probabilistic method to select calculation accelerograms based on

Soil Dynamics and Earthquake Engineering 43 (2012) 174–185

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Soil Dynamics and Earthquake Engineering

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Probabilistic method to select calculation accelerograms based on uniformseismic hazard acceleration response spectra

Antonio Morales-Esteban a,n, Jose Luis de Justo a, Francisco Martınez-Alvarez b, J.M. Azanon c

a Department of Continuum Mechanics. University of Seville, Spainb Department of Computer Science. Pablo de Olavide University of Seville, Spainc Department of Geodynamics, University of Granada, Spain

a r t i c l e i n f o

Article history:

Received 8 March 2012

Received in revised form

19 June 2012

Accepted 8 July 2012

61/$ - see front matter & 2012 Elsevier Ltd. A

x.doi.org/10.1016/j.soildyn.2012.07.003

esponding author. Tel.: þ34616360273; fax:

ail address: [email protected] (A. Morales-Esteban).

a b s t r a c t

A dynamic analysis of a structure requires the previous definition of the accelerograms and the

structure characteristics. The response of a structure subject to a seismic movement can be determined

by two methods: either using the accelerograms recorded near the site, or using visco-elastic response

spectra. The first method should only be used for locations where many accelerograms have been

recorded, and needs a probabilistic calculation to ascertain the design accelerograms. The use of visco-

elastic response spectra is based upon the fact that the response spectrum is the soil movement

parameter better related to the structural response and is more adequate to obtain accelerograms in

regions where the number of records is insufficient. This is the most commonly used method as the

response of structures, in the elastic linear range, can be obtained as the superposition of a few modes

of vibration. A probabilistic method for selecting calculation accelerograms is presented in this paper.

First, the probabilistic hazard equation is solved. Based on the hazard curves obtained, the uniform

seismic hazard acceleration response spectrum (USHARS) is constructed for the location, according to

the type of soil and the required hazard level (exposure time and exceedance probability). Then,

calculation accelerograms are selected. Based on this methodology, real accelerograms, for a return

period of 975 years, have been obtained for San Pedro Cliff (Spain) at the Alhambra in Granada.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction

The dynamic response of a structure affected by a seismicmovement can be estimated by two methods. The first one consistsin defining a theoretical model of the structure and calculating itsdynamic response due to a given movement of its foundation. Theother method, which is approximated, consists in separating thecharacteristic of the structure and the characteristics of the seismicmovement, represented by the response spectra.

To keep a balance between economy and security, currentseismic regulations generally accept that, for large earthquakes,structures might suffer non-linear deformations without collap-sing. The non-linear dynamic analysis more used is the calcula-tion, step by step using accelerograms. This procedure can beused at the linear and non-linear range. A structural analysis of allthe accelerograms considered must be worked out, and a calcula-tion envelope must be obtained. The dynamic calculation envel-ope must be later combined with the static loading envelope.This procedure implies a significant work; it is only used for the

ll rights reserved.

þ34954541007.

design of very important structures and only in the last stages ofthe calculation procedure. In some regions, with a vast historyof large earthquakes, such as Japan and California, a wide networkof recording stations is available and provides many records forlarge earthquakes, for different types of soils and for a wide rangeof distances. In regions of minor seismicity, the network ofrecording stations is not so wide, or is not old enough, so thatthe number of records is insufficient. For the analysis of minorseismicity activity regions, records from other regions are used, orartificial accelerograms are generated.

Between 5 and 10, real or artificial, accelerograms, must beobtained, and must be scaled to a level of severity. The mostcommonly used method consists of scaling the seismic peakacceleration up to a predetermined probabilistic level. However,the potential damage an earthquake can produce is not only afunction of the peak acceleration; there are many alternativessuch as the Arias intensity and the spectral intensity of Housner[24,34] more related to the potential damage.

The use of visco-elastic response spectra, based on the answerof structures at the elastic linear range can be estimated by thesuperposition of a few modes of vibration and is the mostcommonly used method due to its simplicity and appropriateaccuracy.

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A. Morales-Esteban et al. / Soil Dynamics and Earthquake Engineering 43 (2012) 174–185 175

A method to estimate the uniform seismic hazard accelerationresponse spectrum (USHARS) is presented, based on it calculationaccelerograms can be selected.

2. Fundamentals

This section exposes the fundamentals that support the meth-odology applied to calculate the seismic hazard. First, seismichazard is defined. Then, the methods used to calculate the seismichazard are presented and discussed.

Seismic hazard of a location can be defined as the probabilityto equal or exceed a parameter of the soil movement, produced bythe earthquakes that occur on the influence area, during aspecified lapse of time. To unify criteria, UNESCO proposed thecommonly accepted definition, given by UNDRO [43]. Hazard (H)is defined by a probability function of the characteristic para-meter of the soil movement (S) at the location (x) according to:

H¼ P½SðxÞZS0; t� ð1Þ

where P represents the probability of exceeding a threshold value(S0) of the characteristic parameter of the soil movement, duringthe time (t), in years.

Seismic hazard is defined as a probabilistic function, where thevalue of the soil movement, that can be considered dangerous,must be specified and the time of exposure must be established.

The following methods to estimate the seismic hazard may beused: deterministic methods, probabilistic methods, historicaland deductive methods and other methods.

2.1. Deterministic methods

The first methods to establish the seismic hazard of an area ora location were deterministic. The characteristic parameter of thesoil movement used is usually the peak ground acceleration(PGA). The deterministic methods assume the hypothesis thatthe seismicity is stationary, considering that earthquakes in thefuture will be similar to those in the past. The upper limit of themovement, expressed as the maximum value of the parameter, isestimated. These earthquakes can be real earthquakes that in thepast affected the location, or can be deduced from the seismic andtectonic characteristics of the area. The deterministic method canbe divided into zoned or not-zoned, in function of how theseismicity distribution is considered.

The calculation procedure is [39]:

1.
Definition of the influence area of the location, and identifica-tion of the seismic sources or faults within it.
2.
Estimation of the largest earthquakes that have occurred in theinfluence area or at any of the source areas.
3.
Estimation of the seismic parameter at the location, caused bythe maximum potential earthquakes of every area or of thewhole area.
4.
Determination of the hazard at the location, taking the max-imum value generated by the influence areas. Hazard isdefined by the upper limit of the movement at the location.
This method presents some advantages and disadvantages. Itsmain advantage is its easy application. It defines earthquakes thathappened in the past and supposes that similar earthquakes willhappen in the future. Normally, these methods define the mostunfavourable seismic situation (the largest earthquake in theclosest source). However, the probability that these earthquakeswill happen in the future is, generally, unknown. The determi-nistic method estimates the largest earthquake that can affectthe location, while the rest of earthquakes are not considered.

