J Seismol (2012) 16:451–473DOI 10.1007/s10950-012-9281-z

ORIGINAL ARTICLE

Toward a ground-motion logic tree for probabilisticseismic hazard assessment in Europe

Elise Delavaud · Fabrice Cotton · Sinan Akkar · Frank Scherbaum ·Laurentiu Danciu · Céline Beauval · Stéphane Drouet · John Douglas ·Roberto Basili · M. Abdullah Sandikkaya · Margaret Segou ·Ezio Faccioli · Nikos Theodoulidis

Received: 4 August 2011 / Accepted: 24 January 2012 / Published online: 22 February 2012© Springer Science+Business Media B.V. 2012

Abstract The Seismic Hazard Harmonization inEurope (SHARE) project, which began in June2009, aims at establishing new standards for prob-abilistic seismic hazard assessment in the Euro-Mediterranean region. In this context, a logic treefor ground-motion prediction in Europe has beenconstructed. Ground-motion prediction equations(GMPEs) and weights have been determined sothat the logic tree captures epistemic uncertaintyin ground-motion prediction for six different tec-tonic regimes in Europe. Here we present thestrategy that we adopted to build such a logictree. This strategy has the particularity of com-bining two complementary and independent ap-proaches: expert judgment and data testing. A set

E. Delavaud (B) · F. Cotton · C. Beauval · S. DrouetISTerre, Université Joseph Fourier, CNRS, BP 53,38041 Grenoble, Francee-mail: elise.delavaud@sed.ethz.ch

E. Delavaud · L. DanciuSwiss Seismological Service, Institute of Geophysics,ETH Zurich, Sonneggstrasse 5, NO, 8092 Zurich,Switzerland

S. Akkar · M. A. Sandikkaya · M. SegouEarthquake Engineering Research Center, Departmentof Civil Engineering, METU, 06531 Ankara, Turkey

F. ScherbaumInstitute of Earth and Environmental Sciences,University of Potsdam, Karl-Liebknecht-Strasse 24-25,14476 Golm, Germany

of six experts was asked to weight pre-selectedGMPEs while the ability of these GMPEs topredict available data was evaluated with themethod of Scherbaum et al. (Bull Seismol Soc Am99:3234–3247, 2009). Results of both approacheswere taken into account to commonly select thesmallest set of GMPEs to capture the uncertaintyin ground-motion prediction in Europe. For sta-ble continental regions, two models, both fromeastern North America, have been selected forshields, and three GMPEs from active shallowcrustal regions have been added for continentalcrust. For subduction zones, four models, all non-European, have been chosen. Finally, for activeshallow crustal regions, we selected four models,

J. DouglasRIS/RSI, BRGM, 3 avenue C. Guillemin, BP 36009,45060 Orléans Cedex 2, France

R. BasiliIstituto Nazionale di Geofisica e Vulcanologia,Via di Vigna Murata 605, 00143 Rome,Italy

E. FaccioliPolitecnico di Milano, Piazza L. da Vinci, 32, 20133Milan, Italy

N. TheodoulidisITSAK, P.O. Box 53, Finikas 55102 Thessaloniki,Greece

452 J Seismol (2012) 16:451–473

each of them from a different host region but onlytwo of them were kept for long periods. In mostcases, a common agreement has been also reachedfor the weights. In case of divergence, a sensitivityanalysis of the weights on the seismic hazard hasbeen conducted, showing that once the GMPEshave been selected, the associated set of weightshas a smaller influence on the hazard.

Keywords Logic trees · Ground-motionprediction equations · Expert judgment ·Model selection · Seismic hazard assessment

1 Introduction

Following the SESAME (Seismotectonics and Seis-mic Hazard Assessment of the MediterraneanBasin, 1996–2000) project, the Seismic Hazard Har-monization in Europe (SHARE) project (http://www.share-eu.org) is one of the large interna-

tional research initiatives that have been recentlylaunched to harmonize hazard estimates acrosspolitical boundaries and to derive procedurallyconsistent pan-national hazard models. As a re-gional program of the Global Earthquake Model(GEM) project (http://www.globalquakemodel.org), the SHARE project aims at defining meth-ods for seismic hazard and loss assessment in theEuro-Mediterranean region which will becomestandards at global and regional scales.

The team responsible for ground-motion pre-diction in the SHARE project (WP4 group, seeTable 1) has been working on the definition of areference European model that captures the com-plete center, body and range of possible groundmotions in Europe and tackles the unresolvedquestion of regional variations in ground motions.The construction of logic trees that express thisvariability and the associated epistemic uncer-tainty is a multi-step procedure that required acommon effort in characterizing ground shakingin Europe and identifying reliable equations for

Table 1 SHARE WP4 group involved in the building of the logic tree for ground-motion prediction

Coordinators and Elise Delavaud ISTerre, Grenoble, France/ETH, Zürich, SwitzerlandMethodology definition Fabrice Cotton ISTerre, Grenoble, France

Sinan Akkar METU, Ankara, TurkeyFrank Scherbaum Institute of Earth and Environmental Science,

Potsdam, Germany

Experts Julian Bommer Imperial College, London, UKFabian Bonilla IFSSTAR, Paris, FranceHilmar Bungum NORSAR/ICG, Kjeller, NorwayJohn Douglas BRGM, Orléans, FranceEzio Faccioli Politecnico di Milano, Milan, ItalyNikos Theodoulidis ITSAK, Thessaloniki, Greece

Participants Laurentiu Danciu (sensitivity analysis) ETH, Zürich, SwitzerlandCéline Beauval (data testing) ISTerre, Grenoble, FranceStéphane Drouet (models pre-selection) ISTerre, Grenoble, FranceJohn Douglas (models pre-selection) BRGM, Orléans, FranceRoberto Basili (zonation map) INGV, Rome, ItalyAbdullah Sandikkaya (data testing) METU, Ankara, TurkeyMargaret Segou (data testing) METU, Ankara, TurkeyEzio Faccioli (volcanic zones) Politecnico di Milano, Milan, ItalyNikos Theodoulidis (data testing) ITSAK, Thessaloniki, GreeceDonat Fäh ETH, Zürich, SwitzerlandBenjamin Edwards ETH, Zürich, SwitzerlandPierre-Yves Bard ISTerre, Grenoble, FranceKyriazis Pitilakis University of Thessaloniki, Thessaloniki, GreeceMarco Pagani GEM Foundation, Pavia, Italy

J Seismol (2012) 16:451–473 453

the prediction of ground-motion parameters ofinterest together with measures of uncertainties.

Within the large geographical area covered bySHARE, there is a wide variation in terms ofthe magnitude and distance ranges that influenceprobabilistic seismic hazard assessment (PSHA).PSHA in Europe is not only controlled by largemagnitudes. As a matter of fact, probabilistic dis-aggregation analyses indicate that in many seis-mically active regions of Europe, the seismichazard for 10% exceedance in 50 years leveland short vibration periods (fundamental for ul-timate limit state verifications of most structures)tends to be controlled by nearby earthquakes (dis-tance <20 km) in the 4.5 to 5.5 magnitude range.Beauval et al. (2008) showed that in active regionsof France, magnitudes 4 to 5 are also responsiblefor a non-negligible contribution to the hazardeven for return periods as large as 10,000 years.The above observation is commonly found, forexample, for Italian sites in active areas and,obviously, is particularly true for low seismic-ity regions, i.e., north of the Alps (Faccioli andVillani 2009). This is why ground-motion predic-tion equations (GMPEs) that include events withmagnitudes down to Mw 4 in their datasets shouldalso be considered. Concerning the influence ofthe larger magnitudes on hazard, evaluations tendto depend to some extent on the model of earth-quake sources adopted, e.g., whether extendedzones, or fault sources (FS), or smoothed seismic-ity. In active regions of southern Italy (notably theCalabrian Arc), where maximum historical mag-nitudes exceed 7 and which are certainly amongthe most active in the Mediterranean area, recentseismic hazard studies for sites lying within sourcezones indicate that magnitudes >6.5 in the dis-tance range within 20 km dominate hazard only atreturn periods of 5,000 years and vibration periodsof 1 s and larger (Faccioli and Villani 2009). Insuch regions, even at return periods as large as1,500 years and at vibration periods of 1 s, haz-ard is typically controlled by magnitudes ≤ 6.0in the short distance range. On the other hand,again considering southern Italy, sites lying at fewtens of kilometers from the boundaries of modelsource zones are mostly affected by M > 6.5 start-ing from return periods of 1,000 years or so, inthe whole range of vibration periods. If smoothed

seismicity representations are used instead, thingschange to some extent, in that—for a given returnperiod—lower magnitudes tend to dominate.

