  Using data collected by the Askaryan Radio Array (ARA) experiment at the
South Pole, we have used long-baseline propagation of radio-frequency signals
to extract information on the radio-frequency index-of-refraction in South
Polar ice. Owing to the increasing ice density over the upper 150--200 meters,
rays are observed along two, nearly parallel paths, one of which is direct and
a second which refracts through an inflection point, with differences in both
arrival time and arrival angle that can be used to constrain the neutrino
properties. We also observe indications, for the first time, of radio-frequency
ice birefringence for signals propagating along predominantly horizontal
trajectories, corresponding to an asymmetry of order 0.1% between the ordinary
and extra-ordinary paths, numerically compatible with previous measurements of
birefringent asymmetries for vertically-propagating radio-frequency signals at
South Pole. Taken together, these effects offer the possibility of redundantly
measuring the range from receiver to a neutrino interaction in Antarctic ice,
if receiver antennas are deployed at shallow (25 m<z<100 m) depths. Such range
information is essential in determining both the neutrino energy, as well as
the incident neutrino direction.
