Introduction

The eruptive cycle paradigm (inflation–eruption–deflation1) assumes that the influx of new magma and/or volatile exsolution leads to the pressurization of a magmatic reservoir and the inflation of the volcanic edifice. When the internal pressure exceeds the strength of the reservoir wall, the wall breaks, and magma ascends through conduits or dikes toward the surface, feeding the eruption. The subsequent drainage of magma and volatiles from the reservoir releases overpressure, causes edifice deflation, and terminates the eruption. After a repose period of weeks to years, the cycle begins anew. In such a context, long time-series of ground deformation data can capture one or more eruptive cycles, by tracking subsurface fluid (i.e. magma, volatiles, or hydrothermal waters) movements within the crust and allowing quantitative constraints on the geometry, size, and depth range of magmatic reservoirs. Valuable examples come from Soufriere Hills2, Aktun3,4, Westdahl4, Makushin4, Axial Seamounts5, Sierra Negra and Fernandina6,7,8,9, Piton de la Fournaise10. These extensive datasets also help in defining the spatial and temporal patterns of flank instability, a major hazard affecting active volcanoes such as Kilauea (Hawaii, USA), Piton de la Fournaise (Reunion Island), Cumbre Vie (La Palma, Canary Islands), Mt. Etna (Italy), with the triggering of large landslides, tsunamis, and earthquakes11.

A step forward is to track magma stagnation and migration during eruptive cycles by coupling deformation data with tomographic images of the plumbing system. The location and estimation of stored magma volumes provide constraints on deep recharging processes and on the estimation of the magma budget entering/leaving the system. Obtaining consistent budget estimates is crucial to understanding if the replenishment of fresh magma within the stagnation levels occurs continuously or with episodic batches. One of the most desirable aspects is to estimate the volume of magma residing at shallow depths that could be mobilized by episodic supplies or sharp deformation at the volcano.

The exceptionally high volcanic activity continuously monitored by GNSS observations and the detailed definition of the plumbing system by tomography make Mt. Etna a paradigmatic example to compute such volumetric estimates. Mt. Etna is one of the most monitored volcanoes in the world with an almost continuous eruptive activity extending from its summit craters and fairly frequent lava flow eruptions to fissures opened up on its flanks (Fig. 1). The volcano built up since 500 ka12 on the Apennine-Maghrebian accretionary wedge (Fig. 1a) near the Malta escarpment, a fault system separating the thinner Ionian oceanic lithosphere from the thicker continental crust of the Hyblean foreland, at the convergent margin between the Eurasia and Africa plates13. The origin of Mt. Etna is explained either as a passive asthenospheric mantle upwelling through a lithospheric tearing occurring at the south‐western edge of the Calabrian subduction system13,14 or as a laterally feeding from a melt pooling region located below the Malta Escarpment fault system15. The volcano has a central conduit, with five summit craters located westward of the Valle del Bove depression (Fig. 1b). Three rift zones radiate from the summit following the locations and orientations of pyroclastic cones and eruptive fissures (Fig. 1c). Two of them, e.g. the North-East and the South rift zones, defining an overall NE-SE arcuate shape passing through the summit area, have guided the magmatic intrusions and the lateral eruptions in the last 20 years. This arcuate summit rift connects with faults edging a 25 km-wide horseshoe-shaped region (Fig. 1c), i.e. the unstable flank of the volcano16. The seaward motion of this sector of the volcano has been documented since the early 1980s17 and is temporally modulated by vigorous volcanic activity18.

Fig. 1: Location of the study area.
figure 1

a Map of southern Italy. ME Mt. Etna, AMC Apennine-Maghrebian chain, MEF Malta Escarpment fault system. b Sketch map of Mt. Etna volcano showing the urbanized areas (gray polygons) and main faults and tectonic lineaments (dark gray lines). The continuous GNSS network is also reported: yellow diamonds, stations used to constrain the elastic models discussed in this study; dark gray diamonds, remaining stations. The orange dots represent pyroclastic cones, while active faults and tectonic lineaments are reported as gray lines. EDAM–ESLN, EDAM–EMAL, and EDAM–EMGL are reported as black, red, and blue lines, respectively. c Zoom of the summit area of Mt. Etna91. NEC North-East Crater, VC Voragine Crater, BNC Bocca Nuova Crater, SEC South-East Crater, NSEC New South-East Crater.

