“…For instance, while the integrated vertical muon flux (0 • from zenith) is 7 × 10 −3 and 5 × 10 −8 cm −2 sr −1 s −1 above 1 GeV and 1 TeV, respectively (Beringer et al, 2012), the horizontal flux (85 • from zenith) is 1 × 10 −4 and 1.6 × 10 −7 cm −2 sr −1 s −1 above 1 GeV and 1 TeV, respectively (Allkofer et al, 1985). For the purpose of interpolating the measured flux, several groups have formulated approximate equations of the muon energy spectrum as a function of energy and zenith angle (e.g., Gaisser, 2002;Matsuno et al, 1984;Smith and Duller, 1959). However, the systematic difference between them ranges from 10 to 100 % (Lesparre et al, 2010).…”