Ground-Motion Predictions from Empirical ... - GeoScienceWorld

Bulletin of the Seismological Society of America, Vol. 96, No. 3, pp. 984–1002, June 2006, doi: 10.1785/0120050102

Ground-Motion Predictions from Empirical Attenuation Relationships versus Recorded Data: The Case of the 1997–1998 Umbria-Marche, Central Italy, Strong-Motion Data Set by D. Bindi, L. Luzi, F. Pacor, G. Franceschina, and R. R. Castro

Abstract 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 UmbriaMarche 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) ⳱ ⳮ 2.487 Ⳮ 0.534Ml ⳮ 1.280 log10 (R2 Ⳮ 3.942)0.5 Ⳳ 0.268 log10 (PGV) ⳱ ⳮ 1.803 Ⳮ 0.687Ml ⳮ 1.150 log10 (R2 Ⳮ 2.742)0.5 Ⳳ 0.300 and log10 (PGA) ⳱ ⳮ 2.500 Ⳮ 0.544Ml ⳮ 1.284 log10 Rh Ⳳ 0.292 log10 (PGV) ⳱ ⳮ 1.752 Ⳮ 0.685Ml ⳮ 1.167 log10 Rh Ⳳ 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 recordto-record component represents the largest contribution to the model uncertainty.

Introduction Attenuation relations for ground-motion models provide an estimate of ground shaking at a given distance from an earthquake of specified magnitude. For practical engineering

purposes, such relationships should be based on reliable observational data, must be relatively simple, and must involve design variables that can be assessed with some degree of 984

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Ground-Motion Predictions from Empirical Attenuation Relationships versus Recorded Data

confidence. Attenuation relations are based on strong ground motion recorded during previous earthquakes or generated by applying stochastic models. The characteristics of these records depend on a handful of independent parameters such as earthquake magnitude, source-to-site distance, and soil type at the recording site. Thus, the use of them requires more than a simple analysis of how the ground motion varies with distance. The predictive equations are, in fact, also important for probabilistic seismic hazard assessment (Cornell, 1968) and for deterministic seismic hazard analysis. There have been previous reviews and discussions on empirical and theoretical prediction of strong ground motion; among the most notable and recent ones are those by Douglas (2003) and Campbell (2002), for empirical models, and that by Boore (2003), which covers the topic of attenuation relations obtained with seismological models. Specific attenuation relations have been provided for different regions of the world (western North America, eastern North America, European countries, Japan, etc.), and worldwide relations have been devoloped for different tectonic regimes. In Italy, the attenuation relations most widely used for predicting peak ground acceleration (PGA) and peak ground acceleration (PGV) were proposed by Sabetta and Pugliese (1987) and subsequently extended to pseudovelocity spectral ordinates (Sabetta and Pugliese, 1996). These equations are based on 95 accelerometric recordings of 17 earthquakes with various types of focal mechanisms, which occurred in Italy in the time span 1972–1984, and have local or moment magnitudes in the range 4.6–6.8 and epicentral distance up to 100 km. Because of the recent 1997–1998 seismic sequence (maximum magnitude Ml 5.8), and two previous earthquakes (Norcia 1979 Ml 5.9, Gubbio 1984 Ml 5.2), a large accelerogram data set is now available for UmbriaMarche, central Italy. In this study we investigate some issues regarding the attenuation relationships, such as their validation with recorded data, their reliability when applied beyond the range of validity, and the origin of the uncertainties affecting the predictions. We first explore the suitability of the ground models developed for the Italian national territory (Sabetta and Pugliese, 1996) to predict the strong ground-motion parameters in central Italy by following a statistical approach. First we use the likelihood approach of Spudich et al. (1999) to measure the average residuals between observations and predictions and their dependence on magnitude and distance. As a second approach we follow Scherbaum et al. (2004) to measure the goodness of fit. Since we find that the predictions from the Sabetta and Pugliese (1996) ground models overestimate the recorded data in Umbria-Marche region at small magnitudes, we formulate new regional predictive models (UMA05) for the Umbria-Marche area using events within the local magnitude range of 4 to 6 and considering several strong motion parameters such as PGA, PGV, and pseudo velocity response spectrum (PSV). We derive the ground-motion models considering both epicentral and hypocentral distance.

Because the nature of the model uncertainties and the possibility of reducing the standard deviation by adding complexities to the predictive model are a matter of great interest in the scientific community (e.g., Douglas and Smit, 2001; Chen and Tsai, 2002; Sigbjo¨rnsson and Ambraseys, 2003; Bommer et al., 2004; Ambraseys et al., 2005), we also explore the effect of introducing a detailed classification of the strong-motion sites (Luzi et al., 2005) by applying the random effect model (Searle, 1971; Brillinger and Preisler, 1985).

Data Set The acceleration time series, available for the UmbriaMarche area (hereinafter referred to as UMA), are provided by two institutions, namely the Servizio Sismico Nazionale (National Seismic Survey of Italy [SSN] now DPC-USSN) and the Ente per le Nuove Tecnologie, l’Energia e l’Ambiente (ENEA). Table 1 lists the source coordinates and magnitudes of the considered earthquakes (Deschamps et al., 1984; Haessler et al., 1988; Cattaneo et al., 2000; Chiaraluce et al., 2004; Instito Nationale di Geofisica e Vulcanologia [INGV] 2004), and Figure 1 shows the epicenter locations and the recording sites. All the earthquakes occurred during the 1997–1998 Umbria-Marche seismic sequence (SSN, 2002) but four (events 1–4 in Table 1), namely the Ml 5.9 1979 Norcia and the Ml 5.2 1984 Gubbio earthquakes, and two earthquakes of magnitude less than 4.5. Nearly all focal mechanisms are normal, with fault planes parallel to the Apennines trend (northwest–southeast). Only a few events show a strike-slip mechanism. The hypocentral depths are in the 2–8 km range, with the exception of one event (event 39) whose hypocentre is 47 km deep. The selected earthquakes have magnitude greater than 4.0 and distances less than 100 km (Fig. 2). The magnitude scale, which we refer to as Ml in this article, is defined as local magnitude, since this magnitude estimate is available for the totality of the selected events. It is worth noting that the maximum local magnitude of the data set is 5.9 (for the 1979 Norcia earthquake), which is well below the saturation level of about 6.5 on the Ml scale (Lay and Wallace, 1995). Furthermore, since fault geometries are available only for the 3 strongest earthquakes of the data set (events 5, 6, and 26 in Table 1), the attenuation relations are developed for the epicentral and hypocentral distances instead of the closest distance to the fault. For these earthquakes we assume fault dimensions L ⳯ W equal to 6 ⳯ 6 km2, 12 ⳯ 7.5 km2, and 7 ⳯ 5 km2 respectively (Capuano et al., 2000). For the main event of the 1997–1998 sequence (event 6 in Table 1), we find remarkable variations between epicentral and fault distances for the two stations located on the surface projection of the fault, namely CLF and NCR. Otherwise, we find differences lower than 35% for the stations located within 50 km. Since the fault dimensions of earthquakes 5 and 26 are smaller, for these events the discrepancies between epicentral and fault distances are negligible (lower than 15%), with the excep-

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D. Bindi, L. Luzi, F. Pacor, G. Franceschina, and R. R. Castro

Table 1 List of the Events Used for the Analysis Event

dd/mm/yy

hh:mm:ss

Lat ()

Lon ()

Depth (km)