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Results

On an active volcano, the GNSS stations close to the crater area are sensitive to magma movement along the plumbing system, and therefore they represent an efficient way to detect changes in the behavior of the volcano1. This is usually performed by inspecting the motion of one or more stations over time. To this end, we considered the change in distance (or baseline) between some continuous GNSS stations closely located in the summit area to investigate the January 2001–April 2021 period. We selected the EDAM and ESLN long-lived stations, which are located northward and southward of the summit area, respectively (Fig. 1). The EDAM–ESLN baseline time-series records a general lengthening (i.e. a growth of slope distance between the two stations) at a rate of ~20.7 mm/yr. Moreover, it distinctly shows non-linear motion with increasing and/or decreasing rates, well-evidencing the vivid activity of the volcano during the whole considered time interval (Fig. 2a). By inspecting the time-series, we detected several moderate-to-drastic changes in rates with no uniform duration, mostly corresponding to marked variations in the volcanic activity. By coupling these observations with volcanological observations and other GNSS baselines (e.g. EDAM–EMGL and EDAM–EMAL; see the “Methods” section and Supplementary information), we defined a total of 57 different ground deformation phases, consisting of 28 inflation phases, 21 deflation phases, 5 magmatic intrusions and 3 periods with no significant deformation. Roughly speaking, each intrusion/eruptive phase was preceded by a recharge phase characterized by one or more inflation phases (in case of changes in the inflation rate) and then accompanied by a deflation phase during the lava discharge. The inflation phases are characterized by an average duration of ~220 days and cover up to 83.2% (16.85 years) of the entire investigated period. As previously mentioned, some inflations have been defined by a change in the inflation rate within a longer recharge phase (T12–T13, T17–T18, T24–T25–T26–T27, T29–T30, T52–T53, and T55–T56). Since January 2001, the longest recharge phase spans the August 2008–July 2011 (~2.94 years) and the late December 2018–February 2021 (~2.14 years) time intervals. The deflation phases are characterized by an average duration of ~54 days and span up to 18.4% (3.1 years) of the analyzed period. By considering the overall recharge/discharging phases, we defined 19 eruptive cycles (Supplementary Table 1).

Fig. 2: Data and results.
figure 2

Time-series of volcanic activity (at the top: eruptive periods as red boxes, inflation and deflation phases as green and black boxes, respectively; inside the panels: shallow intrusions and lava fountaining episodes as blue and gray vertical lines, respectively) and geophysical data and results. a EDAM–ESLN baseline (see Fig. 1 for stations location). b Time-series of estimated ΔVi, ΔVo, and ΔVb. Estimated average rates are also reported. c Depth variations of the inflation (red) and deflation (blue) modeled sources. These last are sized according to the estimated volume. d Height variations of EPLU (red), EINT (black), and EMEG (blue) stations.

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Some of the inflation and deflation phases are characterized by weak signals and data fail in constraining elastic models (see Supplementary Table 1). By excluding these phases as well as those characterized by magmatic intrusions (generally related to fast migration of magma toward the surface in the last 2–3 km) and/or null deformation, we computed elastic deformation models for 26 inflation and 14 deflation phases (see the “Methods” section). Achieved results for each modeled phase (Figs. 2, 3 and Supplementary Table 1), allow an accurate investigation of the volcano’s behavior over the last 20 years.

