UHE and EHE neutrino induced taus inside the Earth

Tau neutrinos interacting inside the Earth produce $\tau$ leptons which thereafter can decay inside the atmosphere. The propagation of extremely energetic \nut's and $\tau$'s through the Earth is studied by means of a detailed Monte Carlo simulation, taking into account all major mechanisms of \nut interactions and $\tau$ energy loss as well as decay modes. The rates of $\tau$'s emerging from the Earth are determined as a function of $\tau$'s energy for several cosmic neutrino models.