The sources are characterised by the largest earthquake, and notby its recurrence law.

2.2. Probabilistic methods

Later, the probabilistic methods were defined by Cornel [14].The probabilistic methods sum up the contribution of all thepossible earthquakes that can affect a location, and considerrecurrence laws for them. As a result, the probability of exceedingevery value of a parameter of the soil movement expected at thelocation, during a period of time, is estimated. The hazard isrepresented by probability curves. The development of the soilstrong motion prediction models allowed the construction ofdesign spectra, where the probability to exceed all the spectraordinates is considered (and not only peak acceleration). Theuniform hazard spectra represent the predicted values for areturn period of all the spectral ordinates [42]. These methodsare classified into parametric and non-parametric, according tothe statistical distribution adopted.

2.2.1. Non-parametric methods

These methods analyse the hazard according to extreme valuedistribution functions. The most used were defined by Gumbel [23].The method is based on the following steps:

1.
Definition of the area of influence around the location. 2. Calculation of the values of the seismic parameter at the
location, applying attenuation laws to the values of theparameter, that reflect the seismicity of the area during theperiod of time considered.

3.
Adjustment to a distribution of extreme values of the randomparameter, defined with the values of the estimated para-meter, and estimation of the distribution coefficients.
4.
Estimation of the probability of exceeding the extreme value,during the time considered, calculating, thus, the probability.
2.2.2. Parametric methods

The methodology was initially proposed by Cornell [14]. Themethod is based on the existence of different seismogenic areas.First, the influence area is divided into seismogenic areas and theseismicity of every area is adjusted according to a recurrence law.Later, the contribution of all the sources is added to obtain aprobability function that represents the hazard at the location.

The uniform hazard spectrum is a very useful tool for SeismicEngineering, mainly for structures with various degrees of free-dom, for which a uniform hazard level is demanded [5]. Recently,methods to evaluate seismic hazard that combine probabilisticand deterministic characteristics have been proposed. Most ofthese methods are specially developed for the design of seismicstructures at specific locations [40,35,36,32].

Currently, specially for academic studies, deterministic meth-ods [13,30] and probabilistic methods are used [41,21]. Althoughsome regulations suggest the use of both methodologies [25],generally the use of probabilistic methods is prioritised [9],particularly for nuclear security [20,33].

2.3. Historical and deductive methods

Historical methods do not make hypotheses about the char-acteristics of the faults and the seismic parameters that mightcause earthquakes [45]. However, deductive methods makehypotheses about the origin of earthquakes.

A. Morales-Esteban et al. / Soil Dynamics and Earthquake Engineering 43 (2012) 174–185176

2.4. Other methods

Traditional methods for the seismic hazard calculate theprobability of exceeding an established level of the soil movementat the location. On the other hand, these methods do not assessthe joint probability to exceed those levels of the soil movementat multiple locations.

Aforementioned, probabilistic methods allow calculating uni-form hazard spectra, which are better related to the structuralresponse. For this reason, a probabilistic method has been used inthis paper.

Table 1Seismogenic areas of Spain and Portugal.

Area Description

1 Granada basin

2 Penibetic area

3 Area to the East of the Betic system

4 Quaternary Guadix-Baza basin

5 Area of moderate seismicity to the North of the Betic System

6 Area of moderate seismicity including the Valencia basin

7 Sub-betic area

8 Tertiary basin in the Guadalquivir depression

9 Algarve area

10 South-Portuguese unit

11 Ossa Morena tectonic unit

12 Lower Tagus Basin

13 West Portuguese fringe

14 North Portugal

15 West Galicia

16 East Galicia

17 Iberian mountain mass

18 West of the Pyrenees

19 Mountain range of the coast of Catalonia

20 Eastern Pyrenees

21 Southern Pyrenees

22 North Pyrenees

23 North-Eastern Pyrenees

24 Eastern part of Azores–Gibraltar fault

25 North Morocco and Gibraltar field

26 Alboran Sea

27 Western Azores–Gibraltar fault

3. Methodology

In this section the methodology applied to select calculationaccelerograms is presented. First, the probabilistic method isdescribed. Then, the probabilistic method is itemised into its fourparts: the seismicity model, the recurrence model, the attenua-tion law and the probabilistic hazard equation. Later, the prob-abilistic hazard equation is solved and the method to obtain theUSHARS is described. Finally, the equations to select calculationaccelerograms from the USHARS are described.

3.1. Probabilistic method to estimate seismic hazard

Seismic hazard is represented by a hazard function (H) thatindicates the characteristic parameter of the soil movement (S),according to the following equation:

HðS0; tÞ ¼ PðSZS0; tÞ ð2Þ

where P(SZS0;t) is the probability that the characteristic para-meter of the soil movement will exceed a threshold value, S0, atleast once during the time, t.

The arrival of earthquakes to a location is assumed to follow aPoisson’s stationary process [14,45]. Under this hypothesis, thehazard function can be expressed as follows:

HðS0; tÞ ¼ 1�e�lðS0Þt ð3Þ

where l(S0) is the annual rate of times that the parameter (S0) hasbeen exceeded at the location.

To conduct a study of the seismic hazard, a database ofearthquakes that can affect the location must be provided. If thevalue of the characteristic parameter of the soil movement, inevery one of these earthquakes, is known and the database iscomplete, even with the largest earthquakes that can affect thelocation, the annual rate of exceedance could be calculatedaccording to the following formula:

lðS0Þ ¼1

tc

Xk

dðSk�S0Þ ð4Þ

where tc is the duration of the database, Sk is the value of thecharacteristic parameter of the soil movement during the k-th

earthquake of the database, and d is Heaviside�s function:

d Sk�S0ð Þ ¼1-Sk�S0Z0

0-Sk�S0o0

(ð5Þ

Eq. (4) provides a good estimation of l(S0) only if all theearthquakes, that can affect the location, have been presentedvarious times during the period of time the database covers. Thisimplies that the database should have a very long duration,probably of thousands of years [19].

If an instrumental parameter is taken as characteristic of thesoil movement, the annual rate of exceedance l(S0) cannot beobtained by means of (4) as there are no databases of enoughduration.