Fig. 3: Comparison of geodetic results and seismological observations.
figure 3

a Seismicity (M > 1) occurring in the January 2000–April 2021 period (events with M>3.5 are reported as stars); the modeled sources (sized according to the estimated volume and colored in red and blue for inflation and deflation phases, respectively; Supplementary Table 1) are also reported. The gray arrows represent the long-term (2004.42–2018.95) GNSS horizontal velocity field with 95% confidence ellipses84. b Vertical A-A’ section showing the distribution in depth of seismicity and modeled sources. c Vertical A–A’ section through the DVp time-lapse model27. d Vertical A–A’ section through the DVp/Vs time-lapse model. The purple lines (panels c and d) represent the limit of the resolved volume. Note that the volume of transient low Vp corresponds to the deformation modeled sources defining the magma involved during inflations and deflations. The sources correspond to an area of loss of resolution of the Vp/Vs model because S-waves are strongly attenuated during their travel within the magma-filled volume.

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All the sources are located beneath the summit area in the 3–9 km depth interval, with a clear spatial separation between inflation (depth range 4–9) and deflation (depth range 3–6) sources (Fig. 3). Such a different location suggests a connection between two different magmatic reservoirs, along which magma uprising is facilitated during each eruptive cycle.

Another implication is that the volcano has a replenishment phase preceding all eruptions (Fig. 2a). Estimated volume ranges between 1 and 30.8 × 106 m3 for the inflation phases and between 0.7 and 15.4 × 106 m3 for the deflation ones (Supplementary Table 1), highlight a vivid magma movement along the multilevel plumbing system of Mt. Etna. All the modeled sources have a prolate spheroid shape with the average ratio between the minor and major axes of 0.43 and 0.26, for deflation and inflation sources, respectively. These spheroids typically exhibit a predominant vertical elongation (dip > 68°; Supplementary Table 1) and have major axes with a prevalent NE–SW orientation.

Discussion

Plumbing system and magmatic reservoirs

A magmatic system generally consists of one or more regions containing various amounts of melt19,20. These regions develop throughout the crust and can be separated by sub-solidus rocks or be continuous and connected, vertically defining a multi-layered system. Over the last decades, petrological and geophysical data have provided detailed images of the Mt. Etna plumbing system as a gigantic and complex multi-level reservoir extending down to a depth of ca. 30 km. The deeper part has been inferred through petrological data with two main magmatic environments located, respectively, at 19–23 km and below 25 km depth21,22. These two main magmatic environments coincide with a region of low P-wave velocity anomalies23. The shallow (0–9 km) and intermediate depth (10–19 km) portions are dominated by a huge plexus of P-wave high-velocity body located in the central-southern sector of the volcano and extending from 18 km depth to the surface24,25,26,27. In the shallower part, all geodetically detected pressure sources are located along the western border of the high-velocity body, defining at least three different levels of magmatic stagnation and storage, at 0–228,29,30,31, 4–628,32,33,34,35,36, 7–9 km37,38,39, respectively. Most of these levels match well with the ones inferred by petrological studies21,22,40,41,42. In the intermediate part, available petrological data inferred some magmatic environments located in the 10–1240,43,44,45 and 13–16 km depth interval21,22,42,46,47. This last magmatic environment roughly coincides with the magmatic sources related to the long-term uplift of the volcano edifice48. The magmatic reservoirs defining the shallower part of the magmatic system have been identified several times in the last 3 decades, while the ones defining the intermediate and deeper portions have been detected/inferred only occasionally.

We define here with unprecedented detail the spatial distribution of deformation sources for the past two decades of activity (Fig. 3a). We observe a clear spatial separation between the inflation and the deflation sources. In particular, the inflating sources are located beneath the north-western sector of the summit area in the 4–9 km depth range, while the deflating sources are located beneath the south-eastern sector of the summit area in the 3–6 km depth range (Fig. 3b). All these sources are located along the north-western edge of the crustal volume defined by the earthquake distribution at shallow depth (0–6 km) beneath the southern and eastern flanks of the volcano (Fig. 3b). Such a crustal volume mainly corresponds to the high-velocity body detected by the P-wave tomographies (Fig. 3c, d) published in the last two decades24,25,26,27. Therefore, our modeled sources define a northwestern dipping and elongated body where fresh magma likely arises directly from the mantle and interacts with residing magma at shallow depth (Fig. 3b). The sources of deformation match well with the volume at the northern edge of the high-velocity crystallized plexus where transient low-velocities indicated the residence of magma during the most recent large eruptive episodes27. Moreover, the northwestern dipping body closely resembles the active reverse structure beneath Mt. Etna49, therefore suggesting that arising magma is controlled/channeled by inverse faults of the Apennine-Maghrebian accretionary wedge. Some studies have recently proven that magma arising toward the surface is a feasible mechanism also in coeval compressional settings50,51,52. Valuable examples come from Guagua Pichincha, Ecuador53, Socompa, Chile54, and Taapaca, Chile55.

