Geophysical Journal International

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1 Geophysical Journal International Geophys. J. Int. (2011) 187, doi: /j X x Ground deformation at calderas driven by fluid injection: modelling unrest episodes at Campi Flegrei (Italy) A. Troiano, M.G. Di Giuseppe, Z. Petrillo, C. Troise and G. De Natale Istituto Nazionale di Geofisica e Vulcanologia, dept. Osservatorio Vesuviano, Naples, Italy. antonio.troiano@ov.ingv.it Accepted 2011 July 11. Received 2011 July 11; in original form 2010 September 16 1 INTRODUCTION Campi Flegrei is a collapse caldera having a radius of about 6 km, centred at the town of Pozzuoli and including a large part of the metropolitan area of Naples (Fig. 1). It was part of a larger volcanic area which about yr BP was the source of the largest recent ignimbritic eruption in Europe, named the Campanian Grey Tuff, whose pyroclastic currents covered the whole Campania Region under several tens of metres of tuff (Rolandi et al. 2003). About years ago, another large ignimbritic eruption occurred from Campi Flegrei, the so-called Neapolitan Yellow Tuff (Deino et al. 2004). It caused the presently evident caldera collapse and covered the Naples Region with thick tuff deposits, which have been used for centuries as building material in the towns. During the last 5000 years, Campi Flegrei caldera hosted about 60 eruptions, most of them showing hydro-magmatic character (Rossano et al. 2004). Given the extreme urbanisation of this area, this is one of the highest risk volcanoes in the World. Besides eruption activity, Campi Flegrei caldera is characterised, like many other similar areas, by large ground movements. This is well documented during the last 2000 years by marine incrustations on Roman and Middle Ages edifices. Archaeological observations (Parascandola 1947; Dvorak & Mastrolorenzo 1991) point out that the secular trend of ground SUMMARY Campi Flegrei collapse caldera (Italy) is a high-risk volcanic area located close to Naples and includes part of the densely populated city. This area is characterised by large up and down ground displacements. The last large uplift episode caused 3.5 m of cumulative vertical displacement at the centre of the town of Pozzuoli, during the period Up and down ground movements in this area often occur without intercurring eruptions and are similar to what is observed at other calderas worldwide. Here, however, they appear more evident and amplified. Understanding the mechanism of such movements is crucial for hazard assessment and eruption forecast, mainly due to this densely populated area. This paper presents a detailed model for ground displacements due to deep fluid injection in shallower layers. Such a model explains in a natural way the occurrence of uplift and subsidence without eruptions. We show that it is possible to fit observed ground deformation in this area with a thermofluid dynamical model. The model obtained is also consistent with other observations like microgravity changes, changes in CO 2 flux, etc. Here, we suggest that significant uplift and subsidence at calderas can be due to effects of deep fluid injections other than magma. At Campi Flegrei, however, a partial magmatic contribution at the origin of the observed episodes cannot be excluded. Key words: Numerical approximations and analysis; Hydrothermal systems; Explosive volcanism; Calderas. deformation is subsidence centred at Pozzuoli harbour at a rate of about cm yr 1. Superimposed to such secular subsidence, are fast and large uplift episodes, sometimes (as for the only historical eruption of 1538) culminating in an eruptive episode. The 1538 eruption occurred some decades after the beginning of uplift (Di Vito et al. 1987). From 1969 until 1984 the ground level at Pozzuoli harbour rose about 3.5 m, with peak uplift rates of about 1 myr 1 recorded during (De Natale et al. 2006). Several papers have dealt with the interpretation of unrest episodes in this area. Many models involved the mechanical effect of overpressure on a shallow magma chamber (Berrino et al. 1984; Bianchi et al. 1987; Amoruso et al. 2007), whereas several more recent models involved significant effects of fluid-dynamics on the shallow aquifers (De Natale et al. 1991; Gaeta et al. 1998; De Natale et al. 2001; Chiodini et al. 2003; Todesco et al. 2003a,b; De Natale et al. 2006; Gottsmann et al. 2006; Lima et al. 2009; Shirzaei & Walter 2010; D Auria et al. 2011). Although several papers have recently pointed out the importance of fluid circulation in the shallow aquifers, no complete, rigorous numerical model has been proposed in literature that is able to explain the main thermofluid dynamical effects and gives a satisfactory fit to the main data available at Campi Flegrei. Using theoretical modelling of the aquifer system at Campi Flegrei we present the first complete thermofluid dynamical model that is GJI Mineral physics, rheology, heat flow and volcanology C 2011 The Authors 833

2 834 A. Troiano et al. Figure 1. (a) Normalized vertical ground deformations recorded, in several periods of uplift and subsidence, by precision levellings along the levelling route going from Naples to Baia (heavy red line in panel b; redrawn from Troise et al. 2007; 2008). Ground deformations during subsidence have been reversed in sign, to show all episodes positive. Normalization has been obtained by dividing displacements of each curve by its respective maximum value. Error bars have been computed by rigorous network compensation as described by Troise et al. (2007, 2008) and references therein. A strong constancy in the shape of ground displacements, over a very large scale of magnitudes (maxima from 0.02 to 1.77 m), is very evident from the figure; (b) sketch map of Campi Flegrei area with levelling lines (thin red lines), precision levelling route Naples-Baia along which have been measured the displacements shown in (a), location of the continuous GPS (RITE), used in this paper, installed since 2000 (yellow triangle). consistent with ground deformation data in this area as well as with other observations. It points towards the main factors controlling the contribution to ground deformations at calderas as due to input of deep fluids into the shallow geothermal system. Besides giving a robust interpretation of Campi Flegrei unrests, these findings can shed new light into the mechanisms of caldera unrests worldwide. 