We evaluate the goodness of fit of attenuation relations commonly used for the Italian national territory (Sabetta and Pugliese, 1996) by using the maximum likelihood approaches of Spudich et al. (1999) and Scherbaum et al. (2004). According to the classification scheme proposed by Scherbaum et al. (2004), the Sabetta and Pugliese (1996) relationships show consistent discrepancies between the predicted and the observed peak ground acceleration (pga) at rock sites in the Umbria- Marche region, central Italy; however, at soft sites the agreement between observations and prediction is satisfactory. The bias of the residuals, computed with the Sabetta and Pugliese (1996) models for pga, peak ground velocity, (pgv) and pseudovelocity response spectrum (psv) (for Ml = 4–6 and epicentral distances up to 100 km) is negative. This means that on the average, the predictions overestimate the observations, but the overestimation decreases with increasing magnitude. Then, we present regional predictive relations (UMA05) for maximum horizontal pga, pgv, and 5%-damped psv, derived from the strong-motion data recorded in the Umbria-Marche area and classified as to four site categories. The UMA05 attenuation relationships for rock sites are

log10 (PGA) = −2.487 + M1 − 1.280 log10 (R2 + 3.942)0.5 ± 0.268

log10 (PGV) = −1.803 + 0.687M1 − 1.150 log10 (R2 + 2.742)0.5 ± 0.300


log10 (PGA) = −2.500 + 0.544M1 − 1.284 log10Rh ± 0.292

log10 (PGV) = −1.752 + 0.685M1 − 1.167 log10Rh ± 0.297,

where pga is measured in fraction of g and pgv in centimeters per second, Ml is the local magnitude in the range 4–6, R is the epicentral distance in the range 1–100 km, and Rh is the hypocentral distance in kilometers. We used the random effect model (Brillinger and Priesler, 1985; Abrahamson and Youngs, 1992; Joyner and Boore, 1993; Joyner and Boore, 1994) to estimate the component of variance related to the earthquake-to-earthquake, station-to-station, and record-to-record variability, and to quantify the benefit of introducing a site classification in the attenuation model to reduce the variance. The introduction of the site classification in the attenuation model allows a reduction of the station-to-station component of variability (from 0.19 to 0.14 for pga, and from 0.21 to 0.18 for pgv). We also found that the record- to-record component represents the largest contribution to the model uncertainty.

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