In this case, the seismic sources and the attenuation laws of thesoil movement, from the source to the location, must be analysed.The steps to follow with this method were proposed by Cornell [14]:

1.
Seismicity model: definition of the seismogenic areas that canaffect the site. If the seismicity can be considered homogenousin the whole seismogenic area, a unique seismicity source ofglobal influence can be defined.
2.
Recurrence model: the recurrence model in every seismogenicarea must be defined. If it is admitted that the seismicity israndomly distributed and it adjusts to the Gutenberg–Richterlaw with upper truncation, the parameters of the law (a and b)are characteristics of the model. Moreover, for every areamaximum and minimum magnitudes are defined that estab-lish the validity limits of the model.
3.
Attenuation law: attenuation laws to obtain the selectedparameter in function of the distance must be determined inorder to evaluate the seismic hazard. The application of theselaws over the seismicity of every area, represented by itsrecurrence law, allows obtaining the result over the site.
4.
Probabilistic hazard equation: the estimation of the totalhazard is obtained adding up the probabilities obtained bythe result of all the areas that affect the site.
H¼Xn

i ¼ 1

1�e�tl� �

ð6Þ

where l is the annual rate of earthquakes, occurring in any areathat produces a parameter of the soil movement superior to thereference one at the studied site, n is the number of areas and t isthe period of time considered, in years.

The uniform seismic hazard response spectra are those thathave the same probability of being exceeded in all the periods,obtained with the method proposed by Cornell [14].

3.1.1. Seismicity model

Seismicity can be assimilated to a process of punctual eventsthat result from the relaxation of stress that acts over an area.


For its study, the spatial distribution of the earthquakes and itsoccurrence, according to time, must be known.

The areas or seismic sources, named seismogenic areas, arelithosferic volumes associated to certain tectonic characteristics,where earthquakes with similar tectonical origin are supposed tohappen. The process of earthquake generation is spatially andtemporarily homogenous in every area. A seismogenic source,generally, is related to one or a few active faults [4] and itslocation and geometry is of great importance to evaluate itshazard. The task of delimiting seismogenic areas depends on theavailable information of the studied region. When sources corre-spond to inter-plate areas, are associated to large active faults andprobably superficial, it is much easier to identify them. Contrarily,when the sources correspond to intra-plates, that are not asso-ciated to active faults, the task can be very difficult.

When the seismogenetic sources are vast and it is difficult todelimit all the included active faults, it is necessary to establishseismotectonic delimitation, that is, a subdivision of the territoryunder study in areas with a homogenous seismic behaviour froma tectonic point of view.

The model used in this text is based on the seismogenic areasdefined by Morales-Esteban et al. [38]. The twenty seven areasestablished for the Iberian Peninsula are based on tectonic,geological, seismic and gravimetric data. The twenty seven areas

42°N

12°W33°N

36°N

39°N

9°W 6°W

9°W

3°W

45°N12°W

6°W 3°W

12

789

10

11

12

13

14

15

1618

24

25

26

27

Fig. 1. Seismogenic areas of Spain and Portugal. Dots represent earthquakes of momen

magnitude larger than 5.0.

are described in Table 1 and Fig. 1 (Seismogenic areas that mightaffect Spain and Portugal. Dots represent earthquakes of momentmagnitude between 3.0 and 4.0, circles between 4.0 and 5.0, andsolid circles of magnitude larger than 5.0).

3.1.1.1. Seismicity in the Iberian Peninsula. Currently, the convergencedirected NWSE, between Africa and Eurasia, throughout this part ofthe limit between plates, is responsible for the deformation of thecrust of the Iberian Peninsula, the Maghreb, and the adjacent coastalareas of the Mediterranean and the Atlantic [3,31,26]. The plateslimit is not homogenous, with consecutive oceanic and continentalareas in contact and progressive changes in the stress direction. Thearea corresponding to the Iberian Peninsula and the northwest ofAfrica can be considered the most complicated contact area, with amoderate seismicity in relation to the magnitude of the earthquakes.This area is surrounded at both sides by a frequent seismic activitywith very large earthquakes [22,44]. The seismic activity of this areais of great importance as large earthquakes have been produced inthe past such as the Lisbon 1755 earthquake. The coexistence ofcompressive and extensive tectonics, and the interference of theIberian micro-plate [2,12], makes the understanding of the area verycomplicated and many issues of the tectonic structure of the area areprompting discussion among experts. The regional seismicity is

3°E0°

36°N

39°N

0°W 3°E

33°N

42°N

45°N

6°E

6°E

1000 200 300 km

34

5 6

17 19

202122

23

t magnitude between 3.0 and 4.0, circles between 4.0 and 5.0, and solid circles of


diffuse and is not clearly aligned with the current limit between theplate of Eurasia and Africa, at the south of the Iberian Peninsula [11].The seismic activity extends to far away inter-plate areas, such as thenortheast and the centre of the Iberian Peninsula.

The seismicity in Spain and Portugal is characterised by theoccurrence of moderate earthquakes, with a magnitude generally

Table 2Axis orientation, regime of stress, maximum magnitude and predominant type of

faulting for the seismogenic areas of the Iberian Peninsula.

Area Regime Axis orientation Predominant type of faulting Mmax

1 Compressive PEN1701E Normal 7.0


3 Compressive PEN1701E Strike-slip 7.0





8 Compressive PEN1701E Thrust 6.5









17 Compressive TEN451E Strike-slip 5.5











Fig. 2. Axis orientation, stress regime and type of faulting for the

less than 5. Large earthquakes are separated by long periods oftime [10]. Many of the earthquakes are located at the east of theGibraltar Arch and spread over a diffuse area, of approximately500 km wide, centred at the Alboran Sea, containing parts of thesoutheast of Spain, the north of Morocco and Algeria. The limitbetween the plates of Africa and Eurasia is, currently, a matterunder investigation [26]. At the west of Gibraltar, most earth-quakes happen in the southern coast of Portugal next to the limitbetween the plates of Azores and Gibraltar. Other seismic sourcesinclude the northwest of Spain and the Pyrenees. Earthquakesrarely happen in other location. This seismicity so widespreadhappens over geo-tectonic areas with different structure andrheology. At the Iberian Peninsula, at least three different tectonicregimes can be differentiated: stable blocks, alpine mountainbelts and extension basin.

The work by Morales-Esteban [37] has studied the faultingmechanism for the seismogenic areas of the Iberian Peninsulaproposed by Morales-Esteban et al. [38]. In Table 2 and Fig. 2(Axis orientation, stress regime, maximum magnitude and type offaulting for the seismogenic areas defined by Morales-Estebanet al. [38] for the Iberian Peninsula) the orientation, for the 27seismogenic areas, of the main fault axes is shown.

