D'Alessandro A. , Capizzi P., Luzio D., Martorana R., Messina N.

1. Improvement of HVSR technique by cluster analysis D'Alessandro A., Capizzi P., Luzio D., Martorana R., Messina N.

2. HVSR tecnique 1 If the shape of the H/V curves is controlled by the S-wave transfer function within the shallowest sedimentary layers, then both H/V peak frequencis and amplitudes may be straightforward related to subsoil resonance frequencies and site amplification factors. On the other hand, if the shape of the H/V curves is controlled by the polarization of fundamental Rayleigh waves (ellipticity), then only an indirect correlation between the H/V peak amplitude and the site amplification may exist.

3. HVSR Calculation

4. HVSR Calculation Relibility SESAME Criteria

5. How select windows? Time Domain

6. How select windows? Frequency Domain

7. How select windows? Most authors tend to exclude from the computation of the average the non-stationary portion of the recorded noise, thus considering only the low-amplitude part of signal; Some authors (i.e. Mucciarelli (1998)) showed that the use of non-stationary, high-amplitude noise windows improves the capability of the HVSR curve to mimic the response obtained with weak motion recordings of earthquakes.

8. How select windows? Can you use a non-arbitrary approach? Cluster analysis!

9. Cluster Analysis Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called cluster) are more similar (internal cohesion - homogeneity) to each other than to those in other groups (external isolation - separation).

10. Cluster Analysis So, a clustering algorithm is used to group together those objects which are most similar (nearest) to each other. Many clustering algorithms exist, and can be categorized into two main types: Hierarchical methods; Non-hierarchical methods or model based.

11. Cluster Analysis • Advantages of the HierarchicalMethods: • You work from the Similarity/Dissimilarity between the objects to be grouped together. A type of Similarity/Dissimilarity can be chosen which is suited to the subject studied and the nature of the data; • One of the results is the dendrogram which shows the progressive grouping of the data. It is then possible to gain an idea of a suitable number of classes into which the data can be grouped; • Itis an explorativemethod and isnotnecessary to define a priori the number of clusters;

12. AgglomerationCriterion Agglomerative: in agglomerative hierarchical clustering, each object begins the process as the only member of its own cluster. If there are N objects, the process then starts with N clusters. The two most similar objects then combine to form a cluster, producing N-1 clusters in total. This process is repeated until all objects are finally members of a single cluster. Divisive: This is a "top down" approach: all observations start in one cluster, and splits are performed recursively as one moves down the hierarchy.

13. Similarities and Dissimilarities Similarity coefficients: Cooccurrence, Cosine, Covariance (n-1), Covariance (n), Dice coefficient (also known as Sorensen coefficient), General similarity, Gower coefficient, Inertia, Jaccard coefficient, Kendall correlation coefficient, Kulczinski coefficient, Ochiai coefficient, Pearson’s correlation coefficient, Pearson Phi, Percent agreement, Rogers & Tanimoto coefficient, Sokal & Michener coefficient (or simple matching coefficient), Sokal & Sneath coefficient, Spearman correlation coefficient, …... Dissimilarity coefficients: Bhattacharya's distance, Bray and Curtis' distance, Canberra's distance, Chebychev's distance, Chi² distance, Chi² metric, Chord distance, Squared chord distance, Dice coefficient, Euclidian distance, Geodesic distance, Jaccard coefficient, Kendall dissimilarity, Kulczinski coefficient, Mahalanobis distance, Manhattan distance, Ochiai coefficient, Pearson's dissimilarity, Pearson's Phi, General dissimilarity, Rogers & Tanimoto coefficient, Sokal & Michener's coefficient, Sokal & Sneath coefficient, Spearman dissimilarity,…..

14. Similarities and Dissimilarities Normalized Standard Correlation

15. LinkageCriteria Simple linkage: The dissimilarity between A and B is the dissimilarity between the object of A and the object of B that are the most similar. Complete linkage: The dissimilarity between A and B is the largest dissimilarity between an object of A and an object of B. Average linkage: The dissimilarity between A and B is the average of the dissimilarities between the objects of A and the objects of B.

16. Dendrogram A dendrogram is a tree diagram frequently used to illustrate the arrangement of the clusters produced by hierachical clustering.

17. Dataset About 1,000 seismic noise measurements each 46 minutes long

18. Dataset 1

19. Dataset 1

20. Similarity Matrix 1

21. Dendrogram 1

22. Interpretation 1

23. Interpretation 1

24. Interpretation 1

25. Dataset 2

26. Dataset 2

27. Similarity Matrix 2

28. Dendrogram 2

29. Interpretation 2

30. Interpretation 2

31. Interpretation 2

32. Dataset 3

33. MatricedeiDati 3

34. Similarity Matrix 3

35. Dendrogram 3

36. Interpretation 3

37. Interpretation 3

38. Interpretation 3

39. Conclusion and Remarks There no is correspondence between variation in the HVSR content and the high-energy transients in the recordings; Cluster analysis can be used to automatically process HVSR data allowing us to discriminate the part of the signals related to geological structures from those linked to the sources; Extension to the spatial clustering of the HVSR curves to identify homogeneous areas in seismic perspective;