Integrated tomographic methods for seismic imaging ...

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Nov 28, 2017 - Corresponding author. E-mail address: ortensia[email protected] (O. Amoroso). 1 Now at Instituto Volcanológico de Canarias, Tenerife, ...
Journal of Applied Geophysics 156 (2018) 16–30

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Integrated tomographic methods for seismic imaging and monitoring of volcanic caldera structures and geothermal areas O. Amoroso a,⁎, G. Festa a, P.P. Bruno b, L. D'Auria c,1, G. De Landro a, V. Di Fiore d, S. Gammaldi a, S. Maraio e, M. Pilz f, P. Roux g, G. Russo a, V. Serlenga a,2, M. Serra a, H. Woith f, A. Zollo a a

Department of Physics “Ettore Pancini”, University of Naples 'Federico II', Italy Department of Geosciences, Khalifa University of Science and Technology, Abu Dhabi, United Arab Emirates Istituto Nazionale di Geofisica e Vulcanologia, Osservatorio Vesuviano, Italy d Istituto per l'Ambiente Marino Costiero IAMC-CNR, Napoli, Italy e Centro di GeoTecnologie - Università di Siena, Italy f GFZ German Research Center for Geosciences, Helmholtzstr. 7, 14467 Potsdam, Germany g ISTerre, Université Grenoble Alpes, CNRS UMR 5275, rue de la Piscine 1381, F-38058 Grenoble, France b c

a r t i c l e

i n f o

Article history: Received 11 May 2017 Received in revised form 14 October 2017 Accepted 24 November 2017 Available online 28 November 2017 Keywords: Seismic tomography Volcano seismology Seismic attenuation Body waves Surface waves

a b s t r a c t In this paper we present innovative methodologies for seismic monitoring of volcanic structures in space and time (4D) which can possibly evolve toward an unrest stage. They are based on repeated phase and amplitude measurements done on active and/or passive seismic data including shots, vibrations, earthquakes and ambient noise in order to characterize the structure of the volcano and track its evolution through time. The characterization of the medium properties is performed through the reconstruction of an image of the elastic and anelastic properties of the propagation medium crossed by seismic waves. This study focuses on the application of specific tomographic inversion methods to obtain high quality tomographic images. The resolution of the tomographic models is influenced by the number and spatial distribution of data. The expected resolution thus guides the setup of, for example, active seismic surveys. To recognize and monitor changes in the properties of the propagation medium without performing an active survey we identify a fast proxy based on the time evolution of the Vp/Vs ratio. The advantages and limitations of the methods are discussed through synthetic tests, resolution analysis and case studies in volcanic areas such as the Campi Flegrei (southern Italy) and The Geysers geothermal area (California). © 2017 Elsevier B.V. All rights reserved.

1. Introduction Volcanic eruptions have always attracted interest from, media, and scientific community. Scientific studies have led to remarkable progress in the modeling of physical phenomena ruling volcano dynamics, but much remains to be done to reach their complete understanding, and most of all, identify their precursory. One of the most powerful geophysical prospecting methods is seismic tomography. It is an inference technique, which exploits the information contained in the seismic records i.e., arrival times and amplitude of seismic phases to obtain 2D and 3D models of physical parameters such as seismic phase velocity or anelastic attenuation (Lees, 2007). Tomography requires an inverse problem solution to match the model with the

⁎ Corresponding author. E-mail address: ortensia.amoroso@fisica.unina.it (O. Amoroso). Now at Instituto Volcanológico de Canarias, Tenerife, Spain. 2 Now at Consiglio Nazionale delle Ricerche, Istituto di Metodologie per l'Analisi Ambientale, Tito, Italy. 1

https://doi.org/10.1016/j.jappgeo.2017.11.012 0926-9851/© 2017 Elsevier B.V. All rights reserved.

observations (Nolet, 2008; Rawlinson et al., 2010). From the pioneering work of Aki and Lee (1976), methodological advancements in this field allow for the imaging of tectonic and volcanic areas with resolution down to the space scale of the order of tens of meters (De Landro et al., 2017). It is possible to reconstruct the subsurface structure using artificial seismic sources produced, for example, by underground explosions (active seismic) or natural sources such as earthquakes or noise (passive seismic). In the first case, an array of seismic sensors is deployed at surface, close to the region to be studied. The acquisition layout (the relative receiver-source distribution) is designed according to the desired resolution. In passive seismic, both the possible scattered deployment of sensors and the source location are unknowns for the inverse problem. The aim of this paper is to describe methods of seismic tomography used for imaging volcanic structures, with particular attention to inversion strategies. Several case studies of local tomography are presented to provide an overview of the different types of tomographic techniques that are carried out. In particular, we present the application of tomographic techniques to active seismic data sets relative to the volcanic area of

