Ground motion scenarios for the 1997 Colfiorito, central Italy, … · 2019. 11. 4. · 509 ANNALS...

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ANNALS OF GEOPHYSICS, VOL. 51, N. 2/3, April/June 2008

Key words Colfiorito earthquake – kinematic sourcemodelling – ground shaking scenarios

1. Introduction

Following the occurrence of the 1997 Um-bria-Marche seismic sequence, several Italianresearch projects focused on this sector of theApennines to promote a better understanding ofthe regional seismicity and seismic hazard.Among many others, two of them were fundedby the Italian Department of Civil Defense (Di-partimento della Protezione Civile), namely«Development and Comparison amongMethodologies for the Evaluation of SeismicHazard in Seismogenic Areas: Application to

the Central and Southern Apennines» (GNDTProject, 2000-2003) and «Shaking seismic sce-narios in area of strategic and/or priority inter-est» (S3 Project, 2004-2006), hereinafternamed GNDT and S3 projects. In the frame-work of these projects several research activi-ties were focused on the simulation of groundmotions for the Colfiorito main shock (Mw 6.0,September 26th, 1997, 9:40 UTC, hereinafterthe Colfiorito earthquake).

Despite the moderate-magnitude of thisearthquake, the source signature on the patternof observed ground motions is evident (Cultreraet al., 2008). Directivity effects characterize therecorded accelerograms, as shown in fig. 1.This figure illustrates the peak ground acceler-ations (PGAs) recorded during the Colfioritoearthquake as a function of the epicentral dis-tance, and compares them with the empiricalpredictive model proposed for the area by Bin-di et al. (2006). It is evident that the stations lo-cated north of the epicenter show peak acceler-ations systematically larger than the empirical

Ground motion scenarios for the 1997Colfiorito, central Italy, earthquake

Antonio Emolo (1), Giovanna Cultrera (2), Gianlorenzo Franceschina (3), Francesca Pacor (3), VincenzoConvertito (4), Massimo Cocco (2) and Aldo Zollo (1)

(1) Dipartimento di Scienze Fisiche, Università degli Studi «Federico II», Napoli, Italy(2) Istituto Nazionale di Geofisica e Vulcanologia, Roma, Italy

(3) Istituto Nazionale di Geofisica e Vulcanologia, Milano, Italy(4) Istituto Nazionale di Geofisica e Vulcanologia – Osservatorio Vesuviano, Napoli, Italy

AbstractIn this paper we report the results of several investigations aimed at evaluating ground motion scenarios for theSeptember 26th, 1997 Colfiorito earthquake (Mw 6.0, 09:40 UTC). We model the observed variability of groundmotions and the directivity effect through synthetic scenarios which simulate an earthquake rupture propagatingat constant rupture velocity (2.7 km/s). We discuss the variability of kinematic source parameters, such as thenucleation position and the rupture velocity, and how it influences the predicted ground motions and it does notaccount for the total standard deviation of the empirical predictive model valid for the region. Finally, we usedthe results from the scenario studies for the Colfiorito earthquake to integrate the probabilistic and determinis-tic approaches for seismic hazard assessment.

Mailing address: Dr. Antonio Emolo, Dipartimento diScienze Fisiche, Università degli Studi «Federico II», via Cin-tia, 80126 Napoli, Italy; e-mail: [email protected]

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A. Emolo, G. Cultrera, G. Franceschina, F. Pacor, V. Convertito, M. Cocco and A. Zollo

predictions, while the PGAs for the stations lo-cated south of the epicenter lie within one stan-dard deviation of the empirical curves.

The anomalous high accelerations recordedat Nocera Umbra, more than 5 m/s2 on the NScomponent, and at Colfiorito, about 2 m/s2 onthe WE component, have been associated withdominant site effects (Cultrera et al., 2003;Rovelli et al., 2001). However, the differentsource-to-receiver geometry as well as the be-havior depicted in fig. 1, suggested us to inves-tigate the effects related to the rupture history,such as the directivity effects. Indeed, a nearlyNW rupture directivity can explain the ob-served variability of the ground motion aroundthe fault. The relevance of this source effectduring the earthquake has been confirmed byseveral studies aimed at imaging the kinematicrupture history through waveform modeling(e.g., Pino et al., 1999; Zollo et al., 1999; Ca-puano et al., 2000; Hernandez et al., 2004) aswell as by the careful data analysis in Cultreraet al. (2008). The Colfiorito earthquake rup-tured a normal fault SE striking along the

Apenninic direction. Most of the forward andinverse waveform modeling attempts rely on asimilar position of the rupture nucleation pointon the fault plane; it is located at depth close tothe bottom of the fault and to the southernmostedge. The final slip distribution is characterizedby a large slip patch in the southern part of thefault (fig. 2).

