GNGTS 2018 - 37° Convegno Nazionale

636 GNGTS 2018 S essione 3.2 Cluster analysis. Where seismic and electrical surveys were acquired with coincident profiles, cluster analysis techniques were used to facilitate the data interpretation. Cluster analysis is a multivariate technique that makes it possible to group statistical units, characterized by different parameters (in this case, electrical resistivity, seismic velocity, seismic ray density and position in space xz ), which show similar characteristics to each other and dissimilar from those of other groups or clusters. At the end of the procedure, the final clusters should exhibit a high internal consistency (intra-cluster) and high external heterogeneity (inter- cluster). So, if the partition is successful, the objects within the clusters are close to each other, while objects belonging to different clusters are more distant from each other (Barbarito 1999). Generally, in the analysis for grouping it is not necessary to have in mind any interpretative model (Fabbris 1983). Although various studies (Rand 1971; Ohsumi 1980) indicate that different grouping strategies often lead to dissimilar results, however, the criteria for choosing algorithm have not yet been sufficiently explored. We choose a centroid-based algorithm that generally requires the number of clusters, k, and the initial centroid coordinates to be specified in advance. This aspect is considered to be one of the biggest drawbacks of these algorithms. An inappropriate choice of k may yield poor results. The proposed algorithm (Capizzi et al. 2017) does not fix the number of k clusters and choose automatically for each k value the initial centroids from data set. The used algorithm starts the first iteration by choosing the coordinates of the first centroids autonomously, splitting the interval between the minimum and maximum values ​of the used parameters in a number of intervals equal to number of partitions. The distance of each element from the initial nuclei and from the nuclei obtained after each iteration was calculated as the weighted sum of the Euclidean distances of all the considered variables: D=, where a , b , c and d are the weights and dx , dy , dC , dρ and dv are respectively the differences between the parametric xz coordinates, density of the seismic rays, electrical resistivity and P-wave velocity. The results related to the cluster analysis, for k=3, of SRT3 refraction seismic tomography and ERT3 resistivity tomography data are shown in Figure 2(d). In particular, the green cluster represents a layer of fractured limestone formations, whereas the yellow and the blue ones represent the carbonate and the tectonized Upper Jurassic breccias, respectively. Conclusions. The integrated analysis of 2D high-resolution shallow seismic refraction tomographies (SRT) and electrical resistivity tomographies (ERT& IPT) allowed to better define the lateral geometry of the NE-SW trending band composed of intensely tectonized carbonate breccias. Furthermore, the k-means cluster analysis allowed to reconstruct the lateral Fig. 2 - a) ERT3 electrical resistivity tomography; b) IPT3-induced polarization tomography; c) SRT3 Refraction seismic tomography; d) Results of the cluster analysis of SRT3 refraction seismic tomography and ERT3 resistivity tomography data.