(Greece) Earthquake by Zafeiria Roumelioti, Anastasia Kiratzi, and Nikolaos Theodulidis

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 strong ground motion from the 7 September 1999, moment magnitude M 5.9 Athens earthquake. The method includes descritization of the fault plane into a certain number ,spectrum. A slip-distribution model 2מof subfaults, each of which is assigned an x derived from previous studies of this earthquake, is used to specifically account for the source effect. Contributions from all subfaults are then empirically attenuated to the observation sites, where they are summed to produce the synthetic acceleration time history. The method is first calibrated against its ability of reproducing the recordings at 19 strong-motion stations, at epicentral distances ranging from 16 to 61 km. The calibrated model is then applied to calculate synthetics at a large number of grid points covering the area around the fault plane. Simulated peak values are subsequently used to produce synthetic peak ground acceleration and spectral acceleration maps at hard rock. Both peak ground acceleration and spectral acceleration maps 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 in the period range 0.2 to 0.3 sec. Independent geotechnical studies showed considerable site effect at periods 0.5 sec within the meizoseismal area. This result, coupled with the results of the present study, imply that the damage distribution pattern of the 1999 Athens earthquake can be explained by the destructive combination of two factors: the source directivity and the site effect.

Introduction The 7 September 1999, M 5.9 Athens earthquake con- urbs of the city (the municipalities of Thrakomakedones, stitutes another resounding example of the potential destruc- Ano Liosia, Fili, and Menidi), which are located to the east tiveness of moderate-magnitude earthquakes when they oc- of the Fili fault (Fig. 1). In general, damage distribution cur in the proximity of densely populated areas. Reported within the wider epicentral area was irregular (e.g., damage damage places the specific earthquake among the worst nat- within the projection of the fault plane, which is usual for ural disasters in the modern history of Greece. In total, 143 normal-fault earthquakes, was insignificant compared with people were killed, whereas the economic loss is estimated that observed close to the fault’s eastern termination). This to have reached 3% of Greece’s Gross Domestic Product asymmetry toward the meizoseismal area caused speculation (GDP) (Pomonis, 2002). for emergence of directivity phenomena during the earth- The earthquake was related to normal faulting in a quake rupture, which was later confirmed by several studies ,Tselentis and Zahradnik, 2000; Zahradnik and Tselentis) ,57 ס dip ,115 ס northwest–southeast direction (strike ,Louvari and Kiratzi, 2001), about 15 km 2002; Roumelioti et al., 2003a b; Gallovic and Brokesova ;80מס rake northwest of the center of Athens. In the epicentral area, two 2003). normal faults of such orientation are clearly expressed on In the present study we simulate the strong ground mo- the morphology, namely the Thriassio and Fili faults (Fig. tion of the 1999 Athens earthquake by using the widely ap- 1). Among these two structures, the Fili fault is most likely plied stochastic method for finite faults (Beresnev and At- related to the 1999 earthquake (Ganas et al., 2001; Pavlides kinson, 1997). The simulation parameters are first validated et al., 2002), although the rupture did not reach the surface through a posteriori predictions of the available strong- (Papazachos et al., 2001; Baumont et al., 2002; Roumelioti motion records of the examined event and subsequently used et al., 2003b) and, therefore, any conclusions regarding the to assess the strong-motion level at a much larger number causative fault are doubtful. of sites, including the meizoseismal area, for which no re- Most of the damage was observed in the northwest sub- cords are available. Our primary target is to investigate how

1036 Stochastic Strong Ground-Motion Simulation of the 7 September 1999 Athens (Greece) Earthquake 1037

Figure 1. Regional map showing the epicenter of the 1999 Athens earthquake (star symbol) and the locations of the strong motion stations used in the present study. Traces of the Fili and Triassio faults and the area of damage concentration (where the municipalities of Thrakomakedones, Ano Liosia, Fili, and Men- idi are discussed in the text) are also depicted.

