Global variation of body-wave attenuation in the upper mantle from teleseismic P wave and S wave spectra



[1] We constrain the spatial variation of P-wave (tP*) and S-wave (tS*) 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 tP* and tS* values are consistent with PREM's upper mantle velocity and Q structures and conventional tP* and tS* 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 tP* and tS* correlate well with the variations of tS* 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.

1. Introduction

[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].

[3] A number of studies have mapped the global variation of seismic wave attenuation in the upper mantle using surface waves [e.g., Romanowicz, 1995; Billien et al., 2000; Gung and Romanowicz, 2004; Selby and Woodhouse, 2002; Dalton and Ekström, 2006; Dalton et al., 2008] and body waves [e.g., Bhattacharyya et al., 1996; Reid et al., 2001; Warren and Shearer, 2002; Lawrence and Wysession, 2006]. Here we add a new estimate of attenuation in the upper mantle from teleseismic P-wave and S-wave spectra. Using globally distributed stations, we invert ratios of body-wave spectra for the P-wave and S-wave attenuation parameters tP* and tS*. We compare our maps of tP* and tS* to surface-wave Q tomography and attenuation maps inferred from a thermal interpretation of shear-velocity tomography.

2. Spectral Analysis of P and S Waves

[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]:

equation image

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

equation image

the logarithm of the spectral ratio Rij between Oi(ω) and Oj(ω),

equation image

is linearly related to the difference between the attenuation parameters at stations i and j. Here, Δtij* = ti* − tj*.

[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 ΔtP* 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]. ΔtP* (for P-waves) and ΔtS* (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 tP* and tS* in the teleseismic distance range by about 0.2 s and 0.7 s, respectively.

[7] Station-specific tP* and tS* values are determined by least-squares inversion of the ΔtP* and ΔtS* measurements. Since we cannot infer absolute values from spectral ratios, we constrain the mean values of tP* and tS* to be zero. We regularize the inversion by reducing the weight of ΔtP* and ΔtS* 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 tP* and tS* Variations

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

Figure 1.

Spatial variations of (a) tS* and (b) tP* in the upper mantle. The tS* and tP* values have been averaged using overlapping caps with radii of 3°. Note that variations in tS* and tP* are similar. (c) Global heat flow distribution according to Pollack et al. [1993].

[9] The spatial variations of tP* and tS* are similar and the ratio of tP* and tS* 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 tS*/tP* ratio [e.g., Cormier, 1982] (Figure 2). This indicates that variations in tP* and tS* do indeed reflect the lateral variation of intrinsic attenuation in the upper mantle.

Figure 2.

The correlation of tS* versus tP* after correction for epicentral distance. The solid line represents tS* = 4.5tP* as predicted by the PREM velocity and Q structures and the dashed line represents tS* = 3.5tP*, the ratio for conventional tS* to tP* ratio values reviewed by Cormier [1982].

3.2. Joint Inversion for tS*

[10] In Figure 3a, we show the map of tS* by a joint inversion of ΔtP* and ΔtS*. To relate the ΔtP* data to ΔtS* in the upper mantle, we have used

equation image

using velocity structures (VP and VS) 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].

Figure 3.

Spatial variation of tS* in the upper mantle estimated (a) by joint inversion of ΔtP* and ΔtS*, (b) from the surface-wave Q model of Dalton et al. [2008] (tQ*), and (c) from the thermal interpretation of S20RTS (tT*). The correlation coefficient between tS* (Figure 3a) and tQ* (Figure 3b) and between tS* (Figure 3a) and tT* (Figure 3c) are about 0.3.

[11] Figure 3a shows the global distribution of tS* 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, tS* 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: tS* 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, tS* is low in the East African Rift region and high at stations within the western and southern cratons of Africa. In addition, tS* 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 tS* based on the spectral ratios of P- and S-waves with the tS* 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 tS*, and denote it as tQ*, 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 tS*, and denote it as tT*, 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 dVS 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]: QS(T, P) = Q0 exp{gTm(P)/T}, where T and P are absolute temperature and pressure, respectively, Q0 = 0.1ω0.15, g (= 40) is a scaling factor, and Tm is the peridotite solidus. The conversion yields temperature, and corresponding VP, density, QS and QP. Regional models under North America, Europe and Australia converted in a similar manner yielded temperatures that could reconcile observed VP, VS 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).

Figure 4.

Temperatures at depths of (top) 100 km and (bottom) 300 km inferred from S20RTS [Ritsema et al., 1999] using the conversion of Goes et al. [2005]. The temperatures at 100 km reflect surface tectonics. The temperature is relatively low beneath old, stable cratons and relatively high below mid-ocean ridges. The high temperatures behind circum-Pacific subduction zones are likely biased high by high water content in the mantle wedge. At 300 km depth, a weak thermal imprint persists below the base of the cratonic roots, while relatively hot regions have largely lost their correlation with ridge geometry. Narrow subducting slabs are not resolved in this long-wavelength model.

4. Discussion

[14] There is a remarkable similarity between tS*, tQ*, and tT*. 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 tS* values are larger than the variations in tQ* and tT*. 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 tS* but about 0.3 s and 0.5 s for tQ* and tT*, respectively. However, these differences are to be expected given the uncertainties originating from averaging (tS*), the regularization of the inverse problem (tQ*), and uncertainties of the velocity-temperature conversion (tT*).

[16] The correlation between patterns in tS*, 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 QS and VS 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 tS* and tQ* 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 tS* and tQ* 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 VP, VS, and QP below the Izu-Bonin arc [Shito et al., 2006]. To better distinguish between different mechanisms requires an imaging of tS*, tP*, and seismic velocities at more similar resolution and scale than the models we compared here.

5. Conclusions

[18] New maps of tP* and tS*, 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 tS* to tP* is consistent with the PREM ratio of 4.5 and the conventional tS* to tP* ratio of 3.5. Moreover, a joint inversion of the P-wave and S-wave spectral ratios yields lateral variation of tS* that is similar to the predicted tS* variation for a recent surface-wave Q model (tQ*) of the upper mantle and a thermal interpretation of shear-velocity anomalies in the upper mantle (tT*). Combined these observations indicate that the large-scale pattern in tP* and tS* reflects variations in intrinsic shear attenuation.

[19] The high correlation between tS* and tQ* indicates that coherent patterns of attenuation can be constrained from large data sets of horizontally and vertically propagating waves. The similarity between tS*, tQ*, and tT* 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.


[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.