Teleseismic sS and sScS waveforms provide constraints on the attenuation structure above deep seismic zones. We estimate the average Q&bgr; along sS and sScS paths beneath the Lau back arc by comparison wtih S and ScS waveforms. Q is determined using both time and frequency domain analyses of transverse long period records assuming Q is frequency independent. In the frequency domain technique, spectra from reflected (sS or sScS) and direct (S or ScS) waveforms are analyzed using least squares. The time domain method uses a grid search to determine the attenuation operator that, when convolved with the direct phase, produces the best fit to the reflected phase. In both methods the direct phase is convolved with a crustal response function to simulate the crystal interaction of the reflected phase. Large events subject to source directivity effects and source-station combinations involving ray propagation down the subducting slab are not used. The resulting attenuation estimates show low Q values which increase with focal depth, suggesting high attenuation in the upper mantle and a rapid decrease in attenuation below 200--300 km. Lateral variations are also indicated with very high attenuation (Q~20--35) in the upper mantle near the active spreading centers and lower attenuation west of the Lau Ridge. Q-temperature relationships extrapolated from laboratory experiments suggest that the low Q regions represent zones of asthenospheric partial melting. ¿ American Geophysical Union 1990