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SUMMARY Knowledge of attenuation structure is important for understanding subsurface material properties. We have developed a double-difference seismic attenuation (DDQ) tomography method for high-resolution imaging of 3-D attenuation structure. Our method includes two main elements, the inversion of event-pair differential ${t^*}$ ($d{t^*}$) data and 3-D attenuation tomography with the $d{t^*}$ data. We developed a new spectral ratio method that jointly inverts spectral ratio data from pairs of events observed at a common set of stations to determine the $d{t^*}$ data. The spectral ratio method cancels out instrument and site response terms, resulting in more accurate $d{t^*}$ data compared to absolute ${t^*}$ from traditional methods using individual spectra. Synthetic tests show that the inversion of $d{t^*}$ data using our spectral ratio method is robust to the choice of source model and a moderate degree of noise. We modified an existing velocity tomography code so that it can invert $d{t^*}$ data for 3-D attenuation structure. We applied the new method to The Geyser geothermal field, California, which has vapour-dominated reservoirs and a long history of water injection. A new Qp model at The Geysers is determined using P-wave data of earthquakes in 2011, using our updated earthquake locations and Vp model. By taking advantage of more accurate $d{t^*}$ data and the cancellation of model uncertainties along the common paths outside of the source region, the DDQ tomography method achieves higher resolution, especially in the earthquake source regions, compared to the standard tomography method using ${t^*}$ data. This is validated by both the real and synthetic data tests. Our Qp and Vp models show consistent variations in a normal temperature reservoir that can be explained by variations in fracturing, permeability and fluid saturation and/or steam pressure. A prominent low-Qp and Vp zone associated with very active seismicity is imaged within a high temperature reservoir at depths below 2 km. This anomalous zone is likely partially saturated with injected fluids.