Investigating deformation and seismic data and their relationships during the ongoing unrest of Campi Flegrei caldera (Italy)

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Since 2005, the caldera shows a slow but progressive inflation of the ground and an intensification of seismic activity. Here we quantify the decadal accelerating trend together with oscillations of various frequencies overlying it and explore the relationships between deformation and seismic activity over the period 2000-11/2023. Results reveal an accelerating parabolic increase of vertical uplift, with maximum acceleration of ca. 0.74 cm/yr 2 , and a super-exponential increase of number of earthquakes and seismic energy release. Inspection of data gives evidence of a close temporal correlation between rates of deformation and seismicity and of an exponential-type relationship, with an exponent increasing in time, between ground deformation and number of earthquakes. These relationships are consistent with a quasi-elastic behavior of the upper crust of the caldera under an increasing stress and suggest a progressive mechanical weakening of it. Most importantly, they provide evidence of an increasing sensitivity of seismic activity on the caldera inflation and warn on the possibility of significant seismic events in case of continuation, with the same trends and relations, of the bradyseismic crisis in the next years. Earth and environmental sciences/Solid Earth sciences/Volcanology Earth and environmental sciences/Solid Earth sciences/Geophysics Earth and environmental sciences/Natural hazards Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Introduction Campi Flegrei caldera (CFc) is a complex volcanic system characterized by the presence of many explosive craters. These are located within an about 12 km wide caldera generated by at least two main collapses, the Campanian Ignimbrite, about 40,000 years BP, and the Neapolitan Yellow Tuff, about 15,000 years BP 1,2 . Since this latter event, over 70 eruptive vents were active, with the majority of eruptions being explosive. Eruptions were often closely grouped in time and space, over periods ranging from a few centuries to some millennia, and were separated by extended phases of inactivity lasting up to several millennia 3–5 . The most recent eruption, known as the "Monte Nuovo" eruption, occurred in A.D. 1538 after a period of approximately 3,500 years of inactivity and was preceded by an uplift period of some decades 6 . The caldera is home of about 350,000 people thus representing one of the major volcanic risks worldwide. Subsidence and uplift of the caldera ground, known as bradyseism, have been recorded since Roman times. After the Monte Nuovo uplift, the caldera was mostly affected by a dominant sinking and it is likely that the volcano entered a new phase of unrest in the second half of the last century. Since then, the caldera experienced three major bradyseismic crises: in 1950-53, 1969-72 and in 1982-84, resulting in uplifts of about 0.75 m, 1.70 m, and 1.85 m, respectively 7–11 . Seismic activity typically increases during periods of uplift and drastically diminishes during subsidence. Interestingly, the uplift between 1950 and 1952 occurred without any notable felt seismicity 12 . The uplift experienced from 1969 to 1972 coincided with moderate seismic activity, featuring a few perceptible earthquakes and numerous low-magnitude events. However, the period of 1983-84 saw an intense seismic activity and significantly larger earthquakes, with magnitudes reaching a value of 4.0 13,14 . Following the bradyseismic crisis of 1982-84, the caldera experienced about 20 years of subsidence until, since 2005, a slow and progressive increase of ground inflation has been observed 15,16 . Caldera deformation has been characterized by a well-defined bell-shaped pattern of vertical uplift, approximately centered in the town of Pozzuoli, and has been accompanied by a progressive increase of seismic activity 15,17–19 . At the time of writing (December 2023) the ground uplift has reached a level of 118 cm above that of 2005 (hereafter always taken as reference uplift level) and the seismic activity has been largely intensified with two main earthquakes up to magnitude 4.2 and 4.0 in September-October 2023. The increase of deformation and seismic activity has been accompanied by a simultaneous increase of caldera degassing with the reaching of CO 2 fluxes up to about 4,000 t/day just from the Solfatara-Pisciarelli area 15,20 . Bradyseismic activity, including the above-described crises, at CFc has been interpreted by a variety of mechanisms including magmatic intrusions at relatively shallow level (few kilometers) 8,21–26 , poroelastic response to variations of pressure and temperature conditions within the shallow hydrothermal system or the underlying impermeable layers 27–32 , as well as by a combination of superficial and deep processes and sources 33,34 . The whole sequence of unrest since 1950 has been also interpreted as a single long-term process of crustal extension 35,36 . Under this hypothesis the forcing process would be represented by the pressurization of magmatic fluid, either magma or magmatic gases, beneath the so-called “brittle-ductile transition zone” at about 3 km depth 37 . In particular, by applying a model of elastic-brittle rock 38 , the whole unrest sequence has been interpreted in terms of changes of the mechanical behavior of the upper crust of CFc from purely elastic, to quasi-elastic and, finally, to inelastic 36 . The temporal and spatial patterns of deformation and seismicity have been also investigated with specific reference to the most recent uplift phase (2005-ongoing) and in comparison, with previous uplift episodes such as the 1982-84 crisis 19,37,39,40 . In particular, a temporal analysis of the datasets over the period 2000–2020 identified the existence of two distinct overlying trends: a decadal-like acceleration and cyclic oscillations with variable periods ranging from some years to a few months 39 . Inspection of the distribution of seismic activity also highlighted how the ongoing seismicity is mostly located in correspondence of two main depth levels with significantly different mechanical and permeability properties 19,37,41 and on weaker pre-existing structures produced by a variety of processes such as dome resurgence, volcano-tectonic collapses, magma intrusions and migrations 18,40 . The aim of this paper is to analyze the most recent accelerating trends of geophysical data of CFc and, particularly, the close relationships between deformation and seismic data in terms of temporal coupling between the associated trends, their rates and oscillation periods. The datasets used in the analysis are about 2.5-3 years longer with respect to those analyzed in previous similar studies 36,39 thus allowing a more accurate and robust characterization of the rapidly-evolving caldera dynamics. It is just worth mentioning here that more than 70% of seismic events recorded since 2000 have occurred in the last 3 years here investigated, and more than about 85% of the strain release occurred in the same period. The analysis highlights a strong exponential correlation, with exponent increasing with time, between deformation and number of seismic events typical of a quasi-elastic behavior of brittle rocks and indicative of a progressive damage of the shallow crust of CFc 35,38 . Such a correlation is also discussed in relation to the 1982-84 unrest to infer potential differences in the forcing sources and mechanisms associated with the two crises, as well as to investigate a potential evolution of the bradyseismic crisis in case of continuation of the ground inflation and of the observed trends. The datasets used in the study are presented in Section 2 (Datasets) whereas the methods and techniques adopted in the analysis are described in Section 3 (Methods). The results section (Section 4) presents the main findings of the temporal analysis of the geophysical data with specific reference to the last period of the accelerating crisis. In particular, the trend of the data rates, the main periods characterizing the oscillations overlying the time series and the close correlations between deformation and seismic activity are presented. Section 5 discusses the trends and correlations derived also in comparison with an analogous correlation obtained for the 1982-84 crisis and as a basis to describe the potential evolution of the bradyseismic crisis in case of continuation of the observed dynamics. Finally, Section 6 summarizes the main conclusions and insights provided by the study. Datasets The CFc GNSS deformation dataset from 2000 to 11/2023 . The monitoring continuous GNSS network, managed by INGV-Osservatorio Vesuviano (INGV-OV), consists of 27 continuous GNSS stations on land and 4 on seafloor-connected (Fig. 1 -SI) 16,42 . Our analysis considered several of the 11 stations established before 2009, although most of the results are herein presented for the RITE GNSS station at Rione Terra, in the center of Pozzuoli, as representative of the vertical deformation pattern recorded at all other stations. The dataset consists, for each GNSS station, of final daily position time series with the associated uncertainty (estimated to be 1 cm on the vertical component and 0.3 cm in the two horizontal components 16 ). The CFc’s vertical deformation history, since 1983, is illustrated in Fig. 1 a through a combination of leveling and GNSS data 12,16 . Following the last major uplift episode of 1982-84, approximately 20 years of subsidence occurred from 1985 to 2005, causing a vertical drop of about 0.90 m. Subsequently, the CFc resumed its uplift, initially slow but gaining pace over the years. By November 2023, the maximum vertical displacement in the central area nearly reached 118 cm since November 2005 15 , well surpassing the maximum 1985 uplift level. Post-2005, the RITE GNSS station at Rione Terra consistently recorded the most significant uplift. The remaining GNSS stations typically exhibit a bell-shaped decline in vertical displacement outward from the caldera center, alongside a radial symmetry in horizontal displacements centered on Pozzuoli, with peak values situated in a half-annulus of 2–3 km radius 16,43 . It’s important to note that the inversion of GNSS and SAR data places the bell’s center about 500 m into the sea, southwest of the Rione Terra, and a corresponding superficial pressurized source at a depth of about 3–4 km 33,44 . The CFc seismic catalog from 2000 to 11/2023 . The permanent seismic network managed by INGV-OV presently comprises 25 permanent digital stations and 3 permanent analog seismic stations 15 . In our study, we are focusing on the seismic catalog spanning from 2000 to 11/2023, regularly updated by the Osservatorio Vesuviano seismic laboratory 17,19,45 . The catalog we used consists of the earthquakes recorded, between 2000 and 12/2021, at the STH reference station situated near the Solfatara-Pisciarelli area (Fig. 1 -SI), whereas, in the period 1/2022 and 11/2023, it relies on the database SERENADE. In total the catalog includes 16,250 earthquakes. This dataset is consistent with the monthly lists that INGV-OV published in the official monitoring bulletins. Within this dataset, we can assume the completeness magnitude (M c ) equal to about 0.2 19 . To test the sensitivity of some results, in addition to the above-described seismic dataset, we also analyzed the INGV-OV catalog of localized events. In this case, the catalog contains a subset of events with respect to the former catalog, for a total of 8,013 events localized in the 2000–2023 considered period. Figure 1 b shows the number of seismic events per month over the last about four decades. From 1985 to 2005, i.e., during the subsidence phase, seismic activity was sporadic and almost absent within CFc. However, from 2005 onwards, and particularly since 2020, there has been a progressive escalation in seismic activity. Until 2014, earthquakes were infrequent and occurring in clusters of events with low magnitudes. Subsequently, seismic events became more frequent and shallower and those occurring outside of clusters notably increased in magnitude 19,41 . It is worth noting that in the last few years most seismic activity affected a radius of about 2 km centered at the Solfatara-Pisciarelli area, where also a significant increase in fluid flux was recorded 20,46 . However, several earthquakes and swarms also occurred along different volcano-tectonic structures of the caldera including the inner ring fault zone 37,40,41 . Methods The deformation and seismic datasets have been closely analyzed by investigating their temporal evolution (Figs. 2 and 3 ) as well as the behavior of their annual rate (Figs. 4 , 5 and 6 ), with specific reference to the displacement rate, the seismic count rate and the strain release rate (Benioff strain) (see [ 39 ] for more details and a comparison with trends computed over the period 2000–2020). Particular focus has been given here to the analysis of the variations of the most recent period (i.e. 2019-11/2023) given the progressive increase of deformation and seismic activity of the caldera. With reference to the deformation time series, we analyzed the vertical and horizontal displacements of several of the GNSS stations active since 2009 (see Fig. 2 -SI and 3-SI for more information). For the sake of brevity, only the vertical displacement at the RITE GNSS station will be presented in the following. The RITE trends can be considered representative of the vertical displacements estimated at all other GNSS stations as well as of the horizontal displacements at the same locations, computed as the length of the vector defined by the E-W and N-S spatial components. As mentioned above, at these stations the vertical time series are scaled down according to the observed bell-shaped deformation pattern centered in the town of Pozzuoli, whereas the horizontal displacements show their maximum along a circular ring of a few kilometers. It is worth mentioning here that just one GNSS station, located in the area of Mt. Olibano-Academia (named ACAE), has shown, since about 2021, an uplift deficit in comparison to other areas at the same distance from the maximum uplift of the caldera. The analysis and interpretation of this anomaly is the object of another study 47 and will not be further considered in the following. It is also worth noting that in the analysis we always use the absolute vertical displacement values without any correction to account for the background subsidence of the caldera 36 . This in order to avoid the introduction of additional assumptions and errors in the analysis. However, it is important to note that all the non-linear trends and relationships described in the following sections are not affected at all from the introduction of a linear trend describing the subsidence of the caldera. Regarding the seismic count and the strain release in our analysis we mostly refer to all earthquakes recorded. For specific analyses we also consider earthquakes above a given magnitude in order to avoid potential biases due to the incompleteness of the seismic catalogs used. A more complete description of the trends of the above describe time series, F(t) , are obtained by discrete computing of their annual rates F’(t) , rates of change F’’(t) as well as by the application of the Fourier Transform (FT) to identify the main frequencies of the time series. We base the estimate of the annual rate on left-side first-order finite differences so that the value at time t is not anticipating future information 39 . However, it should be noted that, due to considerable oscillations in the data over periods of different lengths, the finite difference approximation displays significant variations based on the chosen time step. Our analysis computes rates using time steps of 2 years, 6 months, and 1 month, thus generating average rates over moving windows of these respective durations. It's worth noting that such rates do not properly capture oscillations with periods shorter than the corresponding time step. Finally, to better identify the main frequencies (and therefore the associated periods) characterizing the deformation and seismic series, a Fourier spectrum is computed for various displacement rates (vertical and horizontal and at different stations) and for the seismic count rate. However, since the annual rate F’(t) displays an increasing trend (see Figs. 3 and 4 ), we consider its rate change F"(t) which is considerably more stationary and estimate the Fourier spectrum of it 39 . Also in this case, given the multiple frequencies contained in the time series, we applied the FT on different periods of time and using appropriate time steps to compute the annual rates, in order to better identify the main frequencies. Results In this section we present the main results of the application of the above-described methods to the datasets presented with specific focus to the period 2019-11/2023. More results are reported in the Supplementary Information (SI). Figure 2 refers to the vertical displacement of the RITE GNSS station from 2000 to 11/2023. The uplift is reported in linear scale (Fig. 2 a), logarithmic scale (Fig. 2 b) and square-root scale (Fig. 2 c). On the curve are reported the so-called “mini-uplifts”, the 7 periods of increased uplift occurred from 2000 to 2013 48 . Since the end of 2005, the trend of the RITE vertical uplift is clearly characterized by a slow acceleration. Since this time (and to 11/2023), there has been a total uplift of about 118 cm of which about 100 cm from 1/2014 and about 45 cm since 1/2021. A better appreciation of the measure of the observed acceleration can be gained from Fig. 2 b which shows the uplift in log-scale. Since about 2008 to 2013, the logarithmic curve shows an increasing trend characterized by short temporary increases reflecting the above-mentioned uplifts, whereas since 2013 to 11/2023 the observed trend is again increasing but with a slower pace. It is worth highlighting that the behavior since 2013 is not linear (i.e., not corresponding to an exponential trend in absolute values) but downward convex, indicating an increasing trend less than exponential. A closer inspection of the curve shows that it could be better described by a polynomial function. In particular, the square root of the curve, as shown in Fig. 2 c, is linearly increasing with R-squared = 99%, indicating a parabolic trend with acceleration of ca. 0.74 cm/yr 2 . Such a parabolic regression fits very well also the linear and log-scale plots as shown in Fig. 2 a,b, and it is negligibly affected by the uncertainty on the data. Very similar features of the deformation trend are also observed in the vertical and horizontal displacements at the other stations, as shown in the SI material (Fig. 2 -SI and 3-SI), making the above considerations valid for all the points investigated. Figure 3 illustrates the trends of the two main seismic variables we analyzed. In particular, Fig. 3 a, and the corresponding Fig. 3 b in log-scale, show the behavior of the total count of seismic events as obtained from the above-described seismic catalog (Fig. 3 a also shows labels marking the size of the 7 greater swarms recorded). Figure 3 b shows a super-exponential behavior of the seismic count from 2006 to 11/2023, in this case corresponding to a super-exponential trend also in absolute values as shown in Fig. 3 a; this is made clear by the upward convex curve in log-scale which also shows a clear increase of the exponential trend since about 2020. The super-exponential trend of seismic count is also evident in Fig. 3 a which shows how more than 65% of events have occurred since 1/2021. Similar super-exponential trends were obtained by using the catalog of localized events. Figure 4 -SI shows the same plots by considering only the earthquakes with M d > 0.5, which are also characterized by a similar super-exponential trend. Similarly, Fig. 3 c and 3 d show the cumulative strain release in linear and log-scale, respectively. In both plots we have labeled some of the most significant events occurred in the last years including the M d = 4.2 occurred on 9/27/2023 which represents the largest earthquake ever measured at CFc. The strain release plot in Fig. 3 c shows a function shape that is macroscopically quite similar to the earthquakes count, though its super-exponential trend is even more evident and gradual (see Fig. 3 d vs 3b). Several strain jumps associated to the most recent earthquakes are also evident. In summary, based on the above figures and analyses, although since the end of 2005 the three variables investigated are all accelerating in time, the ground deformation is better described (particularly since 2013) by a parabolic function whereas the cumulative seismic count and strain release are better described by super-exponential trends. In Fig. 4 we display the annual rate of deformation and seismic data from 2000 to 11/2023. The deformation rate (Fig. 4 a) refers again to the vertical displacement at RITE station whereas the seismic rate (Fig. 4 b) refers to the total number of earthquakes. In these plots the rates are computed by adopting a time step of 6 months to better highlight the oscillations with period longer than this time. In other words, the rates computed can be considered 6-months average rates of the investigated variables. Similar plots have been computed for time steps of 2 years and 1 month to better highlight different oscillation