Though the exact relationship between temperature and seismic attenuation has not been defined, the thermal regime of geothermal systems exhibit high seismic attenuation. The attenuation of a seismic wave is proportional to Q-1, the reciprocal of the quality factor. The reduced spectral ratio technique has been used to infer Q structure. This technique is adapated to study a geothermal system. A generalized discrete linear inversion technique is applied to the observed differential attenuation data Δt* of teleseismic P waves to obtain a discrete Q model. Errors have a large effect on the Q model in a local area. Five sources of errors are involved in the estimation of Δt*. Four levels of random errors are added to synthetic data for eight different assumed models, using 12 events and 11 stations. These data are inverted to assess the effect of the observation errors on the inferred Q structures. For signal to error ratio (S/E) above 5 the models are reproducible; between 5 and 1 a dramatic degradation of fidelity occurs; and at 1 or below, numerous low Q cells are identified as high Q and vice versa. Acquisition of more numerous, better distributed data with lower error improves the quality of the inversion. A two-dimensional Q model of the Geysers-Clear Lake geothermal area is obtained using previously reported attenuation data of six teleseismic events with S/E of 4. A high-attenuation (low Q) zone is found located in the middle crust centered southeast of Mount Hannah, roughly corroborating the gravity and P wave travel time residual models.