3.1.1.2. Seismicity at San Pedro cliff in Granada. Granada basinpresents several sets of faults, most notably those with E–W andNW–SE orientations. Conspicuous NW–SE faults are present in theeastern part and the eastern limit of the basin. These faults arenormal, mostly with a NW–SE orientation, and dipping towards theSW. These NW–SE faults cross-cut and displace previous E–Wfaults, defining the main subsiding areas of the central andeastern part of the basin. Fig. 3 (Annual rate of earthquakes bysquare kilometre and b-value for the seismogenic areas defined byMorales-Esteban et al. [38] for the Iberian Peninsula) shows theb-value and the annual rate of earthquakes by square kilometre forthe 27 seismogenic areas. It can be observed that the annual rate ofearthquakes in the Granada basin (area 1) is clearly the highest.

seismogenic areas defined in [37] for the Iberian Peninsula.

Table 3Annual rate of earthquakes, maximum magnitude and b-value for the seismogenic

areas that affect Spain and Portugal.


However, the b-value is an average (a low b-value implies that theprobability of large earthquakes to happen is high). This means thatearthquakes in Granada are very frequent (clearly the most activeseismogenic area) although, normally, not of large magnitude.

3.1.2. Recurrence model

The seismicity in every seismogenic area is randomly distrib-uted and it adjusts to the Gutenberg–Richter law. In seismichazard studies, the Gutenberg–Richter law must be truncated,with upper and lower limits, to consider the magnitude, Mmax, ofthe largest earthquake that can occur at the source, and to avoidconsidering earthquakes of magnitude less than Mmin, respec-tively. The probability density function of magnitude forGutenberg–Richter law is:

f ðMÞ ¼ beb M�Mminð Þ

1�eb Mmax�Mminð Þð7Þ

The seismicity in every seismogenic area is defined by thefollowing parameters:

Area b-value Annual rate of

earthquakes

Surface

(km2)

Anual rate/ surface

(km2)

Mmax

1.
The maximum and minimum magnitude.
1 1.41 5.14 3835 1.34E-03 7.0
2. 2 1.18 7.82 13,979 5.59E-04 6.5
The annual rate of earthquakes occurrence betweenMmax and Mmin.

3 1.29 4.36 13,251 3.29E-04 7.0
3. The b-value of the Gutenberg–Richter law (b¼b/log e). 4 1.27 2.26 11,957 1.89E-04 6.0
5 1.62 0.87 7066 1.24E-04 5.5

6 2.17 1.38 9735 1.42E-04 6.5

7 1.51 4.32 13,954 3.10E-04 6.0

8 0.92 1.47 22,228 6.63E-05 6.5

9 1.20 0.77 6371 1.21E-04 6.0

10 2.33 2.56 15,717 1.63E-04 5.5

11 1.44 2.35 27,694 8.47E-05 5.5

12 1.01 0.50 9803 5.08E-05 7.0

13 1.29 1.41 13,029 1.09E-04 5.5

14 1.40 1.75 26,049 6.71E-05 5.5

15 2.07 4.02 22,597 1.78E-04 5.5

16 1.54 2.87 15,475 1.85E-04 6.0

17 1.75 1.07 26,993 3.96E-05 5.5

18 1.54 0.58 15,738 3.70E-05 6.0

19 1.90 1.18 16,032 7.35E-05 5.5

20 1.63 1.68 10,622 1.58E-04 6.0

21 1.53 2.63 19,946 1.32E-04 5.5

22 1.48 12.32 22,383 5.51E-04 5.5

23 1.46 2.06 4301 4.78E-04 6.0

24 0.96 13.55 46,329 2.92E-04 7.0

25 0.96 5.85 24,600 2.38E-04 5.5

26 1.14 18.21 48,669 3.74E-04 6.5

27 0.70 15.16 38,955 3.89E-04 8.5

The maximum magnitude in every seismogenic area has beendetermined by Morales-Esteban et al. [38] from seismic andtectonic considerations. The minimum magnitude in all areas is4.5. Lower earthquakes are not considered dangerous. Normally,seismologists only consider earthquakes of magnitude equal orlarger to 5.0. However, not very large earthquakes but close to thesource are known to have caused damage. Moreover, earthquakesin the Iberian Peninsula are known to be of moderate magnitudeand magnitudes over 5.0 are uncommon. The b-value, the

maximum magnitude and the annual rate of earthquakes can beobtained from Table 3.

3.1.3. Attenuation law

Equations for the estimation of the parameters of the soilmovement are a basic tool for the calculation of the seismichazard.

Attenuation laws are functions that relate a parameter of thesoil movement (peak acceleration, spectral acceleration, relativevelocity response spectra, etc.) with the magnitude, the distance

234

5

6

7

8

9

10

13

12

2114

15

16

17

18

19

2011 2223

242526

27

0.00

0.50

1.00

1.50

2.00

2.50

0.00E+00 2.00E-04 4.00E-04 6.00E-04 8.00E

b

Annualrate/

Fig. 3. Annual rate of earthquakes by square kilometre and b-value fo

to the source, and sometimes, with some other variables. After themagnitude, the distance to the source and the type of soil at thelocation, the most used parameter, for attenuation laws, is thetype of fault. From a database of soil movements an attenuationlaw can be obtained through a regression analysis.

The characteristic parameter of the soil movement, used in thistext, is the spectral acceleration (SA). SA is the most suitableparameter to select accelerograms because it is the soil move-ment parameter better related to the structural response.

The equations for the estimate of ground motions fromshallow crustal earthquakes from Morales-Esteban [37] have beenused. These coefficients were obtained from strong motionsrecorded in Europe and the Middle East which are consistentwith the location under study (the Iberian Peninsula). Douglas

1

-04 1.00E-03 1.20E-03 1.40E-03 1.60E-03Area(km2)

r the seismogenic areas defined in [37] for the Iberian Peninsula.


[17] has showed that recorded strong ground motion in theCaucasus region, central Italy, Friuli, Greece and south Icelandshows little evidence for regional differences. However, he foundevidence for regional differences in ground motions betweenEurope and California [18].

