We analyze 1980–2010 ground displacements, to discern similarities or differences between Campi Flegrei (CF) inflations and deflations and highlight possible anomalies in particular areas. We show that the deformation pattern can be decomposed into two stationary (constant over time, except for a mere scaling factor) parts; both of them are satisfied by simple deformation sources. A quasi-horizontal elongated crack (oriented NW to SE, and embedded in an elastic layered half-space at a depth of about 3600 m) satisfies large-scale deformation. All source parameters but potency (volume change) are constant over time. Residual deformation is confined to the area of the Solfatara fumarolic field and satisfied by a small spheroid located at about 1900 m in depth. Again, all source parameters but potency are constant over time. The histories of the two sources are somewhat similar but not equal, supporting the existence of a genuine local deformation source at Solfatara against the emergence of a mere distortion of large-scale deformation. Although reality is probably much more complex, our simple model explains 1980–2010 CF deformation within ground-displacement data errors and is consistent with Solfatara geochemical conceptual models, fumarolic geochemical data, and seismic attenuation imaging of CF. The observation that the CF deformation pattern can be decomposed into two stationary parts is hardly compatible with several recent works which proposed multiple sources with different features acting in different periods, fluid injections implying ample changes of large-scale deformation pattern over time, complex spatio-temporal patterns of distributions of volumetric sources

1] We present exact expressions for the volume change of a pressurized ellipsoidal cavity in an infinite homogeneous elastic medium. The expressions can be used as approximate solutions also for a homogeneous half-space. We show that previously published widely used expressions are correct for spheres but underestimate the ratio of the volume change to the product of pressure and volume in any other case. We discuss the capability to infer the shape of a single ellipsoidal cavity from far-field deformation measurements. Our results indicate that source axis ratios may often be hard to estimate, whereas it may be easier to infer the volume change of the source. We also consider the case of a source region consisting of interconnected pressurized ellipsoidal cavities, neglecting mutually induced stress. If all the cavities share the same shape and orientation, the source is seen in the far field as a single ellipsoidal cavity and it is possible to compute the total volume change from surface displacements. The shape of the apparent single ellipsoid is the same as the shape of the constituting cavities and not of the source region. In any other case a single ellipsoidal cavity might even be unable to give the same surface displacements as the ensemble of cavities. Since sudden volume change of a cavity can generate seismic waves, we discuss the decomposition of the related moment tensor into isotropic, double-couple, and compensated linear-vector dipole force systems in case of magma exchange between two ellipsoidal cavities, giving relations for the moment tensor components.Citation: Amoruso, A., and L. Crescentini (2009), Shape and volume change of pressurized ellipsoidal cavities from deformation and seismic data,

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[1] We carry out a nonlinear joint inversion of P wave first-motion polarities and coseismic surface displacement data of the 1908 Messina earthquake. We model the earthquake using a single planar fault: Slip is at first assumed to be uniform across the whole fault, then independent in a small set of coplanar subfaults, and finally smoothly variable across the fault. The first two steps are accomplished using a global minimization technique. The main features of the retrieved model are very robust and independent of the seismic velocity profile, of the presence of questionable bench marks, and of the assumed residual distribution. The along-strike component of slip is about half the along-dip component, in agreement with the direction of the extensional stress axis retrieved from geological observations. Surface vertical displacement is consistent with tsunami data and with the morphology of the Messina Straits.

From 2006 to spring 2013, Campi Flegrei (CF) caldera, Italy, was mostly uplifting at an increasing rate, particularly high from 2011. We show that the 2011-2013 accelerated uplift and 1980-2010 inflation and deflation phases can be explained by a two-source conceptual model similar to that proposed by Amoruso et al. (2014) (reference model). However, pressurization of the sole thin quasi-horizontal similar to 4000 m deep source, responsible for large-scale 1980-2010 deformation, can explain the whole 2011-2013 deformation, while activity of the shallower Solfatara hydrothermal source, responsible for residual 1980-2010 deformation, appears constant. These results suggest a predominantly magmatic unrest in 2011-2013. Near-real-time comparison of observations and reference model predictions can provide additional information for short-term eruption forecasting at CF; a similar approach could be followed also in other volcanic environments