We have estimated a 1-D permittivity model from a 100m long variable offset GPR in the West Antarctic ice sheet. That model inherits the inaccuracies in depth from the velocity model, which should be corrected before attempting to correlate it with the density log from a close-by borehole. We performed that correction by aligning a synthetic ice density derived from a Maxwell Garnett two-phase mixture model to the ice core density measurements through dynamic time warping. The shifts to bring the permittivity estimates to their proper depths suggest a direct correlation of radar-derived data to borehole depths may suffer from noise to an unknown degree. The present methodology is within reach of a standard GPR survey, having at least one variable offset gather.