periods and are described in the following paragraphs and in the SI. The 6-month average rates clearly emphasize the increasing trends of the two variables and the remarkable oscillations that characterize the analyzed time series. A linear least square fit of the annual rate of uplift at RITE station (Fig. 4 a) produces, from 2005 to 11/2023, a linearized rate slope, i.e. an acceleration of deformation, of about 0.7–0.8 cm/yr 2 regardless of the time step selected for computing the derivative. This is fully consistent with the parabolic fit and the associated acceleration as reported in Fig. 3 . Moreover, the deformation rate trend is characterized by evident oscillations that appear to have larger amplitude since 2012. The period of these oscillations is of the order of 2.8–3.5 years, with secondary maxima at fractions of the intervals 39 . See below for more information on this aspect, based on the FT analysis of the updated catalog. The rate value computed in 9/2023 is also the highest value so far recorded since 1984, thus surpassing the uplift rate computed during the end of 2012 crisis. Figure 4 b similarly shows the seismic count rate. The maximum rate on a 6 months average is ca. 8,000 events/year and was observed at 9/2023. These plots also show an alternation of speed-ups and slow-downs similarly to the ground displacement rate but, in this case, the overall rate trend is accelerating nonlinearly in a super-exponential form. This result was expected, given the super-exponential trend of the seismic count as observed in Figs. 3 a and 3 b. The three most recent peaks are particularly evident and have been observed on March-April 2021, April-May 2022 and August-October 2023, as it will be better illustrated in Fig. 5 . Figure 5 illustrates the same rates shown in Fig. 4 , but now considering just the period 1/2019–11/2023. The two plots well highlight the three main oscillations observed in the two time series and the almost synchronous occurrence of their peaks. Close inspection of the peaks of Dec 2019-Jan 2020, Apr-May 2021, Apr-May 2022, Aug-Oct 2023 shows the existence of a time lag of up to 45 days between the peaks of the two time rates. Due to the noisy behavior of the uplift data, and therefore of the rates computed, as well as the possible occurrence of repeated peaks in the seismic rates, it was not possible to better quantify the distribution of the time lag between the two variable peaks. Such analysis would require a specific filtering of the noisy deformation data which is beyond the target of this analysis. However, the two rates allow to quantify the main “dominant” periods between peaks that result in the range between 1.0 and 1.4 years since 2019, approximately, despite shorter periods are also observed, as shown by the weaker oscillations observed in the seismic rate trend, particularly since May 2022. With the aim of better representing the shorter period oscillations of the signals, Fig. 6 shows the seismic count rate over different periods of time by using a time step of 1 month instead of 6-months, as assumed in Figs. 4 and 5 . In this case, shorter oscillations can be better highlighted and quantified. In particular, Fig. 6 a shows the trend of the seismic rate over the period 1/2019-11/2023 as well as the frequent “secondary” peaks occurring every year. Since 2019, a number of peaks in the range 3–5 per year are observed. A detailed histogram of the seismic event rate per day is instead shown in Fig. 5 b for the year 2023. This shows the features of the four last peaks separated to each other by two periods of approximately 4/4.5 months and one of 40 days, respectively. However, a more accurate estimation of the main periods of the observed oscillations is obtained by the FT of the seismic rate as reported in Figs. 6 c and 6 d. For instance, the application of the FT to the period 1/2022-11/2023 (Fig. 6 d) shows that the dominant oscillation period has a duration of 4.8 months followed by a secondary period of 1.8 months. It is interesting to note that, as proven by the almost synchronous behavior of deformation and seismic rates (illustrated in Figs. 4 and 5 ), the frequencies observed in the seismic rates (reported in Fig. 6 c,d) are closely related to the frequencies observed in the deformation rate patterns. Figure 7 shows the results of the application of the FT to the vertical uplift rate at the RITE GNSS station. In particular, Fig. 7 a shows main periods of about 1.8, 2.5, 2.8 and 5.5 months as emerged from the application of the FT from 2022 to 2023 and rates computed with time step of 1 month. Similarly, Fig. 7 b shows a main period of about 1.3 years computed from 2018 to 2023 with a time step of 6 months, and Fig. 7 c highlights a main period of about 2.9 years computed from 2011 to 2023 with a time step of 2 years. It is also interesting to note that the durations of these main periods are about 10–15% shorter that those estimated by [ 39 ] at the same RITE station over the period 2000–2020. A similar effect has been observed at all other GNSS stations and also in the seismic rate record. We note that the main periods estimated at different locations of the caldera are similar but not identical to those shown in Fig. 7 for the RITE station. In fact, the dominant peaks measured in one location are also clearly discernible as primary or secondary peaks in some of the other sites, suggesting that these differences are the results of multiple spatially irregular effects likely caused by the inhomogeneous distribution of faults/fractures and rock properties in the caldera 37,40,49,50 . The above described coupled behavior of the two geophysical variables can be better analyzed by correlating one signal to the other as done in Fig. 8 . In the two plots, we illustrate the dependence of the cumulative seismic count versus the vertical uplift at the RITE GNSS station. Figure 8 a and 8 b refer, respectively, to the total number of events and to the number of events with magnitude M d > 0.5. The red points in the plots represent the data and the year labels reported on them mark the temporal evolution of the uplift. From the data shown on both plots, it is evident how, since about 2013 up to 11/2023, they are clearly aligned along an accelerating curve. No clear trend was instead observed on the period 2000–2010, part of which has been characterized by subsidence and very weak seismic activity. The correlation between the two data is actually well fitted by using exponential functions. As shown in the SI (Fig. 5 -SI), a single exponential function already represents a good approximation of the observed relationship, i.e., R-squared > 99%. However, given the more accelerating behavior of the data with respect to a single exponential function, we have adopted here a fit with two exponential functions and optimized the “connecting time” between them. In Fig. 6 -SI the mean square distance between data and fitting functions is reported for variable connecting times. The optimized exponential functions fit extremely well the data. It should also be noted that the two exponential functions are characterized by exponents increasing with time for both all seismic events (Fig. 8 a) and events with M d > 0.5 (Fig. 8 b). In particular, the exponents increase from 2.2 to 2.8 in Fig. 8 a, and from 2.8 to 3.9 in Fig. 8 b. It is interesting to note that the optimal connecting time varies from Spring 2020 (Fig. 8 a) to Autumn 2022 (Fig. 8 b), both close to the time the caldera uplift reached the maximum height of 1984 (i.e., Spring 2022). We proved the exponential dependency shown in Fig. 8 to be robust with respect to different assumptions made in the analysis. For instance, the same relationship was obtained, with different fitting exponents, by using: i) different values of magnitude above which seismic events have been counted (up to M d = 2.5), ii) vertical or horizontal displacement at different GNSS stations, iii) the seismic localized catalog described in Section 2.2, or iv) by considering only a seismogenic volume around the area of La Solfatara-Pisciarelli, which is the center of the activity recorded in the caldera since 2005 (see Fig. 7 -SI). Discussion In this section we discuss and analyze closer the strong relationships between deformation and seismicity as emerges in the period 2005-11/2023, and particularly in the period 2019-11/2023, also including a comparison with an analogous relation obtained for the 1982-84 crisis, and discuss the possible evolution of the current bradyseismic crisis under the hypothesis that the caldera will continue to inflate and behave according to the same trends. Figures 4 and 5 clearly show the coupled behavior of deformation and seismic activity at the different time scales. This coupling is well evident both in the long term (i.e., at the decadal scale) as well as in the short/medium terms (i.e., at the week/month/year scales). At the decadal scale, the accelerating deformation of the system, since 2010 well approximated by a parabolic function, is paired with a super-exponential acceleration of the seismic count (either total or above a given magnitude). The reasons for the quasi-parabolic increase of the uplift are beyond the objectives of this manuscript and the analyses here developed. However, the understanding of the cause of this accelerating process is an interesting future goal and questions on the possibility that the driver of the uplift is itself an accelerating cumulative process, such as, for instance the injection of gas or magma in the upper crust from a deeper source. At the shorter time scales, any temporary increase of the deformation rate is closely mirrored, with an apparent time lag up to 30–45 days, in an analogous increase of the seismic rate, with an amplification effect with time clearly visible since 2021 and even more since the beginning of 2023. Such a time gap between the two variables should be also further investigated possibly extending the analysis to shorter time scales (up to days) and to the consideration of the spatial distribution of faults/fractures and the structural features of the caldera. Such a strong dependence between deformation and seismic activity is well described by the relationship between vertical uplift of the caldera (here represented through the RITE station) and the cumulative number of earthquakes, total or above a given magnitude. As shown in Fig. 8 , such relationship can be well represented by two exponential functions, with exponents increasing in time. Such a dependency resembles the well-known behavior of quasi-elastic inhomogeneous materials and rocks under an increasing differential stress, either compressive or tensile, at both low- and high-pressure conditions 35,38,51–54 . Patterns of fracturing of brittle rocks in laboratory clearly show that at low stresses fracturing activity is null or very low and the behavior is close to elastic, i.e., there is a quasi-linear relation between stress and strain. At stresses of about half of the values at bulk failure the fracturing activity begins to increase in an exponential way until the strain has typically reached about 90–95% of the failure value. Under such conditions the stress increases in a non-linear way with respect to strain, producing a curve strain-stress that is downward convex. This condition of the material is also characterized by dilatancy, i.e., an increase of the volume due to a quasi-homogeneous formation of small cracks within the rocks. At larger increasing stresses, the fracturing activity typically accelerates very quickly producing the coalescence of fractures in a major fault and eventually leading to bulk failure of the brittle rock. For specific properties of the rock a variety of strain-hardening or strain-softening type behaviors of the material can also be observed before failure. Eventually, when the amount of stress has reached its maximum value, most of the supplied energy is spent in fracture and fault movements and the behavior of the rock becomes inelastic, i.e., the deformation continues under a constant stress. This regime is typically characterized by a proportional increase of seismic events with deformation. It is important to observe that the nature of the exponential relationship between strain and cumulative seismic count depends on the mechanical properties of the crustal rocks 52,54 . These in turn depend on lithology as well as on the local conditions at depth such as pressure, temperature, water content as well as on other rock properties such as porosity, compaction and alteration of components and minerals. The underground distribution of these properties and conditions are largely unknown for the crust of CFc although several mechanical properties data exist based on measurements on core samples and outcrops 55,56 . Data overall show an elastic-brittle behavior of the CFc rocks although remarkable variations of key properties, such as elastic modulus and Poisson ratio, were measured as a function of porosity, temperature and water saturation conditions. It is therefore important to underline that the empirical relationship between deformation and seismic activity as illustrated in Fig. 8 , and here interpreted as a progressive evolution of the quasi-elastic response of the shallow crust to an increase of stress, should be simply considered as an empirical relation valid for the superficial crust as a whole, i.e. assuming the crustal rocks as a single inhomogeneous medium with a mean elastic-brittle behavior. It should be noted that this relationship also potentially depends on additional processes which are not considered herein and that likely contribute to the deformation observed such as pore-pressure and thermal effects associated with the presence of fluids of magmatic, hydrothermal and exogenous origin in the rock matrix 31,32,57 . The interpreted quasi-elastic behavior of the superficial crust appears, however, largely consistent with previous analyses and interpretations of the ongoing unrest 26,34–36,40 . According to them, the presence of low permeability levels at depths ranging between 1.5 and 3 km could favor the pressurization of the underlying layers due to the accumulation of magmatic gasses, fluids or magma rising from deeper regions. Detailed analyses of the distribution and mechanisms of the ongoing local seismicity also appear to be consistent with a stress concentration caused by the uplift of the central part of the caldera as well as with a possible effect of fluid-driven pore-pressure increase at the reactivated faults involved 18,40,41 . Similarly, the existence of the observed oscillations with variable periods in the geophysical trends investigated could be interpreted as a result of the unsteady fracturing of the crust under the increasing stress due to the pressurization generated by the arrival of deep fluids or magma batches and their complex interplay with the superficial hydrothermal system 20,26,31,32,54 . Nevertheless, a significant difference between the analysis here presented and that of [ 36 ] is the fact that, based on the relation between deformation and number of earthquakes, the latter study claims the reaching of the inelastic regime of the CFc crust since May 2020 (and up to June 2021, corresponding to the end of the period analyzed), due to the establishment of a linear relationship between the two geophysical variables. We hypothesize here that such inconsistency is due to the different time period (about 2.5 years shorter than that analyzed here) over which the two analyses have been made. As a consequence, the present study, although generally consistent with the main conclusion of [ 35 , 36 ] which suggests a progressive weakening of the mechanical properties of the shallow crust of CFc, gives evidence of a stronger sensitivity of the seismic activity on the uplift of the caldera, as will be better described and quantified later on in this section. It is worth underlining that this results is independent from the existing interpretations in terms of rheological behavior of the shallow crust. To gain further insights on the recent dynamics of the caldera, the relationship between deformation and seismic count for the unrest crisis of 1982-84 was also analyzed. This is illustrated in Fig. 9 . Figure 9 a shows the cumulative total number of earthquakes versus the ground uplift as measured at Benchmark 25A of the leveling network (close to Pozzuoli, see Fig. 1 -SI), whereas Fig. 9 b shows the same relationship by considering only earthquakes with M d > 0.5 and the vertical uplift as measured by the tide-gauge at the Pozzuoli harbor (close to the center of the CFc, see again Fig. 1 -SI). Despite the lower quality and amount of data recorded during this past crisis with respect to the current one, in both plots the correlation between the two geophysical variables results quasi-linear, R-squared > 99%, and not exponential. The same relation was obtained by considering different thresholds of magnitude. This is also different from the results of [ 35 , 36 ] who estimated an exponential trend over the period 1982-84 by apparently using a lower number of data points. The interpretation of such different deformation-number of earthquakes relationship with respect to the current crisis (see Fig. 8 ) is not trivial or obvious. However, as mentioned above, a quasi-linear relation between deformation and seismic count is typically indicative of an inelastic mechanical behavior of rocks in which most of deformation is accommodated by the propagation and slip of existing fractures and faults. This process appears consistent with most interpretations of the 1982-84 crisis as caused by an intrusion of magma with the formation of a thin sill at about 3–4 km depth 14,22–25 . We also note that the 1982-84 crisis occurred on a time period much shorter and therefore with deformation and seismic rates about one order of magnitude larger than those characterizing the present crisis. Such a different relationship between deformation and seismic activity appears as further evidence of the different forcing source and/or mechanism associated to the 1982-84 crisis with respect to the present one. Finally, the ongoing trends of deformation and seismic activity, and particularly their so far robust, empirical exponential relationship as illustrated in Fig. 8 , can also be used to gain some insights on the potential evolution of the bradyseismic crisis in case of a further uplift of the caldera with the same trends. From Fig. 8 it is evident how such exponential relationship takes into account and explains the progressively intensifying seismic activity recorded in the last few years due to the continuous, although oscillating, increase of the caldera uplift. Similarly, under the assumption that the same trend of uplift will continue in the future, we could expect a corresponding exponential increase of the number of earthquakes. According to Fig. 8 b, in particular, it emerges that, for instance, a further uplift increase of just 20 cm (i.e., from 1.2 to 1.4 m at the RITE GNSS station) could generate, with the current exponential relationship, a number of M d > 0.5 events larger than that recorded since 2000 (i.e., about 2,000 more events vs the about 1,800 recorded since year 2000, see dashed portion of the exponential curve of Fig. 8 b). A similar consideration can approximately be done also for the total number of earthquakes as shown in Fig. 8 a. Based on the analysis of the distribution of the number of earthquakes as a function of the magnitude M d , it is also possible to define the best fitting parameters of the exponential law (Gutenberg-Richter) describing this distribution. As shown in Fig. 8 -SI, the fitting of the distribution is very good (R-squared > 99%) and the corresponding b -value over the investigated 2000–2023 period is equal to 0.87, by assuming a M c equal to 0.5 (a very similar value was obtained with M c =0.2 but given the discretization of the earthquake magnitude a value of M c =0.5 was preferred). A slightly lower b -value of 0.83 is obtained for the most recent period 2021–2023, whereas, over the period 2007–2020, we obtained a value of 0.95, equal to that obtained by [ 45 ] with a different approach over the same period. We note also that our estimates of the b -value are ca. 5–10% lower than those obtained by previous studies over different previous periods 19,45,58 evidencing a progressive decrease with time. This is also consistent with recent estimates of the b -value of the different volumes of the caldera showing a close relationship between this parameter and the physical and mechanical properties of the rocks and indicating lower b -values just at depths of 2.5-3 km where a caprock with brittle-fragile behavior is located 59 . All this represents further evidence of the overall progressive stress increase and medium weakening of the shallow crust of CFc as clearly observed in many experimental and volcanic systems 19,54,60 . Based on the above-described law of magnitude distribution and the expected number of events of magnitude M d > 0.5 as a function of the ground deformation reached by the caldera, it is also possible to estimate the probability of occurrence of an earthquake above a given magnitude associated to a given future uplift of the caldera. Here we just mention that, based on the above-described data and hypotheses, just a further modest uplift of about 20 cm would be associated with a significant number of expected earthquakes with potential impact in the CFc area. Table 1 -SI details the expected