The joint application of different seismological techniques for seismic noise analysis, and the results of a volcanological and morphostructural survey, have allowed us to obtain a detailed and well constrained image of the shallow crustal structure of the Solfatara volcano (Campi Flegrei caldera, Italy). Horizontal-to-vertical spectral ratios, inversion of surface wave dispersion curves and polarization analysis provided resonance frequencies and peak amplitudes, shear wave velocity profiles and polarization pattern of coherent ambient noise. These results, combined in a unique framework, indicate that the volcanic edifice is characterized by lateral and vertical discontinuities and heterogeneities in terms of shear wave velocity, lithological contrasts and structural setting. The interpretation of the seismological results, with the volcanological and morphostructural constraints, supports the hypothesis that the volcano has been characterized by a complex and intense activity, with the alternation of constructive and destructive phases, during which magmatic and phreatomagmatic explosions built a complex tuff-cone, later reworked by atmospheric agents and altered by hydrothermal activity. The differences in the velocity structure between the central and eastern parts of the crater have been interpreted as resulting from a possible eastward migration of the eruptive vent along the deformational features affecting the area, and to the presence of viscous lava and lithified tuff bodies within the feeding conduits, which are buried under a covering of reworked materials of variable thickness. The observed fault and fracture systems, partially inherited from regional structural setting and exhumed during volcanism and ground deformation episodes also seems to strongly control wave propagation, affecting the noise polarization properties.
 Seismic noise represents an attractive tool to investigate the shallow crustal properties due to the speed and ease of data acquisition and the relative simplicity of analysis. Much information can be extracted by applying both single- and multichannel techniques to microtremor. Single-station methods, such as Horizontal-to-Vertical (H/V) spectral ratio [Nakamura, 1989], have been extensively employed in seismic hazard studies to determine the fundamental resonance frequency and the amplification of a given site [Alfaro et al., 2001; Parolai et al., 2004; Maresca et al., 2006]. Although there is still a debate about the correct interpretation of the H/V ratio, especially regarding the correlation between the peak amplitude and the actual site amplification [Luzón et al., 2001; Malischewsky and Scherbaum, 2004], many efforts have recently been made to prove the effectiveness of the method through numerical simulations [Bonnefoy-Claudete et al., 2006]. Moreover, standard criteria for a correct noise acquisition and rules for the assessment of the reliability of the results have been defined (SESAME European Project, Deliverable D23.12, available from http://sesame-fp5.obs.ujf-grenoble.fr).
 When multiple seismometers are available, array techniques can be used to determine the surface wave dispersion curves and the 1-D path integrated shear wave (S) velocity profile from their inversion. Even in the presence of a complicated medium, 1-D dispersion carries information about the average properties of the earth's crust and its inversion is a good approximation of the velocity structure [Dziewonski and Hales, 1972; Ekström et al., 1997; Ritzwoller and Levshin, 1998]. In addition, detailed 2-D and 3-D images of the crust can be obtained combining several 1-D velocity profiles [Picozzi et al., 2009; Stehly et al., 2009].
 Frequency-Wave number (f-k) [Lacoss et al., 1969] and Spatial Autocorrelation (SPAC) [Aki, 1957, 1965] techniques have become very popular for the analysis of ambient vibrations. The initial limits of the SPAC method related to the circular geometry have been overcome by adapting the method to non-circular configurations [Bettig et al., 2001]. All these techniques have been successfully applied, demonstrating that the inversion of dispersion curves from microtremor data can provide fine resolution of the shallow S-wave velocity model [Bozdağ and Kocauglu, 2005; Di Giulio et al., 2006; Maresca et al., 2006]. Subsurface structure down to a scalelength of the order of 500 m has been retrieved for several volcanoes, such as Masaya [Métaxian et al., 1997], Stromboli [Chouet et al., 1998, Petrosino et al., 1999, 2002], Vesuvius [Saccorotti et al., 2001], Kilauea [Saccorotti et al., 2003] and Arenal [Mora et al., 2006]. High-resolution seismic images of the shallow crust are extremely important in volcanic areas, because the heterogeneous subsurface structure represents a complex propagation medium for seismic waves and clearly influences the wavefield. Some authors have shown that unconsolidated, alternating layers of ash, pumice and lithified rocks generates stronger scattering than in ordinary crust [Wegler and Luhr, 2001; Wegler, 2003; Parsiegla and Wegler, 2008]. Moreover, recent studies based on numerical simulations have demonstrated how different shallow crustal models significantly change the shape of the seismograms of volcanic earthquakes, thus affecting the accuracy of the location and the polarization pattern, and causing bias in the source inversion [Cesca et al., 2008; Bean et al., 2009; Lokmer and Bean, 2010]. Therefore accurate knowledge of the velocity structure is crucial for a correct separation of the observed signal into source and path/site effects, improving the definitions of the mechanisms that trigger and govern volcanic activity.
 An intriguing observation has been recently made by Rigano et al. , who demonstrated that further information about the medium structure is provided by microtremor. These authors, focusing on ambient noise polarization at Mt. Etna, found that its direction was somewhat controlled by the presence of faults, and it was never parallel to the fault strike. Although an influence of faults on the polarization of earthquake ground motion has been found by many authors and been explained in term of a waveguide mechanism [Li et al., 1994; Rovelli et al., 2002; Ben-Zion et al., 2003], the systematic tendency of seismic noise to be polarized has been observed for the first time at Mt. Etna and the mechanism responsible for this characteristic is still not clear. Rigano et al.  suggest, as possible hypotheses to be further investigated, that the noise polarization is caused by anisotropy or by the resonance of seismic waves in the fault zone.
 In this paper we combine spectral ratio, surface wave dispersion inversion and polarization techniques in a unique framework with the aim of extracting a coherent and robust estimate of the fine crustal structure in the first 200 m below the Solfatara volcano. In particular, the H/V spectral ratio technique has provided the resonance frequency and the peak amplitude values for 68 sampled sites; the S-wave velocity profiles in 5 different areas of the crater have been retrieved from the inversion of surface wave dispersion curves estimated by f-k and SPAC methods; the polarization pattern of seismic noise evidences possible correlations with the orientation of the structural features of the volcano. In addition we present results from a detailed volcanological and morphostructural survey aimed at constraining the geophysical interpretation. The seismological techniques, together with the geological information mainly derived from the volcanological and morphostructural survey, have allowed us to obtain a realistic 3-D image of the shallow crustal structure in this area.
