Disaggregation of Probabilistic Ground-Motion Hazard in Italy

Disaggregation of Probabilistic Ground-Motion Hazard in Italy

by Simone Barani, Daniele Spallarossa, and Paolo Bazzurro

Abstract Probabilistic seismic hazard analysis is a process that integrates overaleatory uncertainties (e.g., future earthquake locations and magnitudes) to calculatethe mean annual rate of exceedance (MRE) of given ground-motion parameter valuesat a site. These rates reflect the contributions of all the sources whose seismic activity isdeemed to affect the hazard at that site. Seismic hazard disaggregation provides insightsinto the earthquake scenarios driving the hazard at a given ground-motion level. Thiswork presents the disaggregation at each grid point of the Italian rock ground-motionhazard maps developed by Gruppo di Lavoro MPS (2004), Meletti and Montaldo(2007), and Montaldo and Meletti (2007). Disaggregation is used here to computethe contributions to the MRE of peak ground horizontal acceleration (PGA) and5%-damped 0.2, 1.0, and 2.0 sec spectral acceleration values corresponding to differentmean return periods (MRPs of 475 and 2475 yr) from different scenarios. These sce-narios are characterized by bins of magnitude, M, source-to-site distance, R, andnumber, ε, of standard deviations that the ground-motion parameter is away from itsmedian value for thatM � R pair as estimated by a prediction equation. Maps showingthe geographical distribution of themean andmodal values ofM,R, and ε are presentedfor the first time for all of Italy. Complete jointM–R–ε distributions are also presentedfor selected cities. Except for sites where the earthquake activity is characterized bysporadic low-magnitude events, the hazard is generally dominated by local seismicity.Moreover, as expected, the MRE of long-period spectral accelerations is generally con-trolled by large magnitude earthquakes at long distances while smaller events at shorterdistances dominate the PGA and short-period spectral acceleration hazard. Finally, for agiven site, as the MRP increases the dominant earthquakes tend to become larger and tooccur closer to the site investigated.

Introduction

With his seminal work C. A. Cornell (1968) inventedprobabilistic seismic hazard analysis (PSHA) by introducinga method for evaluating the likelihood of exceedance (oroccurrence) of any level of earthquake ground shaking at a siteduring a given period of time. This is achieved by combiningthe effects of all the possible magnitudes and earthquake loca-tions that could affect the hazard at the site investigated.Although the original approach conceptually still holds, sub-stantial progress has been made to refine the PSHAmethodol-ogy.For example, Power et al. (1981) proposed theuseof logictrees and, subsequently, Kulkarni et al. (1984) and Copper-smith and Youngs (1986) suggested that logic trees provideda convenient framework for the treatment of the uncertaintyboth in the true parameter values in the mathematical modelsadopted and also in thevalidity of themodels themselves. Thisuncertainty is often called epistemic (as opposed to aleatory)because it is due to imperfect knowledge and, at least in prin-ciple, could be reduced by further research. More recently,many studies have emphasized the importance of acknowl-edging anddocumentinguncertainties in PSHA(e.g.,McGuire

andShedlock, 1981;Rabinowitz and Steinberg, 1991;Crameret al., 1996; Senior Seismic Hazard Analysis Committee[SSHAC], 1997; Grünthal and Wahlström, 2001; Cao et al.,2005; Sabetta et al., 2005; Scherbaum et al., 2005; Baraniet al., 2007). Thus, sensitivity and uncertainty analyses havebecome of primary importance in modern PSHA studies be-cause theyallow the identificationof themodels andparametervalues that have the highest influence on the hazard and driveits uncertainty. The knowledge of thosemodels and parametervalues is valuable in guiding focused research efforts to reducesuch an uncertainty and in facilitating a correct understandingand use of PSHA results. In 1988 the National Research Coun-cil (NRC, 1988) pointed out the relevance of seismic hazarddisaggregation (or deaggregation) that becomes an insepa-rable part of a PSHA. Important contributions to seismic hazarddisaggregationmethods and applications were given by Bern-reuter (1992), Chapman (1995),McGuire (1995), Cramer andPetersen (1996), Bazzurro and Cornell (1999), Harmsen et al.(1999), Sokolov (2000), Harmsen (2001), Harmsen and Fran-kel (2001), PeláezMontilla et al. (2002), Halchuk and Adams

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Bulletin of the Seismological Society of America, Vol. 99, No. 5, pp. 2638–2661, October 2009, doi: 10.1785/0120080348

(2004), Hong and Goda (2006), and Cao (2007). The disag-gregation process separates the contributions to the meanannual rate of exceedance (MRE) of a specific ground-motionvalue at a site due to scenarios of givenmagnitudeM, distanceR, and, often, the ground-motion error term ε. This latter quan-tity is defined as the number of standard deviations by whichthe (logarithmic) ground motion generated by a given M–Rpair deviates from the median value estimated by a predictionequation. Thus, this process reveals which earthquake scenar-ios (defined by specific values ofM, R, and ε) control the sitehazard. The knowledge of theM–R–ε groups dominating theseismic hazard at a site is of paramount importance for manyengineering applications for which the hazard curves do notsuffice. For example, it is an important guide for simulatingor selecting appropriate ground-motion time histories fornonlinear dynamic analyses of structures, liquefaction analy-sis of soil, or slope stability studies. Appropriate here refers toaccelerograms that have the characteristics proper of thosescenario events that are more likely to cause the exceedanceof the target ground shaking level at the site. Considering εalong with other disaggregation parameters (i.e., M and R)is also useful to better understand differences between prob-abilistic ground-motion estimates and ground motions fromdeterministic scenarios (Harmsen, 2001). The ε part of the dis-aggregation results may also provide some guidance about theminimum number of standard deviations, σ, at which theground-motion distribution for each scenario could be trun-cated in the PSHA calculations. For example, severe trunca-tions of the ground-motion distribution (e.g., at 1σ) arenever justified and are against empirical evidence of groundmotions 3σ or more above the median in some historicalevents. Such unwise truncations can cause severe underesti-mation of the hazard (Abrahamson, 2006; Bommer and Abra-hamson, 2006). Moreover, once the dominating magnitudesare revealed, it might be desirable to examine in depth the in-fluence of alternative magnitude distributions (e.g., exponen-tial, characteristic) for the magnitude range relevant to thosedominant scenarios (McGuire, 2004). Thus, a comprehensivePSHA should include sensitivity and disaggregation computa-tions to explain what aspects of the PSHA drive the calculatedhazard (e.g., SSHAC, 1997; Grünthal and Wahlström, 2001;McGuire, 2004).

Thework presented here deals with the disaggregation ofthe Italian ground-motion hazard (Gruppodi LavoroMappa diPericolosità sismica [MPS], 2004; Meletti and Montaldo,2007; Montaldo and Meletti, 2007). A new peak ground hor-izontal acceleration (PGA) hazard map on rock for a mean re-turn period (MRP) of 475 yr (the MRP is defined as thereciprocal of the MRE1, thus an MRP of 475 yr is equivalent