Mi

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

19/09/1979 29/04/1984 24/11/1985 05/07/1987 26/09/1997 26/09/1997 26/09/1997 26/09/1997 27/09/1997 27/09/1997 27/09/1997 02/10/1997 03/10/1997 04/10/1997 04/10/1997 04/10/1997 04/10/1997 04/10/1997 06/10/1997 07/10/1997 07/10/1997 12/10/1997 13/10/1997 14/10/1997 14/10/1997 14/10/1997 15/10/1997 16/10/1997 16/10/1997 16/10/1997 16/10/1997 19/10/1997 08/11/1997 09/11/1997 30/11/1997 31/12/1997 07/02/1998 21/03/1998 26/03/1998 03/04/1998 03/04/1998 05/04/1998 02/06/1998 05/06/1998 25/06/1998

21:35:00 05:02:03 06:54:03 13:12:37 09:40:27 00:33:13 09:47:00 13:30:52 08:08:08 17:13:04 19:56:43 10:59:57 08:55:22 06:04:23 06:49:54 15:07:21 16:13:33 18:47:48 23:24:53 01:24:34 05:09:57 11:08:37 11:01:47 16:24:27 23:23:30 15:23:11 22:53:10 04:52:56 04:53:21 17:31:44 12:00:31 16:00:18 15:31:54 19:07:33 11:24:42 16:02:15 00:59:44 16:45:09 16:26:17 07:59:53 07:26:37 15:52:21 23:11:23 21:53:12 00:32:53

42.730 43.250 43.849 43.700 43.016 43.016 43.100 43.016 43.083 43.016 43.033 43.083 43.033 42.927 42.933 42.933 42.933 42.933 43.016 43.016 43.016 42.916 42.900 42.950 42.966 42.883 42.916 42.950 42.939 42.866 43.033 42.966 42.859 42.854 42.839 42.855 42.998 42.951 43.133 43.194 43.166 43.190 43.189 43.184 43.012

12.960 12.520 12.029 12.219 12.850 12.883 12.800 12.933 12.816 12.833 12.850 12.783 12.833 12.916 12.900 12.933 12.933 12.933 12.833 12.850 12.850 12.933 12.966 12.883 12.866 12.966 12.933 12.916 12.912 13.016 12.883 12.850 12.983 12.999 13.001 13.008 12.824 12.914 12.800 12.744 12.766 12.773 12.778 12.787 12.817

6.0 7.0 5.0 5.0 6.3 6.7 2.6 3.9 5.7 5.6 3.8 4.9 4.4 5.8 4.9 4.7 4.2 4.3 5.5 4.7 2.2 4.6 5.2 1.9 4.7 5.2 3.6 3.4 2.5 4.5 1.1 5.1 6.4 2.0 4.0 5.4 3.1 4.1 47.7 3.1 8.7 5.4 3.8 2.6 4.7

5.9 5.2 4.1 4.0 5.8 5.7 4.7 4.3 4.3 4.0 4.0 4.1 5.0 4.0 4.2 4.2 4.6 4.1 5.4 4.2 4.4 5.2 4.0 4.0 4.2 5.6 4.1 4.0 4.0 4.0 4.5 4.1 4.3 4.9 4.0 4.4 4.3 4.6 5.4 4.2 5.0 4.7 4.2 4.2 4.0

tion of one site located inside the fault projection of one event (CLF for the event 5). The accelerograms were base-line corrected, and the effect of the instrument response was removed. The sampling rate of the data was 200 samples/sec. The analog records were filtered in order to remove the high- and low-frequency noise by visually selecting a suitable frequency interval; the average range used was 0.5–25 Hz. The digital records were filtered to remove the low-frequency noise with a bandpass filter having an average threshold of 0.3 Hz and a high-cut frequency at 40 Hz. The larger of the two horizontal peak

Mw

6.0 5.7 4.5 4.3

5.2

4.6 5.4 4.2 4.5 5.2

5.6

4.3 4.2

4.4 5 5.3 4.2 5.1 4.7

Source

Deschamps et al. (1984) Haessler et al. (1988) INGV (2004) INGV (2004) Chiaraluce et al. (2004) Chiaraluce et al. (2004) Chiaraluce et al. (2004) Chiaraluce et al. (2004) Chiaraluce et al. (2004) Chiaraluce et al. (2004) Chiaraluce et al. (2004) Chiaraluce et al. (2004) Chiaraluce et al. (2004) Chiaraluce et al. (2004) Chiaraluce et al. (2004) Chiaraluce et al. (2004) Chiaraluce et al. (2004) Chiaraluce et al. (2004) Chiaraluce et al. (2004) Chiaraluce et al. (2004) Chiaraluce et al. (2004) Chiaraluce et al. (2004) Chiaraluce et al. (2004) Chiaraluce et al. (2004) Chiaraluce et al. (2004) Chiaraluce et al. (2004) Chiaraluce et al. (2004) Chiaraluce et al. (2004) INGV (2004) Chiaraluce et al. (2004) Chiaraluce et al. (2004) Chiaraluce et al. (2004) INGV (2004) Cattaneo et al. (2000) INGV (2004) Cattaneo et al. (2000) Morelli et al. (2000) Morelli et al. (2000) Chiaraluce et al. (2004) Morelli et al. (2000) Chiaraluce et al. (2004) Morelli et al. (2000) INGV (2004) INGV (2004) INGV (2004)

values from an individual recording was used in the analysis. The response spectra were calculated for the component of larger PGA, using a standard damping of 5% at 14 frequencies in the range 0.25–25 Hz (Sabetta and Pugliese, 1996). At any given frequency, the response spectra were computed using only those recordings for which the frequency is within the passband of the applied filter. The number of recordings considered for each frequency is given in Tables 2 and 3. In particular, for frequencies lower than 0.5 Hz, only the digital recordings are considered.

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Recording Sites We analyzed records from 43 strong-motion stations with coordinates and site classifications listed in Table 4. We adopted the site classification previously proposed by Luzi et al. (2005). These authors improved the site characterization by direct verification at the locations and by the acquisition of additional geological and geotechnical information. The locations of the sites were tested and rearranged by the aid of the Italian census data and detailed topographic maps. The depth to bedrock of the most important alluvial valleys was taken from reports in existing literature. The stratigraphy of many stations located on alluvial deposits and shallow alluvium was collected from public offices and private companies. On the base of the improved data set, the stations were grouped into four classes, from AC to DA, where the subscript indicates the corresponding class in the EC8 code (Comite´ Europeén de Normalisation [CEN], 1998): AC: Lacustrine and alluvial deposits with thickness greater than 30 m (Vs30 ⳱ 180–360 m/sec); they form the largest lacustrine plains in the Umbria region. BC: Lacustrine and alluvial deposits with thickness in the range 10–30 m (Vs30 ⳱ 180–360 m/sec); they form narrow alluvial plains or shallow basins. CE: Shallow debris or colluvial deposits (3–10 m) overlaying rock (surface layer with Vs30 360 m/sec); they are located on shallow colluvial covers or slope debris (maximum depth 10 m) set on gentle slopes. DA: Rock (Vs30 800 m/sec); this class identifies stations located either on outcropping rock, or related morphologic features, such as rock crests and cliffs. Figure 1. Distribution of events (circles) and recording stations (squares) in the Umbria-Marche area.