2. Geological Framework
2.1. The Campi Flegrei Caldera
 The Solfatara volcano is located in the central part of the repeatedly collapsed Campi Flegrei caldera (CFc), and is one of the youngest volcanoes formed within this active volcanic field [Rosi and Sbrana, 1987; Orsi et al., 1996; Isaia et al., 2009]. Resurgence affected the central part of the caldera, causing the uplift of a number of differentially displaced blocks, the most uplifted of which is the La Starza marine terrace that has been raised up about 90 m in the past 10 ka [Di Vito et al., 1999]. Resurgence and volcanism in the past 15 ka are strictly related; indeed intense volcanism was preceded and accompanied by intense phases of ground deformation. At least 72 mainly explosive eruptions occurred after the youngest caldera collapse; the last one, Monte Nuovo (1538 AD) was preceded by significant ground uplift, mainly concentrated in the vent area [Di Vito et al., 1987].
 The regional stress field in the Solfatara area, which also controls the volcanism of the CFc, is mainly due to the anticlockwise rotation of the Italian peninsula. This rotation is related to the opening of the Tyrrhenian basin, which occurred through the activation of Plio-Quaternary extensional processes that affected the Tyrrhenian margin of the Apennine chain. The onset of volcanism at about 0.7 Ma [Amato and Montone, 1997, and references therein], reflects a recent extensional pulse, which caused the activation of NW-SE trending normal faults that have downthrown southwestward this margin, and NE-SW trending normal to strike slip faults, which have been interpreted as transverse structures [Liotta, 1991; Faccenna et al., 1994]. A horst-and-graben type structural pattern in the region was generated in relation to this tectonism, and the Campanian plain – in which the CFc is located - represents the largest of these grabens. Within this regional stress field the conditions for magma to form and rise to surface were established. At a regional scale volcanism occurred along a NW-SE trending belt, parallel to the margin of the chain; however the main volcanic vents are located at the intersection between NW-SE and NE-SW trending fault systems, within transverse depressions, and are dominated by caldera-forming eruptions [de Vita et al., 2005, and references therein]. This kind of stress field is characterized by a NE-SW to ENE-WSW trending σ3 (horizontal minimum stress), perpendicular to the main extensional structures, a NW-SE to NNW-SSE trending σ2 (horizontal maximum stress), perpendicular to the main transfer structures, and a vertical σ1 [Amato and Montone, 1997].
2.2. The Solfatara Volcano
 The Solfatara volcano [Di Vito et al., 1999; Isaia et al., 2009] is a tuff cone located at 100 m above sea level, about 2 km NE of the town of Pozzuoli (Figure 1). It was formed at 3,815 ± 55 a b.p. during the third epoch of volcanic activity of the CFc [Di Vito et al., 1999]. Its crater is a 0.5 × 0.6 km sub-rectangular structure, the geometry of which is mainly due to the control exerted by N40–50W and N50E trending fault systems. These systems crosscut the area (Figure 1) and have been active many times, before and after the formation of the crater, likely reactivating pre-existing regional structures during the main volcano-tectonic events that affected the CFc [Orsi et al., 1996, 1999; de Vita et al., 1999]. The morphology of the Solfatara volcano has been interpreted as formed by a multivent activity, which generated a complex sequence that includes the S. Maria delle Grazie Tephra, Mt. Olibano Lavas and Tephra, the Accademia Lava Dome and the Solfatara Tephra [Isaia et al., 2009]. Multivent activity, often characterized by vent migration along structurally controlled fissures, is a quite common feature in the CFc, as it has been reported also for other recent events [Rosi and Sbrana, 1987; de Vita et al., 1999; Isaia et al., 2004, 2009; Orsi et al., 2009; Tonarini et al., 2009; Di Vito et al., 2011].
 Although soil diffuse degassing occurs throughout the entire area of the Solfatara crater [Chiodini et al., 2001], fumarolic activity is mainly concentrated in its southeastern part (Bocca Grande and Bocca Nuova area) at the intersection between the N50W and the N50E trending fractures that border the northeastern and southeastern part of the crater, respectively, and in the northeastern area (Stufe) along the main NW-SE trending fault, cutting the crater. The hydrothermally altered zone also extends outside the crater, along the prolongation of these structures, in areas in which the intersection of fractures belonging to the same systems is clearly evident (Figure 1). The central part of the Solfatara crater is occupied by the Fangaia mud pool, at which the water table emerges and a continuous rising of hydrothermal fluids generates diffuse bubbling. In this area a 0.7 m wide, N50E trending extensional fracture, opened during the 1982–84 bradyseismic crisis [Acocella et al., 1999]. Soil temperature distribution [Chiodini et al., 2001] also shows the direct control exerted by the structures on the heat flux, as demonstrated by the alignment of the highest temperature values along the direction of the main fracture systems, in the northeastern and southeastern parts of the crater, as well as in the Fangaia area [Granieri et al., 2010]. On the contrary, the northwestern sector of the crater is relatively inactive with respect to the heat flux and fumarolic activity.
 Geophysical and hydrogeological investigations at the Solfatara volcano [Bruno et al., 2007] provide images of the shallow and intermediate subsurface of the crater. These authors, using electromagnetic and electrical data, recognized two electrical zones: an outcropping resistive layer (A) overlying a conductive one (B). The latter has an irregular top, crops out in the mud pool area and is up to 20–50 m deep in the northeastern side of the crater. According to Bruno et al.  layer A represents a clayey, non-saturated zone, and layer B corresponds to a hydrothermal aquifer recharged through condensation of geothermal fluids.
 At a deeper level, evidence of a gas or fluid reservoir beneath the Solfatara area comes from the recent seismic attenuation imaging of Campi Flegrei by De Siena et al.  who recognize a vertically extending, high attenuation structure. This result is compatible with that of Battaglia et al.  who observed a high VP/VS anomaly in the southwestern part of the Solfatara, as expected for a strongly fractured medium permeated by fluids.
3. Data Acquisition and Analysis
 In the following subsections we present the results of the volcanological, structural and seismic surveys that we carried out at the Solfatara, and we propose a multidisciplinary approach in which the geological and geophysical measurements integrate to image at a high level of detail the shallow crustal structure of such a complex volcano.
