Maria Elina Belardinelli

Fluids play a fundamental role in controlling deformation, stress redistribution, and seismicity in volcanic and geothermal systems. Variations in pore pressure and temperature associated with hydrothermal circulation can significantly alter the mechanical state of the crust, particularly during unrest episodes in volcanic scenario. Classical analytical models, such as the Mogi point source, have been widely used to interpret surface deformation induced by magmatic intrusions. However, these formulations neglect thermo-poro-elastic coupling and predict an isotropic stress state within the source, thus failing to account for seismicity occurring inside the deformation source.Thermo-poro-elastic (TPE) theory provides a physically consistent framework to describe the coupled effects of fluid pressurization and heating in porous media. Analytical thermo-poro-elastic inclusion models have recently demonstrated their effectiveness in reproducing stress heterogeneities and associated focal mechanisms both internal and external to the source.The inclusion represents a finite, permeable region affected by temperature and pore-pressure variations, while the surrounding medium is assumed to be in isothermal and drained conditions. Nonetheless, at present time, the available solutions for spherical inclusions are derived for an infinite medium, limiting their applicability when surface observations are considered, especially for shallow sources.In this study, we develop new fully analytical solutions for spherical and spherical shell TPE inclusions embedded in a half-space, explicitly accounting for the presence of a free surface. Closed-form expressions are obtained for displacement, strain, and stress fields throughout the domain, including within the source.The problem is formulated under an axisymmetric hypothesis using cylindrical coordinates. Free-surface boundary conditions are enforced through a combination of the image source method and the Galerkin approach. The methodology is first applied to a spherical TPE inclusion representing a pressurized and heated reservoir, and subsequently extended to a spherical magmatic source surrounded by a spherical TPE shell, modeling a mechanically distinct fractured zone surrounding a magma chamber.The results show that the free surface strongly modifies deformation and stress fields compared to full-space solutions. For shallow sources significant differences arise in all mechanical fields. In the spherical shell configuration, thinner shells exhibit enhanced internal shear stress and reduced external deformation, suggesting a higher susceptibility to internal failure.The model is applied to the 2021 unrest episode at Vulcano Island. Using source parameters constrained by previously published we found that significant shear stress concentrations are predicted within and around the source, providing a physically consistent explanation for the clustered shallow seismicity observed near the crater. These results highlight the importance of TPE coupling and free-surface effects in the interpretation of volcanic unrest processes and fluid-driven seismicity.

Gravity observations are widely used in volcanic monitoring to infer subsurface mass redistributions, commonly interpreted in terms of magma intrusion. However, gravity changes may also arise from thermo-poro-elastic (TPE) processes associated with temperature and pore-pressure variations in fluid-saturated reservoirs. Neglecting these effects can lead to ambiguous or misleading interpretations of gravity signals during volcanic unrest.The recent development of TPE inclusion models allows us to describe the mechanical fields induced by fluid-saturated rock volumes undergoing pore-pressure and temperature variations. These sources can coexist with magmatic sources within volcanic systems and are typically located at shallower depths than the deep magmatic reservoir, which acts as the primary engine by releasing hot fluids. These exsolved fluids rise from depth and either accumulate in, or migrate through, overlying brittle rock volumes, which respond to thermal and pore-pressure perturbations and therefore act as secondary sources of deformation and gravity change. In this work, we consider a disk-shaped TPE inclusion, a geometry that has been successfully applied in previous studies to represent deformation fields that are predominantly radial and associated with axisymmetric sources.The results show that gravity variations induced by a TPE inclusion depend strongly on the fluid phase. Both liquid water and gaseous fluids can produce the same significant ground uplift, but lead to different gravity residuals: negative for liquid water and minor but positive for gaseous fluids. In contrast, condensation or vaporization of a thin layer near the surface can generate large gravity changes without notable deformation. As a result, heating and pressurization of a TPE inclusion can mask or weaken the gravitational signature of magma ascent, complicating the interpretation of gravity data and highlighting the need to account for hydrothermal effects when estimating magma volumes during unrest.Gravity data collected over the past decades at the Campi Flegrei caldera (Italy) provide an ideal test site for applying our model and offer intriguing insights into both past and current unrest phases, although our results are applicable to any volcanic system with an active hydrothermal system. These findings highlight the importance of incorporating TPE effects into gravity data interpretation and integrated volcano monitoring strategies. Accounting for them improves our ability to distinguish between magmatic and hydrothermal contributions, leading to more robust assessments of subsurface dynamics and volcanic hazards.