In this paper, we describe the methodology thatwe adopted to build the logic tree for PSHA inEurope. This process is illustrated in Fig. 1. Thegoal of this strategy is to identify the smallest setof GMPEs to capture the epistemic uncertaintyin ground-motion prediction in Europe. The par-ticularity of our approach is that we do not onlytake into account the judgment of experts to selectand rank models but we also use data to guideour choice and weights. Thanks to an increasingamount of strong-motion data, data-driven guidanceis indeed now feasible and can give valuable informa-tion about the ability of GMPEs to predict groundmotion in different regions (e.g., Drouet et al.2007; Allen and Wald 2009; Delavaud et al. 2012).

The structure of this paper follows the adoptedprocedure. First, we show how a list of GMPEsfor each tectonic regime was selected from themany existing models using exclusion criteria. Ina second step, we describe the expert judgment,including the conditions imposed to the experts

Selection of candidate GMPEs

Identification of worldwide GMPEs

Application of the exclusion criteria of Cotton et al. (2006)

Review of the GMPEs applicability range

Adjustment for parameter compatibility

Evaluation of the GMPEs using the criteria of Bommer et al. (2010)

Expert judgment

Logic trees from 6 experts

Testing using data

Rankings of GMPEs basedon Scherbaum et al. (2009)

Proposition of logic trees : WP4 consensus

Selection of the final GMPEs

Proposition of different sets of weights

Sensitivity analysis of the proposed weights on the seismic hazard

Final logic tree

Fig. 1 Process adopted for the construction of the ground-motion logic tree for Europe

454 J Seismol (2012) 16:451–473

and the weights that they chose. We pay particularattention to the rationale behind the choices of theexperts and expose what we learnt from them. Thethird step consists in the testing of the candidateGMPEs using data. GMPEs are ranked accordingto a criteria, the negative average sample log-likelihood, proposed by Scherbaum et al. (2009)and based on information theory. In particular,we estimated to what degree the data supportor reject a model with respect to the state ofnon-informativeness defined by uniform weight-ing. The following section describes how GMPEswere selected taking expert judgment and datatesting into account and different sets of weightsproposed as a consensus within the SHARE WP4group. Finally, we present the results of a sensitiv-ity analysis of the weights on hazard maps to helpus make a final choice. The goal of this paper is to

make the SHARE GMPE logic tree methodologytransparent and reproducible.

2 Pre-selection of ground-motionprediction equations

The pre-selection of GMPEs is first guided bythe seismotectonic description of the area coveredby the SHARE project (Fig. 2). The SHAREsource model also influences ground-motion pre-diction, especially in terms of distance calcula-tion. This source model combines modern sourcetypes (area, fault, and point sources) within alogic tree to account for the inherent uncertaintyin the expert views on seismicity. The sourcelogic tree considers the different source typeswithin the principal methodologies used: the zone-

Fig. 2 Seismotectonic map of the Euro-Mediterraneanarea developed for the SHARE project by WP3.2. 1 SCR,shield (a) and continental crust (b); 2 oceanic crust; 3ASCR, compression-dominated areas (a) including thrustor reverse faulting, associated transcurrent faulting (e.g.,tear faults), and contractional structures in the upperplate of subduction zones (e.g., accretionary wedges),

extension-dominated areas (b) including associated tran-scurrent faulting, major strike-slip faults and transforms(c), and mid oceanic ridges (d); 4 subduction zones shownby contours at 50-km-depth interval of the dipping slab; 5areas of deep-focus non-subduction earthquakes; 6 activevolcanoes and other thermal/magmatic features

J Seismol (2012) 16:451–473 455

based (Cornell 1968) and the kernel-smoothedapproach (Grünthal et al. 2010; Hiemer et al.2011). Final details on the source models can befound within the reports of the SHARE project athttp://www.share-eu.org or within a yet to be writ-ten manuscript on the new Euro-Mediterraneanhazard model.

The pre-selection of GMPEs was realized froman already compiled list by Douglas (2008) thatcontains over 250 published ground-motion mod-els, to retain a subset of the most robust equa-tions for all the existing seismotectonic regimesin the wider European region. Six broad tectonicdomains were identified for ground-motion pre-diction to represent the region covered by theSHARE project (Fig. 2): Stable continental re-gions (SCR) include the shield (Baltic) wherePrecambrian crystalline igneous or metamorphicrocks crop out and are characterized by low waveattenuation and a low deformation rate, and conti-nental crust (most of Europe and Africa) with lowdeformation rate; oceanic crust includes mainlythe eastern Atlantic and small patches in theMediterranean Sea; active shallow crustal regions(ASCR) mainly outline the plate boundaries butoccur also in the continental interiors at placeswith significant rate of deformation; subductionzones (SZ) such as the Calabrian, Hellenic, andCyprus arcs; areas of deep focus non-subductionearthquakes, such as Vrancea (Romania) or theBetics (Spain); and active volcanoes. For this pre-selection, it was decided to apply the seven ex-clusion criteria proposed by Cotton et al. (2006),briefly: (1) the model is from a clearly irrele-vant tectonic regime, (2) the model is not pub-lished in an international peer-reviewed journal,(3) the documentation of model and its underlyingdataset is insufficient, (4) the model has beensuperseded by more recent publications, (5) thefrequency range of the model is not appropriatefor engineering application, (6) the model has aninappropriate functional form, and (7) the regres-sion method or regression coefficients are judgedto be inappropriate. From the existing GMPEs,six models remained for SCR, eight for SZ, 19 forASCR including six regional or local models, onemodel for volcanic zones (McVerry et al. 2006),and one for areas of deep focus non-subductionearthquakes (Sokolov et al. 2008). No model for

the prediction of ground motions from oceaniccrustal earthquakes was available in the interna-tional literature, but models for ASCR and SCRhave been suggested to account for such seismo-tectonic regimes. The engineering needs, evalu-ated at the beginning of the project, were takeninto account by favoring models well calibrated inthe period range between 0.02 and 10 s. Most ofexisting models are, however, not applicable forperiods greater than 3 s, and hence, a specific logictree was built to ensure PSHA computations forperiods between 3 and 10 s.

