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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

A prominent feature of earthquakes is their empirical laws including memory (clustering) in time and space. Several earthquake forecasting models, like the EpidemicType Aftershock Sequence (ETAS) model, were developed based on earthquake…

The scientific process of earthquake forecasting involves estimating the probability and intensity of earthquakes in a specific area within a certain timeframe, based on seismic activity laws and observational data. Epidemic-Type Aftershock…

Geophysics · Physics 2023-10-05 Haoyuan Zhang , Shuya Ke , Wenqi Liu , Yongwen Zhang

The Epidemic Type Aftershock Sequence (ETAS) model is one of the most widely-used approaches to seismic forecasting. However most studies of ETAS use point estimates for the model parameters, which ignores the inherent uncertainty that…

Applications · Statistics 2021-09-14 Gordon J Ross

Self-exciting Hawkes processes are used to model events which cluster in time and space, and have been widely studied in seismology under the name of the Epidemic Type Aftershock Sequence (ETAS) model. In the ETAS framework, the occurrence…

Computation · Statistics 2020-02-06 Aleksandar A. Kolev , Gordon J. Ross

Currently, one of the best performing and most popular earthquake forecasting models rely on the working hypothesis that: "locations of past background earthquakes reveal the probable location of future seismicity". As an alternative, we…

Geophysics · Physics 2020-01-08 Shyam Nandan , Guy Ouillon , Didier Sornette , Stefan Wiemer

Epidemic-Type Aftershock Sequence (ETAS) models are point processes that have found prominence in seismological modeling. Its success has led to the development of a number of different versions of the ETAS model. Among these extensions is…

Applications · Statistics 2022-07-06 Tom Stindl , Feng Chen

Earthquakes are one of the most devastating natural disasters that plague society. A skilled, reliable earthquake forecasting remains the ultimate goal for seismologists. Using the detrended fluctuation analysis (DFA) and conditional…

The Himalayan region, including Nepal, is prone to frequent and large earthquakes. Accurate forecasting of these earthquakes is crucial for minimizing loss of life and damage to infrastructure. In this study, we propose various time-scaled…

Applications · Statistics 2025-08-07 Agniva Das , Muralidharan K

We propose two methods to calibrate the parameters of the epidemic-type aftershock sequence (ETAS) model based on expectation maximization (EM) while accounting for temporal variation of catalog completeness. The first method allows for…

Geophysics · Physics 2022-01-05 Leila Mizrahi , Shyam Nandan , Stefan Wiemer

The ETAS model is widely employed to model the spatio-temporal distribution of earthquakes, generally using spatially invariant parameters. We propose an efficient method for the estimation of spatially varying parameters, using the…

Geophysics · Physics 2017-06-28 Shyam Nandan , Guy Ouillon , Stefan Wiemer , Didier Sornette

As part of an effort to develop a systematic methodology for earthquake forecasting, we use a simple model of seismicity based on interacting events which may trigger a cascade of earthquakes, known as the Epidemic-Type Aftershock Sequence…

Statistical Mechanics · Physics 2015-06-24 A. Helmstetter , D. Sornette

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

The spatio-temporal properties of seismicity give us incisive insight into the stress state evolution and fault structures of the crust. Empirical models based on self-exciting point-processes continue to provide an important tool for…

Geophysics · Physics 2023-03-01 Jack B. Muir , Zachary E. Ross

Performing Bayesian inference for the Epidemic-Type Aftershock Sequence (ETAS) model of earthquakes typically requires MCMC sampling using the likelihood function or estimating the latent branching structure. These tasks have computational…

Applications · Statistics 2024-05-29 Samuel Stockman , Daniel J. Lawson , Maximilian J. Werner

The spatio-temporal Epidemic Type Aftershock Sequence (ETAS) model is widely used to describe the self-exciting nature of earthquake occurrences. While traditional inference methods provide only point estimates of the model parameters, we…

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

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

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

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
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