The spatial separation between the inflation and the deflation sources is more evident at shallow depth, with the latter located beneath the south-eastern sector of the summit area. The continuous south-eastward motion of the unstable flank presumably led to a decrease in the confining pressure and an increase in host-rock porosity beneath the summit area and along the South and North-East rift zones. This mechanism would enable the formation of new pathways/reservoirs in the very shallow crust, also providing a plausible explanation for the south-eastward migration of the shallow deflation sources.

Volume estimation and magma compressibility

Geodetically estimated volumes are commonly considered as the injected volume of a magmatic fluid within the reservoir56. For simplicity, we refer to the positive (inflation) and negative (deflation) volume changes as magma input (ΔVi) and magma output (ΔVo), respectively. The former represents the deeply sourced magma entering into the plumbing system of the volcano, while the latter is the magma leaving the magmatic reservoir because of eruptive onsets at the surface. In the following, our estimated volumes must be considered as minimum estimates since we consider an isotropic elastic half-space medium with a Poisson’s ratio of 0.25.

A large quantity of magma (Fig. 2b, c) entered into the system during the inflation phases preceding the 2002–2003 lateral eruption (ca. 30.8 × 106 m3, T07 in Supplementary Table 1) and the lava fountains occurring during the 16 February–1 April 2021 period (ca. 27.0 × 106 m3, T56 in Supplementary Table 1). For these phases, the modeled sources are located in the 7–8.5 km depth range, at the bottom of the previously defined shallow part (0–9 km) of the plumbing system (Fig. 2c). Both phases follow two eruptive episodes, namely as the July–August 2001 lateral eruption (T06 in Supplementary Table 1) and the late December 2018 one (T54 in Supplementary Table 1) which generated large deformations along the South rift zone and the summit area, leading also to a large scale seaward motion of the eastern flank of the volcano32,57. In this context, the drastic drop in pressure along the upper portion of the plumbing system created a pressure imbalance with the deeper portions, favoring the ascent of fresh magma from depth during the post-eruptive inflations (T07 and T56). The ΔVi time-series (Fig. 2b) also reveals that during the September 2004–February 2013 period, moderate quantities of magma (ca. 13–18 × 106 m3 for each inflation stage) entered in the system every 2.8 ± 0.3 years (e.g. T10, T18, T25, and T30; Supplementary Table 1), suggesting a quasi-cyclic recharge of the lower portion of the shallow plumbing system. Moreover, after a period characterized by inflations with small volume variations (April 2013–April 2015; e.g. T32, T34, T37, and T41), a magma accumulation resumed from May 2015 at increasing rates (T43, T45, T48, T52, T53, T55, and T56; Supplementary Table 1) highlighting impressive pressurization of the shallow plumbing system. Overall, the ΔVi cumulative time-series defines a near-continuous magma accumulation in the feeding system at a rate of 10.7 ± 0.3 × 106 m3/yr (Fig. 2b).