The results of these studies and the availableinformation on the crustal velocity structure al-lowed us to design the numerical calculationsfor evaluating ground shaking scenarios for thetarget earthquake. This was done within theGNDT Project, whose main goal was to devel-op and compare different techniques for groundmotion predictions. Several methodologieswere applied to estimate the ground motion interms of parameters of interest (e.g., peak val-ues, spectral ordinates, and signal integralquantities) associated with the occurrence of acharacteristic earthquake on an identified activefault. Indeed, the calculation of ground shakingscenarios commonly rely on the hypothesis ofthe characteristic earthquake model, which as-

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Fig. 1. Comparison of maximum horizontal PGAs recorded by accelerometers of the Italian Strong MotionNetwork with the UMA05 empirical predictive model of Bindi et al. (2006) for rock sites.

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Ground motion scenarios for the 1997 Colfiorito, central Italy, earthquake

sumes that earthquake ruptures repeatedly oc-cur on the same fault (or fault system) with anearly constant geometry, faulting mechanismsand maximum magnitude. These ideas are sup-ported by numerous paleoseismic studies of ac-tive faults in different tectonic environment(e.g., Pantosti and Valensise, 1990). On the oth-er hand, the rupture history (rupture nucleation,propagation and arrest) is not constant duringseveral seismic cycles (that is, during subse-quent rupture episodes on a given fault), be-cause of the heterogeneity of the frictional andrheological properties and/or the geometrical

complexities of fault zones. The recent 2004Parkfield earthquake represents a key exampleof this behavior.

In this context, we have therefore assumedfor our simulations that the large scale sourcefeatures (i.e., fault geometry and position, focalmechanism and seismic moment) were a prioriknown as a result of previous geological, geo-physical and historical seismicity investiga-tions, while the rupture history is unknown. Thespatial variability of strong ground motions candepend on the heterogeneous distribution ofdifferent source model parameters (position of

Fig. 2. Final slip distribution for the Colfiorito earthquake is represented as contour black lines. The units arecm. The white star represents the position on the fault of the earthquake hypocenter. It is also shown (as whitelines) the subdivision of the bottom half of the fault considered to name the different rupture processes. Nucle-ation points falling in the zone 1, 2, and 3 produce a SE unilateral, bilateral, and NW unilateral directivity, re-spectively.

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the rupture nucleation point, final slip, rupturevelocity, slip duration, etc…) on the fault plane.This implies that a large number of syntheticseismograms must be computed to account forthe complexity of the rupture history in order toobtain a representative collection of strong mo-tion waveforms that can be used for hazard es-timation. Therefore, numerous synthetic seis-mograms are computed for different rupturehistories that are associated with a set of select-ed scenarios whose variability is designed to re-flect the heterogeneity of the rupture process.The advantage of this approach is that the vari-ability of the selected strong ground motion pa-rameter at a given site can be described by thestatistical quantities inferred from the largenumber of available simulations.

In this paper we summarize and discuss themajor results on evaluating ground shakingscenarios for the Colfiorito earthquake. We alsodescribe an original application of the methodproposed by Convertito et al. (2006) to evaluatethe seismic hazard in the study area. Thismethod integrates the probabilistic and deter-ministic approaches and it is aimed at overcom-ing some of their respective limitations. Themain novelty is that, in the frame of the classi-cal PSHA approach, the contribution of earth-quake rupture is evaluated through a determin-istic simulation study. In this way, the time vari-able can be introduced in the deterministic sce-narios in terms of return period and time of in-terest; moreover the source effects (geometry,radiation pattern, and directivity) are consid-ered in the probabilistic approach.

2. Ground motion simulation techniques

The Colfiorito earthquake is modeled usingdifferent numerical approaches that simulateboth approximated and full wave field. We willdiscuss here only the results from two approxi-mated ground motion simulation techniques,i.e., the ASymptotic Method (hereinafter, ASM)and the Deterministic-Stochastic Method (here-inafter, DSM). Although these techniques areapproximated, they are suitable for generatingshaking scenarios close to an extended faultwhere the direct S wave field is generally dom-

inant in amplitude with respect to the reflected,converted, and surface phases.