The magnitude scale used is the moment magnitude, Mw, [29].The use of the moment magnitude avoids the saturation of thetraditional magnitude scales for the larger earthquakes and,consequently, is considered a better measure of the real size ofan earthquake [6]. Earthquakes with Mwo4.5 have been excludedin order to avoid earthquakes that are unlikely to be of engineer-ing significance. Ambraseys et al. [1] in its regression analysis forEurope, only consider earthquakes of magnitude larger than 5.0.However, the minimum in this study has been reduced to 4.5, asthe seismicity in the Iberian Peninsula is moderate and fewearthquakes exceed a moment magnitude of 5.0.

Fault distance has been defined as the minor distance to thesurface projection of the fault as proposed by Joyner and Boore [27]also known as Joyner–Boore distance. Douglas [16] has demon-strated that using the distance to the rupture does not reduce thestandard deviation for ground motion prediction equations.

The scheme proposed by Bommer et al. [7] has been usedto classify the local geology. This scheme uses the averageshear wave velocity, estimated at a depth of 30 m (Vt30). Thereforefour site classes have been used: rock, Vt304750 ms�1; hard soil,360 ms�1oVt30r750 ms�1; soft soil, 180 ms�1oVt30r360 ms�1 and very soft soil, Vt30r180 ms�1.

Currently there are many criteria to classify the faultingmechanisms Boore et al. [8] which can lead to different classifica-tions for the same earthquake [7].

The coeficients to obtain the SA, for the 25 periods calculatedand for the 0, 2, 5, 10 or 20 per cent damping, can be obtainedfrom Morales-Esteban [37]. The predominant type of faulting forevery seismogenic area has been considered for the attenuationlaws according to Table 2.

3.1.4. Probabilistic hazard equation

It is admitted that the arrival at the site of earthquakes thatexceed the reference value, log S0, follows a Poisson stationaryprocess, defined by Gutenberg–Richter law of constant li:

li ¼ ui

Z Mmax

Mmin

Pðlog SZ log S0=M,DÞf ðMÞdM ð8Þ

1

2

47

8

26

3

Fig. 4. Scheme of division of a seismogenic area into

The seismic rate of the punctual source is ui and f(M) is theprobability density function of magnitude (Eq. (7)).

If N punctual seismic sources hit simultaneously the site, therate l of arrivals at the location that exceed the reference valuelog S0 is:

l¼XN

i ¼ 1

li ð9Þ

The probability of exceeding the reference value log S0 duringa time t caused by the simultaneous action of N punctual seismicsources is:

P logSZ logS0; tð Þ ¼ 1�e�lt ð10Þ

Its return period can be obtained from:

T ¼1

l¼

�t

lnð1�PðlogSZ logS0; tÞÞð11Þ

Eq. (8) cannot be applied to the hazard calculation as theseismogenic areas have been modelled as areas and not aspunctual seismic sources. To solve this problem, the seismogenicareas are divided into elements small enough to be assimilated topunctual seismic sources (Fig. 4. Scheme of division of a seismo-genic area into N punctual areas, through an orthogonal mesh).

3.2. Uniform seismic hazard acceleration response spectrum

A computer programme that divides the seismogenic areasinto punctual seismical sources that affect the location thatintegrates numerically Eq. (8) and calculates the exceedanceprobability with Eq. (10) has been developed.

With this method, the probability of exceeding a value of theacceleration response spectra for an established time of exposurecan be calculated. Following this methodology a plot of theseismic hazard is obtained (Fig. 5).

If this process is repeated for various periods of the structureand, for every seismic hazard plot, the value of the spectrum forthe same exceedance probability is obtained, and a uniformseismic hazard acceleration response spectrum (USHARS) can beobtained, point by point, as shown in Fig. 6 (Scheme of construc-tion of a uniform seismic hazard response spectrum from theseismic hazard plots).

1

444

4 44 4444

4 4 4444

44 4444

4 444

42222

1 1 1 1 1 1 1 1 1 111111 1 1 1 1 1 1 1 1 1 111111 1 1 1 1 1 1 1 1 1 111111 1 1 1 1 1 1 1 1 1 111111 1 1 1 1 1 1 1 1 1 111111 1 1 1 1 1 1 1 1 1 111111 1 1 1 1 1 1 1 1 1 111111 1 1 1 1 1 1 1 1 1 111111 1 1 1 1 1 1 1 1 1 111111 1 1 1 1 1 1 1 1 1 11111 1 1 1 1 1 1 1 1 1 1111 1 1 1 1 1 1 1 1 1 111 1 1 1 1 1 1 1 1 1

1 1 1 1

1 1 1 1 1 1 1 1 1 111111 1 1 1 1 1 1 1 1 11111 1 1 1 1 1 1 1 1 1111 1 1 1 1 1 1 1 111 1 1 1 1 1 1 1 1

111

1111

1 111

1 1 111

1

Nc punctual areas, through an ortogonal mesh.


3.3. Selection of calculation accelerograms

The procedure to select design accelerograms is:

1.

Figacc

dum

The time of exposure of the structure is established, accordingto the hazard level.

2.
The admitted exceedance probability is established, normally a5–10%, according to the hazard level.
. 5. Comparison for different exposure time of the seismic hazard plot of the

eleration response spectrum. Granada for a 0.50 s period, in rock, a 5% relative

ping.

P0 P0

T1

S1

S2S3S1

T1 T2

Fig. 6. Scheme of construction of a uniform seismic haza

3.

S

rd r

The USHARS for the location is calculated according to the typeof soil and the required hazard level (time of exposure andprobability of exceeding).

4.
Records from the accelerograms database, registered in thesame type of soil of the location, are examined. The factor ofscale, f, between the logarithm of the USHARS calculated andthe logarithm of the response spectrum which corresponds tothe real spectrum, that minimises the standard deviation, s, iscalculated.
So, if SR is the response spectrum correspondent to the realregister, and SC is the calculated response spectrum, the standarddeviation is:

s¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPlogðf USRÞ�logðSCÞ� �2

25

sð12Þ

The scale factor that minimises the standard deviation is:

f ¼SlogSC�SlogSR

25ð13Þ

The sum is extended to the 25 periods for which the USHARShas been calculated. The records for which the standard deviationis minor are selected.

4. Application to San Pedro cliff

The Alhambra in Granada is one of the most importantnational monuments in Spain. This monument, a World Heritagesite, is located on the top of a red hill that dominates a plain, theGranada basin, where most of the city is placed. One of the mostimportant rivers of the region, River Darro, flows into the basinand is situated on the western part of the city. The Alhambra’swalls are close to the escarpments generated by the incision ofthis river. Slope instability of the escarpments on this side of theAlhambra hill has been a critical problem since the constructionof this palace. In this area, San Pedro Cliff (Fig. 7), a dihedral65.5 m high, is the steepest escarpment of the Alhambra hill. Thiseroding cliff reaches to 23.8 m from the Alhambra palace wall.

