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EarthquakeshakingscenariosforthemetropolitanareaofLisbon

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Soil Dynamics and Earthquake Engineering 28 (2008) 347–364

www.elsevier.com/locate/soildyn

Earthquake shaking scenarios for the metropolitan area of Lisbon

A. Carvalhoa, G. Zonnob,�, G. Franceschinab, J. Bile Serrac, A. Campos Costaa

aNational Laboratory for Civil Engineering, Structural Engineering Department, Lisbon, PortugalbIstituto Nazionale di Geofisica e Vulcanologia, Sezione di Milano-Pavia, Milan, ItalycNational Laboratory for Civil Engineering, Geotechnics Department, Lisbon, Portugal

Received 6 July 2006; received in revised form 19 March 2007; accepted 15 July 2007

Abstract

In this study, we simulate and compare ground motion shaking in the city of Lisbon and surrounding counties (metropolitan area of

Lisbon (MAL)), using two possible earthquake models: the onshore source area of Lower Tagus Valley, M5.7 and M4.7 and the offshore

source area, Marques de Pombal Fault, M7.6, one of the possible source of the 1755 Lisbon earthquake. The stochastic and a new hybrid

stochastic-deterministic approach (DSM) are used in order to evaluate the ground shaking and to characterize its spatial variability.

Results are presented in terms of response acceleration spectra (PSA) and peak ground acceleration (PGA) with respect to bedrock and

surface. Site effects are evaluated by means of equivalent stochastic non-linear one-dimensional ground responses analysis, performed for

a set of stratified soil profile units properly designed to cope with the soil site conditions of MAL region. A sensitive study is carried out

using different input parameters and different approaches in order to give the basic information to evaluate the range of uncertainty in

seismic scenarios.

r 2007 Elsevier Ltd. All rights reserved.

Keywords: Stochastic finite-fault modelling; Ground motion simulation; Response spectra; Deterministic-stochastic method; Non-stationary random

process; Power spectral density function; Local effects; Metropolitan area of Lisbon

1. Introduction

In the framework of the ongoing European project‘‘LESSLOSS—Risk Mitigation for Earthquakes and Land-slides’’, finite-fault seismological models are proposed tocompute the earthquake scenarios for three urban areas—Istanbul (Turkey), Lisbon (Portugal) and Thessaloniki(Greece). The subproject 10, SP10, examines earthquakedisaster scenario predictions and loss modelling for thosementioned cities. In this paper only the earthquakescenario prediction for Lisbon will be presented.

The overall aim of SP10 is to create a tool, based onstate-of-the art modelling software, to provide strongquantified statements about the benefits and costs of arange of possible mitigation actions, to support decision-making by city and regional authorities for seismic riskmitigation strategies [1]. For each case study, groundmotion scenarios are developed for the most probable

e front matter r 2007 Elsevier Ltd. All rights reserved.

ildyn.2007.07.009

ing author.

ess: zonno@mi.ingv.it (G. Zonno).

events for 50 and 500 years return period, locations andmagnitudes derived from historical and geological data andregional studies.The strong ground motion prediction requires the

identification of the position, geometry and rupturemechanism of active faults, the knowledge of local elasticand anelastic structure of the crust and the determinationof amplification effects due to the local site geology.Moreover even in case of an ‘a priori’ fixed fault sourceparameter model, the comparison of synthetic seismogramscomputed with different procedures requires a carefulcheck of the numerical description of the source andpropagation models.The problem of the computation of site transfer

functions to be used to evaluate ground motion at surfaceis also a topic investigated in the project. Some activitiesare devoted to issues mostly related to site characterizationand site response assessments through a comparison ofdifferent methods selected for three countries.The seismic risk of Lisbon derives partly from offshore

sources (Fig. 1, top) that cause large events, such as that

ARTICLE IN PRESS

Fig. 1. TOP: Active faults in SW Iberia (modified from [2]), considerable as probable sources for the 1755 earthquake. MPF—Marques de Pombal Fault,

PSF—Pereira de Sousa Fault, HSF—Horseshoe Fault, GBF—Guadalquivir Bank Faults. Double dot represents location of 1969 earthquake (referred in

the text). DOWN: Neotectonic of the Tagus Valley Region (modified from [3]). VF—Vila Franca Fault, ArR—Arrabida range, AF—Alcochete fault.

Double dot represents location of 1909 Benavente earthquake; the same symbol no bold represents location of the 1531 earthquake referred in the text.

A. Carvalho et al. / Soil Dynamics and Earthquake Engineering 28 (2008) 347–364348

which caused the catastrophic 1755 disaster, and wasdamaging over a very wide area; and partly from localsources (Fig. 1, down) that cause moderate earthquakessituated in or near the metropolitan area of Lisbon (MAL),such as the 1909 Benavente and the 1531 earthquakes,which were locally destructives.

Current methods of predicting ground motions forfuture earthquakes in Portugal should be based on anassumed seismological model of source and propagation

processes [4], meaning advanced ground motion simulationmethods allowing the reproduction of specific sourceeffects like directivity and asperities distributions.A finite-fault simulation approach was used to simulateaccelerometric time series and response spectra for the highfrequency ground motion in the city of Lisbon andsurrounding countries, using a non-stationary stochasticapproach [4] and a new hybrid stochastic-deterministicapproach [5].

ARTICLE IN PRESSA. Carvalho et al. / Soil Dynamics and Earthquake Engineering 28 (2008) 347–364 349

The site effects are evaluated by means of an equivalentstochastic non-linear one-dimensional (1D) ground re-sponse analysis of stratified soil profile using the LNEClosssystem [6]. Given a seismic scenario (magnitude andlocation), the bedrock seismic input and the Local SoilEffect software modules of the system, allow computingthe power spectral density function (PSDF) of the strongground motion at bedrock and at surface level of any site,respectively. In this study, and because the soil units forMAL are desegregated by small administrative divisions(parishes), the evaluation of ground motion scenarios willbe performed at the level of the administrative centre ofparishes.

A sensitive study is performed varying the rupturevelocity, the propagation direction depending on nuclea-tion points and slip distribution in order to give the basicinformation to evaluate the range of uncertainty in seismicscenarios.

The evaluation of the worst-case hazard scenariodepending on level of shaking is done selecting first themore conservative parameters at each parish in terms ofresponse acceleration spectra (PSA) respect to rock site, foreach frequency, and then evaluating site effects for theconservative PSA. The worst case risk scenarios, outsidethe scope of this paper, considering casualties and level ofdamage of buildings will be performed with the applicationof the loss model to the MAL, using the LNECloss system.