to an MRE of 2 × 10�3) was produced for Italy by Gruppodi Lavoro MPS in 2004. The term “rock” indicates sites withaverage shear wave velocity, VS30, in the top 30 m of a soilprofile greater than 750 m=sec. Subsequently, many studieswere developed within the framework of the Dipartimentodi Protezione Civile–Istituto Nazionale di Geofisica e Vulca-nologia (DPC–INGV) S1 project (see the Data and Resourcessection) to supplement that map with a more comprehensivedocumentation beyond the simple PGA hazard estimates.Within the framework of that project, we performed the dis-aggregation of the PGA hazard for nineMRPs (Spallarossa andBarani, 2007). For information on the results, see theData andResources section (Meletti et al., 2007). In this article, wepresent maps showing the geographical distribution of bothmean ( �M, �R, and �ε) and modal (M�, R�, and ε�) values ofthe 3D joint distributions ofM,R, and ε resulting from the dis-aggregation of the values of PGA and 5%-damped spectralacceleration, Sa�T�, at periods, T, of 0.2, 1.0, and 2.0 sec thatare associated with 10% and 2% probability of exceedance in50 yr (MRPs of 475 and 2475 yr, respectively). Themaps werecreated by considering ahomogeneousgrid of 0.05° spacing inlatitude and longitude. For a given MRP, disaggregatingthe exceedance rates for multiple Sa�T� allows us to identify,for example, if common earthquake scenarios dominatethe hazard at all periods or, conversely, whether the hazardat short- and long-period Sa�T� is controlled by differentscenario earthquakes (e.g., McGuire, 1995; Barani et al.,2008). Moreover, for 19 important cities in Italy, we tabulatethe values of both the triplets �M– �R–�ε andM�–R�–ε� of the 3Djoint distributions of M, R, and ε for 0.2 and 1.0 sec spectralacceleration values. For some of these cities we also presentand discuss example joint M–R–ε distributions. Note thatprevious evaluations of the Italian seismic hazard based onthe application of the Cornell approach (e.g., Romeo andPugliese, 1998; Slejko et al., 1998; Albarello et al., 2000;Romeo and Pugliese, 2000) did not provide any informationabout the dominating earthquakes for any site. Finally,although sensitivity analysis is not a central topic of this work,the influence of different disaggregation procedures (i.e., dis-aggregationbyM andR rather than in termsofM,R, andε) andalternative ground-motion attenuation equations on disaggre-gation results are also examined in some detail.

A Note on Models and Input Parameters

Before describing the models and input parameters, it isimportant to provide an overview of the procedure adopted byGruppo di Lavoro MPS (2004) for the evaluation of the Italianseismic hazard. According to the current practice in PSHA, thehazard maps of Italy were developed using the logic treeapproach to account for the epistemic uncertainty in the mod-els and in the parameter values of each model. Specifically,1Incidentally, whenever possible in this article we chose to use annual

rates instead of annual probabilities because the definition of the latterrequires an assumption on the stochastic process of earthquake occurrence(e.g., Poissonian), an assumption that is unnecessary for the topic discussedhere. However, because rates and probabilities when taking on small valuesof engineering significance, such as those discussed here, are, for all prac-

tical purposes, numerically similar, these two terms are used somewhat in-terchangeably. For example, the 475 yr map is also routinely called the 10%in 50 yr exceedance probability map.

Disaggregation of Probabilistic Ground-Motion Hazard in Italy 2639

the logic tree adopted allows modeling the uncertainty in thecatalog completeness time for different magnitude ranges, inthe values of earthquake recurrence parameters andmaximumearthquake magnitude, and in alternative ground-motionpredictive equations. One earthquake catalog, called CPTI04(Gruppo di Lavoro Catalogo Parametrico dei TerremotiItaliani [CPTI], 2004; see the Data and Resources section),and one seismogenetic zonation, named ZS9 (Gruppo diLavoro MPS, 2004; Meletti et al., 2008; see the Data andResources section), were used both in the hazard evaluationsand in this study. Figure 1 shows the geographical distributionof epicenters based on the CPTI04 catalog and the ZS9 seis-mogenetic zonation. Note that ZS9 assigns a prevalentmechanism of faulting (interpreted as the mechanism withthe highest probability of generating future earthquakes) toall its source zones for use in the ground-motion predictionequations (Meletti et al., 2008). Fault sources were not con-sidered in the hazard calculation because the distribution ofthe epicenters appears to be inconsistent with the assumptionof line or planar sources, therefore preventing the attributionof individual historical earthquakes to their causative fault.Consequently, fault sources are not considered in our studyeither. It is worth noting, however, that new and updated dataabout known seismogenic faults in Italy have been recentlypublished (Basili et al., 2008). Should these new data aftercareful evaluation be employed in future seismic hazard as-sessments at a national scale, we will conduct a revision ofthis disaggregation study to evaluate their effects.

Contrary to the recommendations of McGuire et al.(2005) and Musson (2005) and to our opinion, but followingAbrahamson and Bommer (2005), the reference seismic haz-ard maps of Italy were developed in terms of the medianhazard rather than in terms of the mean hazard. Thus, thehazard values disaggregated here correspond to the fiftiethpercentile of the hazard distribution obtained by using a spe-cific logic tree. Because the median hazard is not too sensi-tive to all valid, properly weighted input assumptions(particularly low-likelihood extreme assumptions that leadto high hazard), the disaggregation is performed here using

the branches along the logic tree path that provided thehazard values closest to the reference fiftieth percentilehazard (path 921 of the logic tree adopted for the ItalianPSHA [V. Montaldo and C. Meletti, personal comm.,2007]). In other words, the selected path corresponds tothe model and the parameter values that contribute the most

to the median hazard. This path considers the ZS9 seismo-genetic zonation, a specific set of values of seismicity param-eters (i.e., earthquake recurrence parameters and maximummagnitude) for each source zone (see Table 1), and the rockground-motion attenuation equation by Ambraseys et al.(1996). Note that this relationship was developed usingthe larger of the two horizontal components of severalEuropean ground-motion recordings, and it uses the surfacewave magnitude (MS) to quantify the size of earthquakes andthe Joyner and Boore distance (defined as the shortest dis-tance to the surface projection of the fault rupture [Joynerand Boore, 1981]) as a measure of the source-to-site dis-tance. We have adjusted this equation to account for the styleof faulting by applying the average correction factors pro-posed by Bommer et al. (2003). These multiplicative factorswere also used for the evaluation of the seismic hazard ofItaly. Finally, it is worth observing that we limited our cal-culations to events with source-to-site distances up to 200 kmto avoid breaching the range of applicability of the ground-motion prediction equation adopted.

Basics of 3D Seismic Hazard Disaggregation

In this section we give a brief description of the basicconcepts, definitions, and mathematics of the seismic hazarddisaggregation in terms M, R, and ε (3D disaggregation).A detailed review of different disaggregation procedures(e.g., 1D and 2D disaggregation, geographical disaggregationin terms of latitude and longitude) can be found in Bazzurroand Cornell (1999). However, it is worth specifying that thedisaggregation is performed here for the probability of ex-ceeding the target ground-motion values rather than forthe probability of equaling them (McGuire, 1995).

Disaggregating seismic hazard means to evaluate thecontributions of different scenarios of given M, R, and εto the mean annual rate, λy� , of exceeding a givenground-motion parameter value y� at a site. The contribution,U, to λy� of a particular (M, R, and ε) scenario, such as thatm1 < M < m2, r1 < R < r2, and ε1 < ε < ε2, is given by

U�m1 < M < m2; r1 < R < r2; ε1 < ε < ε2jY > y��

�PNS

i�1 υi�mmin�Rm2m1

Rr2r1

Rε2ε1 fM;R�m; r�fε�ε�P�Y > y�jm; r; ε� dmdr dε

λy�; (1)

where

• NS indicates the number of potential earthquake sources;• υi�mmin� is the annual rate of earthquake occurrence abovea minimum threshold magnitude mmin;

• fM;R�m; r� is the joint probability density function (pdf) ofmagnitude and distance;

2640 S. Barani, D. Spallarossa, and P. Bazzurro

• fε�ε� is the pdf (standardized normal density function) forthe ground-motion error term, ε;

• P�Y > y�jm; r; ε� is the conditional probability of exceed-ing a particular value, y�, of a ground-motion parameter, Y,for a given magnitude, m, distance, r, and ε standard de-viations away from the predicted median ground motion.

