stochastic strong ground-motion simulation of the 7...

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Bulletin of the Seismological Society of America, Vol. 94, No. 3, pp. 1036–1052, June 2004

Stochastic Strong Ground-Motion Simulation of the 7 September 1999

Athens (Greece) Earthquake

by Zafeiria Roumelioti, Anastasia Kiratzi, and Nikolaos Theodulidis

Abstract The stochastic method for finite faults is applied to simulate strongground motion from the 7 September 1999, moment magnitude M 5.9 Athens earth-quake. The method includes descritization of the fault plane into a certain numberof subfaults, each of which is assigned an x�2 spectrum. A slip-distribution model,derived from previous studies of this earthquake, is used to specifically account forthe source effect. Contributions from all subfaults are then empirically attenuated tothe observation sites, where they are summed to produce the synthetic accelerationtime history. The method is first calibrated against its ability of reproducing therecordings at 19 strong-motion stations, at epicentral distances ranging from 16 to61 km. The calibrated model is then applied to calculate synthetics at a large numberof grid points covering the area around the fault plane. Simulated peak values aresubsequently used to produce synthetic peak ground acceleration and spectral accel-eration maps at hard rock. Both peak ground acceleration and spectral accelerationmaps imply energy directivity toward the east, where most of the damage was con-centrated. The directivity effect is most prominent at large periods (�2 sec) and inthe period range 0.2 to 0.3 sec. Independent geotechnical studies showed considerablesite effect at periods �0.5 sec within the meizoseismal area. This result, coupledwith the results of the present study, imply that the damage distribution pattern ofthe 1999 Athens earthquake can be explained by the destructive combination of twofactors: the source directivity and the site effect.

Introduction

The 7 September 1999, M 5.9 Athens earthquake con-stitutes another resounding example of the potential destruc-tiveness of moderate-magnitude earthquakes when they oc-cur in the proximity of densely populated areas. Reporteddamage places the specific earthquake among the worst nat-ural disasters in the modern history of Greece. In total, 143people were killed, whereas the economic loss is estimatedto have reached 3% of Greece’s Gross Domestic Product(GDP) (Pomonis, 2002).

The earthquake was related to normal faulting in anorthwest–southeast direction (strike � 115�, dip � 57�,rake � �80�; Louvari and Kiratzi, 2001), about 15 kmnorthwest of the center of Athens. In the epicentral area, twonormal faults of such orientation are clearly expressed onthe morphology, namely the Thriassio and Fili faults (Fig.1). Among these two structures, the Fili fault is most likelyrelated to the 1999 earthquake (Ganas et al., 2001; Pavlideset al., 2002), although the rupture did not reach the surface(Papazachos et al., 2001; Baumont et al., 2002; Roumeliotiet al., 2003b) and, therefore, any conclusions regarding thecausative fault are doubtful.

Most of the damage was observed in the northwest sub-

urbs of the city (the municipalities of Thrakomakedones,Ano Liosia, Fili, and Menidi), which are located to the eastof the Fili fault (Fig. 1). In general, damage distributionwithin the wider epicentral area was irregular (e.g., damagewithin the projection of the fault plane, which is usual fornormal-fault earthquakes, was insignificant compared withthat observed close to the fault’s eastern termination). Thisasymmetry toward the meizoseismal area caused speculationfor emergence of directivity phenomena during the earth-quake rupture, which was later confirmed by several studies(Tselentis and Zahradnik, 2000; Zahradnik and Tselentis,2002; Roumelioti et al., 2003a b; Gallovic and Brokesova,2003).

In the present study we simulate the strong ground mo-tion of the 1999 Athens earthquake by using the widely ap-plied stochastic method for finite faults (Beresnev and At-kinson, 1997). The simulation parameters are first validatedthrough a posteriori predictions of the available strong-motion records of the examined event and subsequently usedto assess the strong-motion level at a much larger numberof sites, including the meizoseismal area, for which no re-cords are available. Our primary target is to investigate how

Stochastic Strong Ground-Motion Simulation of the 7 September 1999 Athens (Greece) Earthquake 1037

Figure 1. Regional map showing the epi-center of the 1999 Athens earthquake (starsymbol) and the locations of the strong motionstations used in the present study. Traces of theFili and Triassio faults and the area of damageconcentration (where the municipalities ofThrakomakedones, Ano Liosia, Fili, and Men-idi are discussed in the text) are also depicted.

source effect related to this earthquake affected the distri-bution of strong ground motion and whether this factor iscapable of explaining the degree of damage within themeizoseismal area.