2 OBSERVATIONS AND MODELLING OF FAST UPLIFT EPISODES Studies of slow movements at Campi Flegrei began with observations of sea level markers on Roman coastal ruins, which were sensitive to large, secular deformation (Breislak 1792; Forbes 1829; Niccolini 1839; Niccolini 1845; Babbage 1847; Lyell 1872; Gunther 1903). Parascandola (1947) presented the first complete reconstruction of historical ground movements, later modified by Dvorak & Mastrolorenzo (1991), and, in the last few years, by Morhange et al. (1999). Fig. 2 synthesize the ground deformation occurring at Campi Flegrei at different timescales and recorded in different ways (secular, obtained from marine ingression levels on ancient buildings; last decades, obtained by precision levellings; recent, obtained by GPS). The Pozzuoli area has been characterized, since Roman times at least, by a general trend of subsidence at a rate of about cm yr 1. Occasionally, uplift episodes occur, the first one hypothesized in the Middle Ages by Morhange

3 Ground deformation driven by fluid injection 835 Figure 2. Ground movements at Campi Flegrei as a function of time, at different timescales. (a) Secular movements, inferred from the marine ingression levels recorded on ancient Roman and Middle-Age manufacts (redrawn from Bellucci et al. 2006); (b) Vertical ground deformation recorded at Pozzuoli harbour by precision levellings in the last decades (Troise et al. 2008; INGV Report 2010); (c) Recent vertical ground deformation as recorded by the continuous GPS closest to the levelling bench mark at Pozzuoli harbour (RITE in Fig. 1) from 2004 to half 2009 (Troise et al. 2008; INGV Report 2010). et al. (1999) and a second one, well constrained, started about 40 to 100 yr before the only historical eruption in After the 1538 eruption, the subsidence continued at the previous rate, until the end of 1960s, when rapid uplift started again, totaling about 1.7 m between 1969 and 1972 (Casertano 1976; Corrado et al. 1977). Then, 10 years of almost constant ground level (a net subsidence of less than 20 cm) followed until 1982, when renewed uplift raised the ground at Pozzuoli by about 1.8 m until the end of 1984 (De Natale et al. 1991). The last two unrest episodes aroused concern about a possible impending eruption. As a result of such concern, and also because of the risk to buildings caused by earthquakes and static deformation, Pozzuoli was totally evacuated at the end of 1984, after a partial evacuation in Since 1985, ground level subsided at a progressively slower rate, recovering, until 2004, about 80 cm of the previous uplift. Superimposed to such subsidence, several mini-uplift occurred, at intervals of 5 6 yr each other, with maximum uplift in the range 4 11 cm (Gaeta et al. 2003). The pattern of ground deformation during both the recent uplift and subsidence episodes resembled a bell shape, centred at Pozzuoli harbor (Fig. 1). The radial decay of the ground deformation is very rapid, reaching 5 per cent of maximum uplift at 3 km of distance. Such a sharp decay, together with the observation of very constant shape not depending from the amount or sign of ground deformation (see Fig. 1), was attributed by De Natale & Pingue (1993), De Natale et al. (1997) and Gottsmann et al. (2006) to the confining effects of caldera borders. Other key observations, pointed out by Battaglia et al. (2006), indicate that ground deformations and microgravity changes recorded during both uplift and subsidence episodes can be explained by inflow of a fluid into the shallow crust, having density very close to 1 g cm 3, that is, very close to density of water rather than magma. Furthermore, the strongest argument pointing out that fluid inflow and outflow should be a considerable part of ground uplift is the observation of fast subsidence episodes following the sharp uplift phases (about 80 cm between 1985 and 2005). Oscillation of the ground level with consecutive uplift and subsidence episodes, common to other similar calderas like Yellowstone (Arnet et al. 1997) is difficult to interpret in the light of classical magmatic models. It is in fact hardly to justify a deflation phase, when no eruption (with consequent deflation due to magma outflow) occurs at the end of uplift episodes. In addition, the fast subsidence phase following the 1984 uplift has been punctuated by some small uplifts, of maximum amounts between 4 and 11 cm, separated by an almost constant period of 5 6 yr (Gaeta et al. 2003). Each of the small uplifts was also accompanied by microearthquake swarms lasting from days to weeks (Bianco et al. 2004). Several recent

4 836 A. Troiano et al. papers have dealt with modelling of ground deformations as due to thermal and fluid-dynamical effects in shallow aquifers (Gaeta et al. 1998; Troise et al. 2001; Todesco et al. 2003a,b; Rinaldi et al. 2009). The first papers pointing out that the pattern of inflation/deflation should involve thermofluid dynamical effects in shallow aquifers are due to Casertano (1976), De Natale (1989), De Natale et al. (1991), Gaeta et al. (1998) and De Natale et al. (2001). More recently, Battaglia et al. (2006), De Natale et al. (2006), Troise et al. (2006) and Troise et al. ( 2007) presented new evidence and modelling pointing to a complex interaction between deeper magmatic inflow and the effect of shallow fluids in the genesis of both large and small uplift episodes in the area. A somewhat similar hypothesis, supported by InSAR data, was recently presented by Shirzaei & Walter (2010). Chiodini et al. (2001) pointed out the correlation betweenpeakvaluesofco 2 /H 2 O ratios, found in the large fumaroles of Solfatara crater, and the uplift episodes, modeled in terms of episodes of increased CO 2 and water injection in the shallow hydrothermal system. A paper by Todesco & Berrino (2005) further explored the effects of such fluid injection on ground deformations and microgravity changes at the area. However, they modelled local effects of a small circulation system within the Solfatara crater, whereas no paper till now has afforded a through comparison with real unrest data taking into account the whole geothermal system at Campi Flegrei. The mentioned papers, in fact, limited the depth of the simulated geothermal system to 1.5 km and did not afford a complete analysis and fit of ground deformation, microgravity data and other key observations in the framework of global thermofluid dynamical model. 