Despite the growing interest in the continuous monitoring of volcanoes worldwide, accurately forecasting eruptions remains a significant challenge for researchers. As a result, early warning systems frequently fail to provide timely alerts. This is evident in the fatalities caused by recent volcanic eruptions, such as those at Stromboli in 2019 (Andronico et al., 2021) and Whakaari in 2019 (Dempsey et al., 2020). The difficulty arises from the complex, dynamic processes involved, where numerous interconnected (and often unknown) parameters play a role. Nevertheless, analyzing the history of volcanic activitymay reveal characteristic patterns and potential precursors for eruptions. This could not only enhance our understanding of the physical processes occurring within volcanoes but also contribute to the development of more reliable early warning systems.

Identifying potential precursors or regularities in the data is a crucial task, as it may form the basis for early warning systems and event forecasting. For instance, Dempsey et al. (2020) observed an unusual peak in the tremor data recorded at Whakaari several hours to days before an eruption. Later, this finding was applied to several other volcanoes in New Zealand and Alaska by Ardid Segura et al. (2022). For Etna, Langer et al. (2011) detected changes in tremor 1–9 h before the onset of eruptive activity using an unsupervised classification tool (employing self-organizing maps).

The goal of this study is to enhance the characterization of volcanic activity and identify patterns that could contribute to the improvement of early warning systems. The statistical analysis relies on event catalogs generated from seismic data spanning multiple years with various types of events, ranging from major to small eruptions. This approach allowed us to do a long-term comparison of the activity and enhances the statistical significance of the findings.

This type of analysis, particularly focusing on inter-event time analysis and amplitude-frequency relations, has been conducted in various contexts for many volcanoes. Nishimura et al. (2016) compared the amplitude-frequency relations of six volcanoes located in Japan, Indonesia, and Italy for different time periods. However, as some of these volcanoes are less active or not continuously monitored, only a few thousand events were analyzed per volcano. Similarly, Lehr and Rabbel (2021) analyzed data from Villarrica (Chile) to plot the amplitude-frequency relations and derive amplitude distributions. In this case, only 12 days of data were analyzed.

Since volcanic activity can change drastically over extended time periods, using data from longer intervals will provide a more representative analysis. Additionally, the characteristics of large eruptions that occur only a few times per year (or less) can only be investigated by examining sufficiently long time intervals. For instance, Bevilacqua et al. (2020) conducted an extensive analysis of a historical catalog for Stromboli spanning from 1880 to 2020, which included paroxysmal events and major explosions. Further, they executed a detailed inter-event time analysis for this period. However, the inclusion and analysis of smaller events requires instrumentally recorded data, which implies that such an extensive time span cannot currently be considered for this purpose.

This study analyzes data from four volcanoes: Stromboli (Italy), Mount Etna (Italy), Yasur (Vanuatu), and Whakaari (New Zealand). These island volcanoes were selected based on their regular activity and the availability of open, reliable seismic data. Additionally, we focused on volcanoes with at least two operational seismological stations, as illustrated in Figure 1. Exemplary 1-h extracts of data from each volcano are displayed in Figure 2. However, due to the significant variations in volcanic activity over time, these signals are not representative of the entire time span. Each volcano exhibits unique characteristics in its activity.

Stromboli (Italy) is an island volcano situated near Sicily, with documented activity dating back to the 8th century AD (Andronico et al., 2021). It is known for its frequent Strombolian explosions that occur every few minutes and can be observed at several craters within the crater terrace. These medium-sized events, attributed to coalescing and bursting gas bubbles (Nabyl et al., 1997), eject pyroclastic material up to several dozen meters. However, occasional paroxysmal events also occur, posing a serious threat to residents and tourists on the island. The most recent paroxysms occurred in relatively quick succession on July 3, 2019 and August 28, 2019. They ejected material several kilometers from the vents and an eruption column rose to a height of 5 km (Giudicepietro et al., 2020; Andronico et al., 2021). Fortunately, paroxysms are relatively rare, with only 36 occurrences in the last 140 years according to a historical catalog (Bevilacqua et al., 2020). However, paroxysms occurred very irregularly in the past (the longest break in paroxysms is from 1960 to 2002). Their origin is not completely understood (Giudicepietro et al., 2020). Two selected seismic stations (of many others) have been considered on the island, positioned on opposite sides of the volcano and at approximately equal distances from the crater terrace (IV.IST3, IV. ISTR). They have been operational since 2013, with data accessible through the INGV data center (Istituto Nazionale di Geofisica e Vulcanologia, 2005).

