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Foreshocks, observed before some large earthquakes, remain debated in terms of their origins and predictive value. While aftershocks fit well within bottom-up triggering models like ETAS, foreshocks may arise from distinct preparatory processes. Observations suggest real seismic catalogs exhibit more foreshocks than ETAS predicts, and laboratory experiments show that fault heterogeneity enhances foreshock activity. Here, I use a numerical model that reproduces key statistical properties of seismicity to investigate the role of fault heterogeneity. My simulations confirm that increasing interface disorder promotes foreshocks, aligning with laboratory findings and suggesting that fault complexity influences seismic precursors.

Aftershock occurrence is characterized by scaling behaviors with quite universal exponents. At the same time, deviations from universality have been proposed as a tool to discriminate aftershocks from foreshocks. Here we show that the change in rheological behavior of the crust, from velocity weakening to velocity strengthening, represents a viable mechanism to explain statistical features of both aftershocks and foreshocks. More precisely, we present a model of the seismic fault described as a velocity weakening elastic layer coupled to a velocity strengthening visco-elastic layer. We show that the statistical properties of aftershocks in instrumental catalogs are recovered at a quantitative level, quite independently of the value of model parameters. We also find that large earthquakes are often anticipated by a preparatory phase characterized by the occurrence of foreshocks. Their magnitude distribution is significantly flatter than the aftershock one, in agreement with recent results for forecasting tools based on foreshocks. Earth surface continues to slip after large earthquakes at a slow velocity for a period of a year or more. In this study, the authors show how such slow slip before and after large earthquakes relates to the interaction of the brittle zone of the fault with the ductile zone at greater depth.

The epidemic type aftershock sequence (ETAS) model is used as a baseline model both for earthquake clustering and earthquake prediction. In most forecast experiments, the ETAS parameters are estimated based on a short and local catalog, therefore the model parameter optimization carried out by means of a maximum likelihood estimation may be not as robust as expected. We use Bayesian forecast techniques to solve this problem, where non-informative flat prior distributions of the parameters is adopted to perform forecast experiments on 3 mainshocks occurred in Southern California. A Metropolis–Hastings algorithm is employed to sample the model parameters and earthquake events. We also show, through forecast experiments, how the Bayesian inference allows to obtain a probabilistic forecast, differently from one obtained via MLE. Graphical Abstract

Among the most important questions that await an answer in seismology, perhaps one is whether there is a correlation between the magnitudes of two successive seismic events. The answer to this question is considered of fundamental importance given the potential effect in forecasting models, such as Epidemic Type Aftershock Sequence models. After a meta-analysis of 29 papers, we speculate that given the lack of studies carried out with realistic physical models and given the possible bias due to the lack of events recorded in the experimental seismic catalogs, important improvements are necessary on both fronts to be sure to provide a statistically relevant answer.

We investigate the relationship between the cumulative number of earthquakes and ground uplift at the Campi Flegrei caldera (South Italy) during the ongoing unrest (2005-present). While previous studies have explored this correlation, we propose a nonlinear epidemic model that captures new features of the caldera system. Our model describes earthquakes’ occurrence as a cascading process driven by ground deformation. The nonlinearity reflects the reduced efficiency of the triggering mechanism, which contributes to the short duration of seismic swarms. This mechanism may represent a general framework for understanding the occurrence of volcanic earthquakes worldwide.

The Campi Flegrei caldera has experienced several episodes of volcanic unrest during the last few centuries, most notably in 1982–1984 and 2005–present. These periods of unrest are characterized by ground uplift, seismic swarms, and increased degassing. In this study, we compare the seismicity and associated b value variations during the 1982–1984 and 2005–2024 unrest periods. The b value is calculated using the novel b more positive method, which improves upon traditional approaches by analyzing the magnitude difference between successive earthquakes, without the need to estimate the completeness magnitude. Our results show significant differences in the spatial and temporal evolution of b values between the two unrest periods. In particular, the 2005–2024 unrest exhibits a slower ground uplift rate but higher fluctuations in the b value, especially in shallower seismicity, possibly suggesting different underlying mechanisms compared to the 1982–1984 crisis. We also observe distinct regions of increased stress, particularly beneath Pozzuoli harbor and Pisciarelli area for deeper seismicity, during the ongoing unrest. Our findings provide valuable insights into the evolution of Campi Flegrei volcanic systems and highlight the importance of continuous monitoring of the b value as a potential strain meter for describing volcanic activity.

