Instability Induced by Random Background Noise in a Delay Model of Landslide Dynamics

Abstract

In the present paper, we propose a new model for landslide dynamics, in the form of the spring-block mechanical model, with included delayed interaction and the effect of the background seismic noise. The introduction of the random noise in the model of landslide dynamics is confirmed by the surrogate data testing of the recorded ambient noise within the existing landslide in Serbia. The performed research classified the analyzed recordings as linear stationary stochastic processes with Gaussian inputs. The proposed mechanical model is described in the form of a nonlinear dynamical system: a set of stochastic delay-differential equations. The solution of such a system is enabled by the introduction of mean-field approximation, which resulted in a mean-field approximated model whose dynamics are qualitatively the same as the dynamics of the starting stochastic system. The dynamics of the approximated model are analyzed numerically, with rather unexpected results, implying the positive effect of background noise on landslide dynamics. Particularly, the increase of the noise intensity requires higher values of spring stiffness and displacement delay for the occurrence of bifurcation. This confirms the positive stabilizing effect of the increase in noise intensity on the dynamics of the analyzed landslide model. Present research confirms the significant role of noise in landslides near the bifurcation point (e.g., creeping landslides).