source effect related to this earthquake affected the distri- operated by the Institute of Engineering Seismology and bution of strong ground motion and whether this factor is Earthquake Engineering (ITSAK), whereas the Public capable of explaining the degree of damage within the Power Corporation (PPC) of Greece operated three more meizoseismal area. stations (ETNA type). Detailed information on the locations (Fig. 1) and the surface geological conditions at the installation sites, as well Data as PGA values recorded during the examined earthquake are Strong ground motion of the 1999 Athens earthquake given in Table 1. was recorded by a significant number of acceleration stations. However, by the time of the mainshock, all the re- Method cording stations were operating out of the meizoseismal area. Most of the triggered instruments belong to the Institute of In the stochastic method, the Fourier amplitude spec- Geodynamics (G.I.) of the National Observatory of Athens, trum of a seismic signal is represented as the product of a which is operating a strong motion network consisting of spectrum, S(x), that accounts for the effects of the seismic digital instruments (Teledyne A-800 type) to monitor the source and several other filtering functions that represent the construction of the Athens metro. Most of the instruments effects of the propagation path and the recording site. If the are installed below the surface, at different levels of the receiver installation site can be characterized as hard rock, underconstruction metro, and only two stations (MNSA and the shear-wave acceleration spectrum is given by: DMK) can be considered as “free-field.” Between these two מ (2x2 • S(x) • P(x) • e xR/2Qb, (1 ס (stations, MNSA recorded the largest peak ground accelera- A(x -g) in one of the two horizontal compo 0.51 ס tion (PGA nents (oriented N100), a value that was found to be incon- where x is the angular frequency, R is the hypocentral dis- sistent with the low degree of building damage in the tance, Q is the quality factor introduced to account for the neighborhood of the station. Subsequent studies revealed regional inelastic attenuation, and b is the shear-wave ve- that the presence of three underground structures next to the locity. The filtering function P(x) is used for the commonly station’s installation site spuriously enhanced the accelera- observed spectral cutoff above a certain frequency xm. Ac- tion amplitudes in the particular horizontal component up to cording to some scientists, this phenomenon is attributed to a level of 30% (Gazetas et al., 2002). Nevertheless, two more the processes that take place at the source during the occur- stations (KEDE and SPLB) were installed at the basement rence of an earthquake (Papageorgiou and Aki, 1983; Pa- of light buildings (one- to two-stories) and can practically pageorgiou, 1988). Others believe that it is mainly due to be used as “free-field” stations (Gazetas et al., 2001). high-frequency attenuation by the near-surface weathered The rest of the stations (SMA-1 type) that recorded the layer (Hanks, 1982; Anderson and Hough, 1984; Beresnev earthquake belong to the permanent strong-motion network and Atkinson, 1997; Theodulidis and Bard, 1998). In the 1038 Z. Roumelioti, A. Kiratzi, and N. Theodulidis

Table 1 Information on the Strong-Motion Stations Used to Calibrate the Parameters of the Finite-Fault Stochastic Simulation Method in the 1999 Athens Earthquake

Epicentral Station Installation Sensor Depth Latitude Longitude Distance PGA PGA PGA Code Area Installation Site (m) Surface Geology (N) (E) (km) (L) (T) (V) Carrier*

ALIV Aliveri Ground level 0 — 38.400 24.033 53 0.02 0.02 0.01 PPC ATHA 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 ITSAK COR Corinthos Basement/2-story 0 Alluvial 37.937 22.933 59 0.03 0.02 0.02 ITSAK DFNA 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 ITSAK KEDE K.E.D.E. Basement/1-story 0 Marl 37.983 23.717 19 0.26 0.30 0.16 ITSAK KERT Keratsini Basement/2-story 0 — 37.967 23.617 16 0.22 0.19 0.16 PPC LAVR Lavrio Ground level 0 — 37.717 24.050 61 0.04 0.05 0.05 PPC MNSA 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 Seismology and Earthquake Engineering. method described, P(x) has the form of the fourth-order static stress drop (Beresnev and Atkinson, 1997). Dr relates Butterworth ﬁlter: the subfault moment to its ﬁnite dimensions. On the other

hand, K relates the subfault spectrum corner frequency, f c, 1/2מ 8 ם ס P(x) [1 (x/xm)] . (2) to its ﬁnite dimensions, through the relation:

• The function S(x) is calculated as the product of a certain fc Dl (4) , ס K מ deterministic function (usually the x 2 model), which de- b fines the average shape and amplitude of the spectrum, and a stochastic function (e.g., the Fourier spectrum of win- where b is the shear-wave velocity. The parameter K actually dowed Gaussian noise) that accounts for the realistic random controls the level of high-frequency radiation in the simu- character of the simulated ground motion. lated time history and is equal to: The extension of the stochastic model to the finite-fault case requires transformations of the theoretical expressions yz (5) , ס that have been proposed for point sources to account for the K finite dimensions of the sources that produce large earth- p quakes. The fault plane is discretized into a certain number of equal rectangular elements (subfaults) with dimensions where y is the ratio of rupture velocity to shear-wave velocity Dw. Each subfault is then treated as a point source and z is linked to the maximum rate of slip, vm, on the fault ן Dl :spectrum, which can be fully defined by two plane through the equation 2מwith an x parameters: the seismic moment, m0, and the corner frequency, f , of the subfault spectrum. The connection be- 2yz Dr (΂΃΂΃, (6 ס c v tween these two parameters and the finite dimensions of the m e qb subfaults is established through two coefficients, Dr and K, respectively. In detail, assuming the simple case for which where e is the base of the natural logarithm and q is the ס Dl Dw, the subfault moment, m0, can be determined from density. The value of z depends on a convention in the def- the following relation: inition of the rise time as it is introduced in the exponential -model and for standard con 2מfunctions that describe the x 3 • ס .(Beresnev and Atkinson, 1997, 1998) 1.68 ס m0 Dr Dl , (3) ventions z Due to the uncertainties involved in the definition of z, its where Dr is a stress parameter, most closely related to the value is allowed to vary through a parameter called sfact, Stochastic Strong Ground-Motion Simulation of the 7 September 1999 Athens (Greece) Earthquake 1039 which practically consists a “free” parameter during the implementation of the method.

