We invert Rayleigh waves reconstructed from cross-correlations of 18 months of ambient seismic noise recorded by permanent seismological stations run by the Piton de la Fournaise Volcanological Observatory. By correlating noise records between 21 receivers, we reconstruct Rayleigh waves with sufficient signal-to-noise ratio for 210 inter-station paths. We use the reconstructed waveforms to measure group velocity dispersion curves at periods between 1.5 and 4.5 s. The obtained measurements are inverted for two-dimensional group velocity maps and finally for a 3-D S-wave velocity model of the edifice from +2 to −1 km above sea level. Our results clearly show a high velocity body spatially delimited by the borders of the active 10 km wide caldera. The preferential N30°-N130° orientations of this anomaly at −0.5 km below sea-level is an evidence of the preferential paths of magma injections associated to the NE-SE Rift Zones. This structure is surrounded by a low-velocity ring interpreted as effusive products associated to the construction of the Piton de la Fournaise volcano on the flank of the older Piton des Neiges volcano.
 Piton de la Fournaise is a basaltic volcano located on the eastern side of La Réunion island, in the Indian Ocean. Piton de la Fournaise is one of the most active volcanoes in the world. During the past two centuries its average time between consecutive eruptions was about 10 months [Stieltjes and Moutou, 1989]. The 2600 m high and 10 km wide active caldera is characterized by two main radial fracture zones in the directions north 170° and 10° [Bachélery, 1981] (Figure 1a). Those fracture zones are interpreted as active rift zones. However, previous tomographic studies did not show evidence of the rift zone extensions at depth [Nercessian et al., 1996].
 In the last decade, seismic tomographies on volcanoes have provided structural images with an increasing resolution [e.g., Zollo et al., 2002; Tanaka et al., 2002; Yamawaki et al., 2004; Brenguier et al., 2006]. For most of these studies, the objective is either to determine the velocity structure of the entire volcano, or to map details such as possible location of melt material, shallow magma reservoir, or heterogeneities that correlate with seismic activity [Kodaira et al., 2002]. These experiments have an horizontal extent of 10 to 20 km, a depth of investigation of a few km, and a spatial resolution of the order of few km. However, these studies are hampered by irregular distribution of sources (earthquakes or active sources).
 These studies are commonly based on the inversion of P first arrival times and thus do not provide consistent S wave velocity model of the studied structure. The Vp/Vs ratio however appears to be a reliable criterion to assess for the presence of fluid (hydrothermal circulation, magma ascent)[Laigle et al., 2000]. The inversion of surface waves in volcanic domain from array analysis leads to Vs velocity models but suffers from the dependency to the nature of volcanic sources [Ferrazzini et al., 1991; Saccorotti et al., 2003].
 In the field of ultrasonics, it has been shown both theoretically and experimentally that a random wavefield has correlations which, on average, take the form of the Green's function of the media [Weaver and Lobkis, 2001; Lobkis and Weaver, 2001]. In seismology, recent studies also showed that the Rayleigh wave Green's function between pairs of seismographs can be extracted from cross-correlations of coda waves and ambient noise [Shapiro and Campillo, 2004; [Campillo, 2006]. Moreover, some authors used correlations of long ambient seismic noise sequences from regional networks in order to extract and to invert Rayleigh waves to produce high-resolution seismic images of the shallow crustal layers under these networks [Shapiro et al., 2005; Sabra et al., 2005; Kang and Shin, 2006].
 We propose, in this paper, to estimate a 3-D S-wave velocity model of the Piton de la Fournaise volcano. We apply the technique of ambient noise cross correlations to retrieve the Rayleigh wave Green's functions between each pair of seismographs. We use the reconstructed waveforms to measure group velocity dispersion curves and to obtain two-dimensional group velocity maps by tomography. We finally invert these maps for a 3-D S-wave velocity model of the edifice from +2 to −1 km above sea level.
2. Data Processing
 We collected 18 months (Jul. 1999 to Dec. 2000) of continuous seismic noise recorded from the 21 vertical short period stations ran by the Observatoire Volcanologique du Piton de la Fournaise (Figure 1a). One of the advantages of this network is that all stations use the same equipment (available at http://www.ipgp.jussieu.fr/pages/030308.php). This allows us to make inter-stations measurements without dealing with the problem of the instrumental corrections. An example of a noise record at one of the stations (ANR) is shown in Figure 1b. We first filter the data between 1 to 5 s and whiten their spectral amplitude in order to avoid dominance of strong spectral peaks in the noise. We further normalize the data by disregarding completely the amplitudes and by keeping only a one-bit signal [Campillo and Paul, 2003]. This procedure is necessary in order to avoid the dominance, in the correlations, of energetic arrivals such as earthquake signal or storms. Data corresponding to one day are cross-correlated for each station pair. We then reject traces according to a signal to noise ratio criterion (24% rejection on average) and stack the non-rejected traces day per day over 18 months (540 days). An example of reconstructed Rayleigh waves is shown in Figure 1c.
 We then estimate a group velocity dispersion curve for each stacked trace using an automatic Frequency-Time Analysis (FTAN) [Levshin et al., 1989; Ritzwoller and Levshin, 1998]. We manually select the dispersion curves (DP) according to group velocity limits (50% variation around an average DP) and such that the station-to-station distance be longer than one wavelength. We finally obtain 75 reliable dispersion curves and extract group velocities for each trace for periods equal to 2, 2.5, 3, 3.5, 4, and 4.5 s (Figure 2a).