number of earthquakes above various magnitudes in a population of 2,000 events with M d > 0.5 (corresponding to a further uplift of about 20 cm), as a function of the b- value and its associated uncertainty. For instance, by using a b- value equal to 0.87, the magnitude-frequency law would expect 0.82 events with M d ≥ 4.5 on average, and 0.30 events with M d ≥ 5, simply by applying the above-described statistical basis. A b -value equal to 0.83 would produce an increase of ca. 50% expected large events, whereas a b -value equal to 0.95, a decrease of 50% (see Table 1 -SI). These estimates, although based on an extrapolation of the reconstructed distribution of magnitudes to values larger than those so far observed, are qualitatively consistent with analyses of potential seismic activity at CFc based on different data and hypotheses 40,61 . It should be noted, however, that due to the above-described oscillations in time of the rate of deformation, it is not possible to precisely forecast the expected seismic activity as a function of time. For instance, by hypothesizing future deformation rates in the range of values recorded in the last 6 months or 1 year, short-time forecasts of seismic activity, e.g. on a monthly basis, are affected by an uncertainty significantly larger than that associated with medium- and long-term forecasts which are able to filter out oscillations with shorter periods. Nevertheless, the above-described super-exponential decadal trend of seismic activity, also given the time-increasing exponents describing the relationship between deformation and seismic count (see Fig. 8 ), remains suited to be investigated through a probabilistic application of the Failure Forecast Method (FFM), similarly to what done by [ 39 ] for the period 2000–2020, in order to explore the time scale of the evolution of the crisis in case of continuation of the observed trends. In particular, in this new application of FFM the exponent alpha of the seismic rate has been varied between 1.2 and 2 39,62 . The application of the method to the new datasets confirms the main outcomes of the previous analysis providing median values of the waiting times (i.e. the time to be waited to reach the critical time computed since 12/2023) from 0.5 to about 2.5 years with 95%ile values up to about 8 years (see Fig. 9 -SI for more details). It is worth noting that these estimates are remarkably dependent on the period of time used in the regression of the inverse rates, in this case we tested 3 and 10 years. As a consequence, these estimates cannot be considered reliable forecasts of the occurrence of specific volcanic events given the large number of false alarms typically experienced in the application of FFM to real crises. Nevertheless, the analysis is of some interest since it indicates, over the parameter space explored, a relatively fast evolution of the crisis (up to few years as median values) in case of continuation of the observed trends. The bradyseismic scenario above described represents the simple temporal extension of the trends currently observed. Nevertheless, it is uncertain and it represents just one of the plausible evolutions of the ongoing bradyseismic crisis. Based on observation of similar unrest crises at other calderas 35,63 , the interpreted quasi-elastic behavior of the shallow crust could be interrupted at any time, either by evolving into an inelastic regime of the crust or simply due to the occurrence of superficial magmatic intrusions or events, such as phreatic explosions, triggered by some of the complex, and still largely unknown, processes governing the magmatic and hydrothermal systems of CFc 36,37,64 . Similarly, the caldera uplift could, abruptly or more slowly, stop, the seismic activity decrease and the caldera enter into a new period of subsidence 36 . Unfortunately, based on our present understanding, the future evolution of the system is largely controlled by the internal dynamics of the volcanic system of CFc that, at this time, we are unable to observe and forecast accurately. Conclusions Ground deformation and seismic activity are two of the most effective data to understand and monitor volcanic activity. This is because, differently from other variables such as temperature or concentration of gasses, the elastic effects of physical and chemical changes in the underground system are almost instantaneously transmitted to the surface. Their close inspection and analysis are therefore useful for monitoring the volcanic system and to better understand its current state 65 . Based on close inspection and quantitative analyses of deformation and seismic data of CFc and of their relationships, in the period 2000-11/2023 and particularly since 2019, the followings are the main conclusions and insights provided by the study: The temporal evolution of vertical and horizontal deformation (the latter analyzed at several stations within the caldera), number of earthquakes and strain release, continues to be characterized by a decadal-scale trend overlaid with oscillations of varying frequencies. On the decadal scale, deformation rates exhibit an approximately linear growth, i.e., deformation follows a parabolic trend with average acceleration of ca. 0.7–0.8 cm/yr 2 for the vertical uplift at RITE GNSS station, while earthquake occurrence rates increase with a super-exponential trend, similarly to the number of earthquakes. Understanding the cause of such parabolic increase of uplift represents certainly a challenging goal for future investigations and it questions the possibility, among several others, that the driver of the uplift would be itself an accelerating process. Oscillations of various periods are recognizable in both deformation and seismic data. The oscillations of these two parameters appear closely correlated in time, with a variable time delay up to 45 days of seismic activity relative to deformation. Further investigations should be carried out to better quantify this time lag even on shorter time scales. The main periods of these oscillations range from approximately 2 and 5 months (shorter periods) to periods of about 1.5 and 3 years (longer periods). In recent years, there has been a trend towards a reduction in these periods (by about 10–15%, see [ 39 ] for previous estimates). Periods of acceleration and deceleration in geophysical data are therefore characteristic of the dynamics of the recent CFc bradyseism. The current period (December 2023-January 2024 at the time of writing) of reduced seismic activity is not, therefore, necessarily indicative of a major change in the future evolution of the ongoing phenomenon. The relationship between the number of earthquakes and vertical uplift results to be well-represented, since about 2010, by two exponential functions with increasing exponents in time and a transition period between 4/2020 and 9/2022. Such relationship well represents and explains the increasing intensity of seismic activity (number of earthquakes per year) over time, particularly since the beginning of 2020. Such a behavior is different from the linear relationship between these two variables previously suggested [ 36 ] and it is interpreted here in terms of progressive evolution of the quasi-elastic behavior of the shallow crust of CFc. Most importantly, such a relationship, which is independent from the interpretations provided, gives evidence of the increasing sensitivity of seismic activity on the inflation of the caldera. This exponential-type relationship is also different from the linear-type relationships derived for the 1982-84 crisis suggesting that the two crises are characterized by different forcing sources and/or mechanisms. Under the hypothesis that the observed decadal trends persist and the aforementioned relationship between uplift and cumulative number of earthquakes remains valid, a further uplift of the ground could likely be associated with new intense seismic activity, likely at rates even higher than those recorded in 2023. In particular, by assuming just a further uplift of the caldera of 20 cm the magnitude-frequency law would forecast a significant probability of earthquakes with magnitude higher than 4.5. This possibility requires a proper consideration of the seismic hazard and risk in case of continuation of the crisis. Of course, such a scenario is just one of the plausible evolutions of the volcanic system. These insights emphasize the importance of closely monitoring and analyzing the dynamic interplay between deformation and seismic events in the context of the CFc bradyseism to further improve our understanding and forecasting capability of this complex phenomenon. Declarations Data availability The seismic catalogs 18 of CFc are available from the INGV—Osservatorio Vesuviano website at the links: https://doi.org/10.13127/ovcatalogsth_2000_2021 and https://terremoti.ov.ingv.it/gossip/flegrei. The geodetic GNSS dataset 17 of CFc is available from https://zenodo.org/record/6389920#.ZD0GCnbMJD8. Just for the sake of completeness, the two main seismic and geodetic datasets analyzed in the paper are also attached as text files in the supplementary information. Acknowledgements This research was partially funded by the Dipartimento della Protezione Civile (Italy), as part of the INGV-DPC contract B2 2019-2021 and contract A 2022-2024. However, the study does not necessarily represent the official views and policies of the Dipartimento della Protezione Civile (Italy). Preliminary results of this work have been presented during meetings of the Commissione Grandi Rischi, Dipartimento della Protezione Civile (Italy), held in Autumn 2023 and concerning the Campi Flegrei caldera unrest. The authors thank the Committee members for providing useful feedbacks and insights. Author contributions A.B. and A.N. conceived the main conceptual ideas, scientific objectives and methods. A.B. implemented the codes and performed the statistical analysis. A.N. supervised the analysis and wrote the manuscript, A.B. produced the figures and table. P.D.M, F.G., G.M. and P.R. contributed to the development of the scientific objectives and provided and cured the GNSS and seismic records. All authors discussed the results, provided critical feedback and interpretation of findings, commented on the manuscript and gave final approval for publication. Competing interests The authors declare no competing interests. Additional information The online version contains supplementary material in the form of a pdf file with supporting figures and tables discussed in the main text, and two text files with the main deformation and seismic data analyzed in the study. References Rosi, M., & Sbrana, A.. Phlegrean Fields. Quaderni de la ricerca scientifica, 9(114), (1987). Orsi, G. Volcanic and deformation history of the Campi Flegrei Volcanic Field, Italy. In “Campi Flegrei: a restless caldera in a densely populated area”, Book Series:Active Volcanoes of the World, Chap. 1, Springer (2022). Orsi G., Di Vito M.A. & Isaia R. Volcanic hazard assessment at the restless Campi Flegrei caldera. Bull Volcanol 66:514–530. https://doi.org/10.1007/s00445-003-0336-4 , (2004). Bevilacqua, A., Flandoli, F., Neri, A., Isaia, R. & Vitale, S. Temporal models for the episodic volcanism of Campi Flegrei caldera (Italy) with uncertainty quantification. J. Geophys. Res. Solid Earth 121, 7821–7845. https://doi.org/10.1002/2016J B0131 71 (2016). Bevilacqua, A. Macedonio, G., Neri, A., Orsi, G. & Petrosino, P. Volcanic hazard assessment at the Campi Flegrei caldera (Italy), Ch. 12 in Campi Flegrei: A restless caldera in a densely populated area, (Eds Orsi, G., Civetta, L. & D’Antonio, M.) Active Volcanoes of the World, Springer, https://doi.org/10.1007/978-3-642-37060-1_12 (2022a). Di Vito, M. et al. Magma transfer at Campi Flegrei caldera (Italy) before the 1538 AD eruption. Sci. Rep. 6, 32245. https://doi.org/10.1038/srep32245 (2016). Corrado, G., Guerra, I., Lo Bascio, A., Luongo, G. & Rampoldi, R. Inflation and microearthquake activity of Phlegraean Fields, Italy. Bull. Volcanol. 40, 169–188. https://doi.org/10.1007/BF02596998 (1977). Bianchi, R. et al. Modeling of surface deformation in volcanic areas: The 1970–1972 and 1982–1984 crises of Campi Flegrei, Italy. J. Geophys. Res. 92(B13), 14139–14150. https://doi.org/10.1029/JB092iB13p14139 (1987). Berrino, G. et al. Ground deformation and gravity changes accompanying the 1982 Pozzuoli uplift. Bull. Volcanol. 47, 187–200. https://doi.org/10.1007/BF01961548 (1984). Orsi, G. et al. Short-term ground deformations and seismicity in the nested Campi Flegrei caldera (Italy): An example of active block-resurgence in a densely populated area. J. Volcanol. Geotherm. Res. 91, 415–451 (1999). Scarpa, R. et al. Historic unrest of the Campi Flegrei Caldera, Italy. In Ch. 10 Campi Flegrei: A restless caldera in a densely populated area, Active Volcanoes of the World (eds Orsi, G. et al.), Springer, Cham (2022). Del Gaudio, C., Aquino, I., Ricciardi, G. P., Ricco, C. & Scandone, R. Unrest episodes at Campi Flegrei: A reconstruction of vertical ground movements during 1905–2009. J. Volcanol. Geotherm. Res. 195, 48–56. https://doi.org/10.1016/j.jvolgeores.2010.05.014 (2010). Barberi, F., Corrado, G., Innocenti, F. & Luongo, G. Phlegraean Fields 1982–1984: Brief chronicle of a volcano emergency in a densely populated area. Bull. Volcanol. 47, 175–185. https://doi.org/10.1007/BF01961547 (1984). De Natale, G. & Zollo, A. Statistical analysis and clustering features of the Phlegrean Fields earthquake sequence (May 1983-May 1984). Bull. Seism. Soc. Am. 76(3), 801–814 (1986). INGV-OV, Campi Flegrei – Bollettino mensile, novembre 2023, Osservatorio Vesuviano, INGV, https://www.ov.ingv.it/index.php/monitoraggio-e-infrastrutture/bollettini-tutti/mensili-dei-vulcani-della-campania/flegrei/anno-2023-1 (2023). De Martino, P., Dolce, M., Brandi, G., Scarpato, G. & Tammaro, U. The ground deformation history of the Neapolitan volcanic area (Campi Flegrei caldera, Somma-Vesuvius volcano, and Ischia island) from 20 years of continuous GPS observations (2000–2019). Remote Sens. 13, 2725. https://doi.org/10.3390/rs131 42725 (2021). Ricciolino, P. & Lo Bascio, D. Cataloghi sismici dei vulcani campani. Stazione STH Campi Flegrei dal 2000 al 2021 (Cat-STH_2000_2021) (1.0) Data set. Istituto Nazionale di Geofisica e Vulcanologia (2021). Doi: https://doi.org/10.13127/ovcatalogsth_2000_2021 . Giudicepietro, F. et al. Tracking episodes of seismicity and gas transport in Campi Flegrei caldera through seismic, geophysical, and geochemical measurements. Seismol. Res. Lett.; 92 (2A): 965–975. doi: https://doi.org/10.1785/0220200223 (2020). Tramelli, A. et al. Statistics of seismicity to investigate the Campi Flegrei caldera unrest. Sci. Rep. 11, 7211. https://doi.org/10.1038/s41598-021-86506-6 (2021). Chiodini, G., Caliro, S., Avino, R., Bini, G., Giudicepietro, F., Cesare, W.D., Ricciolino, P., Aiuppa, A., Cardellini, C., Petrillo, Z., Selva, J., Siniscalchi, A., Tripaldi, S.. Hydrothermal pressure-temperature control on CO2 emissions and seismicity at Campi Flegrei (Italy). J. Volcanol. Geoth. Res. 107245 https://doi.org/10.1016/j. jvolgeores.2021.107245 (2021). Dvorak, J.J. & Berrino, G. Recent ground movement and seismic activity in Campi Flegrei, southern Italy: episodic growth of a resurgent dome. J. Geophys. Res. Solid Earth 96, 2309–2323. https://doi.org/10.1029/90jb02225 , (1991). Woo, J.Y.L. & Kilburn, C.R.J.. Intrusion and deformation at Campi Flegrei, southern Italy: sills, dikes, and regional extension. J. Geophys. Res. Solid Earth 115. https://doi.org/10.1029/2009jb006913 , 1978 2012, (2010). Macedonio, G., Giudicepietro, F., D’Auria, L., Martini. Sill intrusion as a source mechanism of unrest at volcanic calderas. J. Geophys. Res.: Solid Earth 119, 3986–4000. https://doi.org/10.1002/2013jb010868 , (2014). Giudicepietro, F., Macedonio, G. & Martini, M. A physical model of sill expansion to explain the dynamics of unrest at calderas with application to Campi Flegrei. Front. Earth Sci. 5, 54–65. https://doi.org/10.3389/feart . 2017. 00054, (2017). Troise, C., De Natale, G., Schiavone, R., Somma, R., & Moretti, R. The Campi Flegrei caldera unrest: Discriminating magma intrusions from hydrothermal effects and implications for possible evolution. Earth-Science Reviews 188, 108–122. https://doi.org/10.1016/j.earscirev.2018.11.007 , (2019). Giacomuzzi, G. et al. Tracking transient changes in the plumbing system at Campi Flegrei Caldera. Earth Planet. Sci. Lett. 637, 118744 https://doi.org/10.1016/j.epsl.2024.118744 (2024). Bonafede M. Hot fluid migration; an efficient source of ground deformation; application to the 1982–1985 crisis at Campi Flegrei-Italy. Journal of Volcanology and Geothermal Research, 48, 187–198, (1991). Troiano, A., Di Giuseppe, M. G., Petrillo, Z., Troise, C. & De Natale, G. Ground deformation at calderas driven by fluid injection: modeling unrest episodes at Campi Flegrei (Italy). Geophys. J. Int. 187, 833–847 (2011). Chiodini, G. et al. Evidence of thermal-driven processes triggering the 2005–2014 unrest at Campi Flegrei caldera. Earth Planet Sci. Lett. 414, 58–67. https://doi.org/10.1016/j.epsl.2015.01.012 (2015). Moretti, R., De Natale, G. & Troise, C. A geochemical and geophysical reappraisal to the significance of the recent unrest at Campi Flegrei caldera (Southern Italy). Geochem. Geophys. Geosyst. 18, 1244–1269. https://doi.org/10.1002/2016G C0065 69, (2017). Todesco, M. (2021). Caldera’s breathing: poroelastic ground deformation at Campi Flegrei (Italy). Frontiers in Earth Science 9, 702665. https://doi.org/10.3389/feart.2021.702665 Nespoli, M., Tramelli, A., Belardinelli, M. E., & Bonafede, M. The effects of hot and pressurized fluid flow across a brittle layer on the recent seismicity and deformation in the Campi Flegrei caldera (Italy). Journal of Volcanology and Geothermal Research, 443, 107930 (2023). Amoruso, A., Crescentini, L. & Sabbetta, I. Paired deformation sources of the Campi Flegrei caldera (Italy) required by recent (1980–2010) deformation history. J. Geophys. Res. Solid Earth 119, 858–879. https://doi.org/10.1002/2013JB010392 (2014). Buono, G. et al. New insights into the recent magma dynamics under Campi Flegrei caldera (Italy) from petrological and geochemical evidence. J. Geophys. Res. Solid Earth https://doi.org/10.1029/2021J B0237 73 (2022). Kilburn, C.R.J., De Natale, G. & Carlino, S. Progressive approach to eruption at Campi Flegrei caldera in southern Italy. Nat. Commun. 8, 15312. https://doi.org/10.1038/ncomms15312 (2017). Kilburn, C.R.J., Carlino, S., Danesi, S. & Pino, N.A. (2023). Potential for rupture before eruption at Campi Flegrei caldera, Southern Italy. Commun. Earth & Environment 4:190, https://doi.org/10.1038/s43247-023-00842-1 Danesi, S., Pino N.A., Carlino S., Kilburn C.R.J., Evolution in unrest processes at Campi Flegrei caldera as inferred from local seismicity. Earth Planet. Sci. Lett., 626 (2024) 118530, https://doi.org/10.1016/j.epsl.2023.118530 (2024). Kilburn, C.R.J. Precursory deformation and fracture before brittle rock failure and potential application to volcanic unrest. J. Geophys. Res. Solid Earth 117, B02211. https://doi.org/10.1029/2011JB008703 (2012). Bevilacqua, A. et al. Data analysis of the unsteadily accelerating GPS and seismic records at Campi Flegrei caldera from 2000 to 2020, Sci. Rep. 12:19175, https://doi.org/10.1038/s41598-022-23628-5 (2022b). Scotto di Uccio, F., et al. Delineation and fine-scale structure of active fault zones during the 2014–2023 unrest at the Campi Flegrei Caldera (Southern Italy) from high-precision earthquake locations, ESS Open Archive, doi: 10.22541/essoar.170224505.51315564/v1 (2023). Tramelli, A. et al. The seismicity of Campi Flegrei in the contest of an evolving long-term unrest. Sci. Rep. 12, 2900. https://doi.org/10.1038/s41598-022-06928-8 (2022). De Martino, P. et al. Four years of continuous seafloor displacement measurements in the Campi Flegrei caldera. Front. Earth Sci. 8, 615178. https://doi.org/10.3389/feart.2020.615178 (2020). Bevilacqua, A. et al. Radial interpolation of GPS and leveling data of ground deformation in a resurgent caldera: application to Campi Flegrei (Italy). J. Geod. 94(2), 24. https://doi.org/10.1007/s00190-020-01355-x (2020). Iannaccone, G. et al. Measurements of seafloor deformation in the marine sector of the Campi Flegrei caldera (Italy). J. Geophys. Res., 123, 66–83. https://doi.org/10.1002/2017JB014852 . Giudicepietro, F. et al. Campi Flegrei, Vesuvius and Ischia Seismicity in the context of the Neapolitan volcanic area. Front. Earth. Sci. 9, 662113. https://doi.org/10.3389/feart.2021.662113 (2021). Chiodini, G. et al. Clues on the origin of post-2000 earthquakes at Campi Flegrei caldera (Italy). Sci. Rep. 4472, 2045–2322. https://doi.org/10.1038/s41598-017-04845-9 (2017). Giudicepietro, F., et al. First evidence of a geodetic anomaly in the Campi Flegrei caldera (Italy) ground deformation pattern revealed by DInSAR and GNSS measurements during the 2021–2023 escalating unrest phase. https://dx.doi.org/10.2139/ssrn.4791859 (2024). De Martino, P., Tammaro, U. & Obrizzo, F. GPS time series at Campi Flegrei caldera (2000–2013). Ann. Geophys. 