Data

Strong ground motion of the 1999 Athens earthquakewas recorded by a significant number of acceleration sta-tions. However, by the time of the mainshock, all the re-cording stations were operating out of the meizoseismal area.Most of the triggered instruments belong to the Institute ofGeodynamics (G.I.) of the National Observatory of Athens,which is operating a strong motion network consisting ofdigital instruments (Teledyne A-800 type) to monitor theconstruction of the Athens metro. Most of the instrumentsare installed below the surface, at different levels of theunderconstruction metro, and only two stations (MNSA andDMK) can be considered as “free-field.” Between these twostations, MNSA recorded the largest peak ground accelera-tion (PGA � 0.51 g) in one of the two horizontal compo-nents (oriented N100�), a value that was found to be incon-sistent with the low degree of building damage in theneighborhood of the station. Subsequent studies revealedthat the presence of three underground structures next to thestation’s installation site spuriously enhanced the accelera-tion amplitudes in the particular horizontal component up toa level of 30% (Gazetas et al., 2002). Nevertheless, two morestations (KEDE and SPLB) were installed at the basementof light buildings (one- to two-stories) and can practicallybe used as “free-field” stations (Gazetas et al., 2001).

The rest of the stations (SMA-1 type) that recorded theearthquake belong to the permanent strong-motion network

operated by the Institute of Engineering Seismology andEarthquake Engineering (ITSAK), whereas the PublicPower Corporation (PPC) of Greece operated three morestations (ETNA type).

Detailed information on the locations (Fig. 1) and thesurface geological conditions at the installation sites, as wellas PGA values recorded during the examined earthquake aregiven in Table 1.

Method

In the stochastic method, the Fourier amplitude spec-trum of a seismic signal is represented as the product of aspectrum, S(x), that accounts for the effects of the seismicsource and several other filtering functions that represent theeffects of the propagation path and the recording site. If thereceiver installation site can be characterized as hard rock,the shear-wave acceleration spectrum is given by:

2 �xR/2QbA(x) � 2x • S(x) • P(x) • e , (1)

where x is the angular frequency, R is the hypocentral dis-tance, Q is the quality factor introduced to account for theregional inelastic attenuation, and b is the shear-wave ve-locity. The filtering function P(x) is used for the commonlyobserved spectral cutoff above a certain frequency xm. Ac-cording to some scientists, this phenomenon is attributed tothe processes that take place at the source during the occur-rence of an earthquake (Papageorgiou and Aki, 1983; Pa-pageorgiou, 1988). Others believe that it is mainly due tohigh-frequency attenuation by the near-surface weatheredlayer (Hanks, 1982; Anderson and Hough, 1984; Beresnevand Atkinson, 1997; Theodulidis and Bard, 1998). In the

1038 Z. Roumelioti, A. Kiratzi, and N. Theodulidis

Table 1Information on the Strong-Motion Stations Used to Calibrate the Parameters of the Finite-Fault Stochastic Simulation Method

in the 1999 Athens Earthquake

StationCode

InstallationArea Installation Site

Sensor Depth(m) Surface Geology

Latitude(�N)

Longitude(�E)

EpicentralDistance

(km)PGA(L)

PGA(T)

