## 3 Materials and Methods
### Time Series Decomposition  
In the analyzed case, the sampling process was performed for phenomena defined as continuous, i.e., rock mass movements and radon emissions from the rock mass. We cannot precisely identify the individual processes controlling both phenomena, but with the use of instruments, we can sample the sum of all processes over time. The data obtained from both measurement systems form a time series (a sampled signal--the sum of the influences of various phenomena): geodynamic in the case of the tiltmeters and representing 222 Rn activity concentration in the case of the SRDN-3 radon probes. Subsequently, elements of signal processing theory were applied, including wavelet analysis and Fast Fourier Transform (FFT) filtering. The only difference was the resolution, which in the case of the tested object was expressed in minutes and hours (Figure 4) instead of megahertz. This study was based on time series C consisting of two superimposed signals (1),  
\[\text{C(x)}=\text{f(x)}+\omega\text{(x)} \tag{1}\]  
where f(x) is the signal from the radon detector originating directly from the rock mass movement, and \(\omega\text{(x)}\) is the noise. In the case of electronic systems sampling the function, the sources of noise were identified as interferences inside the device/system, limitations of the transducers and cables, and interferences from external sources. As a result of such a sampling technique, it was possible to collect the values of the function f(x), which contained information about the variability of a particular phenomenon. The function C(x) itself was also the sum of \begin{table}
\begin{tabular}{c c c c c c c c} \hline  & & & & & & & & \\ \hline \multirow{2}{*}{**SRDN-3 No.**} & \multirow{2}{*}{**Average Value**} & \multirow{2}{*}{**Median**} & \multirow{2}{*}{**Minimum**} & \multirow{2}{*}{**Maximum**} & \multirow{2}{*}{**Range**} & \multirow{2}{*}{**Standard**} & \multirow{2}{*}{**Standard Error**} \\  & & & **Value** & **Value** & & & & **Deviation** & **of the Mean** \\  & & & **[Ba/m\({}^{3}\)]** & **[Ba/m\({}^{3}\)]** & **[Ba/m\({}^{3}\)]** & **[Ba/m\({}^{3}\)]** & **[Ba/m\({}^{3}\)]** & **[Ba/m\({}^{3}\)]** \\ \hline
2 & 774 & 725 & 96.5 & 2291 & 2195 & 376 & 1.87 \\
3 & 971 & 911 & 94.8 & 2746 & 2652 & 401 & 1.99 \\
4 & 2521 & 2627 & 101.0 & 5350 & 5249 & 848 & 4.21 \\
5 & 681 & 604 & 96.3 & 2132 & 2036 & 367 & 1.82 \\
6 & 603 & 531 & 95.0 & 2100 & 2005 & 327 & 1.63 \\ \hline \multicolumn{8}{c}{**(B)**} \\ \hline
**ID** & \multirow{2}{*}{**Date**} & \multirow{2}{*}{**Time (UTC)**} & \multirow{2}{*}{**Latitude**} & \multirow{2}{*}{**Longitude**} & \multirow{2}{*}{**Region**} & \multirow{2}{*}{**Depth [km]**} & \multirow{2}{*}{**Magnitude**} \\  & & & & & & & **Type** & **Magnitude** \\ \hline
1 & 22 June 2015 & 04:17:01 & 51.460 & 16.210 & POLAND & 10 & ML & 4.0 \\
2 & 08 July 2015 & 06:53:18 & 51.610 & 16.120 & POLAND & 1 & ML & 4.4 \\
3 & 19 July 2015 & 19:18:04 & 51.570 & 16.110 & POLAND & 1 & ML & 4.1 \\
4 & 29 October 2015 & 02:26:53 & 51.490 & 16.220 & POLAND & 1 & ML & 4.0 \\ \hline \end{tabular}
\end{table} 
Table 1: (**A**) Descriptive statistics of the radon signal dataset recorded from May 2014 to December 2018. (**B**) Information on selected seismic events (based on EMSC database [56]). Figure 4: Raw data from probe SRDN-3 no 2.  
other functions, g(x), h(x)...z(x), which had a direct impact on the phenomenon. The usefulness of the time series was verified using a processing procedure. The first step in processing the time series was to determine the residuals of the signals, whose linear trends had to be identified. The FFT and wavelet analyses of non-stationary series require a special approach [57]. In the analyzed case, removing the linear trend was sufficient. Reduction was required only for the time series of the \({}^{222}\)Rn activity concentration. Due to its characteristics, i.e., a large number of data points and a negligible number of outlier observations, the least squares method was sufficient (Figure 5).