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Monitoring, modelling and forecasting of volcanic hazard -Analytical models of bubble growth

- Bubble growth during decompression of magma:

Bubble growth during decompression of supersaturated melt is controlled by two dimensionless numbers: the ratio of the diffusive and the viscous time scales over the decompression time scale. We explored the conditions for diffusion and viscosity controlled growth and provided analytical solutions for some specific cases. The model solutions, including the division to the growth regimes as function of the two parameters, provide a fast tool for estimation of the state of erupting magma in terms of gas overpressure, supersaturation and gas volume fraction. The model results are in agreement with the conditions of Plinian explosive eruption (e.g. - Mt St Helens, 18 May 1980), where high gas overpressure is expected. The conditions of effusion of lava domes with sudden onset of explosive activity are also in agreement with the model predictions, mostly in equilibrium degassing and partly in overpressure conditions. The results were summarized in a paper published in JVGR.

- The bulk viscosity of bubbly magma and applications for volcanic earthquakes:

We derived expressions for bulk viscosity of suspension of gas bubbles in incompressible Newtonian liquid that exsolves volatiles. When such suspension is subjected to decompression it expands. The dilatational motion and the driving pressure can be used to define the bulk viscosity of the magma. The resulting bulk viscosity is highly non-linear. At the beginning of the expansion process, when gas exsolution is fast, the expansion rate grows exponentially while the driving pressure slightly 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. This is very important since suspensions with negative bulk viscosity may amplify acoustic waves that travel through them. The results were summarized in a paper published in J. of Fluid Mechanics.

The results indicate that following decompression, the conduit releases a lot of energy and at the same time absorbs seismic energy. We developed analytical solutions for the effective bulk viscosity, bubble radius, and gas pressure following the imposing of a sinusoidal pressure wave on a bubbly conduit. A numerical code was also adapted to model the situation. Preliminary results were presented in AGU-EGU meeting in France and at the IUGG meeting in Japan.

- Cyclic activity at Soufrière Hills, Monserrat: degassing induced pressurization and stick-slip extrusion:

The growth of lava domes is often associated with cyclic variations of ground deformation, seismicity and mass flux of gas and magma. These are commonly attributed to cyclic variations of magma pressure and flow patterns of the magma. We examine a model that describes the degassing of supersaturated magma following plugging of the conduit. As magma volume is confined, diffusion of the excess volatiles leads to buildup of gas pressure within the bubbles and to elastic stresses in the deformed conduit walls. The time scale of this process is controlled by diffusion and is of the order of minutes to hours, similar to the measured period of tilt cycles, which are attributed to pressurization of domes. When the difference between magma pressure and ambient pressure exceeds the static friction between the plug and the host rock, the plug starts to extrude, bubbles expand and overpressure is relaxed. The rate of extrusion is controlled by the magmatic pressure and by the friction along shear zones between the plug and the host rock.

We estimate friction using rate and state dependence model and assuming a steady state approximation. The calculated relaxation time of magma overpressure depends on the depth of effective degassing, velocity and friction parameters and is comparable to deflation periods in tilt measurements. When the magma overpressure drops to the dynamic strength of the slip surfaces, the plug sticks to the conduit walls and blocks the vent.

- Fragmentation of bubbly magma in visco-elastic regime:

Explosive eruptions occur when magma fragments in a conduit. The fragmentation process means that the magma does not react as a fluid, but as an elastic substance. We developed a visco-elastic, spheri-symmetrical bubble growth model. The main controlling parameter is the ratio between the Maxwell relaxation time and the stress loading time, known as Deborah number (De). For large Deborah numbers (De>1) the magma will react elastically, and for small ones (De<1) the magma will react as a viscous fluid. For De~1 a bubble growth model that accounts for both viscous flow and elastic strain of the melt around the bubble should be applied. A preliminary numerical growth model was developed and the conditions under which an ascending magma may enter the visco-elastic regime were explored.

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Reported by

Institute of Earth Sciences
The Hebrew University
91904 Jerusalem
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