PGA(V) Carrier*

ALIV Aliveri Ground level 0 — 38.400 24.033 53 0.02 0.02 0.01 PPCATHA Neo Psyhiko Basement/3-story 0 Schist 38.00 23.77 21 0.08 0.10 0.11 G.I.CHAL Chalandri Basement/2-story 0 Alluvial 38.018 23.789 22 0.11 0.16 0.09 ITSAKCOR Corinthos Basement/2-story 0 Alluvial 37.937 22.933 59 0.03 0.02 0.02 ITSAKDFNA Dafni Metro/Level 2 14 Alluvial/Schist 37.95 23.74 23 0.04 0.08 0.04 G.I.DMK Dimokritos Free field 0 Limestone 37.99 23.82 26 0.05 0.08 0.04 G.I.FIX Neos Kosmos Metro/Level 2 15 Alluvial/Schist 37.96 23.73 22 0.09 0.12 0.05 G.I.GYS G.Y.S. Basement/3-story 0 Alluvial 37.996 23.738 19 0.12 0.11 0.05 ITSAKKEDE K.E.D.E. Basement/1-story 0 Marl 37.983 23.717 19 0.26 0.30 0.16 ITSAKKERT Keratsini Basement/2-story 0 — 37.967 23.617 16 0.22 0.19 0.16 PPCLAVR Lavrio Ground level 0 — 37.717 24.050 61 0.04 0.05 0.05 PPCMNSA Monastiraki Free field 0 Alluvial/Schist 37.98 23.73 20 0.23 0.51 0.16 G.I.PNT Pentagono Metro/Level 2 15 Alluvial 38.00 23.79 23 0.09 0.08 0.06 G.I.RFN Rafina Small wooden construction 0 Tertiary Dep./Limestone 38.02 23.99 50 0.08 0.01 0.03 G.I.SGMA Syntagma Metro/Level 1 7 Schist 37.98 23.74 21 0.15 0.24 0.05 G.I.SGMB Syntagma Metro/Level 3 26 Schist 37.98 23.74 21 0.11 0.09 0.09 G.I.SPLA Sepolia Metro/Level 2 13 Alluvial/Schist 38.00 23.71 17 0.25 0.22 0.08 G.I.SPLB Sepolia Basement/2-story 0 Alluvial/Schist 38.00 23.71 17 0.32 0.31 0.19 G.I.THI Thiva Free field 0 Pleistocene Deposits 38.317 23.317 32 0.04 0.03 0.03 ITSAK

*PPC, Public Power Corporation of Greece; G.I., Institute of Geodynamics, National Observatory of Athens; ITSAK, Institute of Engineering Seismologyand Earthquake Engineering.

method described, P(x) has the form of the fourth-orderButterworth filter:

8 �1/2P(x) � [1 � (x/x ) ] . (2)m

The function S(x) is calculated as the product of a certaindeterministic function (usually the x�2 model), which de-fines the average shape and amplitude of the spectrum, anda stochastic function (e.g., the Fourier spectrum of win-dowed Gaussian noise) that accounts for the realistic randomcharacter of the simulated ground motion.

The extension of the stochastic model to the finite-faultcase requires transformations of the theoretical expressionsthat have been proposed for point sources to account for thefinite dimensions of the sources that produce large earth-quakes. The fault plane is discretized into a certain numberof equal rectangular elements (subfaults) with dimensionsDl � Dw. Each subfault is then treated as a point sourcewith an x�2 spectrum, which can be fully defined by twoparameters: the seismic moment, m0, and the corner fre-quency, f c, of the subfault spectrum. The connection be-tween these two parameters and the finite dimensions of thesubfaults is established through two coefficients, Dr and K,respectively. In detail, assuming the simple case for whichDl � Dw, the subfault moment, m0, can be determined fromthe following relation:

3m � Dr • Dl , (3)0

where Dr is a stress parameter, most closely related to the

static stress drop (Beresnev and Atkinson, 1997). Dr relatesthe subfault moment to its finite dimensions. On the otherhand, K relates the subfault spectrum corner frequency, f c,to its finite dimensions, through the relation:

f • DlcK � , (4)b

where b is the shear-wave velocity. The parameter K actuallycontrols the level of high-frequency radiation in the simu-lated time history and is equal to:

yzK � , (5)

p

where y is the ratio of rupture velocity to shear-wave velocityand z is linked to the maximum rate of slip, vm, on the faultplane through the equation:

2yz Drv � , (6)m � �� e qb

where e is the base of the natural logarithm and q is thedensity. The value of z depends on a convention in the def-inition of the rise time as it is introduced in the exponentialfunctions that describe the x�2 model and for standard con-ventions z � 1.68 (Beresnev and Atkinson, 1997, 1998).Due to the uncertainties involved in the definition of z, itsvalue is allowed to vary through a parameter called sfact,


Figure 2. Slip-distribution model for the 1999Athens earthquake. Contours are for 10 cm of slip.Star denotes the hypocentral location, and dots framethe areas of maximum concentration of slip (afterRoumelioti et al., 2003b).

which practically consists a “free” parameter during the im-plementation of the method.

