Introduction

The Campi Flegrei caldera hosts more than 1.5 million people and several productive facilities making it one of the most hazardous regions on Earth1. The volcanism of the caldera has attracted the interest of many studies aimed at defining its extension as well as tracking its eruptive history2,3,4,5,6,7.

Two large-volume caldera-forming eruptions affected the area: the Campanian Ignimbrite (CI), 39 ka years ago, and the Neapolitan Yellow Tuff (NYT), 15 ka years ago8. During CI eruption more than 300 km3 of magma and volcanic ash were emitted. The magma source has been located between 6 and 8 km depth9. The depletion of the magma reservoir produced the Campi Flegrei caldera. As for the NYT eruption, it involved more than 40 km3 of magma and produced a further collapse of the caldera8. The NYT eruption was followed by at least 70 minor eruptions lasting with the historical eruption of Monte Nuovo (1538 AD)8. After the 1538 eruption, the caldera has shown several unrest phases involving periods of uplift and subsidence. From 1950 to 1990 Campi Flegrei suffered three bradiseismic crises with a total uplift of 4.3 m; in 1982–1984 a maximum uplift of 1.86 m was measured followed by a 20-year long period of subsidence. Since 2005, the Campi Flegrei caldera entered a new unrest phase during which a 1.18 m of uplift has been reached in its central part. The uplift has activated both on-land and off-shore faults with the occurrence of largely felt earthquakes that reached a maximum magnitude of md 4.2 in October 2023.

One of the most debated topics in the current scientific literature about Campi Flegrei concerns the source of the unrest and its position. A magmatic chamber at a depth of about 7.5 km was evidenced by ref. 10 but the deformation source is shallower and possibly located between 3 and 5 km of depth below the centre of the caldera11. The causes of the inflation of this source are still under debate. The role of a shallow hydrothermal system that characterises the area12,13,14,15,16 makes the definition of this source very complex because it plays an active part in the inflation and deflation processes. The 1982–84 inflation needs a magmatic source to be justified, being the hydrothermal contribution insufficient to explain the recorded deformation. For the current unrest, some studies tend to favour a magma intrusion at shallow depth17 others favour the over-pressurisation of the hydrothermal system18,19,20 and others invoke both the contributions21.

Volcano-tectonic earthquakes reveal the stress state of a volcano. Indeed, the evolution of the space and time distribution of the seismicity in volcanic areas is driven by fluid circulation and diffusion, the rheology of the crust, and the local and regional stress fields. Moreover, earthquakes are a key parameter in the volcano monitoring system being one of the most important eruption precursors22,23,24,25. Generally, during unrest periods the number of recorded earthquakes increases allowing to perform their statistical analysis, which can lead to a better comprehension of the unrest mechanism and its origin. One of the best-studied and analysed statistical parameters is the b value. The b value represents the scaling parameter of the Gutenberg-Richter relation26:

$$\log (N)=a-bm$$
(1)

where N is the cumulative number of earthquakes with magnitude larger than m. a and b characterise the seismic catalogue and, consequently, the volume where the catalogue is filled in. The b value is generally close to 1 for tectonic areas whereas it assumes larger values in volcanic areas27. It has been shown that its value increases with the medium heterogeneity28 and temperature gradient27,29,30, and it decreases with increasing stress31,32,33,34.

Here we perform the first 3D b tomography of the Campi Flegrei caldera using the method of ref. 35 and a high-quality instrumental seismic catalogue. The obtained results well correlate with the structure of the hydrothermal system and the caprock of the Campi Flegrei revealing the good capability of the b value maps to enlighten the stress state and the rheology of a given volcanic area. Moreover, differently from other geophysical tomography, the b value one can be easily estimated and potentially related to stress state and temperature variations that, in the volcanic field, can be associated with magma migration.

Results

Here we consider the earthquake catalogue collected in the period January 2005–October 2023 corresponding to the last unrest episode. The catalogue contains 7670 events (Fig. 1) with high location quality and magnitude in the range − 1.1 ≤ md ≤ 4.2 where md is the duration magnitude. To obtain a homogeneous catalogue allowing a reliable estimation of the completeness magnitude mc, we converted md in mL (see SI Fig. 2 and methods section).

Fig. 1: The Campi Flegrei seismicity.
figure 1

Seismicity distribution was recorded at Campi Flegrei from January 2005 through October 2023. Symbol size is proportional to the magnitude of the earthquake whereas the colours indicate its depth. The inset depicts the magnitude of the events as a function of time. Grey and blue triangles indicate the seismic stations managed by the Istituto Nazionale di Geofisica e Vulcanologia, Osservatorio Vesuviano, while green triangles the stations of the Rete Accelerometrica Nazionale managed by the Italian Dipartimento della Protezione Civile.

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Applying the ref. 35 method to the Campi Flegrei catalogue the medium was divided into 16 not geometrically homogeneous cells. The cell size varies between 0.68 and 3.14 km. Two of the 16 cells are discarded from the analysis because mmax − mc < 1.5 (see ‘Methods’). Seven of the not excluded fourteen cells exhibit an mc value of 0.28, four of 0.08. For the remaining three cells, mc is 0.68, 0.38 and 0.14 (see SI Table S1). The number of events with m ≥ mc ranges from 217 to 461 allowing a reliable estimation of the b value18. The b standard deviation σb is in the range [0.03,0.13]. For further details see SI Table S1.

