A model, suggested by tbe ray expansion of Roever et al., is constructed to rapidly generate the compressional and shear refracted arrivals, known as head waves, received from a point source on the axis of an ideal fluid-filled borehole. An impulse response is derived, and its frequency characteristics are investigated. The waves are compared to those obtained by the real axis integration method of Tsang and Rader, which results in a complete waveform, including the modes as well as the refracted arrivals. The ray model gives accurate results for the compressional head wave. The shear region of the complete waveform contains strong modal interference, making it difficult to evaluate the quality of the ray model shear wave. A useful filter results from insight provided by the basic structure of the model. This filter can be used to estimate the borehole diameter or formation compressional velocity. It can also remove the second and later compressional arrivals, thus providing an accurate estimate of the source pulse and and a relatively uncorrupted vie of the initial arrival in the shear region.