By considering the ΔVo time-series (Fig. 2b), the largest negative variation (ca. 15.4 × 106 m3; T05 on Supplementary Table 1) occurred during the July–August 2001 eruption, while moderate variations were observed during the 2002–2003 lateral eruption (ca. 8.7 × 106 m3; T09 on Supplementary Table 1), the 2004–2005 eruption (ca. 8.7 × 106 m3; T11 on Supplementary Table 1), and during the early 2021 lava fountains sequence (ca. 11.6 × 106 m3; T57 on Supplementary Table 1). The other deflation phases have been characterized by negative variations generally smaller than 5.0 × 106 m3 (Supplementary Table 1). Overall, the ΔVo cumulative time-series defines a magma discharge occurring at a rate of 3.3 ± 0.3 ×106 m3/yr (Fig. 2b), evidencing how during the investigated time interval only 28.5% of the magma entered into the magmatic system (ΔVi) was drainage during the deflation phases. Therefore, this percentage could be considered a realistic measure of the possible eruptible quantity of magma during each eruptive cycle. By combining the ΔVi and ΔVo quantities over time, we can estimate the balance (ΔVb) between the magma entering and leaving the storage system. Such a balance is not constant over time (Fig. 2b) but showed phases of major magma accumulation and drainage. As previously observed, the balance is positive and defines a net magma supply of 7.4 ± 0.3 ×106 m3/yr (Fig. 2b) resulting in a continuous accumulation of magma along the plumbing system of the volcano, and in turn in the volumetric growth of the volcano edifice. This vigorous and continuous magma accumulation concurs well with the marked eruption frequency increase observed at least since 197558.

Erupted magma is one of the main volcanic outputs and its volume has been compared with the volume change measured by geodetic measurements on several active volcanoes59,60,61,62,63. Observed eruptive volumes are commonly 1–8 times larger than the geodetically modeled ones during volcanic eruptions61,62,63,64,65,66. This is also the case for Mt. Etna, where our estimated magma discharge (ca. 3.3 ± 0.3 × 106 m3/yr) is lower than the one estimated by field measurements and satellite observations67,68,69,70,71. In particular, the average magma output rate of 25 × 106 m3/yr estimated at Mt. Etna for the last 40 years69 is 7.5 times larger than our estimated magma discharge.

Such a general discrepancy is related to new magma influx from the depth during eruptions and/or compressibility of magma. The influx of new magma from deep sources to shallow reservoirs could partially (or totally) balance the magma lost by the shallow reservoir during eruptive events. Alternatively, the deep magma could ascent along the plumbing system to be directly erupted at the surface. Both mechanisms provide a realistic explanation of the observed discrepancy and have been occasionally documented at Mt. Etna32,35. Magma compressibility is also considered a main factor to explain the discrepancies between geodetic and erupted volumes. The compressibility of magma is largely controlled by the high pressures in the Earth’s crust and the presence of highly compressible exsolving volatile phase72. Moreover, additional complexities come from the mechanical properties of the host rock which in turn depend on the presence of fractures and void spaces56. The absence of comprehensive data regarding the compressibility and other critical physical parameters that characterize the bulk magma at Mt. Etna (e.g. density, magma composition, volatile contents in the melt, gas volume fraction, etc.) has hindered establishing well-defined relationships. However, CO2 is thought to become exsolved at considerable depth73, suggesting the presence of a significant amount of volatiles in the magmatic reservoirs at Mt. Etna. Indeed, CO2 emission at Mt. Etna contributes to 10% of the global volcanic emission and greatly exceeds the amount that can be dissolved in the erupted magma74, suggesting external contributions such as mantle-derived fluids and/or assimilation of Mesozoic carbonates75. The development of ground- and satellite-based techniques has notably improved the measurements of SO2 flux over several active volcanoes, increasing the availability of long-time series and catalogs76. By comparing volume estimations derived from thermal and SO2 flux satellite measurements with the geodetically derived ones for the 2004–2007 period, Coppola et al.77 found an excellent correlation and inferred a ratio between the two estimates ranging from 2.4 to 6.5, with a best-fit value of 3.6. This agreement is considerably promising and suggests that more accurate estimations on magma budget may be readily achieved in the future by considering geodetic and geochemical data, along with other observables as ground SO2 flux measurements. However, it also highlights that magma compressibility varies greatly over time, especially during an eruption. Therefore, long-time series of data are needed to achieve accurate estimations. Furthermore, Calvari et al.78, by comparing the volume of erupted magma at Mt. Etna from 2016 to 2020 with respect to the expected one from its average eruptive rate, suggested the accumulation of magma beneath the volcano. This aspect matches well with our results which evidenced an impressive pressurization of the shallow plumbing system of the volcano since May 2015 (Supplementary Table 1).