2. Numerical approaches

Two numerical methods have been adopted for thesimulation of the high frequency ground motion in MAL:the non-stationary stochastic method [4] (hereafter referredto as RSSIM), and the hybrid stochastic-deterministicapproach [5] (hereafter referred to as DSM). The adoptedsimulation techniques take into account finite-fault effectsand are particularly suitable for reproducing high fre-quency properties of the strong ground motion. Moreover,they allow ground motion simulations by specifying arelatively small number of input parameters, representativeof average properties of both seismic source and wavespropagation.

Both methods adopt a point-source-like reference modelfor the amplitude of the acceleration Fourier spectrumobserved at hypocentral distance R from the source,A(o,R). For each circular frequency, o the accelerationspectrum can be represented as

Aðo;RÞ ¼ o2CGðRÞSðoÞApðo;RÞ, (1)

where S(o) is the amplitude displacement far-field sourcespectrum, G(R) is the geometrical spreading factor, and theterm AP(o,R) includes both crustal and near site propaga-tion effects. C is a constant including the free surfaceamplification factor, the average radiation pattern for S

waves, an energy partition factor between the twohorizontal components of the motion and the density andS wave velocity at source.

Following [7,8] the source term is assumed as an omega-square model specified by

SðoÞ ¼M0

1þ ðo=ocÞ2, (2)

where M0 and oc stand for seismic moment and circularcorner frequency, respectively. Moreover, we furtherspecified the distance dependent term AP(o,R) as

Apðo;RÞ ¼ expð�pR=bQðoÞÞFZðoÞPðoÞ, (3)

where the first term includes both an elastic and scatteringattenuation in terms of quality factor Q(o) and FZ(o)is an empirical amplification factor. P(o) accounts forpath-independent high frequency attenuation and isspecified by the k parameter [9] as P(o) ¼ exp(�ok/2) orintroducing the low-pass filtering frequency omax asPðoÞ ¼ ð1þ ðo=omaxÞ

8Þ�1=2.

2.1. The RSSIM synthesis

The RSSIM approach is a non-stationary stochasticsimulation method that synthesizes the ground motiondue to an extended source by means of an appropriatenumber of sub-sources, radiating as o2 point sources. Thismethod has been implemented starting from the classicsimulation code FINSIM [10], widely employed in theseismological literature for simulation of the groundmotion from both moderate and high magnitude earth-quakes [11–16].Like FINSIM, the RSSIM method assumes that the

fault plane is a rectangle, subdivided into an appro-priate number of sub-faults, which are modelled as pointsources characterized by o2 spectrum. The sub-fault moment and corner frequency are derived from thesize of each sub-fault and the number of triggered sub-faults is adjusted so that the specified target moment isachieved.Differently from FINSIM, RSSIM avoids the computa-

tion of acceleration time series representing the contribu-tion of each sub-fault, but synthesizes the ground motiondue to the entire fault from the PSDF radiated by each sub-fault, using the random vibration theory and the extremevalues statistics [17–19].The RSSIM method consists of:

1.

Evaluation of the amplitude acceleration Fourierspectrum, A(o,R), for each sub-fault (see Eq. 1).

2.

Evaluation of the PSDF of the linear response ofsingle degree of freedom systems (SDOF) for inputbase motions produced by each sub-fault:

Given the source duration, Ts, the one-sidedPSDF of acceleration can by derived from A(o,R)

by means of

SaðoÞ ¼1

pAðo;RÞ�� ��2

T s. (4)

ARTICLE IN PRESSA. Carvalho et al. / Soil Dynamics and Earthquake Engineering 28 (2008) 347–364350

Assuming a stationary process, the PSDF of theresponse of each linear SDOFsystemwith a circularnatural frequency on and damping ratio z can becalculated as

Sxðo;on; zÞ ¼ SaðoÞjHxðo;on; zÞj2, (5)

where Hx(o,on,z) is the complex displacement fre-quency response functionrelative to the input absolutebase acceleration and given by

Hxðo;on; zÞ ¼o2

n

�o2n þ 2izonoþ o2

. (6)

3.

Definition of the evolutionary finite-fault responsemoment: Since the kth order moment of the responseis defined as

lkðo;on; zÞ ¼Z 10

okSxðo;on; zÞdo, (7)

for a finite source, subdivided into N sub-faults, thefinite-fault response moment, lTk, can be evaluated asthe sum of all sub-fault response moments, hypothe-sizing that the stochastic processes associated to the N

sub-faults are independent. Therefore:

lTkðo;on; zÞ ¼XN

j¼1

lkjðo;on; zÞ. (8)

It is possible to estimate the evolutionary responsemoments, lT

k(t, o,on,z), introducing the non stationarynature of the response envelope of the SDOF system,by means of an intensity time-modulating responsefunction, y, such that

lTk ðt;o;on; zÞ ¼ y2ðt;on; zÞlTkðo;on; zÞ. (9)

The modulating response function, y, is obviouslydependent on frequency and damping of the SDOFsystem and can be found in Duarte [20]:

yðt;on; zÞ ¼

0 tpt1ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� e�2onzðt�t1Þp

t1otpt2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffie�2onzðt�t2Þ � e�2onzðt�t1Þp

t4t2

8><>: ,

(10)

where t1 represents the starting time of the strongmotion part of the accelerogram and t2 gives thestarting time of the decay part being t2 ¼ T+t1, T theduration of the strong motion.

4.

Synthesis of the total non-stationary response spectrafor a site:

Considering the extreme values statistics and taking T asthe duration of the earthquake, the displacement non-stationary response spectrum (RS), which synthesizes theintegration over the fault of all the delayed sub-sources can

be estimated [17–19]:

RSðT ;o;on; zÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 lnðNcÞ

pþ

0:577216ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 lnðNcÞ

p !

�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffilT0 ðT ;o;on; zÞ

q. ð11Þ

In which N is the number of half-cycles of vibration givenby

Nc ¼ max 2f 0T ; 1:33� �

. (12)

And f0 is the central frequency of the response written as

f 0 ¼1

2plT2 ðT ;o;on; zÞ

lT0 ðT ;o;on; zÞ

" #1=2. (13)

2.2. The DSM synthesis

The DSM approach is a modification of the stochasticpoint source simulation method of Boore [18] (hereafterreferred to as SMSIM), which takes into account finite-fault effects, using synthetic acceleration envelopes com-puted by a simplified formulation of the isochron theory[21,22].Schematically, the synthesis of a time series is a four-step

procedure consisting of [5]

1.

Computation of the deterministic acceleration envelopeof shears waves radiated from an extended fault.

