# Instability Induced by Random Background Noise in a Delay Model of Landslide Dynamics
## 2 Analysis of the Recorded Background Seismic Noise  
In order to confirm the presence of random background seismic noise in a landslide-prone area, we examine the recordings of ambient noise made at the dam \"Zavoj\" (Pirot, Serbia; Figure 1), which is situated in an area composed of dominantly Lower Triassic (T1) sandstones (0.3-0.5 m thick) and claystone (0.1-2 m thick), which build a flysch complex, with the subordinate occurrence of limestones (up to 5 m thick). Considering such geological composition, this area is prone to landslide occurrence, with a massive landslide occurring in 1963, as was already stated in Introduction.  
Figure 2 shows examples of the background seismic noise recorded by accelerograph of ETNA type on 8 April, 17 April, and 18 August 2022, which is publicly available on the website of the Seismological Survey of Serbia [21]. In the present paper, we examine these three recordings by applying surrogate data testing [22].  
The results of surrogate data testing are given in Figure 3. In particular, we tested the first null hypothesis that data represent independent random numbers drawn from some fixed but unknown distribution. For this purpose, we formed 20 surrogate datasets by randomly shuffling the data (without repetition), thus yielding surrogates with exactly the same distribution yet independent construction and estimating zeroth-order prediction error for 100 prediction steps. It is clear from Figure 3 that prediction error \(\varepsilon 0\) for the original dataset is not within the prediction errors for all the tested surrogate datasets, \(\varepsilon\), indicating that starting null hypothesis could be rejected.  
Figure 1: Position of “Zavoj” dam, where the actual accelerograph station is situated.  
Figure 2: Recorded background seismic noise, accelerograph of ETNA type on 8 April 2022 (**a**), 17 April 2022 (**b**), and 18 August 2022 (**c**) [21] at Zavoj dam after WWSSN-SP filter is applied.  
As the second step in our analysis, we tested the null hypothesis that data represent a linear stationary stochastic process with Gaussian inputs. As in the previous case, we formed 20 surrogate datasets by randomizing the Fourier surrogates of the original data and then by computing the inverse transform to obtain randomized time series [23]. The results are shown in Figure 4. Obviously, we could not reject the null hypothesis (at a 95% significance level) since \(\varepsilon_{0}\) is within \(\varepsilon\) for all the tested surrogates.  
Figure 3: Results of surrogate data testing—testing of I hypothesis. The set of curves represents the distribution of prediction errors for the original and 20 surrogate datasets (for 100 prediction steps). The red line denotes prediction error \(\varepsilon_{0}\) for the original dataset, while the black lines denote prediction error \(\varepsilon\) for the surrogate datasets. The first row corresponds to the results of surrogate data testing of the recorded background noise before (**a**) and after (**b**) the event on 17 April 2022 (Figure 2a), the second row corresponds to the results of surrogate data testing of the recorded background noise before (**c**) and after (**d**) the event recorded on 8 April 2022 (Figure 2b), while the third row denotes the results of the analysis of the noise before (**e**) and after (**f**) the event recorded on 18 August 2022 (Figure 2c).