# Instability Induced by Random Background Noise in a Delay Model of Landslide Dynamics
## 1 Introduction
In order to verify the existence and type of the background noise, we first analyze the real observed seismic background noise recorded at the accelerometer station at the dam \"Zavoj\" and its possible influence on the landslide activation in the immediate vicinity of the dam. In particular, the \"Zavoj\" dam is actually founded on one part of the landslide material, which was deposited by the large landslide that occurred in 1963 due to large and sudden snow melting. This landslide dammed the riverbed of the Visocica River and formed a 10 km long natural lake that existed for almost two years. The 36 m high dam was breached on purpose in 1965 by excavating a special 600 m long evacuation tunnel. Later in the period 1983-1989, dam Zavoj was built approximately at the same place as the natural dam. Considering the high susceptibility of this area to activation of landslides, we use this example as convenient for the analysis of the influence of seismic noise on slope stability. It should be emphasized that there are no previous investigations dealing with the effect of ambient noise on possible landslide triggering, although some similar attempts have been recorded. [PERSON] et al. [14] analyzed microseism time series recorded in a broadband seismic station located at the eastern Pyrenees and detected strong evidence of their stochasticity, with no evidence of nonlinearity and determinism. [PERSON] et al. [15] examined two landslides in Western Caprathians (Poland), located 20-30 km from semi-active zones where M \(\leq\) 4.4 earthquakes were previously recorded. As a result of their research, they concluded that low-magnitude earthquakes (M \(<\) 5) are able to induce the occurrence of landslides at distances that are even larger than limiting distances that were previously published as relevant for co-seismic landslides. This indicates the probability that the influence of low magnitude on the landslide triggering may be underestimated in areas that are considered seismically inactive or with low seismic activity. [PERSON] et al. [16] indicated that small earthquakes with MI \(<\) 3.6 maintain a slow-moving landslide in a persistent critical state by preventing the soil from healing. In this way, low-magnitude earthquakes act as a preparatory factor rather than a main triggering parameter. [PERSON] et al. [17]. using results of differential SAR interferometry, indicated an increase in landslide activity after the low-magnitude earthquake. All these examples indicate the importance of low-magnitude events and corresponding low-intensity ground oscillations on landslide activity. In the present paper, we go one step further--we examine the impact of extremely low-level background noise on landslide activity, especially in the case when the slope is on the verge of stability. It is in this case that noise could have a predominant effect, i.e., induces the occurrence of new dynamical features and transitions to different dynamical regimes [18; 19]. The main idea of the research was to examine whether background seismic noise of low intensity has any influence on landslide dynamics and, if so, to analyze the quantitative and qualitative changes of landslide dynamics under the impact of such noise. For this purpose, one needs first to classify the background noise, which is done in this case by analyzing the background noise before and after three small seismic events recorded at an accelerograph placed at the Zavoj dam (Serbia). Once the type of noise is determined, one needs to include this effect in the convenient model of landslide dynamics. In the present paper, we chose the spring-block model of landslide dynamics, with included delay in interaction, as a convenient model for the investigation of the impact of noise on landslide dynamics. The chosen model could be considered an adequate phenomenological model of a landslide recorded in the immediate vicinity of the Zavoj dam.