Selecting the most suitable rupture model for the stochastic simulation of the 1999 Izmit earthquake and prediction of peak ground motions

Soil Dynamics and Earthquake Engineering 42 (2012) 1–16

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Selecting the most suitable rupture model for the stochastic simulation of the 1999 Izmit earthquake and prediction of peak ground motions Esref Yalcinkaya n, Ali Pinar, Oznur Uskuloglu, Serhat Tekebas, Berrak Firat Istanbul University, Engineering Faculty, Geophysical Engineering, 34320 Avcilar, Istanbul, Turkey

a r t i c l e i n f o

abstract

Article history: Received 24 March 2011 Received in revised form 21 March 2012 Accepted 27 May 2012 Available online 17 June 2012

In this study, we use a stochastic finite-fault technique based on a dynamic corner frequency to investigate how the fault and slip models affect the high frequency simulations of the 1999 Izmit (Turkey) earthquake. Seven different rupture models, one of them generated using common fault parameters and random slip distribution are tried to obtain the best matching with the observations. The synthetic seismograms computed in the frequency band 0.1–25 Hz are compared with the observations both in time and frequency domain. Six accelerometric stations located close to the observed surface rupture are chosen for the comparisons considering the fact that the slip contributions are visible at these station records better than the other stations. We also estimated average H/V spectral ratios using the available accelerometric recordings to take into account site amplification at each site. We also acquired ambient noise data at some stations that lack sufficient earthquake records. The results show that none of the rupture models fully simulate the observations at all the stations. Most of the rupture models underestimate the Fourier amplitudes at frequencies lower than 0.4 Hz, whereas overestimate them at higher frequencies. The underestimation may result from a directivity effect which likely causes higher amplitudes on the observed ground motions in low frequency band. While all the rupture models display similar average bias functions, the minimum average error for spectral amplitudes is obtained for the rupture model of Bouchon et al. (2002). The achievement of the random slip distribution model also yields satisfactory results. After we have optimized the rupture model, we have simulated the strong ground motions on a regular grid (0.21  0.21) covering the study area for bedrock conditions. In total, we have estimated peak accelerations and peak velocities at 135 points. The results show that the maximum acceleration values during the Izmit earthquake reached 785 cm/s2, and the largest velocity values were around 75 cm/s. The peak ground accelerations are still smaller than those predicted by the empirical relations but are well above the observed ones. The low accelerations might be attributed to the low stress drop that might be due to the large rupture length. & 2012 Elsevier Ltd. All rights reserved.

1. Introduction The 17 August 1999 Izmit earthquake (Mw 7.4) occurred on the northern strand of the North Anatolian Fault Zone in western Turkey. The hypocenter was located at a depth of 17 km [1]. The surface rupture was well developed over 100 km length [2,3] extending from the eastern Marmara Sea to the southwest of Duzce (Fig. 1). The earthquake caused high casualties and significant structural damage. The officially reported deaths were 18,000 and about 1 million people were trapped under debris. According to the Ministry of Public Works and Settlement, 94,000 buildings either collapsed or were heavily damaged. Total monetary losses of 16 billion USD were reported by the public and

n

Corresponding author. Tel.: þ 90 212 4737070/17572; fax: þ90 212 4737180. E-mail address: [email protected] (E. Yalcinkaya).

0267-7261/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.soildyn.2012.05.018

private sectors. The most common residential building types in the area were three–seven storey reinforced concrete structures with hollow brick infill and with fundamental natural vibration periods between 0.3 and 1 s [4]. The poor quality of construction material, the deficiencies due to the non-compliance with the earthquake code and the nature of the strong motion were the main factors contributing to the damage [5–7]. Despite the destruction, the recorded peak accelerations of the Izmit earthquake are surprisingly smaller than the expectations from an Mw ¼7.4 earthquake [6,8–11]. The unprocessed maximum horizontal accelerations recorded at six near fault stations ranged from 134 cm/s2 to 407 cm/s2. Unfortunately, the locations of these stations do not exactly represent the settlements that were heavily damaged. Indirect evidence exists that violent motions must have occurred, e.g. parked passenger bus was overturned at a filling station near Izmit during the earthquake [6]. Modeling results of Miksat et al. [11] show that only

