GNGTS 2017 - 36° Convegno Nazionale

352 GNGTS 2017 S essione 2.2 The statistical depth identifies the deepest function ( a sort of multivariate median function) and induces a center-out-ward ordering. Several depth notions generalizes unidimensional robust statistics to multivariate data but not all the depths are able to be generalized to functional data, due to the high dimensionality. We focus on Modified Band Depth, MBD ( López-Pintado and Romo, 2009). The choice of MBD in our clustering of waves is motivated by the following reasons: due to high oscillations of the curves, many curves leave their cluster for short intervals and the use of other depth measures does not allow a correct classification. Moreover when there is not a characterization of the clusters in terms of a representative shape, other alternative measures are not able to recognize the different clusters (see López-Pintado and Romo, 2009). Application. The data consist of a set of recordings of the first mainshock of 2012 Emilia sequence (20 May; Mw 6.1). The waveforms are relative to the seismic network RAN (Rete Accelerometrica Nazionale) managed by the Italian Department of Civil Protection, are obtained from ESM/ITACA database (esm.mi.ing.it ; itaca.mi.ingv.it ; Luzi et al., 2016). The signals were recorded by the stations, whose distances from the epicenter are in the range R=(16.1, 343.7) km. The goal is to divide the spatial domain into clusters by extracting information from the shapes of the underlying curves. Fig. 2 - Optimal allocation.