All these features highlight that rapid and accurate estimations of magma budget on active volcanoes like Mt. Etna are of considerable interest and impact on territory management since they can provide useful constraints on possible eruptive events in terms of eruptible magma and volcanic risk assessment.

Height variations and lateral spreading

The elastic models predict a general vertical growth of the volcanic edifice, continuous during almost the entire investigated period. The vertical growth is vigorous, despite episodically being interrupted by local-to-volcano-scale subsidence related to the short-term deflation phases. However, the time-series of vertical components of stations located around the summit area (EPLU and EINT; red and blue time-series in Fig. 2d, respectively) and on the upper western flank of the volcano (EMEG; black time-series in Fig. 2d), show long-term subsidence, despite cyclic (EPLU station) or episodic (EMEG and EINT stations) transients. EPLU and EMEG show a subsidence of ~5 mm/yr and most of the observed vertical motion occurred before the 2002–2003 eruption, while EINT exhibits a near continuous subsidence of ~11 mm/yr. EPLU and EINT stations are externally located with respect to the small N-S elongated graben-like structure inferred by Murray et al.79, therefore their behavior is not (or little) influenced by the strong subsidence measured within the graben (~4 m during the August 1975–September 2018 period). Moreover, the overall subsiding pattern along with the near continuous magma accumulation beneath the volcano suggests that the volumetric growth of the edifice is dominantly horizontal. The long-term picture of Mt. Etna deformation shows an inhomogeneous pattern with the largest rates measured on the eastern flank of the volcano (Fig. 3a). An increase in the horizontal motion moving away from the volcano summit can be recognized, suggesting a gravitational control on the southeastward spreading of the edifice18,57. Such an asymmetric spreading pattern is controlled by the basement topography beneath the volcano and the SE gently dipping shallow interface between rocks and Quaternary sediments12. Moreover, the buttressing of the volcano by the Apennine-Maghrebian chain prevents the spreading toward the north and west. In such a context, the steady-state seaward motion of the eastern flank induces a progressive depressurization of the crust beneath the rift areas, encouraging the deep resourcing of magma and its accumulation in the shallower part of the plumbing volcano, contributing therefore to the endogenous growth of the plutonic complex (the high P-wave velocity body) beneath Mt. Etna volcano.

Conclusions

We demonstrate here that volumetric estimates of the magma budget entering and leaving a volcanic system are now possible and provide constraints in forecasting volcanic activity during sharp episodes or activity climaxes. We tracked magma movements within Mt. Etna’s plumbing system, revealing a continuous magma supply from a depth of ca. 10.7 × 106 m3/yr over a period of almost two decades. The enveloped geometry of the deformation sources suggests that the final rising of magma through the crust is controlled by an NW-dipping interface that we hypothesize is a structure of the compressional belt. About 28.5% of this magma contributed to the decennial effusive activity, providing a valuable constraint on the eruptible quantity of magma during each eruptive cycle. The remaining quantity (ca. 71.5%) is stored within the plumbing system and contributes to the endogenous volumetric growth of the plutonic crystallized mush, and in turn, to the lateral spreading of Mt. Etna.