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Campi Flegrei (Southern Italy) and a passive seismic data set recorded at The Geysers geothermal area (California). 2. Seismic tomography methods for imaging volcanic structures Seismic tomography represents an excellent tool to image crustal heterogeneities (i.e. the position, extension and intensity of anomalies) using either shots and/or local earthquake data (e.g. Zollo et al., 2002; Husen et al. 2003). Very striking results for the P- and S-wave velocity models can be obtained by performing a simultaneous inversion of Pand S-wave arrival times to estimate the event location coordinates, their origin time, and P- and S-wave velocities at the nodes of a discretized 3D volume (Vanorio et al., 2005) as long as a good approximation of the real medium is available as a starting model in the inversion. A useful strategy to minimize the influence of the starting model is adopting a multi-scale approach (e.g. Amoroso et al., 2014; De Landro et al., 2017). While velocities provide information on the elastic properties of rock, the lateral variation of the anelastic parameter Q can be retrieved by the use of attenuation tomography (De Siena et al., 2009; Hauksson and Shearer 2006; Serlenga et al., 2016). Possible time variations of seismic properties can be observed by repeating the tomography in time (i.e. 4D tomography - Patanè et al., 2006; Koulakov et al., 2013). Finally P- and S- wave models with different resolution can be constrained using dispersion curves measured on surface waves either obtained by analyzing the signals generated by shots or by crosscorrelation of ambient noise. 2.1. 3D velocity tomography The most advanced tomographic inversions use an iterative scheme operating a linearized delay-time inversion to estimate both velocity models and earthquake locations (e.g. Latorre et al., 2004 and references therein). First arrival travel times of wavefronts are computed through a finite-difference solution of the eikonal equation (Podvin and Lecomte, 1991) in a finer grid of nodes, consisting of constant slowness nodes computed by tri-linear interpolation from the inversion grid. For each source-receiver pair, travel times are recalculated by numerical integration of the slowness on the inversion grid along the rays traced in the finite-difference travel time field (Latorre et al., 2004). Simultaneously, for each node of the inversion grid, travel time partial derivatives are computed for the P slowness, hypocenter location and origin time. The parameters are inverted using the LSQR method (Paige and Saunders, 1982). Model roughness is controlled requiring that the Laplacian of the slowness must vanish during the inversion procedure (Benz et al., 1996; Menke, 1989). The velocity model is parameterized by a nodal representation, described by a tridimensional grid. 2.2. 3D attenuation tomography using t* and dt* If the velocity model is known and the t⁎ parameter is estimated along the corresponding path, the 3-D attenuation quality factor Q of the medium along this path can be solved by an appropriate inversion method (Lees and Lindley, 1994; Haberland and Rietbrock, 2001; Rietbrock, 2001; Hansen et al., 2004; Martinez-Arevalo et al., 2005; Chiarabba et al., 2009; Bisrat et al., 2014; Amoroso et al., 2017). Since the velocity model is fixed, ray paths do not change in the inversion procedure and the problem is fully linear from a mathematical point of view. Nevertheless, the uncertainties on data, in addition to the mixed-determined nature of the problem (Menke, 1989) ask for the data to be inverted by means of a linearized, iterative, perturbative scheme requiring a starting attenuation model as well as some form of regularization of the inverse problem and constraints. In this model a theoretical calculation of t⁎ is performed to evaluate the residue between observed and expected t⁎ values: Δt⁎ = t⁎obs − t⁎cal. This condition defines the set of equations to be inverted, which are coupled with smoothing and preconditioning conditions to avoid instabilities

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to emerge in the solution. Finally the inversion of the linear system Δt⁎ = HΔη is performed using the LSQR method, where the term H describes the data-kernel, Δη is the perturbation of the reciprocal of the quality factor with respect to the starting attenuation model. Once the Q attenuation model has been obtained, the Root Mean Square (RMS) of residuals is evaluated, and the procedure is reiterated until this value is smaller than a certain threshold. Tomographic attenuation images may be obtained also by differential attenuation measurements (Serlenga et al., 2016), i.e. dt⁎. The problem can be faced using a similar approach to that of Teng (1968), where a thorough dissertation of the problem may be found. For a single source and a set of receivers (j is the reference station, i = 1,N the remaining stations), the data vector is    dt :……………dt  ; 1 n

ð1Þ

where 

dti ¼ t i −t j :

ð2Þ

Let us develop the problem only for the quantity dt⁎1 for sake of simplicity. With fixed velocity and attenuation models, a residual quantity, Δdt⁎1, is obtained as      − t OBS ¼ δt 1 −δt j −t CALC −t CALC Δdt1 ¼ t OBS 1 1 j j

ð3Þ

in which the term Δdt⁎1 may be also defined as the double-difference contribution (Waldhauser and Ellsworth, 2000). In Eq. (3), each term in brackets, δt⁎, represents the residual between observed and computed t⁎ in fixed velocity and attenuation models. In a 3D tomographic grid, each t⁎ residual can be expressed as δt i ¼