P0

T2 T3

2 S3

T3

esponse spectrum from the seismic hazard plots.

(4

Fig. 7. South view of San Pedro Cliff, showing to the right the fault line scarp. Above stand the Alhambra walls and, at the foot, Darro River and Albaicin houses.

Fig. 8. Comparison of the seismic hazard plot of the acceleration response spectra

of period 0.50 s for Granada for different type of soils, for a 5% relative damping

and a time of exposure of 50 years.

Fig. 9. Comparison for different damping ratios of the seismic hazard plot for the

acceleration response spectra. Period 0.20 s, in rock for a time of exposure of

50 years for Granada.


Retreat of this cliff has occurred through superficial slab fallsmainly induced by the floods of the Darro River, the looseningproduced by the extensional tectonic regime, erosion, seepagecoming from the Alhambra palace and earthquakes.

As an example of the methodology presented in this paper,calculation accelerograms for San Pedro Cliff are selected. First,seismic hazard curves for the SA for San Pedro Cliff have beenobtained. Fig. 8 (Comparison of the seismic hazard plot of theacceleration response spectra for different soil types. Site Gran-ada; period 0.50 s; relative damping 5%; time of exposure50 years) shows the curves for a period of 0.5 s, for a 5% relativedamping and a time of exposure of 50 years, as a function of thesoil type. Fig. 9 (Comparison for different damping ratios of theseismic hazard plot for the acceleration response spectra. SiteGranada and rock foundation; period 0.20 s; time of exposure 50years) compares the seismic hazard curves, as a function of therelative damping, for the acceleration response spectra of period

0.20 s and for a time of exposure of 50 years. Fig. 5 compares theseismic hazard curves as a function of the time of exposure(50 and 100 years) in rock, for a period of 0.50 s and a relativedamping of 5%.

Secondly, the type of soil at the location must be known. A siteinvestigation was conducted by Justo et al. [28]. The followinglayers appear from top to bottom in the geological profile:

(1)
Dense conglomerate. Vs¼800 m/s (transverse wave velocity). (2) Very dense conglomerate. Vs¼960 m/s. (3) Moderately dense conglomerate. Vs¼800 m/s. (4) Very dense, gravelly and sandy conglomerate. Vs¼1150 m/s.
.a) One metre thick clay layers, interspersed in layer (4).Vs¼800 m/s.

Talus appears at the foot of the slope, composed of quartzoseand phyllitic blocks, gravel and sand, with predominance of thesand fraction.


The whole Cliff lies over the very dense, gravelly and sandyconglomerate layer. Therefore, the transverse wave velocity at30 m (Vs30) is 1150 m/s. The transverse wave velocity wasobtained through down-hole and cross-hole tests [28].

Thirdly, the methodology described to obtain the USHARS hasbeen applied to San Pedro Cliff, for rock (VsZ750 m/s), for a 5%probability of being exceeded and a time exposure of 50 years,which is equivalent to a return period of 975 years.

Finally, accelerograms from the [15] European earthquakedatabase, that are available on-line, recorded in rock, have beencompared with the USHARS, obtained for San Pedro Cliff. Theaccelerograms selected are those whose standard deviation isminor. A total of 10 accelerograms, whose standard deviation islower to 0.13, have been obtained. The European Strong Motiondatabase provides the fault distance, which is the criteria used tocharacterise the distance from selected site to source in thispaper. The fault distance for the 10 selected accelerograms variesfrom 11 km (record 365) to 65 km (record 5826).

Figs. 10 and 11 represent the USHARS for San Pedro Cliffand the response spectra of the real earthquakes with better

Fig. 10. Seismic hazard acceleration response spectra for San Pedro Cliff. Exceedance

Comparison between the calculated uniform acceleration response spectrum, the spect

and this spectrum scaled to minimise the standard deviation.

Fig. 11. Seismic hazard acceleration response spectra for San Pedro Cliff. Exceedance

Comparison between the calculated uniform acceleration response spectrum, the spe

catalogue and this spectrum scaled to minimise the standard deviation.

adjustment. The scaled spectrum that minimises the standarddeviation has also been plotted. The information about therecords that minimise the standard deviation is shown inTables 4 and 5.

5. Conclusions

A method to select real accelerograms for dynamic calculationanalysis is presented in this paper. This method has beendesigned as a general method for any location of the IberianPeninsula.

The visco-elastic response spectrum has been used to selectdesign accelerograms which is consistent with the number ofaccelerograms available for the Iberian Peninsula. It is known aswell that a response spectrum is the soil movement parameterbetter related to the structural response.

A parametric probabilistic method, based on seismogenicareas, has been used to calculate the seismic hazard. The meth-odology presented in this paper allows the use of other methods

probability 5%; relative damping 5%; rock foundation; time of exposure 50 years.

rum corresponding to record 128, whose fault distance is 19 km, from the catalogue

probability 5%; relative damping 5%; rock foundation; time of exposure 50 years.

ctrum corresponding to record 990 128, whose fault distance is 13 km, from the

Table 4Information about the records whose typical deviation is minor in relation to the

uniform seismic hazard acceleration response spectra for San Pedro Cliff for an

exceedance probability of 5%, a time of exposure of 50 years, rock foundation and a

relative damping 5%.

Earthaquake record 128Seismical dataEarthquake: Friuli (Northern Italy)

Date: 9/15/1976

Magnitude: 6.0 Mw

Record dataStation: Robic (Slovenia)

Type of soil: Rock

Fault distance: 19

f 1.2

s 0.016

SAmax(m/s2) 3.96

Earthaquake record 201Seismical dataEarthquake: Montenegro (Adriatic Sea)

Date: 4/15/1979

Magnitude: 6.9 Mw

Record dataStation: Dubrovnik-Pomorska School (Croatia)

Type of soil: Rock

Fault distance: 61

f 1.15

s 0.087

SAmax(m/s2) 2.68

Earthaquake record 361Seismical dataEarthquake: Umbria (Center of Italy)

Date: 4/19/1984

Magnitude: 5.6 Mw

Record dataStation: Nocera Umbra (Italy)

Type of soil: Rock

Fault distance: 19

f 1.23

s 0.028

SAmax(m/s2) 7.49

Earthaquake record 365Seismical dataEarthquake: Lazio Abruzzo (Southern Italy)

Date: 5/7/1984

Magnitude: 5.9 Mw

Record dataStation: Atina (Italy)

Type of soil: Rock

Fault distance: 11

f 1.12

s 0.13

SAmax(m/s2) 3.83

Earthaquake record 990Seismical dataEarthquake: Lazio Abruzzo, aftershock (Southern Italy)

Date: 5/11/1984

Magnitude: 5.5 Mw

Record dataStation: Atina–Pretura Terrazza (Italy)

Type of soil: Rock

Fault distance: 13

f 1.22

s 0.011

SAmax(m/s2) 6.11

Table 5Information about the records whose typical deviation is minor in relation to the

uniform seismic hazard acceleration response spectra for San Pedro Cliff, an

exceedance probability of the 5%, a time of exposure of 50 years, rock foundation

and a relative damping of 5%.

