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The Large Volume Detector (LVD), hosted in the INFN Laboratori Nazionali delGran Sasso, is triggered by atmospheric muons at a rate of $\sim 0.1$~Hz. Thedata collected over almost a quarter of century are used to study the muonintensity underground. The 50-million muon series, the longest ever exploitedby an underground instrument, allows for the accurate long-term monitoring ofthe muon intensity underground. This is relevant as a study of the backgroundin the Gran Sasso Laboratory, which hosts a variety of long-duration,low-background detectors. We describe the procedure to select muon-like eventsas well as the method used to compute the exposure. We report the value of theaverage muon flux measured from 1994 to 2017: $\mathrm{I_{\mu}^0 = 3.35 \pm0.0005^{stat}\pm 0.03^{sys} \cdot 10^{-4} ~m^{-2} s^{-1}}$. We show that theintensity is modulated around this average value due to temperature variationsin the stratosphere. We quantify such a correlation by using temperature datafrom the European Center for Medium-range Weather Forecasts: we find aneffective temperature coefficient $\mathrm{\alpha_{T}} = 0.94\pm0.01^{stat}\pm0.01^{sys}$, in agreement with other measurements at the same depth. Wescrutinise the spectral content of the time series of the muon intensity bymeans of the Lomb-Scargle analysis. This yields the evidence of a 1-yearperiodicity, as well as the indication of others, both shorter and longer,suggesting that the series is not a pure sinusoidal wave. Consequently, and forthe first time, we characterise the observed modulation in terms of amplitudeand position of maximum and minimum on a year-by-year basis.

Characterization of the varying flux of atmospheric muons measured with the Large Volume Detector for 24 years