Pasolini, C.

Abstract Several different attenuation models have recently been proposed for the Italian region to characterize the decay of macroseismic intensity with the distance from the source. The significant scatter between these relationships and some significant drawbacks that seem to characterize previous approaches (described in a companion article by Pasolini et al., 2008) suggest that the problem needs to be reconsidered. As a first step toward more detailed analyses in the future, this study aimed at developing an isotropic attenuation relationship for the Italian area. Because this attenuation relationship has to be used primarily in probabilistic seismic hazard assessment, major attention was given to evaluating the attenuation relationship in its complete probabilistic form. Another important aspect of this study was the preliminary evaluation of the intrinsic (i.e., independent of the specific attenuation relationship to be used) scattering of data, which represents the lowest threshold for the residual variance that cannot be explained by the attenuation relationship. Furthermore, the peculiar formal features of intensity data and relevant uncertainties were considered carefully. To reduce possible biases, the completeness of the available database was checked and a suitable data selection procedure was applied. Since epicentral intensity cannot be defined unambiguously from the experimental point of view, the attenuation relationship was scaled with a new variable that is more representative of the earthquake dimension. Several criteria were considered when evaluating competing attenuation formulas (explained variance, Bayesian information criteria, Akaike information criteria, etc.). Statistical uncertainty about empirical parameters was evaluated by using standard approaches and bootstrap simulations. The performance of the selected relationship with respect to a control sample was analyzed by using a distribution-free approach. The resulting equation for the expected intensity I at a site located at epicentral distance R is I IE 0:0086 0:0005 D h 1:037 0:027 ln D ln h ; where D R2 p h2, h 3:91 0:27 km, and IE is the average expected intensity at the epicenter for a given earthquake that can be computed from the intensity data (when available) or by using empirical relationships with the moment magnitude Mw or the epicentral intensity I0 reported by the Italian seismic catalog IE 5:862 0:301 2:460 0:055 Mw; IE 0:893 0:254 1:118 0:033 I0: Comparison of the model standard deviation (S.D.) (0.69 intensity degrees) with the intrinsic one (0.62) indicates that this attenuation equation is not far from being optimal.

Abstract We critically analyze the results on seismic intensity attenuation in Italy derived by Albarello and D’Amico (2004) and Gasperini (2001).We demonstrate that, due to the inadequacy of certain underlying assumptions, the empirical relationships determined in those studies did not best reproduce the decay of intensity as the distance from the source increases. We reconsidered some of the relevant concepts and assumptions used in these intensity-attenuation studies (macroseismic epicenter, epicentral intensity, data completeness) to suggest some useful recipes for obtaining unbiased estimates. In particular, we suggest that (1) data for distances from the source at which an intensity below the limit of diffuse perceptibility (≤IV) is expected should be excluded from attenuation computations because such data are clearly incomplete, (2) attenuation equations that include a term proportional to the epicentral intensity I0 with a coefficient different from 1.0 must not be used because they imply a variable offset between I0 and the intensity expected at the epicenter, and (3) epicentral intensities must be recomputed consistently with the attenuation equation because those reported by the Italian catalog do not generally correspond with the intensity predicted at the epicenter by the attenuation relationships so far proposed. Following these suggestions produces a significant reduction in the standard deviation of the model that might lead to a corresponding reduction of the estimates of seismic hazard.