Vol48/04/2005def 797 ANNALS OF GEOPHYSICS, VOL. 48, N. 4/5, August/October 2005 Key words hydrothermal fluids – faults – cracks – fluid pressure – volcanic/hydrothermal areas – seis- micity – Vesuvius – Campi Flegrei 1. Introduction Faults and fractures play a major role in the localization and evolution of hydrothermal flow (Sibson, 1996; Curewitz and Karson, 1997; Riedel et al., 2001). This follows from the nearly ubiquitous close association of faults and hy- drothermal outflows sites, which include hot springs, geysers, fumaroles, and diffuse de- gassing areas (Chiodini et al., 2001a; Craw et al., 2002; Minissale, 2003; Molin et al., 2003). Sim- ilar evidence for fault control on hydrothermal activity is the close association between faults and mineral deposits (e.g., gypsum, anhydrite, quartz) arranged in veins or aligned spots (Han- nington et al., 2001; Singlenton and Criss, 2002; Clark and James, 2003). Fluids may also play a major role in triggering seismicity (Sibson, 2000; Collettini, 2002; Tenthorey et al., 2003). As faults propagate, interact and link, hydrothermal circu- lation may evolve from scattered migrating out- flow sites to stable discharge sites affecting a fault or the whole fault system. Changes in the behavior of hydrothermal outflows near faults may reflect the evolution of the fault zone or of the hydrothermal systems (Chiodini et al., 2001a; Molin, 2003). Then, the estimate of the fluid Estimates of fluid pressure and tectonic stress in hydrothermal/volcanic areas: a methodological approach Guido Ventura (1) and Giuseppe Vilardo (2) (1) Istituto Nazionale di Geofisica e Vulcanologia, Roma, Italy (2) Istituto Nazionale di Geofisica e Vulcanologia, Osservatorio Vesuviano, Napoli, Italy Abstract An analytical approach to estimate the relative contribution of the fluid pressure and tectonic stress in hydrother- mal/volcanic areas is proposed assuming a Coulomb criterion of failure. The analytical procedure requires the coefficient of internal friction, cohesion, rock density, and thickness of overburden to be known from geologi- cal data. In addition, the orientation of the principal stress axes and the stress ratio must be determined from the inversion of fault-slip or seismic data (focal mechanisms). At first, the stress magnitude is calculated assuming that faulting occurs in ‘dry’ conditions (fluid pressure = 0). In a second step, the fluid pressure is introduced per- forming a grid search over the orientation of 1) fault planes that slip by shear failure or 2) cracks that open un- der different values of fluid pressure and calculating the consistency with the observed fault planes (i.e. strike and dip of faults, cracks, nodal planes from focal mechanisms). The analytical method is applied using fault-slip data from the Solfatara volcano (Campi Flegrei, Italy) and seismic data (focal mechanisms) from the Vesuvius volcano (Italy). In these areas, the fluid pressure required to activate faults (shear fractures) and cracks (open fractures) is calculated. At Solfatara, the ratio between the fluid pressure and the vertical stress λ is very low for faults (λ = 0.16) and relatively high for cracks (λ = 0.5). At Vesuvius, λ = 0.6. Limits and uncertainties of the method are also discussed. Mailing address: Dr. Guido Ventura, Istituto Nazionale di Geofisica e Vulcanologia, Via di Vigna Murata 605, 00143 Roma, Italy; e-mail: ventura@ingv.it 798 Guido Ventura and Giuseppe Vilardo pressure required to activate a fault or a crack and of the tectonic stress field acting on a fault is of primary importance for the study of 1) active hy- drothermal systems or paleo-flow systems and b) the analysis of the hydraulic structure of fault zones. This also has implications for the study of the hazard related to the seismic, volcanic, and hydrothermal activity (Sibson, 1998; Saccorotti et al., 2001; Finizola et al., 2002). In this study, we propose an analytical method to obtain semi-quantitative estimates of the magnitude of tectonic stress and fluid pres- sure in fault zones. The method is based on the collection and elaboration (stress inversion) of structural data and/or data from focal mecha- nisms and allow us to estimate the magnitude of the principal tectonic stress (σ1, σ2, and σ3) and fluid pressure Pf in active hydrothermal/tectonic areas. Examples of application to areas character- ized by extensional (Solfatara volcano, Campi Flegrei, Italy) and strike-slip tectonics (Vesuvius, Italy) are provided and the results are discussed. 