It is worth noticing that class AC and BC sites (alluvial and lacustrine deposits) have the same soil category, according to the actual seismic regulations, since they share similar values of Vs30 (180–360 m/sec). In this study we also included the stations that Luzi et al. (2005) disregarded, since they recorded few events.

Statistical Validation of Predictions

Figure 2. the data set.

Magnitude and distance distribution of

The PGA and PGV values predicted by the Sabetta and Pugliese (1996) attenuation relationships (hereinafter referred to as SP96) are compared to the actual values derived from the UMA recordings. To measure the goodness of fit, we follow the approaches of both Spudich et al. (1999) (hereinafter referred as to SPH99) and Scherbaum et al. (2004) (hereinafter referred as to SCM04). Both are based on the concept of a maximum likelihood estimator, which is used to characterize the distribution of the residuals and its central tendency. The residuals are defined as the difference between the logarithms of observed and predicted values and are assumed to be normally distributed. In this article we compare the PGA and PGV predicted by the SP96 attenuation relations with the observed peak values for events with mag-

988


Table 2 UMA05 Coefficients Obtained for PSV (cm/sec) and Larger PGA Component Using Epicentral Distance f (Hz)

a

b

c

h

DA

CB

BC

AC

revent

rrecord

r

N*

0.25 0.32 0.50 0.65 1.00 1.33 2.00 2.56 3.45 4.93 6.63 9.47 15.23 24.50

ⳮ4.734 ⳮ4.720 ⳮ4.235 ⳮ4.069 ⳮ3.446 ⳮ2.989 ⳮ2.285 ⳮ1.862 ⳮ1.462 ⳮ1.197 ⳮ0.900 ⳮ0.883 ⳮ1.168 ⳮ1.560

1.079 1.079 1.015 1.024 0.966 0.899 0.808 0.745 0.675 0.595 0.511 0.507 0.529 0.511

ⳮ0.835 ⳮ0.758 ⳮ0.779 ⳮ0.865 ⳮ1.033 ⳮ1.046 ⳮ1.138 ⳮ1.125 ⳮ1.149 ⳮ1.063 ⳮ1.062 ⳮ1.255 ⳮ1.344 ⳮ1.221

2.000 2.000 2.000 2.000 2.000 2.000 2.706 3.048 2.470 2.098 2.936 4.320 3.665 2.157

0 0 0 0 0 0 0 0 0 0 0 0 0 0

0.035 0.048 0.017 0.001 0.008 ⳮ0.002 ⳮ0.026 ⳮ0.034 0.074 0.228 0.378 0.477 0.426 0.439

ⳮ0.147 ⳮ0.177 ⳮ0.012 ⳮ0.068 ⳮ0.024 ⳮ0.037 ⳮ0.161 ⳮ0.198 ⳮ0.220 ⳮ0.091 ⳮ0.002 0.096 0.110 0.092

0.237 0.248 0.309 0.323 0.339 0.288 0.187 0.098 0.034 0.046 0.073 0.141 0.071 0.042

0.115 0.120 0.133 0.146 0.105 0.092 0.102 0.132 0.138 0.126 0.092 0.097 0.137 0.131

0.254 0.275 0.317 0.311 0.316 0.311 0.306 0.283 0.276 0.289 0.276 0.275 0.250 0.253

0.278 0.301 0.344 0.343 0.333 0.324 0.323 0.313 0.309 0.315 0.291 0.291 0.285 0.285

144 144 224 224 239 239 239 239 239 239 239 239 229 229

*N is the number of records used for each frequency.

Table 3 UMA05 Coefficients Obtained for PSV (cm/sec) and Larger PGA Component, Using Hypocentral Distance f (Hz)

a

b

c

DA

CE

BC

AC

revent

rrecord

r

N*

0.25 0.32 0.50 0.65 1.00 1.33 2.00 2.56 3.45 4.93 6.63 9.47 15.23 24.50

ⳮ4.627 ⳮ4.500 ⳮ4.025 ⳮ3.857 ⳮ3.272 ⳮ2.849 ⳮ2.282 ⳮ1.894 ⳮ1.456 ⳮ1.200 ⳮ0.860 ⳮ0.979 ⳮ1.213 ⳮ1.464

1.100 1.086 1.042 1.045 0.986 0.918 0.839 0.776 0.710 0.616 0.527 0.531 0.563 0.546

ⳮ0.974 ⳮ0.935 ⳮ1.017 ⳮ1.082 ⳮ1.218 ⳮ1.204 ⳮ1.244 ⳮ1.219 ⳮ1.273 ⳮ1.129 ⳮ1.145 ⳮ1.274 ⳮ1.431 ⳮ1.410

0 0 0 0 0 0 0 0 0 0 0 0 0 0

ⳮ0.028 ⳮ0.042 0.027 0.013 0.023 0.013 ⳮ0.023 ⳮ0.037 0.077 0.225 0.387 0.482 0.430 0.449

ⳮ0.131 ⳮ0.173 ⳮ0.008 ⳮ0.054 ⳮ0.006 ⳮ0.018 ⳮ0.142 ⳮ0.181 ⳮ0.205 ⳮ0.083 0.006 0.122 0.133 0.111

0.228 0.249 0.301 0.322 0.342 0.290 0.183 0.096 0.036 0.035 0.066 0.129 0.057 0.032

0.109 0.113 0.117 0.138 0.107 0.104 0.122 0.148 0.150 0.144 0.111 0.130 0.165 0.159

0.260 0.281 0.318 0.316 0.320 0.312 0.303 0.279 0.275 0.288 0.276 0.268 0.246 0.248

0.282 0.303 0.339 0.344 0.338 0.329 0.327 0.316 0.313 0.322 0.300 0.298 0.296 0.295

144 144 224 224 239 239 239 239 239 239 239 239 229 229

*N is the number of records used.

nitudes between 4.6 and 6. To investigate the predictive capability of the SP96 over the whole magnitude range covered by the UMA data set, we also apply the statistical analysis in the range 4 to 6. We use the SP96 site coefficients for stiff sites (average shear velocity 800 m/sec) and for deep alluvium (thickness 20 m and shear-wave velocity between 400 and 800 m/sec) to predict the peak values relevant to DA and AC classes, respectively. Statistical Validation Using SPH99 Spudich et al. (1999) defined the bias between observed and expected ground-motion parameters as the mean value of the residual distribution, computed in a likelihood sense. They also characterized the residuals using basic variables such as the slope of the best-fitting line through a subset of residuals as a function of magnitude M or distance R (slope(M) and slope(R) respectively) (Spudich et al., 1999, Appendix, pp. 1169–1170).

Bias and slopes obtained for PGA and PGV are shown in Table 5 for two magnitude ranges: 45–6, the data set used by SP96, and 4–6, the magnitude range of the UMA05 data set. In the following we discuss the results obtained for the magnitude range 4–6. Figure 3 shows the residuals versus magnitude and base-10 logarithm of distance, as well as the linear fit obtained using the maximum likelihood method. For PGA, the bias is ⳮ0.14 Ⳳ 0.05 for class DA and ⳮ0.09 Ⳳ 0.04 for class AC. The SP96 relation overpredicts the average PGA values by about 27% and 19% for classes DA and AC, respectively. It is also evident that there exists a magnitude dependence of the bias for class DA. As the slope of the maximum likelihood straight line is 0.20 Ⳳ 0.06, the SP96 relations overpredict the PGA more at small magnitudes than at large ones. In particular, SP96 overpredicts, on the average, the data for 4 M 5.5 and underpredicts for M 5.5, as can be seen in Figure 3. For class AC, the slope for the magnitude is less prominent (0.08 Ⳳ 0.05) but not negligible.

