Local Spatial Log-Gaussian Cox Processes for seismic data

In this paper, we propose the use of advanced and flexible statistical models to describe the spatial displacement of earthquake data. The paper aims to account for the external geological information in the description of complex seismic point processes, through the estimation of models with space varying parameters. A local version of the Log-Gaussian Cox processes (LGCP) is introduced and applied for the first time, exploiting the inferential tools in Baddeley (2017), estimating the model by the local Palm likelihood. We provide methods and approaches accounting for the interaction among points, typically described by LGCP models through the estimation of the covariance parameters of the Gaussian Random Field, that in this local version are allowed to vary in space, providing a more realistic description of the clustering feature of seismic events. Furthermore, we contribute to the framework of diagnostics, outlining suitable methods for the local context and proposing a new step-wise approach addressing the particular case of multiple covariates. Overall, we show that local models provide good inferential results and could serve as the basis for future spatio-temporal local model developments, peculiar for the description of the complex seismic phenomenon.