University of Bologna

The deformation and stress fields accompanying dyke injection in rift zones are described in terms of a vertical crack opening in response to internal overpressure, in plane-strain configuration. Previous numerical computations of the displacement field induced by shallow dykes are found to be affected, in some cases, by significant dis- tortion, mainly due to the limited extension of the computational domain, difficultiesin handling the singularities in the proximity of the free surface and an incorrect choice of the reference frame; in particular, it is found that no subsidence can be ascribed to the mere opening of a tensile crack in a homogeneous, elastic half-space. If analytical constant-dislocation models are employed, surface displacements compare reasonably well with crack-model solutions if the upper tip is not too shallow; however, constant dislocation solutions present unphysical singularities along the tips, which distort significantly the near-field stress pattern with respect to crack solutions. If the principal stress axes are computed from crack models, a broad region is found on both sides of the dyke where the induced stress has a nearly vertical intermediate axis while the com- pressive axis is normal to the dyke plane. Strike-slip earthquakes are expected to prevail in this region. Above the upper crack tip, a small region is present where the tensile stress is dominant and the intermediate stress is still vertical. In the proximity of the free surface, typically within a few tens of metres of it, induced tensile stresses are greater than the lithostatic pressure: open fissures might then develop in cohesionless soil or pre-faulted rock. The induced pressure in the host rock is found to be negative (suction) in the proximity of the ground surface and positive at greater depth: fluid flow within the aquifers can be significantly altered by this induced overpressure and by the anisotropic modification of the pre-existing permeability. According to the modified Coulomb failure criterion, in the short term the shallower region, characterized by suction, is strengthened, while the deeper, pressurized region is weakened. These results can explain in a straightforward way the abundance of strike-slip focal mechanisms in vol- canic areas, the switch between tensional and compressional axes inferred from focal mechanisms of earthquakes in connection with a dyke injection episode on Mount Etna, en echelon fracture systems observed at Piton de la Fournaise above the feeding dyke and precursory geochemical anomalies.

Campi Flegrei caldera (Italy) was affected by a new unrest phase during 2011-13. We exploit two COSMO-SkyMed datasets to map the deformation field, obtaining displacement rates reaching 9 cm/yr in 2012 in the caldera center. The resulting dataset is fitted in a geophysical inversion framework using finite element forward models to account for the 3D heterogeneous medium. The best-fit model is a North dipping mixed-mode dislocation source lying at ~5 km depth. The driving mechanism is ascribable to magma input into the source of the large 1982-84 unrest (since similar source characteristics were inferred) that generates initial inflation followed by additional shear slip accompanying the extension of crack tips. The history and the current state of the system indicate that Campi Flegrei is able to erupt again, and the advanced techniques adopted provide useful information for short-term forecasting.

We develop a mathematical model describing dyke propagation in proximity of an elastic discontinuity of the embedding medium. The dyke is modelled as a fluid-filled crack in plane strain configuration employing the boundary element method. The pressure gradient along the crack is assumed proportional to the difference between the densities of the host rock and the fluid. Mass conservation is imposed during propagation and fluid compressibility is taken into account. The path followed by the crack is found by maximizing the total energy release, given by the sum of the elastic and gravitational contributions. The mathematical simulations provide a sort of ‘refraction phenomenon’, that is a sudden change in the direction of propagation when the crack crosses the boundary separating different rigidities: if the dyke enters a softer medium, its path deviates towards the vertical, if the dyke enters a harder medium its path deviates away from the vertical and may even become arrested as a horizontal sill along the interface, if the rigidity contrast is large. Gravitational energy plays a major role during propagation; in particular, in proximity of layer boundaries, this role is enhanced by the shift of the centre of mass due to changes of dyke shape. Mathematical results were validated by laboratory experiments performed injecting tilted air-filled cracks through gelatin layers with different rigidities.