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Table 4 The Recording Stations Name

Annifo Aquilpark Parcheggio Arquata del Tronto Assisi Bevagna Borgo Cerreto Torre Cagli Cascia Cassignano Castelnuovo Assisi Cesi Monte Cesi Valle Colfiorito Colfiorito Casermette Foligno SMI Forca Canapine Forcella Gubbio Gubbio-Piana Leonessa Mascioni Matelica Monte Fiegni Nocera Umbra Nocera Umbra 2 Nocera Umbra P.I. Nocera Umbra Biscontini Nocera Umbra Salmata Norcia Norcia-Altavilla Norcia-Zona Industriale Peglio Pennabilli Pietralunga Rieti Sellano East Sellano West Senigallia Serravalle di Chienti Spoleto Spoleto Monteluco Umbertide Valle Aterno (Moro) Valle Aterno (Valle)

Code

Lat. ()

Lon. ()

Instr.

ANNI PK10 ARQ0 ASSI BVG0 CTR0 CGL0 CSC0 CAG0 CSA0 CESM CESV CLF0 CLC0 FSM0 FHC0 FORC GBB0 GBP0 LNS0 MSC0 MTL0 MNF0 NCR0 NCR2 NOCE NCB0 NCM0 NRC0 NRV0 NRI0 PGL0 PNN0 PTL0 RT10 SELE SELW SNG0 SER0 SPL0 SPM0 UMB0 AQ30 AQ50

43.050 42.346 42.772 43.070 42.932 42.814 43.536 42.719 43.054 43.007 43.000 43.000 43.037 43.028 42.955 42.761 42.950 43.357 43.313 42.565 42.526 43.249 43.063 43.113 43.113 43.110 43.103 43.149 42.791 42.796 42.775 43.695 43.817 43.427 42.430 42.880 42.870 43.685 43.073 42.736 42.722 43.254 42.379 42.377

12.850 13.401 13.294 12.600 12.611 12.915 12.629 13.013 12.829 12.591 12.900 12.890 12.921 12.900 12.704 13.210 12.940 12.602 12.589 12.984 13.346 13.007 13.185 12.785 12.785 12.780 12.805 12.797 13.096 13.089 13.097 12.498 12.261 12.449 12.821 12.930 12.920 13.227 12.953 12.737 12.752 12.256 13.351 13.344

Altus K2 SA16 SMA-1 SSA2 SMA-1 CODISMA SMA-1 SMA-1 SMA-1 SMA-1 Altus K2 Altus K2 SMA-1 A800 SMA-1 SMA-1 Altus K2 SMA-1 SSA1 SMA-1 SMA-1 SMA-1 SMA-1 SMA-1 Etna Altus K2 SSA1 SMA-1 SMA-1 SMA-1 SMA-1 SMA-1 SMA-1 SMA-1 A800 Altus K2 Altus K2 SMA-1 SMA-1 SMA-1 SMA-1 SMA-1 Altus K2 SSA2

Owner

RM-ssn RAN-snn RAN-snn RM-ssn RAN-snn ENEA RAN-snn RAN-snn RAN-snn RAN-snn RM-ssn RM-ssn RAN-snn RM-ssn ENEA RAN-snn RM-ssn RAN-snn RAN-snn RAN-snn RAN-snn RAN-snn RAN-snn RAN-snn RM-ssn RM-ssn RM-ssn RM-ssn RAN-snn ENEA ENEA RAN-snn RAN-snn RAN-snn RAN-snn RM-ssn RM-ssn RAN-snn RAN-snn RAN-snn RAN-snn RAN-snn RAN-snn RAN-snn

Soil Class

CE AC DA DA AC DA DA DA AC CE AC AC AC AC DA DA CE AC AC CE BC DA CE CE BC CE BC AC AC AC CE CE DA AC DA DA CE BC AC DA CE DA AC CE

Owner: RAN-snn, national accelerometric network owned by the National Seismic Survey; RM-ssn, temporary accelerometric network owned by the National Seismic Survey. Coordinates are geographic WGS84.

Regarding the dependence of the bias on the logarithm of the distance, the slope is ⳮ0.22 Ⳳ 0.08 and ⳮ0.18 Ⳳ 0.12 for classes AC and DA, respectively. This means that the SP96 relations overestimate the average PGA values more at large distances than at small distances. The results for PGV are similar to those achieved for PGA, except for the dependence on distance, which is not significantly different from zero. Figure 4 shows the bias and its standard deviation computed for the PSV. The spectral ordinates are generally over-

estimated (bias 0), particularly for the class DA (rock) at frequency f 2 Hz. For class DA, the slope for the magnitude fit is positive and almost constant at all frequencies. It follows that SP96 relations overpredict PSV for small magnitudes more than for large magnitudes, and the trend is the same over the entire analyzed frequency range. For class AC (deep alluvium), the slope is positive for f 8 Hz, but it decreases with frequency. Then, then SP96 model overpredicts PSV for small magnitudes more than large ones, but the relative overestimation diminishes with frequency.

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Table 5

Statistical Validation Using SCM04

Bias and Slope of the Best-Fitting Line as a Function of Magnitude, Slope (M), or Distance, Slope (R), Considering the Sabetta and Pugliese (1996) Models Bias

PGA AC M 4 PGA AC M 4.5 PGA DA M 4 PGA DA M 4.5 PGV AC M 4 PGV AC M 4.5 PGV DA M 4 PGV DA M 4.5

Slope (M)

Slope (R)

ⳮ0.09 Ⳳ 0.04 0.08 Ⳳ 0.05 ⳮ0.004 Ⳳ 0.001 ⳮ0.04 Ⳳ 0.03 ⳮ0.03 Ⳳ 0.08 ⳮ0.005 Ⳳ 0.001 ⳮ0.14 Ⳳ 0.05 0.20 Ⳳ 0.06 ⳮ0.004 Ⳳ 0.003 ⳮ0.06 Ⳳ 0.05 0.10 Ⳳ 0.11 ⳮ0.007 Ⳳ 0.003 ⳮ0.13 Ⳳ 0.05 0.21 Ⳳ 0.09 0.000 Ⳳ 0.002 ⳮ0.05 Ⳳ 0.06 0.04 Ⳳ 0.15 ⳮ0.000 Ⳳ 0.002 ⳮ0.17 Ⳳ 0.03 0.12 Ⳳ 0.06 ⳮ0.000 Ⳳ 0.003 ⳮ0.12 Ⳳ 0.04 0.04 Ⳳ 0.10 0.004 Ⳳ 0.003

Another statistical approach to the problem was proposed by Scherbaum et al. (2004), who first computed the normalized residuals z0 by normalizing each residual to the standard deviation of the ground-motion model. Then, they measured the goodness of fit by computing the probability LH(|z0|) for the absolute value of a random sample from the normalized distribution to fall between the modulus of a particular observed residual z0 and , considering both tails of the error distribution Erf(z) (equation (9) in Scherbaum et al., 2004), that is,

冢

冣

2 |z0| LH (|z0|) ⳱ Erf , ⳱ 冪2 冪p

Figure 3.

