Spatial clustering of earthquakes by data depth

We study the spatial clustering of earthquake epicenters using statistical depth. Data are spatial coordinates of Italian earthquake epicenters recorded in the period 1600 -- 2003 with magnitude greater than $4.5$ $M_w$. In general, data depth provides a centrality ordering according to a reference data set or probability distribution. In the present application, the depth value of a particular location with respect to the spatial distribution of epicenters is interpreted as a measure of seismic risk, i. e., deeper locations have higher risks. Hence, depth contours describe the risk profile of a territory. Both global and local depth functions are used, the former defining a monotonic ranking of the locations covered by the catalogue, the latter aimed at a more flexible ranking, possibly with multiple centers.