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

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1 Bulletin of the Seismological Society of America, Vol. 94, No. 3, pp , 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 of 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 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 concentrated. 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 constitutes another resounding example of the potential destructiveness of moderate-magnitude earthquakes when they occur in the proximity of densely populated areas. Reported damage places the specific earthquake among the worst natural disasters in the modern history of Greece. In total, 143 people were killed, whereas the economic loss is estimated to have reached 3% of Greece s Gross Domestic Product (GDP) (Pomonis, 2002). The earthquake was related to normal faulting in a northwest southeast direction (strike 115, dip 57, rake 80 ; Louvari and Kiratzi, 2001), about 15 km northwest of the center of Athens. In the epicentral area, two normal faults of such orientation are clearly expressed on the morphology, namely the Thriassio and Fili faults (Fig. 1). Among these two structures, the Fili fault is most likely related to the 1999 earthquake (Ganas et al., 2001; Pavlides et al., 2002), although the rupture did not reach the surface (Papazachos et al., 2001; Baumont et al., 2002; Roumelioti et al., 2003b) and, therefore, any conclusions regarding the causative fault are doubtful. Most of the damage was observed in the northwest suburbs of the city (the municipalities of Thrakomakedones, Ano Liosia, Fili, and Menidi), which are located to the east of the Fili fault (Fig. 1). In general, damage distribution within the wider epicentral area was irregular (e.g., damage within the projection of the fault plane, which is usual for normal-fault earthquakes, was insignificant compared with that observed close to the fault s eastern termination). This asymmetry toward the meizoseismal area caused speculation for emergence of directivity phenomena during the earthquake 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 motion of the 1999 Athens earthquake by using the widely applied stochastic method for finite faults (Beresnev and Atkinson, 1997). The simulation parameters are first validated through a posteriori predictions of the available strongmotion records of the examined event and subsequently used to assess the strong-motion level at a much larger number of sites, including the meizoseismal area, for which no records are available. Our primary target is to investigate how 1036

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

3 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 Station Code Installation Area Installation Site Sensor Depth (m) Surface Geology Latitude ( N) Longitude ( E) Epicentral Distance (km) PGA (L) PGA (T) PGA (V) Carrier* ALIV Aliveri Ground level PPC ATHA Neo Psyhiko Basement/3-story 0 Schist G.I. CHAL Chalandri Basement/2-story 0 Alluvial ITSAK COR Corinthos Basement/2-story 0 Alluvial ITSAK DFNA Dafni Metro/Level 2 14 Alluvial/Schist G.I. DMK Dimokritos Free field 0 Limestone G.I. FIX Neos Kosmos Metro/Level 2 15 Alluvial/Schist G.I. GYS G.Y.S. Basement/3-story 0 Alluvial ITSAK KEDE K.E.D.E. Basement/1-story 0 Marl ITSAK KERT Keratsini Basement/2-story PPC LAVR Lavrio Ground level PPC MNSA Monastiraki Free field 0 Alluvial/Schist G.I. PNT Pentagono Metro/Level 2 15 Alluvial G.I. RFN Rafina Small wooden construction 0 Tertiary Dep./Limestone G.I. SGMA Syntagma Metro/Level 1 7 Schist G.I. SGMB Syntagma Metro/Level 3 26 Schist G.I. SPLA Sepolia Metro/Level 2 13 Alluvial/Schist G.I. SPLB Sepolia Basement/2-story 0 Alluvial/Schist G.I. THI Thiva Free field 0 Pleistocene Deposits 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 Butterworth filter: 8 1/2 P(x) [1 (x/x m)]. (2) The function S(x) is calculated as the product of a certain deterministic function (usually the x 2 model), which defines the average shape and amplitude of the spectrum, and a stochastic function (e.g., the Fourier spectrum of windowed Gaussian noise) that accounts for the realistic random character of the simulated ground motion. The extension of the stochastic model to the finite-fault case requires transformations of the theoretical expressions that have been proposed for point sources to account for the finite dimensions of the sources that produce large earthquakes. The fault plane is discretized into a certain number of equal rectangular elements (subfaults) with dimensions Dl Dw. Each subfault is then treated as a point source with an x 2 spectrum, which can be fully defined by two parameters: the seismic moment, m 0, and the corner frequency, f c, of the subfault spectrum. The connection between these two parameters and the finite dimensions of the subfaults is established through two coefficients, Dr and K, respectively. In detail, assuming the simple case for which Dl Dw, the subfault moment, m 0, can be determined from the following relation: 3 m0 Dr Dl, (3) where Dr is a stress parameter, most closely related to the static stress drop (Beresnev and Atkinson, 1997). Dr relates the subfault moment to its finite dimensions. On the other hand, K relates the subfault spectrum corner frequency, f c, to its finite dimensions, through the relation: f Dl c K, (4) b where b is the shear-wave velocity. The parameter K actually controls the level of high-frequency radiation in the simulated time history and is equal to: yz K, (5) p where y is the ratio of rupture velocity to shear-wave velocity and z is linked to the maximum rate of slip, v m, on the fault plane through the equation: 2yz Dr vm, (6) e qb where e is the base of the natural logarithm and q is the density. The value of z depends on a convention in the definition of the rise time as it is introduced in the exponential functions that describe the x 2 model and for standard conventions z 1.68 (Beresnev and Atkinson, 1997, 1998). Due to the uncertainties involved in the definition of z, its value is allowed to vary through a parameter called sfact,