3 NUMERICAL SIMULATIONS 3.1 Thermofluid dynamical modelling In this paper, we present a set of numerical simulations, aimed to study the effects of the fluid inflow and outflow on the ground inflation and deflation of the Campi Flegrei caldera. These simulations have been carried out by the numerical code TOUGH2. This code allows to compute the mass and heat exchange related to multidimensional flows of multiphase (gas and liquid) mixtures of many components within a porous medium of assigned permeability (Pruess 1991; Pruess et al. 1999). It assumes local equilibrium between fluid and rock matrix, through the direct discretization of the balance equations for mass and energy describing the thermodynamic conditions of the system in their integral form, in a scheme called integral finite difference method (Edwards 1972). The solution consist of a set of values assumed by the independent (or primary) thermodynamic variables (Pressure and Temperature) as function of time, at the nodes of the elementary cells discretizing the physical space. All the geometric information for the flow problem is provided through the specification of the cell volumes, interface areas, nodal distances and components of the gravity acceleration in the direction of the line connecting the nodal points. ρ Fluid advection is described by Darcy s law F = K, μ( P ρg) where F is the fluid mass flow rate per unit of cross-sectional area, K is the absolute permeability, μ is viscosity, ρ is density, P is the pressure gradient and g is the gravity acceleration. Darcy s law is written for the case when the pore space contains a single fluid phase, for example a liquid (aqueous) phase. When liquid and gas phases coexist in the pore space of the medium, a multiphase version of Darcy s law is applied. Each one of the two phases flows under its own pressure gradient and body force, but the effective permeability of the medium is reduced with respect to single-phase conditions, because each of the flowing phases has only part of the pore space available. This effect is taken into account by introducing the socalled permeability reduction factors, or relative permeabilities for liquid or gaseous phases, as follows F β = K k rβρ β ( P β ρ β g), μ β where the subscript β indicates, in turn, liquid or gas. The coefficients k rβ represent the reduction in available permeability due to the fact that only a fraction of the pore space is occupied by phase β. The fraction of pore space occupied by a fluid phase is termed its saturation S β, and the relative permeabilities are functions of S β. These are empirically based functions of volumetric saturation of liquid and gas phases, with values varying between 0 and 1. Since relative permeabilities are sensitive to pore and fracture geometry, the appropriate functional relationship will likely vary within the system of interest. Two of the most widely used relationships are the linear and Corey-type curves (Corey 1954; Corey 1957), and the models in the present study incorporate Corey-type relative permeability functions. Heat flux F H includes conductive and convective components: F H = λ T + β h β F β, where λ is the thermal conductivity, T is the temperature gradient and h β is specific enthalpy in phase β; F β is the mass flow rate per unit of cross-sectional area of phase β. The nature and properties of the specific mixture of fluids enter the equations only through appropriate physical parameters (density and viscosity, enthalpy etc.), computed as function of the primary thermodynamic variables through specific TOUGH2 modules. Although hydrothermal fluids are not pure substances, but generally mixtures of several mass components or chemical species, the dominant fluid component is usually water, and for practical reservoir studies it is often reasonable to ignore other components. Following this assumption, most of the simulations conducted in this work include the presence, within the rock matrix, of pure water in liquid or vapour phase or in two-phase conditions. Water properties and phase transitions are calculated, based on the thermodynamic conditions, according to the steam table equation (International Formulation Committee 1967). However, the aqueous phase generally contains solutes such as NaCl and other salts, as well as dissolved incondensable gases, such as CO 2,H 2 Sand noble gases, and constituents of rock minerals such as SiO 2.To analyse the effects of such solutes in the hydrothermal fluids, some of the presented numerical simulations investigate the effect of a CO 2 component in water. If a mass component as CO 2 is present in the pores, simultaneously in the gas phase and in the aqueous (liquid) phase, with mass fractions of χ CO 2 g and χ CO 2 l, respectively, in the mass and energy balance equations, a term depending on the mass flux of CO 2 due to fluid flow, namely F CO 2 = β χ CO 2 β F β, has to be considered. If a gas phase is present, the largest fraction is usually H 2 O although other gases may be present. 3.2 Elastic modelling Once the thermodynamic evolution of the modelled physical domain is simulated by numerical approximation, we use the obtained solution as source term to estimate the deformation of the elastic matrix. The surface deformation is computed by considering the