Finite-Fault Model The finite-fault model of the 1999 Athens earthquake km planar fault discretized into 1-km2 16 ן includes a 14 subfaults. The dimensions and the selected distribution of slip on the fault plane are based on the model proposed by Roumelioti et al. (2003b), which is depicted in Figure 2. The fault-orientation parameters were adopted from the study of Louvari and Kiratzi (2001), whereas hypocenter parameters were taken from Papadimitriou et al. (2002). Stress parameter, Dr, was kept fixed at the value of 50 bars (Kanamori and Anderson, 1975), which is close to the average value of 56 bars derived from simulations of response spectra of recent Greek earthquakes (Margaris and Boore, 1998). For the geometric attenuation we applied a geometric spreading operator of 1/R, and the anelastic attenuation was represented by a mean frequency-dependent quality factor 100f 0.8 ס (for the Aegean Sea and the surrounding area, Q(f (Hatzidimitriou, 1993, 1995), derived from studies of S- wave and coda-wave attenuation. The effect of the near-surface attenuation was also taken into account by diminishing the simulated spectra by the pjf) (Anderson and Hough, 1984). The kappa Figure 2. Slip-distribution model for the 1999מ)factor exp operator, j, was given the values presented in Table 2, de- Athens earthquake. Contours are for 10 cm of slip. pending on the geotechnical characterization of each one of Star denotes the hypocentral location, and dots frame the areas of maximum concentration of slip (after the examined sites. Information on the geotechnical char- Roumelioti et al., 2003b). acterization was combined from the studies of Bouckovalas et al. (2002), Koliopoulos and Margaris (2001), and Theo- dulidis et al. (2004). Most of the station installation sites amplification factors in cases of site-specific simulations. On were characterized as C sites with the exceptions of stations the other hand, although H/V ratio technique has been proven DMK, KERT, ALIV (sites B), and COR (site D). to correctly identify the site resonance, it usually underes- The complete set of parameters used to stochastically timates true amplifications (Bard, 1997; Castro et al., 2001). simulate the 1999 Athens earthquake is presented in Table 3. Therefore, by using H/V ratios, we do not expect the simulated spectra to perfectly match the observed spectra in am- Site Effect plitude, although an adequate match is expected in shape. To assess the level of uncertainty introduced in the sim- Incorporation of site amplification effects in strong- ulated strong-motion amplitudes by the use of the H/V ratios, motion synthetics is usually one of the most troublesome we performed a comparative application of this technique tasks, because site-specific geotechnical information is usu- and the SSR method at a limited number of stations. More ally limited or nonexistent. In the case of the Athens earth- specifically, the two methods were applied at three recording quake, the so-far published geotechnical data are not enough sites (ATHA, CHAL, and PNT in Fig. 1). In all three cases, to allow computations of theoretical transfer functions at a the reference station for the application of the SSR method sufficient number of sites. Furthermore, the vast majority of was station DMK (also in Fig. 1). The outcomes of the par- the strong-motion stations that recorded the earthquake were allel application of the two methods, based on mainshock installed on “soft” sites, and this fact, in combination with data, are compared in Figure 3. In general, a satisfactory the sparse character of the local network, does not allow the agreement in both the shape and the absolute amplitudes of application of the standard spectral ratios (SSR) method to a the amplification functions can be observed in all three ex- sufficient number of stations. Consequently, after assessing amined stations. The amplification level suggested by the the available data, we decided to use the horizontal-to- H/V ratios technique is systematically lower than the corre- vertical (H/V) spectral ratios technique as correction ampli- sponding one suggested by the SSR method. Nevertheless, fication factor versus frequency. By adopting the specific the ratio of the two functions is less than 1.5 in almost all technique we are capable of obtaining H/V ratio amplitudes the examined periods. Furthermore, taking into account the at all the recording sites, which are preferable from empirical relatively large distance between the SSR station pairs (3 to 1040 Z. Roumelioti, A. Kiratzi, and N. Theodulidis

Table 2 Site 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 Յ Յ B 760 VS30 1500 Rock 0.035 Margaris and Boore, 1998 Յ Յ → C 360 VS30 760 Very stiff soil soft rock 0.044 Klimis et al., 1999 Յ Յ D 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 site category.

Table 3 Modeling 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 km W Width, 16 km Depth to upper edge of the fault H 3.3 km

Mainshock moment magnitude MW 5.9 Stress drop stress 50 bars ן ן Number of subfaults along strike and dip NL NW 14 16 Hypocenter location on the fault i0, j0 4,6 Crustal shear wave velocity beta 3.3 km/sec Crustal density rho 2.72 g/cm3 Parameter controlling high-frequency level sfact 1.5 Parameter j kappa As in Table 2

Parameters of the attenuation model Q0 100.0 ס Q(f) Q0*f**eta eta 0.8 Geometric spreading igeom 0 (1/R model) Distance-dependent duration (sec) Equal to source duration (s) for R Յ 40 km R for R 40 km 0.05 ם and to s Site effect namp 1 (H/V) spectral ratios Slip distribution model Earthquake speciﬁc from Roumelioti et al. islip (2003b) (Fig. 2)

