The Large Aperture Seismic Array in eastern Montana was used to measure the travel times and dT/dΔ of earthquake-generated shear waves for the purpose of determining lower-mantle shear velocities. The data were limited to epicentral distances between 27 and 95 degrees. To convert uncertainties in the dT/dΔ measurements to uncertainties in the computed velocities, the data were inverted by a Monte Carlo procedure. The computer randomly generated velocity models, and those which satisfied prescribed travel time and dT/dΔ-versus-Δ limits were considered as possible models for the real earth. The dT/dΔ curve possessed anomalously steep slopes between 27-30 and 65-75 degrees, and the corresponding velocity models had increased gradients between the approximate depths of 700-800 and 1550-2100 kilometers. The slope of the dT/dΔ curve also decreased at about 88 degrees which may indicate a decrease in velocity gradient several hundred kilometers above the core-mantle boundary. For epicentral distances greater than 27 degrees the observed travel times to LASA were greater than the expected J-B times. Although vague, a systematic increase in the observed residuals appeared to exist between 40 and 60 degrees which agreed with the J-B residuals of the computed models.