In asymptotic ray theory, the solution for particle motion is assumed to be an infinite power series of inverse frequency and a vector amplitude, Ān(x, y, z), independent of frequency. A point source with any desired impulse response and radiation pattern is easily incorporated. A synthetic seismogram computer program has been written for a plane-layered homogeneous elastic media using the first or second terms of the expansion where necessary. Multiply converted refracted and reflected phases and also head waves at distances away from the critical angle are included. In addition, the phases are all identified and their amplitude-distance function plotted if desired. The synthetic seismograms are calculated for a model in southern Alberta and another in northwestern Ontario as obtained by deep seismic sounding programs. It is found that reflected phases dominate the seismograms and they are at least as important as head waves in the interpretation of experimental results.