2. Analytical method Jaeger and Cook (1979) present an equation that shows the criteria for Coulomb shear fail- ure along a plane. Rewriting their equation in terms of θ, the angle that the greatest principal stress σ1 makes with the plane of weakness gives (Fournier, 1996) (2.1) where µ is the coefficient of internal friction and C is the cohesion, Note that eq. (2.1) is valid if the fluid pres- sure Pf = 0. If Pf ≠ 0, σ1, σ2, σ3 may be deter- mined assuming a Coulomb criterion of failure and resolving the system of equations (2.2) (normal stress regime), or (2.3a) (strike-slip regime), or (2.3b)gh2 =v t gh1 =v t ( ) ( ) ( ) tan sin C 1 2 2 2V 1 3 3 - = - - + v v n i i n v mv 6 7 @ A ( [ ] ) ( )tan sin C2 2 1 2 31 3 - + = - v v nv n i i6 @ (compressive regime) (2.3c) (2.4) (2.5) where ρ is the rock density, g is the acceleration of gravity, h is the thickness of overburden. This system may be resolved if a) ρ and h are known from geological data; b) R and the ori- entation of the principal stress axes are known from inversion of fault-slip data or focal mech- anisms of earthquakes; and c) θ is determined from the angular relationships between the maximum principal stress and the preferred rupture plane(s). The analytical procedure to solve the system consists of three main steps. In a first step, the stress magnitude is calculated setting λ = 0 and C = 0, and assuming that fault- ing occurs on pre-existing planes of weakness. In a second step, Pf is introduced performing a grid search over the orientation of fault planes that slip by shear failure under different values of λ and calculating the consistency with the observed fault planes (e.g., strike and dip of nodal planes from focal mechanisms) following the procedure of Morris et al. (1996) and Phillips et al. (1997). In this step and in the next step, C and µ are unchanged. In a third step, Pf is varied performing a grid search over the ori- entation of planes that shear under different val- ues of λ and calculating the consistency with the measured (faults) or determined (focal mechanisms) rupture planes. Here below, this method is applied using structural data from the Solfatara crater (Campi Flegrei, Italy) and seis- mic data (focal mechanisms) from the Vesuvius volcano (Italy). In these areas, the fluid pres- sure required to activate faults (shear fractures) and cracks (open fractures) is calculated. 3. Application 3.1. Solfatara crater (Campi Flegrei) The Campi Flegrei is a nested caldera result- ing from two large collapses related to the Cam- ; tan P 2 1 V f = =n i m v ( ) ( ) R 3 2 1 3 = - - v v v v gh3 =v t 799 Estimates of fluid pressure and tectonic stress in hydrothermal/volcanic areas: a methodological approach panian Ignimbrite (39 kyr) and to the Neapoli- tan Yellow Tuff (12 kyr) eruptions (fig. 1a; Orsi et al., 1996). The Campi Flegrei magmatic sys- tem is still active and the last eruption occurred in 1538 A.D. at Monte Nuovo. Faults affecting the Campi Flegrei caldera follow two preferred strikes, NW-SE and NE-SW, which are the same as the faults affecting the Campanian Plain and the inner sectors of the Apennine belt (Hippolyte et al., 1994; Orsi et al., 1996). The Solfatara vol- cano (180 m a.s.l.; fig. 1b) is a 3.8 to 4.1 kyr old tuff-cone located NE of Pozzuoli. The Solfatara crater is affected by two main faults striking NW-SE. Outside the crater area, two NW-SE striking faults cut the eastern sector of the tuff cone (fig. 1b). The Solfatara NW-SE striking fault segments show a maximum meas- ured vertical offset equal to 40 m on the SW cor- ner of the crater. In the crater area, NE-SW and NW-SE striking cracks and fluid-filled veins oc- cur (fig. 1b). Results of a mesostructural study carried out to characterize the Solfatara deforma- tion pattern show that the faults have normal slips with pitch ≥ 75°. They move in response to a nor- mal stress field characterized by a sub-vertical σl = σV (strike 264°, plunge 79°) and a NE-SW striking subhorizontal σ3 (strike 45°, plunge 8°) (fig. 1b). σ2 (strike 316°, plunge 7°) parallels the NW-SE fault strike and R = 0.18 (Chiodini et al., 2001a). This stress configuration is consis- tent with that obtained by Zuppetta and Sava (1993) from the analysis of focal mechanisms of earthquakes which occurred in 1982-1984. To verify if the fluid pressure plays a role in the kinematics of the Solfatara faults, the above Fig. 1a-d. a) Sketch map of the Campi Flegrei caldera (from Orsi et al., 1996). b) Structural map of the Solfatara area and summary of the mesostructural measurement in the Solfatara area. Fault-slip data and orientation of the stress axes are reported right down (Schmidt net, lower hemisphere projection; data from