5 Figure 3. Axial symmetric model domains used for thermofluid dynamical modelling and for surface deformation computation. Right-hand side: finitedifference computational domain for thermofluid dynamical modelling. The inner part of the mesh (r < 1.5 km) is characterized by a permeability K 1, while the external part has a permeability K 2. On the top of the model, temperature and pressure are fixed at atmospheric values, while on the bottom just the temperature is fixed at a 300 C value. Left-hand side: finite element mesh for computation of the ground deformation from the changes of pressure and temperature. The mesh is variable in size, with denser elements close to the centre (in the first 3 km). A white line shows the position of the ring fault system added to the model (see De Natale et al. 1997). White arrows shows the water injection area. changes of pressures and temperatures estimated by the thermalfluid dynamical analysis, as compared to the steady state before the perturbation. To compute the effects of pressure and temperature changes on the surface displacements we use a finite element approach. For such a computation, the caldera volume is subdivided into a dense mesh of volume elements, with denser sampling in the central part (see Fig. 3). At each element we consider the pressure and temperature change, computed by the THOUGH2 analysis, as individual sources. The surface displacement at any point is hence computed as the sum of individual sources of each volume element of the mesh, of the kind T,whereG, ν and α are the shear modulus, Poisson s ratio (drained), and the volumetric thermal expansion coefficient of the saturated porous medium, respectively. The gravity term does not appear in the deformation equations, because the deformation and stresses are referenced to an initial state, which is in static equilibrium. Since the deformed state is also in static equilibrium, the gravity term drops out when the equation is formulated in terms of the change from the initial static state. Finally, we assume that the change in stress has no effect on permeability, porosity or fluid flow. Such a one-way coupling approach (that is, from thermodynamics to deformation but not vice versa) is normally adopted in such simulations (Hurwitz et al. 2007), and differs from a complete and much more cumbersome thermal-poroelastic approach, in which volume deformation affects in turn the porosity and hence the permeability of the system. P + 2G(1+v)α 3(1 2v) 3.3 Physical model The computational model assumed consists of a cylinder with a height of 3 km and a radius of 10 km, as shown in Fig. 3. The inner part of the cylinder (r < 1.5 km), representing the Campi Flegrei caldera, is characterized by a K 1 permeability; a different permeability K 2 is assigned to the outer part of the cylinder, representing the outer caldera hosting rocks. The height of the cylinder, 3 km, represents the maximum depth of the Campi Flegrei aquifers as determined by previous drillings in the area (AGIP 1987). They found, at any drilled site, the critical conditions for water to occur in the depth range km (Rosi & Sbrana 1987). Numerical tests were performed, checking the stability of solutions obtained by varying the radius of the cylinder to verify the absence of significant border effects. Such tests show that, starting from a radius of about 8 km, the results are very stable by increasing Ground deformation driven by fluid injection 837 radius, and practically indistinguishable from a radius of 50 km. We have then chosen a radius of 10 km, which represents a good compromise between maximum stability and minimum computational effort. We assume that the water table coincides with the ground surface and that the topography is flat. In contrast to stratovolcanoes where topography is a major control on hydrodynamics (Hurwitz et al. 2007), topographic gradients in calderas, as such of the Campi Flegrei, are in fact relatively small and the water table is usually close to the ground surface. Flow systems are initialized by assigning, as initial condition, a complete set of primary thermodynamic variables to all grid blocks, in which the flow domain is discretized. Pressure distribution is initially assumed as basically hydrostatic, starting from an atmospheric value at the model surface and linearly increasing with depth down to the bottom of the model. Temperature distribution is also linear, varying from 10 C on surface up to 300 C on the bottom. The model domain represent the hydrothermal system of the caldera, with hydrostatic conditions, overlying a mostly ductile zone where pressures are near lithostatic. In such a way, we take into account the whole depth extension of the aquifer system, down to the depth at which critical temperature is reached and liquid subcritical water is not present anymore. However, we maintain, in the model, lower temperatures so to avoid falling into supercritical conditions, which cannot be handled by any theoretical model. At the top boundary, temperature and pressure are set constant to represent the water table condition. At the bottom of the model, just the temperature is held fixed. Pressure changes are enabled to simulate the effects of large fluid injections in the lower parts of the caldera. Fluid sources are placed at the base of the cylinder, through an area with a radius of 150 m. Pure water or a mixture of water and carbon dioxide are injected at a temperature of 350 Candata fixed rate of injection. Apart from such fluid injections, the cylinder is isolated from the outside and is impervious on the external edges and along the lower base. Values of the parameters characterizing the physical properties of rocks (density, porosity, specific heat and thermal conductivity) are chosen based on literature and data wells (e.g. AGIP 1987; Rosi and Sbrana 1987) and remain constant during simulations; they are reported in Table 1. The computational mesh consists of 2800 cells, divided into 56 columns and 50 rows. The horizontal mesh spacing ranges from some metres, close to the axis of the cylinder, up to several kilometres at the outer edge. Vertical spacing varies from some meters in the higher layer, up to 100 m in the lower slices. 3.4 Campi Flegrei modelling To obtain a correct evaluation of the effects of fluid injection and permeability on the ground movement a suitable steady state must be specified, as the initial condition of the system. To this aim, to isolate the effects on ground deformation due to the fluid injection, Table 1. Rock physical property Rock physical property Density (kg m 3 ) 2000 Thermal conductivity (W m 1 K 1 ) 2,8 Specific heat (J kg 1 K 1 ) 1000 Porosity 2

