Crustal refraction data from the Peace River region of Alberta, Canada, have been analyzed using the spectral ratio method to obtain Q. A total of 1205 first and later arrivals corresponding to turning and reflected P-waves within the crust and upper mantle were studied. Source spectra were estimated from near-offset traces assuming typical sedimentary Q values. The large scatter of measured spectral ratios restricted the resolution to a three-layer model of the crust and upper mantle with Q constant in each layer. This model was obtained using a linear inverse method since the measured spectral ratios and known traveltimes in each layer are linearly related through the attentuation (Q−1) in each layer. A weighted L1 norm was minimized using linear programming, the weights being a measure of the certainty of each spectral ratio. The inversion was performed using the 25% most certain spectral ratios, regardless of magnitude or sign. Model bounds taking account of the scattered data were estimated. The results suggest that Q is between 200 and 500 in the upper crust and greater than 600 in the lower crust and upper mantle. This model is generally consistent with Q obtained from studies on nearby crust.