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Ground-Motion Predictions from Empirical Attenuation Relationships versus Recorded Data: The Case of the 1997–1998 Umbria-Marche, Central Italy, Strong-Motion Data Set

¹ Istituto Nazionale di Geofisica e Vulcanologia
Via Bassini 15
20133 Milano, Italy
 (D.B., L.L., F.P., G.F.)
² Centro de Investigación Científica y de Educación Superior de Ensenada (CICESE)
División Ciencias de la Tierra
Departamento de Sismología
km 107 Carretera Tijuana-Ensenada
22860 Ensenada, Baja California, México
 (R.R.C.)

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 M_l = 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

and

log₁₀ (PGA) = –2.500 + 0.544M₁ – 1.284 log₁₀ R_h ± 0.292

log₁₀ (PGV) = –1.752 + 0.685M₁ – 1.167 log₁₀ R_h ± 0.297,

where PGA is measured in fraction of g and PGV in centimeters per second, M_l is the local magnitude in the range 4–6, R is the epicentral distance in the range 1–100 km, and R_h 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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