Chiodini et al., 2001). The azimuthal distribution of the strike of cracks in different selected sites is plotted on Rose diagrams. Each measurement site does not ex- ceed 40 m2. c, d) Results of the stress field analysis on the Solfatara faults (c; λ = 0.16) and cracks (d; λ = 0.5). Poles to measured fault planes (upper panel) and crack walls (lower panel) are reported as dots (Schmidt net, lower hemisphere). a b d c 800 Guido Ventura and Giuseppe Vilardo described procedure is applied. In a first step, we set λ = 0 and ρ = 2000 kg/m3 (average density of the Flegrei pyroclastics; Barberi et al., 1991). µ was determined measuring the angle θ between the fault planes and the orientation of σ1 deter- mined from the inversion of fault-slip data, i.e. θ∼30°. C was set to zero assuming that faulting occurs on pre-existing planes of weakness. This assumption is justified by the fact that the Solfa- tara faults follow the same trend as the main structural discontinuity affecting the Campi Fle- grei caldera. In a second step, we introduce Pf performing a grid search over the orientation of fault planes that slip by shear failure under different values of λ and calculated the consistency with the NW-SE fault planes following the method of Morris et al. (1996). Both C and µ are unchanged. The ob- tained results (fig. 1c) indicate that 1) at Pf = 0, the variation of the stress magnitude with depth is ∆σ1= 20 MPa/km, ∆σ2= 9 MPa/km and ∆σ3= 6.7 MPa/km; 2) the differential stress is about 13 MPa at 1 km of depth; and 3) Pf required to acti- vate the NW-SE faults is 3.3 MPa/km (fig. 1c). As a result, λ = 0.16. The effective stress magni- tude (σ1eff = σ1−Pf; σ2eff = σ2−Pf; σ3eff =σ3−Pf) are: σ1eff = 17 MPa/km, σ2eff = 6 MPa/km and σ3eff = = 3.7 MPa/km. We conclude that fluids play a mi- nor role in the kinematics of the Solfatara faults. However, both NE-SW and NW-SE cracks and fluid-filled veins occur within the crater area. Then, we vary Pf performing a grid search over the orientation of planes that open (cracks) under different values of λ and calculating the consis- tency with the measured crack parameters (strike and dip of crack wall). Results indicate that Pf re- quired to open both the NW-SE and NE-SW cracks is of about 10 MPa/km (fig. 1d). The cal- culated λ value is 0.5. In summary, the obtained results indicate that Pf < σ3 is required to activate the NE-SW faults by shear, whereas σ2∼Pf >σ3 is required to open the NE-SW and NW-SE striking cracks. 3.2. Vesuvius volcano Vesuvius volcano has been in a quiescent stage since 1944 and is characterized by a low temperature fumarolic activity (Tmax=100°C). The Vesuvius cone is located within a caldera formed during both sub-plinian (e.g. 1631; Rosi et al., 1993) and plininan eruptions (e.g. 79 A.D.; Santacroce, 1987). Two main fault sys- tems striking NW-SE and NE-SW affect the volcanic edifice. Vesuvius seismicity (about 200 events/yr; −0.4 ≤ MD ≤ 3.6) concentrates within the caldera volume and is characterized by swarm type sequences. The hypocentral depths range from the top of the volcanic edi- fice up to about 6 km b.s.l. (fig. 2a). Maximum event clustering occurs between 2 and 3 km b.s.l., at the interface between the sedimentary basement of the volcano (limestones and dolomites) and the intra-caldera volcanic rocks (fig. 2a; Cassano and La Torre, 1987), and where the present-day hydrothermal system is located (Chiodini et al., 2001b). Available focal mechanisms show prevailing strike-slip solu- tions (Vilardo et al., 1996). Correlations be- tween the annual pattern exhibited by the time series of the events number and the seismic en- ergy release indicate that pore pressure varia- tions due to diffusion processes within the hy- drothermal system are responsible for the lubri- fication of pre-existing fractures, so triggering seismicity (Vilardo et al., 1999; Saccorotti et al., 2002). The stress field acting within the Vesuvius volcano was determined by Bianco et al. (1998) and Vilardo et al. (1999) using focal mecha- nisms from 1996-1997 time period. The inver- sion of 60 focal mechanisms of events located at depth between +1 and −6 km a.s.l. and MD between 1 and 3.2 show that the Vesuvius stress field is hetereogeneous. However, the majority of the solutions are consistent with a prevailing strike-slip stress field characterized by subhori- zontal WNW-ESE σ1, NNE-SSW σ3 and sub- vertical σ2. According to Bianco et al. (1998), this configuration reflects the action of the re- gional stress field on the volcano. Here, the 35 available focal mechanisms of events with MD ≥ ≥ 1.5 which occurred between 2 