Granada (Southern Spain) is a place of rare and enigmatic very deep focus earthquakes, the last one on April 11, 2010, with magnitude of 6.3 and depth of 620 km. We use regional broadband recordings to estimate QP and QSin the mantle for frequencies between 0.25 and 8 Hz, computing the spectra of the direct P- and S-waves with their early P- and S coda. We use the spectral decay method, constraining crustalQ to values given in the literature. We obtain robust estimates of QP in 6 frequency bands (0.25, 0.5,1, 2, 4 and 8 Hz) and of QS in 4 bands (0.25, 0.5,1, 2 Hz). QP in the mantle ranges from 13 at 0.25 Hz to 346 at 8 Hz and QS from 59 at 0.25 to 183 at 2 Hz. The frequency dependence is well fitted by Q = Q0fα with α equal to 0.6 for QS and 1.0 for QP, and Q0 equal to 109 for QS and 63 for QP. The QP/QS ratio is less than 1. These are extreme values within the ranges of mantle Q, QP/QS and αvalues reported in the literature, indicating strong scattering attenuation and absence of melt. We propose that such values, rather than being an exception, may approximate the average upper mantle, with solid olivine composition and small-scale heterogeneity.
 In 1954, an unexpected deep (h = 630 km) earthquake [Mw = 7.9] beneath Southern Spain pointed out the existence of deep seismic activity far from any active subduction boundary known at that time [Hodgson and Cock, 1956; Chung and Kanamori, 1976]. Together with the absence of subsequent seismic activity in the same source zone, this quake is recognized as the most peculiar deep earthquake of the last century [Frohlich, 2006]. Three small deep-focus earthquakes (∼4 < M < 5) followed this event in 1973, 1990 and 1993 [Buforn et al., 2004] with hypocenters very close to the 1954 event at less than 25 km epicentral distance. On April 11th, 2010, a larger deep earthquake [h = 620 km; Mw = 6.3] occurred, just in the same source region. Different from the 1954 event, the 2010 earthquake was recorded at a dense regional network of seismic broadband stations, providing an unprecedented amount of on-scale high quality seismograms. Hereafter we denote this earthquake with the acronym DSE.
 All these models have in common the very limited spatial extent of the lithosphere recycling processes beneath the Betic-Rif chain and the Alboran Sea in line with the tight concentration of very deep hypocenters. This represents a fundamental difference to the typical locations of very deep earthquakes in much larger and more active slabs. In particular, the deep Spanish earthquakes provide an interesting opportunity to study upper mantle Q from regional P- and S-wave recordings. Using deep regional earthquakes to study upper mantle attenuation allows for extending attenuation measurements to higher frequency (>1 Hz) compared to teleseismic body waves (<1 Hz), and surface waves (<0.05 Hz). At those high frequencies, effects as scattering, focussing/defocussing or 3D propagation should become more important than or comparable to intrinsic attenuation. While in a typical subduction setting, such waves often carry a significant imprint of the mantle wedge or along-slab propagation, the limited horizontal extension of the upper mantle high-velocity anomaly beneath southern Spain [Spakman and Wortel, 2004] suggests that here the inferred Q values should be more representative of an average upper mantle outside the subduction system. In particular, the stations north of the epicenter are not expected to sample the subduction zone (see Figure 1). Except for Okal , who reports a Qμof 479 between 1 Hz and 3 Hz using a single recording of the 1993 deep Spanish earthquake, there are no previous studies of the attenuation parameters of the upper mantle beneath Spain. We will use P and S waves data generated by the DSE, to contribute in defining the seismic space-averaged total attenuation in the upper mantle beneath Iberia, for useful comparisons with subduction zones around the world.
2. Data and Method
 We analyse seismograms of DSE at 47 broad-band 3-components seismic stations (Figure 1), managed by the Instituto Andaluz de Geofísica (IAG, University of Granada) and Instituto Geografico Nacional (IGN). Epicentral distances range from 29 km to 877 km. Seismograms are sampled at 50 sps for IAG data and 100 sps for IGN data. Examples of the seismic traces utilized in this paper are reported in Figure 2. High frequency (>2 Hz) waves in the early coda of S-waves result to be contaminated by the later P-coda radiation, and thus excluded from the analysis.
