M. Bonafede

Hot fluid migration: an efficient source of ground deformation: application to the 1982–1985 crisis at Campi Flegrei-Italy

Abstract Some solutions of the forced heat advection problem in compressible media are worked out employing a perturbative approach and their implication for thermoelastic deformation are discussed. A sharp temperature front, which migrates at a speed in the order of Darcy flow rate, develops in the medium, giving rise to significant deformation via thermal expansion. A thermally induced pressure source accompanies the temperature front, which may be significant only in very high temperature cases. Results are applied to interpreting the uplift episode of 1982–1984 at Campi Flegrei (C.F.), near Naples, Italy. A mechanism is envisaged for uplift at Campi Flegrei in which a sudden connection is established between a deep, hot, high-pressure fluid reservoir and a shallow, relatively cold, low-pressure aquifer. The inclusion of fluid migration in the deformation model allows simple explanations of several geochemical and geophysical observations made during the bradyseismic crisis. It appears that the proposed mechanism may explain the large observed uplift, without requiring unreasonable pressure increase within the magma chamber. Furthermore, the deformation source may be allowed to be shallower than the magma chamber, as required by any reasonable deformation model at C.F.

Downslope flow models of a Bingham liquid: Implications for lava flows

It is widely recognized that lavas behave as Bingham liquids, which are characterized by a yield stress σϒ and a plastic viscosity η. We consider two models describing downslope flows of a Bingham liquid with different aspect ratios A (= flow height/flow width): model 1 with A ⪡ 1 and model 2 with A ≈ 1. Sufficiently uphill with respect to the front, such flows can be considered as laminar and locally isothermal. For both models, we obtain analytically the steady-state solution of the Navier-Stokes equations and the constitutive equation for a Bingham liquid. We study the flow height and velocity as functions of flow rate, rheological parameters and ground slope. It is found that such flows remain in the Newtonian regime at low yield stresses (σϒ ⪅ 103dyne/cm2), but the transition to the Bingham regime also depends on flow rate and occurs at higher values of σϒ for higher flow rates: for instance, a high aspect ratio flow (model 2) is still very close to the Newtonian regime at σϒ = 104 dyne/cm2, if the flow rate is greater than 105 g/s. In the Bingham regime, flow heights are generally greater and flow velocities are smaller than in the Newtonian regime; moreover, flow heights are independent of flow rate, so that a change in flow rate results exclusively in a velocity change. After assuming a specific temperature dependence of σϒ and η between the solidus and the liquidus temperatures of an ideal Bingham liquid (1000°C and 1200 °C respectively), flow heights and velocities are examined as functions of temperature along the flow. Several effects observed in lava flows are predicted by these models and allow a more quantitative insight into the behaviour of lava flows.

Modelling gravity variations consistent with ground deformation in the Campi Flegrei caldera (Italy)

Abstract In recent years (1970–72 and 1982–84) two inflation episodes took place in the Campi Flegrei caldera (Italy), characterized by significant ground uplift and gravity variations. An elastic half-space model with vertical density stratification is employed to compute the displacement field and the gravity variations produced by the deformation of buried layers, following the inflation of a spherically symmetric deformation source. Contributions to gravity variations are produced by dilation/contraction of the medium, by the displacements of density interfaces (the free surface and subsurface layers) and of source boundaries and, possibly, by new mass input from remote distances into the source volume. Three cases were examined in detail: In case I, the magma chamber is identified as the deformation source and volume and pressure increase in the magma chamber is due to input of new magma from remote distances; in case II deformation is due to magma differentiation within the magma chamber (deformation source with constant mass); in case III the geothermal system is identified as the deformation source and a pressure increase, possibly driven by the exsolution of high temperature and high pressure volatiles in the magma chamber, is assumed to play a dominant role. From the comparison between measured and computed gravity residuals (free-air-corrected gravity variations) we can assess that, in case I, an inflation source with constant density would predict gravity residuals compatible with observations, whereas an expansion at constant mass (case II) would predict gravity residuals much lower than observed. The resolving power of gravity data however prevents accurate assessment of the density of the emplaced material. In case III, the pervasive density increase of the geothermal fluids induced by pressure increase is assumed to be the main source of gravity variations. The average porosity value required for this model to match both the ground deformation and the gravity residuals is found to be ~10%, a value which is compatible with measured porosity values at Campi Flegrei in deep wells. The subsidence phases following both inflation episodes and the gravity residuals during subsidence lead us to consider case III as more plausible, even if a suitable combination of cases I and III cannot be discarded.

Effects of topography and rheological layering on ground deformation in volcanic regions

