Abstract The attenuation of pressure waves in a saturated bubbly magma is examined in a model, coupling seismic wave-propagation with bubble growth dynamics. This model is solved analytically and numerically, including effects of diffusion of volatiles, visco-elasticity and bubble number density. We show that wave attenuation is controlled mainly by the Peclet and Deborah numbers. The Peclet number is a measure of the relative importance of advection to diffusion. The Deborah number is a visco-elastic measure, describing the importance of elasticity in comparison to viscous melt deformation. We solve numerically for wave attenuation for various magma properties corresponding to a wide range of Peclet and Deborah numbers. We show that the numerical solution can be approximated quite well for frequencies above 1 Hz, by an analytical end-member solution, obtained for high Peclet and low Deborah numbers. For lower frequencies, volatile transport should be accounted for, leading to higher attenuation with respect to the analytical solution. However, if the Deborah number is increased, either by longer relaxation time or by higher frequencies, then attenuation decreases with respect to the analytical solution. Therefore, visco-elasticity leads to a significant improvement of the resonating qualities of a magma-filled conduit and widens the depth and frequency ranges where pressure waves will propagate efficiently through the conduit.

Abstract The growth of lava domes is often associated with cyclic variations of ground deformation, seismicity and mass flux of gas and magma. We present a model of cyclic volcanic activity which is controlled by degassing of supersaturated magma, magma flow into the conduit, gas escape from the permeable magma, deformation of the conduit walls and the friction between the walls and the plug at the top of the conduit. When the difference between magma pressure and ambient pressure exceeds the static friction, motion begins, bubbles expand and overpressure relaxes. Bubble expansion builds permeability, allows gas escape and faster depressurization. Depressurization and crystallization of the magma build supersaturation and gas diffusion from melt to bubbles. Gas flux into bubbles and magma flux from the chamber act to increase pressure. The rate of extrusion is controlled by the gas pressure, driving the motion, and by the rate- and state-dependent friction along shear zones between the plug and the host rock. When the magma overpressure drops to the dynamic strength of the slip surfaces, the plug sticks and blocks the vent. As bubble volume is now constant, exsolution of gas from the supersaturated melt leads to pressurization and begins a new cycle.