On March , 2023, three small earthquakes occurred near Umbertide (Central Italy), within 4 hours. Analyzing seismic ambient noise in the frequency band 0.1–1 Hz from six seismometers within 20 km of the M _w 4.5, we detect a significant drop in seismic velocity at the time of occurrence of the seismic sequence. A strain sensitivity analysis suggests that crustal damage was primarily caused by the passage of seismic waves, likely enhanced by the presence of fluids. Analyzing geodetic data from recently installed strainmeters and pore pressure transducers, we highlight the role of elastic strain and fluids in driving deformation during this sequence, suggesting the presence of a pressure source that strongly influences the deformation pattern. We find that fluid‐induced stress may cause the reloading of a few kPa of a co‐seismic asperity within hours, unveiling the contribution of pore pressure sources to the stress budget of seismogenic faults.

On March 9th, 2023, three small earthquakes (3.8≤Mw≤4.5) occurred near Umbertide (Central Italy), within four hours. Analyzing seismic ambient noise in the frequency band 0.1-1 Hz from six seismometers within 20 km of the Mw 4.5, we detect a significant drop in seismic velocity at the time of occurrence of the seismic sequence. A strain sensitivity analysis suggests that crustal damage was primarily caused by the passage of seismic waves, likely enhanced by the presence of fluids. Analyzing geodetic data from recently installed strainmeters and pore pressure transducers, we highlight the role of elastic strain and fluids in driving deformation during this sequence, suggesting the presence of a pressure source that strongly influences the deformation pattern. We find that fluid-induced stress may cause the reloading of a few kPa of a co-seismic asperity within hours, unveiling the contribution of pore pressure sources to the stress budget of seismogenic faults.

The Apennines are a tectonically active belt that has experienced significant earthquakes (Mw6). The largest events primarily occurred along the chain axis, where a complex system of normal faults accommodates 2–3 mm/yr of SW‐NE oriented extension, as precisely measured by a dense Global Navigation Satellite System network. Geodetic strain rates are now frequently used in earthquake hazard models; however, the impact of using such estimates, computed through different methods, for seismic hazard assessments may be difficult to evaluate. This study explores the relationship between geodetic strain rates and seismicity rates in the Apennines using three distinct horizontal strain rate maps and an instrumental seismicity catalog. We find that the principal directions of geodetic strain rate are kinematically consistent with those of strain release. We estimate a spatially heterogeneous seismogenic thickness using the distribution of earthquake depths, and we isolate likely independent seismicity using three different declustering methods. We observe a correlation between independent seismicity rates and the magnitude of strain rate, which can be represented by either a linear or, more accurately, by a power‐law relationship. The variability in the strain‐seismicity relationship depends on the combination of independent seismic catalogs and strain rate maps. This relationship is primarily influenced by the declustering technique more than the choice of the strain rate map and, in particular, by the number of aftershocks excluded during declustering. Seismicity models derived from these combinations were used to estimate and compare the seismic moment release rate with the tectonic moment rate estimated from strain rate maps and seismogenic thickness. Findings indicate that the tectonic moment rate exceeds the seismic moment release rate. We highlight uncertainties and potential causes, one of which could be a possible aseismic release of part of the moment rate.

