Thermo-poro-visco-elastic response of a disk shaped inclusion

The study of deformation sources in volcanic and geothermal fields is a topic of great impor- tance that generates a large debate in the scientific literature. A correct interpretation of the deformation sources acting in a volcanic context is crucial to distinguish between the mechan- ical effects due to the tectonic of the area, the intrusion of new magma and/or the mechanical response of rocks to temperature or pore pressure changes. In the recent literature, thermo- poro-elastic (TPE) inclusions were proposed as possible deformation sources that can explain seismicity and displacements even in absence of the emplacement of new magma. In fact, TPE inclusions allow us to compute the mechanical effects due to temperature and pore-pressure changes brought by the arrival of hot and pressurized fluids permeating a closed volume. In the present work, we improve the modellization of such deformation sources to include the effects of viscoelasticity, which should be expected in high temperature and fluid saturated rocks due to thermall y acti v ated and pressure-solution creep. The analytical thermo-poro-viscoelastic (TPVE) solutions for a disc-shaped inclusion embedded in a uniform viscoelastic medium are obtained through the correspondence principle. Our results can be useful to represent transient effects of both deformation and stress fields that can occur in both volcanic and geothermal areas, which would be difficult to explain otherwise. In fact, TPE inclusion models predict that an increase of uplift occurs simultaneously with an increase of stress, and vice versa. Instead, we shall see that a TPVE inclusion can provide an increase of uplift even in presence of a strongly decreasing deviatoric stress. For this reason, a TPVE inclusion can be suitable to represent a decrease in seismicity rate accompanied by an increase in surface uplift, as observed, for example, during the ’82–’84 unrest phase of Campi Flegrei in Italy.