6 838 A. Troiano et al. a first run of TOUGH2 is performed, starting from the assumed initial conditions, which include hydrostatic equilibrium. The output of this run simulates a realistic, unperturbed steady state for the system to be used as initial state. Starting from such a steady state, we performed a set of TOUGH2 runs, each one characterized by different fluid injection rates, allowing to simulate the inflation or deflation of the model in response to deep fluid injections. As an example, we analyse step by step some of the obtained simulations to characterize the fundamental behaviour of the physical process. First, we investigate an homogeneous cylinder, with a relatively low value of permeability, specified as K 1 = K 2 = m 2. Fig. 4(a) shows the initial condition of the system, that is, the pressure and temperature distribution, with P varying from 0.1 (at z = 0 km) to 30 MPa (at z = 3 km) and T going from 10 C(at surface) up to 300 C (at bottom). Given the radial symmetry, the mesh grid and results are reported on a vertical section of the model, with the left edge coinciding with the cylinder axis. During the simulation, there is no heat exchange with the external volume, nor fluid injection, so the cylinder evolves due to fluid and heat flows in response to internal pressure and temperature gradients. The simulation stops when the system reaches a steady state. Fig. 4(b) shows the corresponding values of the primary thermodynamic variables across the cylinder section; the values here depend substantially on depth. Fig. 4(c) shows the pressure and temperature changes in time, with respect to the initial conditions: a slight adjustment of T and P, due to water density variation is shown, consisting in a Figure 4. Initial conditions of the system. The panels represent the corresponding values of the primary thermodynamics variables across the cylinder section. Panels (a) and (b) report the pressure (right-hand side) and temperature (left-hand side) distribution at the beginning and the end of the simulation time, relative to an homogeneous cylinder (K 1 = K 2 = m 2 ). Panel (c) reports T and P changes with respect to the state (b) and the state (a). Panel (d) report the ending state of a cylinder presenting a permeability contrast K 1 = m 2 ; K 2 = m 2.

7 Ground deformation driven by fluid injection 839 change of T in the range [0 3] C and of P in the range [0 3.5] MPa. Fig. 4(d) shows the final state reached by a model with two different permeabilities K 1 = m 2 ; K 2 = m 2, starting from the same initial conditions. In such a model, the inner part of the cylinder, representing the Campi Flegrei caldera collapse, has an enhanced permeability, one order of magnitude higher, with respect to the host rocks. While pressure still shows a dominant depth dependence, the temperature profile is quite different, showing two distinct equilibrium gradients in the inner and the outer part of the cylinder, each one characterized by a constant gradient behaviour but with different slopes, joining together in a linear way. After determining suitable steady state conditions, we further explore the role of transient deep fluid injections, introducing fluid sources at the centre of the mesh, uniformly distributed across a 150 m radius area. Several injection rates have been used, coupled with different values of inner and outer cylinder permeability. For each permeability model, injection rates giving ground deformations comparable with experimental records are determined. In the first tests, we analyse pure water injection to obtain a good understanding of the system s thermodynamic behaviour; CO 2 effects on the ground displacement are then considered in the further tests. Fig. 5 shows pressure and temperature changes inside the cylinder, in response to transient fluid injection. They represent the final state of the system after three years of constant fluid injection, starting from the steady states described before. Such an injection time is comparable with the characteristic times of large uplift episodes at Campi Flegrei caldera, like the and ones, reported in Fig. 2. In the results shown Fig. 5(a) we consider an homogeneous permeability: K 1 = K 2 = m 2 and note, in the final state, an over-pressured deep zone development. Such a zone is centred above the fluid injection area, at about 2.5 km of depth, extending up to 1 km of distance from the axis of the cylinder. In such a volume, P reaches very high values (several tens of MPa) and the rock temperature rises of some degrees Celsius. A permeability enhancement of the inner part of the system, with K 1 = m 2 ; K 2 = m 2 results again in an over-pressured zone, as shown in Fig. 5(b). In this case, however, almost all the inner cylinder shows a pressure increase, reaching a maximum of just few MPa, thus indicating that the pressure (and consequently the stress) accumulation is strongly dependent from rock permeability values. Lower resistance to fluid flows implies, in fact, a larger over-pressured zone, with lower peak values. This means, as can be inferred from the injection rates, that to obtain a given amount of ground inflation, higher fluid injection rates are needed as permeability increases. A lower resistance to fluid flows also results in a larger zone with increased temperature. An additional increase of the inner cylinder permeability causes a further decrease of the over-pressure levels, dropping to some tens Figure 5. Temperature (left-hand side) and Pressure (right-hand side) changes inside the cylinder, at the final state reached after a 3-yr constant fluid injection, starting from the initial steady state. Only a detail of the first 3 km of mesh length is shown, because the more distant values are constant at the initial value. The three panels are related to: (a) an homogeneous cylinder (K 1 = K 2 = m 2 ). (b) a cylinder presenting a permeability contrast K 1 = m 2 ; K 2 = m 2. (c) a cylinder presenting a permeability contrast K 1 = m 2 ; K 2 = m 2.

