Frequency dependence of long-period t

Multi-phase long-period t * measurements are among the key evidences for the frequency-dependent mantle attenuation factor, Q . However, similarly to Q , poorly constrained variations of Earth’s structure may cause spurious frequency-dependent effects in the observed t *. By using an attenuation-coefficient approach which incorporates measurements of geometric spreading (GS), such effects can be isolated and removed. The results show that the well-known increase of body P -wave t * from ~0.2 s at short periods to ~1–2 s at long periods may be caused by a small and positive bias in the underlying GS, which is measured by a dimensionless parameter γ * ≈ 0.06. Similarly to the nearly constant t * at teleseismic distances, this GS bias is practically range-independent and interpreted as caused by velocity heterogeneity within the crust and uppermost mantle. This bias is accumulated within a relatively thin upper part of the lithosphere and may be closely related to the crustal body-wave GS parameter γ ~ 4–60 mHz reported earlier. After a correction for γ , P-wave t P * becomes equal ~0.18 s at all frequencies. By using conventional dispersion relations, this value also accounts for ~40 % of the dispersion-related delay in long-period travel times. For inner-core attenuation, the attenuation coefficient shows a distinctly different increase with frequency, which is remarkably similar to that of fluid-saturated porous rock. As a general conclusion, after the GS is accounted for, no absorption-band type or frequency-dependent upper-mantle Q is required for explaining the available t * and velocity dispersion observations. The meaning of this Q is also clarified as the frequency-dependent part of the attenuation coefficient. At the same time, physically justified theories of elastic-wave attenuation within the Earth are still needed. These conclusions agree with recent re-interpretations of several surface, body and coda-wave attenuation datasets within a broad range of frequencies.