3.1. Volcanological and Structural Survey
 The volcanological and structural field survey of the Solfatara volcanic edifice carried out in the present work was preceded by a photo aerial analysis and interpretation. It aimed at an optimal description of the pyroclastic sequence associated with the activity of the Solfatara vent area, and at a detailed reconstruction of the crater morphology, structure and deformational history. The reconstructed sequence of the Solfatara Tephra (Table 1) includes a basal breccia, which directly lies above the Mt. Olibano lava dome, and a phreatomagmatic sequence of stratified fine- and coarse-ash surge-beds. The Solfatara Tephra also includes two surfaces of angular unconformity, which subdivide into three portions the entire sequence. The first surface (Angular Unconformity 1 –Table 1) separates the basal breccia from the overlying stratified succession, which is in turn separated into a lowermost, thicker part, and an upper, thinner portion by the second surface (Angular Unconformity 2 – Table 1).
Table 1. Description of the Main Lithological and Stratigraphical Characteristics of the Solfatara Tephra, From Base Upwarda
See the text for discussion. Sections numbers are the same of the structural analysis, reported in Figure 1.
Tephra of vent 2
Fine-ash surge beds with minor pumice fallout layers and lenses, and lithic blocks. The beds are undulated to plane-parallel. This deposit is coarser and thicker in the eastern and northern parts of the crater. It thins radially from vent 2 and drapes unconformably parts of the inner walls of crater 1.
Thickness = 0–13 m. The thickness variation is due to pinch-out of the surge sequence against the inner walls of crater 1.
Thickness = 2–14 m. The thickness variation is due to pinch-out of the surge sequence against the inner walls of crater 1 and to partial draping of crater 1 rim.
Thickness = 3 m.
Thickness = 1.7 m.
Angular Unconformity 2
Tephra of vent 1
Coarse- to fine-ash surge beds and minor scattered or aligned coarse pumice fragments and lithic blocks. The beds are massive to plane parallel, and yellowish to green in color. They contain abundant accretionary lapilli. This deposit is exposed along all the inner crater slopes.
Thickness ≥15 m, base not exposed.
Thickness = 7 m.
Thickness = 6 m.
Thickness = 3.9 m.
Angular Unconformity 1
Very coarse breccia deposit with a fine grained ash matrix. It is composed by variably altered lithic fragments (tuff and lava) and scoria bombs. It is exposed along the eastern inner crater walls.
Thickness = 8 m.
Thickness = ca. 2 m.
Thickness ≥4 m, base not exposed.
 The morphostructural survey highlighted the main morphological features of the area and the mutual relationships among the different fracture systems. The southeastern part of the crater wall is carved into the Mt. Olibano lava dome, which was extruded slightly before the Solfatara activity, whereas its easternmost part is partially deformed by a minor, sub-rounded, rim structure nested within the main crater (Figure 1). The area is affected by dominant NW-SE trending faults and fractures which crosscut the Solfatara area and its external parts, downthrowing to NE (i.e., toward the Agnano plain) the marine deposits of the La Starza marine terrace. Both internal and external slopes of the volcano show rectilinear parts (residual fault scarps), triangular facets and aligned drainage lines (lineation of the northeastern outer slopes). This fault system is intersected by the NE-SW system also well evidenced by rectilinear valleys and slopes, such as the southeastern inner slope of the Solfatara crater, and the valleys crosscutting both the Solfatara volcano and La Starza marine terrace (Figure 1). Also the fracture that opened in the crater floor during the last large bradyseismic event (1982–1984) had this same orientation. Finally the faults and fractures trending around NS and EW are well visible along the outer slopes of the volcano, whereas in the crater floor area they are likely masked by the reworked deposits filling the crater. At a smaller scale the survey suggests that the geometry of the Solfatara crater is only partially inherited from pre-existing fault and fracture systems and their morphological evolution.
 Finally, a meso-structural survey has been carried out in selected sites both inside and outside the Solfatara crater, in order to highlight the mutual relationships among the different fracture systems, and their frequency and possible connection with the main fault systems.
 With the aim of subdividing the study area into homogeneous domains relative to the main morphostructural features (bedding attitude, shape of the slopes, main faults, lithological contrasts), we measured a total of 330 attitudes of fault planes and fractures in 7 sites, in different lithotypes at variable stratigraphic height (Figure 1). The collected data have been statistically analyzed to obtain information about their spatial distribution through the identification of fracture families (principal trends of fractures), which have been defined for each domain by plotting contoured stereo-net pole-frequency and normalized azimuth-frequency (rose) diagrams. A unimodal Gaussian curve-fitting routine is then used for determining peaks in directional data (DAISY software by Salvini et al. ), from which the statistical parameters are derived. We report these results in Figure 2a for each measurement site.
 Almost all the measured features are subvertical, with angles of dip ranging between 70° and 90°. We recognized four main fracture families both inside and outside the Solfatara crater, showing a relatively small dispersal of the strike angle around the direction of the two main fault systems that border the crater. N50W ± 25° and N50E ± 20° trending fractures form two pairs of conjugate systems, compatible with the geometry of the main faults responsible for the quadrangular shape of the Solfatara crater morphology. Although no kinematic indicators have been detected with the present survey, a normal stress field, characterized by a subvertical σ1, subhorizontal NW-SE and NE-SW trending σ2 and σ3, and R = (σ2 − σ3)/(σ1 − σ3) = 0.18, as hypothesized by Chiodini et al. , is consistent with our data.
 Two subordinate N-S and E-W trending systems of fractures, on average characterized by slightly lower angle of dip, ranging between 60° and 80°, have been measured along the high-angle inner slopes of the Solfatara crater, which are affected by gravitational instability phenomena, evidenced by rockfalls and localized translational and rotational sliding of parts of the inward-dipping, stratified, pyroclastic succession. These fractures have been here interpreted as surface deformations, produced to accommodate the movement along the NW-SE and NE-SW fault systems, during the gravitational readjustment of the inner-crater slopes.
