The parameter t* (ratio of body wave travel time to the average quality factor Q) was estimated under various assumptions of the nature of the earthquake sources for short-period P, PcP, and ScP phases originating from earthquakes in the Fiji-Tonga region and recorded at the Warramunga Seismic Array at Tennant Creek (Northern Territory, Australia). Spectral ratios were calculated for the amplitudes of PcP to P and of pP to P. The data reveal a laterally varying Q structure in the Fiji-Tonga region. The high-Q lithosphere descending beneath the Tonga Island arc is overlain above 350 km depth by a wedgelike zone of high attenuation with an average Qα between 120 and 200 at short periods. The upper mantle farther to the west of the Tonga island arc is less attenuating, with Qα, between 370 and 560. Qα is about 500 in the upper mantle on the oceanic side of the subduction zone. The t* estimates of this study are much smaller than estimates from the free oscillation model SL8. This can be partly explained by regional variations of Q in the upper mantle. If no lateral Q variations occur in the lower mantle, a frequency-dependent Q can make the PcP and ScP observations consistent with model SL8. Adopting the absorption band model to describe the frequency dependence of Q, the parameter &tgr;2, the cut-off period of the high-frequency end of the absorption band, was determined. For different source models with finite corner frequencies, the average &tgr;2 for the mantle is between 0.01 and 0.10 s (corresponding to frequencies between 16 and 1.6 Hz) as derived from the PcP data, and between 0.06 and 0.12 s (2.7 and 1.3 Hz), as derived from the ScP data.