According to the ASM method (Zollo et al.,1997), the seismic wave field associated withthe rupture of a finite fault (or fault system) iscomputed by solving numerically the represen-tation integral. Since the technique is aimed atsimulating the high frequency radiation, theGreen functions are computed with the ray the-ory in a 1-D layered crustal medium (Farra etal., 1986). The fault is discretized in rectangu-lar sub-faults whose size is chosen to reduce thenumerical spatial aliasing. The space-time slipdistribution on the fault is obtained assuming aramp time function parameterized by the rup-ture time, the rise time, and the final slip foreach sub-fault. In the original formulation ofZollo et al. (1997), the final slip distribution onthe fault is computed in accordance to the k-squared model (Herrero and Bernard, 1994).The duration of the source time function is as-sumed to be lower than the maximum period ofthe synthetics (low-pass frequency). With thisassumption, the slip velocity function can beconsidered as a Dirac delta function and thenthe omega-squared spectral behavior is pre-served. In this simulation study, we simulatedthe ground motion up to a maximum frequencyof 10 Hz and the corresponding rise time is cho-sen lower than 0.1s.

The other technique (DSM; Pacor et al.,2005) simulates an acceleration envelope by us-ing the isochron formulation (Bernard andMadariaga, 1984; Spudich and Frazer, 1984)for a kinematic source model. The sourceprocess is defined by a nucleation point on arectangular fault plane, from which the rupturepropagates radially outward with a prescribedrupture velocity, and by a slip distribution de-fined in terms of final amount of slip for eachsub-fault. The normalized envelope is then usedto window a Gaussian noise signal which repro-duces the phase incoherency of high frequencyacceleration. The Fourier spectrum of the re-sulting time series is then multiplied by anomega-squared spectrum that contains source,attenuation, and site terms. The target spectrumis site-dependent because its corner frequencyis computed as the inverse of the envelope du-ration as seen by the receiver; thus the corre-

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sponding acceleration time series will containinformation about the directivity effects asmodeled by the isochron formulation. The pa-rameter «distance» also depends on the kine-matic model, being defined by a spatial averageover the fault plane and weighted on the enve-lope function in order to take into account eachsubfault contribution as perceived by the re-ceiver (Pacor et al., 2005). DSM synthetic seis-mograms are reliable at high frequencies (f >0.5 Hz); at lower frequencies the modeling isless accurate, especially in near source condi-tion, where the omega-squared model is a toosimple representation of the observed groundmotion.

Both techniques compute the direct S wavefield, that is dominant in the near-source dis-tance range, allowing a fast computation of syn-thetic seismograms in the frequency band of en-gineering interest [0.5-10Hz]. Conversely, theyare not able to reproduce the wave-field relatedto complex propagation medium with lateralheterogeneities and soft layers. It is importantto note that, since the two techniques imple-ment different numerical representation of therupture on a finite fault, the computed groundmotions will differently depend on the variousparameters used to describe the source kinemat-ics. For instance, in DSM the use of theisochron formalism implies that the ground mo-tion is directly related to the rupture time distri-bution on the fault. The ASM technique also ac-counts for the isochron distribution on the faultplane to sum up the contributions from the indi-vidual subfaults. Moreover, each elementarysynthetic seismogram contains also the Green’sfunction and, in particular, the radiation pattern.Differently, in the DSM method, the radiationpattern is accounted by an average coefficient.

3. Scenarios for the Colfiorito fault

The scenario study for the Colfiorito earth-quake has been performed varying the kinemat-ic parameters describing the rupture process ona fixed fault geometry, focal mechanism, seis-mic moment and crustal structure. More than200 different rupture histories were simulatedwith both ASM and DSM techniques, using dif-

ferent positions of the rupture nucleation, dif-ferent constant rupture velocity values and dif-ferent final slip distributions on the fault. Theadopted fault-geometry, focal mechanism andseismic moment (table I) is inferred from theinversion of near source accelerometric data(Capuano et al., 2000). The crustal velocitymodel (table II) is derived, in the framework ofthe GNDT project, from the 3D velocity struc-ture of the area, obtained by travel-times inver-sion using data from a dense temporary net-work. The attenuation parameters are takenfrom the study of Bindi et al. (2004). These au-thors computed a non-parametric inversion ofstrong motion records in the epicentral area ofthe 1997-1998 Umbria-Marche seismic se-

Table I. Parameters relative to the Colfiorito earth-quake (modified after Capuano et al. 2000).

