The Vadas-Fritts ray-tracing model for convectively generated gravity waves is analyzed using the stationary phase approximation and is interpreted in terms of a ray Jacobian approximated by the density of rays. The Vadas-Fritts model launches rays from the convective source region, with initial conditions for the ray-tracing deduced from a near-field integral representation. In the far-field the rays are binned in space-time grid cells. The contribution of each ray to the spatial wave amplitude is determined by its spectral amplitude and by the local density of rays within the grid cells. The present analysis accomplishes two things. First, the stationary phase analysis gives the formal initial conditions for the ray-tracing, which mostly agree with the Vadas-Fritts initialization but also suggest some refinements. Secondly, the Jacobian and ray-density analysis shows how the Vadas-Fritts model can be generalized to follow a beam of rays with a single moving grid cell.