57(2), S0213. https://doi.org/10.4401/ag-6431 (2014). Vitale, S. & R. Isaia. Fractures and faults in volcanic rocks (Campi Flegrei, Southern Italy): Insights into volcano-tectonic processes, Int. J. Earth. Sci., 103, 801–819, https://doi:10.1007/s00531-013-0979-0 (2014). Bevilacqua, A. et al. Quantifying volcanic hazard at Campi Flegrei caldera (Italy) with uncertainty assessment: I. Vent opening maps. J. Geophys. Res. 120, 2309–2329. https://doi.org/10.1002/2014JB011775 (2015). Mogi, K., Study of the elastic shocks caused by the fracture of heterogeneous materials and its relation to earthquake phenomena, Bull. Earthquake Res. Inst. Tokyo Univ., 40, 125 (1962). Scholz, C.H.. Microfracturing and the inelastic deformation of rock in compression. J. Geophys. Res., Vol. 73, n. 4, 1417–1432 (1968). McGarr, A., Seismic moments and volume changes. J. Geophys. Res., Vol. 81, n. 8, 1487–1494 (1976). Meredith, P. G., I. G. Main, and C. Jones (1990), Temporal variations in seismicity during quasi-static and dynamic rock failure, Tectonophysics, 175, 249–268, doi: 10.1016/0040-1951(90)90141-T . Heap, M. J., Baud, P., Meredith, P. G., Vinciguerra, S., and Reuschlé, T. The permeability and elastic moduli of tuff from Campi Flegrei, Italy: implications for ground deformation modelling. Solid Earth 5, 25–44. doi: 10.5194/se-5-25-2014 , (2014). Vanorio, T., and Kanitpanyacharoen, W. Rock physics of fibrous rocks akin to Roman concrete explains uplifts at Campi Flegrei Caldera. Science 349, 617–621. https://doi:10.1126/science.aab1292 , (2015). Saboo, S., et al. Feedback responses between endogenous and exogenous processes at Campi Flegrei caldera dynamics, Italy. Bull. Volcanol., 86:22 (2024). Siniscalchi, A., et al. Reservoir structure and hydraulic properties of the Campi Flegrei geothermal system inferred by audiomagnetotelluric, geochemical and seismic study. J. Geophys. Res., Solid Earth, 124(6), 5336–5356 (2019). Tramelli, A., Convertito, V., & Godano, C. b value enlightens different rheological behavior in Campi Flegrei caldera. Commun. Earth & Environment, 5:275, https://doi.org/10.1038/s43247-024-01447-y (2024). Farrell, J., Husen, S. & Smith, R. B. Earthquake swarm and b-value characterization of the yellowstone volcano-tectonic system. J. Volcanol. Geoth. Res. 188(1–3), 260–276 (2009). Caputo, M. Two thousand years of geodetic and geophysical observation in the Phlegrean Fields near Naples. Geophys. J. R. Astr. Soc., 56,319–328 (1979). Voight, B. A method for prediction of volcanic eruptions. Nature 332, 125–130. doi: 10.1038/332125a0 (1988). Acocella, V., Di Lorenzo, R., Newhall, C. & Scandone, R. An overview of recent (1988 to 2014) caldera unrest: knowledge and perspectives. Rev. Geophys. 53, 896–955. https://doi.org/10.1002/2015RG0004 92 (2015). Isaia, R. et al. Volcano-tectonic setting of the Pisciarelli fumarole field, Campi Flegrei caldera, southern Italy: Insights into fluid circulation patterns and hazard scenarios. Tectonics 40(5), e2020TC006227 (2021). Rosi, M. et al. Defining the pre-eruptive states of active volcanoes for improving eruption forecasting. Front. Earth Sci. 10, 795700. https://doi.org/10.3389/feart . 2022. 795700 (2022). Additional Declarations There is NO Competing Interest. Supplementary Files SupplementaryInformation.docx DeformationRITEdaily.txt Deformation dataset Seismicity2000Nov2023.txt Seismic dataset Cite Share Download PDF Status: Published Journal Publication published 03 Dec, 2024 Read the published version in Communications Earth & Environment → Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4164255","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":318918448,"identity":"33ace198-de99-4eb3-a0d3-08550a8f62a4","order_by":0,"name":"Andrea Bevilacqua","email":"","orcid":"https://orcid.org/0000-0002-0724-2593","institution":"Istituto Nazionale di Geofisica e Vulcanologia","correspondingAuthor":false,"prefix":"","firstName":"Andrea","middleName":"","lastName":"Bevilacqua","suffix":""},{"id":318918447,"identity":"ce6a5c9c-9383-47c4-a9cc-556d3a549474","order_by":1,"name":"Augusto Neri","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5UlEQVRIiWNgGAWjYLCDAx8MQBRjAxFqEyDUwRkQLY1E6IFqYeaB0Pit4Z+Rfk3y5w8bBnP23oeHbQru2G04wNz+AJ8WiRs5ZdI8CWkMlj3HDQ7nGDxL3nCAkMNu5KRJMyQcZjC4kcYA1HI4WbKBgBZ5oBbJHyAt958xHLYgRovBjfRjEjxgW9gYgORhO35CIWZ45g2zNU9aGo/BmTSGgz0GhxP4mRkbZ+DTInc8/eHNHzY2cgbHjzF/+PHnsD0be/uDD/i0MDDwgKOPB8ZNbGDGrx4I2B+gcO0JahgFo2AUjIIRBwBdXUwXh1u1ZwAAAABJRU5ErkJggg==","orcid":"","institution":"Istituto Nazionale di Geofisica e Vulcanologia","correspondingAuthor":true,"prefix":"","firstName":"Augusto","middleName":"","lastName":"Neri","suffix":""},{"id":318918449,"identity":"9901e268-3706-4d29-aa44-78b99fa6ce65","order_by":2,"name":"Prospero De Martino","email":"","orcid":"","institution":"Istituto Nazionale di Geofisica e Vulcanologia, Osservatorio Vesuviano, Napoli","correspondingAuthor":false,"prefix":"","firstName":"Prospero","middleName":"","lastName":"De Martino","suffix":""},{"id":318918450,"identity":"031ab65a-be82-4154-ad5f-e13137e18d1b","order_by":3,"name":"Flora Giudicepietro","email":"","orcid":"https://orcid.org/0000-0001-6198-8655","institution":"Istituto Nazionale di Geofisica e Vulcanologia","correspondingAuthor":false,"prefix":"","firstName":"Flora","middleName":"","lastName":"Giudicepietro","suffix":""},{"id":318918451,"identity":"8197345e-13ff-4708-b6cc-794d27cad5c2","order_by":4,"name":"Giovanni Macedonio","email":"","orcid":"https://orcid.org/0000-0001-6604-1479","institution":"Istituto Nazionale di Geofisica e Vulcanologia","correspondingAuthor":false,"prefix":"","firstName":"Giovanni","middleName":"","lastName":"Macedonio","suffix":""},{"id":318918452,"identity":"441156fa-08c3-4a54-88fe-d7d8be63b5d1","order_by":5,"name":"Patrizia Ricciolino","email":"","orcid":"","institution":"Istituto Nazionale di Geofisica e Vulcanologia","correspondingAuthor":false,"prefix":"","firstName":"Patrizia","middleName":"","lastName":"Ricciolino","suffix":""}],"badges":[],"createdAt":"2024-03-25 15:13:28","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4164255/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4164255/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s43247-024-01865-y","type":"published","date":"2024-12-03T05:00:00+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":59202829,"identity":"5d9d8975-9b96-43f2-87bd-da828dc27339","added_by":"auto","created_at":"2024-06-27 15:32:51","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":555568,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Overview of the vertical ground displacement at CFc in the period 1983-11/2023. The data merge leveling data, collected at benchmark 25A, and the RITE GNSS station. (b) Overview of the earthquakes recorded at CFc in 1983-11/2023. In (a,b) the data collected in 2000-11/2023 are marked in blue. Data modified from the INGV-OV periodic bulletin of CFc (http://www.ov.ingv.it).\u003c/p\u003e","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4164255/v1/f5b63336c2a740545ee2ba6b.jpeg"},{"id":59202830,"identity":"f8b79dfd-a82d-4745-aaca-8c53c1b42475","added_by":"auto","created_at":"2024-06-27 15:32:51","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":564594,"visible":true,"origin":"","legend":"\u003cp\u003eVertical ground displacement recorded at RITE GNSS station over the period 2020-11/2023. Plots show the GNSS data together with their optimal parabolic fit, obtained by minimizing the mean square distance over the period 1/2010-11/2023. Plot (a) is in linear scale, plot (b) is in logarithmic scale (base 10), and plot (c) is in square-root scale. In all three plots the blue points represent the daily average measure whereas the grey range the associated uncertainty. The labels indicate the occurrence of the mini-uplifts, see text for more explanation.\u003c/p\u003e","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4164255/v1/ad268c4adf0053b2180dcf91.jpeg"},{"id":59202834,"identity":"8300e3d8-bd7d-4d18-8342-de35a63314a1","added_by":"auto","created_at":"2024-06-27 15:32:51","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":461641,"visible":true,"origin":"","legend":"\u003cp\u003eSeismic data over the period 2000-11/2023 analyzed in the paper. Plots (a, b) show the cumulative number of seismic events (the labels indicate the number of earthquakes of the 7 most numerous swarms); plots (c, d) show the cumulative seismic strain release estimation (Benioff strain) (the labels indicate the dates of some of the most intense earthquakes). Plots (a,c) are in linear scale whereas plots (b,d) are in logarithmic scale (base 10).\u003c/p\u003e","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4164255/v1/73a0fae78c11bfc7ff899aed.jpeg"},{"id":59203512,"identity":"58830069-090e-4386-9ce2-68deaeacf1b8","added_by":"auto","created_at":"2024-06-27 15:40:51","extension":"jpeg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":531121,"visible":true,"origin":"","legend":"\u003cp\u003ePlots show the annual rate of the deformation and seismic data from 2000 to 11/2023, respectively. In plot (a) the vertical uplift refers to the vertical displacement recorded at RITE GNSS station. In (a) the labels indicate the occurrence of the mini-uplifts (see text for more explanation) whereas in (b) the number of earthquakes of the 7 most numerous swarms. The annual rates have been computed assuming a time step of 6 months to approximate their derivative and therefore can be considered as 6-months average rates. The ellipse encircles the seismic count in the most recent period 2019-2023, better illustrated in Figure 5.\u003c/p\u003e","description":"","filename":"floatimage4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4164255/v1/ce538291f9fcd50d05b0fc12.jpeg"},{"id":59202840,"identity":"85dbc0f6-e822-4471-8e86-bae0736ab970","added_by":"auto","created_at":"2024-06-27 15:32:51","extension":"jpeg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":528016,"visible":true,"origin":"","legend":"\u003cp\u003eAnnual rate of the geophysical variables over the period 1/2019-11/2023. The plots illustrate the vertical deformation rate at RITE GNSS station (a) and the seismic count rate (b). The rates are still computed with a time step of 6 months as in Fig. 4. The vertical blue bars identify the corresponding peaks of the deformation and seismic rates. Each vertical bar lasts a period of about 30-45 days given the relatively smooth shape of the peak values of the two time series.\u003c/p\u003e","description":"","filename":"floatimage5.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4164255/v1/97b55bc634931519db9c0f20.jpeg"},{"id":59203513,"identity":"d5b111c0-ed93-49b4-8958-d3c4b3314374","added_by":"auto","created_at":"2024-06-27 15:40:51","extension":"jpeg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":780000,"visible":true,"origin":"","legend":"\u003cp\u003eAnnual rates and FT plots of the seismic rate over different periods. Plot (a) shows the seismic count rate over the period 1/2019-11/2023. In this case the rate is computed by assuming a time step of 1 month, instead of the 6 months of Figures 4 and 5, in the estimate of the times series derivative. The plot also shows the 3/5 peaks per year observed in the rate since 2019. Plot (b) shows the histogram of seismic counts per day for the year 2023. Plots (c, d) show the result of the application of the FT to the seismic rate of plot (a) for the identification of the main periods characterizing the seismic rate series in the period 2019-2023 and 2022-2023, respectively.\u003c/p\u003e","description":"","filename":"floatimage6.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4164255/v1/597d1e42ced32faa0fb782c3.jpeg"},{"id":59202832,"identity":"c05f5257-f336-4e0c-abb1-5a27c24b024c","added_by":"auto","created_at":"2024-06-27 15:32:51","extension":"jpeg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":512465,"visible":true,"origin":"","legend":"\u003cp\u003eExamples of Fourier spectrum for the vertical ground displacement recorded at RITE GNSS station. Plot (a) is are calculated on a 1 month moving average over the period 2022-2023, plot (b) is calculated on a 6 month moving average over the period 2018-2023 and plot (c) on a 2 years moving average over the period 2011-2023. The main time periods are marked and labeled in each plot.\u003c/p\u003e","description":"","filename":"floatimage7.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4164255/v1/9756fef15e0a9cacac68ecdf.jpeg"},{"id":59202839,"identity":"ff83bf3f-9c7c-47f4-b408-c3c044d28402","added_by":"auto","created_at":"2024-06-27 15:32:51","extension":"jpeg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":422491,"visible":true,"origin":"","legend":"\u003cp\u003eRelationships between vertical uplift at the RITE GNSS station and cumulative number of seismic events over the period 2000-11/2023. Plot (a) refers to the total number of events as reported in the seismic catalog whereas plot (b) refers to the number of earthquakes with M\u003csub\u003ed \u003c/sub\u003e\u0026gt; 0.5. Data are represented as red dots. Years reported in the labels and as black dots mark the temporal evolution of the uplift. The light and dark blue curves indicate the two exponential functions fitting the data of the two plots, and the corresponding exponents (see text for more explanation).\u003c/p\u003e","description":"","filename":"floatimage8.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4164255/v1/103e5fb5b1abe750b35086fb.jpeg"},{"id":59203515,"identity":"abb76c47-c515-43ea-b6ab-e4e52adbe9a4","added_by":"auto","created_at":"2024-06-27 15:40:51","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":168723,"visible":true,"origin":"","legend":"\u003cp\u003eRelationship between vertical uplift and seismic activity during the 1982-84 unrest crisis. Plot (a) shows as red dots the cumulative total number of earthquakes versus the ground uplift as measured at Benchmark 25A of the leveling network. Plot (b) shows the same relationship by considering only earthquakes with M\u003csub\u003ed \u003c/sub\u003e\u0026gt; 0.5 and the vertical uplift as measured by the tide-gauge at the Pozzuoli harbor (center of the CFc). A few reference dates are reported as horizontal dotted lines in both plots. In both plots the correlation between the two geophysical variables is well fitted by a linear increase.\u003c/p\u003e","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-4164255/v1/24cf8540c30deb26e5f9963b.png"},{"id":70540130,"identity":"32b53576-e6bd-4e29-b876-098b1b8c183c","added_by":"auto","created_at":"2024-12-04 08:07:34","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5037105,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4164255/v1/f79c247d-ccaf-4222-8503-87500e2ad0f4.pdf"},{"id":59202836,"identity":"9950d9b3-2cea-49b1-ac1b-779676b9ba17","added_by":"auto","created_at":"2024-06-27 15:32:51","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":2932866,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"SupplementaryInformation.docx","url":"https://assets-eu.researchsquare.com/files/rs-4164255/v1/52619a225a5ba338bcd8a8ef.docx"},{"id":59202838,"identity":"39fab6ea-8c6f-4729-9662-1df92f29b1e5","added_by":"auto","created_at":"2024-06-27 15:32:51","extension":"txt","order_by":2,"title":"","display":"","copyAsset":false,"role":"supplement","size":250780,"visible":true,"origin":"","legend":"\u003cp\u003eDeformation dataset\u003c/p\u003e","description":"","filename":"DeformationRITEdaily.txt","url":"https://assets-eu.researchsquare.com/files/rs-4164255/v1/a5e1b545ccd53d02a402d89d.txt"},{"id":59203913,"identity":"4b72754c-f4d7-4815-bdbb-cf455ff2b46d","added_by":"auto","created_at":"2024-06-27 15:48:51","extension":"txt","order_by":3,"title":"","display":"","copyAsset":false,"role":"supplement","size":361777,"visible":true,"origin":"","legend":"\u003cp\u003eSeismic dataset\u003c/p\u003e","description":"","filename":"Seismicity2000Nov2023.txt","url":"https://assets-eu.researchsquare.com/files/rs-4164255/v1/5b1e4ce11895036f80622029.txt"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Investigating deformation and seismic data and their relationships during the ongoing unrest of Campi Flegrei caldera (Italy)","fulltext":[{"header":"Introduction","content":"\u003cp\u003eCampi Flegrei caldera (CFc) is a complex volcanic system characterized by the presence of many explosive craters. These are located within an about 12 km wide caldera generated by at least two main collapses, the Campanian Ignimbrite, about 40,000 years BP, and the Neapolitan Yellow Tuff, about 15,000 years BP\u003csup\u003e1,2\u003c/sup\u003e. Since this latter event, over 70 eruptive vents were active, with the majority of eruptions being explosive. Eruptions were often closely grouped in time and space, over periods ranging from a few centuries to some millennia, and were separated by extended phases of inactivity lasting up to several millennia\u003csup\u003e3\u0026ndash;5\u003c/sup\u003e. The most recent eruption, known as the \"Monte Nuovo\" eruption, occurred in A.D. 1538 after a period of approximately 3,500 years of inactivity and was preceded by an uplift period of some decades\u003csup\u003e6\u003c/sup\u003e. The caldera is home of about 350,000 people thus representing one of the major volcanic risks worldwide.\u003c/p\u003e \u003cp\u003eSubsidence and uplift of the caldera ground, known as bradyseism, have been recorded since Roman times. After the Monte Nuovo uplift, the caldera was mostly affected by a dominant sinking and it is likely that the volcano entered a new phase of unrest in the second half of the last century. Since then, the caldera experienced three major bradyseismic crises: in 1950-53, 1969-72 and in 1982-84, resulting in uplifts of about 0.75 m, 1.70 m, and 1.85 m, respectively\u003csup\u003e7\u0026ndash;11\u003c/sup\u003e. Seismic activity typically increases during periods of uplift and drastically diminishes during subsidence. Interestingly, the uplift between 1950 and 1952 occurred without any notable felt seismicity\u003csup\u003e12\u003c/sup\u003e. The uplift experienced from 1969 to 1972 coincided with moderate seismic activity, featuring a few perceptible earthquakes and numerous low-magnitude events. However, the period of 1983-84 saw an intense seismic activity and significantly larger earthquakes, with magnitudes reaching a value of 4.0\u003csup\u003e13,14\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eFollowing the bradyseismic crisis of 1982-84, the caldera experienced about 20 years of subsidence until, since 2005, a slow and progressive increase of ground inflation has been observed\u003csup\u003e15,16\u003c/sup\u003e. Caldera deformation has been characterized by a well-defined bell-shaped pattern of vertical uplift, approximately centered in the town of Pozzuoli, and has been accompanied by a progressive increase of seismic activity\u003csup\u003e15,17\u0026ndash;19\u003c/sup\u003e. At the time of writing (December 2023) the ground uplift has reached a level of 118 cm above that of 2005 (hereafter always taken as reference uplift level) and the seismic activity has been largely intensified with two main earthquakes up to magnitude 4.2 and 4.0 in September-October 2023. The increase of deformation and seismic activity has been accompanied by a simultaneous increase of caldera degassing with the reaching of CO\u003csub\u003e2\u003c/sub\u003e fluxes up to about 4,000 t/day just from the Solfatara-Pisciarelli area\u003csup\u003e15,20\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eBradyseismic activity, including the above-described crises, at CFc has been interpreted by a variety of mechanisms including magmatic intrusions at relatively shallow level (few kilometers)\u003csup\u003e8,21\u0026ndash;26\u003c/sup\u003e, poroelastic response to variations of pressure and temperature conditions within the shallow hydrothermal system or the underlying impermeable layers\u003csup\u003e27\u0026ndash;32\u003c/sup\u003e, as well as by a combination of superficial and deep processes and sources\u003csup\u003e33,34\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe whole sequence of unrest since 1950 has been also interpreted as a single long-term process of crustal extension\u003csup\u003e35,36\u003c/sup\u003e. Under this hypothesis the forcing process would be represented by the pressurization of magmatic fluid, either magma or magmatic gases, beneath the so-called \u0026ldquo;brittle-ductile transition zone\u0026rdquo; at about 3 km depth\u003csup\u003e37\u003c/sup\u003e. In particular, by applying a model of elastic-brittle rock\u003csup\u003e38\u003c/sup\u003e, the whole unrest sequence has been interpreted in terms of changes of the mechanical behavior of the upper crust of CFc from purely elastic, to quasi-elastic and, finally, to inelastic\u003csup\u003e36\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe temporal and spatial patterns of deformation and seismicity have been also investigated with specific reference to the most recent uplift phase (2005-ongoing) and in comparison, with previous uplift episodes such as the 1982-84 crisis\u003csup\u003e19,37,39,40\u003c/sup\u003e. In particular, a temporal analysis of the datasets over the period 2000\u0026ndash;2020 identified the existence of two distinct overlying trends: a decadal-like acceleration and cyclic oscillations with variable periods ranging from some years to a few months\u003csup\u003e39\u003c/sup\u003e. Inspection of the distribution of seismic activity also highlighted how the ongoing seismicity is mostly located in correspondence of two main depth levels with significantly different mechanical and permeability properties\u003csup\u003e19,37,41\u003c/sup\u003e and on weaker pre-existing structures produced by a variety of processes such as dome resurgence, volcano-tectonic collapses, magma intrusions and migrations\u003csup\u003e18,40\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe aim of this paper is to analyze the most recent accelerating trends of geophysical data of CFc and, particularly, the close relationships between deformation and seismic data in terms of temporal coupling between the associated trends, their rates and oscillation periods. The datasets used in the analysis are about 2.5-3 years longer with respect to those analyzed in previous similar studies\u003csup\u003e36,39\u003c/sup\u003e thus allowing a more accurate and robust characterization of the rapidly-evolving caldera dynamics. It is just worth mentioning here that more than 70% of seismic events recorded since 2000 have occurred in the last 3 years here investigated, and more than about 85% of the strain release occurred in the same period. The analysis highlights a strong exponential correlation, with exponent increasing with time, between deformation and number of seismic events typical of a quasi-elastic behavior of brittle rocks and indicative of a progressive damage of the shallow crust of CFc\u003csup\u003e35,38\u003c/sup\u003e. Such a correlation is also discussed in relation to the 1982-84 unrest to infer potential differences in the forcing sources and mechanisms associated with the two crises, as well as to investigate a potential evolution of the bradyseismic crisis in case of continuation of the ground inflation and of the observed trends.