The document discusses kernel density estimation (KDE) methods for analyzing historical seismic damage scenarios to buildings in Potenza, Italy. KDE allows incorporating the spatial component of seismic intensity to better understand damage patterns. The case study applies KDE to historical macroseismic intensity data from Potenza, using different bandwidth approaches and parameters to create KDE maps of expected damage levels. The spatial analysis of past seismic impacts provides information to improve emergency planning and civil defense in case of future earthquakes.

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