Once all the contributions are evaluated, the disaggre-gated hazard (i.e., the contribution to λy� from different dis-crete M–R–ε bins) is represented by the joint probabilitymass function (PMF) of M–R–ε, which is usually summa-rized by its mean ( �M, �R, and �ε) and modal (M�, R�, andε�) values. A closed-form solution for (M�, R�, and ε�) isnot available but �M, �R, and �ε can be calculated as follows:

�M �PNS

i�1 υi�mmin�RRRmfM;R�m; r�fε�ε�P�Y > y�jm; r; ε� dmdr dε

λy�; (2)

�R �PNS

i�1 υi�mmin�RRRrfM;R�m; r�fε�ε�P�Y > y�jm; r; ε�dmdr dε

λy�; (3)

�ε �PNS

i�1 υi�mmin�RRRεfM;R�m; r�fε�ε�P�Y > y�jm; r; ε� dmdr dε

λy�; (4)

where the triple integration covers all possible values of M,R, and ε.

While the mode is a metric with the distinct advantage ofrepresenting the event that most likely generates the exceed-ance of the target ground-motion level at the site considered,it has also the disadvantage of being sensitive to the bin sizeadopted and to being dependent on the disaggregationscheme (e.g., Bazzurro and Cornell, 1999; Abrahamson,2006). The mean, on the other hand, is easier to understandand to compute than the mode; it is independent of the bin-ning size and of the disaggregation scheme but does not nec-essarily represent the most likely M–R–ε event that contrib-utes to the hazard. In some extreme cases the ( �M, �R, and �ε)bin may not even correspond to a feasible event. Because thePMF representation is sensitive to the binning scheme, itmight be convenient to express the results in terms of pdf,which is obtained by dividing the PMF contribution of eachbin by the bin’s size (Bazzurro and Cornell, 1999). The pdfrepresentation, indeed, is independent of the bin’s amplitudebut has the disadvantage that the ordinate of each cell doesnot represent the real contribution to the hazard. In this study,the results are represented in terms of PMF with distance andmagnitude bins of even size. A linear distance binning was

preferred here to other binning strategies, such as logarithmicor pseudologarithmic, which tend to overemphasize thecontributions due to large R values (Cramer and Petersen,1996). The binning scheme applied is generic and appro-priate for most cases. However, we acknowledge thatparticular, nonstandard binning schemes may be prefera-ble to those adopted here for some specific engineeringapplications.

Disaggregation Results

The following sections present the results obtained fromthe disaggregation of the Italian ground-motion hazard fortwo MRPs of 475 and 2475 yr. The discussion of results

is organized as follows. First, for selected Italian cities, ex-ample 3D joint PMFs of M–R–ε are described and the meanand modal values of M, R, and ε tabulated and analyzed.Subsequently, we discuss the geographic distribution (i.e.,disaggregation maps) of �M, �R, �ε, andM�, R�, ε� as obtainedfrom a 3D disaggregation. Gridded values ofM� and R� willbe compared with those obtained by disaggregating the haz-ard in 2D M–R bins. This allows us to study the effect ofdifferent disaggregation procedures on results. Finally, theinfluence of alternative ground-motion predictive equationson results is carefully examined.

Disaggregation of Seismic Hazard for Selected Cities

This section presents example jointM–R–ε distributionsand their central statistics resulting from the disaggregationof the 5%-damped linear elastic Sa�T� values at periods of0.2 and 1.0 sec that correspond to MRPs of 475 and 2475 yrfor three Italian cities, L’Aquila, Rome, and Milan. Thesethree cities have been selected because they are representa-tive of different hazard levels in Italy. Bins of width 0.5 inmagnitude, 10 km in distance, and 0.2 in ε are used.


The 475 yr Sa�0:2 sec� hazard for L’Aquila (Fig. 2) iscontrolled by nearby-distance earthquakes (from 0 to 10 km)of low-to-moderate magnitude (from 4.5 to 6.5). For theseevents, ε is in the range of 0–2, meaning that the dominant

ground motions are within 2σ of the median. Larger andmore distant events dominate the Sa�1:0 sec� value forthe same MRP. In particular, for Sa�0:2 sec�, �M is 5.8, �Ris 9.3 km, and �ε is 1.13. The modal values of magnitude,M� 4:75, and distance, R� � 5 km, are lower than the cor-responding mean values, while ε�, being equal to 1.5, isgreater (note that the modal values are the central valuesof the M, R, and ε bins used in the calculations; hence,M� 4:75 implies that M� is comprised between 4.5 and5.0). The modal value ofM of the 2D joint M–R distributionis 0.5 units greater than that of the 3D PMF. For 1.0 sec re-sponse, �M 6:5, �R � 18:2 km, and �ε � 0:91 while the modaltriplet is M� 6:75, R� � 15 km, and ε� � 0:5. For this peri-od, the modal values ofM and R of the 3D PMF coincide with

Figure 1. (a) ZS9 seismogenetic zonation and (b) distributionof the national seismicity based on the CPTI04 catalog.

Table 1Seismogenic Zone Parameters

Zone Ftype* mmin

† Mmax† υ�mmin�‡ b§

901 undetermined 4.3 5.8 0.045 1.133902 undetermined 4.3 6.1 0.103 0.935903 undetermined 4.3 5.8 0.117 1.786904 strike-slip 4.3 5.5 0.050 0.939905 reverse 4.3 6.6 0.316 0.853906 reverse 4.3 6.6 0.135 1.092907 reverse 4.3 5.8 0.065 1.396908 strike-slip 4.3 5.5 0.140 1.408909 normal 4.3 5.5 0.055 0.972910 reverse 4.3 6.4 0.085 0.788911 strike-slip 4.3 5.5 0.050 1.242912 reverse 4.3 6.1 0.091 1.004913 undetermined 4.3 5.8 0.204 1.204914 undetermined 4.3 5.8 0.183 1.093915 normal 4.3 6.6 0.311 1.083916 normal 4.3 5.5 0.089 1.503917 reverse 4.3 6.1 0.121 0.794918 undetermined 4.3 6.4 0.217 0.840919 normal 4.3 6.4 0.242 0.875920 normal 4.3 5.5 0.317 1.676921 normal 4.3 5.8 0.298 1.409922 normal 4.3 5.2 0.090 1.436923 normal 4.3 7.3 0.645 0.802924 strike-slip 4.3 7.0 0.192 0.945925 strike-slip 4.3 7.0 0.071 0.508926 strike-slip 4.3 5.8 0.061 1.017927 normal 4.3 7.3 0.362 0.557928 normal 4.3 5.8 0.054 1.056929 normal 4.3 7.6 0.394 0.676930 undetermined 4.3 6.6 0.146 0.715931 strike-slip 4.3 7.0 0.045 0.490932 strike-slip 4.3 6.1 0.118 0.847933 reverse 4.3 6.1 0.172 1.160934 reverse 4.3 6.1 0.043 0.778935 strike-slip 4.3 7.6 0.090 0.609936 undetermined 3.7 5.2 0.448 1.219

*Ftype is the prevalent mechanism of faulting.†mmin and Mmax indicate the minimum and maximum

magnitudes, respectively. Magnitudes are given in terms ofMS.‡υ�mmin� is the annual rate of earthquake occurrence above a

minimum threshold magnitude mmin.§b is the negative slope of the Gutenberg–Richter relation

(Gutenberg and Richter, 1944).


those of the 2D PMF. Regarding the disaggregation of the2475 yr Sa�T� at 0.2 and 1.0 sec values, results show thatearthquakes of larger size occurring at slightly shorter dis-tances dominate. In other words, as the MRP increases, thecontrolling earthquakes become larger inM and occur closer

to the site investigated. In detail, events of magnitude from5.0 to 7.0, again occurring at distances between 0 and 10 km,control the 0.2 sec response while the larger contribution tothe 1.0 sec hazard comes from greater magnitude events from6.0 to 7.5, at distances from 0 to 20 km. Mean values of ε are

Figure 2. JointM–R–ε PMFs for L’Aquila obtained from the disaggregation of the Sa�0:2 sec� and Sa�1:0 sec� values corresponding toMRPs of 475 (top row) and 2475 yr (bottom row).


greater than those obtained for an MRP of 475 yr while themodal are either lower (for Sa�0:2 sec�) or greater (forSa�1:0 sec�). For both Sa�0:2 sec� and Sa�1:0 sec�, themodal event of the PMF ofM–R differs from that of the jointdistribution of M–R–ε.

