English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The epidemic-type aftershock sequence model (ETAS) is a simple stochasticprocess modeling seismicity, based on the two best-established empirical laws,the Omori law (power law decay ~1/t^{1+\theta} of seismicity after anearthquake) and Gutenberg-Richter law (power law distribution of earthquakeenergies). In order to describe also the space distribution of seismicity, weuse in addition a power law distribution ~1/r^{1+\mu} of distances betweentriggered and triggering earthquakes. We present an exact mapping between theETAS model and a class of CTRW (continuous time random walk) models, based onthe identification of their corresponding Master equations. This mapping allowsus to use the wealth of results previously obtained on anomalous diffusion ofCTRW. We provide a classification of the different regimes of diffusion ofseismic activity triggered by a mainshock. Specifically, we derive the relationbetween the average distance between aftershocks and the mainshock as afunction of the time from the mainshock and of the joint probabilitydistribution of the times and locations of the aftershocks. Our predictions arechecked by careful numerical simulations. We stress the distinction between the``bare'' Omori law describing the seismic rate activated directly by amainshock and the ``renormalized'' Omori law taking into account all possiblecascades from mainshocks to aftershocks of aftershock of aftershock, and so on.In particular, we predict that seismic diffusion or sub-diffusion occurs andshould be observable only when the observed Omori exponent is less than 1,because this signals the operation of the renormalization of the bare Omorilaw, also at the origin of seismic diffusion in the ETAS model.Comment: 43 pages in revtex, 2 tables, 12 figure

Diffusion of epicenters of earthquake aftershocks, Omori’s law, and generalized continuous-time random walk models