A new magnitude-dependent ETAS model for earthquakes

TL;DR

This paper introduces a novel magnitude-dependent ETAS model for earthquakes, incorporating probabilistic dependence of triggered shocks' magnitudes on their triggers, validated by Italian seismic data and analyzed theoretically for inter-event times.

Contribution

The paper presents a new ETAS model with magnitude dependence, supported by statistical analysis and theoretical derivation of inter-event time distributions.

Findings

The model aligns with Gutenberg-Richter law at any event generation.

Derived inter-event time density for small values using probability generating functions.

Statistical analysis of Italian catalogs supports the magnitude dependence assumption.

Abstract

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 of triggered shocks is assumed to be probabilistically dependent on the triggering events' magnitude. To this aim, we propose a suitable probability density function. This function is such that, averaging on all triggering events' magnitudes, we obtain again the Gutenberg-Richter law. This ensures the validity of this law at any event's generation when ignoring past seismicity. The probabilistic dependence between the magnitude of triggered events' and the one of the corresponding triggering shock is motivated by some results of a statistical analysis of some Italian catalogues. The proposed model has been also theoretically analyzed here. In particular, we focus on the inter-event time which plays a very important role in the assessment of seismic hazard. Using the tool of the probability generating function and the Palm theory, we derive the density of inter-event time for small values.