The huge amount of stocked magma beneath stratovolcanoes raises new questions on whether they could be remobilized to feed eruptions by episodes of sharp deformation or unrest. Increasingly tight constraints on the volume of magma will also substantially improve our understanding of the magmatic systems, revolutionizing the volcanic hazard assessment. At Mt. Etna, the huge quantity of magma would lead to a substantial increase of volcanic activity both from the summit area as well as from the volcano flanks. The occurrence of lateral eruptions dramatically increases the hazard, especially for the potential opening of eruptive fractures on the lower slopes of the volcano80,81, where almost a million people live. Moreover, the continuous magma accumulation increases the probability of a seaward acceleration of the unstable flank of the volcano, and the occurrence of moderate earthquakes at very shallow depths, as already observed during the 2002–2003 and 2018 eruptive events57,82. On a kyrs time scale, the prolonged accumulation of magma in the shallow crust would potentially lead to catastrophic flank instability episodes, triggering in turn tsunamis that can hit the densely populated coasts surrounding the eastern Mediterranean Sea. A similar episode occurred in the early Holocene, probably related to the collapse of the Valle del Bove83.

Achieved results can be easily exported and compared with the ones coming from other densely monitored volcanoes, as well as used to validate/integrate the available information on most of the other worldwide active volcanoes where the monitoring system is spatially and temporally limited.

Methods

GNSS network and data processing

The setting up of a continuous GNSS network at Etna began in November 2000, reaching a configuration of 13 stations in the late summer of 2001 with a daily session of ~8 h. The network geometry was gradually upgraded over the years in order to cover all the slopes of the volcano edifice and to replace the sites destroyed by natural (lava flows) and human (vandalism) activities or affected by local instability, reaching the current configuration of 33 stations (Fig. 1). The upgrade was also coupled with a general improvement of technologies (e.g. receivers, antennas, real-time data streaming and long-term power supply—typically a combination of batteries and solar panels at remote sites), therefore allowing continuous acquisition on sessions of 24 h, at least since early 2005. Raw GNSS observations, collected since November 2000, were processed by using the GAMIT/GLOBK software (http://geoweb.mit.edu/gg/) and by adopting the same strategy described in Palano et al.84. Achieved results as daily coordinates (i.e. time-series) and velocity fields have been referred to the MERF23 frame84. This reference frame allows to isolate the Mt. Etna volcanic deformation from the background tectonic pattern and enable a direct combination and comparison between different deformation phases (inflation, deflation, dike intrusion) affecting the volcano edifice over time.

GNSS time-series analyses and data modeling

Among the available GNSS baseline, we considered the EDAM–ESLN one since it has very few data gaps over the April 2001–April 2021 period (Figs. 1 and 2). This baseline is very sensitive to magma movements along the plumbing system allowing to capture with fine detail any change in the volcano behavior. The baseline is generally affected by lengthening during the inflation phases and shortening during the deflation ones. However, to properly define some deformative phases on periods not adequately covered by the EDAM–ESLN baseline (e.g. T01, T06, T07, T09, and T10), we also considered two additional baselines, namely the EDAM–EMGL and EDAM–EMAL ones (see supplementary material). By inspecting these time-series, we detected several moderate-to-drastic changes in rates with no uniform duration, mostly corresponding to marked variations in the volcanic activity (https://www.ct.ingv.it/index.php/monitoraggio-e-sorveglianza/prodotti-del-monitoraggio/bollettini-settimanali-multidisciplinari). On the basis of geodetic data and volcanological observations (Supplementary Table 2), we defined a total of 57 different ground deformation phases consisting of 28 inflation phases, 21 deflation phases, 5 magmatic intrusions and 3 periods with no significant deformation (Supplementary Table 1). Most of these phases show piecewise linear segments on the analyzed baselines suggesting inflation or deflation with constant rates, while some are characterized by nonlinear segments, denoting complex deformation patterns. These phases include both inflations (T15, T18, T25, T48, T50, and T55) and deflations (T09, T16, T19, T23, T31, and T33), and are related to short-term volcanic activities (e.g. lava fountaining, passive lava effusion, strombolian activity, etc.). The geodetic signals related to these short-term volcanic activities are generally small (with a low signal/noise ratio) and are not pertinent to the general questions addressed in this study. Therefore, in the following, we considered the phases including these short-term volcanic activities as homogeneous in terms of ground deformation patterns. For each detected phase, we estimated the ground deformation field in terms of geodetic velocities by combining the daily GAMIT solutions into a consistent set of station positions and velocities, referred to MERF2384.

