Determining Q in near-surface sedimentary rocks is important both for earthquake seismology and hydrocarbon exploration. Measurements can be performed in the laboratory or in situ. We present an in situ estimation of the relation between QS and QP in a 1.4-km-thick Tertiary sedimentary basin in the Gazli region, Uzbekistan, USSR, using the spectral ratio method. The data consist of three-component accelerograms from aftershocks of the 19 March 1984 MS = 7.0 Gazli earthquake. Theoretically, the spectral ratio between a low-frequency direct S phase and a high-frequency S-to-P converted phase from the basin / basement interface should fit a straight line in log-amplitude-frequency space. The slope of this straight line yields a relation between the average apparent QS and QP for the sedimentary section. Results for stations with well-constrained spectral ratio slopes give a QS between 10 and 25 for QP between 10 and 70. Those with smaller, poorly constrained slopes give relations with a higher QS / QP ratio. These relations are compared with laboratory and in situ measurements of QS and QP and some theoretical relations. Effects of scattering on the apparent Q values are also considered. The well-constrained relations are consistent with a theoretical QP-QS relation with QS = 20 to 25 for QP = 50 to 70, with laboratory measurements on either dry or fully saturated rocks, and some in situ measurements. The poorly constrained relations are incompatible with any theoretical relation or in situ measurement. The poor fit and large QS / QP ratio are attributed to near-surface, frequency-dependent amplification effects.