Analytical model of small fluctuations of compressible magma with Maxwell rheology in the feeding system of a volcano. Part 1. Density oscillations

The analytical mathematical model is presented that describes one of the possible mechanisms for the occurrence of long-period seismic events that are often recorded near active volcanic centers. The feeding system of the volcano is modeled in the simplest form of a cylindrical channel filled with a compressible magmatic melt with the rheology of a Maxwell body. It is shown that such a magmatic body can experience harmonic damped oscillations, the damping coefficient of which is determined by the relaxation time of the magmatic melt. These fluctuations may appear as a response to a density perturbation caused by the influx of denser magma from deep layers or a change in pressure in the supply system of the volcano. The dependence of the natural oscillatory frequency on the physical characteristics of the magmatic melt and the geometric dimensions of the feed channel is shown. When the compressibility of the magmatic melt is taken into account, density perturbations depend on the size of the feeding system and are characterized by periodic oscillations, which are most pronounced near the channel axis. Oscillations are also experienced by the flow velocity component directed along the radius of the cylinder. The source mechanism of the long-period seismic events is discussed. The model is used to describe long-period oscillations recorded near Santiaguito (Guatemala).