Finite-Fault Model

The finite-fault model of the 1999 Athens earthquakeincludes a 14 � 16 km planar fault discretized into 1-km2

subfaults. The dimensions and the selected distribution ofslip on the fault plane are based on the model proposed byRoumelioti et al. (2003b), which is depicted in Figure 2. Thefault-orientation parameters were adopted from the study ofLouvari and Kiratzi (2001), whereas hypocenter parameterswere taken from Papadimitriou et al. (2002). Stress param-eter, Dr, was kept fixed at the value of 50 bars (Kanamoriand Anderson, 1975), which is close to the average value of56 bars derived from simulations of response spectra of re-cent Greek earthquakes (Margaris and Boore, 1998).

For the geometric attenuation we applied a geometricspreading operator of 1/R, and the anelastic attenuation wasrepresented by a mean frequency-dependent quality factorfor the Aegean Sea and the surrounding area, Q(f ) � 100f 0.8

(Hatzidimitriou, 1993, 1995), derived from studies of S-wave and coda-wave attenuation.

The effect of the near-surface attenuation was also takeninto account by diminishing the simulated spectra by thefactor exp(�pjf ) (Anderson and Hough, 1984). The kappaoperator, j, was given the values presented in Table 2, de-pending on the geotechnical characterization of each one ofthe examined sites. Information on the geotechnical char-acterization was combined from the studies of Bouckovalaset al. (2002), Koliopoulos and Margaris (2001), and Theo-dulidis et al. (2004). Most of the station installation siteswere characterized as C sites with the exceptions of stationsDMK, KERT, ALIV (sites B), and COR (site D).

The complete set of parameters used to stochasticallysimulate the 1999 Athens earthquake is presented in Table 3.

Site Effect

Incorporation of site amplification effects in strong-motion synthetics is usually one of the most troublesometasks, because site-specific geotechnical information is usu-ally limited or nonexistent. In the case of the Athens earth-quake, the so-far published geotechnical data are not enoughto allow computations of theoretical transfer functions at asufficient number of sites. Furthermore, the vast majority ofthe strong-motion stations that recorded the earthquake wereinstalled on “soft” sites, and this fact, in combination withthe sparse character of the local network, does not allow theapplication of the standard spectral ratios (SSR) method to asufficient number of stations. Consequently, after assessingthe available data, we decided to use the horizontal-to-vertical (H/V) spectral ratios technique as correction ampli-fication factor versus frequency. By adopting the specifictechnique we are capable of obtaining H/V ratio amplitudesat all the recording sites, which are preferable from empirical

amplification factors in cases of site-specific simulations. Onthe other hand, although H/V ratio technique has been provento correctly identify the site resonance, it usually underes-timates true amplifications (Bard, 1997; Castro et al., 2001).Therefore, by using H/V ratios, we do not expect the simu-lated spectra to perfectly match the observed spectra in am-plitude, although an adequate match is expected in shape.

To assess the level of uncertainty introduced in the sim-ulated strong-motion amplitudes by the use of the H/V ratios,we performed a comparative application of this techniqueand the SSR method at a limited number of stations. Morespecifically, the two methods were applied at three recordingsites (ATHA, CHAL, and PNT in Fig. 1). In all three cases,the reference station for the application of the SSR methodwas station DMK (also in Fig. 1). The outcomes of the par-allel application of the two methods, based on mainshockdata, are compared in Figure 3. In general, a satisfactoryagreement in both the shape and the absolute amplitudes ofthe amplification functions can be observed in all three ex-amined stations. The amplification level suggested by theH/V ratios technique is systematically lower than the corre-sponding one suggested by the SSR method. Nevertheless,the ratio of the two functions is less than 1.5 in almost allthe examined periods. Furthermore, taking into account therelatively large distance between the SSR station pairs (3 to


Table 2Site Categorization and Values of Parameter j Used in the Strong Ground-Motion Simulation

of the 1999 Athens Earthquake

Site Code VS30 (m/sec) Geotechnical Description j Reference

B 760 � VS30 � 1500 Rock 0.035 Margaris and Boore, 1998C 360 � VS30 � 760 Very stiff soil→soft rock 0.044 Klimis et al., 1999D 180 � VS30 � 360 Stiff soil 0.066 Klimis et al., 1999

VS30 gives the value interval of the average S-wave velocity at the top 30 m of the soil column for each sitecategory.

