  We calculate the Doppler broadening of the $W^-$ resonance produced in
$\bar{\nu}_e e^-$ collisions of cosmic anti-neutrinos with $E_{\nu}\approx 6.3
\ PeV$ with electrons in atoms up to Iron. Revisiting this issue is prompted by
recent observations of PeV neutrinos by Ice-Cube. Despite its poor energy
resolution, the $20\%$ Doppler broadening of the resonance due to electronic
motions can produce observable effects via non-linear neutrino absorption near
the resonance. The attendant suppression of the peak cross section allows
$\bar{\nu}_e$ to travel correspondingly longer distances. While this effect is
unlikely to be directly detected in the near future, it may facilitate
terrestrial tomography at depths of $\sim 10 \ km$, complementing deeper
explorations using the more frequent nuclear interactions at lower energies.
