Driving force of lateral permeable gas flow in magma and the criterion of explosive and effusive eruptions
Introduction
A volcanic eruption sometimes produces continuous liquid lava effusively and sometimes ejects various sizes of magma fragments explosively. Explosive eruptions involve the process of magma fragmentation that transforms a bubbly liquid flow of magma into a gassy flow mixed with magma fragments in the conduit (Woods, 1995). The mechanism of magma fragmentation is thus an important factor that determines the eruption style (Sparks, 1978, Alidibirov and Dingwell, 1996, Papale, 1999, Sahagian, 1999). Another important factor is the amount of volatiles that are lost from magma during its ascent motion. Namely, an eruption is made effusive and explosive, respectively, when relatively significant and insignificant amounts of volatiles escape from the ascending magma.
Volatiles in magma may migrate in various ways, including through diffusion and bubble migration. Among them permeable gas flow is probably one of the most effective mechanisms for gas transportation in magma. The coalescence of bubbles in magma is thought to connect the dispersed gas phase and to produce some networks of bubbles that may provide the gas flow with permeable paths (Klug and Cashman, 1996). Accordingly, many studies have focused on methods for estimating the permeability of magma and its dependence on the gas volume fraction theoretically (Saar and Manga, 1999, Blower, 2001) and experimentally (Klug and Cashman, 1996, Klug et al., 2002, Takeuchi et al., 2005, Mueller et al., 2005).
Gas migration in magma has both a vertical component along the ascent motion and a lateral component toward the boundary walls. The vertical gas migration, which is caused by a difference between the ascent velocity of gas and that of the liquid magma, redistributes the gas concentration within the conduit and influences the depth and nature of magma fragmentation (Yoshida and Koyaguchi, 1999, Melnik et al., 2005). The vertical gas migration can even reduce the volume fraction of bubbles due to gas filtration and make the eruption effusive (Melnik and Sparks, 1999). On the other hand, the lateral gas migration reduces the amount of gas in magma at each depth and provides another basic mechanism for the control between explosive and effusive eruptions (Eichelberger et al., 1986, Jaupart and Allegre, 1991, Woods and Koyaguchi, 1994). In this paper we consider the lateral gas transport in magma, assuming that it may play a more important role because of the much shorter path length required for gas removal. An important problem we encounter in this context is the question of what drives the lateral permeable gas flow. To answer this question, we here propose a driving force that originates from the viscous resistance of decompressed magma to gas expansion, and we formulate the corresponding degassing rate.
Once the degassing rate is formulated we can make a computer simulation of the magma ascent process to find the criterion of the eruption style for this specific mechanism of degassing. Many models applicable to the simulation are actually available (Sahagian, 2005). In particular, a model of one-dimensional stationary magma flow has frequently been used for the study of magmatic and eruptive processes (Wood, 1995; Woods and Koyaguchi, 1994, Papale, 2001, Mastin, 2005, Melnik et al., 2005, Macedonio et al., 2005), while non-stationary magma flow has also been analyzed (Melnik and Sparks, 2002, Proussevitch and Sahagian, 2005). In this paper we employ a non-stationary model because we are interested in how the pre-eruptive process leads to different eruption styles. Studies of non-stationary magma flow are necessary to reveal some features of eruptive processes that involve the uncertainties and complexities of non-linear systems (Sparks, 2003).
