Statistical analysis of historical earthquake catalogues: California vs. Italy

摘要

Data depth is a statistical method that allows to order the points of a given space accordingto centrality with respect to an assumed probability distribution. The idea of usingdata depth to study the spatial distribution of earthquake epicenters was put forwardby Small (Small, 1990). More specifically, his intuition was inspired by an illustrationof data depth of directional data. He argued that a possible application was to studythe spatial distribution of earthquake epicenters on the Earth’ surface. California andItaly are, historically, regions with an important seismic activity. The aim of this workis to provide a map of seismic risk for both countries using the relevant earthquakecatalogues. Statistical methods include the centrality ordering (Liu et al, 1999) of datadepth and kernel density estimation (Silverman, 1986). We start with a preliminarydescriptive analysis of the catalogues, then we study the spatial distribution of epicentersand finally we consider the joint distribution of the geographical coordinates andthe magnitude of the shocks to obtain a comprehensive investigation of the data. Thefault structures of California and Italy are very different and our results allow a detailedillustration of the two situations. From the methodological point of view, the result thepresent study provide a first comparison of data depth and kernel density estimation asdata smoothers.