Analysis of stochastic model for nonlinear volcanic dynamics

Abstract

Motivated by important geophysical applications we consider a dynamic model of the magma-plug system previously derived by Iverson et al.∼(2006) under the influence of stochastic forcing. Due to strong nonlinearity of the friction force for a solid plug along its margins, the initial deterministic system exhibits impulsive oscillations. Two types of dynamic behavior of the system under the influence of the parametric stochastic forcing have been found: random trajectories are scattered on both sides of the deterministic cycle or grouped on its internal side only. It is shown that dispersions are highly inhomogeneous along cycles in the presence of noises. The effects of noise-induced shifts, pressure stabilization and localization of random trajectories have been revealed by increasing the noise intensity. The plug velocity, pressure and displacement are highly dependent of noise intensity as well. These new stochastic phenomena are related to the nonlinear peculiarities of the deterministic phase portrait. It is demonstrated that the repetitive stick-slip motions of the magma-plug system in the case of stochastic forcing can be connected with drumbeat earthquakes.