001) in the reconstruction of the eruptive style of historical eruptions (Neri et al, JVGR in press) as well as in the simulation of gas-particle flow patterns observed in laboratory experiments (Neri and Gidaspow, AIChE J 2000).

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The CpiuC (Chamber più Conduit) model

G. Macedonio, A. Neri, J. Martì, and A. Folch

The objective of the CpiuC code is the analysis of the time evolution of the eruption variables (pressure, mass flow rate, vent parameters, etc.) during a sustained magmatic eruption (Macedonio et al., in preparation). To reach this goal simplified 1D isothermal models of magma chamber empting and conduit flow were developed and coupled. The magma chamber model assumes that the chamber is homogeneous in composition although a vertical profile of volatile content (water) can be assumed. The chamber can have a cylindrical, elliptical, or spherical geometry. Inside the chamber, magma is assumed to be in hydrostatic equilibrium both before and during the eruption; i.e. we assume that the velocity field in the chamber does not perturb significantly the hydrostatic pressure field (Martí et al., EPSL 2000). Since the time-scale of the pressure variations at the conduit inlet (of the order of hours) is much longer than the travel time of the magma in the conduit (of the order of a few minutes), we approximated the flow in the conduit as a steady-state flow. As a consequence, the flow is governed by the 1D mass and momentum balance equations under steady-state conditions. The conduit is assumed circular with constant diameter. Bubble nucleation is considered when the homogeneous flow pressure drops below the nucleation pressure given the total water content and the solubility law. Here we assume a simple solubility law of the type , where the exponent n and the constant s are assumed to be independent of pressure and provided as a function of magma composition and temperature (Mastin and Ghiorso, USGS Rep. 2000). Above the nucleation level, bubbles and liquid magma are considered in mechanical equilibrium (i.e. with the same velocity). The fragmentation criterion adopted is based on the reaching of a critical gas volumetric fraction (typically 0.75) whereas, after fragmentation, particles and gas continue to have the same velocity. Above the fragmentation level, the gas-particle mixture accelerates upwards until it reaches the sonic velocity at the conduit exit (choked-flow condition). Due to the hydrostatic hypothesis, the pressure inside the magma chamber monotonically increases from the top to the bottom of the chamber. By considering the pressure at the chamber top as the upper boundary condition, the density and pressure distributions inside the chamber can be easily computed. Moreover, the integration of the density distribution in the chamber allows to obtain the total mass in the chamber as a function of the pressure at the chamber top. The pressure at the chamber top represents, at the same time, the boundary condition for the conduit model that gives the mass flow rate as a function of the pressure at the base of the conduit. As a consequence, the coupled models allow the knowledge of the mass flow rate and vent parameters as a function of the mass of magma in the chamber.

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Soufrière model

A.B. Clarke

The flow of multi-phase magma from the chamber to the surface is poorly understood.  Computational methods are currently being employed to better understand the flow behavior, incorporating effects of gas exsolution, bubble formation, crystal growth, and permeability.  Numerous types of data collected over the course of the eruption of the Soufrière Hills volcano, Montserrat, have aided some of these modeling efforts, however, field data has yet to confirm model results.  Two series of vulcanian explosions in 1997 were observed closely at the Soufrière Hills volcano, 88 in all from August to October.  Each explosion lasted only minutes, producing eruption columns up to 15 km a.s.l and ejecting up to 106 m³ of andesite magma.  Evacuation depths of 1 to 2 km are estimated, along with magma volume flux rates of 9-13 m3/s between explosions.   Magma fragmentation during such vulcanian explosions is thought to occur by a fragmentation wave traveling into the conduit at the local speed of sound, expelling a mixture of solids and gas from the conduit behind it.  Because the fragmentation wave moves at such high speeds, it is assumed that the magma is solidified in its pre-explosive state.  Therefore, the eruptive products should record these pre-eruptive conditions.  We have collected numerous samples from the well-observed events and will use several methods of petrological analysis to constrain the dynamic conditions immediately prior to the vulcanian explosions.  First, experimental studies have established both the equilibrium phase relations of the magma over a range of temperatures and water pressures and the kinetics of crystal nucleation and growth, with the composition of plagioclase feldspar microlites being correlated to final decompression pressure.  The composition and total volume fraction of natural plagioclase feldspars will be measured on a number of samples from a single vulcanian event in order to compare with experimental results and deduce corresponding natural pressures.  Densities of such samples will also be recorded, resulting in a pressure/density profile of the pre-eruptive conduit.  Second, we will attempt to measure water contents and compositions of matrix glass of the same pumices, testing a variety of methods.  These measurements should independently constrain pre-eruptive pressures as well as, along with clast density, help to constrain the amount of volatile loss through porosity of the magma or surrounding country rock.  Results of conduit flow models will then be compared to these data.

