Multiscale processes to describe the Eastern Sicily Seismic Sequences

Abstract

In this paper, a version of hybrid of Gibbs point process models is proposed as method to characterise the multiscale interaction structure of several seismic sequences occurred in the Eastern Sicily in the last decade. Seismic sequences were identified by a clustering technique based on space-time distance criterion and hierarchical clustering. We focus our analysis on five small seismic sequences, showing that two of these are described by an inhomogeneous Poisson process (not significant interaction among events) while the other three clusters are described by a Hybrid-Geyer process (mutiscale interaction between events). The proposed method, although it still needs extensive testing on a larger catalogue, seems to be a promising tool for the characterization of seismogenic sources through the analysis of induced seismicity.

On spatial and spatio-temporal multi-structure point process models

“…[10] introduced the spatial multi-scale Geyer saturation point process that was applied in epidemiology by [46] and in seismology by [77] and [78]. [75] ex-tend the definition and the estimation procedure in the general case of an inhomogeneous spatio-temporal multi-scale Geyer saturation process which density is given by…”

“…Such multi-structure phenomena motivate statisticians to construct new spatial point process models, e.g. in ecology [56,85,72], in epidemiology [46] and in seismology [77,78], mainly based on Gibbs processes, but not only [55]. There are very few spatio-temporal models: [39] and [75] modeled the multi-scale spatio-temporal structure of forest fires occurrences by log-Gaussian Cox processes (LGCP) and multi-scale Geyer saturation process respectively, [47] developed a multi-scale area-interaction model for varicella cases and [51] modelled the locations of muskoxen herds by LGCP with a constructed covariate measuring local interactions.…”

A spatio-temporal multi-scale model for Geyer saturation point process: application to forest fire occurrences

“…The hybrid introduced in (5) is the best choice for a multi-scale generalization of the Geyer saturation process (Baddeley et al, 2013). Model ( 6) is applied with suitable fit on epidemiology data (Iftimi et al, 2017) and earthquake data (Siino et al, 2017;2018b).…”

A spatio-temporal multi-scale model for Geyer saturation point process: Application to forest fire occurrences

“…modelled by the Poisson process [33,34]) or clustering (mostly modelled by Cox processes [16], in particular log-Gaussian Cox processes [41,14,12,20], Poisson Cluster processes [44,13,21] and Shot-Noise Cox processes [11,42,40]) or inhibition (modelled by Strauss processes [60,17], Matérn hard core processes [39,24] and determinantal point processes [38,35]). However, lot of phenomena present interactions at different scales what motivate statisticians to develop new models, mainly spatial models in ecology [36,64,49], epidemiology [30] or seismology [58,59], but very few spatio-temporal models in environment [23] or epidemiology [29] as lately reviewed in [51]. Multi-scale models are mostly based on Gibbs models (see [19] for a recent review on Gibbs models) as they offer a large class of models which allow any of the above mentioned interaction structure.…”

“…The choice of the normalization constant allows to well define a probability density in the case where the product of densities is integrable. In particular, [7] introduced the spatial multi-scale Geyer saturation point process that has then been applied in epidemiology [30] and in seismology [58,59]. [29] extended the hybridization approach to the spatio-temporal framework and introduced the spatio-temporal multi-scale area-interaction process.…”