We have calculated ionospheric perturbations produced by gravity waves at high latitudes. It is shown that gravity waves with reasonable parameters can produce strong ionospheric perturbations in the altitude range of 200--400 km. The ionospheric perturbations become weak above 400 km due to the presence of plasma diffusion. If the horizontal perturbation velocity of the neutrals due to gravity waves increases from 20 m/s at 200-km altitude to 30 m/s at 350-km altitude, the amplitude of the relative ionospheric density perturbations is about 30% below 350 km. A ray tracing program has been used to trace the ionospheric ray paths of HF rays passing through the strong periodic density perturbations resulting from the gravity waves. The paths of HF rays manifest some new and important features. Rays with small elevation angles are focused and reflected by the density undulations in the bottomside F region. These rays can undergo ground scattering at the so-called one-hop range. They can also undergo ground reflection and, as such, usually are assumed to be the rays which access scattering regions at larger range by the one-and-a-half hop propagation mode. In this mode the ratio of the ranges of the high-latitude scatter and the ground scatter is about 3/2. However, there is a significant range of larger elevation angles for which the rays may be trapped in the highly perturbed F region. These Pedersen rays can travel large distances before being scattered and the 3/2 range ratio no longer applies. The ray tracing results presented in this paper provide a reasonable explanation of simultaneous ground scatter and auroral scatter observations made by the Saskatoon SuperDARN HF radar. ¿ 1998 American Geophysical Union