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Episodic Dome Growth and Surface Deformation at Soufriere Hills Volcano, Montserrat, BWI: Constraints from GPS Geodesy

Glen S. Mattioli

GPS geodesy has been ongoing at Soufriere Hills volcano (SHV) since August 1995, when campaign style measurements were started using L1 only code-phase receivers with internal antennas. High-precision campaign GPS was initiated in October 1995 and several campaigns were completed between 1995 and 1997, when the eruptive activity either destroyed the existing benchmarks or prevented their reoccupation.  The SHV CGPS network now consists of 6 dual-frequency code-phase receivers, with Dorn-Margolin choke-ring antennae with identical Lexan radomes, which share a common RF telemetry network.  All GPS data were processed using GIPSY-OASISII to obtain free-network point positions using final orbit, clock, and earth orientation parameters from JPL.  Positions were recast into ITRF97 and these positions were used to calculate component velocities.  Final site velocities for each site are reported relative a fixed Caribbean reference frame (DeMets et al., 2000) and final errors include estimates for the both the plate motion and individual site.

By examination of the individual time series of both the campaign and continuous sites, we have been able to divide the ground deformation observations in several distinct phases, correlated with the type of eruptive behavior manifested at the surface. While the CGPS data is limited in space, and has some important and substantial gaps because of equipment failures (some of which could not be fixed due to hazardous eruptive activity), we find that the entire GPS data set can be usefully discussed in terms of three distinct periods: (1) late 1995 to the end of 1997; (2) early 1998 to late 1999; and (3) early 2000 to at least end of 2001, the last time for which the GPS observations have been analyzed and modeled. The primary criterion used for this distinction is the vertical velocity field.  During the first period (1995-1997), all stations show strong subsidence as a function of radial distance from the SH dome (Mattioli et al., 1998). Although there is a data gap between late fall 1997 and the re-establishment of the CGPS network in early 1998, all sites show inflation at about half the rate observed for the previous period of subsidence. Thus periods of significant surface outflow (1995-1997) are strongly correlated with surface subsidence, while periods of no apparent surface magma flux are strongly correlated with ground surface inflation. Although the exact timing is somewhat equivocal, subsidence resumed at all CGPS sites just prior to the emergence of the Millennium Dome in late November 1999 to early December 1999. 

Data from each of the distinct periods has been inverted using a modified, downhill simplex method for an elastic half-space.  Our code explicitly includes provision for a Mogi-type source and perpendicular opening across a planar dislocation (i.e. dike).  All best-fit models have two distinct sub-surface pressure sources (deep Mogi and shallow dike oriented NW) whose initial geometry and magnitude were not fixed a priori.  Inferred Mogi depths range from 4.0 to 12.0 km, with changing polarity (deflation, inflation, deflation) and deepening in time, and the dimensions and inferred opening displacement of the dike have decreased from an initial maximum of 0.7 m, to 0.3 m, and then 0.1 m in each of the three periods.  The derived average parameters for all three periods are: dike (strike 132N, dip 83, depth 1.9 km, width 2.1 km, length 0.6 km, opening 0.4 m); Mogi (depth 6.9 km, delta V –9.7 x 10⁶ m³); reduced chi-squared (4.4).

The observed open-system versus closed-system behavior at SVH implies that long-term CGPS measurements may be useful in establishing "where individual volcanic systems are," with respect to the volcanic eruption cycle, provided that the phase and amplitude of such time-varying strain can be established for a variety of magmatic systems. Our observations demonstrate that SHV is also affected by longer-period semi-periodic behavior, similar to that reported by Voight et al. (1998) for very short-period fluctuations on the order of 6-14 hr.

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