In order to calculate the acceleration envelope of theseismic radiation produced by an extended fault, asimplified formulation of the representation theoremthrough the isochron theory is solved for a definedkinematic rupture process. The Green functions arecomputed as asymptotic solution of the elastodynamicequation (ray theory) in a flat-layered velocity model. Therupture model is described by specifying a nucleationpoint on a rectangular fault plane, subdivided in a suitablenumber of sub-faults, from which the rupture propagatesradially outward with a prescribed rupture velocity. A slipdistribution over the fault can also be assigned tocomplete the kinematic description of the source. Theacceleration envelopes are smoothed and normalized sothat the integral of the squared envelope is unity.

2.

Generation and windowing of the white noise time-sequence.

Like SMSIM, DSM accounts for stochastic propertiesof acceleration ground motion by generating time seriesof Gaussian white noise. The white noise time-sequenceis then windowed with the acceleration envelope.However, differently from SMSIM, DSM envelopesdo not have a predetermined functional form, but arecalculated deterministically (see step 1), based on thehypothesized rupture model.

3.

Introduction of the point-source-like reference spectrum.The windowed-noise time series is transformed into the

frequency domain through the standard FFT algorithm,

ARTICLE IN PRESSA. Carvalho et al. / Soil Dynamics and Earthquake Engineering 28 (2008) 347–364 351

and multiplied with the point-source-like amplitudespectrum of Eqs. (1) and (2). However, respect toSMSIM, an important modification is introduced inorder to take into account of extended fault properties.The angular corner frequency, oc, the distance, R, andthe average radiation pattern, Ryj, are computed throughthe isochron theory. The standard angular cornerfrequency is substituted by an apparent angular cornerfrequency, oa, which is proportional to the inverse of theapparent duration of rupture as perceived by the receiver.As a consequence, it varies from site to site, thusproducing a spectrum modified by directivity effects, asobserved in the near-field ground motion.

It is noteworthy that this approach makes the cornerfrequency independent of seismic moment and stressdrop, as duration is a function of rupture velocity,nucleation point and fault dimensions. Finally, thedistance and the average radiation pattern characterizingthe extended fault are calculated as averages of the sub-faults distances and sub-faults radiation pattern terms.The computation involves a spatial average over theisochron line for each isochron time, and a weightedtemporal average over the apparent duration [5].

4.

Transformation back to the time domain.The complex acceleration Fourier spectrum is trans-

formed back to the time domain by an IFFT algorithm.Application of steps 1–4 implies that the resultingacceleration time series will show stochastic propertiesof the adopted Gaussian white noise and deterministicproperties of the kinematic finite-fault source modelemployed to compute the acceleration envelopes.

2.3. Non-linear soil site amplifications by an equivalent

stochastic procedure

Both RSSIM and DSM synthesis produce groundshaking scenarios at rock outcropping sites. In order todefine scenarios at locations where different geotechnicalconditions prevail, an adequate transfer function, Ha(o),must be defined to cope with the filtering effect anddissipative nature of local soil propagation medium.

The usual approach to obtain Ha(o) for a specific site, isto conduct several 1D analyses of vertically propagatingshear waves. The randomness of earthquake motion makesit necessary to consider several input acceleration timehistories. These may be interpreted as realizations of anacceleration stochastic process. The input for this analysisconsists of an acceleration time series at bedrock and ageotechnical model consisting of a stack of layers. For eachlayer a set of properties (i.e. density, low strain shearmodulus, secant shear modulus reduction and dampingratio curves) is defined.

Due to the non-linearity of soil behaviour, each of theanalysis incorporates an iterative process in which theshear modulus and the damping ratio of each layer areadjusted according to a representative shear strain. This

adjustment is performed at the end of each run, one periteration. At convergence, a surface output time history isobtained for a given input time history. Should thisapproach be used in the present study a huge number ofruns would be necessary. The total number would be equalto the product of the number of representative geotechnicalprofiles by the number of acceleration time histories and bythe number of iterations.This shortcoming was avoided by adopting an alter-

native iterative stochastic procedure [23]. The earthquakescenarios for each parish are defined by the computation ofthe PSDF of surface acceleration with due consideration oflocal site effects.To use this methodology, both DSM and RSSIM output

(time history and displacement RS, respectively) must bequantified in terms of PSDF at bedrock. Once thedisplacement RS has been achieved (directly from RSSIMand after FFT from DSM) the quantification of PSDF isperformed through an iterative procedure, which is basedon the possibility of computing the maximum values of theRS, from the power spectrum using Eqs. (11) and (7) foreach iteration. To begin the iterative procedure values arechosen for the first PSDF. Then successive procedure cyclesare carried out until a satisfactory approximation of thedesire RS is obtained.The input motion for the 1D analysis is defined by the

rock outcrop PSDF of acceleration, Sr0(o), of the parish.The complex transfer functionHgðoj~h;r;~B; ~GÞi from rockoutcrop acceleration to shear strain g of each layer i isobtained [24], which allows to write the shear strain PSDFas function of the independent variable associated with thecircular frequency o:

SgðoÞi ¼ Hgðoj~h;r;~B; ~GÞiSroðoÞH�gðoj~h;r;~B; ~GÞi. (14)

In which ~h; r*;~B and ~G are parameters vectors of n+1

dimension, representing the height, density, viscous pro-portional damping ratio and the elasticity distortionmodulus, of each stratified soil layer i, respectively.Hgð�Þi and H�gð�Þi are complex conjugate functions.Eq. (14) is only valid under the hypothesis of elastic

linear behaviour of soil meaning that, parameters ð~B; ~GÞishould be kept constant even if they depend on the value ofshear strain g. However, even for low amplitude inputmotion, soil tends to exhibit a non-linear behaviour. In thiscase an equivalent iterative linear secant stiffness approachwas adopted as it is frequently used in other soil dynamicscomputer codes (SHAKE, FLUSH). For that purpose itwill be necessary to have estimates of the peak shear strain

vector g*peak

j whose members i vary from 1 to n for each soil

layer, and jstands for the interaction cycle. Thus shear

strain vector g*peak

j can be interpreted as the control

variables of an iterative process that is schematicallydepicted in Fig. 2.In that figure the procedure in the block Extreme

Statistics determines the estimates of g*peak

j based on the

ARTICLE IN PRESS

Fig. 2. Iterative stochastic procedure adopted, for the consideration of the

non-linearity of soil behaviour. h,r, P, B, and G are initial values of soil

layer parameters representing height, density, viscous damping ratio,

plasticity index and elasticity distortion modulus, respectively. Sr0(o)represents the rock outcrop power spectral density function (PSDF) of

acceleration, Sg(o)j,i the PSDF at each iteration, j, for each stratified layer,

i, and Sa(o) the final PSDF at surface, considering the soil column unit

effect. The same notation stands for the transfer function H(o).