4 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 includes a km planar fault discretized into 1-km 2 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 for 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 taken into account by diminishing the simulated spectra by the factor exp( pjf ) (Anderson and Hough, 1984). The kappa operator, j, was given the values presented in Table 2, depending on the geotechnical characterization of each one of the examined sites. Information on the geotechnical characterization was combined from the studies of Bouckovalas et al. (2002), Koliopoulos and Margaris (2001), and Theodulidis et al. (2004). Most of the station installation sites were characterized as C sites with the exceptions of stations DMK, KERT, ALIV (sites B), and COR (site D). The complete set of parameters used to stochastically simulate the 1999 Athens earthquake is presented in Table 3. Site Effect Incorporation of site amplification effects in strongmotion synthetics is usually one of the most troublesome tasks, because site-specific geotechnical information is usually limited or nonexistent. In the case of the Athens earthquake, the so-far published geotechnical data are not enough to allow computations of theoretical transfer functions at a sufficient number of sites. Furthermore, the vast majority of the strong-motion stations that recorded the earthquake were installed on soft sites, and this fact, in combination with the sparse character of the local network, does not allow the application of the standard spectral ratios (SSR) method to a sufficient number of stations. Consequently, after assessing the available data, we decided to use the horizontal-tovertical (H/V) spectral ratios technique as correction amplification factor versus frequency. By adopting the specific technique we are capable of obtaining H/V ratio amplitudes at all the recording sites, which are preferable from empirical Figure 2. Slip-distribution model for the 1999 Athens earthquake. Contours are for 10 cm of slip. Star denotes the hypocentral location, and dots frame the areas of maximum concentration of slip (after Roumelioti et al., 2003b). amplification factors in cases of site-specific simulations. On the other hand, although H/V ratio technique has been proven to correctly identify the site resonance, it usually underestimates true amplifications (Bard, 1997; Castro et al., 2001). Therefore, by using H/V ratios, we do not expect the simulated spectra to perfectly match the observed spectra in amplitude, although an adequate match is expected in shape. To assess the level of uncertainty introduced in the simulated strong-motion amplitudes by the use of the H/V ratios, we performed a comparative application of this technique and the SSR method at a limited number of stations. More specifically, the two methods were applied at three recording sites (ATHA, CHAL, and PNT in Fig. 1). In all three cases, the reference station for the application of the SSR method was station DMK (also in Fig. 1). The outcomes of the parallel application of the two methods, based on mainshock data, are compared in Figure 3. In general, a satisfactory agreement in both the shape and the absolute amplitudes of the amplification functions can be observed in all three examined stations. The amplification level suggested by the H/V ratios technique is systematically lower than the corresponding one suggested by the SSR method. Nevertheless, the ratio of the two functions is less than 1.5 in almost all the examined periods. Furthermore, taking into account the relatively large distance between the SSR station pairs (3 to

