Abstract
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.
Highlights
It is well-known that the behavior of volcanic systems is enormously complex so that a lot of nonlinear feedbacks lead to multiple states even during a single eruption (Tanaka et al, 2014)
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
An important point of the deterministic behavior is that a certain constant value of the plug velocity u establishes at different pressures p in the state of equilibrium. This equilibrium state persists at different conduit volumes V0 (Fig. 4)
Summary
It is well-known that the behavior of volcanic systems is enormously complex so that a lot of nonlinear feedbacks lead to multiple states even during a single eruption (Tanaka et al, 2014). 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.
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