3. Rayleigh Wave Tomography
 We perform a tomographic inversion of the arrival-time measurements deduced from the group velocity measurements at each period using the algorithm described by [Barmin et al., 2001]. The regularization scheme of this method involves a penalty function composed of a spatial smoothing function and a constraint on the amplitude of the perturbation depending on local path density. Our 2-D model involves 22 × 28 = 616 1 × 1 km cells. The initial velocity is taken as the average of the group velocity measurements at each period. We do not take into account the topography during the inversion procedure. This approximation yields an error <5% on group velocity measurements. However, the group velocity measurements show variations of more than 50% at a each period (Figure 2a). The error caused by the flat topography approximation is, therefore, negligible.
 Because of the sparse ray coverage and the low resolution of the data set, we chose to apply a strong smoothing during the tomographic inversion. The spatial resolution (≈4 km) is constrained by the smoothing condition. The inversion results are thus robust and show a moderate variance reduction varying from 38 to 18% with increasing periods (from 2 to 4.5 s).
 Estimated distribution of Rayleigh wave group velocities at 3 s is shown in Figure 2b within the zone where the model is best resolved. The tomographic image clearly shows a high velocity anomaly 1 km east of the main vent (cratre Dolomieu, Figure 1). We perform a spike test in order to test how well this high velocity anomaly is resolved. The true velocity model is taken as a 3 × 4 km wide high velocity anomaly (Figure 2c). The inversion of the synthetic data shows that the anomaly is well located but its shape is highly smoothed and characterized by a North-West South-East trend due to the similar preferential orientation of rays (Figure 2d). Moreover, the amplitude of the anomaly is attenuated by a factor 3 due to the smoothing condition.
4. Depth Inversion
 We construct dispersion curves for each model cell from the tomographic maps corresponding to periods 2, 2.5, 3, 3.5, 4, and 4.5 s. We fit these curves by polynomial functions in a least-squares sense and invert them using a Monte-Carlo algorithm [Shapiro et al., 1997], the synthetic dispersion curve being calculated using a method by [Herrmann and Al-Eqabi, 1991]. We thus obtain a Vs versus depth velocity profile for each cell. Figures 3a and 3b show depth inversion results of one dispersion curve. Figure 3a illustrates the non-uniqueness of the velocity structures determined by dispersion curve inversion. We average 10 best fitting models for each cell and spatially smooth the 3-D reconstructed velocity model in order to retrieve the average subsurface velocity distribution. Figures 3c and 3d show different velocity profiles corresponding to a near-surface low velocity anomaly (curve 1), a near-surface high velocity anomaly (curve 2), a 1 km below sea level (bsl) low velocity anomaly (curve 3), and a 1 km bsl high velocity anomaly (curve 4). The horizontal location of these profiles is shown on Figure 4.
 We present 6 horizontal slices as well as a 3-D view of the 3-D smoothed model on Figure 4. The results clearly show the presence of a high velocity anomaly which moves westward with depth (+1.3 to −1.1 km above sea level). This structure is surrounded by a low-velocity ring interpreted as effusive products associated to the construction of the Piton de la Fournaise volcano on the flank of the older Piton des Neiges volcano. This high velocity anomaly has also been detected by a previous earthquake and active P-wave tomography on the Piton de la Fournaise volcano [Lankar, 1997]. Recent works also imaged the presence of a high velocity chimney on different volcanoes [Laigle et al., 2000; Tanaka et al., 2002; Zollo et al., 2002; Sherburn et al., 2006; Patanè et al., 2006]. We interpret this anomaly as a solidified intrusive magma body. The high velocity anomaly is also well correlated with the rift zone at sea level (Z = −0.5 km).
5. Discussion and Conclusions
 We used 18 months of seismic noise recorded by the seismological network of the Piton de la Fournaise volcano to reconstruct Rayleigh wave Green's functions between each pair of seismic sensors. We used these waveforms to perform a Rayleigh-wave tomography and invert dispersion curves extracted from group velocity maps in order to build a 3-D S-wave velocity model of the 10 km width active caldera from +2 to −1 km above sea level.
 Our approach relies on a strong quality selection of the data. We apply a strong smoothing condition on our tomographic models to increase the robustness of the inversion. This condition, however, limits the spatial resolution and leads to strongly underestimated amplitudes of the inferred seismic speed anomalies. Our method results in a better resolution in shallow layers than earthquake-based tomographies because it is not limited by the spatial repartition of sources within the volcano that provides with only a very limited number of near-surface paths.
 Our results agree with earthquake and active P-wave tomographies previously performed on this edifice [Lankar, 1997] showing an intrusive high velocity body moving westward from the surface to 1 km below sea level. Imaging these intrusive bodies is of particular interest because the magma path is usually believed to follow their geometry [Laigle et al., 2000; Battaglia et al., 2005].
 This work validates a new technique of 3-D surface waves tomography using correlations of ambient seismic noise. Moreover, we performed a preliminary study showing that, with this data set, using only a few instead of 18 months of seismic noise records will yield similar tomographic results. This method is thus particularly advantageous in the context of temporary seismic arrays because it can return useful information of the near-surface structure even if earthquakes do not occur. This method may also be complementary to prohibitively expensive active seismic source tomography.
 All the data used in this work were collected by the seismological network of the Observatoire Volcanologique du Piton de la Fournaise. We are grateful to the Observatory staff and also to Zacharie Duputel and Luis Rivera for the help with the data. We thank Laurent Stehly, Pierre Gouédard, and Philippe Roux (LGIT) for helpful discussions. We thank Alfred Hirn (IPGP) for discussions about the Piton de la Fournaise P-wave tomography. We are grateful to Olivier Coutant, Jean-Robert Grasso, Kees Wapenaar, and Tae-Seob Kang for constructive comments concerning the manuscript. This work was supported by ANR (France) under contracts 05-CATT-010-01 (PRECORSIS) and COHERSIS.