Mount Etna (Italy), situated on the island of Sicily, is the largest volcano in Europe. Over the past 30 years, it has experienced active and intense explosive and effusive activity, with eruptions characterized by Strombolian activity, lava fountains, and the formation of eruption columns (Bisson et al., 2021). The Istituto Nazionale di Geofisica e Vulcanologia (INGV) (2005) has installed numerous seismic stations in close proximity to the volcano. However, to detect even smaller events, we selected only stations within a radius of approximately 1 km around the central crater (IV.ECNE, IV. ECPN). These two stations have been operational since 2021.

Yasur (Vanuatu) is a volcano on Tanna Island. Its activity is characterized by very frequent Strombolian explosions, which, similar to Stromboli, are connected to the bursting of gas bubbles (Woitischek et al., 2020). Typically, these events last up to 20 s and eject material up to several hundred meters (Marchetti et al., 2013). We analyzed data from the ARC-Vanuatu Seismic Experiment (Pelletier et al., 2011) conducted in 2008-2009, selecting the two closest stations to the crater (ZO.Y31, ZO. Y32).

Whakaari (New Zealand) is a partially submerged andesite volcano forming a small island in the Bay of Plenty. It is currently New Zealand’s most active volcano (Kilgour et al., 2021). Whakaari’s activity primarily consists of phreatic, phreatomagmatic, and magmatic eruptions (Burton et al., 2021), which are caused by the release of pressurized fluids and gas. During volcanic unrest in the central crater cone, hot springs can be found, and the release of steam often produces gas plumes (Kilgour et al., 2021). Here, too, rare violent explosions can occur, as demonstrated by a tragic event in 2019, when 47 tourists were on the island during an eruption, resulting in the deaths of 22 people (Burton et al., 2021). There is one operational station (NZ.WIZ) that has been providing data through GeoNet (GNS Science, 2021) since 2007. Data from another station (NZ.WSRZ), placed on the opposite side of the volcano, are available for the time from 2013 to 2021. However, the signals recorded at this station were found to be very noisy, and therefore they were not used in our analysis. Because of this, we had to alter the catalog creation process slightly (see next section). Nonetheless, Whakaari remains interesting for our analysis due to its longest data record. Furthermore, its activity, distinct from Strombolian eruptions, makes it interesting to compare to the other volcanoes.

Broadband stations were analyzed at all volcanoes, with three channels (HHN, HHE, and HHZ) employed. The instruments used and their sensitivities were consistent across each volcano, respectively. We accounted for instrument sensitivity to obtain velocity seismograms. For further information regarding the sensors and instrument response, please refer to Supplementary Table S1 in the Supplementary Material.

Overall, the figures presented in the previous section demonstrate a clear consistency when comparing the volcanoes based on the frequency of all volcanic events (see Table 1). While Stromboli and Etna exhibit a similar frequency of events (per time interval), Yasur has considerably more. For Whakaari, which has the fewest detected events, it should be noted that the number of low-amplitude events may be overestimated because catalog consolidation (i.e., the comparison of two catalogs from two stations) could not be used due to the second station being excessively noisy.

Figure 5A shows a change in slope in the amplitude-frequency relation for Stromboli towards high-amplitude events. Our previous research (Fenner et al., 2022) already showed this relation for Stromboli, but only for data from 2 years. There, this change in slope was already observed for amplitudes larger than ca. 100 μm/s. This implies that there are more large events compared to the distribution observed for earthquakes and it was suggested that this might be related to a different source mechanism of large events. However, this conclusion was drawn from a sample of just 10 events. In this study, we extend the analysis to 10 years of data and validate the observed change in slope (Figure 5A). The increased sample size allows for more statistically significant results, as we now have over 50 events exceeding 100 μm/s. However, as the majority of detected events (1.4 million) were observed at Stromboli, we cannot rule out the possibility that the change in slope would also appear for the other volcanoes if more data were available. Thus, we do not know if this is a unique property of Stromboli, or if it is more generally applicable. It is also worth noting that the change in slope cannot be explained by distant earthquakes, as they were excluded based on the ISC earthquake catalog.

By further analyzing event types for Stromboli, we primarily attribute the change in slope to high-frequency events (Figure 11). High-frequency volcanic events are typically associated with the movement of magma and volcanic gases leading to fracturing (Wassermann, 2012). However, it is possible that if a more detailed classification into further event types were implemented, more differences might emerge.

In most cases, the amplitude-frequency curve flattens out for low amplitudes. Assuming an exponential distribution for the logarithm of event amplitudes (which is observed for earthquakes and is the underlying distribution for the Gutenberg-Richter law), the slope should continue even for small events. On the one hand, this flattening can be explained by the catalog’s completeness–as the noise level obscures small events, these cannot be detected. On the other hand, Lehr and Rabbel (2021), Nishimura et al. (2016), and Cauchie et al. (2015) found evidence suggesting that the flattening cannot be explained by low detection levels. Instead, it could be related to a different amplitude distribution that decreases for small amplitudes compared to the exponential distribution, resulting in a unimodal distribution (i.e., with a maximum for a certain amplitude). For Yasur, this is the most obvious: the average noise level is much lower than the amplitude where the flattening of the curve begins. The assumption of a different amplitude distribution is further supported by the same distributions observed for jet height or gas masses for other volcanoes (Lehr and Rabbel, 2021).

