GNGTS 2017 - 36° Convegno Nazionale

350 GNGTS 2017 S essione 2.2 Detecting clusters in spatially correlated waveforms F. Di Salvo 1 , R. Rotondi 2 , G. Lanzano 3 1 Dipartimento di Scienze Agrarie Alimentari e Forestali, Università di Palermo, Italy 2 Istituto di Matematica Applicata e Tecnologie Informatiche Enrico Magenes, CNR, Milano, Italy 3 Istituto Nazionale di Geofisica e Vulcanologia , Sezione di Milano, Italy Introduction. Seismic networks often record signals characterized by similar shapes that can also be considered according to their geographic positions. Many techniques have been proposed for the analysis of similarity between seismic waves and in our proposal the functional nature of the data are exploited in order to highlight the temporal dynamics of the signals and investigate their spatial dependence. In the situation under consideration, the observed data y s (t) can be assumed as a realization of a spatio-temporal process, where s is a is the geographic position and t indicates the observed time in a continous interval. An overview of statistical methods for analyzing functional data is shown in Ramsay and Silverman (2005). The data y s (t) are functional in the time dimension and can also be multidimensional: in particular we consider three components of the signal, recorded in three different directions, N-S, E-W and vertical. Therefore, we assume multidimensional curves, as functions of time, d y s (t) , with d=3, recorded, as a set of discrete measurements of spatially interdependent curves. The analysis of functional data provides new perspectives for deriving models and tools for the analysis of high-dimensional data in presence of spatio-temporal structures. Among the proposed methods, functional clustering has been adapted to the case of geographically referenced samples in order to delineate relatively contiguous zones with similar facies. Clustering of spatially correlated curves is a recent field of research; more details are given in Giraldo et al. (2010). Here the key contribution is to incorporate a spatial structure in clusters of waveforms relying on depth measures. A crucial point is represented by the alignment of the curves: functional data not perfectly aligned show peaks and other features at different locations and as a consequence, any pointwise synthesis of curve values become meaningless. A preprocessing step consists in aligning observed curves in order to discard nuisance effects. An application of the proposal is given in the section 3, where the methodology is applied to the set of recordings of the first mainshock of 2012 Emilia sequence (20 May; Mw 6.1). The analysis is performed by using the R software package (R Development Core Team, http://www.R-project.org) The methodology. In applied sciences there is an increasing interest for modeling correlated functional data: it is the case when samples of functions are observed over an interval at discrete time points (temporally correlated functional data) and when these functions are observed in different sites of a region (spatially correlated functional data). The considered methodology is based on waveform clustering dividing the spatial domain into clusters and extracting information from the shapes of the underlying functions. In a sample data the given functions may not be aligned and the mechanism for alignment is an important topic of the analysis. Warping (or aligning) procedures have also great importance in the waveform clustering process, because they reduce a negligible component of amplitude variability, identify nuisance effects in phase variation, that, if ignored, may result in a possible loss of information; the immediate consequence is that the underlying pattern could not be retained. The adopted warping procedure is based on a technique called elastic shape analysis of curves, proposed by Tucker et al. (2013); the technique aims to separate the phase (x-axis) and amplitude (y-axis) of the functional data. An important advantage of this procedure is a relative reasonable computational time, that is a crucial point when data come from dense seismic networks with three components broadband sensors.