Residuals (logarithm of observations minus logarithm of predictions) for

PGA. The predicted values were computed using the Sabetta and Pugliese (1996) re-

lationship. Top: Residual for class AC versus local magnitude (left) and logarithm of the epicentral distance (right). Bottom: The same but for class DA. Black lines represent the bias, white lines represent the maximum likelihood, straight lines and the gray area represent the standard deviation of the maximum likelihood best fits.

冮

eⳮt dt.

|z0| /冪2

2

(1)


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Figure 4.

Dependence of bias on frequency (top panels) and on magnitude (bottom panels), computed considering the Sabetta and Pugliese (1996) relationship for PSV. The results for class DE (rock) are shown on the left, those for class AC (deep alluvium) on the right.

These authors discussed some properties of the LH distribution that make it a good measure of the goodness of fit. Moreover, Scherbaum et al. (2004) used the median of the LH values and some central tendency parameters (mean and median) of the normalized residual distribution, together with the standard deviation, to define a rank ordering that can be adopted to quantify the suitability of a given attenuation relationship for prediction purposes in a given area. In particular, a uniform distribution of LH values between 0 and 1 is expected when the residuals follow a normal distribution with zero mean and unit variance. Figure 5 shows the LH distribution of PGA and PGV for classes AC and DA. The LH distributions for PGA are asymmetric, with median equal to 0.20 and 0.38 for class DA and AC, respectively. The small values of the median can be a consequence of both the negative value of the mean of the residual distribution and the standard deviation of the normalized residual distribution 1, as pointed out by SCM04. SCM04 proposed a categorization scheme to rank a set of

models with respect to their capability to match observed values. They introduced four categories, coded with letters A through D, depending on the values of the median of the LH distribution, and the values of the mean, median, and standard deviation of the distribution of normalized residuals. To exemplify the scheme proposed by SCM04, we recall that models ranked A (highest capability) show a median LH distribution of at least 0.4, and the corresponding normalized residual distributions have an absolute value for both mean and median ⱕ0.25 and standard deviation ⱕ1.125. A model that shows either median LH distribution 0.2, or absolute value of mean and median 0.75, or standard deviation of the normalized residual distribution 1.5, is ranked D and it should be considered unacceptable. Table 6 shows the results for the SP96 model. The models behave differently with respect to the prediction of PGA and PGV. Regarding PGA, SP96 comes out only third in rank (C) for site class AC, and it fails (rank D) in predicting the PGA for site class DA (rock), when magnitudes greater than 4 are

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Figure 5. Distribution of LH values for class AC (top panels) and class DA (bottom panels), computed considering the Sabetta and Pugliese (1996) relationship. The distributions for PGA are on the left, those for PGV on the right. Inside each panel, the value of the median of the LH distribution is shown.

considered. The same conclusion is obtained when M 4.5. The LH distribution (Fig. 5) is strongly asymmetric, as confirmed by a median significantly different from 0.5 (Table 6). High frequency for LH values close to zero means that many residuals correspond to values in the tails of error function distribution. Figure 6 shows the distribution of the normalized residuals (boxes) and the expected normal distribution with zero mean and unit variance (dotted lines). The continuous lines represent the normal distribution having mean and variance constrained to the values derived from the discrete distributions. For both, site classes AC and DA, the model is penalized by its small variance, which influences the LH values, as discussed in SCM04. The obtained values for the standard deviation of the normalized residual distributions (1.33 and 1.66 for site classes AC and DA, respectively) indicate that the standard deviations of the observed PGAs are significantly larger than those predicted by the model (33% and 66% for site classes AC and DA, re-

spectively). Regarding PGV, the model is assigned rank C for both classes AC and DA for M 4, whereas the model for class AC is ranked B for M 4.5. In particular, the model matches satisfactorily the PGV values for site class AC (see also the distribution of normalized residuals in Fig. 6), and only the standard deviation of the normalized residuals (1.125) is not compatible with a ranking of the SP96 in the highest capability (rank A) for M 4.5. In summary, the two statistical approaches used to estimate the goodness of fit of the SP96 attenuation relationships applied to the Umbria-Marche data lead us to the following conclusions: (1) the average residual (bias) is generally negative, that is, the SP96 model overestimates on the average the PGA, PGV, and PSV values, in the magnitude range 4–6 and in the distance range 1–100 km; (2) the slope of bias with magnitude is positive, that is, the SP96 model overpredicts the considered peak ground motions more at low magnitudes than at larger ones, discouraging the extrap-


Table 6 Median of the Distribution of the LH Values and Median, Mean, and Standard Deviation of the Distribution of the Normalized Residuals

PGA AC M 4 PGA AC M 4.5 PGA DA M 4 PGA DA M 4.5 PGV AC M 4 PGV AC M 4.5 PGV DA M 4 PGV DA M 4.5

Median LH

Median Residual

Mean Residual

Std. Dev. Residual

Rank*

0.38 0.51 0.20 0.21 0.36 0.48 0.29 0.30

ⳮ0.33 ⳮ0.15 ⳮ0.71 ⳮ0.47 ⳮ0.003 0.11 ⳮ0.68 ⳮ0.58

ⳮ0.35 ⳮ0.19 ⳮ0.70 ⳮ0.32 ⳮ0.31 ⳮ0.04 ⳮ0.68 ⳮ0.50

1.33 1.24 1.66 1.64 1.28 1.18 1.11 1.11

C B D D C B C C

*The rank is relative to the classification proposed by Scherbaum et al. (2004).

Figure 6.

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olation of SP96 toward lower magnitudes; (3) for PGA, the dependence of bias on distance is evident, since the PGA is overpredicted at large distances more than at small ones; (4) the SP96 model can not be ranked as a good-match model for PGA and PGV values at rock sites in the UMA (class DA); and (5) for deep alluvial sites (class AC), SP96 is classified either in the second (B) or in the third (C) rank, depending on the magnitude range (M 4.5 and M 4 respectively).

Attenuation Relationships for Umbria-Marche: UMA05 We derive new attenuation relationships (hereinafter referred to as UMA05) for UMA, considering the same functional form of the SP96 model:

Distribution of the normalized residuals, computed with the Sabetta and Pugliese (1996) relationship. Dotted lines are the expected normal distribution (i.e., having zero mean and unit standard deviation), while the black lines are the normal distributions, having mean and standard deviation constrained to the value estimated from each discrete distribution.

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log(y) ⳱ a Ⳮ bM Ⳮ c log 冪(R2 Ⳮ h2) Ⳮ e1S1 Ⳮ e2S2 • • • en Sn Ⳳ r

(2a)

log(y) ⳱ a Ⳮ bM Ⳮ c log Rh Ⳮ e1S1 Ⳮ e2S2 • • • en Sn Ⳳ r ,

(2b)

where y is the strong ground-motion parameter, M is the local magnitude, R is the epicentral distance (kilometers), and Rh is the hypocentral distance (kilometers). The base-10 logarithm is considered. The model is characterized by the offset term a, the magnitude coefficient b, the distance coefficient c, and the pseudodepth parameter h. S1, S2, . . . Sn are dummy variables, that take either the value 0 or 1 depending on the soil type and e1, e2, . . . en are the site coefficients, set to zero in case of a rock site (class DA). Finally, r is the standard deviation of the logarithm of the derivative variable. The unknown coefficients in equation (2) can be determined by regression analysis, which gives the best estimates of the coefficients a to ei using a standard fitting algorithm. Following Brillinger and Preisler (1985) and Abrahmson and Youngs (1992), a random effect model can be introduced as log yij ⳱ f (Mi, rij, h) Ⳮ gi Ⳮ eij ,