The b value tomography is displayed in Fig. 2. The map enlightens the presence of three different ranges of b value. The first one (b ∈ (0.7, 1.1)) includes the deepest seismicity, namely all earthquakes at a depth larger than 2 km. However, the same value is observed in a shallow cell (z < 1 km) characterising the Accademia lava dome36 (see Fig. 1). The second range views a b value ∈ [1.1, 1.25] and includes two cells of earthquakes occurring north-east of the Solfatara volcano. The last range relates to events with b > 1.25 and defines what we call the b value anomaly at Campi Flegrei.

Fig. 2: The b value map.
figure 2

b value map from four points of view. The horizontal one can be seen in panel A. Panel B shows the 3D b value distribution as seen from north-east. Panel C and Panel D show the same distribution as seen from south and north, respectively. The points in the map represent the earthquake location belonging to a given cell. The colour code is the b value of the cell to which the earthquake belongs.

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Interestingly, earthquakes tend to occur in zones with smaller (<1.7)37\(\frac{{V}_{p}}{{V}_{s}}\) for any b value range and depth. This result is a general behaviour for any depth: almost no earthquake occurs within the volume with high \(\frac{{V}_{p}}{{V}_{s}}\).

Discussion

It is now well established that the b value is sensitive to the differential stress, the temperature gradient and the degree of fracturing of the crust. In volcanic and geothermal systems, the b value has been proven to be informative about the presence and the extent of magmatic bodies and fluids in the hydrothermal systems38,39,40. In the present study, we have analysed the 3D spatial distribution of the b value at the Campi Flegrei volcanic system and its correlation with the physical properties of the subsurface. The result suggests three main ranges of the b value that can be correlated with well-known structures of the Campi Flegrei volcanic system.

As expected, the smallest values of b are observed for the deepest seismicity confirming that b tends to decrease as z increases26,32,41,42,43,44,45,46,47. This is in accordance with high values of stress found at depths of about 3 km immediately above the deformative source48 and further confirms the inverse relation between b and the differential stress. Moreover, at a depth of about 2–2.5 km, a “natural concrete” rock able to accommodate a large amount of strain before breaking and shearing was found by ref. 49 and named caprock. The presence of fibrous minerals50 makes the caprock more ductile allowing the increase of the stress before generating earthquakes. This is in very good agreement with the observed small b values.

The distribution of the smallest b values can be further discussed in terms of the main known geological structures and stress field. In particular, if the deep on-land events can be associated with the presence of the caprock as described above, those offshore generally occur at higher depth and can be associated with the structures bordering the resurgent dome involved in the bradiseismic episodes51. Interestingly, the offshore events are characterised by reverse fault mechanisms52 that, according to ref. 53, have small b values compared to normal or strike-slip fault mechanisms.

The intermediate b values characterise the earthquakes occurring north-east of the Solfatara volcano, where a system of active faults54 slips under the action of tectonic and volcanic stress generating earthquakes with a b closer to 1, similar to tectonic areas.

The anomalous zone (b > 1.25) can be associated with the presence of high pore-fluid pressures or by a medium having a relevant degree of heterogeneity. Notably, this zone well correlates with low \(\frac{{V}_{p}}{{V}_{s}}\) (<1.7) values37 and high resistivity13,15. It has been interpreted as a porous medium through which fluids, dominated by steam49, can migrate when the caprock breaks allowing their passage from the underlying layers towards the surface. Moreover, this seismicity is located on the intricate faults network characterising the Solfatara-Pisciarelli volcano system51 that moves in response to the local extensive stress field37,52. The surrounding shallow areas are instead characterised by the presence of aquifers13,14,15 where earthquakes seldom occur and the b value can’t be calculated. This result appears to be confirmed by the observations of the heat flow55 that is directly correlated with the shallow b value indicating a preferential way path for the gases where the b value is higher. Conversely, there is no evidence of any correlation with the temperature gradient as measured in the wells drilled at Campi Flegrei during the ‘80s up to a depth of 3000 m55. However, we have to remark that only two of the several wells existing in the area are close to the epicentres of the earthquakes used to estimate the b value.

High values of b (up to 1.5) were found by ref. 56 in the areas characterised by high crustal heterogeneity of the local stress and high thermal gradient in Yellowstone56 suggested that the hydrothermal fluids circulating through the intricate system of cracks and heated from below, as in the hydrothermal systems, would favour the slip of these small cracks and could justify the high b values. In addition, the possible emplacement of magma would induce an expansion in the surrounding crust and would favour a b value increment. Similarly, high b values (b > 1.5) were found by ref. 27 in the area close to the resurgent dome in the Long Valley caldera and were associated with the highly fractured crust. However, in the case of Campi Flegrei, the rock overlying the deformation source, that is the caprock, even if heated by this source, is able to support high stress in accordance with smaller b value. The caprock modulates the transfer of deformation, heat and, possibly, of fluids when breaks to the uppermost more porous and fractured zone characterised by a higher b value.

