Clustering macroseismic fields by statistical data depth functions

The size of historical earthquakes is given by the macroseismic intensity, an ordinal variable expressed by different scales and closely related to the effects produced by an earthquake on humans, buildings and natural environment. The collection of intensity values recorded at sites in the area surrounding the seismic source constitutes the macroseismic field of an earthquake. Our aim is to identify clusters of macroseismic fields according to size and shape of their isoseismals (lines of equal shaking). To this end we consider the modified version of the local half-region depth, a nonparametric method especially suitable for ordering irregular curves (related to isoseismal lines in our application) with many crossing points. Then the most central curve represents the global pattern of intensity decay. To deal with the case of possible multiple centres, a hierarchical algorithm is applied to the dissimilarity matrix based on the local modified half-region depth similarity of a pair of curves. The method is first tested on sets of simulated fields divided into groups whose isoseismal lines differ in shape (circle or ellipse), size, eccentricity, and rotation angle. Then we analyse 31 fields associated with earthquakes of intensity IX, drawn from the Italian Macroseismic Database DBMI11.