A. Carvalho et al. / Soil Dynamics and Earthquake Engineering 28 (2008) 347–364352

hypothesis that the PSDFs Sg(o)i,j are a Gaussian zeromean random processes. In that case estimates of gpeaki;j canbe obtained by

gpeaki;j ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2l0i;j ln

T

2p

ffiffiffiffiffiffiffiffil2i;j

l0i;j

s !� lnðln ð2Þ

" #vuut , (15)

where the stationary moments of 1st and 2nd orders of thestrain are defined as defined in Eq. (7) but for the PSDFsSg(o)i,j defined in Eq. (14).

Once convergence is attained, the transfer functionHa(o) between rock outcrop acceleration and site specificacceleration is defined, and the PSDF of this accelerationcan be computed as

SaðoÞ ¼ Sr0ðoÞjHaðoÞj2, (16)

in which |H(o)|2 represents the transfer function betweenoutcrop acceleration and the absolute acceleration at thetop of the 1D vertically S wave propagation column ofstratified soil medium.

This approach allows a significant saving of calculationtime, roughly a factor of twenty with respect to the usualapproach based on the traditional methods, can beachieved.

Resuming, each seismic input is defined by the rockoutcrop PSDF of acceleration and, given a stratified soilprofile, the new PSDF is computed at the surface levelusing procedure described above (Eqs. (14)–(16)).

3. The case study of metropolitan area of Lisbon

The MAL has been historically stricken by rare, thoughintense, earthquakes, such as the offshore 1755 Lisbonearthquake, the offshore 1969 Gorringe Bank earthquake

(Fig. 1, top), or earthquakes rupturing local intra-platefaults, as the 1531 and the 1909 Benavente earthquake(Fig. 1, down).For this area, the most probable events for the 50 and

500 years return period have been previously assessed[25,26], resulting from a deaggregation of probabilistichazard. This kind of analysis has already been extensivelydiscussed and applied in Portugal, namely in the LisbonMetropolitan region [25], in Azores islands [27] and in abroader geographic region comprising Portugal mainland[28,29].For MAL the seismic deaggregation was assessed by

evaluating hazard marginal distributions in terms ofgeographical coordinates and expected magnitude [25,26].This procedure allows a direct display on map of thelocation of the sources dominating the hazard and,together with the knowledge of the most likely expectedmagnitude, permits a better definition of the specificearthquake causing the greatest hazard to the site [30]. Inthis way, interplate and intraplate seismic scenarios can beindependently assessed.On the basis of deaggregation of probabilistic hazard

there are mainly two seismic sources that could be criticalfor MAL and that are representative of short and longreturn periods, respectively: (a) the onshore source area ofLower Tagus Valley (near Lisbon area) and (b) an offshoresource area, probably associated to the 1755 Lisbonearthquake. Note that the magnitude of the November 1,1755 event, known as the 1755 Lisbon earthquake, wasevaluated as a moment magnitude Mw 8.5 [31] or Mw 8.7[32]. This event generated the largest known tsunami in SWEurope, but its exact location remains controversial.Following [25] three seismic scenarios were considered:

two corresponding to a return period of 500 years, locatedoffshore and onshore and with moment magnitudes 7.6and 5.7, respectively (see Table 2) and the third scenario,corresponding to a return period of 50 years and onshoreMw 4.7 source.Characterization of the geometrical parameters of both

onshore and offshore sources, accounts for tectonic settingsof the regions (Fig. 1). The M7.6 scenario was simulatedconsidering it located in a possible source area of the 1755Lisbon earthquake, an active tectonic structure locatedoffshore Cape St. Vicente named Marques de PombalThrust Fault, MPTF [33,34] (MPF in Fig. 1, top). The M4.7an M5.7 inland seismic scenarios are located in the LowerTagus Valley Fault (LTVF) near to the Vila Franca Fault(VF, Fig. 1, down) [3,35], and very close to a denselypopulated and heavily industrialized area of Lisbon.

3.1. Modelling parameters

Finite-fault simulations require that the fault-planegeometry (length, width, strike, dip, number of subfaultsconsidered and depth to the upper edge), the sourceparameters (seismic moment, slip distribution, stress drop,nucleation point, rupture velocity), the crustal properties of

ARTICLE IN PRESS

35.00

37.00

39.00

41.00

43.00

-12.00 -10.00 -8.00 -6.00

1

2

3

5

4

7

6

35.00

37.00

39.00

41.00

43.00

-12.00 -10.00 -8.00 -6.00

BEN

PAL

SVI

EVMACU

SVF

ACU

Fig. 3. Left: epicentral distribution of the analysed earthquakes records. Circles: intraplate earthquakes. The size of circles is proportional to the value of

magnitude. Triangles: interplates earthquakes. The reference numbers are listed in Table 1. Right: Locations of rock stations used in the calibration

process.

Table 1

List of earthquakes recorded from Portuguese digital network

Event Date Mw Latitude Longitude Source area

1 07–31 1998 4.4 �7.88 38.79 Intraplate

2 09–20 1999 4.7 �9.39 38.59 Intraplate

3 10–16 2000 4.1 �9.23 38.68 Intraplate

4 03–28 2002 4.5 �9.25 38.08 Intraplate

5 07–24 2002 4.8 �11.86 39.11 Intraplate

6 07–29 2003 5.3 �10.26 36.07 Interplates

7 12–13 2004 5.3 �9.96 36.25 Interplates

A. Carvalho et al. / Soil Dynamics and Earthquake Engineering 28 (2008) 347–364 353

the region (geometrical spreading coefficient and anelasticattenuation) and the site-specific soil response informationbe previously specified.

A data set of digital acceleration records obtained fromthe Portuguese accelerometer network at hard-rock sites(Fig. 3, right) was employed to calibrate specific simulationparameters for RSSIM and DSM. The data set includeshorizontal components of ground acceleration records onhard sites, for events with moment magnitudes rangingfrom 4.1 to 5.3 and epicenter distances ranging from 15 to320 km, for a total of 11 records, corresponding to sevenmain events (Table 1). The regional distribution of theearthquakes epicenters is illustrated in Fig. 3 (left). We areaware of the scarcity of data and revision on calibrationwill be carried out with new future events recorded. Thedigitized accelerations time histories were baseline andinstrument corrected and the cutoff frequencies for thehigh-pass and low-pass filtering were 0.4 and 25Hz,respectively.

Parameters were calibrated based on the analysis of thehorizontal components of acceleration records. As twophysical mechanisms of earthquake generations exists inPortugal, namely interplates events originated by themovement between the Eursasian and African plates andintraplate events originated in faults inside the Eurasianplate [25,36], calibration of model parameters was doneseparately with data corresponding to intraplate andinterplates events.

