The clock advance description of the Epidemic Type Aftershock Sequence (ETAS) model

TL;DR

This paper extends the ETAS model to include micro-seismic events by interpreting triggered events as local clock advances, enabling a comprehensive, scale-inclusive seismic modeling without artificial cutoffs.

Contribution

It introduces a novel interpretation of ETAS as a sum of independent, time-adjusted background processes, allowing modeling of all seismic event scales.

Findings

Incorporates micro-seismic events into ETAS model.

Eliminates the need for a small magnitude cutoff.

Provides a scale-inclusive seismic modeling framework.

Abstract

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 model thus becomes the sum of an infinite Markov chain of independent time adjusted background processses. This allows the incorporation of events at all scales. No artificial small magnitude cutoff is needed.