Statistical analysis of historical earthquake catalogues: California vs. Italy

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