Bubble Growth and Pressure Build Up in Ascending Magma: Effects of Surrounding Elastic Medium

In many previous studies on bubble growth, melt pressure in ascending magma was often assumed to be simply decompressed at a constant rate. However, magma generally ascends through a rock and should be stressed from the surrounding medium as the volume of magma increases with bubble growth. In the present study, to examine how elasticity of the surrounding medium play a role on the magma ascent we simulate the bubble growth and pressure change of melt on the basis of a simple magma ascending model. We simplify the magma ascending process as follows. Magma ascends due to buoyancy, and the magma is decompressed as lithostatic pressure decreases. As a result, gas bubbles in the magma start to grow, and the magma increases its volume to get stresses from the surrounding elastic medium. The ascending magma is modeled by a two-dimensional dike filled with compressible viscous melt and numerous tiny spherical gas bubbles. The dike is embedded in the elastic medium. The shape of the dike is characterized by the aspect ratio: a small aspect ratio represents small effective rigidity while a large aspect ratio does large effective rigidity. We suppose uniform magma pressure neglecting a vertical pressure gradient in the dike. Ascent velocity is assumed to be constant, which is expressed by reducing the melt pressure received from the surrounding elastic medium at a constant rate in our calculation. Growth process of the gas bubbles and pressure change of the melt is controlled by diffusion equation of gas, water mass balance on the interface between the gas bubble and melt, equation of motion for bubble radius, and pressure balance equation between the melt and surrounding elastic medium. We calculate temporal changes of the bubble radius and melt pressure for rhyolitic magma under the condition of initial bubble radius of 10_|5 m, the number density of bubbles of 108 /m3, and the initial dike depth of 5 km. We assume the ascent velocity to be 0.01 m/s following the observed ascent velocity of hypocenters of micro-earthquakes associated with lava dome formation. Our simulation results show that the bubble radius and melt pressure are sensitive to the aspect ratio. When the aspect ratio is as small as 0.00001, the bubble radius rapidly increases at a shallow depth of about 0.5 km and reaches 3.3 mm at the surface. The melt pressure gradually decreases with decreasing the lithostatic pressure, and no significant difference between the melt pressure and the lithostatic pressure (hereafter we call overpressure) is observed until the magma reaches the surface. These characteristics are similar to the results reported in the previous studies. On the other hand, for the large aspect ratio of 0.1, large rigidity restricts the bubble growth: the bubble radius is as small as 0.5 mm and the void ratio is 0.074 even at the surface. The melt pressure exceeds the lithostatic pressure when the dike reaches about a depth of 4 km. Overpressure becomes larger as the dike ascends (e.g., 12.5 MPa at a depth of 3 km and 68.4 MPa at the surface). Therefore, our simulation including the elasticity of surrounding medium predicts that the dike can reach a shallow depth without fragmentation which may occur when the void ratio reaches about 0.8. And also, if the surrounding rocks cannot support the overpressure, the dike extends its length to release the stress caused in the surrounding rocks, which may be detected as a noticeable crustal deformation.