X ∂t  i Δη : ∂ηl;n;p l;n;p cube

ð4Þ

In the above equation the subscript i represents the receiver index. The tern of indexes l,n,p, instead, refers to the nodes of the tomographic grid. Let us assume to have a single source attenuation tomographic problem, for which seismic signals have been recorded at N stations. Parameterizing the investigated medium in a 3D tomographic grid described by M nodes, constituting the set of parameters to be determined, the resulting system of double-difference equations could be written in a matrix form:   1    ∂t m ∂t m    ∂t 1 ∂t j j  Δη  1  Δdt   1 −  1  −  1   ∂η1  ηm  …  ∂η1 ∂ηm  ::…         …   ::…      ¼ …………  …   ::…           ::…   …       m  … 1 m ∂t ∂t ∂t  Δdt   ∂t 1   j j n   n −  n − Δη  m  ∂η η ∂η ∂η m m 1 1

ð5Þ

The inversion scheme, as well as the adopted numerical algorithm, is analogous to the one described in the first part of this paragraph, with the exception that absolute t⁎ values are substituted by differential values. 2.3. 4D imaging 2.3.1. Temporal variation of Vp/Vs ratio The Vp/Vs ratio is a quantity directly correlated with the presence of fluids within the crust (Thurber et al., 1995; Amoroso et al., 2017). The analysis of Vp/Vs ratio temporal variations is thus a technique for imaging the large-scale medium properties. It provides complementary

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information with respect to a tomographic inversion procedure and it has the advantage that the results can be computed as soon as the seismogram is available. The Vp/Vs ratio value is computed from the time difference between S- and P-wave arrival times (indicated by tp and ts respectively) at a given station, divided by the P-wave travel-time (ttp) from the hypocenter to the station (Lucente et al., 2010; Wadati, 1933; Kisslinger and Engdahl, 1973; Chiarabba et al., 2009b) using the following formula VP t S −t P ¼1þ VS tt P

ð6Þ

The above relation holds for a uniform Vp/Vs ratio along the travel path (Scholz et al., 1973; Whitcomb et al., 1973). By considering the Vp/Vs ratio temporal variation for several events that occurred in the same source region, and recorded at different pairs of nearby stations, we are able to reveal possible changes in crustal volume of events occurrence (Fig. 1). The basic idea is to analyze the graphs of VP/VS ratio as a function of time for each couple of stations, and to identify both spatial and temporal changes by comparing them to each other. 2.3.2. 4D seismic tomography Time-lapse tomography is a technique that consists in applying the three-dimensional tomography in different time-windows, referred to as epochs. To properly define the epochs, a preliminary 3D reference velocity model and related resolution have to be obtained. These results represent the benchmark for the resolution analysis in the individual epochs. The resolution can be assessed through the ray coverage, the derivative weight sum (DWS - Toomey and Foulger, 1989), the checkerboard test, and the resolution matrix, represented by maps of its diagonal elements and the spreading function (Sj - Michelini and McEvilly, 1991). For each of these, it is possible to define a threshold value that can be used to delimit the model regions that are considered well-resolved. The threshold should be set up specifically for each tomography, for example implementing synthetic tests. The adaptive selection process of the temporal duration of an epoch consists in selecting specific time windows and using the data set recorded within this time interval to achieve a 3D tomography. The solution is evaluated and compared with the one obtained in the 3D reference model. If the resolution is too low with respect to the resolution of the benchmark, the length of the time window has to be increased including more data. In order to have consistent model resolution between the different epochs, the epochs may have different durations.

2.4. Surface wave tomography from phase and group velocity analysis using dense array records The estimation of a 3D model for the investigated area is achieved collecting the 1D models coming from the joint inversion of the dispersion curves in each selected subdomain, where the 1D approximation holds. The local 1D model can be obtained from a joint inversion of group and phase velocities (e.g. using the Geopsy software, Wathelet et al., 2004). The dispersion curves depend on the number of layers, the density and the velocity values for the P- and S-waves in each layer. To properly set the number of layers, recursive test can be performed increasing the number of layers and evaluating the corresponding misfit reduction. An AIC criterion can be applied to define the optimal number of interfaces required to fit the dispersion curves. For a fixed number of layer the solution is sought using a global exploration method such at Neighborhood algorithm (Sambridge, 1999), which divides the parameter space into Voronoi cells and refines the sampling in the regions of the space where the cost function, defined vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u nF uX ðxdi −xci Þ2 as t where xdi is the measured velocity at a given σ 2i n F i¼0 frequency fi, xci is the computed velocity at a given frequency fi, σi is the uncertainty on the measurement of the considered frequency and nF is the number of frequency samples, is smaller than elsewhere. 2.5. Ambient noise In contrast to global tomographic studies we are not seeking for small perturbations to an established reference model but we intend to locate velocity differences and corresponding velocity variations on a small local scale. Opposed to active seismic studies in volcanic environments (De Luca et al., 1997), several approaches have been proposed to extract information about the 3D velocity distribution of seismic waves in shallow structures from temporary recording of seismic noise (Chávez-García and Luzón, 2005; Brenguier et al., 2007; Picozzi et al., 2009) although the use of high frequency seismic noise interferometry implies by far not only a change in scale but also requires a sufficient understanding of the origin of seismic noise and of the spatial and temporal distribution of its sources. Generally, all techniques for retrieving surface wave dispersion curves are based on phase-coherency measurements between pairs (at least two) of signals. Aki (1957) proposed the spatial autocorrelation (SPAC) method, which has been generalized in the extended spatial autocorrelation (ESAC) method by Ohori et al. (2002). If the microtremor wavefield is stochastic and stationary in both time and space (Ohori et al., 2002), the azimuthally averaged correlation function for a single angular frequency ω0 can be calculated by means of  ρðr; ω0 Þ ¼ J 0

Fig. 1. Schematic representation of the rays path for a given sources-stations geometry. The common area of all rays is the source region (red dashed line).

