The Large Volume Detector, hosted in the INFN Laboratori Nazionali del Gran Sasso, is triggered by atmospheric muons at a rate of $\sim 0.1\mathrm{Hz}$. The data collected over almost a quarter of a century are used to study the muon intensity underground. The $5\times {10}^7$ muon series, the longest ever exploited by an underground instrument, allows for the accurate long-term monitoring of the muon intensity underground. This is relevant as a study of the background in the Gran Sasso Laboratory, which hosts a variety of long-duration, low-background detectors. We describe the procedure to select muon-like events as well as the method used to compute the exposure. We report the value of the average muon flux measured from 1994 to 2017: $I_{\mu }^0=3.35\pm 0.0005^{\text{stat}}\pm 0.03^{\text{sys}}\times 10^{-4}{\mathrm{m}}^{-2}{\mathrm{s}}^{-1}$. We show that the intensity is modulated around this average value due to temperature variations in the stratosphere. We quantify such a correlation by using temperature data from the European Center for Medium-range Weather Forecasts: we find an effective temperature coefficient ${\alpha }_T=0.94\pm 0.01^{\mathrm{stat}}\pm 0.01^{\mathrm{sys}}$, in agreement with other measurements at the same depth. We scrutinize the spectral content of the time series of the muon intensity by means of the Lomb-Scargle analysis. This yields the evidence of a 1-year periodicity, as well as the indication of others, both shorter and longer, suggesting that the series is not a pure sinusoidal wave. Consequently, and for the first time, we characterize the observed modulation in terms of amplitude and position of the maximum and minimum on a year-by-year basis.

• Received 25 March 2019

DOI:https://doi.org/10.1103/PhysRevD.100.062002