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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.

Earthquake Occurrence provides the reader with a review of algorithms applicable for modeling seismicity, such as short-term earthquake clustering and pseudo-periodic long-term behavior of major earthquakes.The concept of the likelihood ratio of a set of observations under different hypotheses is applied for comparison among various models.

Earth's crust is continuously subjected to oscillatory stress perturbations due to the solid Earth and ocean tides. The seismic response to such stress modulations carries information on earthquake physics and crustal properties. Experimental and observational studies suggested but could not demonstrate that the strength of tidal modulation of seismicity increases before large earthquakes. We tested this hypothesis by (a) developing a new, comprehensive 10‐year long earthquake catalog preceding the 6 July 2019 magnitude 7.1 Ridgecrest, CA earthquake, and (b) applied our novel method for extracting a statistical signal of tidal modulation. Our results show enhanced tidal sensitivity of seismicity along the fault starting about 1.5 years before the mainshock, corroborating the hypothesis. This observation suggests that small magnitude earthquakes may be used to gain insight into subtle changes in fault conditions, bringing new promise for studying the earthquake preparation process. Plain Language Summary The solid Earth experiences tides, like the ocean, it deforms under the gravitational attraction of the Sun and Moon. This deformation induces an oscillatory stress change in the crust with small peak‐to‐peak amplitudes of the order of 1 kPa (about 1% of the atmospheric pressure). Tidal stresses weakly influence the rate of earthquake occurrence and the characteristics of this modulation carry information on earthquake physics and crustal properties. On the basis of experimental and field observation studies, it has been proposed that the modulation of seismicity by the tides increases before a large earthquake. We tested this hypothesis by analyzing 10 years of seismicity before the M7.1 2019 Ridgecrest, CA earthquake. We first built a new, comprehensive earthquake catalog with our automated method and used our novel method to extract the signal of tidal modulation throughout the study period. We found that seismicity became strongly modulated by the tides about 2 years before the mainshock, thus corroborating the hypothesis. Key Points Seismicity in the Ridgecrest area is modulated by the solid Earth tides Peak seismicity occurs when tidal Coulomb stress or stress rate favors rupture Strength of tidal triggering is gradually increasing in the rupture area about 2 years before the Mw 7.1 2019 mainshock

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

Foreshocks, though well‐documented phenomena preceding many large earthquakes, have limited forecasting utility due to their non‐pervasive occurrence and non‐distinctive characteristics. Using California as an example, we investigate how seismic monitoring capability, particularly the completeness magnitude (Mc${M}_{c}$ ), influences the inferred proportion of mainshocks with foreshocks (Pf${P}_{f}$ ). We test four foreshock identification methods, namely the fixed‐window, nearest neighbor clustering, empirical statistical (ES) methods and the epidemic‐type aftershock sequence (ETAS) model. The fixed‐window method shows Pf${P}_{f}$decreasing with higher Mc${M}_{c}$due to the misclassification of background events as foreshocks. In contrast, clustering and ES methods yield relatively stable Pf${P}_{f}$across different Mc${M}_{c}$values. The ETAS model suggests that many foreshocks in California are associated with aseismic driving processes, but the identification of the processes diminishes at high Mc${M}_{c}$ . These results show that improved seismic monitoring capability does not significantly increase Pf${P}_{f}$but is crucial for distinguishing processes driving foreshocks. Plain Language Summary Foreshocks are seismic events that sometimes occur before large earthquakes. However, they are not always present and do not have clear distinguishing features, limiting their usefulness for earthquake forecasting. We examine how the earthquake monitoring capability affects the observed proportion of large earthquakes that have foreshocks. Using seismic data from California, we apply four foreshock identification methods: the fixed‐window method, nearest neighbor clustering, empirical statistical (ES) methods, and the epidemic‐type aftershock sequence (ETAS) model. Our results show that the fixed‐window method leads to less observations of large earthquakes with foreshocks when the monitoring capability is worse. In contrast, clustering and ES methods provide more stable proportions of large earthquakes with foreshocks even when the monitoring capability varies. And the ETAS model suggests that many foreshocks in Califorina are associated with aseismic processes. However, poor monitoring capability limits the ability to distinguish between foreshocks driven by aseismic processes and those triggered by cascading seismic failure through stress transfer. These findings indicate that while enhanced seismic monitoring does not necessarily lead to a higher proportion of identified foreshocks, it is essential for understanding the underlying physical mechanisms driving foreshock activity. Key Points We assess the impact of magnitude of completeness (Mc${M}_{c}$ ) on multiple foreshock identification methods in California Foreshock dependence on Mc${M}_{c}$is weak in some methods because the magnitude difference between mainshock and largest foreshock is small Foreshocks driven by aseismic processes are numerous in California, but their detectability diminishes at high Mc${M}_{c}$