For the same site, Figure 3 shows the variation of meanand modal values of M, R, and ε with spectral period (wehave taken into account additional periods for this exhibit).Again, the acceleration values disaggregated corresponds toMRPs of 475 (left-hand panels) and 2475 yr (right-hand pan-els). As a comparison, modal values of both the 3D and 2DPMFs are displayed. We denote the mode of a 2D distributionasM�

2D–R�2D while that of a 3D one is simply indicated by the

triplet M�–R�–ε�. For both MRPs considered, local earth-quakes at distances up to 20 km dominate the hazard at bothlower and higher periods. Unlike �R, R�, and R�

2D, which varyvery slightly with period, the mean and modal values of Mincrease more markedly as the spectral period increases. Foran MRP of 475 yr, �M ranges from 5.5 at 0.1 sec to 6.6 at2.0 sec while M� and M�

2D range from 4.75 to 6.75. Note

that the values of �M and M�2D are larger for PGA than for

Sa�0:1 sec� and Sa�0:15 sec�. M� is lower than or equalto M�

2D for a period of up to 0.3 sec, becomes greater thanM�

2D for a period up to 0.75 sec, and, for longer periods (1.0–2.0 sec), coincides with M�

2D. For an MRP of 2475 yr, boththe mean and modal magnitudes dominating the PGA hazardare greater than those controlling the spectral accelerationsup to 0.15 sec. Then, �M,M�, andM�

2D increase progressivelywith period. M� and M�

2D coincide at 0.0, 0.4, 0.75, and1.0 sec. Analyzing ε behavior with period does not revealany particular trend. That is, both �ε and ε� neither increasenor decrease regularly with increasing spectral period. As ex-pected, both mean and modal values of ε tend to increase asthe MRP increases. For an MRP of 475 yr, indeed, the domi-nant ground motions are within 0:5σ–1:5σ of the medianwhile; for an MRP of 2475 yr, they are within 1:1σ–1:9σ.

Figure 4 shows the disaggregation plots for Rome. Herethe 0.2 sec spectral acceleration hazard is entirely dominatedby a single seismic zone (zone 922). Indeed, nearby-distanceevents (up to 10 km) of low magnitude (from 4.0 to 5.0)

Figure 3. Variation of mean and modal values of M, R, and ε with spectral period for L’Aquila. Note that “STDV” in the label on the yaxis of the charts at the bottom of the figure stands for standard deviation.


contribute about 70% and 80% to the Sa�0:2 sec� haz-ard for MRPs of 475 and 2475 yr, respectively. Thus, meanand modal values ofM, R, and ε are close to each other (onlythe values of �ε and ε� resulting from the disaggregation of theSa�0:2 sec� value with 10% probability of exceedance in

50 yr show significant differences). For both MRPs consid-ered, ground motions with ε > 1:0 are necessary to exceedthe target acceleration values. Distributions for 1.0 secresponse are bimodal, clearly reflecting the contribution tothe hazard from both local (zone 922) and distant (zone

Figure 4. JointM–R–ε PMFs for Rome as obtained from the disaggregation of the Sa�0:2 sec� and Sa�1:0 sec� values corresponding toMRPs of 475 (top row) and 2475 yr (bottom row).


923) sources. In such cases or, more generally, if distribu-tions have more than one prominent peak (multimodal dis-tributions), single summary statistics, like the mean and themode, are insufficient to fully describe the seismic threat atthe site. In these cases, it is desirable to document the dif-ferent M–R–ε groups controlling the site hazard. For anMRP of 475 yr, the local event contributing the most to the1.0 sec spectral acceleration hazard corresponds to the modalscenario M� 4:75, R� � 5 km, and ε� � 1:5. The contribu-tion from regional earthquakes is mainly associated withmagnitudes from 6.5 to 7.5 at distances comprised between70 and 120 km. For both close and distant events the ex-pected ground motions are within 2σ of the median. Note,finally, that the mean, because of its nature, correspondsto a triplet having a very low contribution to the hazard(<1:0%) and, therefore, represents an unlikely scenario.Analogous observations can be made analyzing the 3D plotobtained by disaggregating the Sa�1:0 sec� value for anMRP of 2475 yr. It is worth noting, however, that, forlow-magnitude events at distances up to 10 km, ε varies from

1 to 3. Ground motions from larger magnitude earthquakesoccurring at longer distances (from 60 to 130 km), instead,are generally within 2σ of the median. Moreover, the modalvalues of magnitude and distance of the 3D jointM–R–ε dis-tribution strongly differ from those of the 2D PMF. The for-mer, indeed, corresponds to the pair M� 7:25, R� � 95 km,while the latter corresponds to M� 4:75, R� � 5 km.

Figure 5 shows the variation of the mean and modalvalues of M, R, and ε with spectral period for Rome. Foran MRP of 475 yr, �M tends to increase progressively withperiod, while M� and M�

2D assume the same constant valueof 4.75 (except for Sa�0:1 sec�) up to 1.0 sec. Then, M� in-creases abruptly while M�

2D does not vary. An analogous be-havior can be observed analyzing the variation of mean andmodal R values. Thus, the large difference between mean andmodal values of both M and R for periods greater than0.5 sec indicates that more than one scenario contributessignificantly to the site hazard for those spectral periods.Similar observations can be made for an MRP of 2475 yr.Once again, examining the behavior of ε indicates that both

Figure 5. Variation of mean and modal values of M, R, and ε with spectral period for Rome.


the mean and modal values increase as the MRP increases.As an example, in the case of Sa�0:2 sec�, �ε increases from1.26 to 1.73 when the MRP changes from 475 to 2475 yr.Similarly, for the same spectral period, ε� jumps from 0.7

to 1.5. Note that modal values of ε are always lower thanthe mean for both MRPs considered.

Figure 6 shows the 3D PMF of M–R–ε for Milan. In thefirst row, for response accelerations having 10% probability

Figure 6. JointM–R–ε PMFs for Milan as obtained from the disaggregation of the Sa�0:2 sec� and Sa�1:0 sec� values corresponding toMRPs of 475 (top row) and 2475 yr (bottom row).


of exceedance in 50 yr, the left-hand figure (0.2 sec response)shows that the dominating contributions come from low-magnitude events (from 4.0 to 5.5) at distances ranging be-tween 30 and 60 km. For these M–R pairs, ε is generallylower than or equal to 2.0. The modal values of M and Rof the 2D and 3D PMF coincide. The figure to the right(Sa�1:0 sec�) shows that the hazard is controlled by multipleevents that have similar contributions, generally lower than4%. Again, the expected ground motions are approximatelywithin 2σ of the median. In the second row, for an MRP of2475 yr, the 0.2 sec response acceleration is again controlledby low-magnitude events concentrated at about 30–60 kmfrom Milan while both local and distant earthquakes contrib-ute to the 1.0 sec response. In this latter case, two peakscan be identified. They corresponds to the cells M 5:25,R � 45 km (zone 907) and M 6:25, R � 115 km (zone906). The former corresponds to the modal M–R pair ofthe 2D PMF that, again, coincides with that of the 3D distri-bution. For both the 0.2 and 1.0 sec response, ε is in the rangeof 1–3.

