  The vertical sea-level muon spectrum at energies above 1 GeV and the
underground/underwater muon intensities at depths up to 18 km w.e. 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, the growth with energy of inelastic cross sections and pion,
kaon, and nucleon generation in pion-nucleus collisions are taken into account.
For evaluating the prompt muon contribution to the muon flux, we apply 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 homogeneous medium, a semi-analytical
method is used. The simple fitting formulas describing our numerical results
are given. Our analysis shows that, at depths up to 6-7 km w. e., essentially
all underground data on the muon intensity correlate with each other and with
predicted depth-intensity relation for conventional muons to within 10%.
However, the high-energy sea-level data as well as the data at large depths are
contradictory and cannot be quantitatively decribed by a single nuclear-cascade
model.
