# Attenuation of Broadband *P* and *S* Waves in Tonga: Observations of Frequency Dependent *Q*

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## Abstract

—Teleseismic broadband recordings of intermediate and deep focus earthquakes are used to quantify both compression *(Q* _{ <alpha> } and shear(*Q* _{ <beta> }) wave attenuation within the Lau backarc basin. A spectral-ratio method is employed to measure differential attenuation (*<delta>t**) between the depth phases *sS, pP*, and *sP* and the direct *S* and *P* phases over the frequency band 0.05 and 0.5 Hz. We use a stacking algorithm to combine the spectra of several phase pairs from a single event, having similar azimuth and range, to obtain more robust *<delta>t** measurements; these estimates are then used to compute the average *Q* above the focal depth. *Q* _{ <beta> } and *Q* _{ <alpha> } are measured directly from the *sS-S* and *pP-P* phase pairs respectively, however, the interpretation of *<delta>t** measured from *sP-P* requires assumptions about the ratio *Q* _{ <alpha> } * /Q* _{ <beta> }. We find an empirical ratio of *Q* _{ <alpha> } * /Q* _{ <beta> } = 1.93 for this region and use it to compute *Q* _{ <alpha> } and *Q* _{ <beta> } from the *Q* _{ sP } observations. We observe lateral and depth variations in both *Q* _{ β } and *Q* _{ >alpha< } beneath the tectonically active Lau Basin and the geologically older, inactive Lau Ridge and Fiji Plateau. The upper 200 km beneath the Central and Northern Lau Basin show a *Q* _{ <beta> } of 45–57 and a *Q* _{ <alpha> } of 102–121, and *Q* appears to increase rapidly with depth. The upper 600 km beneath the Lau backarc basin has a *Q* _{ <beta> } of 118–138, while over the same depth interval we observe a higher *Q* _{ <beta> } of 139–161 beneath the Lau Ridge and Fiji Plateau. We also find *Q* _{ <alpha> } of 235–303 beneath the northern Lau Basin and a higher *Q* _{ <alpha> } of 292–316 beneath the Fiji Plateau and the Lau Ridge measured directly from *pP-P* phase pairs. These geographic trends in the broadband *Q* measurements correlate with our previous long-period estimates of *Q* _{ <beta> } in this region, however, the broadband measurements themselves are higher by about a factor of two. These observations suggest substantial frequency dependence of *Q* in the upper mantle, beginning at frequencies less than 1.0 Hz and consistent with the power-law form *Q*∝ω^{α} with *<alpha>* between -0.1 and -0.3.

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