Measurements and Modeling of Near-Surface Radio Propagation in Glacial Ice and Implications for Neutrino Experiments

We present measurements of radio transmission in the $\sim$100 MHz range through a $\sim100$ m deep region below the surface of the ice at Summit Station, Greenland, called the firn. In the firn, the index of refraction changes due to the transition from snow at the surface to glacial ice below, affecting the propagation of radio signals in that region. We compare our observations to a finite-difference time-domain (FDTD) electromagnetic wave simulation, which supports the existence of three classes of propagation: a bulk propagation ray-bending mode that leads to so-called "shadowed" regions for certain geometries of transmission, a surface-wave mode induced by the ice/air interface, and an arbitrary-depth horizontal propagation mode that requires perturbations from a smooth density gradient. In the non-shadowed region, our measurements are consistent with the bulk propagation ray-bending mode both in timing and in amplitude. We also observe signals in the shadowed region, in conflict with a bulk-propagation-only ray-bending model, but consistent with FDTD simulations using a variety of firn models for Summit Station. The amplitude and timing of our measurements in all geometries are consistent with the predictions from FDTD simulations. In the shadowed region, the amplitude of the observed signals is consistent with a best-fit coupling fraction value of $2.4$% (0.06% in power) or less to a surface or horizontal propagation mode from the bulk propagation mode. The relative amplitude of observable signals in the two regions is important for experiments that aim to detect radio emission from astrophysical high-energy neutrinos interacting in glacial ice, which rely on a radio propagation model to inform simulations and perform event reconstruction.