GNGTS 2022 - Atti del 40° Convegno Nazionale

22 GNGTS 2022 Sessione 1.1 Fig. 1 - Distribution of epicenters a) and stations b) of the second data set analyzed. The dataset consists of 266 events, 353 stations and 13,952. The different colors on the epicenter indicate the magnitude of the earthquake, while map in b) the reverse triangles are stations in quadrant Q1, blue in Q2, green in Q3 and cyan in Q4. a) b) discarded if the precomputed κ is available for less than half of the considered frequency range (e.g. 6 out of 11 values) and the associated standard deviation is larger than 0.015 s. Nonparametric model. We defined κ avg ( r ) using a nonparametric approach as Anderson (1991), Anderson and Lei (1994), and Fernández et al. (2010), that characterizes the variation of the observed spectral decay parameter with distance. This technique looks for a function that describes the observed values of κ with hypocenter distance without assuming an a priori physical model for mathematical function. The nonparametric method consists of finding a smooth function κ avg ( r ) assuming that κ varies slowly with distance. Using this technique, observed values of κ of earthquakes recorded at different hypocenter distances complement each other and allow definition of κ avg ( r ) at a wide distance range. Independent Estimates of κ s . κ s can be also estimated by single earthquakes by assuming that: κ ( r ) = κ s + κ avg ( r ), For an individual earthquake, the observed values of κ versus distance r are linearly least squared fitted and κ s would correspond to the value of κ at the origin. However, the least- square regression will tend to find the best fit to the mean values of the data and, because κ 0 ≥ 0, κ s will be overestimated. Thus, this estimate of κ s must be corrected by subtracting the mean κ 0 . Results and discussions. Figure 2a shows the nonparametric function κ avg ( r ) and a sample of the observed κ values versus hypocenter distance from four different stations (AQU, AQV, ARRO and ARVD). As we can observe, the shape of κ avg ( r ) is the same for all sites, but it is scaled by the respective value of κ 0 ; for a given distance, κ shows great variability. These observations suggest that it should be a spatial variability of the attenuation between the different source-station paths, already observed in Castro et al. (2000) from the earthquakes