Figure 7 shows thevariationof themean andmodal valuesofM, R, and ε with period for the city of Milan. For both theMRPs considered, �M and �R increase progressively with periodwhile the 2D and 3D modal M and R values show a stepwisetrend. As an example, for the 2475 yr case, M� and M�

2D areequal to 4.75 up to 0.2 sec, then they increase to 5.25 at 0.3 sec,remain constant up to 1.0 sec, and, finally, jump to 6.25 at1.5 sec. For the same MRP, R� and R�

2D assume a nearly con-stant value of 35–45 km up to 1.0 sec, then they increase sig-nificantly and remain constant up to 2.0 sec. Once again, thisindicates that distant sources tend to control long-period spec-tral accelerations while the local seismicity dominates atshorter periods. As expected, for a given spectral period,the mean andmodal values ofR tend to decreasewith increas-ing MRP. Conversely, �ε and ε� tend to increase.

As a summary of this disaggregation exercise, Tables 2and 3 list values of �M, �R, �ε and M�, R�, ε� obtained fromthe disaggregation of the Sa�0:2 sec� and Sa�1:0 sec� valuescorresponding to MRPs of 475 (Table 2) and 2475 yr (Table 3)for the main Italian cities (Fig. 8). The relative influence of

Figure 7. Variation of mean and modal values of M, R, and ε with spectral period for Milan.


Table

2MeanandModal

Valuesof

M,R,andεfortheMainItalianCities

for0.2and1.0secSp

ectral

AccelerationValuesCorresponding

toMRPs

of475yr

City

Sa�0:2

sec�

Sa�1:0

sec�

� MT�0

:2sec

� RT�0:2

sec

� ε T�0

:2sec

M� T�0:2

sec

R� T�0

:2sec

ε� T�0:2

sec

Zon

e(T

�0:2

sec)

� MT�1

:0sec

� RT�1:0

sec

� ε T�1:0

sec

M� T�1:0

sec

R� T�1

:0sec

ε� T�1:0

sec

Zon

e(T

�1:0

sec)

Ancona

0.484

0.117

5.2

9.3

0.99

4.75

51.1

917

5.7

28.6

1.23

5.75

150.9

917

Aosta

0.248

0.051

4.9

16.4

1.01

4.75

5�0

:1909

5.3

33.7

1.35

5.25

150.9

909

Bari

0.196

0.103

6.3

70.7

1.45

6.25

350.7

925

6.8

98.8

1.50

7.25

125

1.3

925

Bologna

0.416

0.102

5.0

9.6

1.11

4.75

50.5

913

5.4

18.6

1.40

4.75

51.3

913

Cam

poBasso

0.609

0.214

5.9

12.7

1.25

4.75

51.3

924

6.7

27.6

1.13

7.25

350.9

927

Catanzaro

0.637

0.231

6.0

10.4

0.98

5.25

50.9

929

6.7

22.8

0.83

6.25

151.3

929

Florence

0.346

0.091

5.1

14.5

1.40

4.75

50.5

916

5.7

34.1

1.54

6.25

250.7

915

Genoa

0.185

0.040

5.0

33.2

1.34

4.75

150.9

911

5.7

72.5

1.46

4.75

151.3

910

L’Aquila

0.648

0.212

5.8

9.3

1.13

4.75

51.5

923

6.5

18.2

0.91

6.75

150.5

923

Milan

0.139

0.026

5.1

65.0

1.88

4.75

451.9

907

5.5

109.0

1.58

5.75

125

1.7

907

Naples

0.412

0.141

5.2

14.1

1.25

4.75

51.1

928

6.6

61.6

1.51

7.25

651.1

927

Palerm

o0.454

0.114

5.0

8.5

1.02

4.75

50.9

933

5.5

23.4

1.23

5.25

50.9

933

Perugia

0.471

0.125

5.2

10.3

1.40

4.75

51.1

919

6.0

33.9

1.47

6.25

150.7

919

Potenza

0.501

0.199

5.9

15.3

1.14

4.75

50.9

927

6.7

30.6

1.08

7.25

250.5

927

Rom

e0.399

0.094

4.7

7.9

1.26

4.75

50.7

922

6.2

73.5

1.54

4.75

51.5

923

Turin

0.158

0.019

5.0

48.8

1.93

4.75

351.9

908

5.3

86.4

1.35

4.75

351.5

908

Trento

0.211

0.059

5.5

47.5

1.64

4.75

352.1

906

6.0

68.9

1.40

6.25

751.1

906

Trieste

0.293

0.084

5.1

23.2

1.51

4.75

151.5

904

5.9

53.9

1.65

5.25

151.5

905

Venice

0.193

0.070

5.7

63.1

1.70

5.75

451.3

905

6.1

73.2

1.50

6.25

450.7

905

Modalvalues

arereported

indicatin

gthecenterof

theM,R

,and

εbins

used

inthecalculations

(e.g.,M

�4:75indicatesthatM

�iscomprised

between4.5and5.0).T

heidentificationnumberof

thesource

zone

contributin

gthemostto

theSa�0:2

sec�

andSa�1:0

sec�

hazard

isalso

indicatedforeach

city.


Table

3MeanandModal

Valuesof

M,R,andεfortheMainItalianCities

for0.2and1.0secSp

ectral

AccelerationValuesCorresponding

toMRPs

of2475

yr

City

Sa�0:2

sec�

Sa�1:0

sec�

� MT�0

:2sec

� RT�0:2

sec

� ε T�0

:2sec

M� T�0:2

sec

R� T�0

:2sec

ε� T�0:2

sec

Zon

e(T

�0:2

sec)

� MT�1

:0sec

� RT�1:0

sec

� ε T�1:0

sec

M� T�1:0

sec

R� T�1

:0sec

ε� T�1:0

sec

Zon

e(T

�1:0

sec)

Ancona

0.88

0.232

5.3

6.2

1.44

5.25

51.1

917

5.7

14.4

1.52

5.75

50.9

917

Aosta

0.445

0.103

4.9

7.5

1.25

4.75

50.9

909

5.3

19.4

1.69

5.25

50.9

909

Bari

0.339

0.200

6.5

50.7

1.73

6.75

351.1

925

6.9

76.8

1.98

6.75

351.3

925

Bologna

0.741

0.194

5.0

6.0

1.53

4.75

51.5

913

5.5

10.5

1.66

5.25

51.5

913

Cam

poBasso

1.066

0.396

6.1

9.1

1.59

5.25

51.7

924

6.8

20.8

1.47

6.75

151.3

927

Catanzato

1.274

0.533

6.4

6.7

1.28

6.25

50.9

929

7.0

14.0

1.11

7.25

150.9

929

Florence

0.584

0.170

5.1

9.2

1.72

4.75

51.3

916

6.0

24.2

1.79

6.25

251.5

915

Genoa

0.325

0.089

4.9

17.8

1.61

4.75

151.7

911

5.8

59.7

1.96

5.25

151.5

911

L’Aquila

1.218

0.456

6.2

6.7

1.45

5.75

51.3

923

6.7

12.6

1.24

6.75

151.5

923

Milan

0.218

0.056

5.2

51.8

2.19

4.75

352.3

907

5.9

103.0

2.02

5.25

452.1

906

Naples

0.739

0.257

5.1

6.6

1.68

4.75

51.7

928

6.8

53.5

1.97

7.25

551.7

927

Palerm

o0.857

0.234

5.1

5.7

1.55

4.75

51.5

933

5.6

14.2

1.61

5.75

50.9

933

Perugia

0.813

0.235

5.3

7.1

1.81

4.75

51.7

919

6.1

25.0

1.79

6.25

151.5

919

Potenza

0.920

0.389

6.1

11.3

1.58

6.75

151.3

927

6.9

21.7

1.42

7.25

251.3

927

Rom

e0.671

0.168

4.7

4.3

1.73

4.75

51.5

922

6.5

73.1

1.99

7.25

951.7

923

Turin

0.242

0.046

5.1

39.2

2.27

4.75

252.3

908

5.7

88.1

1.92

6.25

105

1.1

910

Trento

0.357

0.115

5.8

39.1

1.93

5.25

251.9

906

6.2

57.4

1.76

6.25

651.7

906

Trieste

0.503

0.160

5.1

14.7

1.90

5.25

51.3

904

6.0

46.8

2.10

6.25

451.7

905

Venice

0.336

0.141

6.1

55.3

2.06

6.25

451.5

905

6.3

62.9

2.00

6.25

451.5

905

Modalvalues

arereported

indicatin

gthecenter

oftheM,R

,and

εbins

used

inthecalculations

(e.g.,M

�4:75indicatesthatM

�iscomprised

between4.5and5.0).T

heidentificationnumberof

thesource

zone

contributin

gthemostto

theSa�0:2

sec�

andSa�1:0

sec�

hazard

isalso

indicatedforeach

city.


