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Investigating the frequency dependence of mantle Q by stacking P and PP spectra

Using seismograms from globally distributed, shallow earthquakes between 1988 and 1998, we compute spectra for P arrivals from epicentral distances of 40° to 80° and PP arrivals from 80° to 160°. Selecting records with estimated signal-to-noise ratios greater than 2, we find 17,836 P and 14,721 PP spectra. We correct each spectrum for the known instrument response and for an ω−2 source model that accounts for varying event sizes. Next, we stack the logarithms of the P and PP spectra in bins of similar source-receiver range. The stacked log spectra, denoted as log(DP′) and log(DPP′), appear stable between about 0.16 and 0.86 Hz, with noise and/or bias affecting the results at higher frequencies. Assuming that source spectral differences are randomly distributed, then for shallow events, when the PP range is twice the P range, the average residual source spectrum may be estimated as 2 log(DP′)–log(DPP′), and the average P wave attenuation spectrum may be estimated as log(DPP′) – log(DP′). The residual source spectral estimates exhibit a smooth additional falloff as ω−0.15±0.05 between 0.16 and 0.86 Hz, indicating that ω−2.15±0.05 is an appropriate average source model for shallow events. The attenuation spectra show little distance dependence over this band and have a P wave t¯* value of ∼0.5 s. We use t¯* measurements from individual P and PP spectra to invert for a frequency-independent Q model and find that the upper mantle is nearly 5 times as attenuating as the lower mantle. Frequency dependence in Qα is difficult to resolve directly in these data but, as previous researchers have noted, is required to reconcile these values with long-period Q estimates. Using Q model QL6 [Durek and Ekstrom, 1996] as a long-period constraint, we experiment with fitting our stacked log spectra with an absorption band model. We find that the upper corner frequency f2 in the absorption band must be depth-dependent to account for the lack of a strong distance dependence in our observed t¯* values. In particular, our results indicate that f2 is higher in the top 220 km of the mantle than at greater depths; the lower layer is about twice as attenuating at 1 Hz than at 0.1 Hz, whereas the upper mantle attenuation is relatively constant across this band.