Table 3Modeling Parameters Used to Stochastically Simulate Strong Ground Motion from the

1999 Athens Earthquake

Parameter Symbol Value

Fault orientation �1 Strike, 115�d1 Dip, 57�

Fault dimensions L Length, 14 kmW Width, 16 km

Depth to upper edge of the fault H 3.3 kmMainshock moment magnitude MW 5.9Stress drop stress 50 barsNumber of subfaults along strike and dip NL � NW 14 � 16Hypocenter location on the fault i0, j0 4,6Crustal shear wave velocity beta 3.3 km/secCrustal density rho 2.72 g/cm3

Parameter controlling high-frequency level sfact 1.5Parameter j kappa As in Table 2Parameters of the attenuation model Q0 100.0Q(f ) � Q0*f**eta eta 0.8Geometric spreading igeom 0 (1/R model)Distance-dependent duration (sec) Equal to source duration (s) for R � 40 km

and to s � 0.05 R for R � 40 kmSite effect namp 1 (H/V) spectral ratiosSlip distribution model

islipEarthquake specific from Roumelioti et al.(2003b) (Fig. 2)

5 km instead of the distances less than 1 km usually usedfor the SSR method), it is possible that the amplification levelestimated by the SSR method is slightly overestimated. Toconclude, the comparison in Figure 3 suggests that the H/Vspectral ratios can provide good approximations of the am-plification levels estimated by the SSR method, at least atsites with surface geology similar to the one of the threeexamined stations.

H/V spectral ratios estimates performed during thisstudy were based on strong-motion records of the 1999 Ath-ens mainshock. Nevertheless, we also used aftershock data,wherever available, to compare the resulting amplificationfunctions. In all tests, results from mainshock data werewithin �1 standard deviation of the average function re-sulting from aftershock H/V ratios.

Model Validation

The first step of our analysis includes the validation ofthe stochastic finite-fault model parameters at free-field sta-tions that recorded the earthquake. As previously mentioned

in the case of the Athens earthquake, only three of the re-cording stations can be considered as “free-field”; namely,DMK, SPLB, and KEDE. Among these stations DMK is theonly one installed on hard rock. Soil column at KEDE con-sists of �10 m of alluvial deposits with average shear-wavevelocity of the order of 320–400 m/sec and the underlyingbedrock; whereas, at SPLB, alluvial deposits present a thick-ness of �13 m and average shear-wave velocity of about300 m/sec (Gazetas et al., 2001).

The presence of alluvial deposits at two of the threevalidation stations is expected to have significantly influ-enced the strong-motion recordings. Therefore, during thevalidation procedure it is necessary to include the effect ofthe recording-site conditions. For station DMK this is doneby using empirical amplification factors estimated for ge-neric rock sites (Boore et al., 1993). For stations KEDE andSPLB site-specific amplification functions are estimatedthrough the H/V spectral ratios method (Fig. 4). The low-frequency limit in the amplification functions presented isselected based on the signal-to-noise ratio of the correspond-ing records used in the estimation of the H/V ratios.


Figure 3. Comparison of the amplification func-tions estimated by the SSR and the H/V spectral ratiosmethod at three recording sites (ATHA, CHAL, andPNT from top to bottom). Station DMK was used asreference station for the application of the SSRmethod in all three cases. Amplification functionswere computed based on pseudovelocity (PSV) spec-tra of the mainshock records (damping 5%).

Figure 4. Amplification functions for stationsKEDE (a) and SPLB (b) estimated using the H/Vspectral ratios method.

We assume that the fault dimensions and the details ofthe faulting process, such as the rupture-initiation point andslip distribution on the fault plane, are well constrained byprevious studies. In this case, the only “free” parameter dur-ing the implementation of the method is sfact, which controlsthe strength of high-frequency radiation from each subfault.This parameter controls the value of z (equation 6) and af-

fects the amplitude of the synthetic spectrum at frequencieslarger than the subfault spectrum corner frequency. To selectthe value of this parameter we performed a grid searchwithin the interval 0.5 to 2.0 (Beresnev and Atkinson, 1997).

The effectiveness of the tested values was evaluatedthrough calculations of the model error, which is defined asthe ratio between the average Fourier amplitude spectrum ofthe two horizontal components and the synthetic Fourier am-plitude spectrum (derived through Fast Fourier Transform-ing of the synthetic acceleration time history). As an addi-tional criterion we also examined the relative performanceof the tested values in reproducing the observed PGAs (es-timated as the average of the two horizontal peak values) atthe three validation sites.