3.2. Seismic Array Deployment
 The seismic survey was carried out in April 2007, using Lennartz MarsLite seismic stations equipped with three-component 1-Hz Mark LE3Dlite seismometers for the acquisition of seismic noise. We installed a total of 5 seismic arrays labeled A, B, C, D and E, sampling different areas of the crater (Figure 1). Arrays consisted of 4 sensors, set up with a circular geometry in which a sensor was placed at the center and the remaining three at fixed radius and evenly spaced (120°) around the circumference. Each day we deployed a single array whose configuration was changed by increasing the radius. Arrays A, B and D were designed with radii of 5, 10, 25, 50 and 100 m. Arrays C and E had radii of 5, 10 and 25 m. About 1-h of seismic noise was recorded for each circular configuration with fixed radius and a total of 68 sites were sampled by each sensor. More details about acquisition and data format can be found in Petrosino et al. . Arrays A, D and E were located approximately in the central part of the crater, array B was deployed in the area of the Fangaia, while array C was placed to the north, near the crater rim and the fumarole area (Figure 1) . For each array configuration we calculated the “array transfer function” [Rost and Thomas, 2002] that represents the frequency-wave number spectrum in response to a vertical incident impulse. The array resolution in wavelength that is directly related to the geometry of the array (inter-station distance and aperture) was estimated from the array transfer function [Di Giulio et al., 2006; Wathelet et al., 2008]. The values of minimum (kmin/2) and maximum (kmax) resolvable wavelength are reported in Table 2 for each array configuration.
Table 2. Values of Minimum (kmin/2) and maximum (kmax) Resolvable Wavelength for the Different Array Configurations
Array Radius (m)
3.3. Background Properties of Seismic Noise
 We performed a preliminary study of seismic noise aimed at its spectral and temporal characterization, in order to verify if this signal is suitable for the H/V ratio and surface wave dispersion analyses, and to choose the proper parameters for the application of these techniques.
3.3.1. Nature of the Noise Source and Spectral Characteristics
 Seismic noise at the Solfatara volcano has a predominant anthropogenic nature, as one can easily deduce from the time pattern of the root mean squared (RMS) noise amplitude filtered in the 1–20 Hz frequency band which clearly shows a 24 h periodicity (Figure 3). RMS is calculated over a 1-h long time window; daytime noise amplitude is about 3–4 times greater than that in the nighttime. The data used for the RMS analysis were recorded at SFT station (Figure 1), a permanent installation in the Solfatara crater of the Istituto Nazionale di Geofisica e Vulcanologia (INGV), equipped with a 3-component 1-Hz Mark LE3Dlite sensor. The analyzed samples are relative to an entire week, from Monday to Sunday, in the period 2–8 April 2007. Similar results are obtained by changing the filter frequency band (1–15 and 1–10 Hz). Spectra of noise samples continuously recorded at SFT station show frequency peaks irregularly spread in the 2–20 Hz band. The same evidence was in found analyzing 1-h-long noise samples recorded by 5 representative stations of the temporary arrays deployed within the Solfatara crater (see Figures 5–9 in Petrosino et al. ).
3.3.2. Stationarity of Seismic Noise
 Stationarity of the time series is a fundamental pre-requisite for the application of the present techniques. A check of this assumption is mandatory, as the analysis carried out on time series with a limited time duration. A first element to be addressed is the presence inside the Solfatara crater of many visitors during the day-time, producing transients and disturbances in the seismic recordings. In this condition it is particularly important to verify the stability of the H/V ratio in time, or, equivalently, to check that 1-h-long recordings for each station can be considered a statistically representative sample of the entire process.
 In order to check that hourly and daily cyclic variations of noise amplitude and frequency content, and the presence of transients do not affect the stability of the H/V ratio, we used data continuously recorded by the permanent station SFT. We calculated the H/V ratio over noise samples lasting 1 h, acquired during the week when the seismic survey took place. Each 3-component recording was bandpass filtered in the 1–20 Hz frequency band and an STA/LTA algorithm (with a short-term average, STA, of 1 s and a long-term average, LTA, of 30 s) was applied in order to reject the most energetic transients and disturbances. Time-windows of 40s with an overlap of 30% were selected. The Fourier spectra of the NS and EW components were geometrically averaged to obtain the horizontal component Fourier spectrum and the spectral ratios between the horizontal and vertical components smoothed by a Konno-Ohmachi function [Konno and Ohmachi, 1998] were calculated. Finally, the arithmetic mean of all the H/V ratios over each hourly recording was calculated. Several tests were also performed by changing the bandpass filter (1–15 Hz, 1–10 Hz), the window length (40–80s), the overlap (20–40%) and the Konno-Ohmachi smoothing factor (40–60). All these tests yield similar and stable results. We verified that number and length of the selected time windows ensure the reliability of the H/V curve according to the criteria defined in the SESAME European Project Deliverable D23.12 (available from http://sesame-fp5.obs.ujf-grenoble.fr). Moreover, we also checked that the obtained H/V peak verifies the amplitude and stability conditions indicated in the above-cited report, for an unambiguous and correct identification of the resonance frequency.
 In Figure 4 we show the 168 H/V spectral ratios relative to the period 2–8 April 2007 calculated for the SFT site: the fundamental frequency at about 4.4 Hz and the average peak amplitude of about 12 are stable for all the analyzed period. Slightly variations of these quantities occur within the standard deviation interval, which corresponds to errors on the order of 5–10% for the frequency values and of about 10% for the peak amplitudes.
3.4. Horizontal-to-Vertical Analysis of Array Data
 The H/V spectral ratios were calculated for all the recording points sampled by the 5 arrays, by using the procedure and the parameters previously described for the permanent station SFT. As we have already stated, the seismic noise recordings at the Solfatara crater often contain many transients due to the presence of the numerous tourists that visit the volcano daily. Therefore a careful check of the influence of non-stationary noise on the H/V ratios was performed by using both the raw seismograms and an STA/LTA algorithm to reject disturbances. The comparison of the obtained results show no differences in the resonance frequencies and peak amplitudes calculated in both the ways. This is in agreement with the observations and the numerical simulations by Parolai and Galiana-Merino  which show that transients have no (or little) effect on the H/V ratio. The reliability of the obtained H/V spectral curves and the significance of the retrieved resonance frequencies and peak amplitudes were checked according to the criteria of the SESAME European Project Deliverable D23.12 (available from http://sesame-fp5.obs.ujf-grenoble.fr): all the H/V ratios calculated for the array stations passed the tests. The associated errors are on the order of 5–10% for the frequency values and of about 5–15% for the peak amplitude values. A map (Figure 5) of the resonance frequencies and peak amplitudes was obtained by applying an inverse-distance-to-a-power gridding method that interpolates the H/V data such that the influence of one point relative to another declines with distance from the grid node. In the interpolation procedure we assumed the validity of the H/V ratio over a circle of radius of 30 m. Frequency values relative to the different sampled sites range from 3.6 to 7 Hz. The central and southern parts of the crater, corresponding to the arrays A, B, D and E are characterized by similar values of resonance frequencies (in the 4–5 Hz band), except for the station DR51 located near the inner crater slopes and station BR43 close to the Fangaia mud pool, that show higher values of frequency (6.2 and 7 Hz, respectively). Higher frequencies compared to the average value (from 5.4 up to 7 Hz) are also observed in the northern part, beneath most of the sensors of array C located near the inner crater slopes.