5 km instead of the distances less than 1 km usually used in the case of the Athens earthquake, only three of the re- for the SSR method), it is possible that the amplification level cording stations can be considered as “free-field”; namely, estimated by the SSR method is slightly overestimated. To DMK, SPLB, and KEDE. Among these stations DMK is the conclude, the comparison in Figure 3 suggests that the H/V only one installed on hard rock. Soil column at KEDE con- spectral ratios can provide good approximations of the am- sists of 10 m of alluvial deposits with average shear-wave plification levels estimated by the SSR method, at least at velocity of the order of 320–400 m/sec and the underlying sites with surface geology similar to the one of the three bedrock; whereas, at SPLB, alluvial deposits present a thick- examined stations. ness of 13 m and average shear-wave velocity of about H/V spectral ratios estimates performed during this 300 m/sec (Gazetas et al., 2001). study were based on strong-motion records of the 1999 Ath- The presence of alluvial deposits at two of the three ens mainshock. Nevertheless, we also used aftershock data, validation stations is expected to have significantly influ- wherever available, to compare the resulting amplification enced the strong-motion recordings. Therefore, during the functions. In all tests, results from mainshock data were validation procedure it is necessary to include the effect of standard deviation of the average function re- the recording-site conditions. For station DMK this is done 1ע within sulting from aftershock H/V ratios. by using empirical amplification factors estimated for ge- neric rock sites (Boore et al., 1993). For stations KEDE and Model Validation SPLB site-specific amplification functions are estimated through the H/V spectral ratios method (Fig. 4). The low- The first step of our analysis includes the validation of frequency limit in the amplification functions presented is the stochastic finite-fault model parameters at free-field sta- selected based on the signal-to-noise ratio of the correspond- tions that recorded the earthquake. As previously mentioned ing records used in the estimation of the H/V ratios. Stochastic Strong Ground-Motion Simulation of the 7 September 1999 Athens (Greece) Earthquake 1041

Figure 4. Ampliﬁcation functions for stations KEDE (a) and SPLB (b) estimated using the H/V spectral ratios method.

fects the amplitude of the synthetic spectrum at frequencies larger than the subfault spectrum corner frequency. To select the value of this parameter we performed a grid search within the interval 0.5 to 2.0 (Beresnev and Atkinson, 1997). The effectiveness of the tested values was evaluated through calculations of the model error, which is defined as the ratio between the average Fourier amplitude spectrum of the two horizontal components and the synthetic Fourier amplitude spectrum (derived through Fast Fourier Transform- ing of the synthetic acceleration time history). As an additional criterion we also examined the relative performance of the tested values in reproducing the observed PGAs (estimated as the average of the two horizontal peak values) at the three validation sites. Figure 3. Comparison of the amplification func- Figure 5 shows the model error at each one of the val- tions estimated by the SSR and the H/V spectral ratios idation stations for four representative values of parameter method at three recording sites (ATHA, CHAL, and PNT from top to bottom). Station DMK was used as sfact (0.5, 1.0, 1.5, and 2.0). This figure suggests that the reference station for the application of the SSR smaller overall spectral difference between observations and ס method in all three cases. Amplification functions synthetics (model error closer to unit) appears when sfact were computed based on pseudovelocity (PSV) spec- 1.5. This value corresponds to the average value proposed tra of the mainshock records (damping 5%). by Beresnev and Atkinson (2001a, b) based on simulations of a large number of earthquakes, and it corresponds to “standard” events that do not present unusually high or low We assume that the fault dimensions and the details of slip velocities. the faulting process, such as the rupture-initiation point and Table 4 includes PGA values at the three validation sites slip distribution on the fault plane, are well constrained by for different values of sfact. PGAs written in bold are the previous studies. In this case, the only “free” parameter dur- closest to the corresponding average horizontal values. As it ing the implementation of the method is sfact, which controls can be concluded, the value of 1.5 for parameter sfact is also the strength of high-frequency radiation from each subfault. satisfactory in terms of the overall PGA prediction at the This parameter controls the value of z (equation 6) and af- three examined sites. 1042 Z. Roumelioti, A. Kiratzi, and N. Theodulidis

Table 4 Peak 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 40.1 0.6 17.1 44.6 48.9 0.7 22.9 59.8 69.7 0.8 29.3 76.8 93.9 0.9 36.4 95.7 121.2 1.0 44.0 116.2 151.3 1.1 52.2 138.2 184.1 1.2 60.8 161.7 219.2 1.3 69.8 186.5 256.5 1.4 79.2 212.5 295.6 1.5 88.9 239.6 336.5 1.6 99.0 267.8 378.7 1.7 110.1 296.8 422.2 1.8 121.8 326.7 466.7 1.9 133.9 357.4 512.0 2.0 146.3 388.6 558.0

