Bubble growth processes in magma surrounded by an elastic medium

Gas bubble growth in magma plays an important role in volcanic explosivity, and many previous studies have undertaken theoretical and experimental analyses of gas bubble expansion in melt. These previous studies commonly assume constant ambient pressure, but it is more natural to assume that the magma is stressed by the crust or volcanic edifices as the volume of gas bubbles increases. Here we present a bubble growth model that takes into account the elasticity of the surrounding medium; we use this model to examine temporal changes in the bubble growth process. Our model consists of a two-dimensional dike filled with compressible viscous melt and numerous tiny gas bubbles. We use the cell model proposed by Proussevitch et al. [Proussevitch, A., Sahagian, D. L., Anderson, A. T., 1993. Dynamics of diffusive bubble growth in magmas: isothermal case. J. Geophys. Res. 98, 22283–22307] to describe the interaction between the numerous gas bubbles and the melt. The bubble growth process is formulated by the diffusion equation of volatiles in the melt, the mass balance between bubbles and melt, and the momentum equation of the melt. We also introduce pressure balance equations between the melt and the surrounding elastic medium [Nishimura, T., 2004. Pressure recovery in magma due to bubble growth. Geophys. Res. Lett. 31]. Using the finite difference scheme, we numerically calculate temporal changes in bubble radius and melt pressure within magma subjected to sudden depressurization. Simulation results show that the elasticity of the surrounding medium strongly controls the bubble growth process. Under high effective rigidity, the final bubble radius is several times smaller than for zero rigidity, and the time required for bubble growth is an order of magnitude quicker. Temporal changes in the melt pressure are particularly dependent on the elasticity of the surrounding medium. Melt pressure effectively recovers and even exceeds the given pressure drop for conditions of high rigidity and/or small initial bubble radius. Although bubble growth in magma has previously been investigated mainly from geological samples and theoretical perspectives, our model can quantitatively evaluate pressure changes in magma that can also be detected by seismic and geodetic measurements.