As a second step, these pre-selected GMPEshave been analyzed and compared in order toidentify their weaknesses and limitations in thelight of the criteria set proposed by Bommeret al. (2010). Considering the rapid increasein published GMPEs for ASCR (in particular),Bommer et al. (2010) updated the exclusion cri-teria of Cotton et al. (2006) to reflect the state-of-the-art in ground-motion prediction. The newexclusion criteria especially aim at identifying therobust and well-constrained models based on newquality standards in the formulation and deriva-tion of models as well as considering their ap-plicability range in terms of spectral ordinates,magnitude, and distance. In particular, magnitudeand distance ranges should be large enough sothat the need for extrapolations when conduct-ing PSHA is minimized. In addition, the numberof earthquakes per magnitude and the numberof records per different distance intervals shouldbe maximized. A detailed comparative study be-tween the models of each tectonic regime has beenconducted. In particular, they compared the pre-dicted ground-motion amplitudes by the GMPEsfor different scenarios (in terms of magnitude,distance, and period) and extracted the main char-acteristics of the models that are summarized inTable 2 for SCR, in Table 3 for SZ, and in Table 4for ASCR. In these tables, we report the typeand range for the magnitude and the distance,the spectral period band, as well as the inclu-sion of PGA and/or peak ground velocity (PGV)estimations by the candidate GMPEs. We alsoindicate whether the site classification is based ona continuous function of vS30 or on generic siteclasses in terms of vS30 intervals. The tables alsolist the horizontal component definitions of the

456 J Seismol (2012) 16:451–473

Tab

le2

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J Seismol (2012) 16:451–473 457

Tab

le4

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450

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458 J Seismol (2012) 16:451–473

GMPEs that vary among the models. Moreover,some of the models do not use style of faultingas a predictor variable. In order to combine theGMPEs within a logic tree framework, compo-nent and style-of-faulting adjustments have beenperformed. Horizontal components are convertedusing the conversion coefficients determined byBeyer and Bommer (2006). For models whichdo not consider the style of faulting, adjustmentfactors depending on the proportions of normaland reverse events in the underlying databaseof each model are applied using the approachproposed in Bommer et al. (2003). These fac-tors are given in the tables except for SZ mod-els, which do not explicitly consider the style offaulting but differentiate inslab earthquakes frominterface earthquakes, taking into account boththe mechanism and the depth of the earthquake.The effects of the adjustment strategies are pre-sented in Drouet et al. (2010). Finally, we didnot take non-linear effects into account as theseismic hazard is computed for rock sites. Ourmodel selection is thus focusing on the rock part ofGMPEs.

As a result of the model analysis, the mem-bers of the WP4 team discussed their concernsabout the predictive ability and the weaknessesof the models. Reservations were expressed forthe next-generation attenuation (NGA) modelsof Abrahamson and Silva (2008), Campbell andBozorgnia (2008), and Chiou and Youngs (2008)because they require too many estimator para-meters that are not available in all Europeanearthquake-prone regions. This limitation can bepartially overcome by using the a priori estima-tions of these unknown input parameters given bythe methodology proposed in Kaklamanos et al.(2011). Models that suffer from restrictions inthe definition of predictive variables were alsoquestioned: The SZ model of Garcia et al. (2005)only considers inslab earthquakes, Atkinson andMacias (2009) only consider large interface earth-quakes, the NGA model of Idriss (2008) doesnot cover sites with vS30 values less that 450 m/s,and finally, Kanno et al. (2006) do not provideproportions of normal and reverse faulting eventsthereby preventing style-of-faulting adjustments.The model of Cotton et al. (2008) was also ques-

tioned because it does not include style of faultingas a predictor variable and they might have in-cluded subduction interface events in their ASCRdataset since the selection of earthquakes wasbased on focal depth only. Finally, reservationswere expressed for the models of Tavakoli andPezeshk (2005) and of Ambraseys et al. (2005) asthey are similar to Campbell (2003) and Akkarand Bommer (2010), respectively, and for themodel of Özbey et al. (2004) which was derivedfrom data from the 1999 earthquakes in Turkeythat were recorded within a limited area. Al-though these GMPEs suffer from the above re-strictions, they were considered by the experts andin the testing.

There are obviously large differences in termsof number of GMPEs between the three tec-tonic regimes and also in terms of their host re-gions. For stable continental regions, all the GM-PEs except Douglas et al. (2006) were derivedfrom eastern North America (ENA) data whereasASCR regime includes GMPEs from all overthe world (although mainly California, Europe,and Japan). The selection for subduction zonesincludes no European candidate ground-motionmodel.

Finally, we acknowledge that the pre-selectedGMPEs may not be calibrated homogeneouslyin all the parameter space relevant for PSHA inEurope, especially for low magnitudes (Mw < 5).The development of new GMPEs was beyond thescope of the present project, and for this reasonand the lack of homogeneous local datasets, wehave not applied the calibration of existing modelsusing local data, e.g., following the method byScasserra et al. (2009). We recognize that thereis a need to start to apply these new methods,at least in Turkey and Italy, where local data areavailable.

The pre-selected GMPEs have been subse-quently evaluated in two parallel steps. In one ap-proach, a group of experts were asked to proposethe logic tree weights for these GMPEs. In theother approach, ground-motion records, when-ever available, were used to test the ability of theGMPEs to model the overall trends of the groundmotions in each tectonic region. We present nowthese two complementary approaches.

J Seismol (2012) 16:451–473 459

3 Expert judgment

Since the 1970s, there has been an increasinginterest in the use of expert judgment to helpin decision making by formalizing and quanti-fying expert judgment on problems that involveuncertainties (e.g., Cooke 1991; Goossens et al.2000). Private agencies as well as academia haverecourse to this approach especially when dataare unavailable or inadequate, and this is why ithas been, until recently, the only method used toselect and weigh GMPEs for probabilistic seismichazard assessment. Although guidance for expertjudgment is given by the Senior Seismic HazardAnalysis Committee in Budnitz et al. (1997), thereis no clear standard procedure for the selectionand weighting of GMPEs by experts. In this sec-tion, we present the strategy that we adopted forthe determination of logic tree weights from agroup of experts.

We composed a group of six experts workingin five different countries in academia or publicinstitutions in Europe (see Table 1). Six seemed tobe a good number, to have enough different pointsof view without too much redundancy. They werechosen for their great experience with GMPEs(e.g., some of them developed GMPEs) and alsofor their experience of PSHA in specific countriessuch as Italy, France, or Greece. Four people (thefirst four authors of the present paper) defined theguidelines and the processing of the expert judg-ment. We asked the experts to propose logic treeweights expressing their degree of belief in theability of candidate GMPEs to predict earthquakeground motions in different tectonic regimes inEurope. We did not guide the experts in howto assign their weights (e.g., whether all GMPEsshould be weighted or not), since no clear method-ology was available at that time. However, weasked them to explain the rationale behind theirweighting strategy. Weights had to be assignedfor each tectonic regime (with a differentiationbetween shield and continental crust for SCRand between interface and inslab earthquakes forSZ) for different ranges in spectral frequency ( f ),magnitude (Mw), and distance (d): f ≤ 1/3 Hz,1/3 Hz < f ≤ 25 Hz, or f > 25 Hz; Mw ≤ 5 orMw > 5; and d ≤ 10 km, 10 km < d ≤ 100 km,

100 km < d ≤ 200 km, or d > 200 km. By doingso, we wanted to see whether or not the ex-perts would consider the frequency–magnitude–distance dependency for the logic tree weights.Finally, the experts did not communicate witheach other to have independent alternatives forlogic tree weights. They also did not know aboutthe testing results conducted by using the empir-ical data (see next section). However, they wereprovided with the characteristics of the GMPEsthat are presented.