Looking at the estimated surface geodetic velocities, some of the inflation and deflation phases are characterized by weak signals and perhaps poorly able to constrain elastic models (see Table S1 and figures in the Supplementary material). By excluding these phases as well as those characterized by magmatic intrusions (generally related to fast migration of magma toward the surface in the last 2–3 km) and/or null deformation, in the following, we computed elastic deformation models for 26 inflation and 14 deflation phases.

The surface deformation for each of these phases was used to constrain isotropic half-space elastic inversion models by adopting a uniform approach in order to define all modeled parameters in a robust and unambiguous way over the studied period and to allow a direct comparison between the obtained results. To this end, the inversions were performed by adopting the following uniform approach:

  • to properly model the asymmetric surface ground deformation patterns, as commonly observed at Mt. Etna32, we adopted the analytical formulation related to a spheroidal pressure source85. This source is determined by eight parameters: location (longitude, latitude, and depth) of the center of the spheroid, strike, and dip of the major semi‐axis a, length of the major semi‐axis a, ratio b/a between the minor (b) and major (a) axes, and the pressure change required to produce the observed surface deformation;

  • values of 30 GPa and 0.25 were assumed for the shear modulus (μ) and Poisson’s ratio in the half-space, respectively;

  • since Mt. Etna volcano is characterized by significant topography, the effects of topography have been included in each computation86;

  • both horizontal and vertical GNSS components were inverted by taking into account the weights proportional to the estimated geodetic velocity errors;

  • to obtain realistic estimations of the pressure change parameter, we limited the ratio of the pressure change to the shear modulus within the elastic limits of the surrounding rock;

  • the model parameters optimization was performed by using a genetic algorithms methodology87, an approach which starting with an initial range of models, progressively modifies the solution by incorporating the evolutionary behavior such as the biological systems. The fitness of each solution is measured by a quantitative, objective function, i.e., a measure of the discrepancy (\({\chi }^{2}\)) between the measurements and the predicted values from the model, defined as: \({\chi }^{2}={\sum }_{i}^{N}\frac{{\left[\left({O}_{i}-{P}_{i}\right)\right]}^{2}}{{e}_{i}^{2}}\), where Oi is measured value, Pi is the predicted value from the model, ei is the uncertainty associated to each measured value and i = 1, …., N, the total number of measurements;

  • all sites located on the lower portion of the unstable flank of the volcano (marked as dark gray polygons in Fig. 1b) have been excluded from the inversion because of their continuous seaward motion84. Sites located on the middle-to-upper portion of the unstable flank have been included in the inversion: while they provide a better geometry to constrain the parameters of the modeled source, the expected deformation at their location is generally lower than the observed one, resulting in a poor fit of the model. By using these stations, a possible bias of the parameters of the modeled source would be introduced; however, by considering the general good fit at the stations located externally from the unstable flank of the volcano (Supplementary material), we believe that such a bias can certainly be considered negligible.

For each modeled phase, the volume change of the ellipsoidal cavity has been estimated by adopting the following empirical formulation: \(\triangle V=\frac{3V\triangle P}{4\mu }(\frac{{A}^{2}}{3}-{cA}+d)\) where V is the volume of the ellipsoidal cavity, ∆P is the pressure change, A = b/a represents the geometric aspect ratio between the semi-minor axis b and the semi-major axis a of analytical spheroidal pressure source85. Constants c and d have been determined by the polynomial best fit to the numerical solutions spheroidal88 and have values of 0.7 and 1.37, respectively. The estimated volume can be considered a minimum estimation since we considered a medium with a Poisson ratio of 0.25. The uncertainties of the best fitting parameters were estimated by adopting a Jackknife sampling method89. Best fitting parameters for each modeled phase, along with the estimated uncertainties, are reported in Supplementary Table 1.