Thermo-Poro-Elastic (TPE) inclusions are suitable to model the mechanical effects induced by hot and pressurized hydrothermal fluids pervading a closed volume of rocks. In fact, modeling of TPE deformation sources finds application in both geothermal and vulcanological fields. Some recent works showed that a cylindrical TPE inclusion located at about 2 km of depth contributed to the large and rapid soil uplift observed during the ‘82-’84 unrest phase in the Campi Flegrei caldera. In the present work, we demonstrate that such a source of deformation can be responsible for a significant contribution even in the current unrest phase, that started in 2005 and it is still in progress. We show that the time-series of soil uplift observed in the last years can be reproduced by assuming the rising of hot and pressurized fluids, possibly exsolved by a deep magmatic source, within the same deformation source responsible of the ‘82-’84 unrest. The existence of such a TPE inclusion at Campi Flegrei was supported by previous tomographic studies and it is reinforced by the new analysis of the b-values. In fact, we found a sharp variation of the b-value in correspondence of the depth of the modelled TPE inclusion. The decrease of the b-values is consistent with the fact that within the TPE inclusion the induced shear stress is maximum and the occurrence of larger earthquakes is favored. The results support the existence and the importance of the mechanical effects of fluids flow, during the unrest phases of the Campi Flegrei caldera.

SUMMARY: The study of deformation sources in volcanic and geothermal fields is a topic of great importance 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 mechanical 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 thermally activated 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.

The Po Plain (Northern Italy) has largely subsided due to natural processes and human activities. In particular, in order to reduce subsidence, in the Bologna metropolitan area a politic decision in 2010, imposed a significant reduction of civil water supply from groundwater withdrawal wells. The study area is characterized by an excellent monitoring activity which provides a good spatial and temporal distribution of data coming from continuous GNSS sites, piezometers and rain gauges. In the present work we analyze both GNSS and piezometric data by means of the Principal Component Analysis (PCA). The results of the analysis are then compared with the rainfall time series measured by rain gauges. Thanks to the PCA analysis we can identify: i) a clear increase in the water level following the withdrawal decrease started in 2010 and ii) an anthropic induced surface displacement, which is smaller in magnitude than that induced by rainfall variations. Without the PCA analysis, such a small, but still significant, anthropic effect on vertical displacements would have remained hidden in the raw time series. Our analysis reveals a decrease of about 4 mm/y of vertical velocity in some GNSS sites closest the withdrawal wells. We also found that on large time scales (> 1 month), the vertical displacement induced by rainfall strongly depends on the geological setting: in the mountains a water level increase causes subsidence (elastic response), whereas in the Po Plain it causes uplift (poro-elastic response). Thanks to the PCA analyses, the combined observations of different kind of instruments (GNSS, piezometers and rain gauges) and a basic knowledge of the geological context, we can correctly identify both the anthropic and natural signals on the data.

In volcanic regions ascending magma is subject to depressurization and is generally accompanied by exsolution of volatiles. We blackassume a process in which these volatiles propagate upward across newly fractured and permeable rock layers, bringing a sharp increase of pore pressure and temperature within a thin disk-shaped region (inclusion). Thermo-poro-elastic (TPE) inclusion models provide a mechanism to explain seismicity and deformation induced by p and T changes in absence of new magma emplacement in volcanic contexts. They are also suitable to represent the mechanical effects due to fluid extraction and re-injection in geothermal fields. In the present work analytic solutions are provided for the displacement, strain and stress fields assuming a thermo-poro-elastic unbounded medium. Significant deviatoric stress is generated by positive increments of pore pressure and temperature: the stress field is fully deviatoric outside the TPE inclusion, but a strong isotropic stress component is present within, leading to highly heterogeneous faulting mechanisms: if the disk plane is horizontal, thrust faulting mechanisms are favoured within the TPE disk over optimally oriented faults and normal mechanisms above. The model is easily generalized to a vertically thick disk with variable temperature and pore-pressure changes: then, an extensional environment can be obtained even within the TPE inclusion assuming upward decreasing of pore pressure and temperature changes. The supplied analytical solution may be used to model near-field TPE inclusion effects and to validate more complex numerical modelling.