Parameters (stress drop, kappa, fmax and distance-dependent duration term) were inferred by comparison ofsynthetic and recorded 5% damped pseudo accelerationresponse spectra and adjusted to obtain the best fit to the

data. Due to low to moderate magnitude of the earth-quakes of the database, calibration was done consideringeach earthquake modelling as a Brune point source.Authors remark that a comparison between parametersherein obtained and others from different studies should bemade carefully as a difference in model parameters cannotalways be interpreted as physical differences. In fact, someparameters (p.e. estimates of fmax) will depend strongly onwhat value has been used for others parameters (p.e., Q(f)model).

3.1.1. Source parameters

For each scenario, fault dimensions are calculated usingthe empirical relations for reverse faults [37], relatingmoment magnitude and surface rupture length. The fault-orientation parameters (dip and strike) were inferred fromprevious works [3,4,38].Table 2 lists the main source parameters adopted in all

simulations, and Fig. 4 shows the surface projection of thehypothesized faults. Strong motion prediction variability

ARTICLE IN PRESSA. Carvalho et al. / Soil Dynamics and Earthquake Engineering 28 (2008) 347–364354

was introduced selecting different rupture propagationdirections, rupture velocities and slip distributions. Nuclea-tion points were located in the half deepest part of thefault, hypothesizing Unilateral forward, bilateral andunilateral backward rupture propagation (see Fig. 4, points1, 2 and 3). For the rupture velocity, Vr, we assumedVr ¼ 2.5, 2.7 and 2.9 km/s.

In case of the LTVF Mw 5.7 scenario, due to the smallfault dimension, we assumed a homogeneous slip distribu-tion, while for the MPTF Mw 7.6 scenario simulations wereperformed using a random slip distribution and three

Table 2

Assumed source parameters for three earthquake scenarios

Sources Offshore

Moment magnitude Mw 7.6

L (km)*W (km) 110� 24

Center of fault 36.90N; 9.90W

Strike (degree) 201

Dip (degree) 241

Depth to upper edge of the fault 4.5 km

Number of sub-faults along strike and dip 20� 5

Slip model Random and Gaussia

Fig. 4. Left: geometry of offshore MPTF M 7.6 respect to the MAL (black bo

LESSLOSS project. In this paper only results from the two test parishes S174 a

the left top. Numbers in each fault are the different nucleation points assume

different slip models assuming a Gaussian distribution ofthe slip, centred on the nucleation point 1, 2 or 3 andnamed slips1, 2 and 3, respectively (Fig. 5). The totalamount of slip is the same but with Gaussian distributioncentred on the different nucleation points.

3.1.2. Crustal parameters

Tables 3 and 4 summarize the specific simulationparameters adopted in RSSIM and DSM, respectively.As regard to crustal attenuation properties we adopted

the frequency-dependent quality factor for Tagus Valley

Onshore Onshore

5.7 4.7

8.4� 6.0 2.2� 2.8

38.82N; 9.05W 38.82N; 9.05W

2201 2201

551 551

0.5 km 2.0 km

20� 10 20� 10

n distribution Homogeneous Homogeneous

x). Right: MAL parishes (black dots) and the tested parishes in the aim of

nd S268 will be presented. A spot of the assumed LTVF M5.7 is shown on

d (modified from [39]).

ARTICLE IN PRESS

Fig. 5. Slip models used in M7.6 offshore scenario, assuming a Gaussian distribution of the slip, centred (from the top) on the nucleation point one

(referred as slip 1 in the text), nucleation point 2 (slip2) and nucleation point 3 (slip3).

Table 3

Simulation parameters for the interplates earthquake scenario used in

RSSIM

Crustal thikness, D 25 km

Quality factor, Q(f) 239*f1.06

Geometric attenuation 1/R (Rp1.5Dkm)

1/R0 (1.5DkmoRp2.5Dkm)

1/R0.5 (R 42.5Dkm)

Distance-dependent duration 0.02R (R4300 km)

0 (Ro 300km)

fmax 7Hz

Shear-wave velocity, b 3.5 km/s

Crustal density, r 2.8 g/cm3

Stress drop, Ds 50 bar

Amplification function

Fzi(o) FziðoÞ ¼ 2=ð1þ ðozi=oÞ2Þ o4ozi

fzi ¼ 0.35HZ

Number of subfaults along strike and

dip

20� 5

Slip model Random and Gaussian

distributions

A. Carvalho et al. / Soil Dynamics and Earthquake Engineering 28 (2008) 347–364 355

region and surroundings, Q(f) ¼ 239f1.06, higher rangevalues derived from regional studies of coda-wave attenua-tion [40], and a tri-piece-wise geometric attenuationfunction defined by assuming a crustal seismogenicthickness of 25 km [41].

As regard to site-specific information we expressed thefactor Fz(o) in Eq. (3), as a function that takes into accountof density and S wave velocity changes respect to anhomogeneous propagation model [42,43]:

FzðoÞ ¼2

1þ ðozi=oÞ2

o4ozi. (17)

We employed the impedance function with fzi ¼ 0.35Hz,for interplate events. The latter value is very close tofzi ¼ 0.32Hz, obtained by [43].

Regarding the attenuation operator, P(o), a reasonableprediction of the recorded acceleration response spectra,was found considering the upper crust attenuation as a fmax

filter with fmax ¼ 6–8Hz.DSM simulations were performed with FZ(o) ¼ 1 and

with P(o) defined as a k filter [9]. We estimated thisparameter from the horizontal components of accelerationdata recorded at short hypocentral distances (p35 km), byfitting the high-frequency decay of the accelerationspectrum with a straight line in a log-linear scale. We haveestimated k separately for the two horizontal componentsof the acceleration time histories. A suitable frequencyband (depending on quality of data, generally ranging from5–10 to 20–25Hz) was chosen in order to perform reliable

regressions (Fig. 6). A mean value of k ¼ 0.055 s wasinferred from the analysis of the highest quality records. Byconsidering this estimate as representative of average stiffsoil conditions, we employed the k filter with k ¼ 0.055 s inall DSM simulations.

ARTICLE IN PRESSA. Carvalho et al. / Soil Dynamics and Earthquake Engineering 28 (2008) 347–364356

Fig. 7 shows some examples of comparison betweensimulations and data for horizontal components ofmoderate events recorded at different hypocentre distances.In general, the synthetics are in good agreement withobservations for at least one of the recorded horizontalcomponents.