5 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 V S30 (m/sec) Geotechnical Description j Reference B 760 V S Rock Margaris and Boore, 1998 C 360 V S Very stiff soil soft rock Klimis et al., 1999 D 180 V S Stiff soil Klimis et al., 1999 V S30 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 d 1 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 M W 5.9 Stress drop stress 50 bars Number of subfaults along strike and dip N L N W Hypocenter location on the fault i 0, j 0 4,6 Crustal shear wave velocity beta 3.3 km/sec Crustal density rho 2.72 g/cm 3 Parameter controlling high-frequency level sfact 1.5 Parameter j kappa As in Table 2 Parameters of the attenuation model Q Q(f ) Q 0 *f**eta eta 0.8 Geometric 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 km 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 for the SSR method), it is possible that the amplification level estimated by the SSR method is slightly overestimated. To conclude, the comparison in Figure 3 suggests that the H/V spectral ratios can provide good approximations of the amplification levels estimated by the SSR method, at least at sites with surface geology similar to the one of the three examined stations. H/V spectral ratios estimates performed during this study were based on strong-motion records of the 1999 Athens mainshock. Nevertheless, we also used aftershock data, wherever available, to compare the resulting amplification functions. In all tests, results from mainshock data were within 1 standard deviation of the average function resulting from aftershock H/V ratios. Model Validation The first step of our analysis includes the validation of the stochastic finite-fault model parameters at free-field stations that recorded the earthquake. As previously mentioned in the case of the Athens earthquake, only three of the recording stations can be considered as free-field ; namely, DMK, SPLB, and KEDE. Among these stations DMK is the only one installed on hard rock. Soil column at KEDE consists of 10 m of alluvial deposits with average shear-wave velocity of the order of m/sec and the underlying bedrock; whereas, at SPLB, alluvial deposits present a thickness of 13 m and average shear-wave velocity of about 300 m/sec (Gazetas et al., 2001). The presence of alluvial deposits at two of the three validation stations is expected to have significantly influenced the strong-motion recordings. Therefore, during the validation procedure it is necessary to include the effect of the recording-site conditions. For station DMK this is done by using empirical amplification factors estimated for generic rock sites (Boore et al., 1993). For stations KEDE and SPLB site-specific amplification functions are estimated through the H/V spectral ratios method (Fig. 4). The lowfrequency limit in the amplification functions presented is selected based on the signal-to-noise ratio of the corresponding records used in the estimation of the H/V ratios.

6 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. Figure 3. Comparison of the amplification functions estimated by the SSR and the H/V spectral ratios method at three recording sites (ATHA, CHAL, and PNT from top to bottom). Station DMK was used as reference station for the application of the SSR method in all three cases. Amplification functions were computed based on pseudovelocity (PSV) spectra of the mainshock records (damping 5%). We assume that the fault dimensions and the details of the faulting process, such as the rupture-initiation point and slip distribution on the fault plane, are well constrained by previous studies. In this case, the only free parameter during the implementation of the method is sfact, which controls the strength of high-frequency radiation from each subfault. This parameter controls the value of z (equation 6) and affects 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 Transforming 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 5 shows the model error at each one of the validation stations for four representative values of parameter sfact (0.5, 1.0, 1.5, and 2.0). This figure suggests that the smaller overall spectral difference between observations and synthetics (model error closer to unit) appears when sfact 1.5. This value corresponds to the average value proposed 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 slip velocities. Table 4 includes PGA values at the three validation sites for different values of sfact. PGAs written in bold are the closest to the corresponding average horizontal values. As it can be concluded, the value of 1.5 for parameter sfact is also satisfactory in terms of the overall PGA prediction at the three examined sites.

7 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/sec 2 ) sfact DMK KEDE SPLB Values typed in bold are closest to the average observed horizontal peak ground acceleration. Figure 5. Model error showing the ratio of the observed to simulated amplitude Fourier spectrum at three validation sites (DMK, KEDE, and SPLB from top to bottom) for four representative values of sfact. The resulting synthetic S-wave acceleration time histories, Fourier amplitude spectra, and elastic response spectra (damping 5%) at the three validation stations are presented in Figure 6. Taking into account the simplicity of the applied method, the overall agreement between synthetics and observations is very satisfactory both in the time and frequency domains. The largest misfit is observed in the intermediatefrequency 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 basements, 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 of the mainshock, with the exception of station MNSA where the transversal component, as already mentioned, was affected by surrounding structures and, therefore, only the longitudinal component was used. As derived from Table 1, the examined stations are located at epicentral distances ranging from 16 to 61 km. The closest to the epicenter stations (R 30 km) are all concentrated to the east-southeast of the fault, whereas the more distant stations provide a much better azimuthal coverage. In Figure 8 (a d) we present the results of the stochastic simulations and their comparisons with the observed strong ground-motion recordings. In general, the synthetics are in very good agreement with observations in almost all cases.