Fault length 12 km

Fault width 7.5 km

Bottom depth 8 km

Strike 152°

Dip 38° (~ SW)

Slip –118°

Seismic moment 1.0×1018 Nm

Final slip mean value 0.38 m

Table II. Crustal velocity model used in this simula-tion study.

Layer top Vp Vs Density[km] [km/s] [km/s] [gr/cm3]

0 5.08 2.67 2.56

3 5.75 3.03 2.65

5 6.00 3.16 2.80

7 6.25 3.30 2.80

15 6.50 3.42 2.80

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quence. They found that the attenuation termcan be modelled as

where r is the epicentral distance, β‚ is the aver-age S-wave velocity and QS is the S-wave qual-ity factor (Qs = 49f0.9, in the range 0.5–8.0 Hz,and Qs = 318 for f > 8 Hz. The high-frequencydecay parameter k was set equal to 0.01s (Bin-di et al., 2004).

Synthetic seismograms were computed foreach rupture history at a regular grid of 64 vir-tual receivers, regularly distributed in an area ofabout 60x60 km2 around the fault; the distancebetween adjacent receivers was equal to 7.5 km.In addition, the ground motion is simulated atseven near source sites, where permanent ac-celerometric stations recorded the Colfioritomain shock (ASSI, BVG, CLF, MFN, MTL,and NCR; see fig. 3).

As previously mentioned, we study the vari-ability of predicted ground motions simulatedwith different rupture histories models, definedthrough different final slip distributions, rupturevelocities and positions of the nucleation pointon the fault.

Three values of the rupture velocities arechosen as representative of slow, average andfast ruptures (2.4 km/s, 2.7 km/s and 2.9 km/s);in particular, the rupture velocity 2.7 km/s cor-responds to the ‘true’ value retrieved from datainversion by Capuano et al. (2000).

As far as the location of the nucleation pointis concerned, we have considered three differ-ent potential areas for rupture initiation, all lo-cated on deeper half fault width, and correspon-ding to a bilateral rupture as well as to two uni-lateral ruptures propagating in opposite direc-tions. For each rupture velocity value, rupturescenarios are grouped in 3 classes depending onthe nucleation position (NW unilateral, bilater-al and SE unilateral; fig. 2).

Figure 4 and fig. 5 display PGA and PGVmaps, respectively, computed with both the nu-merical approaches and a constant rupture ve-locity of 2.7 km/s. The bottom panels in fig. 4shows the PGA distribution computed with a

, expA f r r Q f

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rupture velocity equal to 2.4 Km/s. Directivityeffects are more pronounced in the DSM simu-lations, while the effect of radiation pattern ismore evident in the ASM simulations. As ex-pected the directivity effects are more promi-nent for unilateral propagating ruptures. More-over, the rupture style determines the shape andextension of large peak values areas, whosemaximum peaks are comparable in both tech-niques (4 m/s2 for PGA and 0.3 m/s per PGV);in particular, the ground motion variability ob-served for the Colfiorito earthquake is well re-produced when the NW unilateral rupture prop-agating with a 2.7 km/s velocity is considered(in agreement with kinematic source models in-ferred by waveform inversions).

The effect on ground motion of two differ-ent rupture velocities can be also observed forPGA (top and bottom panels of fig. 4): the high-er the rupture velocity the larger the peak val-ues. Moreover, a larger rupture velocity causesa sort of magnification of those areas character-ized by higher shaking levels. Figure 6 showsPGA values as a function of the azimuth meas-ured from the fault strike as illustrated in the in-set. Finite fault effects generate deviations ofPGA azimuthal distribution from the constantscaling predicted by empirical regression laws(Sabetta and Pugliese, 1996, and Bindi et al.,2006): once the magnitude and the distance arefixed, the empirical models provide PGA val-ues independent of azimuth.

The scaling of predicted PGA values as afunction of epicentral distance and their com-parison with the regional-specific predictiveequation retrieved from the 1997-98 Umbria-Marche seismic sequence (UMA2005; Bindi etal., 2006) are displayed in fig. 7. Symbols iden-tify the average values and the average ± one-standard deviation for the PGAs computedthrough DSM. The solid and the dashed curvesdisplay the empirical attenuation law and theone-standard deviation interval, respectively.The agreement between the UMA2005 meancurve and the mean values obtained by the DSMground motion scenarios is quite good even ifthe DSM values slightly underestimate the em-pirical ones. Note, however, that the simulatedvalues are computed at bedrock sites while theempirical predictions are derived from data