ω0 r cðω0 Þ

 ð7Þ

Here, c(ωo) represents the phase velocity, r is the interstation distance and Jo is the zero order Bessel function. Eq. (7) can be applied to averaged correlation functions calculated for a set of narrow frequency bands. In turn, the calculated travel times for the surface wave for individual frequencies were simultaneously inverted by a rapid one-step tomographic algorithm. In its general form, the travel time between a source and a receiver along a ray path element for a continuous slowness s (reciprocal of velocity) is written in an integral form. However, although the ray path is velocity dependent, meaning that travel time inversion is a non-linear problem, deviations of the paths from a straight line will either be of the same order as the dimension of the blocks size or smaller will be less than a quarter of the wavelength. Considering the error level of the input data for shallow seismic surveys, we are sure that a bias of a

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Fig. 2. Acquisition layout of seismic campaign RICEN. Left: location of the two linear arrays used for the 2D seismic reflection-refraction experiments. Data were collected in May 2014 along the NNE striking array and in November 2014 along the WNW trending array. Right: aerial view of the Solfatara crater with location of the recording array. Specifically the 2D array for the 3D tomography is located at the NE boundary of the mud region, named “Fangaia”.

few percent can be tolerated keeping the solution linear (Kugler et al., 2007; Pilz et al., 2012).In turn, the studied medium can be subdivided into smaller blocks, and the problem can be expressed in a simple discrete matrix form (Pilz et al., 2012, 2013). Starting from a homogeneous 3D velocity model, we adopt an iterative procedure based on singular value decomposition for minimizing

the misfit between the observed and theoretical travel times. In particular, as higher frequency sample shallow blocks whereas lower frequencies sample deeper blocks a further constraint on the solution can be introduced by adding a weighting matrix. According to Yanovskaya and Ditmar (1990), for a 3D problem, the weights can be calculated as the product of two functions with one weight depending on the horizontal

Fig. 3. Spatial resolution at surface, superimposed to the map of Solfatara and the acquisition geometry of the experiment. The black box delimits the same area of Fig. 4.

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properties, i.e. the number, the length and the orientation of the ray paths and the other one depending on the depth resolution, i.e. the frequency. A good resolution, meaning a large relative value for the horizontal weight, is achieved if many rays with different azimuths cross the cell. In a simplified way, the horizontal weights are computed by multiplying the ellipticity for the number of rays crossing each cell. The vertical weights account for the different penetration depths of the different frequencies of the surface waves. Consequently, the vertical weights are based on the analytical solution of displacement components for the fundamental mode in a half space (Aki and Richards, 1980). Additionally, for stabilizing the iteration process and for reducing the risk of divergence, an adaptive bi-weight estimation (Tukey, 1974; Arai

and Tokimatsu, 2004) can be applied. The solution is constrained to smoothly vary in the horizontal domain, meaning that the slowness of each cell is related to the value of the slowness of all the surrounding cells. As the vertical weights are based on a continuous functional form, this ensures that the slowness also smoothly varies vertically. For each cell, the individual weights and the corresponding surface wave velocity values are updated after each iteration until a reasonable compromise between the reduction of the root-mean-square error between the observations and the predictions and the norm of the solution is reached. The final 3D velocity model is obtained from the inversion of the cross-correlations based on a singular value decomposition technique (e.g., Arai and Tokimatsu, 2004; Pilz et al., 2012).

Fig. 4. Model resolution estimation. a) Map view showing RDE at several depths ranging between 0 and 70 m. b) Map view showing the Sj spread function with depth ranging between 0 and 70 m.

