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[1] We constrain the spatial variation of P-wave (t_{P}*) and S-wave (t_{S}*) attenuation by inverting 190,000 teleseismic P- and S-wave spectra up to 0.8 Hz. These spectra are derived from 250 deep earthquakes recorded at 880 broadband global and regional network stations. The variance and ratios of t_{P}* and t_{S}* values are consistent with PREM's upper mantle velocity and Q structures and conventional t_{P}* and t_{S}* values. High attenuation is resolved beneath stations in tectonically active regions characterized by high heat flow. Low attenuation marks stable continental regions. The maps of t_{P}* and t_{S}* correlate well with the variations of t_{S}* computed and inferred from (1) the most recent surface-wave Q model and (2) a thermal interpretation of shear-wave velocity tomography. This indicates that maps of body- and surface-wave attenuation reflect intrinsic attenuation and variable temperature in the mantle.

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[2] Models of the elastic velocity structure of the mantle have advanced our knowledge of mantle dynamics [e.g., Romanowicz, 2008], but are by themselves insufficient to obtain complete descriptions of the physical state of Earth's interior. Anelasticity models can provide important complementary information. Anelasticity has a much stronger sensitivity to temperature and water content than elastic velocities, a lower sensitivity to composition and a different sensitivity to melt [e.g., Anderson, 1967; Karato and Jung, 1998; Hammond and Humphreys, 2000; Jackson et al., 2002; Faul et al., 2004; Shito et al., 2006].

[4] The attenuation parameter t* is defined as the ratio between the body-wave traveltime t and the quality factor Q along the (ray) path L [e.g., Stein and Wysession, 2003]:

If we write the spectrum O(ω) as the product of the source spectrum S(ω) and the attenuation function e^{−ωt*/2},

the logarithm of the spectral ratio R_{ij} between O_{i}(ω) and O_{j}(ω),

is linearly related to the difference between the attenuation parameters at stations i and j. Here, Δt_{ij}* = t_{i}* − t_{j}*.

[5] To isolate the influence of intrinsic attenuation on t* from other sources such as crustal amplification, scattering, focusing and defocusing, we use large number of spectral ratio measurements. Our data set comprises 190,000 P- and S-wave spectral ratios from broadband recordings of 250 earthquakes with magnitudes larger than 6. The earthquake focal depths are larger than 200 km to ensure short source-time functions and to avoid interference of the direct P- and S-waves with the surface reflections pP, sP, and sS. We analyze the spectra at teleseismic distances (30°–85°) to avoid waveform complexities from triplication in the transition zone and diffraction along the core-mantle boundary. We select 10–30 s long segments of P-wave and S-wave signals with impulsive onsets, low-amplitude coda, high signal-to-noise ratios, and similar waveforms for the same earthquakes. To minimize the variations of spectra due to varying source azimuths, we measure Δt_{P}* for station pairs that have similar azimuths.

[6] We determine lnR(ω) up to a frequency of 0.8 Hz using the multiple-taper spectral analysis method of Lees and Park [1995]. Δt_{P}* (for P-waves) and Δt_{S}* (for S-waves) and 2σ uncertainties are estimated by linear regression of ln R(ω). We apply a correction using the results of Hwang and Ritsema [2011] to account for the systematic increase of t_{P}* and t_{S}* in the teleseismic distance range by about 0.2 s and 0.7 s, respectively.

[7] Station-specific t_{P}* and t_{S}* values are determined by least-squares inversion of the Δt_{P}* and Δt_{S}* measurements. Since we cannot infer absolute values from spectral ratios, we constrain the mean values of t_{P}* and t_{S}* to be zero. We regularize the inversion by reducing the weight of Δt_{P}* and Δt_{S}* measurements with large 2σ uncertainties and measurements for large inter-station distances. Details of the Δt* measurements and uncertainties are given by Hwang et al. [2009] and Hwang and Ritsema [2011].