A lesson that we learned from the experts isthat assigning weights to GMPEs is not straight-forward, especially for such a large number ofmodels and with distinctions in terms of fre-quency, magnitude, and distance. We also real-ized that the time limit imposed for the entiredecision process was quite limited for this task(5 weeks). In particular, some experts raised thepossibility of assigning zero weights to some of theGMPEs, indirectly raising the question of whatlogic tree weights represent. This led to a livelydiscussion between the WP4 members and theexperts during a meeting where experts presentedtheir weighting strategy. Experts had a commonapproach: They selected a set of models whichenabled them to capture epistemic uncertainty asmuch as possible. For some of the experts, a smallnumber of GMPEs (two to four) was sufficient(not all models are used although they could beappropriate). On the other hand, some expertsselected many or all the candidate GMPEs as-signing small weights (<0.1) for the less favorableones. Although logic trees are now widely used,we realized that it is not clear yet how weightsshould be assigned and what they should be as-sumed to represent. Scherbaum and Kühn (2011)recently showed the importance of treating logictree weights as probabilities instead of simply asgeneric quality measures of GMPEs, which aresubsequently normalized. In particular, they showthe danger of using a performance/grading matrixapproach (independently assigning of grades todifferent quality criteria) where the normalizationprocess can lead to an apparent insensitivity tothe weights. In order to achieve consistency witha probabilistic framework, Scherbaum and Kühn(2011) proposed to assign weights in a sequential

460 J Seismol (2012) 16:451–473

fashion (e.g., if the first GMPE of three selectedgets a 0.6 weight, then the sum of the weights forthe two remaining models is 0.4).

The first conclusion of the experts was that thenumber of selected GMPEs should be kept assmall as possible (between two and five) to pre-vent the logic tree for ground-motion predictionbeing too complex, which is especially importantfor such a wide area considered by the SHAREproject. In addition, most of the experts gaveweights that are independent of the magnitude,distance, and frequency, except for long periods(3 s < T ≤ 10 s) for ASCR. The main moti-vation behind this choice was to prevent havinga discontinuity due to the transition from onelogic tree to another one in the uniform hazardspectra produced by PSHA. The experts selectedGMPEs which are sufficiently robust to cover awide range of magnitudes, distances, and spectralperiods. Such GMPEs are indeed better able tocapture the magnitude scaling of ground motionthat decreases when magnitude increases (Cottonet al. 2008; Atkinson and Morrison 2009). More-over, Bommer et al. (2007) strongly recommendednot to apply GMPEs outside and even close totheir magnitude limits. Finally, GMPEs developedfrom limited datasets are more likely to incorpo-rate random earthquake effects (biases) into theirmodels. Therefore, global predictive models werepreferred as compared to regional ones. Finally,experts assigned equal weights for the models thatthey are not familiar with or for which they lacksufficient information.

For stable continental regions, selecting themodels was a particular challenge as all but oneare derived for ENA and inadequate informationabout their applicability for Europe is known.Experts made no distinctions between shield andcontinental crust. Of the six GMPEs proposedfor SCR, the expert selection ranged betweenretaining three or all six. The SCR models byCampbell (2003) and Toro et al. (1997) were se-lected by all experts. The choice of GMPEs forsubduction zones was also a challenging task sincenone of the pre-selected GMPEs were derivedusing empirical data from Europe. Due to thisparticular reason, the experts preferred choosingthe global SZ models that cover a wide range ofmagnitude and distance intervals. Only one expert

considered interface and inslab models separatelyin ranking whereas three experts considered thespectral period ranges while assigning weights.The experts selected two to five GMPEs amongthe eight models proposed for SZ. Only onemodel was selected by all the experts, the model ofAtkinson and Boore (2003). Contrary to the SCRand SZ regions, the excessive number of GMPEsfor the shallow crustal active regions challengedthe expert judgment. Regional ASCR models(e.g., Massa et al. 2008; Kalkan and Gülkan 2004;Danciu and Tselentis 2008) were either excludedor given small weights (less than 0.1). The ex-pert choices lean toward global and pan-Europeanmodels in the ranking of ASCR GMPEs. Of theentire expert group, only two of them consid-ered magnitude–distance–frequency ranges whileassigning weights. The experts selected betweenthree to ten GMPEs among the 18 candidate mod-els. The GMPEs by Akkar and Bommer (2010)and of Boore and Atkinson (2008) were the com-monly selected models by all experts. Tables 8, 9,and10 summarize the choice of each expert for thethree tectonic regimes under the Category basedon expert judgment.

4 Data testing

To complement the expert opinions describedabove, testing of the candidate GMPEs againstempirical data was undertaken. The goal of thisphase was to judge the applicability of candidatemodels by evaluating their probability to havegenerated the available data. We used the data-driven method developed by Scherbaum et al.(2009) that implemented an information theoreticapproach for the selection and the ranking ofGMPEs. The method derived a ranking crite-rion from the Kullback–Leibler (KL) divergence,which denotes the information loss when a modelg defined as a distribution is used to approximatea reference model f (Burnham and Anderson2002). The KL divergence between two modelsrepresented by their probability density functionsf and g is defined as:

D( f, g) = E f[log2( f )

] − E f[log2(g)

](1)

J Seismol (2012) 16:451–473 461

where Ef is the statistical expectation taken withrespect to f .

In the case of GMPE selection, f representsthe data-generating process (nature) and is onlyknown through observations. Consequently, theterm Ef

[log2( f )

]called the self-information of f

cannot be calculated. However, the second term,−Ef

[log2(g)

], can still be approximated via the

observations. This approximation is the negativeaverage sample log-likelihood, noted LLH anddefined by:

LLH(g, x) := − 1

N

N∑

i=1

log2 (g(xi)) (2)

where x = {xi}, i = 1, ..., N are the empirical dataand g(xi) is the likelihood that model g has pro-duced the observation xi. In the case of GMPE se-lection, g is the probability density function givenby a GMPE to predict the observation producedby an earthquake defined by a magnitude M (andby other characteristics such as the style of fault-ing) at a site i that is located at a distance R fromthe source.

We used the LLH divergence as a criterion torank the candidate GMPEs. Due to its negativesign, the negative average sample log-likelihood isnot a measure of closeness but a measure of thedistance between a model and the data-generatingprocess. A small LLH indicates that the candidatemodel is close to the process that has generatedthe data while a large LLH corresponds to amodel that is less likely of having generated thedata.

In order to interpret the rankings, weights ob-tained from the LLH values were compared tothe uniform weight wunif = 1

M , where M is thenumber of GMPEs. This comparison tells us towhat degree the data support or reject a modelwith respect to the state of non-informativeness.It is expressed by the data support index (DSI)which gives the percentage by which the weight ofa model is increased (positive DSI) or decreased(negative DSI) by data. The DSI of model gi withLLH-value based weight wi is:

DSIi = 100wi − wunif

wunif, (3)

where

wi = 2−LLH(gi,x)

∑Kk=1 2−LLH(gk,x)

(4)

This ranking method has been recently used byDelavaud et al. (2012) to test the global applicabi-lity of GMPEs for active shallow crustal regions.The LLH divergence was computed for 11 GM-PEs for different regions and magnitude and dis-tance ranges to assess their validity domain.

The LLH-based weights defined by Eq. 4 can-not be automatically regarded as probabilities asthe LLH values are independently determined foreach model (Kolmogorov’s axioms of mutual ex-clusiveness and collective exhaustiveness are notrespected) and only subsequently made to sum upto one (see Scherbaum and Kühn 2011, for moredetails about this subject). Therefore, we advisenot to directly use them as logic tree weights butto use them in combination with expert judgment.The purpose of using empirical data was not to re-place expert judgment but rather to help the judg-ment process by providing additional informationabout the applicability of GMPEs, especially inregions where no indigenous model exists.

