173 citations · 942 across the 29 of their papers we have counts for
9 papers · 1 filter
Statistics of seismic cluster durations
A. Saichev, D. Sornette
Using the standard ETAS model of triggered seismicity, we present a rigorous theoretical analysis of the main statistical properties of temporal clusters, defined as the group of e…
Fertility Heterogeneity as a Mechanism for Power Law Distributions of Recurrence Times
A. Saichev, D. Sornette
We study the statistical properties of recurrence times in the self-excited Hawkes conditional Poisson process, the simplest extension of the Poisson process that takes into accoun…
Theory of Earthquake Recurrence Times
A. Saichev, D. Sornette
The statistics of recurrence times in broad areas have been reported to obey universal scaling laws, both for single homogeneous regions (Corral, 2003) and when averaged over multi…
"Universal" Distribution of Inter-Earthquake Times Explained
A. Saichev, D. Sornette
We propose a simple theory for the ``universal'' scaling law previously reported for the distributions of waiting times between earthquakes. It is based on a largely used benchmark…
Renormalization of the ETAS branching model of triggered seismicity from total to observable seismicity
A. Saichev, D. Sornette
Several recent works point out that the crowd of small unobservable earthquakes (with magnitudes below the detection threshold ) may play a significant and perhaps dominant ro…
Distribution of the Largest Aftershocks in Branching Models of Triggered Seismicity: Theory of the Universal Bath's law
A. Saichev, D. Sornette
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…
Power Law Distributions of Seismic Rates
A. Saichev, D. Sornette
We report an empirical determination of the probability density functions of the number of earthquakes in finite space-time windows for the California cata…
Power law distribution of seismic rates: theory and data
A. Saichev, D. Sornette
We report an empirical determination of the probability density functions P(r) of the number r of earthquakes in finite space-time windows for the California catalog, over fixed sp…
Anomalous Power Law Distribution of Total Lifetimes of Branching Processes Relevant to Earthquakes
A. Saichev, D. Sornette
We consider a branching model of triggered seismicity, the ETAS (epidemic-type aftershock sequence) model which assumes that each earthquake can trigger other earthquakes (``afters…