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a few strong motion observations around the Izmit earthquake fault are not adequate to describe how the ground moved in the immediate vicinity of the fault rupture. After large earthquakes the simulation methods are frequently used to understand ground motions, damage and rupture characteristics caused by earthquakes. Stochastic finite-fault modeling is widely used in prediction of strong ground motions (e.g. [12–15]). In this method, the finite source is represented by a rectangular plane, subdivided into subfaults. Each subfault is treated as a point source and radiates a o-squared spectrum. The ground motion at an observation point is obtained by summing up the contributions of several subfaults. A simple kinematic model [16] is used to simulate the rupture propagation, which is assumed to start at the hypocenter and propagate out radially. Propagation effects are modeled by using the observed regional ground-motion amplitudes and durations as functions of distance. Recently, Motazedian and Atkinson [17] introduced a new finite-fault model with a dynamic corner frequency where the total energy radiated from the fault is conserved regardless of the subfault size and the relative amplitudes of the lower frequencies could be controlled. In this study, we use stochastic finite-fault technique based on a dynamic corner frequency and the computer program EXSIM developed by Motazedian and Atkinson [17] to simulate the ground-motion records of the 17 August 1999 Izmit earthquake. Stochastic method is generally used to produce the high frequency components of the ground motions. While acceleration waveforms including high frequency vibrations, velocity and displacement waveforms are sensitive to lower frequencies. At the same time, velocity and displacement waveforms at the nearfault stations may include long-period directivity pulse and permanent displacement effect, respectively. Therefore, the simulation of the velocity and displacement waveforms requires hybrid methods. We limited our work of stochastic modeling to acceleration waveforms. In the first part of the paper, we tried to optimize the rupture parameters characterizing the earthquake. We tested seven

different rupture models comparing the simulations with the observations at six near field accelerometric stations. In the second part, we used the rupture model giving the best matching with the observations to reproduce the ground motions at totally 23 stations that recorded the Izmit earthquake. After we established a successful model, we computed peak accelerations and peak velocities for the whole region, and checked the matching with the ground motion prediction equations.

2. Data The 1999 Izmit earthquake was recorded at 38 strong ground motion stations operated by ERD (Earthquake Research Department), KOERI (Kandilli Observatory and Earthquake Research Institute), and ITU (Istanbul Technical University). From these, only 23 stations were used in this study, because some stations were triggered by S wave or have spikes or peculiar waveforms. In addition, the accelerograms with amplitudes less than 30 cm/s2 of peak ground acceleration (PGA) have been excluded due to low signal/noise ratio. The stations used in this study are shown in Fig. 1. Table 1 summarizes the station coordinates, ‘‘Joyner-Boore’’ distance (Rjb) and the site classifications according to VS30 measurements and surface geology. Site classifications for the strong motion stations were obtained from Sandikkaya et al. [18], Rathje et al. [19], and the institutions operating the stations. As shown in the table, while most of the stations take place on C and D site classes according to the NERHP site classification, the IZT, MSK, MCD and YKP stations are located on rock sites corresponding to A and B site classes. In comparison with synthetic data, all data were band-passfiltered with a fourth-order Butterworth filter with corner frequencies of 0.1 and 25 Hz. This frequency range is applicable for stochastic simulations and engineering studies. Although signal/ noise ratio is generally sufficient in this range, the limits can show minor differentiations depending to station environment; for example, the lower frequency limit rises to 0.2–0.3 Hz at some

Fig. 1. The epicentral region of the Izmit earthquake is illustrated. The strong ground motion stations used in this study are shown with triangles. The observed surface rupture (black lines) and the epicenter (star) of the earthquake are also presented on the map.

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Table 1 Strong motion stations that recorded the August 17, 1999 Izmit earthquake and some of the parameters used in the simulations. The six near field stations used to optimize the rupture parameters are shown in italics. PGA values for the horizontal components are obtained from the data filtered between 0.1 and 25 Hz. Rjb distances and PGA values for the simulations are calculated for the BOU model (see text for explain). No.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Station Code

ARC ATK ATS BRS BTS BUR CNA DHM DUZ FAT GBZ GYN IST IZN IZT KUT KMP MCD MSK SKR YKP YPT ZYT

Coordinates (No–Eo)

40.824–29.361 40.989–28.849 40.981–28.692 40.183–29.127 40.992–27.979 40.261–29.068 41.024–28.759 40.982–28.820 40.844–31.149 41.020–28.950 40.786–29.450 40.397–30.783 41.058–29.010 40.442–29.717 40.767–29.917 39.419–29.997 41.003–28.928 41.065–28.990 41.104–29.019 40.737–30.380 41.081–29.011 40.764–29.760 40.986–28.908

Rjb (km)

11.55 38.32 47.21 59.64 102.08 51.27 46.24 39.32 22.14 36.73 7.33 35.87 38.95 33.09 5.22 144.47 35.88 40.17 43.72 1.89 71.70 4.89 35.13