Although the amount of empirical ground-motion data is rapidly increasing worldwide, wefaced some limitations while testing GMPEs withthe compiled data. We considered the distributionof empirical ground-motion data in terms of mag-nitude and distance. We also accounted for thereduction in available data size in terms of theirusable period range in order to reduce the filtercutoff influence on the spectral ordinates. Thecountry-based distribution of the data was alsoconsidered to examine the similarities betweenthe original datasets of the tested GMPEs and ourdatabase used for testing these GMPEs becausewe wanted to prevent biased evaluations due tosimilarities between our dataset and those of theGMPEs. A homogenous dataset was not availablefor SCR, and therefore, no tests for this tectonicregime were made.

For subduction zones, we had available a re-stricted dataset that only consisted of inslab strike-slip earthquakes along the Hellenic arc with a totalnumber of 65 recordings. Moment magnitudes ofSZ data range from 5.2 to 6.7, their depth mainlyvaries from 40 to 90 km, and the hypocentral

462 J Seismol (2012) 16:451–473

Table 5 Ranking of the candidate GMPEs for subductionzones based on LLH values for PSA at 0.05, 0.3, 0.5, 0.8, 1,1.5, and 2 s

Subduction zones—PSA 0.05 to 2 s

Rank LLH DSI Model

1 1.979 29.57 Lin and Lee (2008)2 1.988 28.76 Zhao et al. (2006)3 2.206 10.71 Youngs et al. (1997)4 2.499 −9.641 Kanno et al. (2006)5 2.500 −9.704 McVerry et al. (2006)6 3.344 −49.70 Atkinson and Boore (2003)

distances are mostly from 70 to 300 km. All theGMPEs from Table 3 have been tested against thisGreek dataset except for the models of Atkinsonand Macias (2009) and Garcia et al. (2005). Theformer model only considers interface events withmagnitudes greater than 7.5 whereas the lattermodel is only derived for inslab earthquakes andhence its applicability for PSHA is limited. Noneof the tested GMPEs used Greek data for theirderivations. Rankings have been performed forpseudo-spectral accelerations (PSAs) at spectralperiods between 0.05 and 2 s. Table 5 shows the

ranking using the chosen spectral periods. Thefirst two models in the ranking are the modelsof Lin and Lee (2008) and Zhao et al. (2006).These modes were derived from the data pertain-ing to northern Taiwan and Japan, respectively.They are equally supported by the Greek datawith a DSI of about 29% each. On contrary,the global model of Atkinson and Boore (2003)appears particularly inconsistent with the presentGreek dataset with a DSI of about −50%. TheAtkinson and Boore (2003) model was sensitiveto the changes in the period range considered asit predicted the Greek ground motions fairly wellfor periods below 0.16 s. The overall results ofthe testing for subduction zones are summarizedin Table 9 under the Category based on data-testing results. They are presented in more detailin Beauval et al. (2012).

For active shallow crustal regions, we consid-ered two databases that are composed of record-ings from Europe (DB1) and from other ASCRaround the world (DB2). The majority of record-ings in DB1 are in the magnitude and distancerange: 4 < Mw < 7 and 1 km < RJB <200 km,

Fig. 3 Distribution of thedatabase DB1 (Europeandatabase) in terms ofJoyner–Boore distance(RJB) and magnitude.For illustrative purposes,the recordings withRJB < 0.1 km are plottedas 0.1 km

DB1 (1533 recordings)

RJB (km)

0.1 1 10 100

Mw

2

3

4

5

6

7

8

GreeceItalyTurkeyOthers

J Seismol (2012) 16:451–473 463

Fig. 4 Distribution of thedatabase DB2(Non-Europeandatabase) in terms ofJoyner–Boore distance(RJB) and magnitude.For illustrative purposes,the recordings withRJB < 0.1 km are plottedas 0.1 km

DB2 (1755 recordings)

RJB (km)

0.1 1 10 100

Mw

2

3

4

5

6

7

8

TaiwanUSAOthers

respectively. Due to the lack of large magnitudeevents in DB1, GMPEs were also tested againstDB2 which is mainly composed of magnitudesbetween 6 and 8. The main assumption while run-ning these analyses was the weak regional depen-dence of GMPEs. Both databases were extractedfrom the SHARE strong-motion databank (Akkaret al. 2010) that is compiled from various original

databases (Ambraseys et al. 2004; Luzi et al. 2008;Chiou et al. 2008; Cotton et al. 2008; Sandikkayaet al. 2010). The European dataset is presented inFig. 3. It contains 1,533 recordings, mainly fromTurkey. The major reason for the larger numberof Turkish recordings is the fact that the other Eu-ropean databases do not contain site classificationin terms of vS30 and lack complete information on

Table 6 Ranking of thecandidate GMPEs forASCR based on LLHvalues for PSA at 0.1, 0.2,0.5, 1, and 2 s from DB1(European database)

Active shallow crustal regions—DB1—PSA 0.1 to 2 s

Rank LLH DSI Model

1 2.378 68.29 Bindi et al. (2010)2 2.396 66.20 Cauzzi and Faccioli (2008)3 2.427 62.67 Cotton et al. (2008)4 2.588 45.49 Akkar and Bommer (2010)5 2.680 36.50 Douglas et al. (2006)6 2.800 25.61 Zhao et al. (2006)7 2.938 14.15 Chiou and Youngs (2008)8 3.158 1.99 Ambraseys et al. (2005)9 3.271 −9.38 Danciu and Tselentis (2008)10 3.869 −40.13 Abrahamson and Silva (2008)11 4.121 −49.72 Boore and Atkinson (2008)12 4.785 −68.27 Campbell and Bozorgnia (2008)13 4.921 −71.12 Kalkan and Gülkan (2004)14 5.332 −78.28 Massa et al. (2008)

464 J Seismol (2012) 16:451–473

Table 7 Ranking of thecandidate GMPEs forASCR based on LLHvalues for PSA at 0.1, 0.2,0.5, 1, and 2 s from DB2(non-European database)

Active shallow crustal regions—DB2—PSA 0.1s to 2s

Rank LLH DSI Model

1 1.558 29.49 Akkar and Bommer (2010)2 1.592 26.43 Chiou and Youngs (2008)3 1.620 24.00 Boore and Atkinson (2008)4 1.672 19.65 Abrahamson and Silva (2008)5 1.678 19.15 Kalkan and Gülkan (2004)6 1.710 16.45 Campbell and Bozorgnia (2008)7 1.761 12.50 Bindi et al. (2010)8 1.813 8.477 Danciu and Tselentis (2008)9 1.835 6.81 Cauzzi and Faccioli (2008)10 1.850 5.75 Zhao et al. (2006)11 2.331 −24.25 Ambraseys et al. (2005)12 2.545 −34.67 Douglas et al. (2006)13 2.897 −48.82 Cotton et al. (2008)14 3.288 −60.97 Massa et al. (2008)

some of the distance measures used by the can-didate GMPEs. Other observations mostly comefrom Italy and Greece. The non-European datasetis presented in Fig. 4. It mostly contains recordingsfrom the USA and Taiwan that were extractedfrom the NGA database. Rankings based on PSAsat five spectral periods (0.1, 0.2, 0.5, 1, and 2 s)are presented in Tables 6 and 7 for DB1 andDB2, respectively. A total of 14 GMPEs havebeen tested: all the models in Table 4 exceptfor the GMPEs of Idriss (2008), Kanno et al.(2006), Özbey et al. (2004), McVerry et al. (2006),

and Pankow and Pechmann (2004). The Italianmodel of Bindi et al. (2010) is ranked first, closelyfollowed by two non-European models, Cauzziand Faccioli (2008) and Cotton et al. (2008),with DSIs larger than 60%. The testing resultsof the Akkar and Bommer (2010) model appearto be quite robust as it is well ranked for bothdatasets DB1 and DB2. The model of Kalkan andGülkan (2004) and the NGA models are betterable to predict ground motions from the largeearthquakes that compose DB2 than ground mo-tions from DB1. The results of the data testing for

Table 8 Expert choicesand the final logic treesfor stable continentalregions

Names in bold are theselected modelsWS weighting scheme

Category based on expert judgment Models

Models supported by all the experts Campbell (2003)Toro et al. (1997)

Models chosen by a majority of experts Atkinson and Boore (2006)Douglas et al. (2006)Atkinson (2008)

Models chosen by a minority of experts

Models not chosen by the experts Tavakoli and Pezeshk (2005)

Selected models for shield WS

Campbell (2003) 0.5Toro (2002, unpublished) 0.5

Selected models for continental crust WS

Campbell (2003) adjusted to 800 m/s 0.2Toro (2002, unpublished) adjusted to 800 m/s 0.2Akkar and Bommer (2010) 0.2Cauzzi and Faccioli (2008) 0.2Chiou and Youngs (2008) 0.2

J Seismol (2012) 16:451–473 465

active shallow crustal regions are summarized inTable 10 under the Category based on data-testingresults.