local zones and of regional sources farther from the site mightbe deduced from the data of Tables 2 and 3. For example, atcities such as Ancona, Bologna, Catanzaro, Palermo, Perugia,and Rome, the similarity of �M and M�, and that between �RandR� (Table 2), indicates that a single source zone surround-ing these cities dominates the Sa�0:2 sec� hazard at the 475 yrMRP level. The events controlling the Sa�0:2 sec� hazardat these locations are generally characterized by low-to-moderatemagnitudes (from 4.5 to 6.0) at distances up to about10 km. For these cities, the dominant groundmotions are gen-erally within 1:4σ of the median. On the other hand, for theremaining sites, the differences between the mean and modalvalues ofM and R indicate that more than one event contrib-utes significantly to the hazard. In particular, as the discrep-

ancy between �R and R� increases, the hazard tends to becontrolled by both the local and regional seismicity, suggest-ing a bimodal distribution. Thus, the noticeable difference be-tween �R and R� at Bari, Genoa, Milan, Turin, Trento, andVenice indicates that both close and distant earthquakes affectthe Sa�0:2 sec� hazard and should be taken into account toproperly derive time histories for engineering analysis and de-signat agivenMRP.Furthermore, for these cities, thedominantgroundmotions are generally within 2σ of themedian. For thesameMRPof 475 yr, variationswith spectral period of both themean and modal values of M, R, and ε reveal that differentscenario events control the hazard at short (T � 0:2 sec) andmoderate (T � 1:0 sec) periods. Thedifference is evident, forexample, at Campobasso, Florence, L’Aquila, Milan, Naples,

Figure 8. Map of Italy with the location of the cities considered in Tables 2 and 3.


Perugia, Potenza, and Trento where closer, low-to-moderatemagnitudes dominate the 0.2 sec hazard but larger magnitudeevents from distant sources control the Sa�1:0 sec� values.Similar observations can be made from Table 3, which showsthe mean and modal values of M, R, and ε controlling theSa�T� hazard at 0.2 and 1.0 sec for the 2475 yr MRP. Asobserved previously, the hazard at long MRPs tends to becontrolled by closer and larger earthquakes.

Disaggregation Maps

Figures 9, 10, and 11 present maps showing the geo-graphic variation of both the mean and modal values ofM, R, and ε extracted from the 3D joint PMFs conditionedon exceeding the 475 yr values of PGA and the 5%-dampedSa�0:2 sec�, Sa�1:0 sec�, and Sa�2:0 sec�. The maps arecontours based on values computed for each node of a gridwith spacing of 0.05° in latitude and longitude. Specifically,the left- and right-hand columns of these three figures displaythe geographic distribution of the mean and modal values ofM, R, and ε, respectively, resulting from the disaggregationof the four ground-motion parameters mentioned previously.These maps should be inspected in conjunction with prob-abilistic seismic hazard maps (for more information, seethe Data and Resources section) and with the seismicity dis-tribution depicted in Figure 1b.

Maps of �M andM� (Fig. 9) confirm the results presentedin the previous section, which show that the values of bothparameters tend to increase as the spectral period increases.Given the similar behavior for Sa�0:2 sec� and PGA (i.e.,PGA behaves as a high-frequency ground motion), as wellas for the 1.0 and 2.0 sec response, in the following discussionwe will focus on maps for Sa�0:2 sec� and Sa�1:0 sec� only.Except for two areas in the eastern sector in Northern Italy,mapped values of �M for the 0.2 sec response vary between4.5 and 5.5, while M� assumes a nearly constant value of4.5–5.0. The largest values of both theseM statistics are con-centrated in two low-seismicity areas located in the northeastwhere the hazard is controlled by source zones 905 and 906(see Fig. 1), two tectonic provinces where strong earthquakeswith magnitudes larger than 6.0 occurred in the past (thelargest event is thewell-knownFriuli earthquake that occurredon 6May 1976 with magnitudeMS 6:4). Note that the largestdifferences in the distributions of the mean and modal valuesare generally concentrated in areas that in the past were af-fected only by sporadic low-magnitude earthquakes (e.g., eastof zone 908) and within source zones 905 and 906 where thehazard is dominated by local seismicity. For the same spectralperiod, an analogous spatial distribution can be observed incentral Italy where, again, �M andM� vary from 4.5 to 5.5 andfrom 4.5 to 5.0, respectively, almost everywhere. In southernItaly, the geographic distribution of �M results are substantiallysmoother than that ofM� because averaging takes into accountthe contribution of both the local and regional seismicity.Generally, �M ranges from5.5 to 7.0whileM� is strongly local,assuming values from 5.0 to 6.5 in areas (e.g., zones 927 and

929) that in the past were struck by strong earthquakes (thelargest one is the 1908 Messina earthquake of magnitudeMS 7:2) and values from 6.5 to 7.5 in some onshore and off-shore areas characterized by low-seismic activity. For a 1.0 secresponse, �M varies from 4.5 to 6.0 in northwestern Italywhere, except for the Ligurian Sea and adjacent areas, itcan be up to 0.5 units greater than M�. The distribution ofthe mean and modal values, instead, is similar in the northeastwhere the dominant magnitudes are up to 6.5. �M and M� as-sume larger values in central Italy where they are up to 7.0 and7.5, respectively. �M is between 6.5 and 7.0 almost everywherein southern Italy and reaches its maximum (7:0 < �M <7:5) inthe southern Tyrrhenian Sea where the hazard is controlled bydistant sources (e.g., zone 929). Modal values are slightlygreater with their maxima in areas (e.g., near Bari, south ofPotenza, central Sicily southeast of Palermo, TyrrhenianSea, and Ionian Sea) that historically have had only smallearthquakes. Both �M andM� are lowest in northern Sicily nearPalermowhere both local sources (zone 933) and events at dis-tances up to 60 km contribute significantly to the Sa�1:0 sec�hazard.

Again, maps of the mean and modal distances (Fig. 10)show that �R and R� increase with increasing spectral period(this behavior is more evident for �R). Analogous to what isobserved in Figure 9, maps for PGA and a 0.2 sec responseand for Sa�1:0 sec� and Sa�2:0 sec� are similar to each other.Except for verymildly seismic areas, theSa�0:2 sec�hazard isgenerally controlled by local seismogenetic zones. Close-distance sources (e.g., R ≤ 20 km) dominate the hazard bothinhighly seismic areas (e.g., zones 905, 923, 927, and929) andat sites where seismic activity is prevalently characterized bysmall-to-moderate but quite frequent events (e.g., zones 912,917, 918, and 921). Sources at larger distances dominate theSa�0:2 sec� hazard in the northwest (east of Turin), northeast(north of Trento), near Bari in southern Italy, in Sicily south-east of Palermo, and offshore. For a 1.0 sec response, the geo-graphic distributions of �R differ significantly from that of R�

because the mean, contrary to the mode, is strictly affected bycontributions from the regional seismicity. �R is generally be-tween 10 and 60 km and is larger, as much as 200 km, in areaswhere earthquakes are rare (e.g., nearBari). On the other hand,except for low-seismicity areas, R� is smaller than or equal to10 km almost everywhere in the north and exhibits slightlygreater values in central and southern Italy.

