Generalized ray expansions of the P, SH, and SV displacement potentials resulting from a point-source dislocation are evaluated at the surface of a layered half-space. The Cagniard-de Hoop technique is used to obtain the transient response. The results of this analysis are used to construct synthetic seismograms for a shear dislocation on a vertical fault plane. Comparisons of synthetic and observed seismograms for the Borrego Mountain earthquake (April 9, 1968) at teleseismic distances indicate an equivalent point-source depth of 9 km with the far-field time function approximated by a step function with an exponential decay. This time function fits both the P and S wave forms. The apparent shift in corner frequency between the P and S waves for shallow events, as reported by some investigators, is explained by surface reflections.