 We measure the decay of spectral amplitude of the ground velocity (for P and S waves) with source-to-station distance [Sato and Fehler, 1998, pp. 110–111], which, as well known, depends on the total-Q (QP and QSfor P and S waves, respectively). The spectral amplitude is estimated through Fast Fourier Transform. The amplitude spectral density is calculated for time-windows 60 seconds long, starting respectively at the P- and S- wave onset. We use spectra of vertical component for P-waves and log-averaged spectra of the two horizontal components for S-waves. Pre-event noise spectra are calculated and compared with signal spectra. Signal-to-noise ratio results always greater than 5 at 8 Hz, and much greater than this value for decreasing frequency. The spectral Log-average is evaluated over the horizontal components and finally the integral of the spectral amplitude is calculated in 6 frequency bands, respectively from 0 to 0.35, from 0.35 to 0.7, from 0.7 to 1.4, from 1.4 to 2.8, from 2.8 to 5.6 and from 5.6 to 12 Hz. Central frequencies for each band are 0.25, 0.5, 1.0, 2.0, 4.0 and 8.0 Hz. To estimate the contribution of the seismic attenuation in the crust, we use total-Q for S-waves in southern Spain calculated byAkinci et al.  (QSC = 34.8f1.0). We assume that total-Q for P-waves is a half of total-Q for S-waves in the crust, an average of the experimental values through the world [Sato and Fehler, 1998, Figure 5.3], and use this estimate as a constraint for calculating the correspondent quality factors, QPM and QSM in the mantle. The equation which associates the integral of the spectral amplitude for P and S waves (as a function of frequency SP,S(f)) to the quality factor is
where Kincludes source-, site-, instrument-transfer functions and velocity model;T is the travel time (M and Cindicate respectively mantle and crust and subscripts P and S respectively compressional and shear waves). The left hand side of this equation represents the measured quantities as a function of travel time (calculated through ray-tracing).Equation (1) for all the stations, and for P and S waves, represents a largely overdetermined system of N equations for 2 unknowns (K and QP, SM) that can be solved, after Log-linearization, with an optimization algorithm. We use here the weighted least squares approach, described by the following matrix equation for any value of the frequency,f.
where m(f) is the vector containing the unknowns, G(f) is the 2-column coefficient matrix (first column elements = 1; second columns elements = − πf(Ti,P,SM) where Ti,P,SMis the travel time in the mantle at the i-th receiver).Wis the matrix containing the weights. After many tests for different weighting matrices, we observe that unweighted- are comparable to weighted-solutions and selected W = unity.d(f) is the data matrix, whose elements (i = 1,...N) are
We solved system (2) for each frequency, separately for P and S. Errors on the estimates of QP and QS are obtained using as Covariance matrix the diagonal matrix associated with the variances in the spectral estimates.
 From the results displayed in Figure 3, we obtain a frequency dependence well expressed by QP,SM = Q0fα. Q0 is Q at 1 Hz and α the dependence with the frequency of Q. QP,SM and α has been estimated using least squares minimization. The results show that for QPM, Q0 = 63 ± 1 and α = 1.0 ± 0.1 (correlation coefficient = 0.98) taking into account the whole frequency range (Figure 4). The restricted frequency range available for QSM makes the estimate of the QSM frequency dependence less stable than that for QPM. Results for QSM give Q0 = 109 ± 1 and α = 0.6 ± 0.1 (correlation coefficient = 0.95, Figure 4). The above results for α are higher than the estimates obtained by Shito et al.  for the upper mantle beneath Japan and at the upper bound of values reported by Cheng and Kennett . From lab-experiment on solid olivine samples,α = 0.2 − 0.4 [e.g., Jackson et al., 2002, 2004], tending to 0 when partial melting is present [Faul et al., 2004]. Higher α values suggest a solid olivine composition of the mantle path above the source in Southern Spain and the presence of strong scattering attenuation [e.g., Shito and Shibutan, 2003].
