High energy neutrino detection via radio emission from the interaction vertex is an efficient method for neutrino energies between $10^{16}$ eV and $~10^{20}$ eV. The ARIANNA radio "Askaryan" detectors are located in the Antarctic ice just beneath the surface. Neutrino observation requires that radio pulses propagate to the surface with minimum distortion by the ice and firn medium. Using the residual hole from the South Pole Ice Core Project, radio pulses were sent at 1Hz from a transmitter located up to 1.7km below the snow surface. We quantify the direction reconstruction abilities of ARIANNA and refractive bending of signal trajectories in the firn using radio pulse data from 2018. After deconvolving the raw signals for amplifier and antenna response and correcting for cable delays, the electric fields reveal no significant distortion,e.g. birefringence, due to ice propagation. These studies also suggest that the polarization of the electric field, which is required to measure the direction of the neutrino, is not altered by the natural ice medium to a significant extent.