3. Results

3.1. Lateral t_{P}* and t_{S}* Variations

[8] Since t_{P}* and t_{S}* are affected by wave scattering and near-surface ‘site-responses', we investigate the average values of t_{P}* and t_{S}* within overlapping circles with radii of 3° (Figures 1a and 1b). The averaging of the data brings out the large-scale patterns of t_{P}* and t_{S}* that reflect global tectonics and that are similar to the global heat flow variations (Figure 1c).

[9] The spatial variations of t_{P}* and t_{S}* are similar and the ratio of t_{P}* and t_{S}* variances (∼4) is consistent with the expected ratio of 4.5 for the upper mantle Q structure of PREM [Dziewonski and Anderson, 1981] and the conventional value of 3.5 for the t_{S}*/t_{P}* ratio [e.g., Cormier, 1982] (Figure 2). This indicates that variations in t_{P}* and t_{S}* do indeed reflect the lateral variation of intrinsic attenuation in the upper mantle.

3.2. Joint Inversion for t_{S}*

[10] In Figure 3a, we show the map of t_{S}* by a joint inversion of Δt_{P}* and Δt_{S}*. To relate the Δt_{P}* data to Δt_{S}* in the upper mantle, we have used

using velocity structures (V_{P} and V_{S}) of PREM and assuming that Δt* is due to laterally varying Q in the upper mantle only and that bulk attenuation is negligible [e.g., Anderson and Given, 1982].

[11]Figure 3a shows the global distribution of t_{S}* in a map that has been smoothed by cap-averaging. High attenuation characterizes tectonically active collision zones, rift zones and back-arc regions, while low attenuation is found below stable continental cores. For example, t_{S}* is relatively high in the tectonically-active western North America and low in the platforms of central and eastern North America. A similar contrast is also apparent in Europe: t_{S}* is higher in western Europe than in the Baltic shield region. Station density is lower in other regions but a pattern consistent with tectonics persists. For example, t_{S}* is low in the East African Rift region and high at stations within the western and southern cratons of Africa. In addition, t_{S}* is high in the back-arc regions of the western Pacific subduction zones.

3.3. Comparison With Seismic Tomography

[12] We compare the map of t_{S}* based on the spectral ratios of P- and S-waves with the t_{S}* variation computed by integrating through two Q models for the upper 400 km of the mantle using (1). In Figure 3b, we show the distribution of t_{S}*, and denote it as t_{Q}*, predicted by the model QRFSI12 [Dalton et al., 2008] for the upper mantle. QRFSI12 is a spherical harmonic degree-12 model of shear attenuation derived using fundamental-mode Rayleigh-wave amplitudes in the long-period range (50–250 s). The data set of Rayleigh-wave amplitudes are corrected for source, instrument, and focusing effects.

[13] In Figure 3c, we show t_{S}*, and denote it as t_{T}*, for the Q structure based on a thermal interpretation of S20RTS [Ritsema et al., 1999] shear-velocity anomalies with respect to the Ocean Reference Model of Ritsema and Allen [2003]. For the conversion from dV_{S} to temperature anomalies we assume that the mantle has a homogeneous pyrolitic composition and that below a PREM lithospheric structure, the average velocity profile corresponds to a mantle adiabat with a potential temperature of 1300°C. Elastic velocities are calculated using a finite-strain approach [Cammarano et al., 2003; Goes et al., 2005] with a correction for anelastic effects using an Arrhenius-type pressure and temperature-dependent Q formulation [Karato, 1993; Goes et al., 2005]: Q_{S}(T, P) = Q_{0} exp{gT_{m}(P)/T}, where T and P are absolute temperature and pressure, respectively, Q_{0} = 0.1ω^{0.15}, g (= 40) is a scaling factor, and T_{m} is the peridotite solidus. The conversion yields temperature, and corresponding V_{P}, density, Q_{S} and Q_{P}. Regional models under North America, Europe and Australia converted in a similar manner yielded temperatures that could reconcile observed V_{P}, V_{S} and surface heat flow [Goes et al., 2000, 2005; Goes and van der Lee, 2002]. The long-wavelength thermal structure inferred from S20RTS has reasonable temperatures varying between 600°C and 1450°C at 100 km depth and 1200–1550°C at 300 km depth (Figure 4).