Figure 5 shows the model error at each one of the val-idation stations for four representative values of parametersfact (0.5, 1.0, 1.5, and 2.0). This figure suggests that thesmaller overall spectral difference between observations andsynthetics (model error closer to unit) appears when sfact �1.5. This value corresponds to the average value proposedby Beresnev and Atkinson (2001a, b) based on simulationsof a large number of earthquakes, and it corresponds to“standard” events that do not present unusually high or lowslip velocities.

Table 4 includes PGA values at the three validation sitesfor different values of sfact. PGAs written in bold are theclosest to the corresponding average horizontal values. As itcan be concluded, the value of 1.5 for parameter sfact is alsosatisfactory in terms of the overall PGA prediction at thethree examined sites.


Figure 5. Model error showing the ratio of the ob-served to simulated amplitude Fourier spectrum atthree validation sites (DMK, KEDE, and SPLB fromtop to bottom) for four representative values of sfact.

Table 4Peak Ground Acceleration Values at Three Validation Sites

for Different Values of sfact.

Peak Ground Acceleration (cm/sec2)

sfact DMK KEDE SPLB

0.5 12.1 31.4 40.10.6 17.1 44.6 48.90.7 22.9 59.8 69.70.8 29.3 76.8 93.90.9 36.4 95.7 121.21.0 44.0 116.2 151.31.1 52.2 138.2 184.11.2 60.8 161.7 219.21.3 69.8 186.5 256.51.4 79.2 212.5 295.61.5 88.9 239.6 336.51.6 99.0 267.8 378.71.7 110.1 296.8 422.21.8 121.8 326.7 466.71.9 133.9 357.4 512.02.0 146.3 388.6 558.0

Values typed in bold are closest to the average observed horizontal peakground acceleration.

The resulting synthetic S-wave acceleration time histo-ries, Fourier amplitude spectra, and elastic response spectra(damping 5%) at the three validation stations are presentedin Figure 6. Taking into account the simplicity of the appliedmethod, the overall agreement between synthetics and ob-servations is very satisfactory both in the time and frequencydomains. The largest misfit is observed in the intermediate-

frequency domain (0.2 to 0.4 sec) of the response spectracorresponding to station DMK. Nevertheless, this particularstation is located on the elongation of the fault model towardthe east and, according to our tests, the simulation resultsare sensitive to the uncertainty included in the adopted faultstrike.

In the second step of our analysis the validated param-eters are further tested through simulations at a much largernumber of stations that recorded the 1999 Athens earth-quake. These stations had been installed inside the under-construction Athens metro or in multistory building base-ments, at depths of several meters; therefore, some of therecordings may have been affected by the surroundingstructures.

As in the validation procedure, stochastic simulationswere performed using the parameters presented in Table 3.Site effect at each station was taken into account by usingthe corresponding amplification functions estimated by theH/V spectral ratios technique (Fig. 7). Amplification func-tions were estimated using all three acceleration componentsof the mainshock, with the exception of station MNSAwhere the transversal component, as already mentioned, wasaffected by surrounding structures and, therefore, only thelongitudinal component was used.

As derived from Table 1, the examined stations are lo-cated at epicentral distances ranging from 16 to 61 km. Theclosest to the epicenter stations (R � 30 km) are all concen-trated to the east-southeast of the fault, whereas the moredistant stations provide a much better azimuthal coverage.

In Figure 8 (a–d) we present the results of the stochasticsimulations and their comparisons with the observed strongground-motion recordings. In general, the synthetics are invery good agreement with observations in almost all cases.


Figure 6. Comparison between observed and synthetic acceleration time histories(left), amplitude Fourier spectra (center), and elastic response spectra (5% damping)(right) at the three validation stations.

Underprediction of strong-motion duration at more distantstations (e.g., LAVR and THI) can be attributed to insuffi-ciencies of the seismic wave attenuation and duration modelsand complexity of the propagation paths. Further study anddiscrimination between these three factors was consideredunnecessary and beyond the scope of this article, which ba-sically aims in forward calculating strong ground motion atdistances less than 40 km from the causative fault plane. Ofparticular interest are the simulation results at station MNSA(Fig. 8c), where the synthetic acceleration waveform differssignificantly from the observed transversal component,

which has been affected by factors not taken into account inthe simulation procedure (nearby structures). On the con-trary, the synthetic waveform matches satisfactorily the ob-served longitudinal component.