(3)

where yij is the ground-motion parameter; f(M, r, h) is the attenuation equation with the basic variables Mi as the magnitude of event i, rij as the epicentral distance from source i to site j, and h as the vector of model coefficients. gi represents the interevent variation, and eij represents the intraevent variation. gi and eij are assumed to be independent, normally distributed variables with variances revent2 (earthquake-to-earthquake component of variance) and rrecord2 (record-to-record component of variance), respectively. The variance r2 in equation (2) is given by the sum revent2 Ⳮ rrecord2. The dependence on the recording site can be also considered, and the random effect model takes the form log yij ⳱ f (Mi, rij, h) Ⳮ e⬘ij Ⳮ uj ,

(4)

where uj represents the interstation error, assumed to be independent normally distributed with variance rstation2, and e⬘ij represents the intrastation variability with variance rrecord2, in analogy to the intra-event term. In this case, the variance r2 in equation (2) is given by the sum rstation2 Ⳮ rrecord2. We refer to the model in equation (3) as REM-Ev and to the model in equation (4) as REM-St. The Appendix gives the details of the applied schemes. UMA05 Relationships for PGA and PGV

and Analysis of Uncertainties The UMA05 attenuation relationships are developed for PGA and PGV using the REM-Ev and REM-St regression

schemes previously discussed. Moreover, we assess the effectiveness of the considered site classification by performing the regression for each model twice: in the first regression (R1), we do not introduce any site classification, that is, the coefficients ei in equation (2) are not considered; while in the second regression (R2), each station is associated to one of the four site classes, as previously described. The results are shown in Table 7 and confirm that the values of a, b, c, h, and r for R1 or R2 do not depend on the scheme REM-St or REM-Ev adopted for describing the uncertainty, but the two schemes differ in the value of each component of variance. Especially when the high-frequency parameter PGA is considered, we find c-values higher than unity. In fact, the attenuation term in equation (2) also accounts for the effect of the anelastic attenuation. Moreover, the values of the coefficient b for the magnitude term are higher than those obtained in the SP96 ground model. Values of b greater than 0.5 have also been recently found by Frisenda et al. (2005), who calibrated ground models for PGA and PGV in northwestern Italy for magnitudes lower than 4 and epicentral distances up to 100 km. They found 0.76M–0.018M2 and 0.87M–0.042M2 for PGV and PGA, respectively. Most of the worldwide attenuation relationships are derived for magnitudes higher than 5.5, and b-values are generally lower than 0.5; therefore the results of Frisenda et al. (2005) and those of the present study could suggest a stronger dependence of PGA and PGV on magnitude, since the ground models are derived considering low-magnitude values (6). Even though the coefficients and the total standard deviation computed with the REM-Ev or REM-St methods are the same, the use of both allows us to discuss the origin of the uncertainties in UMA05. Let us first consider the regression carried out without any site classification (R1). By applying the REM-Ev model and considering PGA as the target parameter, the earthquaketo-earthquake component of variability has a standard deviation revent ⳱ 0.119, while the standard deviation of the record-to-record component is rrecord ⳱ 0.282. Then, the contribution of the interevent variability to the total standard deviation r ⳱ (revent2 Ⳮ rrecord2)1/2 ⳱ 0.306 is negligible. By applying model REM-St, the station-to-station component of variability is remarkable, being the standard deviation rstation ⳱ 0.191, compared to the record-to-record standard deviation of rrecord ⳱ 0.234. Let us now introduce the site classification (regression R2). In the case of the REM-Ev model, the introduction of a set of site coefficients reduces the standard deviation of the record-to-record error distribution (from 0.282 to 0.241), while in the case of the REM-St model the introduction of the site classification reduces the standard deviation of the station-to-station component (from 0.191 to 0.145). The total standard deviation is reduced from 0.306 to 0.268 and from 0.302 to 0.274 for REM-Ev and REM-St, respectively, which corresponds to a reduction of the uncertainty of the predicted mean PGA of about 7%. For PGV, the introduction

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Table 7 Regression Coefficients and Standard Error for UMA05 PGA

a

b

c

h

DA

CE

BC

AC

revent

rstation

rrecord

r

Rem-Ev R2 Rem-Ev R1 Rem-St R2 Rem-St R1

ⳮ2.487 ⳮ2.188 ⳮ2.487 ⳮ2.188

0.534 0.477 0.534 0.479

ⳮ1.280 ⳮ1.202 ⳮ1.280 ⳮ1.202

3.94 3.79 3.94 3.79

0.000 — 0.000 —

0.365 — 0.365 —

0.065 — 0.065 —

0.053 — 0.053 —

0.117 0.119 — —

— — 0.145 0.191

0.241 0.282 0.232 0.234

0.268 0.306 0.274 0.302

ⳮ1.803 ⳮ1.668 ⳮ1.803 ⳮ1.668

0.687 0.665 0.687 0.665

ⳮ1.150 ⳮ1.083 ⳮ1.150 ⳮ1.083

2.74 2.18 2.74 2.18

0.000 — 0.000. —

0.232 — 0.232 —

ⳮ0.0624 — ⳮ0.0624 —

0.174 — 0.174 —

0.138 0.138 — —

— — 0.176 0.208

0.2668 0.2855 0.2458 0.2445

0.300 0.317 0.303 0.321

PGV

Rem-Ev R2 Rem-Ev R1 Rem-St R2 Rem-St R1

R1 and R2 indicate whether site classification is considered (see text for explanation).

of the site classification reduces the total standard deviation from 0.321 to 0.303 and from 0.317 to 0.300 for REM-St and REM-Ev, respectively (Table 7). By assuming that the distributions of errors are independent, the total variance is given by r2 ⳱ revent2 Ⳮ rstation2 Ⳮ v2, where revent measures the correlation between errors for the same earthquake at different stations (interevent component), rstation measures the correlation between the errors for different earthquakes recorded at the same station (interstation component), and v is the standard deviation of the error distribution that accounts for all the other sources of uncertainties. Since for regression R2 applied to PGA we obtained r ⳱ 0.27, revent ⳱ 0.12, and rstation ⳱ 0.14, it follows that v is equal to 0.20. A decrease of revent can be achieved by reducing the epistemic uncertainty affecting the source term in the regression model, by adding variables to model the variability of earthquake source parameters, such as stress-drop dependence on magnitude or different focal mechanisms. A further reduction of revent should be obtained, improving the quality of the parameters that affect the basic variables (e.g., the accuracy of the magnitudes and hypocentral parameters estimations). On the other hand, rstation could be reduced by considering more sophisticated site classification or site models. In our case, revent is fairly small, as expected, since most of the earthquakes belong to the same seismic sequence. Moreover, the adopted site classification allows a reduction of rstation of the same order of revent. Then, the highest source of variability of UMA05 is v, and a significant reduction of the total standard deviation can be achieved by reducing this component of variability. Future investigations will aim to reduce v by adding complexities to the attenuation model, for instance, the inclusion of a term accounting for the anelastic attenuation in the UMA. Site-to-Site Error We have seen that the introduction of the site classification in the attenuation model reduces r from 0.30 to 0.27 for PGA. The benefits of using a detailed site classification can be appreciated more by observing the distribution of the