8 840 A. Troiano et al. of MPa in almost all the inner cylinder, as shown in Fig. 5(c). In fact, a higher flow velocity, due to higher permeability, leads to a more complex rock s heating pattern, characterized by a slight heating close to the surface and by a sharp contrast at the border of the inner cylinder. In all the examples the pressure increase is mostly limited, in the 3 yr of injection time, just in the inner part of the cylinder. In this permeability and over-pressure link a key role is played by the presence or absence of convective cells in the cylinder. Larger permeability values accelerate the convection cells development that tends to equilibrate the system, precluding the high-pressure values obtained, on the contrary, when rock permeability is smaller. 4 GROUND DEFORMATION INDUCED BY DEEP FLUID INJECTION Surface ground deformation has been computed by considering both the effects of over-pressure and of rocks heating caused by the higher temperature fluid flow. We first concentrate on the pattern of maximum vertical deformation as a function of time. Fig. 6 shows the computed vertical ground displacements related to several combinations of inner and outer permeability, K 1 and K 2. The ground inflation is obtained from a constant injection of pure water, named I 1, lasting 3 yr (related to the inflating part of the curve, placed in the grey box) and a subsequent decrease to a lower value I 2 (generating a ground deflation, related to the second part of the curve); for comparison, the observed time evolution of maximum ground deformation, in the period 1982 today, is also shown. As we said before, the fluid injection rate has been selected in a proper way to adequately fit the maximum vertical displacement recorded in the harbour of Pozzuoli town, the closest on-land point to the centre of Campi Flegrei caldera, at the end of 1984; again, we note that higher injection rates correspond to higher inner permeability. The best fit of the experimental curve is obtained by the couple of permeability values K 1 = m 2 ; K 2 = m 2 ; substantially lower values of the inner permeability give rise to a slower ground deflation while higher values induce a too fast decay of the relaxation curves. Much higher values of K also implies a strong misfit of the first part of the curve, related to the ground inflation period. Besides large and long-lasting episodes of ground uplift, Campi Flegrei caldera ground displacements are also characterized by the occurrence of some smaller uplift episodes, which, in the displacement curve 1982 today (Fig. 2), appear superimposed to the general subsidence trend started in Such episodes, first studied in a more specific way by Gaeta et al. (2003), have been called in their work mini-uplifts. They occurred in 1989, 1994, 2000 and 2006, and involved maximum ground uplift in the range 4 cm to 11 cm, with durations of few months and associated seismic swarms (Gaeta et al. 2003). They are barely visible in the global deformation curve of Fig. 2, because it has been obtained by discontinuous levelling campaigns. However, starting from 2000, the last ones have been continuously recorded by GPS networks installed in the area (Troise et al. 2008). The best recorded one, occurred in , is shown in Fig. 7, and has been here modelled in terms of the same mechanism of deep fluid injection used to model the large uplift episodes. Fig. 7 shows the vertical GPS signal recorded at the station RITE, the closest one to the centre caldera at that time, then characterized by maximum vertical deformation. Continuous curves of Fig. 7 represent theoretical models obtained with different values of permeabilities K 1 and K 2. Ground deformations responses to smaller fluid injection, required to fit the smaller amount of maximum displacement, show a similar behaviour with respect to what has been already discussed for the major event. However, mini uplifts are characterized by a faster subsidence rate after the maximum uplift, which requires, to be fitted satisfactorily, a permeability value in the inner cylinder higher of a factor 5 to 10 with respect to the value found for large uplift episodes (Figs 6 Figure 6. Vertical displacement at surface, at the origin of the axial-symmetrical scheme, as due to liquid injection at the base. Colour lines are related to several models, differing in the combination of the inner and outer permeability, K 1 and K 2. The blue line represents observed vertical displacements recorded at Campi Flegrei area in the period Injection rates, I 1 and I 2, are also shown in figure, for each model. A continuos injection of pure water, lasting 3 yr, give rise to an inflation of the models. The water injection rate, I 1, is suitably selected for every model, to obtain a good match of the corresponding displacement curve with the experimental one. A deflation of the models corresponds instead to a minor fluid injection phase. The reduced water injection rates, I 2, are adequate to fit the experimental deformation of the models after the simulated time of almost 30 yr.

