We present a technique that greatly improves the precision in measuring temporal variations of crustal velocities using an earthquake doublet, or pair of microearthquakes that have nearly identical waveforms and the same hypocenter and magnitude but occur on different dates. We compute differences in arrival times between seismograms recorded at the same station in the frequency domain by cross correlation of short windows of signal. A moving-window analysis of the entire seismograms, including the coda, gives Δ(t), the difference in arrival times versus running time along the seismogram. The time resolution of the method is an order of magnitude better than the digitization interval. The Δ(t) technique is illustrated with a pair of microearthquakes, M=1.7 and 2.0, that occurred before and after the Coyote Lake, California, earthquake (M=5.9) of August 6, 1979, and on the same segment of the Calaveras fault that ruptured during the earthquake. The coda wave arrivals for some stations are progressively delayed for the second earthquake in the doublet, so that its seismogram appears as a stretched version of the earlier event. We interpret this systematic variation in Δ(t) along the coda as a change in the average S velocity in the upper crust in the time interval between the two doublets. S wave velocities appear to have decreased by 0.2% in an oblong region 5--10 km in radius at the south end of the aftershock zone.