Since 1993, geodetic data obtained by different techniques (GPS, EDM, SAR, levelling) have detected a consistent inflation of the Mt. Etna volcano. The inflation, culminating with the 1998– 2001 strong explosive activity from summit craters and recent 2001 and 2002 flank eruptions, is interpreted in terms of magma ascent and refilling of the volcanic plumbing system and reservoirs. We have modelled the 1993–1997 EDM and GPS data by 3-D pressurized sources to infer the position and dimension of the magma reservoir. We have performed analytical inversions of the observed deformation using both spheroidal and ellipsoidal sources embedded in a homogeneous elastic half-space and by applying different inversion methods. Solutions for these types of sources show evidence of a vertically elongated magma reservoir located 6 km beneath the summit craters. The maximum elevation of topography is comparable to such depth and strong heterogeneities are inferred from seismic tomography; in order to assess their importance, further 3-D numerical models, employing source parameters extracted from analytical models, have been developed using the finite-element technique. The deformation predicted by all the models considered shows a general agreement with the 1993–1997 data, suggesting the primary role of a pressure source, while the complexities of the medium play a minor role under elastic conditions. However, major discrepancies between data and models are located in the SE sector, suggesting that sliding along potential detachment surfaces may contribute to amplify deformation during the inflation. For the first time realistic features of Mt. Etna are studied by a 3-D numerical model characterized by the topography and lateral variations of elastic structure, providing a framework for a deeper insight into the relationships between internal sources and tectonic structures.

Deformation of the ground surface in volcanic areas is generally recognized as a reliable indicator of unrest, possibly resulting from the intrusion of fresh magma within the shallow rock layers. The intrusion process is usually represented by a deformation source such as an ellipsoidal pressurized cavity, embedded within a homogeneous and elastic half-space. Similar source models allow inferring the depth, the location and the (incremental) volume of the intrusion, which are very important parameters for volcanic risk implications. However, assuming a homogeneous and elastic rheology and, assigning a priori the shape and the mechanism of the source (within a very restricted “library” of available solutions) may bias considerably the inference of source parameters. In complete generality, any point source deformation, including overpressure sources, may be described in terms of a suitable moment tensor, while the assumption of an overpressure source strongly restricts the variety of allowable moment tensors. In particular, by assuming a pressurized cavity, we rule out the possibility that either shear failure may precede magma emplacement (seismically induced intrusion) or may accompany it (mixed tensile and shear mode fracture). Another possibility is that a pre-existent weakness plane may be chosen by the ascending magma (fracture toughness heterogeneity). We perform joint inversion of levelling and EDM data (part of latter are unpublished), collected during the 1982-84 unrest at Campi Flegrei caldera: a 43% misfit reduction is obtained for a general moment source if the elastic heterogeneities computed from seismic tomography are accouted for. The inferred source is at 5.2 km depth but cannot be interpreted as a simple pressurized cavity. Moreover, if mass conservation is accounted for, magma emplaced within a shallow source must come from a (generally deeper) reservoir, which is usually assumed to be deep enough to be simply neglected. At Campi Flegrei, seismic tomography indicates that the “deep” magma source is rather shallow (at 7-8 km depth), so that its presence should be included in any thorough attempt to source modeling. Taking into account a deflating source at 7.5 km depth (represented either as a horizontal sill or as an isotropic cavity) and an inflating moment source, the fit of both levelling and EDM data improves further (misfit reduction 80%), but still the best fitting moment source (at 5.5 km depth) falls outside the range of pressurized ellipsoidal cavities. The shallow moment source may be decomposed in a tensile and a shear dislocation. No clue is obtained that the shear and the tensile mechanisms should be located in different positions. Our favourite interpretation is in terms of a crack opening in mixed tensile and shear mode, as would be provided by fluid magma unwelding pre-stressed solid rock. Although this decomposition of the source is not unique, the proposed solution is physically motivated by the minimum overpressure requirement. An important implication of this new interpretation is that the magma emplaced in the shallow moment source during the 1982-84 unrest was not added to already resident magma at the same position.

Deformation sources in volcanic areas are generally modeled in terms of pressurized tri-axial ellipsoids or pressurized cracks with simple geometrical shapes, embedded in a homogeneous half-space. However, the assumption of a particular source mechanism and the neglect of medium heterogeneities bias significantly the estimate of source parameters. A more general approach describes the deformation source in terms of a suitable moment tensor. Ratios between moment tensor eigenvalues are shown to provide a strong diagnostic tool for the physical interpretation of the deformation source and medium heterogeneities may be accounted for through 3D finite element computations. Leveling and EDM data, collected during the 1982–84 unrest episode at Campi Flegrei (Italy), are employed to retrieve the complete moment tensor according to a Bayesian inversion procedure, considering the heterogeneous elastic structure of the volcanic area. Best fitting moment tensors are found to be incompatible with any pressurized ellipsoid or crack. Taking into account the deflation of a deeper magma reservoir, which accompanies the inflation of a shallower source, data fit improves considerably but the retrieved moment tensor of the shallow source is found to be incompatible with pressurized ellipsoids, still. Looking for alternative physical models of the dislocation source, we find that the best fit moment tensor can be best interpreted in terms of a mixed mode (shear and tensile) dislocation at 5.5 km depth, striking EW and dipping by ~25°–30° to the North. Gravity changes are found to be compatible with the intrusion of ~60–70·10^6 m^3 of volatile rich magma with density ~2400 kg/m^3.