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3. Application on real datasets 3.1. Campi Flegrei caldera and the Solfatara volcano Campi Flegrei is a volcanic polygenetic complex located along the western coast of Southern Italy, 15 km west of Naples (De Natale et al., 1987). The Campi Flegrei volcanic field is a partly submerged nested calderic system whose current shape is directly linked to its eruptive history. The greatest events occurred about 39,000 (Campanian Ignimbrite) and 15,000 years ago (Neapolitan Yellow Tuff) (Deino et al., 2004; De Vivo et al., 2001).The current activity of this volcanic system consists mainly in widespread fumaroles inside and at the border of caldera, thermal spring activities as well as ground deformation episodes. In this regard, the subsidence trend of the last five centuries has been sometimes interrupted by unrest episodes characterized by short-term ground uplift. Actually, two large bradyseismic crises occurred in the last 40 years: the former between 1969 and 1972, the latter between 1982 and 1984 (Beaducel and De Natale, 2004; Battaglia et al., 2006; Del Gaudio et al., 2010). Both of them were accompanied by a shallow seismicity in the range 1–4.2 and brought to a cumulative uplift of about 3.5 m in a 10–15 km wide circular area (del Pezzo et al., 1987; De Natale et al., 1995; de Lorenzo et al., 2001; De Natale et al., 2006; Zollo et al., 2008; Amoruso et al., 2014; Carlino et al., 2015). As a consequence of these episodes, the risk of an imminent eruption was perceived by the population living in the active portion of the supervolcano (about 350,000 people) (Di Renzo et al., 2011; Capuano et al., 2013). On these grounds, in recent years the interest of the scientific community greatly increased in order to gain insight into the interior of the volcano. To this purpose, in the recent past several subsurface images of the Campi Flegrei caldera were obtained by means of different seismic methodologies (de Lorenzo et al., 2001; Zollo et al., 2008; Judenherc and Zollo, 2004; Zollo et al., 2008; Battaglia et al., 2008; Dello Iacono et al., 2009, De Siena et al., 2010, Serlenga et al., 2016). Among the most studied areas of this volcanic field, there is the Solfatara volcano, which is one of the craters of the Campi Flegrei caldera with a diameter of about 0.6 km. It is believed to be the top of a hydrothermal plume (Chiodini et al., 2001), being the shallow hydrothermal system of the Campi Flegrei caldera fed by the interaction between the meteoric water and heat from depth. Solfatara often experiences episodes of degassing, with very intense emission of hydrothermal–magmatic gases and high heat flow, ascending along faults bounding the crater (Chiodini et al., 2001).

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The shallow part of this volcanic structure was investigated through the seismic campaign RICEN (Repeated InduCed Earthquake and Noise), recording both active seismic data and ambient noise. Active seismic data were recorded using a single 6400 kg IVI-MINIVIB® vibroseis truck, which delivers a maximum theoretical peak force of ~ 27 kN at each sweep. For the two 2D seismic profiles a nominal source spacing of 4 m was used, with vibration points located halfway between geophones (Fig. 2, left panel). At each vibration point, two, 15 s long, 5–150 Hz sweeps were stacked and recorded respectively by a 216channel and 240-channel, with spacing between the individual sensors of 2 m. The source-receiver configuration allowed sampling a wide range of offsets, from a minimum of only 0.5 m to a maximum of 453 m. 3D data were acquired on a regular grid, composed of a 240channel array. For the regular 3D array we used 10 parallel sub-arrays of 24 channels each, oriented roughly with a NE strike. Inline spacing of geophones was 5 m, while cross-line spacing was 10 m. This yielded a 120 × 100 m2 wide grid of geophones (Fig. 2, right panel). Vibration points are located along parallel lines located midway between two parallel geophone lines. Nominal source spacing was 20 m, within the rectangular grid of four adjacent geophones. Ambient noise data were continuously acquired for three days at 50 stations on a larger area, spanning the entire crater. A data set with N100,000 seismograms was collected and preliminary used to infer a 1D model of the elastic and anelastic properties of Solfatara. Starting from an initial dataset of 21,315 automatically determined P-wave first arrival time picks, 17,847 data have been manually selected to be used to obtain a 3D P-wave tomographic image. In order to retrieve a P wave attenuation model, a further manual selection of the dataset has been performed by discarding signals with a low signal-to-noise ratio. To remove the source effect from the signal, the velocity seismograms have been cross-correlated with the sweep (Brittle et al., 2001). The cross-correlated traces have been cut in a window of 0.128 s around the P-wave arrival time and zero-padded up to a total duration of 0.256 s. Then, the velocity signals have been integrated in the time domain and the displacement spectra have been computed. The natural logarithm of the spectral amplitudes as a function of the frequency has been fit with a straight line in the frequency range 40–125 Hz in order to obtain for each source-receiver couple the t⁎ value. 3.1.1. Resolution test and ray coverage In order to evaluate the spatial resolution of a 3D model for the source-receiver geometry of the RICEN experiment at Solfatara volcano,

Fig. 5. Ray coverage. a) Ray distribution in the XY plane, b) ray distribution in the XZ, plane, c) 1D velocity model used for ray tracing.

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Fig. 6. 3D attenuation tomography synthetic test. a) Attenuation model used in the synthetic test. The triangles represent the receivers, whereas the black points identify the shots. b) 1D P wave velocity model used for ray-tracing. c) Synthetic dt⁎ data used for the inversion.

we performed a numerical computation of the resolution matrix through spike tests. For this analysis, a 1D velocity model for the area was inferred from the previous study of Bruno et al. (2007) up to 70 m depth. The velocity model is specified at the nodes of a cubic lattice of 10 m spacing. We added a velocity perturbation of 400 m/s to each grid node and computed the synthetic travel times that were used as input data for the tomographic inversion. In Fig. 3 we show the diagonal elements of the resolution matrix (RDE) overlapped to the map of Solfatara Volcano, and the station/ source distribution. The resolution is closely related to the sourcereceiver geometry. In fact, the resolution is maximum in the area covered by the array.

