We invert a global phase-anomaly database of intermediate- to long-period Rayleigh waves, recently updated with increased coverage in the European-Mediterranean region, on a global scale with a higher resolution parameterization in the region of interest. We first compare phase-velocity inversions based on ray and finite-frequency theory and derive for each a corresponding set of local phase-velocity dispersion curves (one per model pixel) between 35 s to 300 s period. Effects of the two different theories on the three-dimensional upper-mantle structure are investigated by inverting each dispersion curve for radial shear-velocity profiles. The combination of a gradient-descent method and a random-Monte-Carlo model search provides an estimated shear-velocity model with associated uncertainties for depths between 40 km to 400 km. While differences between ray-theoretical and finite-frequency models are small compared to model uncertainty, comparisons with independent models favor the finite-frequency one.
 It is unclear how such differences in phase-velocity distributions reflect differences in the underlying seismic structures. Identifying a one-dimensional seismic velocity profile from a local dispersion curve is a nonlinear, non-unique problem [Knopoff, 1972]. An exploration of the solution space more thorough than those afforded by linearized inversions becomes therefore necessary, to identify a most likely seismic profile and estimate its uniqueness. Focusing on the well sampled European-Mediterranean region [Fry et al., 2008], we use Rayleigh-wave phase-velocity maps derived by both ray and numerical finite-frequency theory [Peter et al., 2007] to build a new set of dispersion curves which, in a second step, are inverted for radial Vs (shear velocity) profiles. We then compare the resulting three-dimensional shear-velocity models with earlier studies of the region's seismic structure.
 The global dispersion database of Ekström et al. , updated by Boschi and Ekström , was further expanded by Fry , applying the same measurement technique as Ekström et al.  to recordings of both Love and Rayleigh waves from MidSEA, SDSNet, TomoCH and GRSN stations [see Fry et al., 2008, and references therein]. This results in a particularly dense coverage over Europe and the Mediterranean Basin. We invert a total of 677,234 measurements of Rayleigh waves at all available periods between 35 s and 300 s and epicentral distances between 15° and 165°, and for both minor and major arcs.
 We invert for local phase velocities with a global multiple-resolution parameterization, where Europe and the Mediterranean region are parameterized with blocks of approximately equal size of 1° × 1°, everywhere else by 3° × 3° blocks. At each period from 35 s to 300 s, we use a least-squares algorithm [Paige and Saunders, 1982] to find a phase-velocity map derived by both ray- and finite-frequency theory. For the latter, we computed sensitivity kernels entirely numerically as described and illustrated by Peter et al. , in the assumption that the Earth structure be relatively smooth. Our choice of solution is based on an analysis of the L-curves after deriving sets of solution models with different strength of the smoothness damping constraint (no other regularization was applied). For each theory, we compare the inversion solutions corresponding to points of equal curvature on the L-curve [Peter et al., 2007].
 Dispersion curves derived from these phase-velocity maps are assembled for each inversion pixel within Europe and the Mediterranean region (900 locations total). At each pixel, we next invert the corresponding dispersion curve to find Vs in six distinct layers (40–60 km, 60–100 km, 100–150 km, 150–220 km, 220–310 km and 310–400 km). In the assumption of a perfectly elastic upper mantle (i.e., neglect of attenuation), we use Knopoff's method [Schwab and Knopoff, 1970], to calculate a synthetic dispersion curve for each seismic profile generated by our search algorithm. The search algorithm consists of a gradient-descent inversion [Tarantola, 2005] subsequently refined by a Monte-Carlo search.
 The starting seismic profile combines PREM [Dziewonski and Anderson, 1981] vertically polarized Vs, compressional velocity Vp, and density for the mantle together with a crustal description from Crust-2.0 [Bassin et al., 2000], where ocean and Moho depths have been interpolated from the more detailed ones given in the European crustal model EuCrust-07 [Tesauro et al., 2008].
 In the Monte-Carlo refinement, we generate ∼105 radial profiles by randomly perturbing the values of Vs at each layer up to 10%, while keeping density and P-velocity fixed [Deschamps et al., 2008]. Limited to some locations, we verified that even after increasing the number of sampled solutions to ∼107, our final result remains stable.
 Our cost function χ2, accounting for the observational error σj (estimated by Ekström et al.  and converted to phase velocity) at each period Tj and for the difference between “observed” cobs(Tj) and computed c(Tj) phase-velocity, is defined as:
where ′ denotes derivation with respect to period and η acts as a weighting parameter for the second term, chosen so that the shapes and offsets of the dispersion curves are fit equally well. For all solution profiles for which the phase-velocities lie within one standard deviation of the observational error, we calculate a probability p that depends on the corresponding χ2 value:
where k is a normalization constant. Our final preferred profile coincides with the weighted (with weight p) average of all those profiles, accompanied by the corresponding standard deviations [Deschamps et al., 2008].