Table 4

Simulation parameters for the intraplate earthquake scenario used in

DSM

Crustal thikness, D 25 km

Quality factor, Q(f) 239*f1.06

Geometric attenuation 1/R (Rp1.5Dkm)

1/R0 (1.5DkmoRp2.5Dkm)

1/R0.5 (R42.5Dkm)

Distance-dependent duration 0.02 R (R4300 km)

(Ro300km)

K 0.055 s

Shear-wave velocity, b 3.5 km/s

Crustal density, r 2.8 g/cm3

Number of subfaults along strike and

dip

20� 10

Slip model Homogeneous

Number of trials 30

Fig. 6. k estimations from the slope of the high frequency acceleration spectru

shown in the left and right panels, respectively. Top and bottom events refer

3.2. A sensitivity analysis

Both methods, DSM and RSSIM, adopted in this studyand in the framework of LESSLOSS project, allowcomputing synthetic ground motion for direct S-wave fieldat bedrock sites and are suitable to generate shakingscenarios near an extended fault. Nevertheless it is authorsbelieve that FINSIM is worldwide known and a referencetool for a comparison of new approaches. A sensitivityanalysis will be performed using both adopted methodol-ogies and FINSIM.

3.2.1. Nucleation points

Fig. 8 presents a comparison of the response spectraobtained at one test parish (S174, in Fig. 4) using RSSIM,FINSIM and the DSM methods for the onshore sourceLTVF M 5.7 (DSM) and offshore source MPTF M7.6(RSSIM), for two different nucleation points (1 and 3) withthe same velocity rupture (2.5 km/s) and the same slipdistributions (homogeneous for the onshore scenario andslip2, in Fig. 5, for the offshore scenario).Fig. 8 emphasizes the predicted effects of rupture

directions on strong ground motions and remarks theimportance of using methodologies that can account for

m. EW and NS amplitude Fourier Spectra of the direct S wave pulse are

to distances events of 15 and 35 km, respectively.

ARTICLE IN PRESS

0.1 1 10 100

Frequency [Hz]

0.01

0.1

1

10

Acc [cm

/s2]

Event 2

M = 4.7

R = 40 km

0.1 1 10 100

Frequency [Hz]

0.01

0.1

1

10

Acc [cm

/s2]

Event 4

M = 4.5

R = 80 km

Event 3

M = 4.1

R = 18 km

0.1 1 10 100

Frequency [Hz]

0.1 1 10 100

Frequency [Hz]

0.01

0.1

1

10

Acc [cm

/s2]

100

0.01

0.1

1

10

Acc [cm

/s2]

Event 1

M = 4.4

R = 108 km

Event 5

M = 4.8

R = 243 km

0.1 1 10 100

Frequency [Hz]

0.01

0.1

1

10

Acc [cm

/s2]

0.1 1 10 100

Frequency [Hz]

0.1 1 10 100

Frequency [Hz]

100

0.01

0.1

1

10

Acc [cm

/s2]

Event 7

M = 5.3

R = 280 km

Event 6

M = 5.3

R = 335 km

Fig. 7. Example of response spectra comparison between synthetic and observed data. Straight line are the simulated results, dot and dashed line are both

horizontal components of the recorded accelerogram. (Dot: component N–S; dashed: component E–W).

A. Carvalho et al. / Soil Dynamics and Earthquake Engineering 28 (2008) 347–364 357

directivity effects. In fact at site S174, the parish closer tothe LVTF, and considering DSM method, the PSA valuesobtained with nucleation point 3 (backward directivity) aremuch lower (by a factor about 2) than the ones computedconsidering nucleation point 1 (forward directivity). Indeedthe DSM reproduces the high frequency directivityeffects by means of the apparent corner frequency, fa,which is included in the computation of the accelerationspectrum. Due to the assumed functional form of thehypothesized source model, an fa2 dependence of the highfrequency level of the acceleration spectrum is obtained.Sites experiencing backward and forward directivity arecharacterized by low and high values of fa, respectively,which implies marked differences in the simulated spectralacceleration. FINSIM and RSSIM capture directivityeffects, too, but in the high frequency range, and with lessvariability than DSM.

3.2.2. Rupture velocities

Fig. 9 shows the simulated spectra for the two selectedparishes (S174 and S268, Fig. 4) for different rupturevelocity of 2.5 and 2.9 km/s. For FINSIM calculations, wehave not used the relation Vr ¼ 0.8 b between rupturevelocity and shear velocity, but instead fixed it in thecode avoiding the coupling between the two physicalparameters.

An increase of directivity effects can be observed forincreasing values of the rupture velocity, more pronouncedfor the onshore scenario. For the offshore scenario, due to

the great distances between source and parish, the effect ofthe rupture velocity is almost undetectable.High frequency simulations are particularly sensitive to

the adopted value of the k filter. When values representa-tive of rock or stiff soil sites are used, the simulated strongmotion is strongly dependent on the hypothesized rupturevelocity [44]. In the case of Lisbon, due to the high valueadopted for the k parameter, the effect of the rupturevelocity on the ground shaking is almost undetectable(Fig. 9).

3.2.3. Slip distribution

Sensitivity analysis considering different slip distribu-tions is presented in Fig. 10, for the offshore scenario andusing the S174 parish as a tested site. For the onshore caseit was considered, as stated before, a homogeneous slip.Simulations were performed using the three slip distribu-tions of Fig. 5 and a random slip distribution, assuming abilateral rupture (nucleation point 2) and the same velocityrupture Vr ¼ 2.5 km/s.As it is remarked in Fig. 10, slip model is a very

important source of variability in ground motion simula-tion, even considering the offshore scenario, in the far field.Accelerations values (Table 5) increases around 30%, inthe high frequency range, considering a slip distributioncentred on the nucleation point moving from south tonorth of fault, in strike direction (Fig. 4). The random slipdistribution, for all range of frequencies, seems an averageassumption when the slip distribution of an earthquake is

ARTICLE IN PRESS

103

102

101

101

100

10010-1

10-1

Frequency [ Hz ]

Simulation Earthquake LTVF M 5.7 for the site S174

DSM (NP = 1) DSM (NP = 3) FINSIM (NP = 1) FINSIM (NP = 3)

P

SA

[ c

m/s

ec**

2 ]

(5

% d

am

pin

g)

Simulating Eathquake MPTFM7.6 for the site S174

0.1

1

10

100

1000

0.1 1 10 100

Frequency [Hz]

RSSIM (NP = 1, slip2)

RSSIM (NP = 3, slip2)

FINSIM (NP = 1, slip2)

FINSIM (NP = 3, slip2)

P

SA

[ c

m/s

ec**

2 ]

(5

% d

am

pin

g)

Fig. 8. Comparison of response spectra PSA (5% damping), for the S174

parish, for nucleation points 1 and 3 and velocity rupture of 2.5 km/s. Up:

DSM and FINSIM, for the onshore M5.7 scenario; down: RSSIM and

FINSIM, for the offshore M7.6 scenario.