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

frequency domain (0.2 to 0.4 sec) of the response spectra corresponding to station DMK. Nevertheless, this particular station is located on the elongation of the fault model toward the east and, according to our tests, the simulation results are sensitive to the uncertainty included in the adopted fault strike. In the second step of our analysis the validated parameters are further tested through simulations at a much larger number of stations that recorded the 1999 Athens earthquake. These stations had been installed inside the underconstruction Athens metro or in multistory building base- ments, at depths of several meters; therefore, some of the recordings may have been affected by the surrounding structures. As in the validation procedure, stochastic simulations were performed using the parameters presented in Table 3. Site effect at each station was taken into account by using the corresponding amplification functions estimated by the H/V spectral ratios technique (Fig. 7). Amplification functions were estimated using all three acceleration components Figure 5. Model error showing the ratio of the ob- of the mainshock, with the exception of station MNSA served to simulated amplitude Fourier spectrum at where the transversal component, as already mentioned, was three validation sites (DMK, KEDE, and SPLB from affected by surrounding structures and, therefore, only the top to bottom) for four representative values of sfact. longitudinal component was used. As derived from Table 1, the examined stations are located at epicentral distances ranging from 16 to 61 km. The The resulting synthetic S-wave acceleration time histo- closest to the epicenter stations (R 30 km) are all concen- ries, Fourier amplitude spectra, and elastic response spectra trated to the east-southeast of the fault, whereas the more (damping 5%) at the three validation stations are presented distant stations provide a much better azimuthal coverage. in Figure 6. Taking into account the simplicity of the applied In Figure 8 (a–d) we present the results of the stochastic method, the overall agreement between synthetics and ob- simulations and their comparisons with the observed strong servations is very satisfactory both in the time and frequency ground-motion recordings. In general, the synthetics are in domains. The largest misfit is observed in the intermediate- very good agreement with observations in almost all cases. Stochastic Strong Ground-Motion Simulation of the 7 September 1999 Athens (Greece) Earthquake 1043

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 distant which has been affected by factors not taken into account in stations (e.g., LAVR and THI) can be attributed to insuffi- the simulation procedure (nearby structures). On the con- ciencies of the seismic wave attenuation and duration models trary, the synthetic waveform matches satisfactorily the ob- and complexity of the propagation paths. Further study and served longitudinal component. discrimination between these three factors was considered Figures 9 and 10 reflect a statistical analysis on our re- unnecessary and beyond the scope of this article, which ba- sults. In Figure 9 we present ratios of average observed hor- sically aims in forward calculating strong ground motion at izontal PGA to synthetic PGA versus epicentral distance for distances less than 40 km from the causative fault plane. Of the total of the 19 examined stations. In Figure 10 we show particular interest are the simulation results at station MNSA corresponding ratios of spectral acceleration (SA) values as (Fig. 8c), where the synthetic acceleration waveform differs a function of epicentral distance, as well, and for represen- significantly from the observed transversal component, tative period values of 0.12, 0.35, and 1.08 sec. As derived 1044 Z. Roumelioti, A. Kiratzi, and N. Theodulidis

Figure 7. Amplification functions for strong motion stations whose records of the 1999 Athens earthquake are simulated using the validated parameters of Table 3. All amplification functions have been calculated using the H/V spectral ratios method. from these two figures, the misfit between observed and syn- sites towards the strike-opposite direction, which locally thetic PGA and SA values is less than a factor of 1.5 for the reaches 50% (i.e., close to Thrakomakedones). majority of stations and throughout the entire range of epi- Synthetic accelerograms were further used to calculate central distances covered by our data. elastic response spectra (5% damping) and peak spectral acceleration (PSA) values were used to produce PSA synthetic Application of the Validated Model maps. Figure 12 shows the synthetic maps for representative (and 3.0 sec ,2.0 ,1.0 ,0.35 ,0.2 ,0.1 ס period values (T In the final step of our analysis, the validated parameters covering the simulated period range. By comparing the re- of the stochastic model are used to perform “blind” predic- sulting maps one can conclude different levels of asymmetry tions of strong ground motion within the meizoseismal area toward the meizoseismal area. At indermediate periods (1.0 of the 1999 Athens earthquake. For this purpose we set up sec) it is difficult to notice any asymmetry in the radiated a grid of 1200 points covering the wider epicentral area, with energy toward this area. On the contrary, the asymmetry is a distance of 0.02 between successive points. Synthetic ac- profound at longer periods (3 sec) and at short periods (0.1 celerograms were calculated for each one of these points by to 0.35 sec). This result is in agreement with the results of assuming hard rock site conditions to emphasize the source spectral analysis performed on regional broadband data of effect. PGA values were subsequently used to produce the the 1999 Athens earthquake (Roumelioti, 2003), which re- synthetic PGA map, which is presented in Figure 11, along vealed increased spectral content at the same period intervals with the projection of the upper edge of the fault model and toward east-northeast stations. The estimated absolute values its hypothetical continuation toward the surface. As can be of strong ground motion are of moderate magnitude to ad- concluded from Figure 11, PGA values at hard rock did not equately explain the extensive damage observed within the exceed 0.35 g. Largest values are observed along the surface meizoseismal area. Nevertheless, they imply increased levels projection of the upper edge of the fault, while a slight asym- of radiated energy at certain period intervals, which may metry of the strong motion field is observed toward the have been combined with other factors, such as site and to- meizoseismal area (Ano Liosia, Menidi, Thrakomakedones). pographic relief effects (Anastasiadis et al., 1999; Marinos This asymmetry corresponds to a significant increase of PGA et al., 1999; Bouckovalas and Kouretzis, 2001; Gazetas, values within the meizoseismal area relative to the mirror 2001; Gazetas et al., 2001, 2002). We mention that in the Stochastic Strong Ground-Motion Simulation of the 7 September 1999 Athens (Greece) Earthquake 1045

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) 1046 Z. Roumelioti, A. Kiratzi, and N. Theodulidis