5 Ground-motion logic tree

Based on the results of both the expert judgmentand the testing, a consensus set of GMPEs wasdetermined for each tectonic regime. Tables 8, 9,and 10 were used to guide the selection, especiallywhen expert judgment and empirical data testingresults were available. Models supported by theempirical data testing and the experts’ choices(first category) were selected while the modelsthat were not supported by the data testing andnot chosen by the experts (fourth category) havebeen rejected. For the rest of the models (sec-ond and third categories), discussions were heldbetween the experts and ground-motion model-

ing group to decide on their rejection or selec-tion. Weights were also determined but differentpropositions were retained for sensitivity analyses.

For stable continental regions, for which notesting could be performed due to a lack of data,a distinction between shield and continental crustwas taken into account. For shields, the two mod-els supported by all the experts were selected withequal weights: Toro’s (2002, unpublished) modelwhich is an updated version of Toro et al. (1997)and the model by Campbell (2003). For continen-tal crust, three GMPEs for ASCR were adopted(Akkar and Bommer 2010; Cauzzi and Faccioli2008; Chiou and Youngs 2008) in addition to themodels of Toro (2002, unpublished) and Campbell(2003). This accounts for uncertainty in knowingif ground motions in continental crust are morelike those in ASCR or in SCR. Equal weightswere assigned to the five GMPEs selected forcontinental crust. The Toro (2002, unpublished)

Table 9 Expert choices,data-based testing results,and logic trees forsubduction zones

Names in bold are theselected models. Thepreferred WS is shownin boldWS weighting scheme

Category based on expert judgment Models

Models supported by all the experts Atkinson and Boore (2003)

Models supported by a majority of experts Youngs et al. (1997)Zhao et al. (2006)

Category based on data-testing results Models

Models supported by the testing Lin and Lee (2008)for long periods (T > 0.16s) Zhao et al. (2006)

Models supported by the testing Atkinson and Boore (2003)for short periods (T ≤ 0.16s) Zhao et al. (2006)

Category based on expert judgment Modelsand data-testing results

Models supported by the data testingand the experts choices

Models chosen by a majority Zhao et al. (2006)of experts and supportedby the data-testing results

Models chosen by a minority McVerry et al. (2006)of experts or with a low Atkinson and Macias (2009)data-testing result Garcia et al. (2005)

Models not supported by the data-testingand not chosen by the experts

Selected models WS1 WS2

Zhao et al. (2006) 0.4 0.25Atkinson and Boore (2003) 0.2 0.25Youngs et al. (1997) 0.2 0.25Lin and Lee (2008) 0.2 0.25

466 J Seismol (2012) 16:451–473

Table 10 Expert choices,data-based testing results,and logic trees for activeshallow crustal regions

Names in bold are theselected models. Thepreferred WS is shownin boldWS weighting scheme

Category based on expert judgment Models

Models supported by all the experts Boore and Atkinson (2008)Akkar and Bommer (2010)

Models supported by a majority of experts Cauzzi and Faccioli (2008)Zhao et al. (2006)

Category based on data-testing results Models

Models supported by the testing (European dataset) Bindi et al. (2010)Cauzzi and Faccioli (2008)

Models supported by the testing Akkar and Bommer (2010)(non-European dataset) Chiou and Youngs (2008)

Category based on expert judgment and Modelsdata-testing results

Models supported by the data testing and bythe experts choices

Models chosen by a majority of experts and Akkar and Bommer (2010)supported by the data-testing results Cauzzi and Faccioli (2008)

Models chosen by a minority of experts or with a low Abrahamson and Silva (2008)data-testing result Ambraseys et al. (2005)

Campbell and Bozorgnia (2008)

Models not supported by the data testing and Idriss (2008)not chosen by the experts McVerry et al. (2006)

Pankow and Pechmann (2004)Kalkan and Gülkan (2004)Danciu and Tselentis (2008)Massa et al. (2008)

Selected models for periods T ≤ 3 s WS1 WS2 WS3 WS4 WS5 WS6 WS7Akkar and Bommer (2010) 0.30 0.30 0.40 0.25 0.30 0.35 0.10Cauzzi and Faccioli (2008) 0.30 0.20 0.20 0.25 0.25 0.35 0.40Zhao et al. (2006) 0.20 0.20 0.20 0.25 0.20 0.10 0.10Chiou and Youngs (2008) 0.20 0.30 0.20 0.25 0.25 0.20 0.40

Selected models for periods 3 s < T ≤ 10 s WSCauzzi and Faccioli (2008) 0.5Chiou and Youngs (2008) 0.5

and Campbell (2003) models were decided tobe adjusted for the generic rock site conditionin Europe, established within the framework ofSHARE project that is described with a shear-wave velocity of vrock = 800 m/s and κ = 0.03 fol-lowing Van Houtte et al. (2011). The proposedweighting scheme for SCR is presented in Table 8.

For subduction zones (Table 9), the results ofthe empirical data testing and the choices of theexperts were quite divergent. Only the model ofZhao et al. (2006) was supported by the majorityof experts and the data-testing results. This modelhas been selected. The McVerry et al. (2006)model was neither supported by the experts nor

the empirical data testing, and consequentially, itwas rejected. The models of Atkinson and Boore(2003) and Youngs et al. (1997) that were the con-sensus selection of the experts as well as the Linand Lee (2008) and Zhao et al. (2006) models thatwere ranked the best in the testing were consid-ered in the weighting scheme. A weight of 0.4 wasassigned to the Zhao et al. (2006) model whereasthe other three models were weighted equallywith 0.2. An other weighting scheme where thefour selected GMPEs have equal weights hasbeen proposed. We decided to make a sensitivitystudy to investigate the differences between thetwo weighting schemes. No difference in weights

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Table 11 Weightingscheme (WS) for activeregions in oceanic crust(same as for ASCR). Thepreferred WS is shownin bold

Selected models for periods T ≤ 3 s WS1 WS2 WS3 WS4 WS5 WS6 WS7Akkar and Bommer (2010) 0.30 0.30 0.40 0.25 0.30 0.35 0.10Cauzzi and Faccioli (2008) 0.30 0.20 0.20 0.25 0.25 0.35 0.40Zhao et al. (2006) 0.20 0.20 0.20 0.25 0.20 0.10 0.10Chiou and Youngs (2008) 0.20 0.30 0.20 0.25 0.25 0.20 0.40

Selected models for periods 3 s < T ≤ 10 s WSCauzzi and Faccioli (2008) 0.5Chiou and Youngs (2008) 0.5

between interface and inslab earthquakes wasmade, due to a lack of data. However, this maybe a critical issue in PSHA, and further researchis needed in the future. The proposed weightingschemes are presented in Table 9.