Simulation Earthquake LTVF M 5.7 for the sites S174 and S268

DSM (NP = 2, Vr = 2.5 km/sec) DSM (NP = 2, Vr = 2.9 km/sec)

Simulation Earthquake MPTF M 7.6 for the sites S174 and S268

RSSIM (NP = 2, Vr = 2.5 km/sec) RSSIM (NP = 2, Vr = 2.9 km/sec)

P

SA

[ c

m/s

ec**

2 ] (

5%

dam

pin

g)

103

102

101

100

10-1

P

SA

[ c

m/s

ec**

2 ] (

5%

dam

pin

g)

103

102

101

100

10-1

Frequency [ Hz ]

10110010-1

Frequency [ Hz ]

10110010-1

Fig. 9. Sensitivity of response spectra to alternative rupture velocities (2.5

and 2.9 km/s) using the same nucleation point 2. Up: onshore M5.7

scenario, using DSM; down: offshore M7.6 scenario, using RSSIM.

A. Carvalho et al. / Soil Dynamics and Earthquake Engineering 28 (2008) 347–364358

not known or for predictions of strong ground motions forfuture earthquakes.

To have a complete picture of sensitivity of DSM andRSSIM to different nucleation points, rupture velocitiesand slip models, Fig. 11 shows result for the tested parishesconsidering all scenarios evaluated (three nucleationpoints, three rupture velocities and three slip models). Asit is visible, the onshore scenario presents great variabilitybetween different scenarios, while for the offshore scenariothere is no so great sensitivity to the different models, dueto the great distance between source and sites.

3.3. Evaluation and analysis of seismic scenarios

In the framework of subproject 10 of LESSLOSS, resultshave been provided in terms of time series, PSA and maps

of different shaking parameters as PGA, PGV and PGDfor each scenario [45].Regarding the seismic scenarios performed for the

onshore source LTVF, response spectra have beenproduced for each parish of MAL based upon 30 trialsfor time histories using DSM and an average timeduration. For the seismic scenarios performed for theoffshore source MPTF we have computed directly responsespectra at the bedrock using RSSIM.The peak ground acceleration (PGA) obtained with

DSM method applied to the onshore source LTVF M 5.7is shown on the left side of Fig. 12, for the threedifferent nucleation points, considering a rupture velocityof 2.7 km/s and an homogeneous slip distribution. Thedirectivity effects due to different rupture propagation onthe fault are well marked: in the case of nucleation point 1

ARTICLE IN PRESSA. Carvalho et al. / Soil Dynamics and Earthquake Engineering 28 (2008) 347–364 359

(top left) higher peak values are shown in the parisheslocated southern to the fault, as this case involves rupturetowards these parishes, while in nucleation point 3 case(bottom left) higher peak values are shown in parisheslocated northeastern to the fault, as in this case rupturepropagates away from the southern parishes. The case ofbilateral rupture (centre, left) shows a radial patternaround the fault.

Simulating Eathquake MPTF M7.6 for the site S174

1

10

100

1000

0.1 1 10 100

Frequency [Hz]

PS

A [

cm

/se

c**

2]

(5

%d

am

pin

g)

RSSIM (NP = 2, Slip1)

RSSIM (NP = 2, Slip2)

RSSIM (NP = 2, Slip3)

RSSIM (NP=2, random Slip)

Fig. 10. Sensitivity of response spectra to different slip distribution, for

the offshore M7.6 scenario, using RSSIM.

100 102

Frequency [ Hz ]

100

102

PS

A [

cm

/sec**

2 ]

Inland Source LTVF M 5.7

site S174

100 102

Frequency [ Hz ]

100

102

PS

A [ c

m/s

ec**

2 ]

site S268

Fig. 11. Response spectra, at bedrock, for the S174 parish, considering the nine

offshore source.

PGA values obtained with RSSIM method applied tothe offshore source MPTF M 7.6 are illustrated onthe right of Fig. 12, considering a rupture velocity of2.7 km/s and a random slip distribution. As it can be seen,there is no spatial pattern related to directivity. For thethree different ruptures considered, higher values arefound in the southern parishes of MAL and lower valuesare found in the northern parishes. There is, however,a difference in peak values, higher peak PGA valuesresulting from the scenario considering nucleation point 1,meaning an upward propagation for all parishes, and lowervalues resulting from the scenario considering nucleationpoint 3, meaning a backward propagation, with longerduration.Fig. 12 indicates also that the simulated ground motion

for MAL has great geographic variability. This variability

100 102

Frequency [ Hz ]

100

102

PS

A [

cm

/sec**

2 ]

Offshore Source MPTF M 7.6

site S174

100 102

Frequency [ Hz ]

100

102

PS

A [ c

m/s

ec**

2 ]

site S268

scenarios performed using DSM for the inland source and RSSIM for the

Table 5

PGA (cm/s2) values for the three different nucleation points and four slip

distributions considered in the sensitivity analysis of offshore scenario, for

S174 and S268 parishes

Sites S268 S174

Slip\NP NP 1 NP 2 NP 3 NP 1 NP 2 NP 3

Slip 1 126.82 90.12 66.12 94.10 66.92 49.17

Slip 2 139.98 101.27 72.69 102.46 74.17 53.31

Slip 3 163.20 121.74 85.33 117.86 87.97 61.70

Random 147.23 107.20 77.96 106.06 78.01 55.19

ARTICLE IN PRESS

Inland source LTVFM = 5.7

bedrock bedrock

Offshore source MPTFM = 7.6

Nu

cle

atio

n p

oin

t 1

N

ucle

ation p

oin

t 2

Nucle

ation p

oin

t 3

PGA [cm/s^2]<3535 - 4040 - 4545 - 5050 - 6060 - 7575 - 9090 - 110110 - 130>130

PGA [cm/s^2]<3535 - 4040 - 4545 - 5050 - 6060 - 7575 - 9090 - 110110 - 130>130

PGA [cm/s^2]<3535 - 4040 - 4545 - 5050 - 6060 - 7575 - 9090 - 110110 - 130>130

PGA [cm/s^2]0 - 1010 - 2020 - 4040 - 6060 - 100100 - 150150 - 200200 - 300300 - 500>500

100 100 Kilometers 100 100 Kilometers

100 100 Kilometers100 100 Kilometers

100 100 Kilometers 100 100 Kilometers

PGA [cm/s^2]0 - 1010 - 2020 - 4040 - 6060 - 100100 - 150150 - 200200 - 300300 - 500>500

PGA [cm/s^2]0 - 1010 - 2020 - 4040 - 6060 - 100100 - 150150 - 200200 - 300300 - 500>500

Fig. 12. Left: PGA maps, obtained with DSM method, for the inland source LTVF M 5.7. Right: PGA maps, obtained with RSSIM method, for the

offshore source MPTF M 7.6. Maps are relative to alternative nucleation points with rupture velocity of 2.7 km/s and homogeneous slip for onshore

scenarios and random slip for offshore scenarios.