Earthaquake record 5826Seismical dataEarthquake: Strofades (Jonic Sea)

Date: 11/18/1997

Magnitude: 6.6 Mw

Record dataStation: Kyparrisia-Agriculture Bank (Greece)

Type of soil: Rock

Fault distance: 65

f 1.13

s 0.129

SAmax(m/s2) 2.76

Earthaquake record 6265Seismical dataEarthquake: Southern Iceland

Date: 6/17/2000

Magnitude: 6.5 Mw

Record dataStation: Burfell Hydroelectric Station (Iceland)

Type of soil: Rock

Fault distance: 25

f 1.16

s 0.076

SAmax(m/s2) 2.58

Earthaquake record 6270Seismical dataEarthquake: Suthern Iceland

Date: 6/17/2000

Magnitude: 6.5 Mw

Record dataStation: Ljosafoss Hydroelectric Station (Iceland)

Type of soil: Rock

Fault distance: 32

f 1.23

s 0.026

SAmax(m/s2) 2.06

Earthaquake record 6331Seismical dataEarthquake: Southern Iceland, aftershock

Date: 6/21/2000

Magnitude: 6.4 Mw

Record dataStation: Flagbjarholt (Iceland)

Type of soil: Rock

Fault distance: 22

f 1.17

s 0.057

SAmax(m/s2) 1.90

Earthaquake record 7480Seismical dataEarthquake: St. Die (France)

Date: 2/22/2003

Magnitude: 4.7 Mw

Record dataStation: Bremgarten (Germany)

Type of soil: Rock

Fault distance: –

f 1.25

s 0.058

SAmax(m/s2) 8.45


to calculate the seismic hazard. However, in this paper theparametric probabilistic method has been used to present ageneral method for the Iberian Peninsula. This method is appro-priate for Spain and Portugal as the seismicity is diffuse andmoderate. However, for any location with enough informationavailable, other methods could be used. On a first attempt, theauthors tried to use specific attenuation laws for the IberianPeninsula. However, there were not enough records to carry out a

consistent regression analysis. So, the European Strong MotionDatabase was used for the attenuation laws.

To select accelerograms the time of exposure of the structure,the type of soil at the location and the admitted exceedanceprobability must be established in order to obtain the seismichazard curves. With the hazard curves the USHARS can be plottedand the design accelerograms can be selected.


An example of the method proposed has been conducted forSan Pedro Cliff. A total of 10 design accelerograms have beenselected. It can be observed that the standard deviation for theselected accelerograms is very low (a minimum of 0.011 forrecord 990 and minor to 0.06 for 5 of the 10 accelerograms)showing thus the robustness of the method.

Acknowledgements

The financial support given by the Spanish Ministry of Scienceand Technology, projects BIA-2004-01302, BIA 2010-20377 andTIN-68084-C02 and by the Junta the Andalucıa, project P07-TIV-02611 are acknowledged. The authors also want to acknowledgeDr. Antonio Jesus Martın for providing the Spanish database ofearthquakes.

References

[1] Ambraseys NN, Douglas J, Sarma SK, Smit PM. Equations for the estimation ofstrong ground motions from shallow crustal earthquakes using data fromEurope and the Middle East: horizontal peak ground acceleration andspectral acceleration. Bulletin of Earthquake Engineering 2005;3:1–53.

[2] Andeweg B, de Vicente G, Cloetingh S, Giner J, Munoz-Martın A. Local stressfield and intraplate deformation of Iberia: variations in spatial and temporalinterplay of regional stress sources. Tectonophysics 1999;305:153–64.

[3] Argus DF, Gordon RG, DeMets C, Stein S. Closure of the Africa–Eurasia–NorthAmerica plate motion circuit and tectonics of the Gloria fault. Journal ofGeophysical Research 1989;94:5585–602.

[4] Basili R, Valensise G, Vannoli P, Burrato P, Fracassi U, Mariano S, et al. TheDatabase of Individual Seismogenic Sources (DISS), version 3: summarizing20 years of research on Italy’s earthquake geology. Tectonophysics2008;453(1–4):20–43.

[5] Bernreuter DL, Savy JB, Mensing RW, Chen JC. Seismical hazard characteriza-tion of 69 nuclear plant sites east of the Rocky Mountains. Technical ReportNUREG/CR-5250. Lawrence Livermore National Laboratory. U.S. NuclearRegulatory Commission; 1989.

[6] Bolt BA. Earthquakes and geological discovery. New York: Scientific AmericanLibrary; 1993.

[7] Bommer JJ, Douglas J, Strasser FO. Style-of-faulting in ground-motionprediction equations. Bulletin of Earthquake Engineering 2003;1(2):171–203.

[8] Boore DW, Joyner WB, Fumal T. Estimation of response spectra and peakacceleration from western North American earthquakes: an interim report.Technical Report 93-509. U.S. Geological Survey Open-File; 1993.

[9] Boore DW, Joyner WB, Fumal T. The 2000 NEHRP recommended provisionsfor seismic regulations for new buildings and other structures (FEMA 368)and the accompanying commentary (FEMA 369). Technical Report 446.Building Seismic Safety Council (BSSC); 2000.

[10] Buforn E, Udıas A, Colombas A. Seismicity, source mechanism and tectonicsof the Azores–Gibraltar plate boundary. Tectonophysics 1988;152:89–118.

[11] Buforn E, Sanz de Galdeano C, Udıas A. Seismotectonics of the Ibero–Maghrebian region. Tectonophysics 1995;248:247–61.