Fig. 4 shows both RDE and the spread function Sj, which gives a measure of the order of magnitude of the off diagonal elements of the resolution matrix. For this analysis we did not consider data errors and we assumed that all stations recorded all events, i.e., we considered a total amount of 25,920 P-arrival times with respect to the 21,315 preliminary picks. According to this analysis, the model has a good resolution up to 40 m depth. In fact, RDE is larger than 0.7 down to 40 m depth in the central part of the investigated area, whereas, at larger depth, the number of well resolved nodes drastically drops down. The spread function has a pattern very similar to that of the RDE. This behavior is indicative of the fact that the off-diagonal elements are small and there is little

Fig. 7. Results of 3D attenuation tomography synthetic test. a) Tomographic images at different depths retrieved after 8 iterations. Grey regions indicate areas not covered by rays. b) Relative error of the tomographic results. c) RMS as a function of the number of iterations. A stable value is achieved after 8 iterations. d) Residuals after the first iteration (blue histogram) and after the 8th iteration (green histogram).

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Fig. 8. Results of the inversion obtained using the software Geopsy. On the left and central panels, the retrieved dispersion curves for the group and phase velocities respectively, superimposed with the measured ones (the black lines). On the right panel, the S-wave models explored by the inversion procedure and the average model (dotted black line). The colors refer to the misfit value.

correlation between parameters. As a confirmation of the results, in Fig. 5 the plot of the ray coverage in the vertical and horizontal planes are shown. 3.1.2. Synthetic test of 3D attenuation tomography of Pozzuoli bay area using dt* data A three-dimensional Qp tomography of offshore part of Campi Flegrei caldera was already performed in the very recent past by inverting differential t⁎ measurements, with the method described in Section 2.2 (Serlenga et al., 2016), Nevertheless, a synthetic test is here described to further show the reliability of a three-dimensional attenuation tomography based on the inversion of dt⁎ measurements. The adopted source-receiver configuration allowed investigating a tomographic volume of 13 × 13 × 5 km3. It is the same layout used for the active seismic experiment SERAPIS, in September 2001, in the Pozzuoli Bay, southern Italy (Judenherc and Zollo, 2004). The node spacing of the tomographic grid in the described synthetic test is 500

× 500 × 250 m3. Seismic rays were traced in a 1D velocity model obtained by averaging the depth-dependent P wave velocity model of Battaglia et al. (2008). Synthetic attenuation model is characterized by a low-Qp annular anomaly (Qp = 100) located at depths between 500 m and 1.5 km in a homogeneous attenuation medium (Qp = 500). In the tomographic volume 14,450 synthetic dt⁎ are computed (Fig. 6). The tomographic inversion of synthetic data is run using a homogeneous Qp = 300 structure as starting model. The inversion is stopped at the 8th iteration and provides the tomographic images as shown in Fig. 7. The attenuation anomaly is fully recovered from a geometrical point of view. Nevertheless, due to the poor ray coverage, high relative errors (about 40%) affect the volume around the annular anomaly at depth of 1.25 km and 1.5 km. 3.1.3. Surface wave tomography Phase and group velocity estimated on the array of Fig. 2, right panel, are inverted to obtain a 3D model of the area, from combination of local

Fig. 9. Slices of the 3D model at different depths. Results beyond 12 m are not shown because of the lack of resolution.

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Fig. 10. Horizontal cross sections of the Solfatara volcano in terms of S-wave velocity after inverting 2 h of seismic noise.

1D models. In each sub-array, the inversion of phase and group velocity using a global exploration technique (Wathelet et al., 2004) furnishes more models that almost equally fits the measured dispersion curves. Therefore, it is more reasonable to infer statistical properties from the family of solutions, having the similar misfits to the experimental dispersion curves. At each depth, the final model was selected as the one resulting from the average of all the models with misfit b15% with respect to the minimum one (Fig. 8). This choice will produce a final non-layered model, which presents a smooth variation with

depth. In this analysis only the S wave model is constrained by the dispersion curves, as these curves are poorly affected by variations of both P-velocity and density. The maximum penetration depth is about 12 m (Fig. 8 right panel). The 3D S-wave velocity model obtained from the collection of all the 1D models is represented in Fig. 9, in slices at fixed depths. The most remarkable trend is the presence of low-velocity anomalies due to the water that permeates the westernmost area, outcropping to the surface in the Fangaia.

Fig. 11. Distribution of induced seismicity recorded at The Geysers. Black triangles indicate the seismic stations of the Lawrence Berkeley National Laboratory (LBNL) Geysers/Calpine seismic network used in this study, and grey triangles are additional stations from the Northern California Seismic Network (NCSN) in the region (modified after Convertito et al., 2012).