9 Ground deformation driven by fluid injection 841 Figure 7. Vertical displacements at surface, at the origin of the axial-symmetrical scheme, due to fluid injection at the bottom of the model, computed to simulate a sample mini-uplift episode ( ). Colour lines are related to several models, differing in the combination of the inner and outer permeability, K 1 and K 2. The blue dots represent the values of the vertical displacements recorded by the continuos GPS in RITE (Fig. 1) between 2000 and Injection rates, I 1 and I 2, are also shown in figure, for each model. The grey area shows the inferred duration of continuous injection of pure water to fit data. and 7). This kind of phenomenon could possibly be originated from occasional permeability enhancements, caused by cracks opening in the rock matrix. Another important test for the model is to look at the shape of ground deformation as a function of the distance from the injection centre. The decay of ground displacements with the distance, in a homogeneous medium, is controlled by the effective source depth (Mogi 1958). However, De Natale & Pingue (1993) and De Natale et al. (1997) put in evidence that, at calderas, the presence of slip discontinuities associated to the bordering ring faults makes the ground displacement strongly concentrated within the collapsed area, so the decay with distance is almost independent from the source depth in a large depth interval. Fig. 8 shows the curves of ground displacements obtained by the best fluid-dynamical models, respectively with homogeneous (Fig. 8a) and heterogeneous (Fig. 8b) permeability. The third panel, Fig. 8(c), shows the ground displacements obtained including the effects of discontinuities at the caldera borders. The position of such discontinuities, chosen in agreement with De Natale et al. (1997) results, is also shown superimposed to the mesh of Fig. 3. The mathematical conditions imposed on these discontinuities simulating ring faults enclosing the collapsed volume, are: shear stress σ = 0; normal displacement ε>0, implying that only fracture opening is allowed (see also De Natale & Pingue 1993). Each couple of vertical horizontal curves refers to a given time during the injection, which may correspond to the inflation or deflation phase. What is evident from the figures is that the spatial shape of ground deformation depends on the time, in a more marked way during the deflation phase, that is, after the injection rate is decreased to the lower limit. In particular, also the ratio H/V between maximum horizontal and maximum vertical displacement (Fig. 8d) critically depends from time. The values of this parameter range between 0.35 and 0.41, showing a maximum increase during the deflation phase and for the model with lower innermost permeabilities. The shape parameter H/V has been identified by Troise et al. (2007) as the most critical parameter to detect the shape and depth of the deformation sources. Moreover, Battaglia et al. (2006) identified a substantial increase of the H/V ratio during the deflation phase, with respect to the first part of the inflation phase. What is also evident is that, for such kind of model, the effect of ring faults is practically negligible. This is reasonable because the most important part of the deformation source is located at lower depth with respect to the bottom part of the ring faults. This is very different from the case in which a source deeper than the faults bottom, simulating a magma chamber, pushes the upper volume from below, causing a larger uplift of the volume enclosed by the ring faults, due to induced passive differential slip along the ring faults. When the source is located well within the ring fault cone, it deforms the caldera volume essentially the same way as if it was in a homogeneous intact volume, because the force induced on the ring faults is not dominantly shear, but normal. The trend shown by our model is then in substantial agreement with the observations, although the observed increase measured by Battaglia et al. (2006) is stronger (H/V up to ). It is also very important to compare the resulting shapes of predicted ground deformation, as a function of distance, with the observed ones. This is done in Fig. 9, where vertical (panel a) and horizontal (panel b) theoretical displacement curves as a function of distance from the source epicentre are shown, compared with observed data collected by precision levellings and EDM in various periods (Troise et al. 2007; 2008). Although the ground displacement curves change their shape during the time, and more markedly during the subsidence phase, the observed data collected in several deformation periods are well enclosed within the set of theoretical curves, also showing almost the same level of variability. An exception is the displacement along the line Baia- Miseno, which, in the period , was significantly higher than expected from the theoretical model. The last test which has been carried out pertains the effects of aco 2 mass fraction present in the injected fluid. Such a test is important because of the observations of Chiodini et al. (2001, 2003) pointing out that peaks of CO 2 and of CO 2 /H 2 O occur after about 6/7 months from peaks of ground uplifts. Although they have shown, in several papers (e.g. Chiodini et al. 2003; Todesco et al.

10 842 A. Troiano et al. Figure 8. Curves of ground displacements obtained by the best fitting thermofluid dynamical models with homogeneous (a), heterogeneous (b) and permeability (c), respectively. Curves in (c) are computed with the further effect of displacement discontinuities simulating the collapse caldera ring faults. Each couple of vertical horizontal curves refers to a given time during the injection, which may correspond to the inflation or deflation phase. The ratio H/V between maximum horizontal to maximum vertical displacement, as a function of time, is also shown (d), for the three models (point markers for the homogeneous model, square markers for the heterogeneous model and diamond markers for the heterogeneous model with discontinuities). 2003a), which such changes are consistent with injection peaks of a mixture of the two fluids, we have repeated here such tests. This is mainly because our models differ from their ones, for some details related to the permeability and, much more, for the depth of fluid injection, which they put much shallower, at 1.5 km. Results of the simulations carried out in this paper are reported in Fig. 10. In this figure, a comparison is shown between the ground displacement related to injection of pure water and CO 2 H 2 O mixture (with a 1:10 ratio), at a bottom of a cylinder characterized by permeabilities K 1 = m 2 ; K 2 = m 2. Only minor changes of the curves