By analyzing the inter-event time distributions for different amplitudes (Figure 8), we found no evidence of any periodic recurrence of events for any given amplitude across all the volcanoes studied. Similarly, the classification of event types for Stromboli revealed no distinct recurrence time per event type (Supplementary Figure S2 in Supplementary Material). Instead, we observed a log-normal distribution for the inter-event time across all volcanoes, a pattern also reported in other studies (Cauchie et al., 2015). Given that Strombolian eruptions are often attributed to the coalescence and bursting of gas bubbles (Nabyl et al., 1997), we may infer that the formation of these gas bubbles within the magma column also follows a log-normal distribution.

As suspected from the analysis of the amplitude-frequency relations (Figure 5), the distributions are indeed unimodal. However, for all volcanoes, the noise level is close to the center of the distribution. Based on this observation, the true maximum (if it exists) could be at lower amplitudes. Since the noise level constraints the detection of smaller events, the true distribution remains unknown from the catalogs. For Whakaari, the high number of events close to the noise level can be attributed to the fact that we did not use catalog consolidation for this volcano as the second station was deemed unsuitable due to its elevated noise level.

There appears to be an alternating pattern between the two event types. In summary, the frequency content of the events preceding both paroxysms was high until 1 month before the first paroxysm. Subsequently, more low-frequency events occurred. This anomaly commences 1 month before the first paroxysm. This observation aligns with the findings from (Giudicepietro et al., 2020), who analyzed the polarity and fractal dimension of the signal and noticed a significant change 1 month prior to the first paroxysm. Similar behavior has also been observed in other volcanoes, such as the Augustine Volcano in Alaska (Buurman and West, 2010). To establish whether these anomalies observed in event types before and after paroxysms are consistently related to large eruptions, further analysis is essential.

In the inter-event time distribution as a function of the amplitude (Figure 8) there appears to be a bimodal event distribution. This observation is unfortunately based on only a small number of events, which could potentially affect the significance of the finding. The two dominant recurrence times seem to be 100 min and 140 days. This long-term periodicity was already documented in volcanic activity. For instance, a study by Qu et al. (2011) suggests the presence of multiple oscillations (10–100 years). Also, similar patterns were observed by Srivastava et al. (2021) in a two-to-three-year periodicity in large earthquakes. However, the analysis for Whakaari relies solely on data from one station, and more research and data are necessary to gain more robust insights.

Our selection of volcanoes was primarily guided by data availability, which resulted in a focus on volcanoes associated with convergence/subduction tectonic regimes. However, it would be important to consider volcanoes located in divergent plate boundaries or intraplate volcanoes as well. Future studies could aim to incorporate different types of volcanoes. Further, this study was primarily focused on open-conduit volcanoes. However, closed-vent volcanoes with regular seismic activity could be considered for analysis in a similar way. AWESAM does not differentiate between event types and we expect that it could detect events from closed systems in the same way. Therefore, comparing open and closed systems could yield additional insights and reveal possible differences. Also, this work does not consider the impact of different types of volcanic activity (e.g., phreatic and magmatic eruptions). However, we plan to address this aspect in future research.

The comparison of the seismo-volcanic event catalogs from four volcanoes (Stromboli, Mount Etna, Yasur, and Whakaari) facilitates some interesting conclusions about their volcanic activity. Using the same tool for all volcanoes enables a meaningful comparison. All four volcanoes, despite their different type and frequency of events, show similar characteristics. For example, the amplitude-frequency relation, the inter-event time distributions and the amplitude distributions show similar trends.

We have confirmed the change in slope for Stromboli in the amplitude-frequency relation (Figure 5A), a phenomenon previously observed in another study (Fenner et al., 2022). This implies that there are an unusually high number of very high-amplitude events. With an increased number of events now, the result holds more statistical significance. With this analysis, it is further possible to determine the average recurrence time of events with specific amplitudes for each volcano.

Additionally, we examined the double paroxysm in 2019 at Stromboli. It appears that there was a higher occurrence of HF events before the paroxysms, while LP events were more prominent after the paroxysms.

In conclusion, the event-detection methodology presented can be applied to volcano monitoring. It offers the possibility to quickly identify and analyze relevant events, particularly when multiple stations are available for catalog consolidation in near real-time. The analysis of inter-event times and amplitude statistics offers the detection and characterization of volcanic unrest phases, similar to RSAM analysis (Endo and Murray, 1991), and can provide enhanced constraints for early warning systems.