## 3 Results and Discussion
### Long-Period Data  
For long-period data, the barometric coefficient \(\beta_{P}\) was established. During investigations, only data collected on the ten most quiet days of every month were used. The list of those days was acquired from the International Quiet Days (IQD) database ([[http://wdc.kugi.kyoto-u.ac.jp/qddays/](http://wdc.kugi.kyoto-u.ac.jp/qddays/)]([http://wdc.kugi.kyoto-u.ac.jp/qddays/](http://wdc.kugi.kyoto-u.ac.jp/qddays/)) accessed on 14 February 2021) [17]. Figure 6a presents relative deviation of the muon count rate \(\frac{\Delta I}{I}\) as a function of pressure deviation \(\Delta\)P. The blue markers represent all data from the period studied, while the red markers represent data recorded only on IQD days. The correlation coefficient between these values and the pressure changes indicates strong negative correlation (\(r_{1,TOP}=-0.75\)). The \(\beta_{P}\) coefficient was determined by a least squares fit, and its value was \(\beta_{P,TOP}=-0.168(2)\) %/hPa. The value was used to correct the data and to eliminate the dependence of the muon flux intensity on the atmospheric pressure using the Equation (2). The obtained results are presented in Figure 6b. The value of the correlation coefficient after data correction \(r_{2,TOP}=-0.08\) confirms a significant reduction in this dependence. In the case of the FRONT detector, analyses were performed to allow an estimate of \(\beta_{P,FRONT}=-0.153(2)\) %/hPa, which reduced the data correlation from \(r_{1,FRONT}=-0.72\) to \(r_{2,FRONT}=0.09\). Figure 4: (**a**) Autocorrelation function of time intervals between events registered at the TOP scintillator. As shown, there is no correlation in the examined series. (**b**) Discrete Fourier transform analysis of the sequence of counts registered by detector TOP in 1 s. No significant periodicities were found. Similar results were obtained for other detectors: BOTTOM, FRONT, REAR and SIDE. Figure 7a shows the normalized intensity of the muon flux registered by the detector TOP before correction for changes in atmospheric pressure (which are depicted in Figure 7b). The pressure corrected data demonstrated in Figure 7c,d for scintillator TOP and FRONT, respectively, show less variability. It should be noted that seasonal variation is still clearly visible; however, seasonal changes do not affect the final results for the analyzed period (20 months). Figure 5: Distribution of 471 coincidence events registered by TOP, BOTTOM, FRONT and REAR detectors. To obtain the data, a Gaussian distribution has been fitted (\(\mu=32\) ns; \(\sigma=12\) ns). Figure 6: Determination of the barometric coefficient for the data recorded by the TOP detector. (**a**) Relative deviation of muon count rate as a function of pressure deviation for all data (blue markers) and for International Quiet Days (IQD) data—red markers. The correlation coefficient between the IQD data and the pressure variations was \(r_{1}=-0.75\). Obtained barometric coefficient \(\beta_{P}=-0.168\) %/hPa. (**b**) Pressure corrected data; correlation coefficient reduced to \(r_{2}=-0.08\). Fast Fourier transform analysis was conducted on the pressure-corrected data, and the obtained results are presented in Figure 8.  
In the case of the TOP detector, the FFT algorithm allowed identification of the diurnal periodicity (24 h) with harmonics components (12 h and 8 h) of muon flux caused by the rotation of the Earth and its relative motion in the solar magnetic field, modulated by solar wind [18,19]. Furthermore, a periodic component with a period of around 27 days was identified. This variability is associated with the effect of the Sun's rotation, causing variations in both intensity of solar wind particles and their speed [18,20]. In addition, a periodicity of about 68 days is noticeable in the frequency spectrum but its origin is unclear. [PERSON] et al. (2016) [21] conducted a frequency analysis of the eight-year time series of muon flux recorded during the MARIACHI experiment.