Figure 1 shows examples of our phase-velocity maps at four different periods (40 s, 75 s, 150 s and 250 s) with important discrepancies between ray- and finite-frequency-theory-derived maps visible for longer periods at 150 s and 250 s [Fry et al., 2008]. Although the sensitivity of Rayleigh waves at the shortest period we consider (35 s) has highest sensitivity mostly below the Moho [Boschi and Ekström, 2002], their sensitivity to the crust is still considerable. We constructed an artificial Vs profile, with crustal layers derived from Crust-2.0 and EuCrust-07 but an artificial upper mantle, and computed a corresponding “synthetic” dispersion curve by Knopoff's method. We then inverted this synthetic dispersion curve with starting profiles different from the original “input” model. Figure 2a illustrates results of two such tests with crustal structure fixed either to PREM crust or to our crustal model based on Crust-2.0 and EuCrust-07 (as was used to generate the synthetics). It is clear that (i) even if the starting model for the inversion is very wrong (gray dashed line) the input model can be retrieved properly, but (ii) only if the crustal model is reliable. In the absence of an accurate crustal model, retrieved upper-mantle structure is dubious down to ∼200 km depth.
 The three-dimensional models derived by ray and finite-frequency theory exhibit differences under Southern Italy and the Hellenic arc at depths between 150–400 km. Figure 2b shows one of the Vs profiles from the “observed” dispersion curves derived by finite-frequency or ray theory for a location in Southern Italy (41.5°N, 16.5°E). In both cases, crustal structure is fixed to our crustal model based on Crust-2.0 and EuCrust-07. Between 60 km and 100 km, both models show a positive anomaly, which at 100–150 km changes to a low-velocity layer. The inversion of the finite-frequency dispersion curve shows higher anomalies at depths between 150–310 km. Figures 3 and 4combine all the Vs perturbations (and their standard deviations) found as described. Standard deviations grow with depth and vary up to 6%, which indicates a decreased resolving power in the dispersion curves.
 Comparisons between our ray-theoretical and finite-frequency results confirm the important differences pointed out by Fry et al. . At the longest periods, our finite-frequency maps exhibit stronger anomalies than those derived by Fry et al.  via analytical finite-frequency kernels. We additionally find that the crustal structure plays an important role in the correct determination of the uppermost ∼200 km of the radial Vs profiles, confirming the findings of Waldhauser et al. . Including shorter surface-wave periods from noise correlations could allow us to extend our model search and invert simultaneously for crustal layer parameters [Panza et al., 2007]. In both Vs-models (Figure 3) we find the same prominent features as Boschi et al.  and Marone et al. . Although our models show a strong, high-velocity anomaly under the Hellenic Arc at 60–150 km depths, related to the Dinarides-Hellenides subduction, the dip angle is only poorly resolved. At 220–310 km depth, a high Vs-anomaly stretching along the Southern Apennines up to Northern Italy is identified in the finite-frequency inversion, while in the ray-theoretical model this anomaly seems to be shifted eastwards under the Adriatic sea.
 Our estimated model error (Figure 2) is between 2% to 6%, obscuring most ray-theory vs. finite-frequency discrepancies. Yet, error estimates from Ekström et al.  are conservative, and there are suggestive hints that the finite-frequency method is indeed enhancing resolution. With respect to the ray-theory solution, the finite-frequency one is more coherent with Vp structure found in a tectonic reconstruction of the temperature field [de Jonge et al., 1994]: compare, e.g., Figure 3 (layer at 220–310 km) with Figure 6 of Boschi et al. . In the same depth range, a fast anomaly under the Central Alps, associated with past subduction, also found by Schmid et al. , is reproduced more clearly in our finite-frequency model than in the ray-theoretical one: compare, in particular, our Tunisia-Central Europe cross-section of Figure 4 with Figure 8 of Boschi et al. .
 We inverted a new phase-anomaly database [Fry et al., 2008] of intermediate to long-period Rayleigh waves, confirming (at 150 s period) the presence of a distinct high-phase-velocity zone between Southern Italy and the Hellenic Trench in finite-frequency inversions, which is shifted to the Balkan coastline for ray-theoretical inversions. We constructed three-dimensional shear-velocity models by inverting dispersion curves, found at each location in the European-Mediterranean region, from the previously obtained phase-velocity maps derived by ray- and finite-frequency theory. In general, differences are small compared to a conservative estimate of model error, but a tectonic reconstruction [de Jonge et al., 1994] of the region's temperature field supports our finite-frequency model. Including dispersion measurements at shorter wave periods and basing the inversion on refined models of the crust will allow to reduce the error bar on tomographic results, and eventually quantify the improvement achieved via the finite-frequency approach.
 We thank John Woodhouse for giving us access to the large computational facility at the Department of Earth Sciences, Oxford University. We also gratefully acknowledge support from the European Commission's Human Resources and Mobility Programme, Marie Curie Research Training Networks.