  To better understand the effect of ice properties on the capabilities of
radio experiments designed to measure ultra-high energy neutrinos (UHEN), we
recently considered the timing and amplitude characteristics of radio-frequency
(RF) signals propagating along multi-kilometer, primarily horizontal
trajectories through cold Polar ice at the South Pole. That analysis indicated
satisfactory agreement with a model of ice birefringence based on c-axis data
culled from the South Pole Ice Core Experiment (SPICE). Here we explore the
geometrically complementary case of signals propagating along primarily
vertical trajectories, using published data from the Askaryan Radio Array (ARA)
experiment, supplemented by a re-analysis of older RICE experimental data. The
timing characteristics of those data are in general agreement with the same
birefringence model. Re-analysis of older RICE data also confirm the
correlation of signal amplitudes reflected from internal-layers with the
direction of ice flow, similar to previous observations made along a traverse
from Dome Fuji to the Antarctic coast. These results have two important
implications for radio-based UHEN experiments: i) owing to birefringence, the
timing characteristics of signals propagating from neutrino-ice interactions,
either vertically or horizontally, to a distant receiver may be used to infer
the distance-to-vertex, which is necessary to estimate the energy of the
progenitor neutrino, ii) the measured reflectivity of internal layers may
result in previously-unanticipated backgrounds to UHEN searches, requiring
significantly more modeling and simulations to estimate.
