Calculation of the Underground Muon Intensity Crouch Curve from a Parameterization of the Flux at Surface

Utilizing only the vertical muon intensity of the Gaisser parameterization of the muon flux at the surface and propagating this energy spectrum underground according to statistical ionization and radiative energy losses, it is possible to calculate the underground muon intensity Crouch curve. In addition, the primary spectral index of the Gaisser parameterization can be adjusted from $E^{-2.7}$ to $E^{-2.643}$ simply by minimizing the deviation from the Crouch curve. For chemical compositions other than standard rock, the propagation of the spectrum underground can be repeated with a different muon energy loss in the material. The resulting underground muon intensity curve represents a consistent conversion of the Crouch curve to the local rock, fully accounting for the energy dependence of the muon $dE/dx$.