interstation error. Figure 7 shows the distribution of interstation error before (gray circles) and after (empty triangles) the introduction of the site classification. Each abscissa corresponds to a different station, and the stations are grouped according to the four site classes. The main improvements for PGA are achieved for class CE, which exhibits the highest observed PGA values (see the site coefficients in Table 7), especially for the Nocera group of stations (stations corresponding to abscissas from 19 to 21). For these stations, the reduction of error varies from 0.1 to 0.2 log10 units (corresponding to a reduction of about 20% to 35%). The large reductions of site-to-site component of variance for some specific sites is worthy of attention, since it could strongly improve the reliability of predictions when the attenuation models are used for evaluating the hazard at that site. For PGV, the introduction of the site classification reduces the standard deviation from 0.32 to 0.30. For this parameter, the maximum PGV values correspond to classes AC and class CE (see site coefficients in Table 7). The error decreases for most of the stations, and in particular, the error decreases as much as 20% for classes AC and CE. The introduction of the site classification reduces the error of the predicted PGA and PGV for most of the sites classified as DA (rock). For example, Figure 7 shows that the error on PGV diminishes for more than 0.1 log10 units for stations MNF0 (Monte Fiegni), FORC (Forca Canapina), and CESM (Cesi Monte). On the other hand, for a few stations, the interstation error increases after the introduction of the site classification. An example is the station installed at Assisi (ASSI, abscissa 2 in Fig. 7). The reason for the increase of the error probably lies in the different behavior of the site amplification for this station with respect to the average behavior of stations belonging to class DA. In particular, ASSI is classified as DA, but it exhibits strong amplification due to topography (Castro et al., 2004), which could affect the PGV values. It is also worth noting the large differences among the errors shown in Figure 7 for PGV of class AC. In particular, station GBP0 (Gubbio Piana, abscissa 37) and CSA0 (Castelnuovo Assisi, abscissa 39) show errors of about 0.3 log10 unit (predictions underestimate observations), while the error for station CLC0 (Colfiorito Caser-

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class (Luzi et al., 2005). These differences are probably due to the location of CLC, since this station is installed near the edge of an alluvial basin, while most of class AC stations are installed closer to the middle of the basin, where it has been recognized that 2D and 3D effects play an important role (Rovelli et al., 2001; Luzi et al., 2005). In summary, any assumed site classification can only account for some aspects of site response. On the other hand, more sophisticated site classification models are justified only when they are well constrained by the available data. Since the ultimate goal of an attenuation model is to be applied in the seismic engineering framework for design purposes, a simplified but robust model is preferable. Nevertheless, research studies that address the problem of modeling specific site effects, such as topographic effects for rock sites or 2D and 3D effects for alluvial basins, could be useful to better understand the source of uncertainties for specific areas.

Earthquake-to-Earthquake Error

Figure 7.

Interstation distribution error for PGA (top) and PGV (bottom). Each abscissa corresponds to a different station (the code of each station is given in the legend on right) and the ordinates are the value of uj of equation (5). The stations are grouped into four site classes (AC, BC, CE, and DA). Gray-filled circles are the error obtained without any site classification, whereas white triangles represent the interstation error affecting the regression that accounts for site classification.

mette, abscissa 41) is about ⳮ0.2 (predictions overestimate observations). The large overestimation of ground motion for Gubbio Piana is consistent with the recently derived attenuation relationships for the European territory reported by Ambraseys et al. (2005). The introduction of site classification in our relations reduces only slightly the interstation error of class AC. The reason for such differences probably lies in the different site amplification behavior among stations belonging to the same soil class, as already noted for ASSI. Station CLC0 is classified as AC but its amplification, at frequencies close to 1 Hz, is much lower in amplitude than the amplification of most stations belonging to the same

Figure 8 exemplifies the earthquake-to-earthquake component of error versus magnitude and focal depth. The error varies between ⳮ0.2 and 0.2 for all earthquakes, but there is one case for which the error is about ⳮ0.35. This earthquake differs from all the others with regard to its focal depth (Figure 8, bottom panel). Since the pseudodepth h in the UMA05 model (equation 2) was determined using shallow earthquakes (depth 10 km), the error for the deeper earthquake is larger and negative, since the predictions are computed at a distance significantly smaller than the true hypocentral distance. This earthquake was not considered in the data set used for performing the regressions presented in Tables 2 and 7. It is worth noting that the errors for the Ml 5.9 1979 Nocera and Ml 5.2 1984 Gubbio earthquakes are of the same order of what obtained for the earthquakes of the 1997–98 seismic sequence, suggesting the absence of significant differences in the source properties among these earthquakes.

UMA05 Relationship for PSV The UMA05 attenuation relationship has been developed for the PSV using the Rem-Ev regression scheme. The PSV (centimeters per second) is calculated for 14 frequencies, from 0.25 to 25 Hz, as proposed by Sabetta and Pugliese (1996), with 5% damping. Tables 2 and 3 list the results in terms of regression coefficients and standard deviation, for both the epicentral and hypocentral distances. Figure 9 displays the PSV spectral ordinates for two magnitudes and distances, and different soil classes. An increase in magnitude, at a fixed distance, produces an increase of spectral content at low frequencies (as predicted by the Brune model, 1970), while an increase of distance at fixed magnitude causes a scaled decrement of the spectral ordinates. While the behaviour of PSV with magnitude is as one would expect,


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Comparison between SP96 and UMA05

Figure 8.

Interevent error distribution for PGA versus magnitude (top panel) and versus depth (bottom panel). Black circles correspond to earthquakes not belonging to the 1997–1998 sequence.

classes CE and DA show weaker attenuation with distance at low frequencies than at high frequencies (Fig. 9, right panel). This indicates that the role of the anelastic attenuation has to be investigated further. In general, the spectral shape of different soil classes at fixed magnitude and distance differ substantially. Class DA has its higher spectral content in the frequency range of 2–6 Hz, while class CE sites show amplification at about 8 Hz. Class AC shows the higher spectral content for low frequencies (0.8–1.5 Hz) in correspondence to the soil transfer function maximum (Castro et al., 2004). Class BC sites are not reported, since very few observations are available.

Figure 10 shows the mean PGA and PGV Ⳳ 1 standard deviation predicted by the UMA05 model (thick lines) and the SP96 model (thin lines). The attenuation functions plotted were calculated for two fixed magnitudes (Ml 4.6 and 5.8) at rock sites (class DA). Figure 10 shows that the SP96 model tends to overestimate PGA and PGV at large epicentral distances (R 10 km), in accordance with the results of the statistical methods applied to the residual distributions. In particular, the mean of SP96 for M 4.6 is greater than the mean of UMA05 over the entire distance range analyzed. For magnitude 5.8 a better agreement is observed, and in particular, for PGV, SP96 predicts values similar to those of UMA05 at distances larger than 10 km. It is worth noting that, for magnitude 5.8, SP96 predicts lower mean values for both PGA and PGV at distances shorter than 10 km. In Figure 11 the differences between the logarithm of SP96 and UMA05 are shown against magnitude and distance, considering the PGA and PGV for class DA. Figure 11 confirmes that SP96 overpredicts PGA and PGV, although the overprediction diminishes with magnitude, and for PGA, it increases with distance. To verify whether the difference between the attenuation relationships could be related to the different focal mechanisms of the earthquakes included in regression analysis, we adjusted the SP96 to account for the style of faulting (Bommer et al., 2003). The average correction factors vary from 0.89 to 1.02 for both PGA and spectral ordinates computed at difference frequencies, indicating that the observed differences between UMA05 and SP96 cannot be ascribed to the different style of faulting of the earthquakes characterizing the data set used to obtain SP96. Figure 12 shows the comparison between the PSV predicted by UMA05 and SP96 at 20 km for two magnitudes (4.6 and 5.8) and two soil classes (DA and AC). For rock sites (class DA) SP96 predicts higher amplitudes, particularly at low frequencies, since it overestimates the observed values, as discussed before. The discrepancy between UMA05 and SP96 decreases with frequency for any given magnitude, in agreement with the behavior of the bias shown in Figure 5. The difference also decreases with magnitude for both soil sites, and good agreement of predicted PSV is observed for M 5.8, with only a slight difference at low frequencies. The comparison for class AC (deep alluvium) is also illustrated in Figure 12. This figure shows that SP96 overpredicts the PSV more at intermediate frequencies, although the disagreement with UMA05 diminishes with magnitude. The agreement for M 5.8 is satisfactory, with a slight underprediction of SP96. For f 9 Hz, a good agreement for the entire range of magnitude analyzed is observed, confirming the results obtained in the statistical analysis (Fig. 4, right panel). Some discrepancies between SP96 and UMA05 can be ascribed to the data set used to derive the former. The SP96 strong-motion data set includes data coming from the 1980