Earthquakes are one of the natural disasters that pose a major threat to human lives and property. Earthquake prediction propels the construction and development of modern seismology; however, current deterministic earthquake prediction is limited by numerous difficulties. Identifying the temporal and spatial statistical characteristics of earthquake occurrences and constructing earthquake risk statistical prediction models have become significant; particularly for evaluating earthquake risks and addressing seismic planning requirements such as the design of cities and lifeline projects based on the obtained insight. Since the 21st century, the occurrence of a series of strong earthquakes represented by the Wenchuan M 8 earthquake in 2008 in certain low-risk prediction areas has caused seismologists to reflect on traditional seismic hazard assessment globally. This article briefly reviews the development of statistical seismology, emphatically analyzes the research results and existing problems of statistical seismology in seismic hazard assessment, and discusses the direction of its development. The analysis shows that the seismic hazard assessment based on modern earthquake catalogues in most regions should be effective. Particularly, the application of seismic hazard assessment based on ETAS (epidemic type aftershock sequence) should be the easiest and most effective method for the compilation of seismic hazard maps in large urban agglomeration areas and low seismic hazard areas with thick sedimentary zones.

Earthquake forecast and risk assessment are of key importance in reducing casualties and property losses. However, they have not been fully achieved due to the complexity of earthquakes. Numerous studies have explored the correspondence of the b-value with changes in effective stress, leveraging temporal and spatial variations to identify precursor characteristics of destructive events in both natural and induced seismic activities. However, robust interpretation of predictive b-values hinges on rigorous estimation, as biased results can mislead conclusions. This paper provides a comprehensive review of spatiotemporal b-value estimation methods alongside statistical significance tests. A pilot b-value analysis of natural earthquakes and induced seismicity manifested the valid impression. The expansion of monitoring datasets with the development of acquisition technology or dense array and advanced estimation methodology will augment the utility of b-value analysis in seismic research and hazard assessment.

Foreshock analysis promises new insights into the earthquake nucleation process and could potentially improve earthquake forecasting. Well‐performing clustering models like the Epidemic‐Type Aftershock Sequence (ETAS) model assume that foreshocks and general seismicity are generated by the same physical process, implying that foreshocks can be identified only in retrospect. However, several studies have recently found higher foreshock activity than predicted by ETAS. Here, we revisit the foreshock activity in southern California using different statistical methods and find anomalous foreshock sequences, that is, those unexplained by ETAS, mostly for mainshock magnitudes below 5.5. The spatial distribution of these anomalies reveals a preferential occurrence in zones of high heat flow, which are known to host swarm‐like seismicity. Outside these zones, the foreshocks generally behave as expected by ETAS. These findings show that anomalous foreshock sequences in southern California do not indicate a pre‐slip nucleation process, but swarm‐like behavior driven by heat flow. Plain Language Summary Many studies have observed that large earthquakes are preceded by smaller events, called foreshocks. If they have distinctive characteristics that make them recognizable in an ongoing sequence in real time, they can significantly improve the forecasting capability of large earthquakes. To investigate the nature of foreshocks, we compare actual seismicity with the expectation of the most skilled earthquake forecasting model, which assumes that foreshocks are not different from other earthquakes. We find that discrepancies between reality and expectation mostly affect foreshock sequences that anticipate moderate mainshocks with magnitudes below 5.5. We find that those anomalous foreshock sequences tend to occur more often where the heat flow is high. Those zones are already known for the occurrence of swarm‐like sequences, which are prolonged episodes of seismicity without a dominant event. Outside these zones, the observed foreshock activity is explained well by the forecasting model. These findings indicate that anomalous foreshock sequences are not indicating impending large earthquakes but are influenced by the heat flow. Key Points We compare the foreshock activity in southern California with the expectation of the best‐performing class of earthquake clustering models Sequences with an anomalous excess of foreshocks are associated mostly with moderate mainshocks and preferentially with high heat flow We neither find evidence against the cascade nucleation hypothesis nor in favor of the pre‐slip nucleation hypothesis

Following the Kahramanmaras earthquake on February 6th, 2023, which significantly impacted central Turkey, hundreds of aftershocks within the first two weeks have continued to trigger widespread panic, forcing residents to evacuate their homes. The ongoing uncertainty surrounding the duration and magnitude of these aftershocks has heightened public anxiety. This report aims to provide an estimation of the magnitude of potential aftershocks and assess the likelihood of severe seismic events by analyzing statistical data from events recorded in the affected area during the 16 days following the main shock. Utilizing MATLAB, the time series of these aftershocks were examined. A statistical model was developed to correlate Aftershock Magnitude (AM) with the time interval between consecutive events and the time elapsed since the main shock. Findings indicate a consistent trend in AMs over time, enabling us to predict upper and lower magnitude bounds with 95% certainty. The analysis suggests that significant seismic activity is unlikely to continue in the near future, potentially alleviating immediate concerns among residents.