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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

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

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

Aftershocks of aftershocks - and their aftershock cascades - substantially contribute to the increased seismicity rate and the associated elevated seismic hazard after the occurrence of a large earthquake. Current state-of-the-art…

Geophysics · Physics 2024-11-07 Leila Mizrahi , Dario Jozinović

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 Epidemic-Type Aftershock Sequences (ETAS) model and its variants effectively capture the space-time clustering of seismicity, setting the standard for earthquake forecasting. Accurate unbiased ETAS calibration is thus crucial. But we…

Geophysics · Physics 2025-06-23 Jiawei Li , Didier Sornette , Zhongliang Wu , Jiancang Zhuang , Changsheng Jiang

Earthquake signals are non-stationary in nature and thus in real-time, it is difficult to identify and classify events based on classical approaches like peak ground displacement, peak ground velocity. Even the popular algorithm of STA/LTA…

Signal Processing · Electrical Eng. & Systems 2021-01-19 Tonumoy Mukherjee , Chandrani Singh , Prabir Kumar Biswas

Earthquake catalog declustering is the procedure of separating event clusters from background seismicity, which is an important task in statistical seismology, earthquake forecasting, and probabilistic seismic hazard analysis. Several…

Geophysics · Physics 2025-04-14 Robert Shcherbakov , Sidhanth Kothari

Forecasting the full distribution of the number of earthquakes is revealed to be inherently superior to forecasting their mean. Forecasting the full distribution of earthquake numbers is also shown to yield robust projections in the…

Geophysics · Physics 2019-03-19 Shyam Nandan , Guy Ouillon , Didier Sornette , Stefan Wiemer

Seismicity and faulting within the Earth crust are characterized by many scaling laws that are usually interpreted as qualifying the existence of underlying physical mechanisms associated with some kind of criticality in the sense of phase…

Geophysics · Physics 2021-03-31 Shyam Nandan , Sumit Kumar Ram , Guy Ouillon , Didier Sornette

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

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

Earthquake forecasting and prediction have long and in some cases sordid histories but recent work has rekindled interest based on advances in early warning, hazard assessment for induced seismicity and successful prediction of laboratory…

Geophysics · Physics 2022-10-13 Laura Laurenti , Elisa Tinti , Fabio Galasso , Luca Franco , Chris Marone

For decades, classical point process models, such as the epidemic-type aftershock sequence (ETAS) model, have been widely used for forecasting the event times and locations of earthquakes. Recent advances have led to Neural Point Processes…

Geophysics · Physics 2026-03-12 Samuel Stockman , Daniel Lawson , Maximilian Werner

Geoscience and seismology have utilized the most advanced technologies and equipment to monitor seismic events globally from the past few decades. With the enormous amount of data, modern GPU-powered deep learning presents a promising…

Geophysics · Physics 2021-09-14 Bo Feng , Geoffrey C. Fox

Numerical weather forecasting using high-resolution physical models often requires extensive computational resources on supercomputers, which diminishes their wide usage in most real-life applications. As a remedy, applying deep learning…

Machine Learning · Computer Science 2023-10-06 Selim Furkan Tekin , Arda Fazla , Suleyman Serdar Kozat

This study introduces a deep learning-based framework for forecasting weather-related traffic crash risk using heterogeneous spatiotemporal data. Given the complex, non-linear relationship between crash occurrence and factors such as road…

Applications · Statistics 2026-03-06 Abimbola Ogungbire , Srinivas Pulugurtha

We evaluate the forecasting performance of a deep learning model, originally introduced as a pattern-extraction framework, that operates on the spatiotemporal evolution of seismic b-values in a short-term forecasting context. Model output…

Geophysics · Physics 2026-03-04 Jonas Köhler , Wei Li , Johannes Faber , Georg Rümpker , Nishtha Srivastava

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

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