Figure 11 shows the geographical variation of the meanand modal values of ε. Contrary to the maps of the mean andmodal M and R, which show very similar distributions forPGA and Sa�0:2 sec�, those of �ε and ε� present some differ-ences and, therefore, are both discussed. For PGA, �ε is be-tween 0.5 and 1.0 both at sites with higher PGA hazard(e.g., zones 905, 923, 927, 929, and 935 where the PGAvalues for an MRP of 475 yr are greater than 0.225g) andin areas affected by quite frequent, small magnitude events(e.g., zones 912, 917, 921, and 933 where the PGA valuescorresponding to an MRP of 475 yr ranges from 0.125 to0.20g). Mean values of ε rise up to 2.0 (and even to 2.5


Figure 9. Maps of mean (left-hand column) and modal (right-hand column) magnitude, M, values obtained from the 3D disaggregationof the 475 yr values of PGA, Sa�0:2 sec�, Sa�1:0 sec�, and Sa�2:0 sec�.


Figure 10. Maps of mean (left-hand column) and modal (right-hand column) distance, R, values obtained from the 3D disaggregation ofthe 475 yr values of PGA, Sa�0:2 sec�, Sa�1:0 sec�, and Sa�2:0 sec�.


Figure 11. Maps of �ε (left-hand column) and ε� (right-hand column) obtained from the 3D disaggregation of the 475 yr values of PGA,Sa�0:2 sec�, Sa�1:0 sec�, and Sa�2:0 sec�. Note that “STDV” in the legend stands for standard deviation.


at some sites in the northwest) in areas that are almost aseis-mic (e.g., northwestern Italy near Turin, northeastern Italynear Trento, near Bari, Tyrrhenian, and Ionian Sea) wherethe PGA is lower than 0.05g. The distribution of ε�, althoughit appears more grained, does not differ substantially fromthat of �ε. The main differences concentrate in the southernTyrrhenian Sea and the Ionian Sea where ε� is about 0.5 unitslower than �ε. For a 0.2 sec response, the mean and modalvalues of ε are slightly greater (no more than 0.5 units) thanfor PGA. Again, the largest values (from 1.5 to 2.5) concen-trate in areas characterized by very low-seismic activitywhile in higher seismic hazard regions, �ε and ε� range be-tween 0.5 and 1.5. The mean and modal values of ε decreasefor Sa�1:0 sec� and increase again for Sa�2:0 sec�.2 Forthese spectral periods, maps of the mean and modal ε differsignificantly from each other. Except for regions character-ized by a high-seismic hazard level (e.g., Calabrian arc andsouthern Sicily near the Etna volcano), for a 1.0 sec response,�ε is generally between 1.0 and 1.5 almost everywhere inItaly. The geographical distribution of ε�, instead, varieswidely from site to site. As was the case for �ε, ε� is alsominimum in high-seismic hazard areas where it is generallylower than 1.0. For a 2.0 sec response, the geographical dis-tribution of ε� values is very similar to that for Sa�1:0 sec�.The map of �ε, instead, presents some differences mostly innorthern and central Italy where mean values of ε are slightlygreater than those for a 1.0 sec response.

Influence of 2D and 3D Disaggregation Schemeon Results

As mentioned previously, for some sites the bivariate(M�

2D, R�2D) values do not coincide with the M and R modal

values extracted from the 3D joint PMF. To quantify the effectof the 2D and 3D disaggregation procedures at a nationalscale, we have calculated and mapped the ratio of the 2D tothe 3D modal values of M and R (Fig. 12). The left- andright-hand columns of the figure correspond to maps result-ing from the disaggregation of the Sa�0:2 sec� andSa�1:0 sec� values for an MRP of 475 yr while rows showthe geographical distribution of M�

2D=M� and R�

2D=R�. The

maps are very grained, indicating that both magnitude anddistance ratios vary significantly from one site to another.Therefore, it is difficult to relate the geographical variationof M�

2D=M� and R�

2D=R� to the seismicity distribution

(Fig. 1b) and the hazard maps for each spectral period. Ingeneral, the modal M and R values of the 2D PMF coincidewith those of the corresponding 3D distribution at most ofthe gridded points. Specifically, for a 0.2 sec response, thebivariate (M�

2D, R�2D) differs from the M and R modal values

of the 3D PMF at approximately 25% of the points. For this

period, the largest differences betweenM� and M�2D concen-

trate in southern Italy near l’Aquila, where M�2D is up to 1

unit greater than M�, in the southern Tyrrhenian Sea, whereM�

2D is about 0.5–1 units lower thanM�, along the Calabrianarc (i.e., zones 927 and 929), whereM�

2D can be either lower(zone 927) or higher (zone 929) than M�, and near the Etnavolcano (zone 935) in Sicily. Differences between R� andR�2D do not concentrate in specific areas. Note that about

80% of sites where R�2D=R

� differs from unity show valuesof R� greater than R�

2D. For a 1.0 sec response, modal M–Rpairs of the 2D and 3D PMFs differ in about 32% of the cases.Again, the main differences in modal magnitudes are concen-trated in central and southern Italy where M�

2D is generally(0.5–1.0 magnitude units) lower than or equal to M�. R� isgreater than R�

2D at 86% of the sites, most of which arelocated in areas characterized by a medium-to-high seismichazard level (0:125g < Sa�1:0 sec� < 0:25g). At most ofthese points, R�

2D is about half the value of R�.

Effect of Alternative Attenuation Relationships

As specified in the section titled A Note on Models andInput Parameters, the ground-motion predictive equation ofAmbraseys et al. (1996), which contributes the most to thereference median hazard, was employed to derive referencedisaggregation maps. However, other attenuation relation-ships based on national (Sabetta and Pugliese, 1996) and re-gional (De Natale et al., 1988; Patanè et al., 1994, 1997;Malagnini et al., 2000, 2002; Morasca et al., 2006) ground-motion data were used to assess the Italian seismic hazard. Inthis study, we evaluate the influence of an alternative attenu-ation equation on disaggregation results. Specifically, wecompare the mean and modal values of M, R, and ε calcu-lated by applying the Sabetta and Pugliese (1996) equationwith the reference values mapped in Figures 9, 10, and 11 forSa�0:2 sec� and Sa�1:0 sec�. More specifically, the compar-ison is based on the ratio of the mean and modal values ofM,R, and ε obtained from Sabetta and Pugliese (1996) (denotedas SP96) to those from Ambraseys et al. (1996) (see Fig. 13).The mean values of M and R obtained by using the two pre-dictive equations are similar at most of the gridded pointswhile the values of �εSP96 and �ε differ substantially in someregions. In the Sa�1:0 sec� case, for example, �MSP96 and �Massume nearly the same value almost everywhere in centraland southern Italy and never differ by more than 0.4 magni-tude units. The largest differences are concentrated offshoreand in low-seismicity areas in northern Italy. At these sites,using the equation by Sabetta and Pugliese (1996) providesmagnitude values that are slightly greater than the referenceones. For the same spectral period, �RSP96 and �R differ bymore than 10 km in only 1.2% of cases. Except for veryfew sites south of Palermo and off the Sicilian coast, theSabetta and Pugliese (1996) equation provides mean distancevalues that are lower than those calculated with the Ambra-seys et al. (1996) relationship. As mentioned previously,unlike the mean values of M and R, �εSP96 and �ε differ from

2Note that, for these two spectral periods, the maps show values of �ε andε� lower than �2:5. These values, which should be disregarded, correspondto sites where the spectral acceleration values provided by the seismic hazardmaps were erroneously set to zero.


one another at most of the gridded points. The �εSP96=�ε ratio isalways lower than unity and reaches the lowest values inareas characterized by high-seismic hazard level, such asthe Calabrian arc (source zones 927 and 929) and the areaof the Etna volcano in southern Sicily (zone 935), where dif-ferences between �εSP96 and �ε are up to about 0.4.