PGA (cm/s2) NSobs

EWobs

Sim

218 100 253 59 108 98 174 91 326 183 225 133 52 95 158 49 88 53 44 – 36 344 104

140 157 187 45 92 109 137 79 362 151 137 117 45 139 225 64 129 67 41 381 37 282 111

146 110 100 67 65 107 126 99 384 204 182 82 50 81 274 43 128 58 59 615 30 359 118

stations. However, we do not consider using different filter ranges for those stations, because it does not cause a significant effect on the results. The window of strongest shaking (S wave) which has a length of 10–15 s was selected for each record, and then transformed to frequency domain via the fast Fourier transform. The amplitude spectra of the Fourier transform were smoothed with a Konno and Ohmachi [20] filter using a coefficient of 20 for the bandwidth. The peak accelerations for each station computed from processed data are reported in Table 1. The north–south component of SKR station was out of order during the earthquake.

3. Rupture models Several researchers have extensively studied the fault rupture process of the Izmit earthquake and inferred spatial and temporal slip distribution on the causative fault plane (e.g. [11,21–33]). The well-known six rupture models of Izmit earthquake are considered in this study, namely, the BOU model [22], the CAK model [23], the DEL model [24], the REL model [29], the SEK model [30], and the YAG model [33]. In addition, we construct a new model, namely, the RAN model, based on common fault parameters and random slip distribution. The objective of the RAN model is to see what happens when we use a simple rupture model that has average fault dimensions established considering all the slip models but with random slip distribution. To evaluate the success of the RAN model compared to the well defined six slip distribution models, the Izmit earthquake would be beneficial for future studies especially for the cases where no detailed slip distribution is available. Fig. 2 provides map views of the epicentral region of Izmit earthquake including the projection of all seven rupture models and the location of the strong motion instruments. The finitesource rupture models were retrieved from the database of Mai [34]. The main differences between the models are the locations of the high-slip patches across the fault plane and the dimensions of the ruptured fault. Table 2 summarizes the basic parameters pertaining to the selected rupture models with reference to the

Kappa (j)

VS30 (m/s)-(NEHRP)

Site function

0.045 0.035 0.035 0.055 0.020 0.045 0.020 0.030 0.050 0.015 0.055 0.045 0.035 0.045 0.055 0.035 0.030 0.020 0.020 0.050 0.035 0.070 0.040

500 (C) 220 (D) 175 (E) 457 (C) (D) (E) 350 (D) (D) 282 (D) (E) 701 (C) 347 (D) 595 (C) 197 (D) 826 (B) 243 (D) (D) (B) (B) 412 (C) (A) 300 (D) (C)

Not used H/V H/V H/V H/V H/V H/V H/V H/V H/V Not used Not used Not used H/V Not used H/V H/V Not used Not used Not used Not used Not used H/V

researchers. These model parameters will be used for the generation of the synthetic ground motions on selected locations in the immediate vicinity of the tectonic fault. 3.1. The BOU model Bouchon et al. [22] used five strong motion stations (ARC, YPT, IZT, SKR and DZC) to infer the spatial and temporal slip distribution on idealized fault plane. The faulting model proposed by Bouchon et al. [22] consists of eight segments, which are inferred from the surface breaks and the aftershock distribution. The total length and width of the rupture is 155 km and 18 km, respectively. They found that the rupture propagated at the subRayleigh speed of about 3 km/s on the western and eastern segments of the fault, but that the central segment broke at supershear speed of about 4.8 km/s. The largest slip values (up to 6.7 m) were computed in the vicinity of YPT and SKR stations. 3.2. The CAK model C - akir et al. [23] use combined tectonic field observations and synthetic aperture radar (SAR) data to determine an improved model of the slip associated with the 1999 Izmit earthquake. Their faulting model has 160 km length and 28 km width. Their model indicates heterogeneous slip with three main zones of higher slip. The largest slip is 5.5 m located near the YPT and SKR stations. 3.3. The DEL model Delouis et al. [24] investigate the space–time distribution of slip of the Izmit earthquake by inverting synthetic aperture radar (SAR) interferometry and Global Positioning System (GPS) data, together with teleseismic broadband and near field strong-motion records. Surface offsets are used as an added constraint. The earthquake rupture is simulated by four segments whose strike and intersection with the surface coincide with the main surface breaks. The total length and width of the segments are 172.5 km and 22.5 km, respectively. Two of the segments in the

