We used shear waves, generated by an air-powered source at the ground surface and recorded in a borehole, to estimate the shear-wave quality factor at strong-motion station Gilroy no. 2. We find similar values of Q using both the decay of the spectra with depth and the slope of the spectral ratio at two depths; we find no evidence of a frequency dependence of Q. The mean value of Q over the depth range 10 to 115 m is close to 10. The use of this value over the depth of the borehole and the observed travel time of 0.358 sec gives a cumulative attenuation factor t* of 0.036 sec for the upper 180 m of the Quaternary alluvium. This is comparable to the differential decay between Gilroy no. 2 and a rock site 1.9 km away (Gilroy no. 1), as measured from the decay of the high-frequency spectra of accelerograms from large earthquakes, plotted on a log-linear scale: t* = 0.05, 0.04, and 0.03 sec for the 1979 Coyote Lake, 1984 Morgan Hill, and 1989 Loma Prieta earthquakes, respectively. The similarity between the attenuations measured from the low-strain surface source and those from the larger amplitude earthquake sources suggests that increases of damping due to nonlinear wave propagation effects are limited.