## 1. Introduction

[2] The frequency dependence of seismic wave attenuation is often ignored in seismological studies of attenuation (for review see *Romanowicz and Durek* [2000]), but it is important for several reasons. First, most laboratory attenuation studies show power-law dependence *Q**f*^{α} (*f*: frequency) with α = 0.2–0.4 for most solid materials [e.g., *Jackson*, 2000]. If indeed *Q* depends on frequency, then *Q* estimation from a broad range of frequency should incorporate the frequency dependence of *Q*. Second, the frequency dependence of *Q* in partially molten peridotites appears to be different from that in solid olivine [*Jackson et al.*, 2004; *Faul et al.*, 2004]. Therefore the presence of partial melt could be detected through the frequency dependence of *Q*. Third, recent studies suggest a close connection between *Q* and long term rheology [e.g., *Karato and Spetzler*, 1990; *Jackson*, 2000] but the exact relation depends on the frequency dependence of *Q* (*Q* ∝ η^{β}, β ∝ α). Therefore one needs to know the frequency dependence of *Q* to convert seismic measurements to the long term viscosity.

[3] Most previous studies of frequency dependent seismic wave attenuation rely on differences in attenuation estimated from several discrete frequency bands [e.g., *Sipkin and Jordan*, 1979; *Flanagan and Wiens*, 1998]. However, because widely separated frequency bands were used, the frequency dependence of attenuation within the gaps is unconstrained. To verify a power-law model for *Q*, we need spectrum estimates over a continuous frequency band.

[4] Two previous studies on frequency dependent *Q* have used continuous spectrum estimates. *Ulug and Berckhemer* [1984] used a *S*–*P* spectral ratio method in the frequency range 0.03–1.5 Hz. They proposed an absorption band model with a power-law *Q* ∝ *f*^{α} with an exponent 0.25 < α < 0.6 in the frequency range up to 1 Hz. *Cheng and Kennett* [2002] also used the *S*–*P* spectral ratios to obtain a power-law with an exponent of 0.2 < α < 1.0 in the frequency range up to 6.0 Hz. Their results suggest significant spatial variation of the frequency dependence. For both these studies, the upper range of possible α is inconsistent with laboratory experimental results [e.g., *Berckhemer et al.*, 1982; *Jackson et al.*, 2002] in the frequency range 10^{−4}–30 Hz. Also, there is no evidence from the laboratory studies for a change of the frequency dependence within the measured frequency range. The *S*–*P* spectral ratio used in the previous two studies is potentially powerful, however in the data set we report in this paper, the *S*–*P* spectral ratio can be biased at higher frequency (>2.5–3.0 Hz) due to the persistence of *P* coda energy in the *S* wave arrival window. Although the bias threshold (2.5–3.0 Hz in our case) should change from site to site, large values of α (α > 0.6) in *Ulug and Berckhemer* [1984] and *Cheng and Kennett* [2002] might come from the contamination of the *P* coda energy.

[5] The aim of this study is to determine the frequency dependence of *Q* using a more reliable continuous spectrum estimate over a broader frequency band to better understand the physical mechanism of *Q* in Earth's upper mantle.