Employing a 3D finite element method, we develop an algorithm to calculate gravity changes due to pressurized sources of any shape in elastic and inelastic heterogeneous media. We consider different source models, such as sphere, spheroid and sill, dilating in elastic media (homogeneous and heterogeneous) and in elasto-plastic media. The models are oriented to reproduce the gravity changes and the surface deformation observed at Campi Flegrei caldera (Italy), during the 1982-1984 unrest episode. The source shape and the characteristics of the medium have great influence on the calculated gravity changes, leading to very different values for the source densities. Indeed, the gravity residual strongly depends upon the shape of the source. Non negligible contributions also come from density and rigidity heterogeneities within the medium. Furthermore, if the caldera is elasto- plastic, the resulting gravity changes exhibit a pattern similar to that provided by a low effective rigidity. Even if the variation of the source volumes is quite similar for most of the models considered, the density inferred for the source ranges from ∼400 kg/m3 (super critical water) to ∼3300 kg/m3 (higher than trachytic basalts), with drastically different implications for risk assessment.

The Emilia-Romagna seismic sequence in May 2012 was characterized by two mainshocks which were close in time and space. Several authors already modeled the geodetic data in terms of the mechanical interaction of the events in the seismic sequence. Liquefaction has been extensively observed, suggesting an important role of fluids in the sequence. In this work, we focus on the poroelastic effects induced by the two mainshocks. In particular, the target of this work is to model the influence of fluids and pore-pressure changes on surface displacements and on the Coulomb failure function (CFF). The fluid flow and poroelastic modeling was performed in a 3D half-space whose elastic and hydraulic parameters are depth dependent, in accordance with the geology of the Emilia-Romagna subsoil. The model provides both the poroelastic displacements and the pore-pressure changes induced coseismically by the two mainshocks at subsequent periods and their evolution over time. Modeling results are then compared with postseismic InSAR and GPS displacement time series: the InSAR data consist of two SBAS series presented in previous works, while the GPS signal was detected adopting a variational Bayesian independent component analysis (vbICA) method. Thanks to the vbICA, we are able to separate the contribution of afterslip and poroelasticity on the horizontal surface displacements recorded by the GPS stations. The poroelastic GPS component is then compared to the modeled displacements and shown to be mainly due to drainage of the shallowest layers. Our results offer an estimation of the poroelastic effect magnitude that is small but not negligible and mostly confined in the near field of the two mainshocks. We also show that accounting for a 3D fault representation with a nonuniform slip distribution and the elastic-hydraulic layering of the half-space has an important role in the simulation results.

The 1982-84 unrest episode at Campi Flegrei was characterized by huge deformation (about 1.8 m uplift) located inside the caldera and significant gravity variations correlated with the elevation changes (about -213 $\mu$Gal/m). Due to the bell shape of the uplift, the source is usually interpreted to have a fixed spherical shape. In the present study, we combine simple point source mechanisms (dipoles and double couples) to represent arbitrary sources such as sphere, ellipsoid or sill. The models are realized by Finite Element and the medium may be characterized by elastic heterogeneities. We study the deformation detected by leveling and EDM techniques by coupling the FE forward models with an inversion procedure. The potential point sources are contained in a volume of 8$\times$8$\times$8 km$^3$ located beneath Pozzuoli, the site of maximum displacement. We calculate the displacement field at each data point for each basic mechanism and we compare the result with the observed value. From the inversion of geodetic data we retrieve the best-fitting source parameters, without fixing the shape a priori. The best-fitting source is located beneath Pozzuoli at about 4.8 km b.s.l. and undergoes to horizontal compression and vertical dilatation.

A model is proposed to explain the spatial distribution of foreshocks of the June 17th 2000, M s 6.6 earthquake in the South Iceland Seismic Zone (SISZ) and the high stress drop of the mainshock. Fluids of magmatic origin, ascending at near-lithostatic pressure through a low permeability layer perturb the regional stress field, inhibiting fluid flow laterally, where a high strength asperity is left. The asperity is modeled as elastic, embedded within a medium with low effective rigidity. Regional stresses due to tectonic motions are perturbed by the presence of the asperity, enhancing the production of hydrofractures and foreshocks in the NW and SE quadrants and increasing considerably the shear stress within the asperity, leading to the NS striking mainshock.