\u003c/p\u003e \u003cp\u003eThe datasets used in the study are presented in Section 2 (Datasets) whereas the methods and techniques adopted in the analysis are described in Section 3 (Methods). The \u003cspan refid=\"Sec4\" class=\"InternalRef\"\u003eresults\u003c/span\u003e section (Section 4) presents the main findings of the temporal analysis of the geophysical data with specific reference to the last period of the accelerating crisis. In particular, the trend of the data rates, the main periods characterizing the oscillations overlying the time series and the close correlations between deformation and seismic activity are presented. Section 5 discusses the trends and correlations derived also in comparison with an analogous correlation obtained for the 1982-84 crisis and as a basis to describe the potential evolution of the bradyseismic crisis in case of continuation of the observed dynamics. Finally, Section 6 summarizes the main conclusions and insights provided by the study.\u003c/p\u003e"},{"header":"Datasets","content":"\u003cp\u003e \u003cem\u003eThe CFc GNSS deformation dataset from 2000 to 11/2023\u003c/em\u003e.\u003c/p\u003e \u003cp\u003eThe monitoring continuous GNSS network, managed by INGV-Osservatorio Vesuviano (INGV-OV), consists of 27 continuous GNSS stations on land and 4 on seafloor-connected (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e1\u003c/span\u003e-SI)\u003csup\u003e16,42\u003c/sup\u003e. Our analysis considered several of the 11 stations established before 2009, although most of the results are herein presented for the RITE GNSS station at Rione Terra, in the center of Pozzuoli, as representative of the vertical deformation pattern recorded at all other stations. The dataset consists, for each GNSS station, of final daily position time series with the associated uncertainty (estimated to be 1 cm on the vertical component and 0.3 cm in the two horizontal components\u003csup\u003e16\u003c/sup\u003e). The CFc\u0026rsquo;s vertical deformation history, since 1983, is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e1\u003c/span\u003ea through a combination of leveling and GNSS data\u003csup\u003e12,16\u003c/sup\u003e. Following the last major uplift episode of 1982-84, approximately 20 years of subsidence occurred from 1985 to 2005, causing a vertical drop of about 0.90 m. Subsequently, the CFc resumed its uplift, initially slow but gaining pace over the years. By November 2023, the maximum vertical displacement in the central area nearly reached 118 cm since November 2005\u003csup\u003e15\u003c/sup\u003e, well surpassing the maximum 1985 uplift level.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003ePost-2005, the RITE GNSS station at Rione Terra consistently recorded the most significant uplift. The remaining GNSS stations typically exhibit a bell-shaped decline in vertical displacement outward from the caldera center, alongside a radial symmetry in horizontal displacements centered on Pozzuoli, with peak values situated in a half-annulus of 2\u0026ndash;3 km radius\u003csup\u003e16,43\u003c/sup\u003e. It\u0026rsquo;s important to note that the inversion of GNSS and SAR data places the bell\u0026rsquo;s center about 500 m into the sea, southwest of the Rione Terra, and a corresponding superficial pressurized source at a depth of about 3\u0026ndash;4 km\u003csup\u003e33,44\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cem\u003eThe CFc seismic catalog from 2000 to 11/2023\u003c/em\u003e.\u003c/p\u003e \u003cp\u003eThe permanent seismic network managed by INGV-OV presently comprises 25 permanent digital stations and 3 permanent analog seismic stations\u003csup\u003e15\u003c/sup\u003e. In our study, we are focusing on the seismic catalog spanning from 2000 to 11/2023, regularly updated by the Osservatorio Vesuviano seismic laboratory\u003csup\u003e17,19,45\u003c/sup\u003e. The catalog we used consists of the earthquakes recorded, between 2000 and 12/2021, at the STH reference station situated near the Solfatara-Pisciarelli area (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e1\u003c/span\u003e-SI), whereas, in the period 1/2022 and 11/2023, it relies on the database SERENADE. In total the catalog includes 16,250 earthquakes. This dataset is consistent with the monthly lists that INGV-OV published in the official monitoring bulletins. Within this dataset, we can assume the completeness magnitude (M\u003csub\u003ec\u003c/sub\u003e) equal to about 0.2\u003csup\u003e19\u003c/sup\u003e. To test the sensitivity of some results, in addition to the above-described seismic dataset, we also analyzed the INGV-OV catalog of localized events. In this case, the catalog contains a subset of events with respect to the former catalog, for a total of 8,013 events localized in the 2000\u0026ndash;2023 considered period.\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e1\u003c/span\u003eb shows the number of seismic events per month over the last about four decades. From 1985 to 2005, i.e., during the subsidence phase, seismic activity was sporadic and almost absent within CFc. However, from 2005 onwards, and particularly since 2020, there has been a progressive escalation in seismic activity. Until 2014, earthquakes were infrequent and occurring in clusters of events with low magnitudes. Subsequently, seismic events became more frequent and shallower and those occurring outside of clusters notably increased in magnitude\u003csup\u003e19,41\u003c/sup\u003e. It is worth noting that in the last few years most seismic activity affected a radius of about 2 km centered at the Solfatara-Pisciarelli area, where also a significant increase in fluid flux was recorded\u003csup\u003e20,46\u003c/sup\u003e. However, several earthquakes and swarms also occurred along different volcano-tectonic structures of the caldera including the inner ring fault zone\u003csup\u003e37,40,41\u003c/sup\u003e.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003eThe deformation and seismic datasets have been closely analyzed by investigating their temporal evolution (Figs.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e2\u003c/span\u003e and \u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e3\u003c/span\u003e) as well as the behavior of their annual rate (Figs.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e4\u003c/span\u003e, \u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e5\u003c/span\u003e and \u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e6\u003c/span\u003e), with specific reference to the displacement rate, the seismic count rate and the strain release rate (Benioff strain) (see [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e] for more details and a comparison with trends computed over the period 2000\u0026ndash;2020). Particular focus has been given here to the analysis of the variations of the most recent period (i.e. 2019-11/2023) given the progressive increase of deformation and seismic activity of the caldera.\u003c/p\u003e \u003cp\u003eWith reference to the deformation time series, we analyzed the vertical and horizontal displacements of several of the GNSS stations active since 2009 (see Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e2\u003c/span\u003e-SI and 3-SI for more information). For the sake of brevity, only the vertical displacement at the RITE GNSS station will be presented in the following. The RITE trends can be considered representative of the vertical displacements estimated at all other GNSS stations as well as of the horizontal displacements at the same locations, computed as the length of the vector defined by the E-W and N-S spatial components. As mentioned above, at these stations the vertical time series are scaled down according to the observed bell-shaped deformation pattern centered in the town of Pozzuoli, whereas the horizontal displacements show their maximum along a circular ring of a few kilometers. It is worth mentioning here that just one GNSS station, located in the area of Mt. Olibano-Academia (named ACAE), has shown, since about 2021, an uplift deficit in comparison to other areas at the same distance from the maximum uplift of the caldera. The analysis and interpretation of this anomaly is the object of another study\u003csup\u003e47\u003c/sup\u003e and will not be further considered in the following.\u003c/p\u003e \u003cp\u003eIt is also worth noting that in the analysis we always use the absolute vertical displacement values without any correction to account for the background subsidence of the caldera\u003csup\u003e36\u003c/sup\u003e. This in order to avoid the introduction of additional assumptions and errors in the analysis. However, it is important to note that all the non-linear trends and relationships described in the following sections are not affected at all from the introduction of a linear trend describing the subsidence of the caldera.\u003c/p\u003e \u003cp\u003eRegarding the seismic count and the strain release in our analysis we mostly refer to all earthquakes recorded. For specific analyses we also consider earthquakes above a given magnitude in order to avoid potential biases due to the incompleteness of the seismic catalogs used. A more complete description of the trends of the above describe time series, \u003cem\u003eF(t)\u003c/em\u003e, are obtained by discrete computing of their annual rates \u003cem\u003eF\u0026rsquo;(t)\u003c/em\u003e, rates of change \u003cem\u003eF\u0026rsquo;\u0026rsquo;(t)\u003c/em\u003e as well as by the application of the Fourier Transform (FT) to identify the main frequencies of the time series.\u003c/p\u003e \u003cp\u003eWe base the estimate of the annual rate on left-side first-order finite differences so that the value at time \u003cem\u003et\u003c/em\u003e is not anticipating future information\u003csup\u003e39\u003c/sup\u003e. However, it should be noted that, due to considerable oscillations in the data over periods of different lengths, the finite difference approximation displays significant variations based on the chosen time step. Our analysis computes rates using time steps of 2 years, 6 months, and 1 month, thus generating average rates over moving windows of these respective durations. It's worth noting that such rates do not properly capture oscillations with periods shorter than the corresponding time step.\u003c/p\u003e \u003cp\u003eFinally, to better identify the main frequencies (and therefore the associated periods) characterizing the deformation and seismic series, a Fourier spectrum is computed for various displacement rates (vertical and horizontal and at different stations) and for the seismic count rate. However, since the annual rate \u003cem\u003eF\u0026rsquo;(t)\u003c/em\u003e displays an increasing trend (see Figs.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e3\u003c/span\u003e and \u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e4\u003c/span\u003e), we consider its rate change \u003cem\u003eF\"(t)\u003c/em\u003e which is considerably more stationary and estimate the Fourier spectrum of it\u003csup\u003e39\u003c/sup\u003e. Also in this case, given the multiple frequencies contained in the time series, we applied the FT on different periods of time and using appropriate time steps to compute the annual rates, in order to better identify the main frequencies.\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003eIn this section we present the main results of the application of the above-described methods to the datasets presented with specific focus to the period 2019-11/2023. More results are reported in the Supplementary Information (SI).\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e2\u003c/span\u003e refers to the vertical displacement of the RITE GNSS station from 2000 to 11/2023. The uplift is reported in linear scale (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e2\u003c/span\u003ea), logarithmic scale (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e2\u003c/span\u003eb) and square-root scale (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e2\u003c/span\u003ec). On the curve are reported the so-called \u0026ldquo;mini-uplifts\u0026rdquo;, the 7 periods of increased uplift occurred from 2000 to 2013\u003csup\u003e48\u003c/sup\u003e. Since the end of 2005, the trend of the RITE vertical uplift is clearly characterized by a slow acceleration. Since this time (and to 11/2023), there has been a total uplift of about 118 cm of which about 100 cm from 1/2014 and about 45 cm since 1/2021. A better appreciation of the measure of the observed acceleration can be gained from Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e2\u003c/span\u003eb which shows the uplift in log-scale. Since about 2008 to 2013, the logarithmic curve shows an increasing trend characterized by short temporary increases reflecting the above-mentioned uplifts, whereas since 2013 to 11/2023 the observed trend is again increasing but with a slower pace. It is worth highlighting that the behavior since 2013 is not linear (i.e., not corresponding to an exponential trend in absolute values) but downward convex, indicating an increasing trend less than exponential. A closer inspection of the curve shows that it could be better described by a polynomial function. In particular, the square root of the curve, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e2\u003c/span\u003ec, is linearly increasing with R-squared\u0026thinsp;=\u0026thinsp;99%, indicating a parabolic trend with acceleration of ca. 0.74 cm/yr\u003csup\u003e2\u003c/sup\u003e. Such a parabolic regression fits very well also the linear and log-scale plots as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e2\u003c/span\u003ea,b, and it is negligibly affected by the uncertainty on the data. Very similar features of the deformation trend are also observed in the vertical and horizontal displacements at the other stations, as shown in the SI material (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e2\u003c/span\u003e-SI and 3-SI), making the above considerations valid for all the points investigated.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e3\u003c/span\u003e illustrates the trends of the two main seismic variables we analyzed. In particular, Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e3\u003c/span\u003ea, and the corresponding Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e3\u003c/span\u003eb in log-scale, show the behavior of the total count of seismic events as obtained from the above-described seismic catalog (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e3\u003c/span\u003ea also shows labels marking the size of the 7 greater swarms recorded). Figure\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e3\u003c/span\u003eb shows a super-exponential behavior of the seismic count from 2006 to 11/2023, in this case corresponding to a super-exponential trend also in absolute values as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e3\u003c/span\u003ea; this is made clear by the upward convex curve in log-scale which also shows a clear increase of the exponential trend since about 2020. The super-exponential trend of seismic count is also evident in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e3\u003c/span\u003ea which shows how more than 65% of events have occurred since 1/2021. Similar super-exponential trends were obtained by using the catalog of localized events. Figure\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e4\u003c/span\u003e-SI shows the same plots by considering only the earthquakes with M\u003csub\u003ed\u003c/sub\u003e \u0026gt; 0.5, which are also characterized by a similar super-exponential trend.\u003c/p\u003e \u003cp\u003eSimilarly, Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e3\u003c/span\u003ec and \u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e3\u003c/span\u003ed show the cumulative strain release in linear and log-scale, respectively. In both plots we have labeled some of the most significant events occurred in the last years including the M\u003csub\u003ed\u003c/sub\u003e = 4.2 occurred on 9/27/2023 which represents the largest earthquake ever measured at CFc. The strain release plot in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e3\u003c/span\u003ec shows a function shape that is macroscopically quite similar to the earthquakes count, though its super-exponential trend is even more evident and gradual (see Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e3\u003c/span\u003ed vs 3b). Several strain jumps associated to the most recent earthquakes are also evident.\u003c/p\u003e \u003cp\u003eIn summary, based on the above figures and analyses, although since the end of 2005 the three variables investigated are all accelerating in time, the ground deformation is better described (particularly since 2013) by a parabolic function whereas the cumulative seismic count and strain release are better described by super-exponential trends.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e4\u003c/span\u003e we display the annual rate of deformation and seismic data from 2000 to 11/2023. The deformation rate (Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e4\u003c/span\u003ea) refers again to the vertical displacement at RITE station whereas the seismic rate (Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e4\u003c/span\u003eb) refers to the total number of earthquakes. In these plots the rates are computed by adopting a time step of 6 months to better highlight the oscillations with period longer than this time. In other words, the rates computed can be considered 6-months average rates of the investigated variables. Similar plots have been computed for time steps of 2 years and 1 month to better highlight different oscillation periods and are described in the following paragraphs and in the SI.\u003c/p\u003e \u003cp\u003eThe 6-month average rates clearly emphasize the increasing trends of the two variables and the remarkable oscillations that characterize the analyzed time series. A linear least square fit of the annual rate of uplift at RITE station (Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e4\u003c/span\u003ea) produces, from 2005 to 11/2023, a linearized rate slope, i.e. an acceleration of deformation, of about 0.7\u0026ndash;0.8 cm/yr\u003csup\u003e2\u003c/sup\u003e regardless of the time step selected for computing the derivative. This is fully consistent with the parabolic fit and the associated acceleration as reported in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eMoreover, the deformation rate trend is characterized by evident oscillations that appear to have larger amplitude since 2012. The period of these oscillations is of the order of 2.8\u0026ndash;3.5 years, with secondary maxima at fractions of the intervals\u003csup\u003e39\u003c/sup\u003e. See below for more information on this aspect, based on the FT analysis of the updated catalog. The rate value computed in 9/2023 is also the highest value so far recorded since 1984, thus surpassing the uplift rate computed during the end of 2012 crisis.\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e4\u003c/span\u003eb similarly shows the seismic count rate. The maximum rate on a 6 months average is ca. 8,000 events/year and was observed at 9/2023. These plots also show an alternation of speed-ups and slow-downs similarly to the ground displacement rate but, in this case, the overall rate trend is accelerating nonlinearly in a super-exponential form. This result was expected, given the super-exponential trend of the seismic count as observed in Figs.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e3\u003c/span\u003ea and \u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e3\u003c/span\u003eb. The three most recent peaks are particularly evident and have been observed on March-April 2021, April-May 2022 and August-October 2023, as it will be better illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e5\u003c/span\u003e illustrates the same rates shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e4\u003c/span\u003e, but now considering just the period 1/2019\u0026ndash;11/2023. The two plots well highlight the three main oscillations observed in the two time series and the almost synchronous occurrence of their peaks. Close inspection of the peaks of Dec 2019-Jan 2020, Apr-May 2021, Apr-May 2022, Aug-Oct 2023 shows the existence of a time lag of up to 45 days between the peaks of the two time rates.