The atmospheric muon and neutrino fluxes at energies from 10 GeV to 10 PeV are calculated with the Kimel–Mokhov (KM), SIBYLL 2.1, EPOS LHC, and QGSJET-II hadronic models for known parameterizations of the cosmic ray spectra by Zatsepin--Sokolskaya and Hillas–Gaisser. The calculations with the KM, EPOS LHC, and SIBYLL 2.1 models are agree well with the measurements of the atmospheric muon spectra in IceCube and IceTop experiments. The measurement of high-energy muon spectra indicates the presence of the prompt muon component at energies above 500 TeV, which is well reproduced in calculations with the quark-gluon string model. The calculations of the atmospheric muon neutrino spectrum performed for the KM, EPOS LHC, and SIBYLL 2.1 models give good fit with the measurement data of IceCube, ANTARES, and Super-Kamiokande experiments.
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