Section snippets
Escape of gas through permeable flow
Coalescence of bubbles in vesiculating magma is considered to create permeability which serves to connect the dispersed gas phase (Klug and Cashman, 1996). Laboratory measurements of permeability for some artificial silicate melts that have been decompressed at high temperatures actually confirm that permeable networks of bubbles can be created in ascending magmas (Burgisser and Gardner, 2005, Takeuchi et al., 2005). Permeable gas flow thus can be an important mechanism contributing to the
Magma flow model
To examine the degassing mechanism formulated above we make a computer simulation of the magma ascent process. For the simulation we employ a model of one-dimensional conduit flow in which the ascent velocity, the bulk magma density and other quantities are averaged over the conduit cross-section at each depth (Fig. 2). This approximation has been employed in many previous studies of both stationary (Woods and Koyaguchi, 1994, Woods, 1995, Papale, 2001, Mastin, 2005, Melnik et al., 2005,
Parameters for the numerical calculation
Some parameters that appear in the model for our simulation involve large uncertainty. In particular, the nature of permeable gas flow in magma has not yet been constrained very well. If the inertial effects play an important role in the gas flow, the Darcy's law itself should be modified (Rust and Cashman, 2004). Furthermore, actual gas flow in natural liquid magma may behave differently than predicted from permeability measurements for the quenched samples. For these reasons, we prefer to
Results of the simulation
In this section some results of the numerical calculations are presented using the dimensionless variables that are denoted here by the same notations as the original. Fig. 3 demonstrates one of the typical results of calculated time-dependent magma flow. In this figure spatial distributions of the mass ratio of the total volatiles m (left), the gas volume fraction ψ (center) and the magma ascent velocity v (right) are shown at every dimensionless time step of 0.8. The area occupied by bubbly
Criterion of the eruption style
In this section the dimensionless degassing factor is denoted by D′ to discriminate it explicitly from the original dimensional form D defined in Eq. (12). Recalling the unit for scaling in Table 1, D′ is written asThis expression of D′ consists of multiplication of the three dimensionless factors. The first factor involving T, pr and ρr can be regarded almost as a constant of about 0.1. The second factor changes over a wide range in proportion to the magma viscosity η,
Discussion
Our criterion of the eruption style (Fig. 10) predicts that effusive eruptions should occur in the condition of relatively higher viscosity. This conclusion seems to conflict with the knowledge that low-viscous basaltic magmas usually participate in silent effusive eruptions while explosive eruptions are generally produced by more felsic magmas having higher viscosities. The effect of viscosity in this criterion may be partly compensated by the effect of permeability, because measured
Acknowledgements
I would like to thank Dr. Margaret Mangan and an anonymous reviewer for helpful suggestions to improve the paper. This study was supported by Grants-in-Aid for Scientific Research by MEXT, Scientific Research in Priority Areas 422.
References (43)
Water and magma: a mixing model
Geochim. Cosmochim. Acta
(1975)- et al.
Explosive basaltic volcanism of the Chikurachki Volcano (Kurile arc, Russia): insights on pre-eruptive magmatic conditions and volatile budget revealed from phenocryst-hosted melt inclusions and groundmass glasses
J. Volcanol. Geotherm. Res.
(2005) - et al.
Gas content, eruption rate and instabilities of eruption regime in silicic volcanoes
Earth Planet. Sci. Lett.
(1991) - et al.
Temporal evolution of flow conditions in sustained magmatic explosive eruptions
J. Volcanol. Geotherm. Res.
(2005) - et al.
The generation of gas overpressure in volcanic eruptions
Earth Planet. Sci. Lett.
(1999) The controlling effect of viscous dissipation on magma flow in silicic conduits
J. Volcanol. Geotherm. Res.
(2005)- et al.
Dynamics of magma flow inside volcanic conduits with bubble overpressure buildup and gas loss through permeable magma
J. Volcanol. Geotherm. Res.
(2005) - et al.
The trigger mechanism of low-frequency earthquakes on Montserrat
J. Volcanol. Geotherm. Res.
(2006) - et al.
Bubbledrive-1: a numerical model of volcanic eruption mechanisms driven by disequilibrium magma degassing
J. Volcanol. Geotherm. Res.
(2005) - et al.
Permeability of vesicular silicic magma: inertial and hysteresis effects
Earth Planet. Sci. Lett.
(2004)
Volcanic eruption mechanisms: insights from intercomparison of models of conduit processes
J. Volcanol. Geotherm. Res.
The dynamics of bubble formation and growth in magmas: a review and analysis
J. Volcanol. Geotherm. Res.
Forecasting volcanic eruptions
Earth Planet. Sci. Lett.
A new regime of volcanic eruption due to the relative motion between liquid and gas
J. Volcanol. Geotherm. Res.
Magma fragmentation by rapid decompression
Nature
Factors controlling permeability–porosity relationships in magma
Bull. Volcanol.
Experimental constraints on degassing and permeability in volcanic conduit flow
Bull. Volcanol.
Non-explosive silicic volcanism
Nature
Fragmentation of magma during Plinial volcanic eruptions
Bull. Volcanol.
Explosive volcanism may not be an inevitable consequence of magma fragmentation
Nature
Fragmentation of a porous viscoelastic material: implications to magma fragmentation
J. Geophys. Res.
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