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Figure 9.

PSV computed considering the UMA05 attenuation relationship. Left: PSV for R ⳱ 20 km and two different magnitudes (4.5 and 5.8), considering three different soil classes (AC, CE, DA). Right: PSV for M 5.8, two different distances (10 and 60 km), and the same soil classes.

Figure 10. Comparison between Sabetta and Pugliese (1996) and UMA05 relationships. PGA (top panels) and PGV (bottom panels) versus distance are shown, considering two magnitudes (M 4.6 on left and M 5.8 on right). Predictions for rock sites (class DA) are considered. Thin black lines and gray area represent the mean Ⳳ 1 standard deviation of the Sabetta and Pugliese (1996) relationships, whereas thick black, lines represent mean Ⳳ 1 standard deviation of UMA05.


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Figure 11. Differences between the logarithm of SP96 and UMA05 predictions versus magnitude (left) and distance (right), for PGA (top panels) and PGV (bottom panels). Each circle corresponds to a DA (rock) recording in the UMA data set.

Irpinia earthquake (M 6.8), which is a multiple shock event, and the recorded accelerograms have atypical long durations and very high low-frequency amplitudes. Nevertheless we can compare the PGA and PGV values of the Irpinia earthquake with the UMA05 predictions for a rock site and magnitude 6.9. The good agreement among observations and predictions (Fig. 13) suggests that we could extend the UMA05 toward higher magnitudes. In addition the records of the Irpinia earthquake might be used to enlarge the data set recorded during the Umbria-Marche sequence with the aim of deriving an attenuation relationship valid for the extensional areas of the central Apennines.

Conclusions Attenuation relationships are often applied in regions and ranges of model parameters different from those used to calibrate them. When new regional strong-motion data sets are available, they should be used for validating existing

relationships developed in other countries with similar seismotectonic context. The statistical approaches of Spudich et al. (1999) and Scherbaum et al. (2004) are effective tools for such a task. In this study we used the strong-motion data set recorded in Umbria-Marche, central Italy, during the 1997– 1998 seismic sequence to evaluate the goodness of fit of the Sabetta and Pugliese (1996) relations, which are usually applied for the Italian territory. SP96 is mainly controlled by two earthquakes, since 9 out of 17 come from the 1976– 1977 Friuli sequence and 3 out of 17 from the 1980–1981 Irpinia earthquake. Moreover, SP96 is based on few data recorded at close distance ranges (R 10 km), and restrictive criteria have been used to select the data, leading to a model with small standard deviation. A discussion about the selectivity of the SP96 can be found in Bommer and Scherbaum (2005). Adopting the classification proposed by Scherbaum et al. (2004), the comparison between predictions computed

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Figure 12. PSV computed for SP96 (Sabetta and Pugliese, 1996) and UMA05 (this study), for two different magnitudes (4.5 and 5.8) at 20 km. Left: Predictions for site class DA (rock). Right: Predictions for site class AC (deep alluvium).

Figure 13. Comparisons among the PGA (left) and PGV (right) recorded for the 23 November 1980 Irpinia earthquakes (black circles) and the values predicted by the Sabetta and Pugliese (1996) and UMA05 relationships. Predictions for M 6.9 and rock sites (class DA) are considered. The thin black lines and gray area represent the mean Ⳳ 1 standard deviation of the relationships SP96, whereas the thick black lines represent mean Ⳳ 1 standard deviation of UMA05.

with the SP96 attenuation relationships and observations in the UMA shows that SP96 is not the best model for groundmotion predictions at rock sites in the UMA. However, it can be ranked as a fairly good model for predicting peak values at deep alluvium (class AC). We observed that, in general, the SP96 is penalized by its small standard deviation, which underestimates the variability of the ground-motion parameters observed in the UMA. The analysis of the residuals shows that the bias is generally negative, that is, the SP96 model overestimates, on the average, the PGA, PGV, and PSV values, in the magnitude range 4–6 and in the distance range 1–100 km. The bias diminishes with magnitude and, for PGA, increases with distance. SP96 works better for magnitudes M 5.5, while the use of this model should be dis-

couraged for M 5. Regarding the performance with distance, SP96 works better in the range 10 R 50 km, while it overestimates peaks at larger distances and underestimates peaks for large earthquake at distances 10 km. For all these reasons, new attenuation relationships (UMA05) for PGA, PGV, and PSV in Umbria-Marche region were developed in the range 1–100 km and for magnitude between 4 and 6. We used the random effect model to quantify the earthquake and site components of variance. The introduction of site classification reduces the site-to-site component of variability, but the standard deviation of the attenuation relations is only slightly reduced since the most relevant component of variability does not depend on the specific site or event.

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Acknowledgments We thank S. Parolai for useful discussions. We also thank J. Bommer, an anonymous reviewer, and associate editor G. Atkinson for their valuable comments and suggestions. This work was partially funded by the Italian Dipartmento della Protezione Civile in the frame of the 2004–2006 agreements with Istituto Nazionale di Geofisica e Vulcanologia—INGV.

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Appendix In the following, JB# means equation number of Joyner and Boore (1993), and AY# means equation number of Abrahamson and Youngs (1992). We applied the algorithm for REM-Ev (equation 3) as follows: 1. Estimate the model parameter values h using a fixed effects procedure.

1002 2. Given h, start a search on the parameter c ⳱ revent2/ (revent2 Ⳮ rrecord2). a. Compute the normalized variance-covariance matrix V (JB10). b. Compute r2 ⳱ revent2 Ⳮ rrecord2 (JB15) that maximizes the likelihood function (JB14). c. Compute the likelihood value (JB14) given c, r2, h. d. Evaluate the c value corresponding to the maximum likelihood of point 2.3. 3. Given h, revent2, and rrecord2, estimate gi (interevent variability) by equation AY10. 4. Given gi, estimate new h set using step 1, for (ln yij ⳮ gi); 5. Repeat steps 2, 3, 4 until the likelihood in step 2d is maximized The first step is performed by applying the LSQR algorithm (Paige and Saunders, 1982) to a linearized version


of the original attenuation model. The algorithm for model REM-St (equation 4) is obtained by substituting rstation for revent and uj for gi.

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Manuscript received 18 May 2005.