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12°12' 12°24 ' 12°36' 12°48' 13°00' 13°12' 13°24 '

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Fig. 3. Strong motion stations that recorded the Colfiorito earthquake (ASSI: Assisi, BVG: Bevagna, CLF:Colfiorito, CSA: Castelnuovo di Assisi, CSC: Cascia, FHC: Forca Canapina, GBB: Gubbio, GBP: Gubbio pi-ana, LNS: Leonessa, MNF: Monte Fiegni, MTL: Matelica, NCR: Nocera Umbra, NRI: Norcia zona industriale,NRV: Norcia Altavilla, PGL: Pegli, PNN: Pennabilli, RTI: Rieti, SNG: Senigallia, TOR: Cerreto Torre). Trian-gles and squares correspond to digital and analog seismic stations, respectively. The fault surface projection(grey rectangle) and the focal mechanism of the Colfiorito earthquake, shown in the figure are from Capuano etal. (2000).

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Fig. 4. Maps of mean synthetic PGA obtained for the Colfiorito earthquake using the DSM and the ASM sim-ulations. Top panels: unilateral SE/NW nucleation for a constant rupture velocity of 2.7 km/s; middle panels: bi-lateral nucleation a constant rupture velocity of 2.7 km/s; bottom panels: unilateral SE/NW nucleation for a con-stant rupture velocity of 2.4 km/s. For all rupture models, the mean value of PGA is computed at each site fromthe distribution of peak values obtained from synthetics simulated by moving the nucleation point on the bottomhalf of the Colfiorito fault.

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Fig. 5. Maps of mean synthetic PGV obtained for the Colfiorito earthquake using the DSM and the ASM sim-ulations. Top panels: unilateral SE/NW nucleation for a constant rupture velocity of 2.7 km/s; bottom panels: bi-lateral nucleation for a constant rupture velocity of 2.7 km/s. For all rupture models, the mean value of PGV iscomputed at each site from the distribution of peak values obtained from synthetics simulated by moving the nu-cleation point on the bottom half of the Colfiorito fault.

recorded at rock sites that could be affected byamplification effects (Bindi et al., 2004; 2006).

The comparison of PGA standard devia-tions shown in fig. 7 indicates that numericalsimulations produce a PGA variability greaterthan that resulting from the UMA2005 empiri-cal regression law. This means that the variabil-

ity introduced in kinematic source parameters(slip distributions, rupture velocity values andnucleation point position) produces ground mo-tions whose peaks are comparable with the em-pirical models in terms of average values butwith larger standard deviation. One possible ex-planation is that the simulations are performed

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sampling many different rupture models of thesame fault (more than 200) and using a verydense grid of observers.

The previous comparisons allowed us to se-lect the source model which best fits the ob-served ground motions. Figure 8 shows theFourier spectra of ground acceleration comput-ed from time histories recorded at six nearsource stations during the Colfiorito earth-quake.

The spectra are compared with the deter-ministic simulation performed by the DSMtechnique for an unilateral (toward NW) rup-ture model with vR=2.7 km/s.

The synthetic spectra include the site trans-fer functions estimated with different methods,depending on the available information: forCLF and MTL, the transfer functions were

computed by 1D theoretical transfer functions(Rovelli et. al., 2001; Di Giulio et al., 2003;Luzi et al., 2005). Empirical transfer functionsfrom the non-parametric spectral inversion(Bindi et al.; 2004) were adopted for ASSI andBVG. Finally the horizontal-to-vertical spectralratios, computed on signal windows includingthe strong motion phases, were used to quanti-fy the strong and complex local effects at NCR(Cultrera et al., 2003). No site effects are ex-pected at MNF since the accelerometric stationis located on rock site.

The agreement between observed and simu-lated spectra is quite good, especially at theMNF, CLF and NCR stations.

The mismatch at the other stations could bemainly ascribed to inappropriate transfer func-tions chosen to describe the local effects and to

Fig. 6. PGA as a function of azimuth at 10 km epicentral distance predicted by synthetic simulations and byground motion predictive equations. DSM and ASM simulations obtained with the unilateral SE/NW nucleationand with two values of the rupture velocity are compared with empirical predictions of Sabetta and Pugliese(1996) and UMA2005 (Bindi et al., 2006) for a M6 earthquake. Shaded area indicates ±1std of UMA2005, andthe inset shows the geometry adopted for the computation.

