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Forecast models in statistical seismology are commonly evaluated with log-likelihood scores of the full distribution P(n) of earthquake numbers, yet heavy tails and out-of-range observations can bias model ranking. We develop a tail-aware…

Geophysics · Physics 2026-02-24 Jiawei Li , Qingyuan Zhang , Didier Sornette

In statistical seismology, the Epidemic Type Aftershocks Sequence (ETAS) model is a branching process used world-wide to forecast earthquake intensity rates and reproduce many statistical features observed in seismicity catalogs. In this…

Geophysics · Physics 2023-01-09 Lorenzo Cristofaro , Roberto Garra , Enrico Scalas , Ilaria Spassiani

This article proposes a spatiotemporal point process model that enhances the classical Epidemic-Type Aftershock Sequence (ETAS) model by incorporating a renewal main-shock arrival process, which we term the renewal ETAS (RETAS) model. This…

Methodology · Statistics 2021-12-16 Tom Stindl , Feng Chen

The rapid proliferation of deep-learning-based detection and association methods has greatly expanded automatically generated earthquake catalogs, but has also introduced false detections, mis-associated arrivals, and poorly constrained…

Geophysics · Physics 2026-03-03 Ziye Yu , Jinqing Sun , Yuqi Cai , Zemin Liu , Pingping Wu , Xin Liu , Jiayan Tan

Several recent works point out that the crowd of small unobservable earthquakes (with magnitudes below the detection threshold $m_d$) may play a significant and perhaps dominant role in triggering future seismicity. Using the ETAS branching…

Geophysics · Physics 2007-12-04 A. Saichev , D. Sornette

In meteorology, engineering and computer sciences, data assimilation is routinely employed as the optimal way to combine noisy observations with prior model information for obtaining better estimates of a state, and thus better forecasts,…

Geophysics · Physics 2009-08-12 M. J. Werner , K. Ide , D. Sornette

Testing earthquake forecasts is essential to obtain scientific information on forecasting models and sufficient credibility for societal usage. We aim at enhancing the testing phase proposed by the Collaboratory for the Study of Earthquake…

Applications · Statistics 2026-02-03 Jonas R. Brehmer , Kristof Kraus , Tilmann Gneiting , Marcus Herrmann , Warner Marzocchi

Without rigorous attention to the completeness of earthquake catalogs, claims of new discoveries or forecasting skills cannot be deemed credible. Therefore, estimating the completeness magnitude (Mc) is a critical step. Among various…

Geophysics · Physics 2025-09-12 Xinyi Wang , Jiawei Li , Ao Feng , Didier Sornette

The conditional intensity function of a point process is a useful tool for generating probability forecasts of earthquakes. The epidemic-type aftershock sequence (ETAS) model is defined by a conditional intensity function, and the…

Applications · Statistics 2014-12-08 Takao Kumazawa , Yosihiko Ogata

Machine learning regression can predict macroscopic fault properties such as shear stress, friction, and time to failure using continuous records of fault zone acoustic emissions. Here we show that a similar approach is successful using…

We present a new method of data clustering applied to earthquake catalogs, with the goal of reconstructing the seismically active part of fault networks. We first use an original method to separate clustered events from uncorrelated…

Geophysics · Physics 2015-05-19 Guy Ouillon , Didier Sornette

Earthquakes in seismological catalogs and acoustic emission events in lab experiments can be statistically described as a linear Hawkes point process, where the spatio-temporal rate of events is a linear superposition of background…

Geophysics · Physics 2020-05-05 Jordi Baró

The development of new earthquake forecasting models is often motivated by one of the following complementary goals: to gain new insights into the governing physics and to produce improved forecasts quantified by objective metrics. Often,…

Geophysics · Physics 2023-01-19 Leila Mizrahi , Shyam Nandan , William Savran , Stefan Wiemer , Yehuda Ben-Zion

We present the "condensation" method that exploits the heterogeneity of the probability distribution functions (PDF) of event locations to improve the spatial information content of seismic catalogs. The method reduces the size of seismic…

Geophysics · Physics 2015-09-02 Y. Kamer , G. Ouillon , D. Sornette , J. Woessner

Earthquake nowcasting has been proposed as a means of tracking the change in large earthquake potential in a seismically active area. The method was developed using observable seismic data, in which probabilities of future large earthquakes…

Geophysics · Physics 2024-06-21 John B. Rundle , Geoffrey Fox , Andrea Donnellan , Lisa Grant Ludwig

In this short paper we propose to extend the ETAS model to micro-seismic events. For that we interpret the triggered events in an ETAS model as individual local clock advances of an independent background process. The solution of the ETAS…

Geophysics · Physics 2025-01-07 Matthias Holschneider

The epidemic-type aftershock sequence model (ETAS) is a simple stochastic process modeling seismicity, based on the two best-established empirical laws, the Omori law (power law decay ~1/t^{1+\theta} of seismicity after an earthquake) and…

Statistical Mechanics · Physics 2009-11-07 A. Helmstetter , D. Sornette

Over the past decades much effort has been devoted towards understanding and forecasting natural hazards. However, earthquake forecasting skill is still very limited and remains a great scientific challenge. The limited earthquake…

Many point process models have been proposed for describing and forecasting earthquake occurrences in seismically active zones such as California, but the problem of how best to compare and evaluate the goodness of fit of such models…

Applications · Statistics 2015-01-27 Andrew Bray , Ka Wong , Christopher D. Barr , Frederic Paik Schoenberg

Short-term earthquake clustering is one of the most important features of seismicity. Clusters are identified using various techniques, generally deterministic and based on spatio-temporal windowing. Conversely, the leading rail in…

Geophysics · Physics 2024-08-30 I. Spassiani , S. Gentili , R. Console , M. Murru , M. Taroni , G. Falcone