\u003c/p\u003e \u003cp\u003eDue to the noisy behavior of the uplift data, and therefore of the rates computed, as well as the possible occurrence of repeated peaks in the seismic rates, it was not possible to better quantify the distribution of the time lag between the two variable peaks. Such analysis would require a specific filtering of the noisy deformation data which is beyond the target of this analysis. However, the two rates allow to quantify the main \u0026ldquo;dominant\u0026rdquo; periods between peaks that result in the range between 1.0 and 1.4 years since 2019, approximately, despite shorter periods are also observed, as shown by the weaker oscillations observed in the seismic rate trend, particularly since May 2022.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eWith the aim of better representing the shorter period oscillations of the signals, Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e6\u003c/span\u003e shows the seismic count rate over different periods of time by using a time step of 1 month instead of 6-months, as assumed in Figs.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e4\u003c/span\u003e and \u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e5\u003c/span\u003e. In this case, shorter oscillations can be better highlighted and quantified. In particular, Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e6\u003c/span\u003ea shows the trend of the seismic rate over the period 1/2019-11/2023 as well as the frequent \u0026ldquo;secondary\u0026rdquo; peaks occurring every year. Since 2019, a number of peaks in the range 3\u0026ndash;5 per year are observed. A detailed histogram of the seismic event rate per day is instead shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e5\u003c/span\u003eb for the year 2023. This shows the features of the four last peaks separated to each other by two periods of approximately 4/4.5 months and one of 40 days, respectively. However, a more accurate estimation of the main periods of the observed oscillations is obtained by the FT of the seismic rate as reported in Figs.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e6\u003c/span\u003ec and \u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e6\u003c/span\u003ed. For instance, the application of the FT to the period 1/2022-11/2023 (Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e6\u003c/span\u003ed) shows that the dominant oscillation period has a duration of 4.8 months followed by a secondary period of 1.8 months.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIt is interesting to note that, as proven by the almost synchronous behavior of deformation and seismic rates (illustrated in Figs.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e4\u003c/span\u003e and \u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e5\u003c/span\u003e), the frequencies observed in the seismic rates (reported in Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e6\u003c/span\u003ec,d) are closely related to the frequencies observed in the deformation rate patterns. Figure\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e7\u003c/span\u003e shows the results of the application of the FT to the vertical uplift rate at the RITE GNSS station. In particular, Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e7\u003c/span\u003ea shows main periods of about 1.8, 2.5, 2.8 and 5.5 months as emerged from the application of the FT from 2022 to 2023 and rates computed with time step of 1 month. Similarly, Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e7\u003c/span\u003eb shows a main period of about 1.3 years computed from 2018 to 2023 with a time step of 6 months, and Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e7\u003c/span\u003ec highlights a main period of about 2.9 years computed from 2011 to 2023 with a time step of 2 years. It is also interesting to note that the durations of these main periods are about 10\u0026ndash;15% shorter that those estimated by [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e] at the same RITE station over the period 2000\u0026ndash;2020. A similar effect has been observed at all other GNSS stations and also in the seismic rate record.\u003c/p\u003e \u003cp\u003eWe note that the main periods estimated at different locations of the caldera are similar but not identical to those shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e7\u003c/span\u003e for the RITE station. In fact, the dominant peaks measured in one location are also clearly discernible as primary or secondary peaks in some of the other sites, suggesting that these differences are the results of multiple spatially irregular effects likely caused by the inhomogeneous distribution of faults/fractures and rock properties in the caldera\u003csup\u003e37,40,49,50\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe above described coupled behavior of the two geophysical variables can be better analyzed by correlating one signal to the other as done in Fig.\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e8\u003c/span\u003e. In the two plots, we illustrate the dependence of the cumulative seismic count versus the vertical uplift at the RITE GNSS station. Figure\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e8\u003c/span\u003ea and \u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e8\u003c/span\u003eb refer, respectively, to the total number of events and to the number of events with magnitude M\u003csub\u003ed\u003c/sub\u003e \u0026gt; 0.5. The red points in the plots represent the data and the year labels reported on them mark the temporal evolution of the uplift. From the data shown on both plots, it is evident how, since about 2013 up to 11/2023, they are clearly aligned along an accelerating curve. No clear trend was instead observed on the period 2000\u0026ndash;2010, part of which has been characterized by subsidence and very weak seismic activity.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe correlation between the two data is actually well fitted by using exponential functions. As shown in the SI (Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e5\u003c/span\u003e-SI), a single exponential function already represents a good approximation of the observed relationship, i.e., R-squared\u0026thinsp;\u0026gt;\u0026thinsp;99%. However, given the more accelerating behavior of the data with respect to a single exponential function, we have adopted here a fit with two exponential functions and optimized the \u0026ldquo;connecting time\u0026rdquo; between them. In Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e6\u003c/span\u003e-SI the mean square distance between data and fitting functions is reported for variable connecting times. The optimized exponential functions fit extremely well the data. It should also be noted that the two exponential functions are characterized by exponents increasing with time for both all seismic events (Fig.\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e8\u003c/span\u003ea) and events with M\u003csub\u003ed\u003c/sub\u003e \u0026gt; 0.5 (Fig.\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e8\u003c/span\u003eb). In particular, the exponents increase from 2.2 to 2.8 in Fig.\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e8\u003c/span\u003ea, and from 2.8 to 3.9 in Fig.\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e8\u003c/span\u003eb. It is interesting to note that the optimal connecting time varies from Spring 2020 (Fig.\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e8\u003c/span\u003ea) to Autumn 2022 (Fig.\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e8\u003c/span\u003eb), both close to the time the caldera uplift reached the maximum height of 1984 (i.e., Spring 2022).\u003c/p\u003e \u003cp\u003eWe proved the exponential dependency shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e8\u003c/span\u003e to be robust with respect to different assumptions made in the analysis. For instance, the same relationship was obtained, with different fitting exponents, by using: i) different values of magnitude above which seismic events have been counted (up to M\u003csub\u003ed\u003c/sub\u003e = 2.5), ii) vertical or horizontal displacement at different GNSS stations, iii) the seismic localized catalog described in Section 2.2, or iv) by considering only a seismogenic volume around the area of La Solfatara-Pisciarelli, which is the center of the activity recorded in the caldera since 2005 (see Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e7\u003c/span\u003e-SI).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eIn this section we discuss and analyze closer the strong relationships between deformation and seismicity as emerges in the period 2005-11/2023, and particularly in the period 2019-11/2023, also including a comparison with an analogous relation obtained for the 1982-84 crisis, and discuss the possible evolution of the current bradyseismic crisis under the hypothesis that the caldera will continue to inflate and behave according to the same trends.\u003c/p\u003e \u003cp\u003eFigures \u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e4\u003c/span\u003e and \u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e5\u003c/span\u003e clearly show the coupled behavior of deformation and seismic activity at the different time scales. This coupling is well evident both in the long term (i.e., at the decadal scale) as well as in the short/medium terms (i.e., at the week/month/year scales). At the decadal scale, the accelerating deformation of the system, since 2010 well approximated by a parabolic function, is paired with a super-exponential acceleration of the seismic count (either total or above a given magnitude). The reasons for the quasi-parabolic increase of the uplift are beyond the objectives of this manuscript and the analyses here developed. However, the understanding of the cause of this accelerating process is an interesting future goal and questions on the possibility that the driver of the uplift is itself an accelerating cumulative process, such as, for instance the injection of gas or magma in the upper crust from a deeper source. At the shorter time scales, any temporary increase of the deformation rate is closely mirrored, with an apparent time lag up to 30\u0026ndash;45 days, in an analogous increase of the seismic rate, with an amplification effect with time clearly visible since 2021 and even more since the beginning of 2023. Such a time gap between the two variables should be also further investigated possibly extending the analysis to shorter time scales (up to days) and to the consideration of the spatial distribution of faults/fractures and the structural features of the caldera.\u003c/p\u003e \u003cp\u003eSuch a strong dependence between deformation and seismic activity is well described by the relationship between vertical uplift of the caldera (here represented through the RITE station) and the cumulative number of earthquakes, total or above a given magnitude. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e8\u003c/span\u003e, such relationship can be well represented by two exponential functions, with exponents increasing in time. Such a dependency resembles the well-known behavior of quasi-elastic inhomogeneous materials and rocks under an increasing differential stress, either compressive or tensile, at both low- and high-pressure conditions\u003csup\u003e35,38,51\u0026ndash;54\u003c/sup\u003e. Patterns of fracturing of brittle rocks in laboratory clearly show that at low stresses fracturing activity is null or very low and the behavior is close to elastic, i.e., there is a quasi-linear relation between stress and strain. At stresses of about half of the values at bulk failure the fracturing activity begins to increase in an exponential way until the strain has typically reached about 90\u0026ndash;95% of the failure value. Under such conditions the stress increases in a non-linear way with respect to strain, producing a curve strain-stress that is downward convex. This condition of the material is also characterized by dilatancy, i.e., an increase of the volume due to a quasi-homogeneous formation of small cracks within the rocks. At larger increasing stresses, the fracturing activity typically accelerates very quickly producing the coalescence of fractures in a major fault and eventually leading to bulk failure of the brittle rock. For specific properties of the rock a variety of strain-hardening or strain-softening type behaviors of the material can also be observed before failure. Eventually, when the amount of stress has reached its maximum value, most of the supplied energy is spent in fracture and fault movements and the behavior of the rock becomes inelastic, i.e., the deformation continues under a constant stress. This regime is typically characterized by a proportional increase of seismic events with deformation.\u003c/p\u003e \u003cp\u003eIt is important to observe that the nature of the exponential relationship between strain and cumulative seismic count depends on the mechanical properties of the crustal rocks\u003csup\u003e52,54\u003c/sup\u003e. These in turn depend on lithology as well as on the local conditions at depth such as pressure, temperature, water content as well as on other rock properties such as porosity, compaction and alteration of components and minerals. The underground distribution of these properties and conditions are largely unknown for the crust of CFc although several mechanical properties data exist based on measurements on core samples and outcrops\u003csup\u003e55,56\u003c/sup\u003e. Data overall show an elastic-brittle behavior of the CFc rocks although remarkable variations of key properties, such as elastic modulus and Poisson ratio, were measured as a function of porosity, temperature and water saturation conditions. It is therefore important to underline that the empirical relationship between deformation and seismic activity as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e8\u003c/span\u003e, and here interpreted as a progressive evolution of the quasi-elastic response of the shallow crust to an increase of stress, should be simply considered as an empirical relation valid for the superficial crust as a whole, i.e. assuming the crustal rocks as a single inhomogeneous medium with a mean elastic-brittle behavior. It should be noted that this relationship also potentially depends on additional processes which are not considered herein and that likely contribute to the deformation observed such as pore-pressure and thermal effects associated with the presence of fluids of magmatic, hydrothermal and exogenous origin in the rock matrix\u003csup\u003e31,32,57\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe interpreted quasi-elastic behavior of the superficial crust appears, however, largely consistent with previous analyses and interpretations of the ongoing unrest\u003csup\u003e26,34\u0026ndash;36,40\u003c/sup\u003e. According to them, the presence of low permeability levels at depths ranging between 1.5 and 3 km could favor the pressurization of the underlying layers due to the accumulation of magmatic gasses, fluids or magma rising from deeper regions. Detailed analyses of the distribution and mechanisms of the ongoing local seismicity also appear to be consistent with a stress concentration caused by the uplift of the central part of the caldera as well as with a possible effect of fluid-driven pore-pressure increase at the reactivated faults involved\u003csup\u003e18,40,41\u003c/sup\u003e. Similarly, the existence of the observed oscillations with variable periods in the geophysical trends investigated could be interpreted as a result of the unsteady fracturing of the crust under the increasing stress due to the pressurization generated by the arrival of deep fluids or magma batches and their complex interplay with the superficial hydrothermal system\u003csup\u003e20,26,31,32,54\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eNevertheless, a significant difference between the analysis here presented and that of [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e] is the fact that, based on the relation between deformation and number of earthquakes, the latter study claims the reaching of the inelastic regime of the CFc crust since May 2020 (and up to June 2021, corresponding to the end of the period analyzed), due to the establishment of a linear relationship between the two geophysical variables. We hypothesize here that such inconsistency is due to the different time period (about 2.5 years shorter than that analyzed here) over which the two analyses have been made. As a consequence, the present study, although generally consistent with the main conclusion of [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e] which suggests a progressive weakening of the mechanical properties of the shallow crust of CFc, gives evidence of a stronger sensitivity of the seismic activity on the uplift of the caldera, as will be better described and quantified later on in this section. It is worth underlining that this results is independent from the existing interpretations in terms of rheological behavior of the shallow crust.\u003c/p\u003e \u003cp\u003eTo gain further insights on the recent dynamics of the caldera, the relationship between deformation and seismic count for the unrest crisis of 1982-84 was also analyzed. This is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig18\" class=\"InternalRef\"\u003e9\u003c/span\u003e. Figure\u0026nbsp;\u003cspan refid=\"Fig18\" class=\"InternalRef\"\u003e9\u003c/span\u003ea shows the cumulative total number of earthquakes versus the ground uplift as measured at Benchmark 25A of the leveling network (close to Pozzuoli, see Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e1\u003c/span\u003e-SI), whereas Fig.\u0026nbsp;\u003cspan refid=\"Fig18\" class=\"InternalRef\"\u003e9\u003c/span\u003eb shows the same relationship by considering only earthquakes with M\u003csub\u003ed\u003c/sub\u003e \u0026gt; 0.5 and the vertical uplift as measured by the tide-gauge at the Pozzuoli harbor (close to the center of the CFc, see again Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e1\u003c/span\u003e-SI). Despite the lower quality and amount of data recorded during this past crisis with respect to the current one, in both plots the correlation between the two geophysical variables results quasi-linear, R-squared\u0026thinsp;\u0026gt;\u0026thinsp;99%, and not exponential. The same relation was obtained by considering different thresholds of magnitude. This is also different from the results of [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e] who estimated an exponential trend over the period 1982-84 by apparently using a lower number of data points.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe interpretation of such different deformation-number of earthquakes relationship with respect to the current crisis (see Fig.\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e8\u003c/span\u003e) is not trivial or obvious. However, as mentioned above, a quasi-linear relation between deformation and seismic count is typically indicative of an inelastic mechanical behavior of rocks in which most of deformation is accommodated by the propagation and slip of existing fractures and faults. This process appears consistent with most interpretations of the 1982-84 crisis as caused by an intrusion of magma with the formation of a thin sill at about 3\u0026ndash;4 km depth\u003csup\u003e14,22\u0026ndash;25\u003c/sup\u003e. We also note that the 1982-84 crisis occurred on a time period much shorter and therefore with deformation and seismic rates about one order of magnitude larger than those characterizing the present crisis. Such a different relationship between deformation and seismic activity appears as further evidence of the different forcing source and/or mechanism associated to the 1982-84 crisis with respect to the present one.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFinally, the ongoing trends of deformation and seismic activity, and particularly their so far robust, empirical exponential relationship as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e8\u003c/span\u003e, can also be used to gain some insights on the potential evolution of the bradyseismic crisis in case of a further uplift of the caldera with the same trends. From Fig.\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e8\u003c/span\u003e it is evident how such exponential relationship takes into account and explains the progressively intensifying seismic activity recorded in the last few years due to the continuous, although oscillating, increase of the caldera uplift. Similarly, under the assumption that the same trend of uplift will continue in the future, we could expect a corresponding exponential increase of the number of earthquakes. According to Fig.\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e8\u003c/span\u003eb, in particular, it emerges that, for instance, a further uplift increase of just 20 cm (i.e., from 1.2 to 1.4 m at the RITE GNSS station) could generate, with the current exponential relationship, a number of M\u003csub\u003ed\u003c/sub\u003e \u0026gt; 0.5 events larger than that recorded since 2000 (i.e., about 2,000 more events vs the about 1,800 recorded since year 2000, see dashed portion of the exponential curve of Fig.