Analytical Model of Small Fluctuations of Compressible Magma With Maxwell Rheology in the Feeding System of a Volcano. Part 2. Oscillations of Vertical Velocity

Abstract

The analytical solution for vertical magma movements in a volcanic conduit within the occurrence of low-frequency volcanic seismic events is presented. Magma is described by Maxwell's compressible body model. When the density of the magmatic melt is disturbed, for example, when dense magma enters from deep layers or the melt degasses at a certain depth, density oscillations may occur in the channel as a reaction to this event. For the magma conduit of the simplest cylindrical shape, the magma density and two components of the velocity of movement are subject to oscillations. In this case, the vertical component of the velocity experiences forced oscillations, both under the influence of density oscillations and under the influence of the initiating disturbance. All these oscillations are harmonic damped oscillations, the damping coefficient of which is determined by the relaxation time of the magmatic melt, and the natural frequency depends on the physical characteristics of the magmatic melt and the geometric dimensions of the conduit. Melt density oscillations lead to periodic variations in the lithostatic pressure drop, which in turn causes vertical movements of the melt, the most amplitude along the axis of the magma conduit. The model is used to describe crater surface displacements observed on the surface of the Santiaguito volcano crater.