4. Discussion

[14] There is a remarkable similarity between t_{S}*, t_{Q}*, and t_{T}*. This indicates that surface-wave amplitudes and body-wave spectra are affected by the same long-wavelength variation in attenuation even though the wavelengths and propagation directions of surface-waves and body-waves are entirely different.

[15] The variations in t_{S}* values are larger than the variations in t_{Q}* and t_{T}*. For example, the contrast between western North America and stable North America and between western Europe and the Baltic region is about 0.7 s in t_{S}* but about 0.3 s and 0.5 s for t_{Q}* and t_{T}*, respectively. However, these differences are to be expected given the uncertainties originating from averaging (t_{S}*), the regularization of the inverse problem (t_{Q}*), and uncertainties of the velocity-temperature conversion (t_{T}*).

[16] The correlation between patterns in t_{S}*, surface heat flow, tectonics and shear-velocity anomalies suggest attenuation is largely the result of thermally activated creep. The conclusion that temperature exerts the main control on global Q_{S} and V_{S} structures is consistent with other studies [Artemieva et al., 2004; Dalton et al., 2009; Dalton and Faul, 2010]. Our analyses illustrate that the maps of t_{S}* and t_{Q}* can be explained by variations of intrinsic attenuation consistent with a temperature variation as that depicted in Figure 4.

[17] Other factors such as the presence of melt below mid-ocean ridges and a melt-depleted composition of cratonic roots likely have additional influence [Artemieva et al., 2004; Dalton et al., 2009; Dalton and Faul, 2010]. The back-arc high t_{S}* and t_{Q}* anomalies that coincide with low shear velocities, which we have interpreted as high temperatures, may partially reflect high water content compatible with an interpretation of regional V_{P}, V_{S}, and Q_{P} below the Izu-Bonin arc [Shito et al., 2006]. To better distinguish between different mechanisms requires an imaging of t_{S}*, t_{P}*, and seismic velocities at more similar resolution and scale than the models we compared here.

5. Conclusions

[18] New maps of t_{P}* and t_{S}*, derived from 190,000 teleseismic, global P-wave and S-wave spectra, exhibit a coherent large-scale spatial variation that is consistent with heat flow and tectonic variations. The ratio of t_{S}* to t_{P}* is consistent with the PREM ratio of 4.5 and the conventional t_{S}* to t_{P}* ratio of 3.5. Moreover, a joint inversion of the P-wave and S-wave spectral ratios yields lateral variation of t_{S}* that is similar to the predicted t_{S}* variation for a recent surface-wave Q model (t_{Q}*) of the upper mantle and a thermal interpretation of shear-velocity anomalies in the upper mantle (t_{T}*). Combined these observations indicate that the large-scale pattern in t_{P}* and t_{S}* reflects variations in intrinsic shear attenuation.

[19] The high correlation between t_{S}* and t_{Q}* indicates that coherent patterns of attenuation can be constrained from large data sets of horizontally and vertically propagating waves. The similarity between t_{S}*, t_{Q}*, and t_{T}* suggests that the patterns of Figure 3 predominantly reflects variable attenuation in the upper few hundred kilometers of the mantle. The patterns are consistent with a thermal structure of the mantle as inferred from shear velocity anomalies.

Acknowledgments

[20] We thank the two anonymous reviewers for their constructive comments. This research was funded by NSF grant EAR–0944167. Data were provided by the IRIS/DMC.

[21] The Editor thanks the two anonymous reviewers for their assistance in evaluating this paper.