\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e8\u003c/span\u003eb). A similar consideration can approximately be done also for the total number of earthquakes as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e8\u003c/span\u003ea.\u003c/p\u003e \u003cp\u003eBased on the analysis of the distribution of the number of earthquakes as a function of the magnitude M\u003csub\u003ed\u003c/sub\u003e, it is also possible to define the best fitting parameters of the exponential law (Gutenberg-Richter) describing this distribution. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e8\u003c/span\u003e-SI, the fitting of the distribution is very good (R-squared\u0026thinsp;\u0026gt;\u0026thinsp;99%) and the corresponding \u003cem\u003eb\u003c/em\u003e-value over the investigated 2000\u0026ndash;2023 period is equal to 0.87, by assuming a M\u003csub\u003ec\u003c/sub\u003e equal to 0.5 (a very similar value was obtained with M\u003csub\u003ec\u003c/sub\u003e=0.2 but given the discretization of the earthquake magnitude a value of M\u003csub\u003ec\u003c/sub\u003e=0.5 was preferred). A slightly lower \u003cem\u003eb\u003c/em\u003e-value of 0.83 is obtained for the most recent period 2021\u0026ndash;2023, whereas, over the period 2007\u0026ndash;2020, we obtained a value of 0.95, equal to that obtained by [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e] with a different approach over the same period. We note also that our estimates of the \u003cem\u003eb\u003c/em\u003e-value are ca. 5\u0026ndash;10% lower than those obtained by previous studies over different previous periods\u003csup\u003e19,45,58\u003c/sup\u003e evidencing a progressive decrease with time. This is also consistent with recent estimates of the \u003cem\u003eb\u003c/em\u003e-value of the different volumes of the caldera showing a close relationship between this parameter and the physical and mechanical properties of the rocks and indicating lower \u003cem\u003eb\u003c/em\u003e-values just at depths of 2.5-3 km where a caprock with brittle-fragile behavior is located\u003csup\u003e59\u003c/sup\u003e. All this represents further evidence of the overall progressive stress increase and medium weakening of the shallow crust of CFc as clearly observed in many experimental and volcanic systems\u003csup\u003e19,54,60\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eBased on the above-described law of magnitude distribution and the expected number of events of magnitude M\u003csub\u003ed\u003c/sub\u003e \u0026gt; 0.5 as a function of the ground deformation reached by the caldera, it is also possible to estimate the probability of occurrence of an earthquake above a given magnitude associated to a given future uplift of the caldera. Here we just mention that, based on the above-described data and hypotheses, just a further modest uplift of about 20 cm would be associated with a significant number of expected earthquakes with potential impact in the CFc area. Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e-SI details the expected number of earthquakes above various magnitudes in a population of 2,000 events with M\u003csub\u003ed\u003c/sub\u003e \u0026gt; 0.5 (corresponding to a further uplift of about 20 cm), as a function of the \u003cem\u003eb-\u003c/em\u003evalue and its associated uncertainty. For instance, by using a \u003cem\u003eb-\u003c/em\u003evalue equal to 0.87, the magnitude-frequency law would expect 0.82 events with M\u003csub\u003ed\u003c/sub\u003e \u0026ge; 4.5 on average, and 0.30 events with M\u003csub\u003ed\u003c/sub\u003e \u0026ge; 5, simply by applying the above-described statistical basis. A \u003cem\u003eb\u003c/em\u003e-value equal to 0.83 would produce an increase of ca. 50% expected large events, whereas a \u003cem\u003eb\u003c/em\u003e-value equal to 0.95, a decrease of 50% (see Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e-SI). These estimates, although based on an extrapolation of the reconstructed distribution of magnitudes to values larger than those so far observed, are qualitatively consistent with analyses of potential seismic activity at CFc based on different data and hypotheses\u003csup\u003e40,61\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eIt should be noted, however, that due to the above-described oscillations in time of the rate of deformation, it is not possible to precisely forecast the expected seismic activity as a function of time. For instance, by hypothesizing future deformation rates in the range of values recorded in the last 6 months or 1 year, short-time forecasts of seismic activity, e.g. on a monthly basis, are affected by an uncertainty significantly larger than that associated with medium- and long-term forecasts which are able to filter out oscillations with shorter periods.\u003c/p\u003e \u003cp\u003eNevertheless, the above-described super-exponential decadal trend of seismic activity, also given the time-increasing exponents describing the relationship between deformation and seismic count (see Fig.\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e8\u003c/span\u003e), remains suited to be investigated through a probabilistic application of the Failure Forecast Method (FFM), similarly to what done by [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e] for the period 2000\u0026ndash;2020, in order to explore the time scale of the evolution of the crisis in case of continuation of the observed trends.\u003c/p\u003e \u003cp\u003eIn particular, in this new application of FFM the exponent alpha of the seismic rate has been varied between 1.2 and 2\u003csup\u003e39,62\u003c/sup\u003e. The application of the method to the new datasets confirms the main outcomes of the previous analysis providing median values of the waiting times (i.e. the time to be waited to reach the critical time computed since 12/2023) from 0.5 to about 2.5 years with 95%ile values up to about 8 years (see Fig.\u0026nbsp;\u003cspan refid=\"Fig18\" class=\"InternalRef\"\u003e9\u003c/span\u003e-SI for more details). It is worth noting that these estimates are remarkably dependent on the period of time used in the regression of the inverse rates, in this case we tested 3 and 10 years. As a consequence, these estimates cannot be considered reliable forecasts of the occurrence of specific volcanic events given the large number of false alarms typically experienced in the application of FFM to real crises. Nevertheless, the analysis is of some interest since it indicates, over the parameter space explored, a relatively fast evolution of the crisis (up to few years as median values) in case of continuation of the observed trends.\u003c/p\u003e \u003cp\u003eThe bradyseismic scenario above described represents the simple temporal extension of the trends currently observed. Nevertheless, it is uncertain and it represents just one of the plausible evolutions of the ongoing bradyseismic crisis. Based on observation of similar unrest crises at other calderas\u003csup\u003e35,63\u003c/sup\u003e, the interpreted quasi-elastic behavior of the shallow crust could be interrupted at any time, either by evolving into an inelastic regime of the crust or simply due to the occurrence of superficial magmatic intrusions or events, such as phreatic explosions, triggered by some of the complex, and still largely unknown, processes governing the magmatic and hydrothermal systems of CFc\u003csup\u003e36,37,64\u003c/sup\u003e. Similarly, the caldera uplift could, abruptly or more slowly, stop, the seismic activity decrease and the caldera enter into a new period of subsidence\u003csup\u003e36\u003c/sup\u003e. Unfortunately, based on our present understanding, the future evolution of the system is largely controlled by the internal dynamics of the volcanic system of CFc that, at this time, we are unable to observe and forecast accurately.\u003c/p\u003e"},{"header":"Conclusions","content":"\u003cp\u003eGround deformation and seismic activity are two of the most effective data to understand and monitor volcanic activity. This is because, differently from other variables such as temperature or concentration of gasses, the elastic effects of physical and chemical changes in the underground system are almost instantaneously transmitted to the surface. Their close inspection and analysis are therefore useful for monitoring the volcanic system and to better understand its current state\u003csup\u003e65\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eBased on close inspection and quantitative analyses of deformation and seismic data of CFc and of their relationships, in the period 2000-11/2023 and particularly since 2019, the followings are the main conclusions and insights provided by the study:\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe temporal evolution of vertical and horizontal deformation (the latter analyzed at several stations within the caldera), number of earthquakes and strain release, continues to be characterized by a decadal-scale trend overlaid with oscillations of varying frequencies. On the decadal scale, deformation rates exhibit an approximately linear growth, i.e., deformation follows a parabolic trend with average acceleration of ca. 0.7\u0026ndash;0.8 cm/yr\u003csup\u003e2\u003c/sup\u003e for the vertical uplift at RITE GNSS station, while earthquake occurrence rates increase with a super-exponential trend, similarly to the number of earthquakes. Understanding the cause of such parabolic increase of uplift represents certainly a challenging goal for future investigations and it questions the possibility, among several others, that the driver of the uplift would be itself an accelerating process.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eOscillations of various periods are recognizable in both deformation and seismic data. The oscillations of these two parameters appear closely correlated in time, with a variable time delay up to 45 days of seismic activity relative to deformation. Further investigations should be carried out to better quantify this time lag even on shorter time scales. The main periods of these oscillations range from approximately 2 and 5 months (shorter periods) to periods of about 1.5 and 3 years (longer periods). In recent years, there has been a trend towards a reduction in these periods (by about 10\u0026ndash;15%, see [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e] for previous estimates). Periods of acceleration and deceleration in geophysical data are therefore characteristic of the dynamics of the recent CFc bradyseism. The current period (December 2023-January 2024 at the time of writing) of reduced seismic activity is not, therefore, necessarily indicative of a major change in the future evolution of the ongoing phenomenon.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe relationship between the number of earthquakes and vertical uplift results to be well-represented, since about 2010, by two exponential functions with increasing exponents in time and a transition period between 4/2020 and 9/2022. Such relationship well represents and explains the increasing intensity of seismic activity (number of earthquakes per year) over time, particularly since the beginning of 2020. Such a behavior is different from the linear relationship between these two variables previously suggested [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e] and it is interpreted here in terms of progressive evolution of the quasi-elastic behavior of the shallow crust of CFc. Most importantly, such a relationship, which is independent from the interpretations provided, gives evidence of the increasing sensitivity of seismic activity on the inflation of the caldera. This exponential-type relationship is also different from the linear-type relationships derived for the 1982-84 crisis suggesting that the two crises are characterized by different forcing sources and/or mechanisms.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eUnder the hypothesis that the observed decadal trends persist and the aforementioned relationship between uplift and cumulative number of earthquakes remains valid, a further uplift of the ground could likely be associated with new intense seismic activity, likely at rates even higher than those recorded in 2023. In particular, by assuming just a further uplift of the caldera of 20 cm the magnitude-frequency law would forecast a significant probability of earthquakes with magnitude higher than 4.5. This possibility requires a proper consideration of the seismic hazard and risk in case of continuation of the crisis. Of course, such a scenario is just one of the plausible evolutions of the volcanic system.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eThese insights emphasize the importance of closely monitoring and analyzing the dynamic interplay between deformation and seismic events in the context of the CFc bradyseism to further improve our understanding and forecasting capability of this complex phenomenon.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe seismic catalogs\u003csup\u003e18\u003c/sup\u003e\u003csup\u003e\u0026nbsp;\u003c/sup\u003eof CFc are available from the INGV\u0026mdash;Osservatorio Vesuviano website at the links:\u0026nbsp;https://doi.org/10.13127/ovcatalogsth_2000_2021\u0026nbsp;and\u0026nbsp;https://terremoti.ov.ingv.it/gossip/flegrei. The geodetic GNSS dataset\u003csup\u003e17\u003c/sup\u003e of CFc is available from https://zenodo.org/record/6389920#.ZD0GCnbMJD8. Just for the sake of completeness, the two main seismic and geodetic datasets analyzed in the paper are also attached as text files in the supplementary information.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis research was partially funded by the Dipartimento della Protezione Civile (Italy), as part of the INGV-DPC contract B2 2019-2021 and contract A 2022-2024. However, the study does not necessarily represent the official views and policies of the Dipartimento della Protezione Civile (Italy). Preliminary results of this work have been presented during meetings of the Commissione Grandi Rischi, Dipartimento della Protezione Civile (Italy), held in Autumn 2023 and concerning the Campi Flegrei caldera unrest. The authors thank the Committee members for providing useful feedbacks and insights.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eA.B. and A.N. conceived the main conceptual ideas, scientific objectives and methods. A.B. implemented the codes and performed the statistical analysis. A.N. supervised the analysis and wrote the manuscript, A.B. produced the figures and table. P.D.M, F.G., G.M. and P.R. contributed to the development of the scientific objectives and provided and cured the GNSS and seismic records. All authors discussed the results, provided critical feedback and interpretation of findings, commented on the manuscript and gave final approval for publication.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAdditional information\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe online version contains supplementary material in the form of a pdf file with supporting figures and tables discussed in the main text, and two text files with the main deformation and seismic data analyzed in the study.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eRosi, M., \u0026amp; Sbrana, A.. Phlegrean Fields. Quaderni de la ricerca scientifica, 9(114), (1987).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eOrsi, G. Volcanic and deformation history of the Campi Flegrei Volcanic Field, Italy. In \u0026ldquo;Campi Flegrei: a restless caldera in a densely populated area\u0026rdquo;, Book Series:Active Volcanoes of the World, Chap. 1, Springer (2022).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eOrsi G., Di Vito M.A. \u0026amp; Isaia R. Volcanic hazard assessment at the restless Campi Flegrei caldera. Bull Volcanol 66:514\u0026ndash;530. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s00445-003-0336-4\u003c/span\u003e\u003cspan address=\"10.1007/s00445-003-0336-4\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e, (2004).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBevilacqua, A., Flandoli, F., Neri, A., Isaia, R. \u0026amp; Vitale, S. Temporal models for the episodic volcanism of Campi Flegrei caldera (Italy) with uncertainty quantification. J. Geophys. Res. Solid Earth 121, 7821\u0026ndash;7845. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1002/2016J B0131\u003c/span\u003e\u003cspan address=\"10.1002/2016J B0131\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e 71 (2016).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBevilacqua, A. Macedonio, G., Neri, A., Orsi, G. \u0026amp; Petrosino, P. Volcanic hazard assessment at the Campi Flegrei caldera (Italy), Ch. 12 in Campi Flegrei: A restless caldera in a densely populated area, (Eds Orsi, G., Civetta, L. \u0026amp; D\u0026rsquo;Antonio, M.) Active Volcanoes of the World, Springer, \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/978-3-642-37060-1_12\u003c/span\u003e\u003cspan address=\"10.1007/978-3-642-37060-1_12\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2022a).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDi Vito, M. et al. Magma transfer at Campi Flegrei caldera (Italy) before the 1538 AD eruption. Sci. Rep. 6, 32245. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/srep32245\u003c/span\u003e\u003cspan address=\"10.1038/srep32245\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2016).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCorrado, G., Guerra, I., Lo Bascio, A., Luongo, G. \u0026amp; Rampoldi, R. Inflation and microearthquake activity of Phlegraean Fields, Italy. Bull. Volcanol. 40, 169\u0026ndash;188. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/BF02596998\u003c/span\u003e\u003cspan address=\"10.1007/BF02596998\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (1977).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBianchi, R. et al. Modeling of surface deformation in volcanic areas: The 1970\u0026ndash;1972 and 1982\u0026ndash;1984 crises of Campi Flegrei, Italy. J. Geophys. Res. 92(B13), 14139\u0026ndash;14150. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1029/JB092iB13p14139\u003c/span\u003e\u003cspan address=\"10.1029/JB092iB13p14139\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (1987).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBerrino, G. et al. Ground deformation and gravity changes accompanying the 1982 Pozzuoli uplift. Bull. Volcanol. 47, 187\u0026ndash;200. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/BF01961548\u003c/span\u003e\u003cspan address=\"10.1007/BF01961548\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (1984).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eOrsi, G. et al. Short-term ground deformations and seismicity in the nested Campi Flegrei caldera (Italy): An example of active block-resurgence in a densely populated area. J. Volcanol. Geotherm. Res. 91, 415\u0026ndash;451 (1999).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eScarpa, R. et al. Historic unrest of the Campi Flegrei Caldera, Italy. In Ch. 10 Campi Flegrei: A restless caldera in a densely populated area, Active Volcanoes of the World (eds Orsi, G. et al.), Springer, Cham (2022).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDel Gaudio, C., Aquino, I., Ricciardi, G. P., Ricco, C. \u0026amp; Scandone, R. Unrest episodes at Campi Flegrei: A reconstruction of vertical ground movements during 1905\u0026ndash;2009. J. Volcanol. Geotherm. Res. 195, 48\u0026ndash;56. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.jvolgeores.2010.05.014\u003c/span\u003e\u003cspan address=\"10.1016/j.jvolgeores.2010.05.014\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2010).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBarberi, F., Corrado, G., Innocenti, F. \u0026amp; Luongo, G. Phlegraean Fields 1982\u0026ndash;1984: Brief chronicle of a volcano emergency in a densely populated area. Bull. Volcanol. 47, 175\u0026ndash;185. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/BF01961547\u003c/span\u003e\u003cspan address=\"10.1007/BF01961547\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (1984).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDe Natale, G. \u0026amp; Zollo, A. Statistical analysis and clustering features of the Phlegrean Fields earthquake sequence (May 1983-May 1984). Bull. Seism. Soc. Am. 76(3), 801\u0026ndash;814 (1986).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eINGV-OV, Campi Flegrei \u0026ndash; Bollettino mensile, novembre 2023, Osservatorio Vesuviano, INGV, \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.ov.ingv.it/index.php/monitoraggio-e-infrastrutture/bollettini-tutti/mensili-dei-vulcani-della-campania/flegrei/anno-2023-1\u003c/span\u003e\u003cspan address=\"https://www.ov.ingv.it/index.php/monitoraggio-e-infrastrutture/bollettini-tutti/mensili-dei-vulcani-della-campania/flegrei/anno-2023-1\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2023).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDe Martino, P., Dolce, M., Brandi, G., Scarpato, G. \u0026amp; Tammaro, U. The ground deformation history of the Neapolitan volcanic area (Campi Flegrei caldera, Somma-Vesuvius volcano, and Ischia island) from 20 years of continuous GPS observations (2000\u0026ndash;2019). Remote Sens. 13, 2725. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3390/rs131 42725\u003c/span\u003e\u003cspan address=\"10.3390/rs131 42725\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2021).