Figures 9 and 10 reflect a statistical analysis on our re-sults. In Figure 9 we present ratios of average observed hor-izontal PGA to synthetic PGA versus epicentral distance forthe total of the 19 examined stations. In Figure 10 we showcorresponding ratios of spectral acceleration (SA) values asa function of epicentral distance, as well, and for represen-tative period values of 0.12, 0.35, and 1.08 sec. As derived


Figure 7. Amplification functions for strong motion stations whose records of the1999 Athens earthquake are simulated using the validated parameters of Table 3. Allamplification functions have been calculated using the H/V spectral ratios method.

from these two figures, the misfit between observed and syn-thetic PGA and SA values is less than a factor of 1.5 for themajority of stations and throughout the entire range of epi-central distances covered by our data.

Application of the Validated Model

In the final step of our analysis, the validated parametersof the stochastic model are used to perform “blind” predic-tions of strong ground motion within the meizoseismal areaof the 1999 Athens earthquake. For this purpose we set upa grid of 1200 points covering the wider epicentral area, witha distance of 0.02� between successive points. Synthetic ac-celerograms were calculated for each one of these points byassuming hard rock site conditions to emphasize the sourceeffect. PGA values were subsequently used to produce thesynthetic PGA map, which is presented in Figure 11, alongwith the projection of the upper edge of the fault model andits hypothetical continuation toward the surface. As can beconcluded from Figure 11, PGA values at hard rock did notexceed 0.35 g. Largest values are observed along the surfaceprojection of the upper edge of the fault, while a slight asym-metry of the strong motion field is observed toward themeizoseismal area (Ano Liosia, Menidi, Thrakomakedones).This asymmetry corresponds to a significant increase of PGAvalues within the meizoseismal area relative to the mirror

sites towards the strike-opposite direction, which locallyreaches 50% (i.e., close to Thrakomakedones).

Synthetic accelerograms were further used to calculateelastic response spectra (5% damping) and peak spectral ac-celeration (PSA) values were used to produce PSA syntheticmaps. Figure 12 shows the synthetic maps for representativeperiod values (T � 0.1, 0.2, 0.35, 1.0, 2.0, and 3.0 sec)covering the simulated period range. By comparing the re-sulting maps one can conclude different levels of asymmetrytoward the meizoseismal area. At indermediate periods (1.0sec) it is difficult to notice any asymmetry in the radiatedenergy toward this area. On the contrary, the asymmetry isprofound at longer periods (3 sec) and at short periods (0.1to 0.35 sec). This result is in agreement with the results ofspectral analysis performed on regional broadband data ofthe 1999 Athens earthquake (Roumelioti, 2003), which re-vealed increased spectral content at the same period intervalstoward east-northeast stations. The estimated absolute valuesof strong ground motion are of moderate magnitude to ad-equately explain the extensive damage observed within themeizoseismal area. Nevertheless, they imply increased levelsof radiated energy at certain period intervals, which mayhave been combined with other factors, such as site and to-pographic relief effects (Anastasiadis et al., 1999; Marinoset al., 1999; Bouckovalas and Kouretzis, 2001; Gazetas,2001; Gazetas et al., 2001, 2002). We mention that in the


Figure 8. Comparison between observed and synthetic acceleration time histories(left), amplitude Fourier spectra (center) and elastic response spectra (5% damping)(right) at 16 examined strong-motion stations. (continued)


Figure 8. Continued


Figure 9. Ratios of average observed horizontalPGA to synthetic PGA at the 19 examined stations, asa function of epicentral distance, R.

Figure 11. Synthetic PGA map at hard rock forthe 1999 Athens earthquake. The upper edge of thefault model (continuous line) and the projection of itscontinuation toward the surface (dashed line) are alsoshown. Monastiraki is located at the center of Athens,whereas the remaining three depicted sites are amongthe most heavily damaged ones.

Figure 10. Ratios of average observed horizontalspectral acceleration to the corresponding syntheticvalue at the 19 examined stations, as a function ofepicentral distance, R. Ratios are shown for discreteperiod values of 0.12, 0.35, and 1.08 sec (from top tobottom).

central part of Ano Liosia PGA amplification due to localsoil conditions was estimated to be of the order of 60%,whereas the largest PSA amplification was of the order of 2at period �0.17 sec (Gazetas et al., 2001).