A. Carvalho et al. / Soil Dynamics and Earthquake Engineering 28 (2008) 347–364360

is evaluated dividing the maximum and minimum valuesobtained for each frequency, at all parishes of MAL, for alldifferent scenarios.

The range of values of each different nucleation pointand the ratio values are synthesized in Fig. 13. As it isshown, the onshore scenario is very sensitive to directivityand has great scatter of peak values, PGA values varyingfrom 10 cm/s2 in some parishes to 500 cm/s2 in othersmeaning that higher values are locally obtained and thatseismic actions attenuates too fast with distance. The

higher ratio (higher scatter) is observed considering thenucleation point 3 (see Fig. 4).Fig. 14 presents the worst case-shaking scenario (con-

sidering the three nucleation points, the three slip distribu-tion for the offshore scenario and the three rupturevelocity), in terms of PGA at bedrock and at groundsurface, for the three considered sources. For a bettercomparison, we used the same scale legend.The worst-case scenario is defined considering, in each

parish, the maximum value of shaking parameters of all

ARTICLE IN PRESS

100 102

Frequency [ Hz ]

100

102

P

SA

[ c

m/s

ec**

2 ]

Inland Source LTVF M 5.7

code 023

100 102

Frequency [ Hz ]

100

102

P

SA

[ c

m/s

ec**

2 ]

Offshore Source MPTF M 7.6

code 123

100 102

Frequency [ Hz ]

100 102

Frequency [ Hz ]

100 102

Frequency [ Hz ]

100

102

P

SA

[ c

m/s

ec**

2 ]

100

102

100

102

P

SA

[ c

m/s

ec**

2 ]

R

atio [

PS

AM

/PS

Am

]

code 023

code 022

code 021

code 021

10-1

100

101

R

atio [

PS

AM

/PS

Am

]100 102

Frequency [ Hz ]

100 102

Frequency [ Hz ]

100 102

Frequency [ Hz ]

100

102

P

SA

[ c

m/s

ec**

2 ]

100

102

P

SA

[ c

m/s

ec**

2 ]

code 121

code 123

code 122

code 121

code 022 code 0122

Fig. 13. Response spectra, at bedrock, for all parishes of MAL, considering scenarios performed using DSM for the onshore source and RSSIM for the

offshore source. Numbers refer to the simulated shaking scenarios, using the conventional code IJK specified as follows: I ¼ 0; 1 for homogeneous and

heterogeneous slip distribution, respectively; J ¼ 1,2 and 3 for Vr ¼ 2.5, 2.7 and 2.9 km/s, respectively; K ¼ 1,2 and 3 for nucleation point 1, nucleation

point 2 and nucleation point 3, respectively, as shown in figure 4.

A. Carvalho et al. / Soil Dynamics and Earthquake Engineering 28 (2008) 347–364 361

scenarios considered in the simulations. For each parish,the worst case response spectra is obtained selecting,for each frequency, the maximum spectral ordinate amongthe values generated by the hypothesized scenarios atbedrock.

The RS of each parish was transformed into PSDF, atthe bedrock, using the classical theory of stationaryrandom process already described. Site effects were, then,evaluated following the numerical approach explained

elsewhere in this paper and using an available database,containing information on stratified soil profile units forMAL. Each soil unit considers the thickness of shallowlayers, shear waves velocity, density and plastic index. Thisdatabase was built in the framework of the projectconducted by the Portuguese civil protection authority,for which it was conducted a geological-geotechnicalsurvey that allowed the characterization of stratified soilprofile units for MAL with a fair level of detail.

ARTICLE IN PRESS

Worst case scenario

bedrock

Worst case scenario

surface

M4.7

, in

land

M5.7

, in

land

M7.6

, offshore

0-10 10-20 20-40 40-60 60-100 100-150 150-200 200-300 300-500 >500

PGA [cm/^s2]

Fig. 14. Worst-case scenarios at the bedrock and ground surface, for the onshore and offshore sources.

A. Carvalho et al. / Soil Dynamics and Earthquake Engineering 28 (2008) 347–364362

Fig. 14 evidences that the nonlinear soil amplification isquite pronounced, particularly in the south of LTVFwhere soft soil sites prevail. As it is shown, local effectscan amplify PGA values by approximately a factor of 2.PGA values computed for bedrock in Lisbon city canincrease from 0.12 to 0.25 g and up to 0.5 g in surround-ings, for the onshore scenario, and from 0.045 g to 0.090 gand 0.13 g in some parishes of MAL for a M7.6 offshorescenario.

Higher values of PGA for almost all parishes ofMAL come from the interplate scenario (the farther one)except for the parishes that are localized in or nearLTVF.

4. Conclusions

In the framework of the LESSLOSS project we haveestimated ground motion scenarios in the frequency bandof engineering interest (0.5–20Hz) for the MAL.Two numerical methods have been adopted for the

prediction of strong ground motion due to extended faults:a hybrid stochastic-deterministic approach (deterministic-stochastic method (DSM); [5]) and a non-stationarystochastic finite-fault simulation method (RSSIM; [4]).A sensitivity analysis was carried out for the two

methodologies and the variability of ground motion wasstudied. On the seismological point of view, many equally

ARTICLE IN PRESSA. Carvalho et al. / Soil Dynamics and Earthquake Engineering 28 (2008) 347–364 363

probable shaking scenarios were simulated by varyingnucleation point, rupture velocity and slip distribution. Thedifferent scenarios used produced high variability inground motion simulations, mainly dependent on theassumed position of the hypocenter on the fault plane(nucleation point), which controls the rupture directivity.

Selected scenarios resulted from previous regionalstudies. The shaking scenarios are computed in terms ofPSA, time series, and PGA at bedrock and ground surfacelevel. Results are here presented in terms of PGA maps, foroffshore and onshore scenarios.

The overall variability due to both source and site effectwas accounted for by considering the worst shakingscenarios for all the parishes of the MAL. Local siteeffects have been considered based on information onstratified soil profile units for MAL and it come out that itamplify the synthetic PGA values by approximately afactor of 2.

This study sets out the basis of the earthquake scenariosfor MAL and may act as the basis for a loss estimationstudy. The worst-case scenarios were selected with pur-poses of generating precautionary scenarios, which can actas a demand of the local administrators.

Acknowledgements

This study was performed with the financial support ofthe European Commission through the LESSLOSS FP6Integrated Project Risk Mitigation for Earthquakes andLandslides, No.: GOCE-CT-2003-505488. The first authoris grateful to Fundac- ao para a Ciencia e a Tecnologia, fromwhich the author has a grant. Some work and preliminaryresults were presented in the ‘‘250th anniversary of the 1755Lisbon earthquake’’, 4–10 November 2005, Portugal.

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