QPM/QSM ratio calculated in the present paper in the range between 0.25 Hz and 2 Hz is less than 1.0 (0.21, 0.51, 0.77 and 0.91 at 0.25 Hz, 0.5 Hz, 1.0 Hz and 2.0 Hz, respectively). Taking into account that QP/QS for a Poisson solid with null bulk attenuation (QK−1) is close to 2.25 [Jackson, 2007], the present result showing significantly smaller ratio (QPM/QSM < 1.0) suggests the presence of melt and/or scattering attenuation in the mantle beneath Spain [Budiansky et al., 1983]. QPM/QSM values found in Southern Spain are lower than: a) those calculated in Central Alaska by Stachnik et al.  (QP/QS = 1.1 − 1.4), b) those calculated in Tonga-Fiji region [Roth et al., 1999] (QP/QS values between 1.7 and 2.2), c) those calculated in the Philippines mantle wedge [Shito and Shibutan, 2003], and at the lower bound of values reported for the Marianas subduction system (∼0.8–2.1 [Pozgay et al., 2009]).
 To support our initial hypothesis that our estimates of QP,SM, QPM/QSM and α approximate average mantle conditions, we repeat the calculations excluding several stations that potentially may register waves propagating through the high velocity anomaly. Therefore we exclude seven stations at short distances that show the largest positive residuals in the regression for QSM at 2 Hz (Figure 3). For this data set, we found QPM in the mantle ranging from 13 at 0.25 Hz to 346 at 8 Hz and QSM from 59 at 0.25 to 183 at 2 Hz. α becomes 0.7 for QSM and remains 1.0 for QPM, while QPM/QSM ratios become 0.20, 0.47, 0.66 and 0.76 at 0.25 Hz, 0.5 Hz, 1.0 Hz and 2.0 Hz, respectively. These estimates are very close to the results for the full data set, suggesting that the average values are not significantly contaminated by propagation through the subduction system.
 In the present paper we estimate attenuation parameters (QP,SM) for the upper mantle beneath the Iberian peninsula using the spectral decay method for direct P and S waves in the frequency range of 0.25 to 8 Hz by using a complete and dense data set from broad band seismograms of the 11 April 2010 deep (h = 620 km) Spanish Mw = 6.3 earthquake. We found a highly attenuative mantle with very low values of QP,SM in the frequency range analyzed, similar to those measured in active volcanic arcs. A large frequency dependence of the quality factor is observed, with α ∼ 1.0 for QPM and ∼0.6 for QSM. QPM/QSM ratios are remarkably low (<1.0). Our estimates are close to the extremes of the range of previously reported QP,SM, QPM/QSM and α for the upper mantle.
 The combination of small QPM/QSM and large α favours an interpretation in terms of scattering attenuation as the dominant mechanism, compared to a classic mantle wedge setting, where melting processes, thermal perturbations and an environment rich in fluids should translate into much smaller values of α ∼ 0. Our data suggest a solid, randomly heterogeneous propagation medium producing high attenuation (low values of QPM and QSM). We propose that such conditions may be characteristic of the upper mantle outside subduction systems.
 Digital data used in this work has been kindly provided by “Red Sísmica de Andalucía” managed by the Instituto Andaluz de Geofísica, “Red Sísmica Nacional” managed by Instituto Geográfico Nacional. This research has been partially supported by Spanish project CGL2008-01830-BTE, CGL2008-01660 and CGL2011-29499-C02-01, the Junta de Andalucía P09-RNM-5100 and by the Consolider Ingenio 2010 project TOPO-IBERIA CSD2006-00041. Edoardo del Pezzo has been partly supported by University of Granada for a 1-month stage at Instituto Andaluz de Geofísica and partly by the DPC-INGV UNREST and SPEED, and by Italian Ministry of Education and Research PRIN projects.
 The Editor and the authors thank Raul Castro and Azusa Shito for assisting with the evaluation of this paper.