Figure 8. Continued Stochastic Strong Ground-Motion Simulation of the 7 September 1999 Athens (Greece) Earthquake 1047

Figure 8. Continued 1048 Z. Roumelioti, A. Kiratzi, and N. Theodulidis

Figure 8. Continued Stochastic Strong Ground-Motion Simulation of the 7 September 1999 Athens (Greece) Earthquake 1049

Figure 9. Ratios of average observed horizontal PGA to synthetic PGA at the 19 examined stations, as a function of epicentral distance, R. Figure 11. Synthetic PGA map at hard rock for the 1999 Athens earthquake. The upper edge of the fault model (continuous line) and the projection of its continuation toward the surface (dashed line) are also shown. Monastiraki is located at the center of Athens, whereas the remaining three depicted sites are among the most heavily damaged ones.

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

Discussion and Conclusions The stochastic finite-fault method was applied to simulate acceleration records of the 1999 Athens earthquake and to assess the source effect on the distribution of strong ground motion within the meizoseismal area where no records are available. Model parameters were first validated against their ability to reproduce the acceleration records at three free-field strong motion stations. The validated parameters were further tested through simulations of records at 16 stations located at epicentral distances ranging from 16 to 61 km and finally used to produce synthetic PGA and PSA maps that cover the meizoseismal and adjacent areas. Observed acceleration time histories, Fourier amplitude spectra, and elastic response spectra were successfully simulated in almost all cases. The synthetic PGA map suggested that the highest PGA values at bedrock occurred along the projection of the upper edge of the fault, whereas a slight asymmetry was observed toward the meizoseismal area. Al- though this asymmetry is not as clear as the one derived from InSAR or long-period seismological data (Kontoes et al., 2000; Roumelioti et al., 2003b), it implies a significant increase of the PGA values toward the meizoseismal area, which locally reached 50% of the values observed in the opposite Figure 10. Ratios of average observed horizontal direction. Nevertheless, PGA values at bedrock are still gen- spectral acceleration to the corresponding synthetic erally low (0.35 g) and could only explain the high level value at the 19 examined stations, as a function of epicentral distance, R. Ratios are shown for discrete of damage in this area if combined with other factors, e.g., period values of 0.12, 0.35, and 1.08 sec (from top to the site effect. We indicatively mention that the use of em- bottom). pirical amplification factors of site classes C and D (Klimis 1050 Z. Roumelioti, A. Kiratzi, and N. Theodulidis