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

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

10 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)

11 1046 Z. Roumelioti, A. Kiratzi, and N. Theodulidis Figure 8. Continued

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

13 1048 Z. Roumelioti, A. Kiratzi, and N. Theodulidis Figure 8. Continued

14 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 Figure 10. Ratios of average observed horizontal spectral acceleration to the corresponding synthetic value at the 19 examined stations, as a function of epicentral distance, R. Ratios are shown for discrete period values of 0.12, 0.35, and 1.08 sec (from top to bottom). 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. Although 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 direction. Nevertheless, PGA values at bedrock are still generally low ( 0.35 g) and could only explain the high level of damage in this area if combined with other factors, e.g., the site effect. We indicatively mention that the use of empirical amplification factors of site classes C and D (Klimis

15 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 approximately a factor of 2. This means that PGA values computed for bedrock conditions within the meizoseismal area (0.13 to 0.2 g according to Fig. 11) can increase up to 0.4g, a value that is in accordance with the mean modified Mercalli intensity (MMI) estimated for the areas of Ano Liosia, Menidi, and Thrakomakedones (VIII IX; see as derived from empirical relations between MMI and PGA (Theodulidis, 1991; Theodulidis and Papazachos, 1992; Wald et al., 1999). Synthetic PSA maps are also asymmetrical toward the meizoseismal area. The asymmetry appears more distinctively at periods longer than 2 sec and within the range 0.2 to 0.3 sec. This result is comparable with direct measurements of the spectral content of regional broadband waveforms (Roumelioti, 2003). The sharp asymmetry observed at 0.2 sec is extremely interesting in terms of explaining the damage distribution pattern, as most of the buildings damaged by the earthquake were two- or three-story constructions with resonances close to 0.2 sec. On the other hand, site-effect studies within the meizoseismal area suggest that site effect was also significant in this period range (Gazetas et al., 2001). By combining these pieces of information we conclude that the destructiveness of the 1999 Athens earth-

16 Stochastic Strong Ground-Motion Simulation of the 7 September 1999 Athens (Greece) Earthquake 1051 quake was probably due to an unfortunate combination of source and site effects within a limited strong-motion period range. The results of this study stem from a rough representation of all three factors controlling the strong ground motion, namely the earthquake source, the propagation path, and the site effect. Despite the simplicity of the model, synthetic strong-ground motion is in agreement with all the available seismological, geodetic, and geotechnical information and adequately explains the damage distribution pattern of the examined earthquake. Nevertheless, deeper understanding of the faulting process and its effect on the distribution of damage requires finer modeling (e.g., inclusion of an area-specific 3D velocity model, additional geotechnical data to characterize recording site conditions, and investigation of the temporal characteristics of the rupture process). Acknowledgments We acknowledge the partial financial support of the General Secretariat of Research and Technology (GSRT) of the Ministry of Development of Greece and of the Earthquake Planning and Protection Organization (EPPO) of Greece (no. 70/3/5484). Thanks are due to our colleagues of the Geodynamic Institute of the National Observatory of Athens for providing part of the data used and to Igor Beresnev for kindly offering the simulation code and valuable advice. The article also benefited from careful reviews by Z. Wang and V. Sokolov. References Anastasiadis, An., M. Demosthenous, Ch. Karakostas, N. Klimis, B. Lekidis, B. Margaris, Ch. Papaioannou, C. Papazachos, and N. Theodoulidis (1999). The Athens (Greece) earthquake of September 7, 1999: preliminary report on strong motion data and structural response, Anderson, J. G., and S. E. Hough (1984). A model for the shape of the Fourier amplitude spectrum of acceleration at high frequencies, Bull. Seism. Soc. Am. 74, Bard, P.-Y. 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