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This paper gives the technical solutions of implementing the space-time epidemic-type aftershock sequence (ETAS) model for short-term (1-day) earthquake forecasts for the all-Japan region in the Collaboratory for the Study of Earthquake Predictability (CSEP) project in Japan. For illustration, a retrospective forecasting experiment is carried out to forecast the seismicity in the Japan region before and after the Tokachi-Oki earthquake (M 8.0) at 19:50:07 (UTC) on 25 September 2003, in the format of contour images. The optimal model parameters used for the forecasts are estimated by fitting the model to the observation records up to the starting time of the forecasting period, and the probabilities of earthquake occurrences are obtained through simulations. To tackle the difficulty of heavy computations in fitting a complicated point-process to a huge dataset, an “off-line optimization” and “online forecasting” scheme is proposed to keep both the estimates of model parameters and forecasts updated according to the most recent observations. The results show that the forecasts have captured the spatial distribution and temporal evolution of the features of future seismicity. These forecasts are tested against the reference Poisson model that is stationary in time but spatially inhomogeneous.

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.

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

The majority of earthquakes occur unexpectedly and can trigger subsequent sequences of events that can culminate in more powerful earthquakes. This self-exciting nature of seismicity generates complex clustering of earthquakes in space and time. Therefore, the problem of constraining the magnitude of the largest expected earthquake during a future time interval is of critical importance in mitigating earthquake hazard. We address this problem by developing a methodology to compute the probabilities for such extreme earthquakes to be above certain magnitudes. We combine the Bayesian methods with the extreme value theory and assume that the occurrence of earthquakes can be described by the Epidemic Type Aftershock Sequence process. We analyze in detail the application of this methodology to the 2016 Kumamoto, Japan, earthquake sequence. We are able to estimate retrospectively the probabilities of having large subsequent earthquakes during several stages of the evolution of this sequence. Forecasting aftershock earthquakes is a critical step in improving seismic hazard mitigation. The authors here combine Bayesian methods with extreme value theory to tackle this problem - and manage to estimate the maximum magnitude of an expected earthquake as well as the arrival times in a pre-defined window.

This study investigates the missing data problem in the Japan Meteorological Agency catalog of the Kumamoto aftershock sequence, which occurred since April 15, 2016, in Japan. Based on the assumption that earthquake magnitudes are independent of their occurrence times, we replenish the short-term missing data of small earthquakes by using a bi-scale transformation and study their influence on the maximum likelihood estimate (MLE) of the epidemic-type aftershock sequences (ETAS) parameters by comparing the analysis results from the original and the replenished datasets. The results show that the MLEs of the ETAS parameters vary when this model is fitted to the recorded catalog with different cutoff magnitudes, while those MLEs remain stable for the replenished dataset. Further analysis shows that the seismicity becomes quiescent after the occurrence of the second major shock, which can be regarded as a precursory phenomenon of the occurrence of the subsequent M J 7.3 mainshock. This relative quiescence is demonstrated more clearly by the analysis of the replenished dataset. Graphical abstract (Left 6 panels) Illustration of applying the replenishing algorithm to the short missing of aftershocks in the Kumamoto aftershock sequence. (Right 6 panels) ETAS parameters estimated from the Kumamoto aftershock sequence with different magnitude thresholds. See text for details.

In this study, we have developed and implemented a new technology capable of probabilistically selecting phase arrival times and determining the initial polarity of seismic waveforms without the requirement of prior information. In this new method, the arrival time is determined through an eigen-equation associated with the probability distribution of the noise level, which is then used to calculate the probability of the polarity. We have tested this method using synthetic waveforms as well as records from well-established databases. The results demonstrate a high degree of concurrence with manually picked arrival times and polarities (98% accuracy) in the local seismic catalog. This suggests that the proposed method can provide consistent and unified judgments in phase picking tasks. In comparison, this method has shown comparable reliability to existing neural-network-based AI methods while maintaining greater portability due to its lack of dependence on training data. Graphical abstract

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.

In the present paper, a new method referred to as the Poisson probability map (PMAP) method is presented for identifying and visualizing seismic quiescence. With the PMAP, the P-value is defined as the probability that consecutive earthquakes occur according to a homogeneous Poisson process: the smaller the P-value, the less frequently the longer time interval is observed, i.e. the more significant the seismic quiescence. The PMAP method was applied to the sequence which preceded the Kurile Islands earthquake that occurred on 15 November 2006 [Mw = 8.3 and the centroid = (154.33 °E, 46.71 °N)]. The seismic quiescence is identified by a small P-value of 9.0 × 10–5 that was found to start in 1990.1, which lasted for 15.4 years and ended in 2005.5 within a circular area centered at (153.8 °E, 47.1 °N) and with a radius of 26 km. This seismic quiescence has not previously been recognized using any other method.

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

The paper gives first-order residual analysis for spatiotemporal point processes that is similar to the residual analysis that has been developed by Baddeley and co-workers for spatial point processes and also proposes principles for second-order residual analysis based on the viewpoint of martingales. Examples are given for both first- and second-order residuals. In particular, residual analysis can be used as a powerful tool in model improvement. Taking a spatiotemporal epidemic-type aftershock sequence model for earthquake occurrences as the base-line model, second-order residual analysis can be useful for identifying many features of the data that are not implied in the base-line model, providing us with clues about how to formulate better models.