Related papers: Topological properties of epidemic aftershock proc…
Using the ETAS branching model of triggered seismicity, we apply the formalism of generating probability functions to calculate exactly the average difference between the magnitude of a mainshock and the magnitude of its largest aftershock…
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…
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…
We present a new kind of critical stochastic finite-time-singularity, relying on the interplay between long-memory and extreme fluctuations. We illustrate it on the well-established epidemic-type aftershock (ETAS) model for aftershocks,…
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…
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…
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…
The Hawkes process is a versatile stochastic model for point patterns that exhibit self-excitation, that is, the property that an event occurrence increases the rate of occurrence for some period of time in the future. We present a Bayesian…
We consider an epidemic-type aftershock model (ETAS($F$)) for a large class of distributions $F$ determining the number of direct aftershocks. This class includes Poisson, Geometric, Negative Binomial distributions and many other. Assuming…
Many time series in natural and social sciences can be seen as resulting from an interplay between exogenous influences and an endogenous organization. We use a simple (ETAS) model of events occurring sequentially, in which future events…
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…
Hawkes process is one of the most commonly used models for investigating the self-exciting nature of earthquake occurrences. However, seismicity patterns have complicated characteristics due to heterogeneous geology and stresses, for which…
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…
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…
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…
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…
Short-term earthquake clustering is one of the most important features of seismicity. Clusters are identified using various techniques, generally deterministic and based on spatio-temporal windowing. Conversely, the leading rail in…
Let $V_M,(m_0)$ be the number of m>M aftershocks caused by $m_0$ event. We consider the $V_M,(m_0)$ distribution within epidemic-type seismicity models, ETAS(F). These models include the Gutenberg-Richter law for magnitude and Utsu law for…
This paper extends the existing fractional Hawkes process to better model mainshock-aftershock sequences of earthquakes. The fractional Hawkes process is a self-exciting point process model with temporal decay kernel being a Mittag-Leffler…
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…