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 conditions, i.e, no site effets have been taken into account. et al., 1999) amplifies the synthetic PGA values by approx- tively at periods longer than 2 sec and within the range 0.2 imately a factor of 2. This means that PGA values computed to 0.3 sec. This result is comparable with direct measure- for bedrock conditions within the meizoseismal area (0.13 ments of the spectral content of regional broadband wave- to 0.2 g according to Fig. 11) can increase up to 0.4g, a value forms (Roumelioti, 2003). The sharp asymmetry observed that is in accordance with the mean modified Mercalli inten- at 0.2 sec is extremely interesting in terms of explaining the sity (MMI) estimated for the areas of Ano Liosia, Menidi, damage distribution pattern, as most of the buildings dam- and Thrakomakedones (VIII–IX; see www.itsak.gr), as de- aged by the earthquake were two- or three-story construc- rived from empirical relations between MMI and PGA (Theo- tions with resonances close to 0.2 sec. On the other hand, dulidis, 1991; Theodulidis and Papazachos, 1992; Wald et site-effect studies within the meizoseismal area suggest that al., 1999). site effect was also significant in this period range (Gazetas Synthetic PSA maps are also asymmetrical toward the et al., 2001). By combining these pieces of information we meizoseismal area. The asymmetry appears more distinc- conclude that the destructiveness of the 1999 Athens earth- Stochastic Strong Ground-Motion Simulation of the 7 September 1999 Athens (Greece) Earthquake 1051 quake was probably due to an unfortunate combination of effects in the 7 September 1999 Athens (Greece) earthquake, Soil source and site effects within a limited strong-motion period Dyn. Earthquake Eng. 21, 671–687. Bouckovalas, G. D., G. P. Kouretzis, and I. S. Kalogeras (2002). Site- range. specific analysis of strong motion data from the September 7, 1999 The results of this study stem from a rough represen- Athens, Greece earthquake, Nat. Hazards 27, 105–131. tation of all three factors controlling the strong ground mo- Castro, R. R., A. Rovelli, M. Cocco, M. Di Bona, and F. Pacor (2001). tion, namely the earthquake source, the propagation path, Stochastic simulation of strong-motion records from the 26 September and the site effect. Despite the simplicity of the model, syn- 1997 (MW 6), Umbria-Marche (Central Italy) earthquake, Bull. Seism. Soc. Am. 91, 27–39. rupture model parametric 2מthetic strong-ground motion is in agreement with all the Gallovic, F., and J. Brokesova (2003). The k available seismological, geodetic, and geotechnical infor- study: example of the 1999 Athens earthquake, Stud. Geophys. Geo- mation and adequately explains the damage distribution pat- daet. (submitted for publication). tern of the examined earthquake. Nevertheless, deeper un- Ganas, A., G. Papadopoulos, and S. B. Pavlides (2001). The 7 September derstanding of the faulting process and its effect on the 1999 Athens 5.9 Ms earthquake: remote sensing and digital elevation model inputs towards identifying the seismic fault, Int. J. Remote distribution of damage requires finer modeling (e.g., inclu- Sensing 22, 191–196. sion of an area-specific 3D velocity model, additional geo- Gazetas, G. (2001). The 1999 Parnitha (Athens) earthquake: soil effects on technical data to characterize recording site conditions, and distribution of damage, in Lessons Learned from Recent Strong Earth- investigation of the temporal characteristics of the rupture quakes, A. Ansal (Editor), International Society of Soil Mechanics process). and Geotechnical Engineering, Istanbul, Turkey, 5–18. Gazetas, G., N. Gerolimos, P. Kallou, I. Anastasopoulos, M. Apostolou, P. Psarropoulos, D. Asimaki, E. Protopapa, C. Goudas, S. Benekos, J. Sarraf, Ch. Saumatsou, and E. Efstathopoulou (2001). Numerical and Acknowledgments experimental evaluation of ground acceleration within the meizoseismal area of the Parnitha earthquake 7-9-99, Final report, Earthquake We acknowledge the partial financial support of the General Secre- Planning and Protection Organization (in Greek) Athens, Greece. tariat of Research and Technology (GSRT) of the Ministry of Development Gazetas, G., P. V. Kallou, and P. N. Psarropoulos (2002). Topography and of Greece and of the Earthquake Planning and Protection Organization soil effects in the Ms 5.9 Parnitha (Athens) earthquake: the case of (EPPO) of Greece (no. 70/3/5484). Thanks are due to our colleagues of the Ada´mes, Nat. Hazards 27, 133–169. Geodynamic Institute of the National Observatory of Athens for providing Hanks, T. C. (1982). fmax, Bull. Seism. Soc. Am. 72, 1867–1879. part of the data used and to Igor Beresnev for kindly offering the simulation Hatzidimitriou, P. M. (1993). Attenuation of coda waves in Northern code and valuable advice. The article also benefited from careful reviews Greece, Pure Appl. Geophys. 140, 63–78. by Z. Wang and V. Sokolov. Hatzidimitriou, P. M. (1995). S-wave attenuation in the crust in Northern Greece, Bull. Seism. Soc. Am. 85, 1381–1387. Kanamori, H., and D. L. Anderson (1975). Theoretical basis of some em- References pirical relations in seismology, Bull. Seism. Soc. Am. 65, 1073–1095. Klimis, N., B. Margaris, and P. Koliopoulos (1999). Site dependent am- Anastasiadis, An., M. Demosthenous, Ch. Karakostas, N. Klimis, B. Lek- plification functions and response spectra in Greece, J. Earthquake idis, B. Margaris, Ch. Papaioannou, C. Papazachos, and N. Theodou- Eng. 3, no. 2, 237–247. lidis (1999). The Athens (Greece) earthquake of September 7, 1999: Koliopoulos, P. K., and B. N. Margaris (2001). The 1999 Athens (Greece) preliminary report on strong motion data and structural response, earthquake: energy and duration—related response spectral charac- www.itsak.gr/report.html. teristics of different site conditions, in Proc. 4th Conf. Geotechn. Eng. Anderson, J. G., and S. E. Hough (1984). A model for the shape of the Soil Dyn., March 2001, San Diego, California, Paper no. 10.31. Fourier amplitude spectrum of acceleration at high frequencies, Bull. Kontoes, C., P. Elias, O. Sykioti, P. Briole, D. Remy, M. Sachpazi, G. Veis, Seism. Soc. Am. 74, 1969–1993. and I. Kotsis (2000). Displacement field and fault model for the Sep- Bard, P.-Y. (1997). Local effects on strong ground motion: basic physical tember 7, 1999 Athens earthquake inferred from ERS2 satellite radar phenomena and estimation methods for microzoning studies, in interferometry, Geophys. Res. Lett. 27, 3989–3992. SERINA—Seismic Risk: An Integrated Seismological, Geotechnical Louvari, E., and A. Kiratzi (2001). Source parameters of the 7 September and Structural Approach, ITSAK, Thessaloniki, Greece, 229–299. 1999 Athens (Greece) earthquake based on teleseismic data, J. Balkan Baumont, D., F. Courboulex, O. Scotti, N. S. Melis, and G. Stavrakakis Geophys. Soc. 4, 51–60.