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the simplyfied simulation techniques. A de-tailed description of geotechnical site charac-terisation of these stations is reported in Luzi etal. (2005). BVG is located on deep lacustrineand alluvial deposits (> 30m) of the Valle Um-bra basin and complex 2D and 3D effects areexpected. MTL is installed on the alluvial de-posits of a shallow basin with thickness < 30 mand the 1D profile is derived from penetromet-ric test data. Finally ASSI is installed next tothe St. Francesco Cathedral and peak amplifica-tion could be related to interaction with thestructure.

4. Seismic hazard assessment: integratingprobabilistic and deterministic approaches

The results obtained with the deterministicsimulations have been integrated in the proba-bilistic approach, following Convertito et al.(2006).

The Probabilistic Seismic Hazard Analysis(PSHA), developed by Cornell (1968), is wide-ly used for evaluating the impact on earth-quakes-prone areas associated with the occur-rence of seismic events. The PSHA techniqueis largely applied in regions where the charac-teristics of the seismogenetic structures, re-sponsible for large earthquakes, are not wellknown and then the application of determinis-tic approaches to the seismic hazard is not fea-sible. Moreover, when a single causative faultand a maximum-magnitude earthquake occur-ring on it are considered, it is not easy to definea recurrence relationship and the activity ratedue to the non-completeness of seismic cata-logues. To overcome these limitations, Conver-tito et al. (2006) compute the probability of oc-currence of earthquakes by assuming the char-acteristic earthquake model (Schwartz andCoppermith, 1984), while the activity rate isobtained by the Youngs and Coppersmith(1985) approach.

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Fig. 7. Average PGA with ± one standard deviation of the computed scenarios compared with UMA2005ground motion prediction equation (Bindi et al., 2006).

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Another limitation of the classical PSHAformulation is that the earthquake effects aredescribed by predictive empirical equationsproviding the required ground motion estimatesas a function of parameters like the earthquakemagnitude, the source-to-site distance, the siteconditions (e.g., Sabetta and Pugliese, 1996;Abrahamson and Silva, 1997). However, theempirical models account only roughly forsource properties (in general, through the mag-nitude and in some case by a coefficient that de-pends on the receiver’s position with respect tothe fault; i.e. hanging-wall or foot-wall record-ing sites), propagation (through the distance),and site effects (through a coefficient). Thisrepresentation of the source contribution doesnot account for the variability of the radiatedground motions that we have shown before. Inother words, this representation of the source

contribution is reliable only for recording siteslocated at distances from the source larger ofequal to the fault dimension (far field, farsource approximation). We emphasize that nearsource radiation requires us to account for thesource complexity and dynamic heterogeneityin order to properly model the high frequency(larger than 1 Hz) ground motions. To this goalthe method proposed by Convertito et al.(2006) takes into account the effects of rupturehistory and source heterogeneities through de-terministic modelling of the waveforms radiat-ed by an extended fault. In the following wediscuss the application of this modified PSHAapproach to the Colfiorito main shock.

In the framework of the classical PSHA ap-proach, the hazard is evaluated computing thehazard integral (Cornell, 1968) that, for the i-thseismic source zone, provides the frequency of

Fig. 8. Comparison of DSM synthetic and observed acceleration spectra at 6 near-source stations. NS and WEhorizontal components are plotted with dashed and solid thin lines, respectively. DSM synthetics are plotted withsolid thick line.

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exceedance Ei of a fixed threshold value A0 fora given ground motion parameter A as

(1)

where fR(r)dr represents the probability of oc-currence of an earthquake at a distance betweenr and r+dr from the target site. The probabilitydensity function fR(r) has no analytical formula-tion except that in simple cases. The Probabili-ty Density Function fM(m) provides the proba-bility of occurrence of an earthquake having amagnitude in the range (m, m+dm). Finally, thecoefficient αi represents the average rate ofearthquake occurrence for the ith seismogenet-ic zone and, in general, is estimated from seis-mic catalogues.

If a single causative fault is considered for ascenario-like analysis, the hazard integral needssome modifications because the PDFs fR(r) andfM(m) and the seismic activity rate αi have noobvious formulations. First of all, consideringthat the fault geometry is known (table I), andassuming that the rupture process at the sourceinvolves the whole fault plane, we can use adefinition of distance as the minimum distancefrom the surface projection of the fault plane(Joyner and Boore, 1981). In this way, for anygiven receiver, the source-to-site distance isfixed aside from the location of the nucleationpoint and then there is no more need to consid-er a PDF for it in the hazard integral. If thecharacteristic-earthquake model is assumed, thePDF fM(m) is characterized by a constant prob-ability of occurrence of earthquakes havingmagnitude in the neighborhood of the magni-tude of the characteristic earthquake (M6.0 forthe Colfiorito fault). Moreover, the characteris-tic earthquake dos not occur at the exclusion ofother size events that are accounted in the PDFfM(m) as non-characteristic part. In otherwords, the fM(m) is a truncated exponential upto the characteristic magnitude value and it isconstant for larger magnitudes (see the fig. 1 inthe paper by Convertito et al., 2006). In thesame way, Youngs and Coppersmith (1985)provide the expressions for evaluating the seis-mic activity rates both for the non-characteris-

, ,

.