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3.1.4. Ambient noise tomography results Using the vertical cross-correlations and a fraction of 2 h of the entire noise data set, the inversion results after 500 iterations are shown in Fig. 10. At first glance one can notice the occurrence of strong lateral velocity variations. The topmost layer just below the surface is characterized by S-wave velocities ranging from 120 m/s for the northeastern part of the Solfatara crater close to the vegetation cover and associated background values of ground temperature and gas flux up to velocities of 200 m/s for the south-western part in agreement with the results of Serra et al. (2016). However, the penetration depth of their study was limited to the uppermost 10 to 15 m. A significant increase of the S-wave velocity starts immediately below the shallow deposits in the southern and central part at depths of around 10 and 20 m (Fig. 10), probably at the lower boundary of the unconsolidated shallow deposits. The lower velocity area remains confined in the northern and south-eastern part of the crater. At a depth of around 35 m, the S-wave velocity in the southern area increases up to 850 m/s. At these depths, the volume is divided in a higher velocity part (corresponding to the fumaroles area) and a lower one (corresponding to the northern

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edge), with a transition central zone. High S-wave velocities and corresponding resistivity and gas flux values emphasize a highly resistive body indicating that resistivity changes at this depth are related to high temperature gas saturation (Byrdina et al., 2014; Pilz et al., 2017). This large velocity contrast and the measured velocity values might assure the hypothesis of the presence of a small volcanic edifice (most probably a tuff-cone) formed in a smaller crater in the eastern sector during the phreatomagmatic activity (Petrosino et al., 2012). Below 40 to 45 m, the S-wave velocity increases up to 1200 m/s in the south-western area. The absolute depth of the velocity contrasts and the corresponding estimated S-wave velocities are robust and compatible with the findings of previous studies (Petrosino et al., 2006, 2012). 3.2. The Geysers geothermal area The Geysers geothermal field is located 120 km north of San Francisco. It has been actively exploited since the 1960s and is now the most productive geothermal area in the world. The geothermal field is monitored by a dense seismic network maintained by the

Fig. 12. P and S-wave velocity models. a), Map view of P-wave velocity model at 0, 1.5, 2, 3, 3.5 and 4 km depth from 3D travel time tomography. The seismic stations are imposed on the 0 km depth layers as open triangles, whereas black dots in all panels represent the earthquake locations. Regions not covered by ray-paths are in grey. The solid white contour lines identify the model regions where derivative weight sum (DWS) is N5000. The images indicate the presence of a strong lateral variation of seismic velocity along the NW-SE direction. b) Map view of S-wave velocity model at 0, 1, 2, 3, 3.5 and 4 km depth. Again, the images indicate the presence of a strong lateral variation of seismic velocity along the NW-SE direction.

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Lawrence Berkeley National Laboratory Calpine (BG) and by the Northern California Seismic Network (NCSN). The BG network consists of 32 three-component stations, 29 of which were used for the present study (black triangles in the Fig. 11). The analysis is here focused on natural and induced seismicity recorded from August 2007 to October 2011. The whole dataset contains about 15,000 events with magnitude ranging between 1.0 and 4.5. We selected only 1320 events for which at least 20 high-quality P-wave picks are available. Several authors have noted a difference in the seismicity features along the north-west -south-east direction (Convertito et al., 2012; Picozzi et al., 2017). In particular, Beall and Wright (2010) identified a clear “M ≥ 4.0 dividing line”, which splits the whole field into two different seismic areas. The north-western area (ZONE1) contains all the epicenters of the earthquakes with magnitude larger than 4.0, whereas

the southeastern one (ZONE2) is characterized by lower magnitude earthquakes. In ZONE1 the normal steam dominated reservoir (at temperature ~ 240 °C) is underlined by a high temperature steam dominated reservoir (HTR) at 260–360 °C (see Fig. 14, right part). The top of the shallower steam reservoir is located at about 1 km depth. The top of felsite (granitic intrusion), which underlines much of the steam reservoir, is shallower in ZONE2 compared to ZONE1. 3.2.1. 3D body-wave seismic tomography The 3D P- and S-wave velocity models are obtained from the tomographic inversion of the first P- and S-wave arrival times. The selected stations and events distribution allowed us to investigate a volume of 36 × 25 × 5 km3. The velocity model is parametrized by trilinear interpolation on a tridimensional grid with node spacing of 1 × 1 × 0.5 km3. The inversion starts from the 1D velocity model, optimized for the area,

Fig. 13. Cross-section of P and S-wave velocity models and Vp/Vs ratio.The earthquakes are projected onto the NW-SE cross-section depicted by the black line in the first panel of Fig. 12. The blue solid line indicates the top of the steam reservoir, the orange line the top of felsite and the red line corresponds to the top of the high-temperature reservoir as reported by Beall and Wright (2010). a) Vertical cross-section along the NW-SE transect crossing the P-wave velocity model. b) Vertical cross-section along NW-SE transect crossing the S-wave velocity model. c) Vp/Vs ratio images along the NW-SE transect.