Maps for modal values are not presented because they arehighly grained and, therefore, do not allow any meaningfulgeneralizations about any possible relationwith the seismicitydistribution. It is worth noting, however, that also modalvalues of ε strongly depend on the attenuation equation usedwhile those of M and R exhibit only minor variations thatare generally smaller than the bin amplitude considered inthe calculations.

Summary and Conclusions

The article has presented the results of the disaggrega-tion of the Italian ground-motion hazard maps for rock con-ditions developed by Gruppo di Lavoro MPS (2004), Melettiand Montaldo (2007), and Montaldo and Meletti (2007).These maps have been officially adopted as reference mapsby the Italian government (Ministero delle Infrastrutture e deiTrasporti, 2008). We identified the contributions of earth-quake scenarios to the mean rates of exceeding PGA and 0.2,1.0, and 2.0 sec spectral acceleration (Sa�T�) values asso-

ciated with MRPs of 475 and 2475 yr at a grid of locationscovering the entire Italian territory. The maps showingthe geographical distribution of the mean ( �M, �R, and �ε) andmodal (M�, R�, and ε�) values of the 3D joint PMFs ofM–R–ε have been presented and compared with thoseobtained from a 2D disaggregation. It is worth noting, how-ever, that these maps show the mean and modal values ofM–R–ε only. The complete joint M–R–ε distributions insome cases can have multiple peaks, some of which contrib-ute about the same amount as the mode to the hazard. There-fore, it is suggested that joint 3D PMFs be evaluated forsite-specific analyses because they are more informative thantheir central statistics.

As observed by other researchers (e.g., Harmsen et al.,1999; Peláez Montilla et al., 2002), disaggregation resultsdepend strictly on the seismicity distribution—that is, on theproximity to sources where the seismicity is mainly concen-trated. Distant, larger magnitude events dominate the hazardin areas characterized by a low-seismic activity. Conversely,nearby seismicity is often the major contributor to the hazardat sites located in high-seismicity regions or in zones wherethe seismic activity is characterized by weak-to-moderate butquite frequent events. At these sites, joint M–R–ε distribu-tions tend to be unimodal and values of �ε and ε� are generallysmaller than those observed in low-seismicity areas. More-over, the larger the MRP (or, conversely, the smaller the

Figure 12. Maps showing the ratio of the 2D to 3D modal values of magnitude (top panels) and distance (bottom panels).


MRE), the greater the contribution from closer, higher mag-nitude events. It was also observed that as the MRP increases,both the mean and modal values of ε tend to slightly increase.An analysis of the trend of the disaggregation results withspectral period (T) shows that the mean rate of exceedinglong-period spectral accelerations is generally controlledby earthquakes that are larger in size and farther from thesite than those dominating the PGA and short-period spectralacceleration hazard.

As discussed in many articles (e.g., Bommer et al.,2005; Sabetta et al., 2005; Scherbaum et al., 2005), ground-motion predictive equations have a large impact on finalhazard estimates. Hence, in this study we have also analyzedthe sensitivity of disaggregation results to the choice of the

attenuation relationship. Although limited in scope, our re-sults revealed that applying different attenuation relation-ships induces changes in the disaggregation results that, atleast in this case, are not very significant (perhaps withthe exception of the values of ε). We found that differencesin the mean and modal values ofM and R are generally smal-ler than the bin amplitude considered in the calculations(Δm � 0:5,Δr � 10:0 km). Larger differences, often twiceas large as the bin amplitude (Δε � 0:2), were observed inthe mean and modal values of ε that, therefore, dependstrongly on the attenuation equation used.

To summarize, the M–R–ε disaggregation maps pre-sented here can be helpful to both private and public stake-holders for many applications. For example, they can be used

Figure 13. Sensitivity maps showing the ratio of mean M, R, and ε values resulting from the disaggregation of the 475 yr Sa�0:2 sec�and Sa�1:0 sec� values obtained using the Sabetta and Pugliese (1996) (indicated by SP96) and the Ambraseys et al. (1996) ground-motionpredictive equations.


by structural engineers to select appropriate ground-motionrecords for testing the adequacy of the design of new struc-tures or the response of existing ones. Geotechnical engi-neers can also select ground-motion records consistent withthe M and R values shown here for site amplification, lique-faction, and slope stability studies. Local governments canuse such maps, for instance, to select scenarios for assessingtheir preparedness to conduct postevent emergency re-sponses (e.g., the Shake Out exercise conducted in SouthernCalifornia on November 2008, see the Data and Resourcessection for more information).

To conclude, it is worth mentioning again that the seis-mic hazard maps that we used for our disaggregation exer-cise do not account for the contribution of either faults orsubduction zones. The recently released version of the Data-base of Individual Seismogenic Sources (DISS) (Basili et al.,2008), which collects data (e.g., fault length, fault width,slip rate, and maximum magnitude) about known activefaults in Italy, was not adopted in the development of thehazard maps considered here. This is because of the largeuncertainty affecting such data (e.g., for most faults in DISS,the slip rates vary from 0.1 to 1:0 mm=yr) and the missinginformation about which historical events were caused bywhich fault (DISS indicates only the largest historical eventfor each fault). Studying the effects of faults on the dominantearthquake scenarios is beyond the scope of this article. In-terested readers are referred to the work of Barani and Spal-larossa (2008) that incorporates faults and area sources intoan updated seismic source model for PSHA in Italy. Thatpreliminary study revealed that at sites near seismogenicfaults (up to a distance of about 30 km) the contributionfrom area sources is low and the hazard is almost exclu-sively controlled by fault sources. Thus, at these sites, incor-porating faults into the earthquake source model provides(mean and modal) values of M and R that are, respectively,higher and lower than those presented here. As the source-to-site distance increases, the fault contributions tend to de-crease rapidly and the area sources dominate the hazard.These are only preliminary considerations and further re-search is needed before fault data can be confidently usedin future PSHA studies for Italy. Research efforts shouldfocus on analyzing the sensitivity of the hazard to differentsets of fault characteristic parameter values (e.g., faultlength, fault width, slip rate, and maximum magnitude) andalternative magnitude distributions (e.g., exponential andcharacteristic).

Data and Resources

The CPTI04 catalog can be downloaded at the followingWeb address: http://emidius.mi.ingv.it/CPTI04/ (last ac-cessed June 2009). A file providing the geographical coor-dinates of the ZS9 seismogenetic zonation can bedownloaded at the following Web address: http://zonesismiche.mi.ingv.it/elaborazioni/ (last accessed June2009). For information on the DPC–INGV S1 project, see

the Web site http://esse1.mi.ingv.it (last accessed June2009). Results of the disaggregation of the PGA harzardfor nine MRPs can be consulted on the interactive Web sitehttp://esse1-gis.mi.ingv.it/ (last accessed June 2009). Infor-mation on the Shake Out exercise is available at http://www.shakeout.org (last accessed June 2009).

Acknowledgments

We thank an anonymous reviewer and the associate editor, M. C.Chapman, for their thorough review and helpful comments. We wish to ac-knowledge the use of the Generic Mapping Tools software package by Wes-sel and Smith (1991) to produce most of the figures in this article. This studywas supported and funded by the DPC-INGV S1 Project (http://esse1.mi.ingv.it).

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Dipartimento per lo Studio del Territorio e delle sue RisorseUniversity of GenoaViale Benedetto XV5-16132 Genova, [email protected]@dipteris.unige.it

(S.B., D.S.)

AIR Worldwide CompanySan Francisco, Californiapbazzurro@air‑worldwide.com

(P.B.)

Manuscript received 1 December 2008







Disaggregation of Probabilistic Ground-Motion Hazard in Italy

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