For active shallow crustal regions (Table 10),two models were supported by both the experts andthe empirical data testing: the models of Akkarand Bommer (2010) and Cauzzi and Faccioli(2008). These models were directly consideredin the logic tree weighting scheme. In addition,we selected two other models: the Zhao et al.(2006) model, which was favored by the majorityof the experts, and the NGA model of Chiouand Youngs (2008), which was supported bythe testing using non-European recordings. Thisselection is in agreement with the recent studyconducted by Delavaud et al. (2012) to test theglobal applicability of GMPEs using the globaldataset of Allen and Wald (2009). For PGAand PSA at 1 Hz in Europe and the MiddleEast, the four best-ranked models accordingto Delavaud et al. (2012) are the models ofAkkar and Bommer (2010), Chiou et al. (2010),Cauzzi and Faccioli (2008), and Berge-Thierryet al. (2003) that are followed by the models ofChiou and Youngs (2008) and Zhao et al. (2006).Note that the model of Chiou et al. (2010) is anextension of the Chiou and Youngs (2008) modelfor small-to-moderate magnitudes. It is consistentwith the Chiou and Youngs (2008) model for largemagnitudes (Mw ≥ 6) but has new coefficientsfor smaller magnitudes. This result suggests thatDelavaud et al. (2012) would have ranked firstthe four models that we selected for ASCR ifthey had not considered the model of Chiouet al. (2010) and the model of Berge-Thierryet al. (2003). The model of Chiou et al. (2010)was not published when we started the selection

of GMPEs. It is also defined only for a limitednumber of periods. We considered moreoverthat the model of Berge-Thierry et al. (2003) isobsolete. For longer periods, between 3 and 10 s,only the models of Cauzzi and Faccioli (2008)and Chiou and Youngs (2008) were selected andgiven equal weights (0.5) because the Akkar andBommer (2010) and Zhao et al. (2006) modelsare not defined for periods up to 10 s. For periodslower than 3 s, different weighting schemeshave been proposed, as shown in Table 10. Theweighting scheme WS6 was, however, preferredthat assigns higher weights to the two modelsthat are supported by both the experts and theempirical data testing. It was also decided tomake a sensitivity analysis to better understandthe influence of the weights on the computedhazard.

For active regions in oceanic crust, GMPEsfrom ASCR were chosen (Table 11). For areasof deep focus non-subduction earthquakes, suchas Vrancea (Romania) or the Betics (Spain), wedecided to use the GMPEs selected for subduc-tion instead of the empirical model of Sokolovet al. (2008), which is directly derived from therecordings of Vrancea. The model by Sokolovet al. (2008) is too complex for regional PSHAbecause it models azimuthal variations of groundmotion (Table 12). Finally, for volcanic zones,

Table 12 Weighting scheme for Vrancea (same as for SZ)

Selected models WS1 WS2

Zhao et al. (2006) 0.4 0.25Atkinson and Boore (2003) 0.2 0.25Youngs et al. (1997) 0.2 0.25Lin and Lee (2008) 0.2 0.25

The preferred WS is shown in boldWS weighting scheme

468 J Seismol (2012) 16:451–473

Table 13 Weighting scheme (WS) for volcanic zones

Selected models WS

Faccioli et al. (2010) 1

it was decided to adopt an approach similar tothat implemented in Italy when creating the cur-rently applied set of seismic hazard maps (seeMontaldo et al. 2005) rather than using themodel of McVerry et al. (2006), which onlyseeks to model higher attenuation in volcaniczones rather than ground motions from volcano-related events. This approach consists of intro-ducing separate GMPEs within a seismic sourcezone of limited extension surrounding a volcanowith well-documented historical evidence of dam-aging earthquakes, such as the Mount Etna vol-cano, in Sicily. Such GMPEs should be able todeal with events of shallow focal depth, from2 to 5 km. An analysis expressly carried outon acceleration records from recent moderateearthquakes (3.2 < Mw <4.5) of recent years inItaly, notably in the Mount Amiata (southernTuscany) and Mount Etna areas, has shownthat the use of the recent attenuation model ofFaccioli et al. (2010) was appropriate, and its

adoption was therefore agreed to by WP4 ofSHARE (Table 13).

With logic trees containing between two andfive GMPEs for each tectonic regimes (exceptfor volcanic zones), the SHARE WP4 groupaimed at better taking epistemic uncertaintiesinto account. In comparison, for the SESAMEproject which provided the first homogeneousassessment of seismic hazard for the wholeMediterranean region, only three GMPEs wereconsidered: the model of Ambraseys et al. (1996)for all crustal sources, the model of Musson (1999)for Vrancea, and the model of Papaioannou andPapazachos (2000) for intermediate-depth seismicactivity sources in the Hellenic Arc (Jiménez et al.2001).

6 Sensitivity analysis

Logic tree and sensitivity analyses are generallyrun simultaneously. The results of a preliminarysensitivity analysis usually offer guidance for aniterative revision of the final logic tree structure(Scherbaum et al. 2005; Bommer and Scherbaum2008). As different weighting schemes were pro-

Table 14 Percentagedifferences for ASCR forthree ground-motionintensity measure types,two seismic source types,and two return periods.The maximum for eachground-motion intensitymeasure type, sourcetype, and return period ishighlighted in bold

Weighting schemes Area source Fault source

475 years (%) 2,475 years (%) 475 years (%) 2,475 years (%)

PGAPreferred WS vs. WS1 3.27 3.36 4.22 3.97Preferred WS vs. WS2 (+)7.68 5.95 5.38 5.88Preferred WS vs. WS3 6.96 5.20 7.82 6.66Preferred WS vs. WS4 6.39 5.43 5.79 5.10Preferred WS vs. WS5 5.45 4.33 4.57 4.25Preferred WS vs. WS7 4.44 (−)6.49 (−)8.59 (−)9.51

PSA (0.2s)Preferred WS vs. WS1 3.28 3.55 4.21 4.60Preferred WS vs. WS2 7.80 6.84 6.42 5.79Preferred WS vs. WS3 8.93 7.86 10.71 9.78Preferred WS vs. WS4 5.91 6.00 5.63 5.87Preferred WS vs. WS5 5.49 5.12 5.07 5.02Preferred WS vs. WS7 (−)11.04 (−)8.83 (−)14.57 (−)14.26

PSA (1s)Preferred WS vs. WS1 3.53 4.49 3.31 4.34Preferred WS vs. WS2 3.59 7.31 2.65 6.38Preferred WS vs. WS3 3.73 7.35 2.48 4.56Preferred WS vs. WS4 4.68 (−)7.50 4.72 7.46Preferred WS vs. WS5 3.02 5.89 2.88 5.32Preferred WS vs. WS7 (+)4.95 4.60 (−)5.88 (−)7.48

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posed for SZ and ASCR, a sensitivity analysis wasnecessary to explore the impact of the assignedweights on the final hazard results. We brieflyreport the main results of this analysis and referto Danciu (submitted for publication) for moredetails.

The sensitivity analysis was performed by con-sidering the selected GMPEs for each tectonicregime (as presented in Tables 9 and 10) anda set of fictitious seismic sources. Two types ofseismic sources were considered: an area sourcezone (ASZ) and a FS. A fictitious ASZ was usedto simulate the seismicity in an ASCR and alsoon subduction intraslab sources. A virtual FS wasused to model an active shallow crustal fault aswell as a subduction interface source.