 As regards the H/V peak amplitudes, we observe that the Fangaia area, corresponding to array B, shows low values ranging from 2.5 to 5, with exception of stations BR42 and BR52 that fall outside the mud pool area and have slightly higher amplitudes. The part of the crater to the north of the Fangaia, exhibits higher peak amplitudes, with values ranging from 7 to 15. The area where array D is set up shows a highly heterogeneous behavior: the H/V amplitudes at the northern stations (DR53, DR43 and DR33) are comparable with those that characterize the central and northern part of the crater, while high peak values (up to 24) are observed in correspondence of the central stations (DR11, DR21, DR32, DR31). Moreover, for the eastern station DR51 we obtain a low peak amplitude, comparable to those of the Fangaia area.
3.5. Dispersion Curves Estimates
 We assumed that the vertical motion component of noise wavefield (in the frequency range we considered) at the Solfatara is dominated by Rayleigh waves. This is justified by the observation that the origin of high frequency seismic noise is mainly related to anthropogenic activity (as shown in section 3.3) and therefore the sources are mostly located at the surface [Bonnefoy-Claudet, 2004]. Under this hypothesis, we used three different methods to estimate the dispersion curves of Rayleigh waves propagating through the array: the Frequency–Wave number (f-k) technique [Lacoss et al., 1969], the Spatial Autocorrelation (SPAC) technique [Aki, 1957] and its modification (MSPAC) proposed by Bettig et al. .
3.5.1. Frequency-Wave Number Analysis
 In the f-k method the power spectral density is calculated as
where k = (kx, ky) is the wave number vector, ω is the angular frequency, R(ω) is the cross-spectral matrix, e(k) is the steering vector containing the phase shift and eH(k) is its Hermitian conjugate. The maximum of the spectral estimator at a given frequency is searched in the wave number plane (kx, ky) and the corresponding wave number vector is used to calculate the horizontal slowness (the inverse of the apparent velocity):
In order to apply the f-k technique we bandpass filtered the 1-h long recordings (vertical component) in the 1–15 Hz range, choosing values of center frequency, fc, with the step of 0.1 Hz and bandwidth defined as 0.9 fc–1.1 fc. The time window was selected equal to 30 times the central period of the analyzed band, and the overlap between successive windows was set to 30%. For each frequency band, the f-k spectrum was computed over a grid with size equal to kmax and step less than kmin/4 (Table 2). The maximum corresponds to the best slowness value. A histogram of the slowness obtained for all the selected time-windows at a fixed frequency was constructed in order to calculate the mean value and its associated statistical error [Ohrnberger et al., 2004].
 The phase velocity dispersion curve of the fundamental mode of Rayleigh waves was obtained for each array by plotting the velocity values as a function of frequency and selecting the part of the curve bounded by the resolution limits defined through kmin and kmax (Table 2). Actually, each array configuration with fixed radius defines the dispersion pattern in a limited frequency band: the smaller the radius, the higher the frequency range for which the dispersion branch is valid. Therefore, the total dispersion over the whole frequency band of 1–15 Hz was finally obtained by joining the 5 dispersion curves (or 3 in case of array C and E) estimated for each configuration with fixed radius (Figure 6). The phase velocity ranges from 100 m/s at high frequency to about 1000 m/s at frequency of 2 Hz. Phase velocity values are well retrieved from 15 Hz down to 4.5–5 Hz (which roughly corresponds to the average H/V peak estimated from Nakamura's technique [Nakamura, 1989]), while below 5 Hz velocity data are more scattered. This could be due to the increasing loss of coherency with the increasing array aperture (particularly evident for radii equal to 50 and 100 m). Moreover some authors have pointed out the difficulty to obtain the part of the dispersion curve just below the resonance frequency of a site [Di Giulio et al., 2006; Wathelet et al., 2008, and references therein]. Comparing the dispersion curves for the 5 arrays one can note that at least for frequencies greater than 5 Hz, the array C (the northern one) is characterized by higher velocities with respect to those of the arrays A, D and E located in the central part of the crater. On the other hand, the array B deployed in the Fangaia area shows intermediate values. Below 5 Hz, these differences in the phase velocity values are no longer appreciable.
3.5.2. SPAC and MSPAC Analyses
 For an array of receivers in a circular configuration, Aki  demonstrated that the phase velocity, for signals on the vertical component and filtered in a narrow frequency band around ω0, can be obtained by fitting a zeroth-order Bessel function, to the azimuthal average of the spatial correlation coefficients, , according to
with r the radius of the array, J0 the zeroth-order Bessel function and c(ω0) the phase velocity.
 Extension of Aki's SPAC method to a non-circular array [Bettig et al., 2001] consists in averaging, for each individual target frequency, the correlation coefficients evaluated at subsets of M station pairs whose distances range between r − dr and r + dr. A generic configuration can be then reviewed as a family of concentric rings. In such a frame, equation (3) becomes
where J1 is the first-order Bessel function.
 We applied both the classical and modified SPAC (MSPAC) methods, using the same parameters to calculate the average correlation coefficients. Since the final results are similar and the errors associated to the MSPAC dispersion curves are significantly smaller, we decided to illustrate only MSPAC analysis.