Discussion and Conclusions

The stochastic finite-fault method was applied to sim-ulate acceleration records of the 1999 Athens earthquake andto assess the source effect on the distribution of strongground motion within the meizoseismal area where no re-cords are available. Model parameters were first validatedagainst their ability to reproduce the acceleration records atthree free-field strong motion stations. The validated param-eters were further tested through simulations of records at16 stations located at epicentral distances ranging from 16to 61 km and finally used to produce synthetic PGA and PSAmaps that cover the meizoseismal and adjacent areas.

Observed acceleration time histories, Fourier amplitudespectra, and elastic response spectra were successfully sim-ulated in almost all cases. The synthetic PGA map suggestedthat the highest PGA values at bedrock occurred along theprojection of the upper edge of the fault, whereas a slightasymmetry was observed toward the meizoseismal area. Al-though this asymmetry is not as clear as the one derived fromInSAR or long-period seismological data (Kontoes et al.,2000; Roumelioti et al., 2003b), it implies a significant increaseof the PGA values toward the meizoseismal area, which lo-cally reached 50% of the values observed in the oppositedirection. Nevertheless, PGA values at bedrock are still gen-erally low (�0.35 g) and could only explain the high levelof damage in this area if combined with other factors, e.g.,the site effect. We indicatively mention that the use of em-pirical amplification factors of site classes C and D (Klimis


Figure 12. Synthetic PSA maps at selected periods for the 1999 Athens earthquake.In agreement with the previous figure, synthetic values correspond to hard rock con-ditions, i.e, no site effets have been taken into account.

et al., 1999) amplifies the synthetic PGA values by approx-imately a factor of 2. This means that PGA values computedfor bedrock conditions within the meizoseismal area (0.13to 0.2 g according to Fig. 11) can increase up to 0.4g, a valuethat is in accordance with the mean modified Mercalli inten-sity (MMI) estimated for the areas of Ano Liosia, Menidi,and Thrakomakedones (VIII–IX; see www.itsak.gr), as de-rived from empirical relations between MMI and PGA (Theo-dulidis, 1991; Theodulidis and Papazachos, 1992; Wald etal., 1999).

Synthetic PSA maps are also asymmetrical toward themeizoseismal area. The asymmetry appears more distinc-

tively at periods longer than 2 sec and within the range 0.2to 0.3 sec. This result is comparable with direct measure-ments of the spectral content of regional broadband wave-forms (Roumelioti, 2003). The sharp asymmetry observedat 0.2 sec is extremely interesting in terms of explaining thedamage distribution pattern, as most of the buildings dam-aged by the earthquake were two- or three-story construc-tions with resonances close to 0.2 sec. On the other hand,site-effect studies within the meizoseismal area suggest thatsite effect was also significant in this period range (Gazetaset al., 2001). By combining these pieces of information weconclude that the destructiveness of the 1999 Athens earth-


quake was probably due to an unfortunate combination ofsource and site effects within a limited strong-motion periodrange.

The results of this study stem from a rough represen-tation of all three factors controlling the strong ground mo-tion, namely the earthquake source, the propagation path,and the site effect. Despite the simplicity of the model, syn-thetic strong-ground motion is in agreement with all theavailable seismological, geodetic, and geotechnical infor-mation and adequately explains the damage distribution pat-tern of the examined earthquake. Nevertheless, deeper un-derstanding of the faulting process and its effect on thedistribution of damage requires finer modeling (e.g., inclu-sion of an area-specific 3D velocity model, additional geo-technical data to characterize recording site conditions, andinvestigation of the temporal characteristics of the ruptureprocess).

Acknowledgments

We acknowledge the partial financial support of the General Secre-tariat of Research and Technology (GSRT) of the Ministry of Developmentof Greece and of the Earthquake Planning and Protection Organization(EPPO) of Greece (no. 70/3/5484). Thanks are due to our colleagues of theGeodynamic Institute of the National Observatory of Athens for providingpart of the data used and to Igor Beresnev for kindly offering the simulationcode and valuable advice. The article also benefited from careful reviewsby Z. Wang and V. Sokolov.

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Department of GeophysicsAristotle University of Thessaloniki54124 Thessaloniki, Greece

(Z.R., A.K.)

Institute of Engineering Seismology and Earthquake EngineeringP.O. Box 5355102 Thessaloniki, Greece

(N.T.)

Manuscript received 14 October 2003.

stochastic strong ground-motion simulation of the 7...

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