For z > 3.5 km we do not observe any on-land seismicity. There the source of the inflation is located and an elastic to ductile transition is inferred17,19,48.

On the basis of our results, we propose a schematic model reported in Fig. 3 showing the whole system as coming from our interpretation of the b value and its relation with the principal known features as inferred from geophysical analyses1013,14,15,49.

Fig. 3: Sketch model of the Campi Flegrei.
figure 3

Model of the Campi Flegrei volcanic system as deduced by b value and other geophysical tomographies10,13,14,15,49. Black dots indicate the earthquakes contained in the Campi Flegrei catalogue recorded in the period January 2005–October 2023. Arrows indicate the fluid path and surface heat flow. The dashed coloured lines indicate the measured temperature at the wells drilled in the 80s55. Brown and blue lines represent the offshore and on-land faults, respectively together with the typical associated projected fault mechanism.

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Our results enlighten that the correlation between the b value and volcanic system provides valuable insights into volcanic processes and behaviour when analysed jointly with geological and geophysical information. The ref. 35 method joined with the ref. 57 one, allowed us to obtain the first 3D high-resolution image of the b value at Campi Flegrei. The spatial b value variations reveal a very clear correlation with different rheological behaviour of the rocks. Since changes in the b value may reflect variations in stress levels, magma movement, or the presence of fluid migration within the volcanic edifice our results can be used as a reference model to evidence future meaningful variations indicating the evolution of the volcano toward a critical status. Monitoring changes in the b value can help assess volcanic hazards, identify periods of volcanic unrest, and improve volcanic risk mitigation strategies.

Methods

Evaluating the m L values

The md is routinely evaluated by the INGV-Osservatorio Vesuviano for all the earthquakes for which it is possible to measure the duration. This latter may be in fact affected by the level of the noise. At present time the md ranges, at Campi Flegrei, from –1.6 to 4.2. Moreover, the same institution is currently evaluating mL by using the relation calibrated by ref. 58. The available catalogue indicates that mL cannot be effectively estimated for a magnitude lower than 1.5 possibly due to the seismic noise level that does not allow for measurement of the Wood-Anderson peak displacement. The direct comparison of mL with md (Fig. 4) reveals the linear relationship between the two magnitude scales indicating that for the events analysed in this study, there is a slight underestimation of md with respect to mL. The slope of the linear fit is indeed slightly different from 1. This implies that md should be corrected following the fit. This effectively improves the estimation of mc (see SI Fig. 2).

Fig. 4: Magnitude conversion relationship.
figure 4

mL as a function of md. The red line represents the linear fit whose result is reported in the figure.

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The transformation relationship is obtained by fitting a linear model providing mL = 0.23(±0.11) + 0.86 (±0.05)md with a correlation coefficient r = 0.86. Notice that, due to this correction, the local magnitudes are not binned anymore at 10−1 but at 0.086. This makes the Utsu59 correction term in the maximum likelihood60b estimation, negligible.

The extrapolation of the fit to magnitudes smaller than 1.5 is guaranteed by the small confidence interval (at a significance level of 95%) Δ = 0.1 for the fitted linear slope. Indeed the standard error for extrapolated mL is ≃ 0.1 in the range − 1 < md < 1 and smaller than 0.1 for 1 < md < 1.5.

Building independent cells

We divide the Campi Flegrei seismicity into independent cells using the method described in detail in ref. 35. The method selects the largest event in the catalogue not yet assigned to a cell and includes in the cell, around the chosen earthquake, n ± ntol events. Following ref. 61, here we use, n = 500 and ntol = 30.

The cells are not geometrically homogeneous and, for the Campi Flegrei catalogue the cell size—defined as 0.5 times the maximum distance between events in the cell—varies between 0.68 and 3.14 km. When mmax − mmin < 1.5, the cell is discarded from the analysis. This choice appears to be a good compromise to have sufficient cells to allow for an interpretation of the observed b values. However, this does not occur in any case for the Campi Flegrei catalogue.

Evaluating the completeness magnitude

Reference 62 defined the completeness magnitude mc as a threshold magnitude and all earthquakes are reported in the catalogue if m ≥ mc. Its value is very important for an unbiased estimation of the b value. Indeed if mc is underestimated, the b value is underestimated. Conversely, an overestimated mc will reflect into a reduced magnitude interval leading, possibly, to an incorrect estimation of the b value.

Following ref. 57 and ref. 63 we evaluate the variability coefficient cv (defined as \(\frac{{\sigma }_{m-{m}_{th}}}{\langle m-{m}_{th}\rangle }\) where \({\sigma }_{m-{m}_{th}}\) is the standard deviation of m − mth) as a function of a threshold magnitude mth. When cv is larger than a given threshold, mth = mc. This threshold value has been, here, fixed at 0.9 because for such a value the GR distribution can be assumed homogeneous (see SI Fig. 1).

Evaluating the b value

In each cell, the b value for the events has been evaluated using the maximum likelihood method60 and its standard deviation σb following64.