Atmospheric muon flux at sea level, underground, and underwater

The vertical sea-level muon spectrum at energies above 1 GeV and the muon intensities at depths up to 18 km w.e. in different rocks and in water are calculated. The results are particularly collated with a great body of the ground-level, underground, and underwater muon data. In the hadron-cascade calculations, we take into account the logarithmic growth with energy of inelastic cross sections and pion, kaon, and nucleon generation in pion-nucleus collisions. For evaluating the prompt-muon contribution to the muon flux, we apply the two phenomenological approaches to the charm production problem: the recombination quark-parton model and the quark-gluon string model. To solve the muon transport equation at large depths of a homogeneous medium, we used a semianalytical method, which allows the inclusion of an arbitrary (decreasing) muon spectrum at the medium boundary and real energy dependence of both continuous and discrete muon energy losses. The method is checked for accuracy by direct Monte Carlo calculation. Whenever possible, we give simple fitting formulas describing our numerical results.