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Fig. 2. The fault models and the slip distributions used in the study. While the projections of the original fault models on the free surface are drawn by black lines, the projections of the idealized fault planes for this study are shown by blue lines (a single fault segment with east–west strike). Short information about the models is presented on the upper right corner of the map. The triangles show the near field stations. The stars indicate the location of the epicenter and its projection on the fault plane for each model. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

original model overlap 15 km. Therefore, the fault length of the adapted model in Fig. 2 is 15 km shorter. Their study shows that the Izmit rupture is dominated by bilateral breaking of a central asperity located between 10 km west of YPT station and SKR

station, with slip reaching 6–8 m in the depth range of 6–12 km. A second area of large slip is located to the west of DUZ station. Supershear rupture propagation was not required for modeling the waveforms considered in their study.

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Table 2 Basic parameters pertaining to the selected rupture models with reference to the researchers. Parameters

Bouchon et al. [22]

C - akir et al. [23]

Delouis et al. [24]

Reilinger et al. [29]

Sekiguchi and Iwata [30]

Yagi and Kikuchi [33]

Our model

Mw Epicenter (No/Eo) Depth (km) Strike (o) Dip (o) Rake (o) Fault length (km) Fault width (km) Subfaults (Nx–Nz) Rupture vel. (km/s) fmin–fmax (Hz) Data*

7.59 40.73/29.99 17.5 Variable 90 180 155 18 155–18 Variable 0.0–0.5 SM

7.47 40.70/29.91 17 Variable 89 180 160 28 32–7 – – SAR–GPS

7.56 40.76/29.97 11.25 Variable 85 180 172.5 22.5 23–5 Variable 0.0–0.5 SM–GPS–SAR–TS

7.42 40.76/29.97 14.3 Variable 90 180 153 18.2 59–7 – – GPS

7.44 40.71/29.91 16 Variable 90 180 141 23.3 47–8 Variable 0.1–1.0 SM

7.4 40.70/29.91 16.2 268 86 180 93.6 21.6 24–6 Variable 0.01–0.8 SM–TS

7.4 40.73/29.97 17 270 90 180 150 20 50–6 2.8

n

SM, strong motion; TS, teleseismic; GPS, global position system; SAR, synthetic aperture radar.

3.4. The REL model Reilinger et al. [29] used GPS observations and elastic halfspace models to estimate the distribution of co-seismic slip along the Izmit earthquake rupture. They used the mapped co-seismic surface rupture to determine the location of the fault used in their model. Beneath Izmit Bay they used the distribution of aftershocks and fault maps based on submarine and coastal morphology to locate the co-seismic fault model. Their fault model includes five segments with total length and width of 153 km and 18.2 km, respectively. Their results indicate that co-seismic fault slip falls off rapidly below 12–15 km and concentrates along three high-slip patches that roughly coincide with the three structurally distinct central fault segments (Golcuk, West Sapanca, and East Sapanca). The highest slip occurs within the upper 10 km of the crust, and it reaches 5.7 m on the western Golcuk segment and 4.7 m on the West Sapanca segment to the east of the epicenter. 3.5. The SEK model Sekiguchi and Iwata [30] applied the multiple time-window linear waveform inversion technique to study the source process of the Izmit earthquake using strong-motion data. The fault plane model based on the surface rupture and the aftershock distribution consists of four planar and vertical surfaces with slightly different strike directions. The total length and width of the rupture are 141 km and 23.3 km, respectively. They found out that the best source model is characterized by an asperity that is about 35 km east of the epicenter and near the SKR station, triggered by the first time-window front with 5.8 km/s, close to P-wave velocity. The first time-window propagation velocities west of the hypocenter and east of SKR are expected to be 3.0 km/s. The slips on the eastern segment and the waveforms at DUZ station are not sufficiently modeled by their source model because of the interference of waveform records by an aftershock and insufficient station coverage. 3.6. The YAG model Yagi and Kikuchi [33] examine the rupture process of the 1999 Izmit earthquake using both near-field strong motion data and teleseismic body wave data. They applied a multi-time window inversion to the data to determine the spatio-temporal distribution of fault slip. They assumed that faulting occurs on a single fault plane and that the slip angle is stable during the rupture. Their fault length and width is 93.6 km and 21.6 km, respectively. The rupture process is characterized by an asymmetric bilateral rupture propagation and smooth slip. It consists of two major