E A A f r f m

p A m r A m r dr dm

i i R

MR

M0

0

$

$

α=] ] ]

^

g g g

h7 A

##

tic and characteristic parts of the PDF fM(m).In conclusion, the hazard integral for a giv-

en site located at a distance r* from the surfaceprojection of the fault plane can be rewritten(Convertito et al., 2006), in the case of the char-acteristic-earthquake model, as

(2)

mc being the ‘characteristic’ magnitude while∆m defines the range in which the fault behav-iour can be considered characteristic. Youngsand Coppermith (1985) suggested ∆m = 0.5.

For evaluating the frequency of exceedanceE through the computation of the hazard inte-gral (equation 2), the level reached by the se-lected ground motion parameter A and the asso-ciated probability of exceedance p of thethreshold value A0 are needed. For this purpose,the scenario study performed for the Colfioritofault allows the computation of the earthquakeeffects, in terms of PGA, assuming a log-nor-mal statistical distribution for the selectedground motion parameter. In particular, weused the mean PGA and the associated variabil-ity inferred from the whole set of ruptureprocesses simulated varying the slip distribu-tion and the position of the nucleation point.The maps of PGA and of the associated Coeffi-

cient of Variation we used

are shown in fig. 9. The CoV parameter is away to show how the variability at the source intransferred to the ground motion variability.

As an example, we shown in fig. 10 thehazard map obtained by the approach proposedby Convertito et al. (2006) when the character-istic earthquake model is assumed, for a returnperiod T = 50,000 years. In the same figure it isalso reported for comparison the hazard mapcomputed by using the Abrahamson and Silva(1997) ground motion predictive equation forPGA. We used the Abrahamson and Silva(1997) empirical equation in order to separatesites locate in the fault foot-wall from those lo-

CoVPGA

100 PGA

1 2σ=b l

,

.

,

E A A

p A m r

f m

A m r dm* *

c Mc

m

m m

0

0

c

c

$

$

α=D+

] ]

^

g g

h7 A

#

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522


cated in the hanging-wall. The hazard map ob-tained from synthetic PGAs reproduces themain features of the mean PGA map of fig. 9,

thus accounting for the kinematic source pa-rameters (fault geometry, radiation pattern, anddirectivity).

Fig. 9. (a) Map of simulated PGA (mean values). (b) Map of the Coefficient of Variation. Results were obtainedby the ASM simulation technique. The rectangles in the figures represent the surface projection of the fault(modified after Convertito et al., 2006).

Fig. 10. Hazard map for PGA associated with the Colfiorito fault and corresponding to T=50,000 return peri-od. Contour lines for PGAs larger then 1 m/s2 are shown. The grey rectangles represent the surface projection ofthe fault. (a) Hazard map for the characteristic earthquake model and PGAs simulated by the ASM technique.(b) Hazard map for the characteristic earthquake model and PGAs estimated by the Abrahamson and Silva(1997) predictive relation. (modified after Convertito et al. 2006).

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5. Conclusive remarks

The geophysical data collected during theUmbria-Marche, Italy, seismic sequence (1997-98) represent a unique database which allowsus to improve the seismic hazard assessment forthe region. In particular, strong ground motionrecords of the Colfiorito main shock (Septem-ber 26th, 1997, 9:40 UTC, Mw6.0) reveal thatstations located north of the epicenter recordedpeak accelerations systematically larger thenthose recorded at stations located to the south(Cultrera et al., 2008). Moreover, the accelero-grams recorded at NCR (Nocera Umbra) andCLF (Colfiorito) are characterized by a relative-ly high peak ground acceleration, not capturedby empirical predictive models. The former ob-servation suggests that rupture directivity to-ward the NW played a dominant role, while thesecond observation can be explained in terms oflocal site amplifications.