[12] Calvert A, Sandvol E, Seber D, Barazangi M, Roecker S, Mourabit T, et al.Geodynamic evolution of the lithosphere and upper mantle beneath theAlboran region of the western Mediterranean: constraints from traveltomography. Journal of Geophysical Research 2000;105:10871–98.

[13] Chandler AM, Cham LS, Lam NTK. Deterministic seismic hazard parametersand seismic risk implications for the Hong Kong region. Journal of Asian EarthSciences 2001;20:59–72.

[14] Cornell CS. Engineering seismic risk analysis. Bulletin of the SeismologicalSociety of America 1968;58:1583–606.

[15] European Earthquake Database. /http://www.isesd.cv.ic.ac.ukS.[16] Douglas J. A critical reappraisal of some problems in engineering seismology

(doctoral dissertation). UK: University of London; 2001.[17] Douglas J. An investigation of analysis of variance as a tool for exploring

regional differences in strong ground motions. Journal of Seismology2004;8(4):485–96.

[18] Douglas J. Use of analysis of variance for the investigation of regionaldependence of strong ground motions. In: Proceedings of the world con-ference on earthquake engineering. Paper no. 29; 2004b.

[19] Ebel JE, Kafka AL. A Monte Carlo approach to seismic hazard analysis. Bulletinof the Seismological Society of America 1999;89:854–66.

[20] Garcıa-Monge J, Beltran F, Sanchez-Cabanero JG. Seismic margin assessmentof Spanish nuclear power plants: a perspective from industry and regulators.In: Proceedings of the OECD-NEA workshop on the seismic re-evaluation ofall nuclear facilities; 2001. pp 26–27.

[21] Giardini D, Grunthal G, Shedlock K, Zhang P The GSHAP global seismic hazardmap. International Handbook of Earthquake and Engineering Seismology,IASPEI; 2003.

[22] Gr�acia E, Pall�as R, Soto JI, Comas M, Moreno X, Masana E, et al. Active faultingoffshore SE Spain (Alboran Sea): implications for earthquake hazard assess-ment in the Southern Iberian Margin. Earth and Planetary Science Letters2006;241(3–4):734–49.

[23] Gumbel JE. Statistics of extremes. Columbia University Press; 1958.[24] Housner GW. Spectrum intensities of strong motion earthquakes. In: Pro-

ceedings of the symposium on earthquake and blast effects on structures;1975. pp 25–33.

[25] International Code Council (ICC). International Building Code. TechnicalReport 631; 2000).

[26] Jimenez-Munt I, Fernandez M, Torne M, Bird P. The transition from linear todiffuse plate boundary in the Azores–Gibraltar region: results from a thin-sheet model. Earth and Planet Science Letters 2001;192:175–89.

[27] Joyner W, Boore DM. Peak horizontal acceleration and velocity from strong-motion records including records from the 1979 Imperial Valley, California,earthquake. Bulletin of the Seismological Society of America 1981;71(6):2011–38.

[28] Justo JL, Azanon JM, Azor A, Saura J, Durand P, Villalobos M, et al.Neotectonics and slope stabilization at the Alhambra, Granada, Spain.Engineering Geology 2008;100:101–19.

[29] Kanamori H. The energy release in great earthquakes. Journal of GeophysicalResearch 2001;80(20):2981–7.

[30] Kayabali K, Akin M. Seismic hazard map of Turkey using the deterministicapproach. Engineering Geology 2003;69(1–2):127–37.

[31] Kiratzi AA, Papazachos CB. Active crustal deformation from the Azores triplejunction to the Middle East. Tectonophysics 1995;243:1–24.

[32] Kochkin VG, Crandell JH. New Madrid seismic zone: overview of earthquakehazard and magnitude assessment based on fragility of historic structures.Partnership for advancing technology in housing. Technical Report 110, PATHResearch Center, Upper Marlboro; 2003.

[33] Konno T. Present and future seismic safety guideline for Npps in Japan.Transactions SMiRT 2001;16:1117.

[34] Lin JP, Mahin SA. Effect of inelastic behavior on the analysis and design ofearthquake resistant structures. Earthquake Engineering Research Center.Berkeley: University of California; 1985.

[35] Marcellini A, Daminelli R, Franceschina G, Pagani M. Regional and localseismic hazard assessment. Soil Dynamics and Earthquake Engineering2001;21:415–29.

[36] McGuire RK. Deterministic versus probabilistic earthquake hazards and risks.Soil Dynamics and Earthquake Engineering 2001;21:377–84.

[37] Morales-Esteban A. Seismic hazard. Attenuation laws and earthquake timeseries analysis (doctoral dissertation, Spanish). University of Seville /http://fondosdigitales.us.es/media/thesis/1286/Q_Tesis_AME.pdf, 2010S.

[38] Morales-Esteban A, Martınez-Alvarez F, Troncoso A, de Justo JL, Rubio-Escudero C. Pattern recognition to forecast seismic time series. ExpertSystems with Applications 2010;37(12):8333–42.

[39] Powell GH, Allahabadi R. Seismic damage prediction by deterministicmethods: concepts and procedures. Earthquake Engineering and StructuralDynamics 2008;16(5):719–34.

[40] Romeo R, Prestininzi A. Probabilistic versus deterministic hazard analysis: anintegrated approach for sitting problems. Soil Dynamics and EarthquakeEngineering 2000;20:75–84.

[41] Romeo R, Pugliese A. Seismicity, seismotectonics and seismic hazard of Italy.Enginering Geology 2000;55:241–66.

[42] Trifunac MD, Lee VM, Anderson JG. Methods for introduction of geologic datainto characterization of active faults and seismicity and upgrading of the URStechnique. Technical Report NUREG/CR, vol. 2. Nuclear regulatory commis-sion; 1987.

[43] UNDRO. Natural disasters and vulnerability analysis. Technical report. ReportExpert Group Meeting, Geneva; 1979.

[44] Vanucci G, Gasperini P. The new release of the database of EarthquakeMechanisms of the Mediterranean Area (EMMA Version 2). Annals ofGeophysics 2009;47:307–34.

[45] Veneziano D, Cornell CA, O’Hara T. Historical methods of seismic hazardanalysis. Technical Report NP-3438. Electric Power Research Institute, PaloAlto, California; 1984.

http://www.isesd.cv.ic.ac.uk

http://fondosdigitales.us.es/media/thesis/1286/Q_Tesis_AME.pdf, 2010

http://fondosdigitales.us.es/media/thesis/1286/Q_Tesis_AME.pdf, 2010

probabilistic method to select calculation accelerograms based on

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