The seismic shear phase SS is considered as a tool in the reconnaissance of the Earth. The Hibert transform is empirically verified as a reasonable mimic of the distortion incurred at the internal caustic in the propagation of SS. Travel times are obtained by a waveform correlation technique for 26 well-recorded SHSH waves from the 1968 Borrego Mountain earthquake. Significant variation is found in the travel-time residuals for paths reflected under the Canadian shield. A correlation of the variation with tectonic sub-province is suggested. The data are sufficiently precise to indicate lateral heterogeneity of several percent in the upper mantle velocities within the Canadian shield.