and 5 km b.s.l. from the data set of Vilardo et al. (1999), which refers to 1996-1997 seismicity, are selected. The fault plane solutions are characterized by subvertical nodal planes following two main strikes: NNW-SSE and NE-SW (fig. 2b). The inversion (Sperner et al., 1993) of the selected 801 Estimates of fluid pressure and tectonic stress in hydrothermal/volcanic areas: a methodological approach fault plane solutions is consistent with a strike- slip stress configuration characterized by σ1= 91° and 7° (trend and plunge), σ2 = 219° and 79°, σ3= 360° and 8° (fig. 2b), and R = (σ2+ −σ3)/(σ1−σ3) = 0.24. In a first step, we calculate stress magnitude in depth by setting σV = σ2 (strike-slip configuration), λ = 0 and ρ = 2600 kg/m3 (mean density of the Vesuvius lavas; Fig. 2a-c. a) Schematic cross sections of the Vesuvius volcano (form Cassano and La Torre, 1987, modified) with circles representing the hypocentral location of the 1986-1997 earthquakes. Number of events versus depth is also reported. b) Azimuthal distribution of angular parameters of nodal planes from 35 focal mechanisms of earthquakes with MD ≥ 1.5 occurred in 1996-1997 period, and distribution of P and T axes and of the principal stress axes. c) Results of the stress field analysis on the nodal planes from earthquakes (λ = 0.6). a b c 802 Guido Ventura and Giuseppe Vilardo Cassano and La Torre, 1987). µ was determined measuring the angle θ between the strike of nodal planes and the orientation of σ1. C was set to zero assuming that faulting occurs on pre- existing planes of weakness. This assumption is justified by the fact that the nodal planes follow the same trends as the main structural disconti- nuity affecting the volcano basement. In a sec- ond step, we introduced Pf performing a grid search over the orientation and slip direction of planes which slipped under different values of λ and calculating the consistency with the nodal planes following the procedure of Morris et al. (1996) and Phillips et al. (1997). The results obtained (fig. 2c) are: µ = 0.18 and λ = 0.6. Ef- fective principal stresses (σ1eff = σ1−Pf ; σ2eff = = σ2−Pf ; σ3eff = σ3−Pf ) vary with depth with the following gradients: ∆σ1eff = 17.3 MPa/km, ∆σ2eff = 10 MPa/km and ∆σ3eff = 7.6 MPa/km. We conclude that fluid pressure plays a major role in triggering Vesuvius seismicity. 4. Discussion and conclusions The proposed analytical method is based on the assumption that some geotechnical data (e.g., cohesion; density) of the rocks are known. In the above reported examples, we assume that faulting occurs on pre-existing zones of discon- tinuity and set C = 0. However, this may be not true in hydrothermal zones, where self-sealing processes in fractures are common and mineral- filled fractures (veins) may act as barriers to fluid flow (e.g., Thentorey et al., 2003). In ad- dition, we assume no variations of density with depth. In the cases of Vesuvius and Campi Fle- grei, this is a reasonable assumption because significant variations in density with depth are lacking at least in the first 2-3 km below the volcano axis (Cassano and La Torre, 1987; Rosi and Sbrana, 1987). However, this may be an over-simplification in many hydrothermal and/or volcanic areas because of the occurrence of strong layering within both the shallow and deeper parts of the crust. An additional problem concerns the occurrence of areas subjected to heterogeneous stress sources. This is the case of volcanoes, whose structural features generally result from the superimposition of gravity, tec- tonic and magmatic induced stress. In this pic- ture, a procedure of data selection must be im- plemented to select brittle structures related to tectonic and fluid-induced stresses alone, with- out the contribution of gravity. Taking into ac- count the above reported limitations, the results of analysis presented here may give useful in- formation on the relative contribution of tecton- ic stress and fluid pressure in triggering faulting and cracking in volcanic/hydrothermal areas. Examples from Solfatara and Vesuvius show that hydrothermal fluids play a major role in triggering Vesuvius seismicity and in opening of the Solfatara cracks, whereas they play a mi- nor role in the dynamics of the Solfatara faults. In particular, the Solfatara cracks may open on- ly by fluid overpressure, i.e. by hydrofractur- ing. These results are consistent with the con- clusions from independent geochemical and seismological studies on Solfatara and Vesuvius (Chiodini et al., 2001a,b; Saccorotti et al., 2001, 2002). 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