 Considering all the possible station pairs, we arranged a set of 2 rings, each containing 3 station pairs for every array configuration. As for the f-k analysis, we filtered the vertical component of 1-h-long signals in the band 1–15 Hz. For each ring, we used 60-s-long time windows with an overlap of 30%, to calculate the average correlation coefficient. The obtained series, containing 100 samples linearly spaced over 1–15 Hz frequency band, were used to fit equation (4). The Rayleigh wave fundamental mode dispersion curves, c(ω0), were obtained by picking the maxima of the semblance function, calculated in the fitting procedure, in the slowness-frequency plane. The frequency range of the dispersion curves for each configuration is determined by the resolution limits kmin and kmax (Table 2). The error associated with the dispersion at a given frequency value was calculated by the spreading of the semblance maxima corresponding to that frequency. The total dispersion curve for each array was finally obtained with the same procedure used in f-k method (Figure 7). The dispersion curves retrieved from MSPAC and f-k methods are comparable. Therefore all the general observations made for f-k curves hold, although the dispersion patterns obtained by the MSPAC technique are less scattered below 5 Hz. Since the MSPAC curves are affected by smaller errors, they were chosen to be inverted for the S-wave velocity model.
3.6. Dispersion Curve Inversion
 For each array we inverted the dispersion curves obtained from MSPAC analysis, jointly with the corresponding average H/V resonance frequency, whose value depends on the layer thickness and the shear wave velocity [Kramer, 1996] and therefore can be used as a constraint in the inversion procedure. In order to obtain the 1-D S-wave velocity profiles we used the neighborhood algorithm [Sambridge, 1999] as implemented by Wathelet et al. [2004, 2005, 2008]. This algorithm performs a stochastic search over the parameter space, defined by S- and P-wave velocities, top depths, densities and Poisson's ratios of the subsurface layers. The goodness of results is evaluated through minimizing misfit function, defined as
where xdi and xci are the experimental and theoretical velocity, respectively, at frequency fi, σi is the uncertainty of the considered frequency sample, nF is the number of frequency samples at frequency fi.
 The inversion of dispersion data is a non-unique problem, i.e., several velocity profiles can be retrieved from the same dispersion curve by using different parameterizations, in particular the number of layers and the half-space depth. To overcome this difficulty we evaluated the misfit value over a wide range of parameterizations and for each one we performed a set of 5 inversions to check the robustness of the results [Di Giulio et al., 2012]. For each array and each parameterization we obtained a set of 5 best models with associated 5 minimum misfit values. Then, to select the most likely velocity profile, we analyzed the behavior of the minimum misfit as the parameterization varies, taking into account that (1) the minimum misfit as a function of the number of layers reaches a minimum in correspondence of the more realistic number of layers [Renalier et al., 2010; Di Giulio et al., 2012] and (2) the half-space depth increases with the number of layers and starts to scatter around the actual depth [Renalier et al., 2010]. We illustrate these behaviors in Figure 8; on the left, the minimum misfit shows a clear minimum in correspondence of 2 layers for the array A and C, 3 for array B and 1 for array E; on the right, the corresponding half-space depth can be easily identified. The behavior of the array D is ambiguous. Although an absolute minimum for the minimum misfit can be recognized, none of the parameterizations inside the range 2–4 number of layers dominates (green triangles in Figure 8, on the left). The final profile ensembles for each array were obtained in correspondence of the previous minima and they are plotted in Figure 9, where the most likely S-wave velocity profiles are shown in the middle panels. In the left panels we show the theoretical dispersion curves for the Rayleigh fundamental mode and the experimental ones, with the respective error bars. A good agreement is obtained for the array A, B, C and E. The mismatch occurred for the array D is to be attributed to a poorly constrained depth for the second layer. The right panels of Figure 9 report the theoretical ellipticity curves, calculated for the velocity profiles, that fit the H/V peaks inside the standard deviations (gray vertical bars).
 Since our final goal is to retrieve a shallow 3-D S-wave velocity model for the Solfatara crater by combining the results obtained from the inversion procedure, we estimated the statistical level of significance associated to each depth and velocity of the 5 1-D profiles by using a Monte Carlo algorithm. We generated 100 random dispersion curves inside the error bars for each array and inverted them following the same procedure previously described. This procedure constitutes a test which quantifies how well the inversion algorithm reconstructs synthetic models when the dispersion curves are perturbed. The obtained mean velocity profiles and their associated standard deviations are shown in Figure 9 (black continuous and dashed lines, respectively, in the middle panels) superimposed to the velocity profile ensembles. A first consideration on these results is that the mean profiles coincide with the best 1-D profiles, confirming the goodness of the inversion procedure and the Gaussian structure of the errors. The errors on the velocity in the first 12 m of depth, calculated with Monte Carlo method are at most of the order of 10% of the estimate. This evidence suggests that the procedure utilized is sensitive to the crustal heterogeneity (vertical and horizontal) close to the surface. Conversely, resolution decreases as depth increases. Finally, the D array shows a low precision (53%) in the determination of the subsurface structure under the hypothesis of parallel-plane layers (with constant velocity) at intermediate depths. Although poorly constrained, this velocity structure is indicative of the average properties of the medium beneath the array D.
 In order to obtain a 3-D velocity model corresponding to the volume below the 5 arrays, we applied an inverse-distance-to-a-power gridding method to the 5 mean 1-D velocity profiles. The velocity data are weighted during the interpolation process, such that the influence of one point relative to another declines with distance from the grid node coincident with the array centers. For the generation of the grids we used circular domains with the same geometrical dimension of the corresponding array, leaving the zone without data as blank. We performed the following resolution tests to ensure that the algorithm does not introduce artificial patterns in the velocity spatial distribution. (1) All the volume is set at a uniform velocity. (2) In turn, one model underneath one array, is left unchanged and the remaining volume is set at a uniform velocity. (3) In turn, one model underneath one array, is slightly varied and the other four models remain unchanged. All the tests do not show spurious patterns. It has to be said that our 3-D model preserves the good original vertical resolution of the 1-D profiles, while the position of the horizontal velocity discontinuities are only constrained by the array aperture since the 1-D models do not carry information about their horizontal extent.
