GNGTS 2019 - Atti del 38° Convegno Nazionale

GNGTS 2019 S essione 2.1 313 set of distances from the epicenter to the sites where the same intensity I s is recorded. All this information was collected in a matrix to which a hierarchical agglomerative method for cluster analysis was then applied obtaining 4 classes A, B, C, and D with similar attenuation trends decreasing in steepness. So, given an earthquake of intensity I 0 belonging, for instance, to the class B, the parameters p j are estimated on the basis of the intensity records related to all the other earthquakes of the same class and with the same epicentral intensity [Zonno, Rotondi, Brambilla (2009)]. Anisotropic attenuation trend. Actually, it is well-known that, drawing the isoseismal lines of many earthquakes, the attenuation trend appears quite complex and not simply circular. Since it was observed that more rapid decay can be visibly recognizable along the direction perpendicular to that of the fault, it can be appropriate to use an elliptical shape for the isoseismal lines when information on the fault rupture that caused an earthquake, in particular on the direction and length of the rupture, is available [Agostinelli and Rotondi (2016)]. The solution we found to do that, consists in a plane transformation that turns the ellipse of major axis equal to the fault rupture into the circle of radius equal to the width of the first bin; then one repeats the estimation procedure in the transformed plane and then one associates the estimated probability distribution of the intensity I s that will be felt at a site to the original position of that site [Rotondi et al. (2016)]. The problem arises when we do not have information on the causative fault, e.g. when the fault does not appear on the surface, being completely hidden underneath surface rock layers (blind fault). Taking into account that the shape of the area of highest intensity is generally elongate along the direction of the active fault plane, we propose to deduce the fault dimensions from those of the ellipsoid hull (or spanning ellipsoid) that includes all the sites with I 0 - I s ≤1, i.e. the ellipsoid of minimal area such that all given points lie just inside or on the boundary of the ellipsoid. The idea is not new because already in 1973 Shebalin proposed to estimate the dimension and orientation of a seismogenic fault based on the ellipticity of the highest degree isoseismals; however, his and other researchers’ work relied only on hand-drawn, hence inherently arbitrary, isoseismals. Our solution is closer to the attempt made by De Rubeis et al . (1992), that is, we obtain information just on strike and dimensions of the meizoseismal area by running an algorithm of the free R software. The method has been first tested on some volcanic earthquakes of Etna area for which the fault is known [Azzaro et al. (2013)] and the positive results were also supported by the scoring criteria used to compare the different estimated damage scenarios. Then we have also applied the algorithm to the macroseismic field of some strong Italian earthquakes. References Agostinelli, C. and Rotondi, R. (2016). Analysis of macroseismic fields using statistical data depth functions: considerations leading to attenuation probabilistic modelling, Bull. Earth. Eng., 14, 1869--1884, doi:10.1007/ s10518-015-9778-2 Azzaro, R., D’Amico, S., Rotondi, R., Tuvè, T. and Zonno, G. (2013). Forecasting seismic scenarios on Etna volcano (Italy) through probabilistic intensity attenuation models: A Bayesian approach, Journal of Volcanology and Geothermal Research, 251, 149-157 De Rubeis, V., Gasparini, C., Maramai, A., Murru, M. and Tertulliani, A. (1992) The uncertainty and ambiguity of isoseismal maps, Earthquake Eng. Struct. Dyn. 21, 509-523 Rotondi R., Zonno G. (2004). Bayesian analysis of a probability distribution for local intensity attenuation, Annals of Geophysics, 47, 5, 1521-1540. Rotondi, R., Varini, E. and Brambilla, C. (2016). Probabilistic modelling of macroseismic attenuation and forecast of damage scenarios, Bull. Earth. Eng., 14, 1777--1796, doi:10.1007/s10518-015-9781-7 Zonno G., Rotondi R. and Brambilla C. (2009) Mining Macroseismic Fields to Estimate the Probability Distribution of the Intensity at Site, BSSA, 9}, 5, 2876-2892, doi: 10.1785/0120090042, http://hdl.handle.net/2122/5039