The activities performed in the frameworkof the GNDT Project gave us the opportunity toinvestigate the observed pattern of ground mo-tion waveforms and to perform a systematicstudy on ground shaking scenarios comparingdifferent simulation techniques. In this paper,we present the main results of this simulationattempts and the computed shaking scenariosfor the Colfiorito earthquake using two simula-tion techniques, i.e., ASM (Zollo et al., 1997)and DSM (Pacor et al., 2005).

The variability of ground motion parametersobtained with both techniques is comparable orsmaller than the standard deviation associatedwith the empirical predictive model UMA2005(Bindi et al., 2006), even if both simulationmethods are approximated. As expected, ourmodeling results are strongly dependent on theposition of nucleation point (directivity effect),on faulting style and on the adopted rupture ve-locity value: the higher the rupture velocity thehigher the peak ground motions.

The ground motions observed during theColfiorito earthquake are well reproduced whenan unilateral rupture propagation toward the NWis considered, with a rupture velocity of about2.7 km/s. The data can be modeled only in someparticular frequency bands due to the relevantamplification associated with the site effects,

which require the use of appropriate site transferfunctions in the modeling. In general, the sce-nario studies preformed for the Colfiorito earth-quake highlighted that the extended fault effects(e.g., the rupture directivity) are important alsoin the case of moderate size earthquake. Thisconclusion encouraged us to carry out a system-atic study on the ground motion variability dueto the source parameters for moderate magnitudeearthquakes, which was performed in the frame-work of the S3 Project.

The inferred main source features of theColfiorito earthquake have also been used in arecent technique aimed at integrating probabilis-tic and deterministic approaches for seismic haz-ard assessment. The deterministic approach al-lows us to compute ground shaking scenarios foran earthquake occurring on a given, well known,causative fault. In the case of the Colfiorito sce-narios, we have shown that it is possible in thisway to properly include source and propagationeffects in simulated ground motions. On the oth-er hand, the deterministic scenarios represent asort of ‘static’ results that are of poor use forprobabilistic hazard assessment, because it is notpossible to include the earthquake recurrencetime in the computation.

The technique proposed by Convertito et al.(2006) is based on the site-dependent evaluationof the probability of exceedance for the chosenstrong motion parameters (e.g., peak quantities,and spectral ordinates). The probability is ob-tained from the statistical analysis of the synthet-ic waveforms data base produced for a largenumber of possible rupture histories occurringon a characteristic earthquake fault. The integrat-ed technique is aimed at overcoming some of thelimitations of both purely probabilistic and pure-ly deterministic approaches for seismic hazardassessment. In particular, it allows us to accountfor the return period and elapsed time in the de-terministic scenarios and for the source charac-teristics and their effects on the ground motions(as the geometry, the radiation pattern, and thedirectivity) in the probabilistic technique. Due tothe availability of synthetic seismograms, theanalysis can be extended to any desired groundmotion parameter. Moreover, the site effects canbe easily taken into account if the transfer func-tions are available.

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The combined study of a deterministic and aprobabilistic approaches to compute groundshaking scenarios for the Colfiorito earthquakeallows us to point out the importance of source-to-receiver geometry and heterogeneity of sourceparameters on extended faults also for moderatemagnitude seismic events. Indeed, despite thesmall dimension of the causative faults, the di-rectivity effects strongly affect the observed pat-tern of PGA values. Once rupture directivity isproperly taken into account, the deterministicsimulation methodologies are able to reproducethe average Fourier spectra of ground accelera-tion, the spatial pattern of recorded PGA as wellas the variability of ground motion parameterswith distance. This corroborates the relevance ofincluding the outcomes of deterministic groundmotion predictions in probabilistic hazard as-sessment to specific target sites.

Acknowledgments

The research activities presented in this articlewere supported by the projects «Sviluppo econfronto di metodologie per la valutazionedella pericolosità sismica in aree sismoge-netiche: applicazione all’Appennino centrale emeridionale», GNDT 2000-2003, and «Scenaridi scuotimento e di danno atteso in aree di in-teresse prioritario e/o strategico», S3 Project,DPC-INGV 2004-2006. The authors thank allthe people (such as D. Bindi, G. Festa, L. Luzi,E. Priolo, A. Saraò, P. Suhadolc, and A.Vuan,among many others) involved in these projectswho collaborate to the simulation studies relat-ed to the Colfiorito earthquake. The careful re-vision made by J. Burianek and anonymous re-viewer improved the manuscript. We also thankthe Editorial Board of Annals of Geophysicsthat welcomed our paper.

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