Related papers: Predictability in the ETAS Model of Interacting Tr…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
The driving concept behind one of the most successful statistical forecasting models, the ETAS model, has been that the seismicity is driven by spontaneously occurring background earthquakes that cascade into multitudes of triggered…
Using the simple ETAS branching model of seismicity, which assumes that each earthquake can trigger other earthquakes, we quantify the role played by the cascade of triggered seismicity in controlling the rate of aftershock decay as well as…
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…
We consider a branching model of triggered seismicity, the ETAS (epidemic-type aftershock sequence) model which assumes that each earthquake can trigger other earthquakes (``aftershocks''). An aftershock sequence results in this model from…
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…
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…
Aftershock sequences are of particular interest in seismic research since they may condition seismic activity in a given region over long time spans. While they are typically identified with periods of enhanced seismic activity after a…