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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

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

We propose a new version of the ETAS model, which we also analyze theoretically. As for the standard ETAS model, we assume the Gutenberg-Richter law as a probability density function for background events' magnitude. Instead, the magnitude…

Probability · Mathematics 2015-04-23 Ilaria Spassiani , Giovanni Sebastiani

Most point process models for earthquakes currently in the literature assume the magnitude distribution is i.i.d. potentially hindering the ability of the model to describe the main features of data sets containing multiple earthquake…

Applications · Statistics 2026-04-13 Louis Davis , Boris Baeumer , Ting Wang

The essence of the cumulative effect of a round-the-world seismic echo is that the echo can serve as a trigger for a second tremors in the epicentral zone of the earthquake that gave rise to the echo. According to the classification of…

Geophysics · Physics 2024-04-30 A. V. Guglielmi , O. D. Zotov

Mainshocks are often followed by increased earthquake activity (aftershocks). According to the Omori-Utsu law, the rate of aftershocks decays as a power law over time. While aftershocks typically occur in the vicinity of the mainshock,…

Geophysics · Physics 2023-10-05 Yongwen Zhang , Maor Elbaz , Shlomo Havlin , Yosef Ashkenazy

Short and long range interactions between earthquakes are attracting increasing interest. Scale invariant properties of seismicity in time, space and energy argue for the presence of complex triggering mechanisms where, like a cascade…

Geophysics · Physics 2007-05-23 Patrizia Tosi , Valerio De Rubeis , Vittorio Loreto , Luciano Pietronero

In models of triggered seismicity and in their inversion with empirical data, the detection threshold m_d is commonly equated to the magnitude m_0 of the smallest triggering earthquake. This unjustified assumption neglects the possibility…

Geophysics · Physics 2007-05-23 D. Sornette , M. J. Werner

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 acoustic emission activity associated with recent rock fracture experiments under different conditions has indicated that some features of event-event triggering are independent of the details of the experiment and the materials used…

Geophysics · Physics 2018-01-17 Jordi Baró , Jörn Davidsen

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

We present an analytical solution and numerical tests of the epidemic-type aftershock (ETAS) model for aftershocks, which describes foreshocks, aftershocks and mainshocks on the same footing. The occurrence rate of aftershocks triggered by…

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

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

We investigate the spatial distribution of aftershocks and we find that aftershock linear density exhibits a maximum, that depends on the mainshock magnitude, followed by a power law decay. The exponent controlling the asymptotic decay and…

Geophysics · Physics 2009-07-17 E. Lippiello , L. de Arcangelis , C. Godano

Earthquakes are complex physical processes driven by the stick-slip motion of a sliding fault. After the main quake, a series of aftershocks typically follows. These are loosely defined as events that follow a given event and occur within…

Geophysics · Physics 2022-12-12 Pinaki Kumar , Roberto Benzi , Jeannot Trampert , Federico Toschi

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…

Induced seismicity has emerged as a source of a significant earthquake hazard associated with recent development of unconventional energy resources. Therefore, it is imperative to develop stochastic models that can accurately describe the…

Geophysics · Physics 2024-10-08 Robert Shcherbakov

Earthquake aftershock identification is closely related to the question "Are aftershocks different from the rest of earthquakes?" We give a positive answer to this question and introduce a general statistical procedure for clustering…

Geophysics · Physics 2010-03-01 Ilya Zaliapin , Andrei Gabrielov , Vladimir Keilis-Borok , Henry Wong

We find the static displacement, stress, strain and the modified Columb failure stress produced in an elastic medium by a finite size rectangular fault after its dislocation with uniform stress drop but a non uniform dislocation on the…

Geophysics · Physics 2007-05-23 R. Console , F. Catalli