Four ground-motion intensity measures wereconsidered: peak ground acceleration, PGV, andpseudo-acceleration spectra at the spectral peri-ods of 0.2 and 1.0 s. Seismic hazard maps for eachweighting scheme were obtained for two referencereturn periods: 475 and 2,475 years, the formercorresponding to 10% probability of exceedancein 50 years and the latter indicating a 2% prob-ability of exceedance in 50 years. Additionally,individual hazard maps for each GMPE wereproduced. All the resulting hazard maps wereestimated for a reference rock site, defined byvS30 = 800 m/s. The seismic hazard software(Pagani et al. 2010) developed within the proto-type of GEM, namely the GEM1 project, was usedfor the calculations. Details of the source char-acterization and hazard calculation settings arepresented in more detail in Danciu (submitted forpublication).

The difference between the hazard maps ofthe preferred weighting schemes and those com-

puted from alternative weights was quantifiedby the mean of the percentage differences. Per-centage difference for each grid point was com-puted by:

PerDiff(%) = WS(proposed) − WS(preferred)

WS(preferred)× 100

(5)

where WS(preferred) are the estimated expectedground motion at each grid point from the pre-ferred weighting scheme and WS(proposed) con-tains the values using the alternative weightingschemes. For example, for active crustal regions,the preferred weighting scheme is WS6 and the al-ternative weighting schemes are WS1, WS2, WS3,WS4, WS5, and WS7 as reported in Table 10.Maps showing the percentage difference wereproduced for all ground-motion intensity mea-sures and for the specified return periods. Due tothe limited space, the percentage difference mapsare not reproduced herein, but a summary of thepercentage differences for PGA, PSA (0.2 s), andPSA (1 s) for different weighting schemes is shownin Table 14 for ASCR and in Table 15 for SZ.

For ASCR, the sensitivity analysis shows thatthe absolute difference between the preferredand the proposed weighting schemes varies withinthe range of 5% to 10% for the ASZ and 5%to 15% for the FS. Most of the differences oc-cur when the proposed weighting scheme WS7is compared with the preferred one (WS6). Theexamination of individual hazard maps for eachselected GMPE suggest that the equations pro-posed by Akkar and Bommer (2010) and Chiouand Youngs (2008) dominate the hazard in theareal zones of active shallow crustal tectonic

Table 15 Percentage difference values for SZ for three ground-motion intensity measure types, two seismic source types,and two return periods

Weighting schemes Subduction inslab Subduction interface

475 years (%) 2,475 years (%) 475 years (%) 2,475 years (%)

PGAPreferred WS vs. WS2 (−)8.80 6.81 6.87 (−)6.97

PSA (0.2s)Preferred WS vs. WS2 (−)8.70 8.51 6.83 (−)8.00

PSA (1s)Preferred WS vs. WS2 (−)4.00 1.67 5.45 (−)6.21

The maximum for each source type and return period is highlighted in bold

470 J Seismol (2012) 16:451–473

regimes because they yield higher values whencompared to the other remaining two GMPEs(roughly 30% larger). Cauzzi and Faccioli (2008)and Chiou and Youngs (2008) predict largerground motions in shallow crustal fault sources(roughly 60% larger than the other two GMPEs),thus dominating the hazard for such cases.

In the case of subduction zone, the percent-age difference varies between 4% and 10%. Thedifferences decrease with increasing period valuesfor subduction inslab sources. Contrary to thisobservation, the hazard differences become largeras the vibration period increases for subductioninterface cases. By contrast, for subduction inter-face sources, the difference increases as the returnperiods increase. Zhao et al. (2006) and Youngset al. (1997) were found to be responsible for thelarger values in the seismic hazard for the subduc-tion sources (predicting roughly six times largerground motions than the other two GMPEs).

The overall results of the sensitivity analysis ondifferent weighting schemes suggest that for theconsidered seismic sources, there is a moderateimpact on the hazard results. Sabetta et al. (2005)also concluded that if four or more GMPEs areused in the logic tree, the assigned weights do notsignificantly affect the hazard results. Scherbaumet al. (2005) also indicated that the selection ofthe GMPEs seems to be more important thanthe choice of weighting strategy. In essence, thepractical conclusion of this preliminary sensitivityanalysis led us to keep the present structure ofthe ground-motion logic tree together with thepreferred weights.

7 Conclusions

Although it is now common practice to treat un-certainty in ground-motion prediction with a logictree approach, there is no standard procedure thatdescribes how the tree should be constructed. Inthis paper, we shared our experience on this sub-ject by presenting the strategy that was adopted tobuild a logic tree for Europe within the SHAREproject. This task involved roughly a dozen in-stitutions with the goal, in a limited amount oftime (18 months), to commonly define a logic tree

that would capture the center, body, and range ofground motion in six different tectonic regimes inthe Euro-Mediterranean region.

The principal idea that guided our strategy wasto gather as much knowledge as possible from in-dependent sources and different methods. Basedon the characteristics of the available GMPEsdetermined by Douglas (2008), recently updatedby Douglas (2011), we first identified the bestcandidates using the rejection criteria of Cottonet al. (2006) and Bommer et al. (2010). Afterward,expert judgment highlighted the sets of GMPEsthat were, according to the experts, capable ofcapturing epistemic uncertainties, while testing us-ing observational data showed GMPEs capableof closely predicting past ground motions. Theintegration of these different approaches was un-dertaken to propose logic trees that were thensubjected to a sensitivity analysis to see the impacton the seismic hazard.

From this experience, we have learnt lessonsand identified weaknesses in our methodology.First, a great effort should be dedicated to thecollection of data and meta-data in order to getas much information as possible from the GMPEtesting. In our case, data were not sufficient tocover the center, body, and range of ground mo-tions in Europe. Secondly, the procedure for theselection and weighting of GMPEs by expertsshould be clearly defined. Within the SHAREproject, most experts required more guidance andinformation (e.g., What do weights represent?How will they be used afterward?). Selecting GM-PEs and assigning weights is still not an obvioustask, although Scherbaum and Kühn (2011) haverecently proposed a method. To build a logic treeis not to give a quality measure to each candidateGMPE independently from the others but ratherto identify the set of models that together, with acertain weighting, can capture the perceived epis-temic uncertainty. In the context of the SHAREproject that covers a large area, the set of GMPEshad to be the smallest one.

The robustness of the proposed logic tree is acrucial property. For ASCR, the SHARE GMPEselection is in agreement with the data testing ofDelavaud et al. (2012) who used an independentdataset to rank candidate GMPEs for Europe andMiddle East. Their study also showed that for this

J Seismol (2012) 16:451–473 471

particular dataset, the recent model of Chiou et al.(2010) but also the model of Berge-Thierry et al.(2003) were both able to predict ground motion inEurope and Middle East reasonably well. Regularupdates of the logic tree should be planned to takenew data and new GMPEs into account.

Each project is unique and it is importantto be aware of its particularities. However, wethink that the procedure described above is re-producible and that at least it contributed to thereflections on the way a logic tree for ground-motion prediction should be built.

Acknowledgements The main part of this work has beenfunded by the EC-Research Framework programme FP7,Seismic Hazard Harmonization in Europe, contract num-ber 226967. The authors would like to warmly thankJulian Bommer, Hilmar Bungum, and Fabian Bonilla fortheir expert role and their key contribution to the ground-motion prediction equation evaluation and weighting. Wethank an anonymous reviewer and Jochen Woessner fortheir comments on the first draft of this article. This paperalso benefited from the feedbacks and interaction withDonat Fäh, Ben Edwards, Marco Pagani, Kyriazis Pitilakis,Pierre-Yves Bard, and Carola Di Alessandro. This workstrongly benefited from the constant support of JochenWoessner and Domenico Giardini, manager and coordina-tor of the SHARE FP7 project.

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