(2002). Slip distribution of the MW 5.9, 1999 Athens earthquake in- Margaris, B. N., and D. M. Boore (1998). Determination of Dr and j0 from verted from regional seismological data, Geophys. Res. Lett. 29, doi response spectra of large earthquakes in Greece, Bull. Seism. Soc. Am. 10.1029/2001GL014261. 88, 170–182. Beresnev, I. A., and G. M. Atkinson (1997). Modeling ﬁnite-fault radiation Marinos, P., G. Bouckovalas, G. Tsiambaos, G. Protonotarios, N. Sabata- from the xn spectrum, Bull. Seism. Soc. Am. 87, 67–84. kakis, and collaborators (1999). Damage distribution in the western Beresnev, I. A., and G. M. Atkinson (1998). FINSIM: a FORTRAN pro- part of Athens after the 7-9-99 earthquake, Newsletter of the European gram for simulating stochastic acceleration time histories from ﬁnite Center on Prevention and Forecasting of Earthquakes 3, 37–39. faults, Seism. Res. Lett. 69, 27–32. Papadimitriou, P., N. Voulgaris, I. Kassaras, G. Kaviris, N. Delibasis, and ס Beresnev, I., and G. Atkinson (2001a). Subevent structure of large earth- K. Makropoulos (2002). The MW 6.0, 7 September 1999 Athens quakes: a ground motion perspective, Geophys. Res. Lett. 28, 53–56. earthquake, Nat. Hazards 27, 15–33. Beresnev, I., and G. Atkinson (2001b). Correction to Subevent structure of Papageorgiou, A. S. (1988). On two characteristic frequencies of acceler-

large earthquakes: a ground motion perspective (correction), Geo- ation spectra: patch corner frequency and fmax, Bull. Seism. Soc. Am. phys. Res. Lett. 28, 4663. 78, 509–529. Boore, D., W. Joyner, and T. Fumal (1993). Estimation of response spectra Papageorgiou, A. S., and K. Aki (1983). A speciﬁc barrier model for the and peak acceleration from Western North American earthquakes: an quantitative description of inhomogeneous faulting and the prediction interim report, U.S. Geol. Surv. Open-File Rept. 93–509. of strong ground motion. I. Description of the model, Bull. Seism. Bouckovalas, G. D., and G. P. Kouretzis (2001). Stiff soil ampliﬁcation Soc. Am. 73, 693–722. 1052 Z. Roumelioti, A. Kiratzi, and N. Theodulidis

Papazachos, C. B., B. G. Karakostas, G. F. Karakaisis, and Ch. A. Pa- ground motion on magnitude: distance, site geology and macro- ס paioannou (2001). The Athens 1999 mainshock (MW 5.9) and the seismic intensity for shallow earthquakes in Greece. I. Peak horizontal evolution of its aftershock sequence, in Proc. of the 9th Int. Conf. of acceleration, velocity and displacement, Soil Dyn. Earthquake Eng. the Geological Society of Greece, September 2001, Athens, 1581– 11, no. 7, 387–402. 1586. Theodulidis, N. I., I. Kalogeras, C. Papazachos, V. Karastathis, B. Margaris, Pavlides, S. B., G. Papadopoulos, and A. Ganas (2002). The fault that Ch. Papaioannou, and A. Skarlatoudis (2004). HEAD v1.0, a unified ס caused the Athens September 1999, Ms 5.9 earthquake: field ob- Hellenic Accelerogram Database, Seism. Res. Lett. 75, 36–45. servations, Nat. Hazards 27, 61–84. Tselentis, G.-A., and J. Zahradnik (2000). The Athens earthquake of 7 Pomonis, A. (2002). The mount Parnitha (Athens) earthquake of September September 1999, Bull. Seism. Soc. Am. 90, 1143–1160. 7, 1999: a disaster management perspective, Nat. Hazards 27, 171– Wald, D. J., V. Quitoriano, T. H. Heaton, and H. Kanamori (1999). Rela- 199. tionships between peak ground acceleration, peak ground velocity and Roumelioti, Z. (2003). Contribution to the simulation of strong ground mo- modified Mercalli intensity in California, Earthquake Spectra 15, no. tion, with emphasis on the near field, in the Aegean Sea and the 3, 557–564. adjacent areas, Ph.D. Thesis, Aristotle University of Thessaloniki, Zahradnik, J., and G.-A. Tselentis (2002). Modeling strong-motion acce- Greece (in Greek). lerograms by PEXT method, application to the Athens 1999 earth- Roumelioti, Z., D. Dreger, A. Kiratzi, and N. Theodoulidis (2003b). Slip quake, in Proc. XXVIII Gen. Ass. Eur. Seism. Comm., Genoa, Italy, distribution of the 7 September 1999 Athens earthquake inferred from 1–6 September 2002 (CD-ROM). an empirical Green’s function study, Bull. Seism. Soc. Am. 93, 775– 782. Department of Geophysics Roumelioti, Z., A. Kiratzi, N. Theodoulidis, I. Kalogeras, and G. Stavra- Aristotle University of Thessaloniki

kakis (2003a). Rupture directivity during the September 7, 1999 (MW 54124 Thessaloniki, Greece 5.9) Athens (Greece) earthquake inferred from forward modeling of (Z.R., A.K.) strong ground motion, Pure Appl. Geophys. 160 no. 12, 2301–2318. Theodulidis, N. (1991). Contribution to the study of strong ground motion Institute of Engineering Seismology and Earthquake Engineering in Greece, Ph.D. Thesis, Aristotle University of Thessaloniki, Greece. P.O. Box 53 Theodulidis, N., and P.-Y. Bard (1998). Dependende of fmax on site ge- 55102 Thessaloniki, Greece ology: A preliminary study of Greek strong-motion data, in Proc. 11th (N.T.) European Conference on Earthquake Engineering 1, 269–274. Theodulidis, N. P., and B. C. Papazachos (1992). Dependence of strong Manuscript received 14 October 2003.