Analysis of stochastic model for nonlinear volcanic dynamics

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.

Stochastically-induced dynamics of earthquakes

“…The main idea of this paper is to describe the temporal evolution of earthquake sequences using a phenomenological population nonlinear model. Such an approach is essentially analogous to the non-linear dynamics of various biological and physical processes and phenomena studied earlier 26,27,28,29,30,31,32,33,34 . The model under consideration, containing positive and negative a) feedback, is simple enough to understand the factors being included.…”

Stochastic sensitivity analysis of volcanic activity

“…It is now well known that the dynamics of volcanic activity is a complex unpredictable process due to nonlinearities that can lead to various evolutionary scenarios during an erupting volcano. [1][2][3] To describe the different stages of the same volcanic eruption, as well as to predict volcanic dynamics, it is necessary to use various methods of mathematical modeling. In this regard, an important task is the formulation and study of various mathematical models of volcanic activity.…”

Феноменологическая модель генерации землетрясений сейсмического режима «drumbeats», сопровождавших извержение вулкана Кизимен в 2011–2012 гг

“…В другой работе [4] для этого извержения предложена модель затухающего генератора, на основе падающего трения. Для сложных нелинейных течений (суспензии, многофазные жидкости) функция силы трения F(u) может иметь Nобразную форму, которая рассмотрена в применении к выжиманию экструзивной пробки.…”

“…При малых скоростях выжимания экструзии (u) функция трения F(u) монотонно возрастает, с резким падением, а после резкого скачка u, снова возрастает. Поведение системы и ее переход в устойчивый предельный цикл, контролируется поведением F(u), при этом изменчивость динамики системы приводит или к моностабильному (равновесному или циклическому) или к бистабильному (равновесный и циклический) режимам, что наблюдалось при извержении в. Сент-Хеленс [4].…”

“…33. no. 4 The eruption of the Kizimen volcano in 2011-2012 characterized by stable, almost uniform squeezing of a viscous lava flow with a volume of 0.3 km 3 . The formation of the lava flow was accompanied by the occurrence of quasiperiodic earthquakes of the "drumbeats" mode with energy classes K s < 7, recorded at long time intervals.…”