11 Ground deformation driven by fluid injection 843 Figure 9. Curves of theoretical vertical and horizontal displacements as a function of distance from the symmetry axis, as due to fluid injection at the model bottom, for the best-fitting parameters. Light grey curves indicate displacements during the inflation phase, grey ones displacements during the deflation phase. (a) Vertical displacements at different times during the injection (continuous curves). Also shown, superimposed (small solid circles), are the observed vertical displacement data in several periods since ; (b) Horizontal displacements at different times during the injection (continuous curves). Also shown, superimposed (small solid circles), are the observed horizontal displacement data in several periods from 1982 to Figure 10. Time-dependent vertical displacements due to fluid injection at the bottom of the mesh, for the best-fitting parameters. Blue line represents the values of the vertical displacements observed at the Campi Flegrei area in the period Red line is related to a continuos injection of pure water, lasting 3 yr, at an injection rate, I 1, followed by a phase of injection at a reduced rate I 2. Green line is related to injection of a water and CO 2 mixture. Related injection rates are shown in figure. The H 2 O/CO 2 ratio is 10/1. are evident, from pure water to water/carbon dioxide mixture. This indicates that, more than fluid composition, the ground displacement behaviour is determined by the fluid injection rates and times. Fig. 11 shows the modelled peaks of CO 2 emission resulting in a time-lag of about 6 months with respect to peaks of ground deformation, highly consistent with the experimental observations (Chiodini et al. 2001). 5 DISCUSSION The modelling and results presented in this paper allow to describe, in a thorough and complete way, the main effects on ground deformations due to deep fluid injection in the shallow geothermal system of Campi Flegrei caldera. The models obtained in this paper, for the first time with this kind of formulation, take into account the whole depth extension of the aquifer system, down to the depth at which critical temperature is reached and no liquid water can exist. The basic model here described is an input of deeper fluids into the shallower aquifer system; the deep fluid injection is then suddenly decreased to a lower value, eventually equal to zero. One of the key points of our results concerns the effect of permeability values. They appear to be strongly affecting the time decay of ground deformation once the injection is decreased. This implies, in turn, that permeability values needed to explain observed ground deformation at Campi Flegrei, in the framework of the present model, are well constrained by the data. Inferred values range, for large to small uplift episodes, from to m 2. We tested two types of models: the first one homogeneous, the second one consisting of a more permeable cylinder embedded into a less permeable one (simulating encasing rocks). The second kind of model is consistent with higher permeability characterising the inner caldera rocks, due to intense fracturing. Also in this case, permeability values of the inner caldera cylinder appear well constrained at the mentioned values. It is noteworthy that inferred permeability values are in good agreement with values actually measured on rock samples (e.g. Peluso & Arienzo 2006). Such a result is not obvious, because it is well

12 844 A. Troiano et al. Figure 11. Top panel: The displacement curves of Fig. 10 are reported for comparison. There is an evident lag of about 6 months among the CO 2 emission peak with respect to the displacement peak value. Bottom panel: CO 2 fluxes at surface related to the model involving a H 2 O CO 2 mixture presented in Fig. 10 (green line). known that in situ permeability, possibly conditioned by rock fracturing, can be very different from laboratory measurements made on intact rock samples, whose permeability is conditioned by porosity and pore connectivity. Another important result is that the fluid injection rate needed to explain the amount of uplift cumulated in about 2.5 yr during the large unrest is roughly consistent with the amount of water equivalent inferred to simulate the observed microgravity changes accompanying the uplift (Battaglia et al. 2006). It is hence important to point out the main improvements of the analyses performed in this paper, as compared with former ones. The main improvement with respect to previous papers dealing with a thermofluid dynamical modelling is that, for the first time, we succeeded to give a formal good fit to both large and small uplift/subsidence episodes, in turn constraining the minimum permeability values. The model appears good both to simulate the time evolution of maximum deformation and to reproduce the shape of ground displacements as a function of the distance from the centre point (the one at which maximum vertical deformation occurs). The main conceptual difference of our analyses with respect to former results is that we model the whole geothermal system of Campi Flegrei caldera, extending down to the critical water temperature, to interpret any scale of ground deformation episodes. The depth at which critical temperature is reached in this area, is well constrained by former drillings data (AGIP 1987), to be in the range km. For comparison, former articles (e.g. Todesco et al. 2003a,b; 2010 and references therein) were rather devoted to model the local aquifers of Solfatara crater, to interpret the observed patterns of CO 2 fluxes. For this reason, former papers used, as the depth of 1.5 km for the aquifer in which fluid is injected. Such depth reflects the bottom of the shallower Solfatara geothermal system (Chiodini et al. 2003), but certainly not the maximum depth of aquifers at Campi Flegrei. To explain also the increase in CO 2 flux following the peaks of ground uplift, we have modelled, in a way similar to Todesco et al. (2003a, b), the injection at the base of aquifers of a mixture of 90 per cent of H 2 O and 10 per cent of CO 2. Results show that, in such way, we are able to explain the observed correlation between peaks of uplift and peaks of CO 2, with the correct time lag of about 6 months. Again, such results are obtained with the same realistic values for rock permeability, and share almost the same features of results obtained with pure water injection. This paper is then the first one giving a complete fit to the observed pattern of deformation during both large and small unrest episodes, using a realistic physical model, which involves thermofluid dynamical effects in a porous medium. The largest episode, namely the unrest, can be modelled by an increase of fluid injection amounting to 8 kt d 1, superimposed to a background injection rate of 1.15 kt d 1. For comparison, small uplift episodes like the one (see Lanari et al. 2004) require about 1.8 kt d 1 of peak injection rate. However, small uplift episodes show a sharper and complete subsidence, which reports the ground level to the former values (Figs 1 and 7). While the complete recovering of ground deformation can be explained with the return of injection rates exactly to previous values, the sharper subsidence rate requires permeability values higher than those inferred for large uplift episodes. Recalling that such minimum permeability values are inferred for a sudden decrease of injection rates, two explanations are possible for such discrepancy. The first one could be that, during large uplift episodes, the decrease of fluid injection rates after attaining peak values is not sudden, but more gradual to give the same subsidence rate with higher permeability values. The second one is that small uplift episodes only involve part of the aquifer system (for instance the shallower levels) characterized by a higher average permeability with respect to the whole system. Another feature which is clearly visible, in Fig. 8, is the slight time dependence of the theoretical shape of deformation during injection, which is due to the progressively shallower levels reached by injected fluids and is more marked during the deflation phase. Such dependence is hard to discriminate using observed data, which in fact fit the model rather well, including a slight variability in shape for different episodes overall similar to the variability range shown by theoretical predictions. Once the feasibility of the thermofluid