 In Figure 10 we show the S-wave velocity horizontal slices at the different depths. A wide spatial variability of the velocity between 0 m (station plane) and 12 m depth is retrieved (Figures 10a–10e). In the range 0–5.0 m (Figure 10a) we can distinguish the velocity variation from 120 m/s for the eastern part of the crater (array A and D) to 200 m/s for the western part. Then an increase of the S-wave velocity starts in the southern area at depths between 5.0 and 5.5 m (Figure 10b), involving also the northern sector in correspondence of depths 5.5–7.2 m (Figure 10c), where a maximum velocity of 400 m/s is reached beneath the array C. The lower velocity area remains confined in the central part of the crater. Between 7.2 and 12 m (Figure 10d) the velocity in the eastern area increases up to 650 m/s. At these depths the volume results divided in a higher velocity part (to the east, corresponding to the fumaroles below the array D) and a lower one (corresponding to the western edge below the array E), with a transition central zone. From 12 to 17 m (Figure 10e) the velocity increases up to 1300 m/s in the western area. Figure 10f shows the volume between 17 and 28 m with an increase up to 900 m/s of the velocity below the array B. Depths 28–40 m are represented in Figure 10g, where the higher velocity area in the northwestern sector (up to 1400 m/s below the array C) bounds the center of the crater, characterized by lower velocities (500 m/s) beneath the array A. Figures 10h and 10i represent the volume, explored only by arrays A, B and D, below 40 m depth which is the limit of resolution for the array E and C [Midzi, 2001]. The 60–150 m depths (Figure 10h) are characterized by a higher velocity in the center and northeast area, with values between 1000 and 1900 m/s, while lower velocity corresponds to the array D (about 650 m/s). The final slice (below 150 m) that represents the velocity values just above the limit of detection (about 200 m) for the array A, B and D, shows a higher velocity (1700–1900 m/s) area in correspondence of the array A and B, and a lower velocity region (1000 m/s) below the array D.
3.7. Polarization Analysis
 We investigated the polarization properties of seismic noise by applying the covariance matrix method [Jurkevics, 1988] to the three-component seismograms. Through a diagonalization procedure, the following parameters are estimated:
 1. The rectilinearity, defined as RL = 1 − (λ2 + λ3 /2λ1), with λ1 > λ2 > λ3 the eigenvalues of the covariance matrix. RL takes values between 0 (pure spherical motion) and 1 (pure rectilinear motion).
 2. The azimuth of the polarization vector. It is the angle between the projection on the horizontal plane of the polarization vector and north, measured clockwise.
 3. The incidence angle between the polarization vector and the vertical axis.
 The samples of seismic noise were filtered by applying a bandpass a-causal Butterworth filter in different frequency ranges (1–10, 5–10, 5–15 Hz); polarization parameters were estimated using 1-s-long sliding window with overlap of 50%. Similar polarization patterns were found independently of the frequency band, therefore we discuss the results of the analysis in the 1–10 Hz range.
 We selected the stations for which the distribution of RL has a 70% of values equal or greater than 0.5, because in this case the angular parameters are associated with surface and body waves, while for RL less than 0.5 they lose their significance. The incidence angles from the polarization analysis are in the range 80°–90°, confirming the shallow propagation of the noise wavefield. Moreover, narrow azimuthal distributions of the polarization vector are shown in the rose diagrams of Figure 11. The representation in terms of the vectorial field (Figure 11) was obtained using the mean value of the azimuth for each site and applying an inverse-distance-to-a-power gridding method. The interpolation was limited to a circle of radius of 30 m around each station. The magnitude of the vectors was set proportional to the inverse of the standard deviation of the azimuth mean value. Results of the analysis evidence the tendency of ambient noise to be polarized. In the central and northern part of the crater, going from the west to the east, the horizontal polarization vector is first oriented NW-SE, then it seems to switch to a roughly N-S direction, and finally it assumes a E-W orientation. In particular, the array D is affected by the greatest inter-station variability of the azimuth of the polarization vector. In the Fangaia area, the azimuths retrieved for stations BR43, BR00 and BR52 show a preferred orientation along the NW-SE direction, while station BR33 has a NE-SW polarization. However, this anomalous wave propagation occurs locally, beneath the station located just above the edge of the mud pool.
 In the present paper we combine the results obtained from seismic noise analysis with those from a volcanological and morphostructural study of the Solfatara volcano, in order to reconstruct the formation and evolution processes of the volcano and to model its shallow crustal structure. Figure 12 is an interpretative cross-section, based on the results of the volcanological, morphostructural and seismological investigations.
 The volcanological features described in section 3.1 suggest that the eruption that generated the Solfatara volcano was a complex and likely long-lasting event, during which a former crater (Crater 1; Figures 1 and 12) was formed during the early phreatomagmatic and magmatic explosions, which occurred in the area of the preexisting Mt. Olibano lava dome, generating the breccia deposits and the lower part of the overlying pyroclastic sequence. The upper part of the sequence, which lies above the uppermost angular unconformity, was generated by a series of phreatomagmatic explosions in the latest stages of the Solfatara eruption, likely after a pause in the activity. Its thickness and grain-size variations suggest a provenance from a smaller, ring-shaped vent area (Crater 2; Figures 1 and 12), nested within the previous main crater. This eastward vent migration is likely controlled by the intersection of the NW-SE and NE-SW trending fault systems that crosscut the Solfatara area, as evidenced by the structural survey. The Solfatara area, located along the northeastern boundary of the La Starza resurgent block, is largely deformed by these two fault systems, and by the subordinate N-S and E-W trending systems of fractures, that we interpreted as surface deformations, produced to accommodate the movement along the main NW-SE and NE-SW fault systems, during the gravitational readjustment of the differentially deformed blocks. Both internal and external slopes of the volcano show rectilinear parts and triangular facets related to the deformation that occurred during and after the eruption along these features. This deformation has also been evident during recent bradyseismic events, when the opening of a NE-SW trending fracture occurred in the area of the Fangaia mud pool [Acocella et al., 1999; Orsi et al., 1999; Vilardo et al., 2010].
 The intense volcanic and deformation activity has generated a complex volcanic edifice characterized by high vertical and horizontal heterogeneity, due to the overlapping of nested craters (Figure 12), which have been variably filled by heterogeneous reworked deposits, produced by the morphologic evolution of the inner slopes of the Solfatara edifice. These deposits are thickest in the central part of the main crater and progressively thin outward, draping the inner flanks of the edifice. The last observation fits quite well with the results of H/V analysis that shows higher resonance frequency values in the northeastern part of the crater, approaching the internal crater slopes, when compared to the central area. Moreover, the detected shear wave velocities for the shallower layers are typical of loose and unconsolidated pyroclastic deposits [Nunziata et al., 1999].
 Another interesting observation concerns the low peak amplitude values obtained from the H/V analysis in the Fangaia area, here interpreted as due to the presence of deposits saturated by hydrothermal fluids. This interpretation is supported by the results of electrical resistivity profiles [Bruno et al., 2007]. Indeed, as observed by some authors [Yang and Sato, 2000; Yang, 2006], ground motion amplification (and thus the amplitude ratios) is significantly affected by the saturation conditions of the medium.