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRicciolino, P. \u0026amp; Lo Bascio, D. Cataloghi sismici dei vulcani campani. Stazione STH Campi Flegrei dal 2000 al 2021 (Cat-STH_2000_2021) (1.0) Data set. Istituto Nazionale di Geofisica e Vulcanologia (2021). Doi: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.13127/ovcatalogsth_2000_2021\u003c/span\u003e\u003cspan address=\"10.13127/ovcatalogsth_2000_2021\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGiudicepietro, F. et al. Tracking episodes of seismicity and gas transport in Campi Flegrei caldera through seismic, geophysical, and geochemical measurements. Seismol. Res. Lett.; 92 (2A): 965\u0026ndash;975. doi: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1785/0220200223\u003c/span\u003e\u003cspan address=\"10.1785/0220200223\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2020).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTramelli, A. et al. Statistics of seismicity to investigate the Campi Flegrei caldera unrest. Sci. Rep. 11, 7211. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/s41598-021-86506-6\u003c/span\u003e\u003cspan address=\"10.1038/s41598-021-86506-6\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2021).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChiodini, G., Caliro, S., Avino, R., Bini, G., Giudicepietro, F., Cesare, W.D., Ricciolino, P., Aiuppa, A., Cardellini, C., Petrillo, Z., Selva, J., Siniscalchi, A., Tripaldi, S.. Hydrothermal pressure-temperature control on CO2 emissions and seismicity at Campi Flegrei (Italy). J. Volcanol. Geoth. Res. 107245 https://doi.org/10.1016/j. jvolgeores.2021.107245 (2021).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDvorak, J.J. \u0026amp; Berrino, G. Recent ground movement and seismic activity in Campi Flegrei, southern Italy: episodic growth of a resurgent dome. J. Geophys. Res. Solid Earth 96, 2309\u0026ndash;2323. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1029/90jb02225\u003c/span\u003e\u003cspan address=\"10.1029/90jb02225\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e, (1991).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWoo, J.Y.L. \u0026amp; Kilburn, C.R.J.. Intrusion and deformation at Campi Flegrei, southern Italy: sills, dikes, and regional extension. J. Geophys. Res. Solid Earth 115. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1029/2009jb006913\u003c/span\u003e\u003cspan address=\"10.1029/2009jb006913\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e, 1978 2012, (2010).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMacedonio, G., Giudicepietro, F., D\u0026rsquo;Auria, L., Martini. Sill intrusion as a source mechanism of unrest at volcanic calderas. J. Geophys. Res.: Solid Earth 119, 3986\u0026ndash;4000. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1002/2013jb010868\u003c/span\u003e\u003cspan address=\"10.1002/2013jb010868\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e, (2014).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGiudicepietro, F., Macedonio, G. \u0026amp; Martini, M. A physical model of sill expansion to explain the dynamics of unrest at calderas with application to Campi Flegrei. Front. Earth Sci. 5, 54\u0026ndash;65. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3389/feart\u003c/span\u003e\u003cspan address=\"10.3389/feart\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e. 2017. 00054, (2017).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTroise, C., De Natale, G., Schiavone, R., Somma, R., \u0026amp; Moretti, R. The Campi Flegrei caldera unrest: Discriminating magma intrusions from hydrothermal effects and implications for possible evolution. Earth-Science Reviews 188, 108\u0026ndash;122. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.earscirev.2018.11.007\u003c/span\u003e\u003cspan address=\"10.1016/j.earscirev.2018.11.007\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e, (2019).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGiacomuzzi, G. et al. Tracking transient changes in the plumbing system at Campi Flegrei Caldera. Earth Planet. Sci. Lett. 637, 118744 \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.epsl.2024.118744\u003c/span\u003e\u003cspan address=\"10.1016/j.epsl.2024.118744\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBonafede M. Hot fluid migration; an efficient source of ground deformation; application to the 1982\u0026ndash;1985 crisis at Campi Flegrei-Italy. Journal of Volcanology and Geothermal Research, 48, 187\u0026ndash;198, (1991).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTroiano, A., Di Giuseppe, M. G., Petrillo, Z., Troise, C. \u0026amp; De Natale, G. Ground deformation at calderas driven by fluid injection: modeling unrest episodes at Campi Flegrei (Italy). Geophys. J. Int. 187, 833\u0026ndash;847 (2011).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChiodini, G. et al. Evidence of thermal-driven processes triggering the 2005\u0026ndash;2014 unrest at Campi Flegrei caldera. Earth Planet Sci. Lett. 414, 58\u0026ndash;67. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.epsl.2015.01.012\u003c/span\u003e\u003cspan address=\"10.1016/j.epsl.2015.01.012\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2015).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMoretti, R., De Natale, G. \u0026amp; Troise, C. A geochemical and geophysical reappraisal to the significance of the recent unrest at Campi Flegrei caldera (Southern Italy). Geochem. Geophys. Geosyst. 18, 1244\u0026ndash;1269. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1002/2016G\u003c/span\u003e\u003cspan address=\"10.1002/2016G\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e C0065 69, (2017).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTodesco, M. (2021). Caldera\u0026rsquo;s breathing: poroelastic ground deformation at Campi Flegrei (Italy). Frontiers in Earth Science 9, 702665. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3389/feart.2021.702665\u003c/span\u003e\u003cspan address=\"10.3389/feart.2021.702665\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNespoli, M., Tramelli, A., Belardinelli, M. E., \u0026amp; Bonafede, M. The effects of hot and pressurized fluid flow across a brittle layer on the recent seismicity and deformation in the Campi Flegrei caldera (Italy). Journal of Volcanology and Geothermal Research, 443, 107930 (2023).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAmoruso, A., Crescentini, L. \u0026amp; Sabbetta, I. Paired deformation sources of the Campi Flegrei caldera (Italy) required by recent (1980\u0026ndash;2010) deformation history. J. Geophys. Res. Solid Earth 119, 858\u0026ndash;879. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1002/2013JB010392\u003c/span\u003e\u003cspan address=\"10.1002/2013JB010392\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2014).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBuono, G. et al. New insights into the recent magma dynamics under Campi Flegrei caldera (Italy) from petrological and geochemical evidence. J. Geophys. Res. Solid Earth \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1029/2021J B0237\u003c/span\u003e\u003cspan address=\"10.1029/2021J B0237\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e 73 (2022).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKilburn, C.R.J., De Natale, G. \u0026amp; Carlino, S. Progressive approach to eruption at Campi Flegrei caldera in southern Italy. Nat. Commun. 8, 15312. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/ncomms15312\u003c/span\u003e\u003cspan address=\"10.1038/ncomms15312\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2017).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKilburn, C.R.J., Carlino, S., Danesi, S. \u0026amp; Pino, N.A. (2023). Potential for rupture before eruption at Campi Flegrei caldera, Southern Italy. Commun. Earth \u0026amp; Environment 4:190, \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/s43247-023-00842-1\u003c/span\u003e\u003cspan address=\"10.1038/s43247-023-00842-1\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDanesi, S., Pino N.A., Carlino S., Kilburn C.R.J., Evolution in unrest processes at Campi Flegrei caldera as inferred from local seismicity. Earth Planet. Sci. Lett., 626 (2024) 118530, \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.epsl.2023.118530\u003c/span\u003e\u003cspan address=\"10.1016/j.epsl.2023.118530\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKilburn, C.R.J. Precursory deformation and fracture before brittle rock failure and potential application to volcanic unrest. J. Geophys. Res. Solid Earth 117, B02211. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1029/2011JB008703\u003c/span\u003e\u003cspan address=\"10.1029/2011JB008703\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2012).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBevilacqua, A. et al. Data analysis of the unsteadily accelerating GPS and seismic records at Campi Flegrei caldera from 2000 to 2020, Sci. Rep. 12:19175, \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/s41598-022-23628-5\u003c/span\u003e\u003cspan address=\"10.1038/s41598-022-23628-5\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2022b).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eScotto di Uccio, F., et al. Delineation and fine-scale structure of active fault zones during the 2014\u0026ndash;2023 unrest at the Campi Flegrei Caldera (Southern Italy) from high-precision earthquake locations, ESS Open Archive, doi: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.22541/essoar.170224505.51315564/v1\u003c/span\u003e\u003cspan address=\"10.22541/essoar.170224505.51315564/v1\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2023).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTramelli, A. et al. The seismicity of Campi Flegrei in the contest of an evolving long-term unrest. Sci. Rep. 12, 2900. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/s41598-022-06928-8\u003c/span\u003e\u003cspan address=\"10.1038/s41598-022-06928-8\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2022).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDe Martino, P. et al. Four years of continuous seafloor displacement measurements in the Campi Flegrei caldera. Front. Earth Sci. 8, 615178. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3389/feart.2020.615178\u003c/span\u003e\u003cspan address=\"10.3389/feart.2020.615178\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2020).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBevilacqua, A. et al. Radial interpolation of GPS and leveling data of ground deformation in a resurgent caldera: application to Campi Flegrei (Italy). J. Geod. 94(2), 24. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1007/s00190-020-01355-x\u003c/span\u003e\u003cspan address=\"10.1007/s00190-020-01355-x\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2020).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eIannaccone, G. et al. Measurements of seafloor deformation in the marine sector of the Campi Flegrei caldera (Italy). J. Geophys. Res., 123, 66\u0026ndash;83. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1002/2017JB014852\u003c/span\u003e\u003cspan address=\"10.1002/2017JB014852\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGiudicepietro, F. et al. Campi Flegrei, Vesuvius and Ischia Seismicity in the context of the Neapolitan volcanic area. Front. Earth. Sci. 9, 662113. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3389/feart.2021.662113\u003c/span\u003e\u003cspan address=\"10.3389/feart.2021.662113\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2021).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChiodini, G. et al. Clues on the origin of post-2000 earthquakes at Campi Flegrei caldera (Italy). Sci. Rep. 4472, 2045\u0026ndash;2322. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/s41598-017-04845-9\u003c/span\u003e\u003cspan address=\"10.1038/s41598-017-04845-9\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2017).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGiudicepietro, F., et al. First evidence of a geodetic anomaly in the Campi Flegrei caldera (Italy) ground deformation pattern revealed by DInSAR and GNSS measurements during the 2021\u0026ndash;2023 escalating unrest phase. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://dx.doi.org/10.2139/ssrn.4791859\u003c/span\u003e\u003cspan address=\"10.2139/ssrn.4791859\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDe Martino, P., Tammaro, U. \u0026amp; Obrizzo, F. GPS time series at Campi Flegrei caldera (2000\u0026ndash;2013). Ann. Geophys. 57(2), S0213. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.4401/ag-6431\u003c/span\u003e\u003cspan address=\"10.4401/ag-6431\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2014).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eVitale, S. \u0026amp; R. Isaia. Fractures and faults in volcanic rocks (Campi Flegrei, Southern Italy): Insights into volcano-tectonic processes, Int. J. Earth. Sci., 103, 801\u0026ndash;819, \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi:10.1007/s00531-013-0979-0\u003c/span\u003e\u003cspan address=\"https://doi:10.1007/s00531-013-0979-0\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2014).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBevilacqua, A. et al. Quantifying volcanic hazard at Campi Flegrei caldera (Italy) with uncertainty assessment: I. Vent opening maps. J. Geophys. Res. 120, 2309\u0026ndash;2329. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1002/2014JB011775\u003c/span\u003e\u003cspan address=\"10.1002/2014JB011775\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2015).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMogi, K., Study of the elastic shocks caused by the fracture of heterogeneous materials and its relation to earthquake phenomena, Bull. Earthquake Res. Inst. Tokyo Univ., 40, 125 (1962).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eScholz, C.H.. Microfracturing and the inelastic deformation of rock in compression. J. Geophys. Res., Vol. 73, n. 4, 1417\u0026ndash;1432 (1968).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMcGarr, A., Seismic moments and volume changes. J. Geophys. Res., Vol. 81, n. 8, 1487\u0026ndash;1494 (1976).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMeredith, P. G., I. G. Main, and C. Jones (1990), Temporal variations in seismicity during quasi-static and dynamic rock failure, Tectonophysics, 175, 249\u0026ndash;268, doi:\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/0040-1951(90)90141-T\u003c/span\u003e\u003cspan address=\"10.1016/0040-1951(90)90141-T\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHeap, M. J., Baud, P., Meredith, P. G., Vinciguerra, S., and Reuschl\u0026eacute;, T. The permeability and elastic moduli of tuff from Campi Flegrei, Italy: implications for ground deformation modelling. Solid Earth 5, 25\u0026ndash;44. doi:\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.5194/se-5-25-2014\u003c/span\u003e\u003cspan address=\"10.5194/se-5-25-2014\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e, (2014).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eVanorio, T., and Kanitpanyacharoen, W. Rock physics of fibrous rocks akin to Roman concrete explains uplifts at Campi Flegrei Caldera. Science 349, 617\u0026ndash;621. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi:10.1126/science.aab1292\u003c/span\u003e\u003cspan address=\"https://doi:10.1126/science.aab1292\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e, (2015).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSaboo, S., et al. Feedback responses between endogenous and exogenous processes at Campi Flegrei caldera dynamics, Italy. Bull. Volcanol., 86:22 (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSiniscalchi, A., et al. Reservoir structure and hydraulic properties of the Campi Flegrei geothermal system inferred by audiomagnetotelluric, geochemical and seismic study. J. Geophys. Res., Solid Earth, 124(6), 5336\u0026ndash;5356 (2019).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTramelli, A., Convertito, V., \u0026amp; Godano, C. b value enlightens different rheological behavior in Campi Flegrei caldera. Commun. Earth \u0026amp; Environment, 5:275, \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/s43247-024-01447-y\u003c/span\u003e\u003cspan address=\"10.1038/s43247-024-01447-y\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (2024).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFarrell, J., Husen, S. \u0026amp; Smith, R. B. Earthquake swarm and b-value characterization of the yellowstone volcano-tectonic system. J. Volcanol. Geoth. Res. 188(1\u0026ndash;3), 260\u0026ndash;276 (2009).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eCaputo, M. Two thousand years of geodetic and geophysical observation in the Phlegrean Fields near Naples. Geophys. J. R. Astr. Soc., 56,319\u0026ndash;328 (1979).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eVoight, B. A method for prediction of volcanic eruptions. Nature 332, 125\u0026ndash;130. doi:\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1038/332125a0\u003c/span\u003e\u003cspan address=\"10.1038/332125a0\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (1988).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAcocella, V., Di Lorenzo, R., Newhall, C. \u0026amp; Scandone, R. An overview of recent (1988 to 2014) caldera unrest: knowledge and perspectives. Rev. Geophys. 53, 896\u0026ndash;955. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1002/2015RG0004\u003c/span\u003e\u003cspan address=\"10.1002/2015RG0004\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e 92 (2015).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eIsaia, R. et al. Volcano-tectonic setting of the Pisciarelli fumarole field, Campi Flegrei caldera, southern Italy: Insights into fluid circulation patterns and hazard scenarios. Tectonics 40(5), e2020TC006227 (2021).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRosi, M. et al. Defining the pre-eruptive states of active volcanoes for improving eruption forecasting. Front. Earth Sci. 10, 795700. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3389/feart\u003c/span\u003e\u003cspan address=\"10.3389/feart\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e. 2022. 795700 (2022).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-4164255/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4164255/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eCampi Flegrei is the largest active caldera in Europe and it is home of more than 350,000 people. Since 2005, the caldera shows a slow but progressive inflation of the ground and an intensification of seismic activity. Here we quantify the decadal accelerating trend together with oscillations of various frequencies overlying it and explore the relationships between deformation and seismic activity over the period 2000-11/2023. Results reveal an accelerating parabolic increase of vertical uplift, with maximum acceleration of ca. 0.74 cm/yr\u003csup\u003e2\u003c/sup\u003e, and a super-exponential increase of number of earthquakes and seismic energy release. Inspection of data gives evidence of a close temporal correlation between rates of deformation and seismicity and of an exponential-type relationship, with an exponent increasing in time, between ground deformation and number of earthquakes. These relationships are consistent with a quasi-elastic behavior of the upper crust of the caldera under an increasing stress and suggest a progressive mechanical weakening of it. Most importantly, they provide evidence of an increasing sensitivity of seismic activity on the caldera inflation and warn on the possibility of significant seismic events in case of continuation, with the same trends and relations, of the bradyseismic crisis in the next years.\u003c/p\u003e","manuscriptTitle":"Investigating deformation and seismic data and their relationships during the ongoing unrest of Campi Flegrei caldera (Italy)","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-06-27 15:32:46","doi":"10.21203/rs.3.rs-4164255/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"communications-earth-and-environment","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"commsenv","sideBox":"Learn more about [Communications Earth and Environment](https://www.nature.com/commsenv/)","snPcode":"","submissionUrl":"","title":"Communications Earth \u0026 Environment","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Communications Series","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"7f34a311-cf98-4b3c-8082-1dcd4ef31b86","owner":[],"postedDate":"June 27th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":33723263,"name":"Earth and environmental sciences/Solid Earth sciences/Volcanology"},{"id":33723264,"name":"Earth and environmental sciences/Solid Earth sciences/Geophysics"},{"id":33723265,"name":"Earth and environmental sciences/Natural hazards"}],"tags":[],"updatedAt":"2024-12-04T08:07:28+00:00","versionOfRecord":{"articleIdentity":"rs-4164255","link":"https://doi.org/10.1038/s43247-024-01865-y","journal":{"identity":"communications-earth-and-environment","isVorOnly":false,"title":"Communications Earth \u0026 Environment"},"publishedOn":"2024-12-03 05:00:00","publishedOnDateReadable":"December 3rd, 2024"},"versionCreatedAt":"2024-06-27 15:32:46","video":"","vorDoi":"10.1038/s43247-024-01865-y","vorDoiUrl":"https://doi.org/10.1038/s43247-024-01865-y","workflowStages":[]},"version":"v1","identity":"rs-4164255","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4164255","identity":"rs-4164255","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}