  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.