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which is also used for the initial earthquake locations (Emolo et al., 2012). The misfit function, defined as the sum of the squared time delays (RMS), is a posteriori analyzed to check the convergence, which is reached after 8 iterations, where the final RMS value is equal to 0.1 s, with an RMS reduction of 50%. The tomographic P- and S-wave velocity models shown in Fig. 12 a,b respectively, seem to delineate the main geological features of the field. For example, the isovelocity curves at 5.4 km/s for Vp and 3.2–3.4 km/s for Vs (see Fig. 13) correspond to the top of the felsite (Thompson, 1989). Most of the seismicity in ZONE1 is clustered between 2.5 and 4.5 km depth, whereas the seismicity in ZONE2 is shallower. The Vp/Vs ratio throughout the reservoir reveals strong deviations from the expected value of 1.73. A high V p /V s anomaly is present in ZONE1 where the highest temperature in the field is measured (Beall and Wright, 2010) and the most of seismicity occurs (Fig. 13).

3.2.2. 4D velocity imaging Time variations of the seismic properties of the hosting medium can be observed by means of the variations of the Vp/Vs ratio evaluated at single stations and through time-lapse tomography (4D tomography). The whole catalogue was divided in consecutive epochs of 6 months with an overlapping of 2 months for the analysis. A technique for the large scale medium properties identification was applied, which can provide complementary information with respect to tomographic analysis The method allows to evaluate the temporal variations of the Vp/Vs ratio, using the arrival times of the P and S phases as seismological observables and then relate the ratio to the directional properties of the fluid diffusion process. Taking into account separately the events belonging to the two zones (Fig. 15) and the catalogue subdivision defined above, the Vp/Vs ratio was evaluated for each event at each station. For each epoch an interpolated color map of the mean values of the ratio at each station is presented to show its spatial variation.

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Vp/Vs ratios range from 1.65 to 1.85, in agreement with the work of Gunasekera et al. (2003). The assumption of this technique is that the Vp/Vs ratio is constant along the ray path, so that the value found at the stations may be considered the combination of the contributions of the anomalies at different depths. The plots in Fig. 14 represent the 1D Vp/Vs ratio trends for some stations of the network that show similar patterns. Even these plots indicate a high variability of the Vp/Vs ratio in the different time intervals. For some stations it varies from values lower than 1.7 to 1.8, the former value being attributed to the depletion of pore liquid water and the replacement with steam, the latter being associated to the presence of liquid water (Gritto et al., 2013). The 4D tomography consists in applying the 3D tomography at consecutive epochs. The model inferred by considering the whole dataset was used as starting model in the inversion. The model parametrization is the same as for the initial model. We evaluated the results in terms of Vp and Vs, and their percentage variation with respect to the initial model (Fig. 15). For each model the DWS is computed to determine the well resolved regions. The 4D tomographic images show for all the epochs a variation that does not exceed 10%. The presence of some anomalies seems to be rather recurrent. This is the case for example of the + 5% anomaly at the epochs from A and B and −3% anomaly at the epochs D, F, I and L. The observed changes in velocity might be correlated to the field operations, such as fluid injection or steam production, which are not constant during each year, but show seasonal variation (e.g. Convertito et al., 2012). Finally, the inferred time variation in the velocity pattern (Vp,Vs, and Vp/Vs ratio) suggests a non- isotropic fluid diffusion in the whole geothermal field. 4. Conclusions In this paper we have presented four recent, integrated methods for high-resolution seismic tomographic imaging of volcanic structures. Methods differ in the input data type used and inversion strategies. The first method is the body-wave velocity tomography performed

Fig. 14. Vp/Vsratio vs time epoch. The four panel show the Vp/Vs as a function of time epoch for different stations, grouped according to the similarity of their trends.

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Fig. 15. Cross-sections of 4D seismic tomography results. Each panel shows the tomographic model, for each time epoch, projected onto the NW-SE cross-section plotted as a black line in the first panel of Fig. 19. The first and second columns represent the Vp and Vs the variation with respect to the 3D Vp and Vs model calculated on the entire period respectively (see Fig. 13.) The fifth column represents the Vp/Vs ratio model.

with a linearized approach. We have also shown how to assess the resolution of the final model. The second method, attenuation tomography, uses t* absolute and dt* relative measurement, using iterative inversion approaches. The last two methods proposed are the surface wave and shear wave tomography obtained from active shots and environmental noise. The advantages, limitations, and domains of applicability of these methods have been shown through practical examples applied to data provided by both seismic exploration campaigns and, synthetic passive seismic data.

Acknowledgements This paper was carried out within the framework of the MedSuv project, which received funding from the European Union Seventh Programme for research, technological development and demonstration, under grant agreement no. 308665 and SERA project, grant agreement no. 730900, EU Framework Programme H2020-INFRAIA-2016-2017/ H2020-INFRAIA-2016-1. The authors wish to thank the editor and the reviewers, including L. De Siena, for their valuable comments, which have contributed to improve the quality of the manuscript. A Post-

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