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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 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

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…

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

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

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

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 2023-10-24 Ian Baughman , John B Rundle , Tianjin Zhang

Point processes have been dominant in modeling the evolution of seismicity for decades, with the Epidemic Type Aftershock Sequence (ETAS) model being most popular. Recent advances in machine learning have constructed highly flexible point…

Geophysics · Physics 2023-10-04 Samuel Stockman , Daniel J. Lawson , Maximilian J. Werner

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

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

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 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

The ETAS models are currently the most popular in the field of earthquake forecasting. The MCMC method is time-consuming and limited by parameter correlation while bringing parameter uncertainty. The INLA-based method "inlabru" solves these…

Applications · Statistics 2025-10-17 Ziwen Zhong

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 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

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…

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
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