Abstract The ground deformation produced by a spherical overpressure source in a heterogeneous elastic and/or viscoelastic medium is investigated by numerical models based on the finite element method. Sources are assumed to be located at different depths beneath Mount Etna, Sicily, Italy, the structure of which is approximated as axially symmetric. Finite element modelling allows to incorporate in the analysis realistic features such as topographic relief and the laterally heterogeneous multi-layered structure inferred from seismic tomography. In order to avoid introducing artifacts in the solution, great care was taken to calibrate the computational domain necessary to reproduce analytical results accurately. An elastic analysis, performed initially, shows significant changes of the deformation field with respect to homogeneous half-space solutions: topography induces slight but detectable changes in the deformation field; in particular the maximum value of the vertical component is shifted away from the symmetry axis. When introducing the elastic heterogeneities, the ground deformation is found to be more confined to the proximity of the axis and its amplitude is mostly sensitive to the presence of low rigidity layers above the source. The ratio of maximum radial to vertical deformation is significantly larger for deeper sources. A further development of the model includes the study of inelastic properties assuming a Maxwell viscoelastic rheology for different layers. If the viscoelastic rheology is applied only to layers deeper than the source, the solutions are affected in different ways according to the distance of the source from the viscoelastic layer. If a viscoelastic layer is present above the source, a very large amplification (by more than 100%) of the surface deformation is predicted by the model; moreover, uplift transients are found to be followed by subsidence, without invoking any decrease in source overpressure. The most striking effects are observed when the source is embedded within a viscoelastic layer: in this case a static equilibrium configuration is not attained and, in the long term, both components of deformation reverse their signs in proximity to the axis. Furthermore, the surface deformation becomes nearly independent of source depth, in the long term. Simple physical explanations are proposed for the different cases.

Geodetic constraints to the source mechanism of the 2011–2013 unrest at Campi Flegrei (Italy) caldera

Campi Flegrei caldera (Italy) was affected by a new unrest phase during 2011–2013. We exploit two COSMO-SkyMed data sets to map the deformation field, obtaining displacement rates reaching 9 cm/yr in 2012 in the caldera center. The resulting data set is fitted in a geophysical inversion framework using finite element forward models to account for the 3-D 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 1982–1984 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.

Stress diffusion across laterally heterogeneous plates

Stress diffusion following a major dislocation event may provide significant contributions to the stress field present in the neighbouring regions. Seismic regularities observed in the southern Adriatic region are used in the present paper to constrain possible physical models of stress diffusion. Lateral variations in the rheological structure of the lithosphere-asthenosphere system are considered. A diffusion equation with variable diffusivity is obtained using the Elsasser approximation, which describes migration of the stress field after a dislocation event. Approximate solutions of this equation are worked out in the long wavelength limit, showing that diffusion is faster where the lithosphere is thicker and slower where it is thinner. Lithosphere thinning accordingly provides a higher amplitude and longer duration diffusional stress following a dislocation event. This behaviour is particularly evident in a transient regime.

On the Interpretation of Slow Ground Deformation Precursory to the 1976 Friuli Earthquake

During three years preceding the 1976 Friuli earthquake, a continuous southward ground tilt was recorded by a tiltmeter placed near Tolmezzo, 15 km north-west of the epicentre of the impending earthquake. The cumulative ground tilt amounted to as much as 3 minutes of arc. Since the tiltmeter was placed in the proximity of an active fault, such a tilt can be explained if the fault slipped aseismically on its shallower section during the same three year period. Aseismic slip on the fault might have been caused by the same mechanism which concentrated stress in the region and eventually produced the 1976 earthquake.

Stress Relaxation in the Earth and Seismic Activity.

Consideration of the models described in the preceding pages shows that a sound theoretical basis exists for a physical understanding of post-seismic ground deformations and several other phenomena associated with the asthenosphere relaxation. Since the asthenosphere seems to be involved in a direct way in the seismic mechanism, the knowledge of its rheological properties becomes an essential point to understand the seismic mechanism too. Once a reasonable knowledge of the asthenosphere behaviour is achieved, the models can tell us how the system lithosphere-asthenosphere will evolve after an earthquake or a similar perturbation of the stress field. It will be necessary to compute the stress pattern not only at the Earth surface, but also at the depth where the faults lay. By knowing how stress changes in space and time through the lithosphere, one might predict, for instance, the arrival of a stress wave on a seismogenetic structure: this wave might trigger an earthquake in this zone, if favourable conditions are found.

Heat diffusion and size reduction of a spherical magma chamber

An analytical solution is derived for the size reduction of a spherical magma chamber cooling by conduction. The use of moving boundary conditions and the constraint of a spherical symmetry allow one to ignore the details of the heat redistribution processes which take place within the magma chamber. The dependence of the solution on the initial conditions is investigated. A simple solution is found for short time, which is shown to be valid for times long enough to make it useful in the volcanological context. Moreover, the general solution confirms that the hydrothermal contribution to heat transfer in Phlegraean Fields cannot be extremely important.

A porous-flow model of flank eruptions on Mount Etna

Abstract A porous flow model for magma migration from a deep source within a volcanic edifice is developed. The model is based on the assumption that an isotropic and homogeneous system of fractures allows magma migration from a common localized source to the surface of the volcano. The evolution of the free surface of magma (i.e. the locus where magma pressure equals the atmospheric pressure) is reproduced through a first-order perturbation approach to the non-linear equations governing the migration of incompressible fluids through a porous medium. It is argued that flank eruptions should preferably concentrate in those regions where the topography is lower than the theoretical free surface of magma, since, in this case, less pressure is necessary at the source to accomplish magma migration to the surface against gravity and viscous friction. Comparisons of the theoretical free surface with several topographical sections of Mt. Etna, where eruptive fractures and vents preferably concentrate, seem to confirm the assumption. Even if the model does not pretend to reproduce the topographic surface, the comparison is excellent along the southern and southeastern sections of Mt. Etna, where flank eruption take place over the widest range of altitudes; in this sector, modulations in the eruption site density correlate well with even minor differences between free surface and topography. Along other sections of Mt. Etna, the free surface and the topography are not always in close agreement, but the density of eruption vents generally concentrates in regions where the topography is lower than the free surface, the only notable exception being the northeastern rift.