Third International Workshop on "Geographical Analysis, Urban Modeling, Spatial Statistics"

1. Kernel Density Estimation Methods for a Geostatistical Approach in Seismic Risk Analysis: the Case Study of Potenza Hilltop Town (southern Italy) Maria Danese * , **, Maurizio Lazzari * , Beniamino Murgante ** International Conference on Computational Science and Its Applications (ICCSA 2008) - 30June -3July 2008 - Perugia, Italy * National Counsil of Research Archaeological and Monumental Heritage Institute, ** Università degli Studi della Basilicata, Dipartimento di Architettura, Pianificazione ed Infrastrutture di Trasporto

2. The problem: the seismic approach Program of prevision, prevention and protection Seismic event consequences evaluation and damages quantification Analysis of seismic damage scenarios

3. Analysis of seismic damage scenarios: instruments European Macroseismic Macroscale 1998 Vulnerability classes Damage levels Historical macroseismic scenarios Relationships between macroseismic intensity and damage levels

5. Methods: the Kernel Density Estimation (KDE)

7. KDE: intensity and its measures First order effects (Absolute location) Second order effects ( Relative location ) Properties of a spatial distribution* *Gatrell et al. (1996)

8. KDE: kernel functions

9. KDE: grid resolution

10. KDE: bandwidth Smaller Bandwidth (Levine, 1999) Greater Bandwidth (Levine, 1999) Relation between the bandwidth dimension and the study area

11. KDE: bandwidth approaches

12. KDE: a method for the right choose of bandwidth Nearest-Neighbor Index Nearest-Neighbor Expected Distance NNI > 1  observed distance is higher than the expected distance; events are more scattered than expected. NNI < 1  observed distance is smaller than expected distance Nearest-Neighbor Observed Distance

13. KDE: classification of results

14. The case of study: Potenza hilltop town 1857 1930 1980 Over-consolidated clayey substratum Sandy-conglomerate deposit lays Narrow asymmetrical ridge

15. The case of study: Potenza hilltop town

17. The case of study: parameters selection Intensity choice 6 5 D5 5 4 D4 3 3 D3 2 2 D2 1 1 D1 Intensity in northern sector Intensity in middle-southern sector Damage level

18. The case of study: parameters selection Kernel choice Cell size choice 0.1m

19. The case of study: parameters selection Bandwidth choice 6.8 Nearest neighbour mean calculated for whole point pattern Fixed for whole point pattern 1 KD map t (m) Methods used to estimate t Bandwidth approach Case

20. The case of study: parameters selection Bandwidth choice Sum of two resultant raster 3.9 6.8 D1-2-3 damage level: average of building’s minimum semi-dimension. D4-5 damage level: nearest neighbour mean calculated for whole point pattern. Two different fixed bandwidths 2 KD map t (m) Methods used to estimate t Bandwidth approach Case

21. The case of study: parameters selection Bandwidth choice Sum of two resultant raster 1.4÷9.9 6.8 4.1 D1-2-3 damage level: building’s minimum semi- Dimension D4-5 damage level: Building’s area ≤ mean + sd nearest neighbour mean calculated for whole point pattern Building’s area > mean + sd nearest neighbour mean calculated for whole point pattern multiplied by correction. One KDE with Fixed method, one with Adaptive method 3 KD map t (m) Methods used to estimate t Bandwidth approach Case

22. Results