 Immediately below the shallow deposits, the shear wave velocity modeling again shows the presence of both vertical and horizontal discontinuities. In particular, the eastern sector corresponding to Crater 2 (Figures 1 and 12), is characterized by high velocity values, which are typical of lithified tuffs [Nunziata et al., 1999]. The observed values and the contrasts with the surrounding areas corroborate the hypothesis of the presence at shallow depth of a small volcanic edifice, likely a tuff-cone, formed during the phreatomagmatic activity of Crater 2, and emplaced above sediments filling the Crater 1 (Figure 12). The lateral and vertical lithological and structural discontinuities, due to the superposition of the products related to this multivent activity would be ultimately the cause of the observed spatial variability in the H/V peak amplitudes. In addition the high heterogeneity of this sector of the crater possibly affects the phase velocity array measurements [Bodin and Maupin, 2008], making inadequate, at intermediate depths, the parallel-plane layers modeling and thus producing a less constrained velocity structure.
 At a greater depth, a complex high-velocity body has been observed in the northwestern sector of Crater 1 (Figures 10 and 12). The recorded horizontal and vertical velocity variations suggest the presence of lithified bodies surrounded by soft sediments, which can be interpreted as lava bodies, emplaced inside Crater 1 and later overlain by the soft and likely reworked sediments that fill the crater.
 The deepest volume explored by the seismic arrays is characterized by the highest velocity values in the central part of the Solfatara volcano, and by slightly lower values toward east, in the Fumarole sector. This is also in agreement with the presence of lava bodies within the larger and older Crater 1, and tuffs within Crater 2. Velocity values increase with depth, likely due to a generalized improvement in the mechanical characteristics of the rocks.
 The results of the morphostructural analysis of the Solfatara volcano evidence the interplay between two conjugate N50W and N50E trending main fracture systems that define the geometry of the inner-crater slopes, and two N-S and E-W trending subordinate systems, induced by the gravitational readjustment of the slopes. This complex structural pattern could control the direction of the polarization vector of seismic noise, as suggested by Rigano et al. . In fact a clear relationship between the direction of the polarization vector and fault trend arises in the Fangaia area (Figures 1 and 11). Here the average azimuth shows a preferred orientation along a NW-SE direction, which is approximately orthogonal to the trend of the main feature affecting this sector of the crater. Normal polarization pattern could be consistent with the near-surface anisotropy or with a resonance mechanism of seismic waves in the fault [Rigano et al., 2008]. In the northern part of the Solfatara crater, along an E-W profile the orientation of the horizontal polarization vector varies from roughly orthogonal to parallel to the direction of the fractures. In this latter case the observed parallel pattern could be interpreted in terms of fault-trapped surface waves and channeled in the waveguide [Rovelli et al., 2002; Lewis et al., 2005]. However, due to the complex interplay among the variable fracture systems in this part of the crater, their contribution to the noise polarization cannot be discriminated. Moreover, the results could also be affected by the high degree of heterogeneity characterizing the local lithology, and by the presence of the buried rim of Crater 2.
 The Solfatara volcano has represented a good test-site to reconstruct the shallow crustal structure from the application of different seismological techniques for the analysis of seismic noise, combined with the results of volcanological and morphostructural investigations. In a sort of continuous feed-back process, the surface geology of this area has been used to provide physical constraints needed for the correct interpretation of spectral ratio resonance frequencies and peak amplitudes, S-wave velocity model and polarization pattern, which in turn has led to constraints on the subsurface structure of the volcano and its geological evolution.
 At the Solfatara volcano, seismic noise has provided a great deal of information about the medium properties whose knowledge is thus essential for seismologists, when a proper separation into source, path and site effects is needed for a correct interpretation of volcanic earthquake source. This is particularly important at this volcano, where long-period seismic events associated to the activity of the hydrothermal system occur in the top 500 m [Cusano et al., 2008].
 The S-wave velocity structure inferred in the present study provides a detailed 3-D model for the Solfatara subsurface down to a depth of about 200 m. Previous models calculate 1-D S-wave velocity profiles from active seismic data, with a maximum resolution down to a depth of 32 m [Bruno et al., 2007], or they represent an average 1-D profile for an area including not only the Solfatara volcano but also the town of Pozzuoli [Petrosino et al., 2006], hence with a lower spatial resolution compared to the present results. Moreover our study confirms that, as observed by Rigano et al. , polarization of seismic noise is sensitive to the presence of faults and could be indicative of the orientation of the fracture systems. In the future, this interesting result could be further improved by replacing single stations with very small arrays, in order to perform array-averaged polarization measurements.
 The joint interpretation of the S-wave velocity model, together with the results of the polarization analysis and the volcanological and morphostructural observations, contributes not only to imaging the shallow crustal structure of the volcano at a small scale, but also to put some constraints on its geological evolution. A new evolutionary model of the Solfatara volcano in which the volcano has been characterized by a long-lasting multivent activity, due to vent migration along structurally controlled fissures. The geometry of at least two tuff-cone craters, later intruded by viscous lava domes and filled by tephra and reworked sediments, is clearly shown by both the geological and seismological survey carried out with this study.
 The outcomes presented in our paper improve the knowledge of the Solfatara volcano, thus contributing to evaluate and assess volcanic hazard in a densely populated area like the Campi Flegrei volcanic complex, and to support further geophysical and volcanological researches. These outcomes should encourage new surveys at active volcanoes and to adopt such a multidisciplinary approach.
 The Administration of the Solfatara Volcano is acknowledged for having allowed us to deploy the seismic instruments in the Naturalistic Park. We wish to thank Mariacira Veneruso, Lucia Zaccarelli and Vincenzo Torello who greatly helped us in the field work, and Francesca Bianco and Roberto Scarpa for their useful suggestions. Bill Fry, Catherine Lewis Kenedi and an anonymous reviewer are acknowledged for their comments that helped us in improving the manuscript. Most part of data analysis was done by using Geopsy and Dinver software (available from http://www.geopsy.org/). This work was carried out in the framework of the projects entitled ‘SPeeD’ and ‘UNREST’ (Civil Defense of Italy and the Istituto Nazionale di Geofisica e Vulcanologia), and PRIN (Italian Ministry of Education). Data and results of preliminary analyses are fully available upon request to firstname.lastname@example.org.