The Epidemic Type Aftershock Sequence (ETAS) model is a widely used tool for cluster analysis and forecasting, owing to its ability to accurately predict aftershock occurrences. However, its capacity to explain the increase in seismic activity prior to large earthquakes—known as foreshocks—has been called into question due to inconsistencies between simulated and experimental catalogs. To address this issue, we introduce a generalization of the ETAS model, called the Epidemic Type Aftershock Foreshock Sequence (ETAFS) model. This model has been shown to accurately describe seismicity in Southern California. In this study, we demonstrate that the ETAFS model is also effective in the Italian catalog, providing good agreement with the instrumental Italian catalogue (ISIDE) in terms of not only the number of aftershocks, but also the number of foreshocks—where the ETAS model fails. These findings suggest that foreshocks cannot be solely explained by cascades of triggered events, but can be reasonably considered as precursory phenomena reflecting the nucleation process of the main event.

The transmissibility of an infectious disease is usually quantified in terms of the reproduction number R t representing, at a given time, the average number of secondary cases caused by an infected individual. Recent studies have enlightened the central role played by w ( z ), the distribution of generation times z , namely the time between successive infections in a transmission chain. In standard approaches this quantity is usually substituted by the distribution of serial intervals, which is obtained by contact tracing after measuring the time between onset of symptoms in successive cases. Unfortunately, this substitution can cause important biases in the estimate of R t . Here we present a novel method which allows us to simultaneously obtain the optimal functional form of w ( z ) together with the daily evolution of R t , over the course of an epidemic. The method uses, as unique information, the daily series of incidence rate and thus overcomes biases present in standard approaches. We apply our method to one year of data from COVID-19 officially reported cases in the 21 Italian regions, since the first confirmed case on February 2020. We find that w ( z ) has mean value z ¯ ≃ 6 days with a standard deviation σ ≃ 1 day, for all Italian regions, and these values are stable even if one considers only the first 10 days of data recording. This indicates that an estimate of the most relevant transmission parameters can be already available in the early stage of a pandemic. We use this information to obtain the optimal quarantine duration and to demonstrate that, in the case of COVID-19, post-lockdown mitigation policies, such as fast periodic switching and/or alternating quarantine, can be very efficient.

Volcanic seismic swarms, clusters of earthquakes without a distinct mainshock, are commonly linked to magma and fluid movements rather than tectonic stress transfer. Magma and hydrothermal fluid migration can perturb the ambient stress field and trigger volcano-tectonic (VT) seismicity on surrounding structures, either through dike propagation or inflation and associated stress changes. We analyze nine seismic catalogs from eight volcanic systems, including two unrest periods at Campi Flegrei, to investigate the spatial organization of swarm activity. Using a standardized declustering method and stacking radial distance distributions from the largest-magnitude event in each swarm, we identify a consistent two-regime spatial pattern across most volcanoes: an approximately uniform density at short distances and an exponential decay at larger scales. The transition scale varies among volcanoes and may reflect local structural or physical constraints, while the decay slope decreases with volcano size. Santorini represents an exception, suggesting site-specific influences. These empirical regularities provide new observational benchmarks for physical models of swarm dynamics and may inform the development of improved forecasting tools for volcanic seismicity.

The identification of seismic clusters is essential for many applications of statistical analysis and seismicity forecasting: uncertainties in cluster identification leads to uncertainties in results. However, there are several methods to identify clusters, and their results are not always compatible. We tested different approaches to analyze the clustering: a traditional window-based approach, a complex network-based technique (nearest neighbor—NN), and a novel approach based on fractal analysis. The case study is the increase in seismicity observed in Molise, Southern Italy, from April to November 2018. To analyze the seismicity in detail with the above-mentioned methods, an improved template-matching catalog was created. A stochastic declustering method based on the Epidemic Type Aftershock Sequence (ETAS) model was also applied to add probabilistic information. We explored how the significant discrepancies in these methods’ results affect the result of NExt STrOng Related Earthquake (NESTORE) algorithm—a method to forecast strong aftershocks during an ongoing cluster—previously successfully applied to the whole Italian territory. We performed a further analysis of the spatio-temporal pattern of seismicity in Molise, using the Principal Component Analysis (PCA), the ETAS algorithm, as well as other analyses, aimed at detecting possible migration and diffusion signals. We found a relative quiescence of several months between the main events of April and August, the tendency of the events to propagate upwards, and a migration of the seismicity consistent with a fluid-driven mechanism. We hypothesize that these features indicate the presence of fluids, which are also responsible for the long duration of the sequence and the discrepancies in cluster identification methods’ results. Such results add to the other pieces of evidence of the importance of the fluid presence in controlling the seismicity in the Apennines. Moreover, this study highlights the importance of refined methods to identify clusters and encourages further detailed analyses when different methods supply very different results. Graphical Abstract