fault segments, a rupture propagating to the west and a second rupture propagating to the east. The maximum dislocation and the maximum dislocation velocity are 6.3 m and 2.7 m/s, respectively, both found at the former segment. 3.7. The RAN model The relation between rupture length and earthquake size given in Wells and Coppersmith [35] yield a rupture length of 84 km for Mw ¼7.4. This length is smaller than the surface ruptures associated with the Izmit earthquake [2]. Therefore, the parameters of the RAN model are chosen as the most pronounced values related with the Izmit earthquake. As mentioned before, the role of the RAN model is to test the success of a rupture model which has ‘‘pronounced’’ parameters and random slip distribution and to see how it competes with the other slip models derived from a modeling of co-seismic data. The length and width of the rupture are selected as 150 km and 20 km, respectively. In this model, the slip distribution is randomly produced by a code. The rupture velocity is chosen as a standard rupture velocity of 2.8 km/s.

4. Stochastic finite-fault modeling In the stochastic finite-fault method, typical approach is to simulate the ground motion for a large earthquake by simulating the rupture of several small earthquakes as subevents that comprise a large fault rupture event (e.g. [16,36–38]). The subsources are modeled as stochastic point sources [39,40]. The shear wave acceleration spectrum of the ijth subfault, Aij(f), is expressed in terms of source, path and site effects as Aij ðf Þ ¼

M 0ij Hij Ryj FV 4prb

3

ð2pf Þ2 ½1þ ðf =f 0ij Þ2 

epf k epf Rij =Q ðf Þb GðRij ÞDðf Þ

ð1Þ

where M0ij, f0ij and Rij are the ijth subfault seismic moment, corner frequency and distance from the observation point, respectively. Hij is a scaling factor that aims to conserve the energy of highfrequency spectral level of subfaults [17]. Ryj is the radiation pattern (average value of 0.55 for shear waves), F is the free surface amplification (taken as 2 for SH wave), V is the partition of total shear wave energy into horizontal components (0.71), r is the density, and b is the shear wave velocity. Q(f) is the quality factor, G(Rij) is the geometric spreading factor, D(f) is the site amplification and the term exp( pfk) is a high-cut filter to model the spectral decay at high frequencies described with the kappa (k) factor of soils. The stochastic method multiplies a theoretical and/or empirical shear wave acceleration spectrum with the spectrum of band limited windowed Gaussian noise. Transformation to the time

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domain produces an earthquake time series. By summing up properly the scaled point source simulations in the time domain, an extended fault-plane source can be modeled AðtÞ ¼

nl X nw X

Aij ðt þ Dt ij Þ

ð2Þ

i¼1j¼1

where Dtij is the relative delay time for the wave radiated from the ijth subfault to reach the observation point, nl and nw are the number of subfaults along the length and width of the main fault. Beresnev and Atkinson [41,42] explored the implications of subsource size on the radiated spectrum. Motazedian and Atkinson [17] introduced a new variation based on a ‘‘dynamic corner frequency’’. In this implementation, the corner frequency (f0) is a function of time, and the rupture history controls the frequency content of the simulated time series of each subfault  1=3 Ds f 0ij ðtÞ ¼ 4:9  106 b ð3Þ M 0ave N R ðtÞ where M0ave ¼M0/N is the average seismic moment of subfaults, NR(t) is the cumulative number of ruptured subfaults at time t, Ds is the stress drop. The rupture begins with a high corner frequency and progresses to lower corner frequencies as the ruptured area grows. Limiting the number of the active subfaults (the percentage of pulsing area, which is the maximum possible area of the fault radiating seismic waves divided by the total area of the fault) in the calculation of the dynamic corner frequency influences the spectral shape at intermediate frequencies. The dynamic corner frequency concept allows the simulations to be independent of subfault size and provides for conservation of seismic moment. Motazedian and Atkinson [17] developed a FORTRAN code for this approach based on the earlier program FINSIM by Beresnev and Atkinson [43]; the new program is called EXSIM. Like most other stochastic finite fault approaches, EXSIM does not assign a directivity effect to individual subfaults, but the effects of rupture propagation along the fault (from subfault to subfault) are assumed to mimic the overall directivity effect [44]. Mavroeidis and Papageorgiou [45] have introduced a mathematical method to include directivity effect in stochastic technique. This approach has been programmed as an option in the EXSIM. In this study, however, we could not use this option because it has not been tested yet sufficiently in the latest version of EXSIM (EXSIM_beta).

5. Simulation parameters The modeling parameters used for the simulations of the Izmit earthquake are given in Table 3. Source parameters including the fault dimensions, the hypocenter, moment magnitude, subfault size, and slip distribution are taken from the chosen models described in the previous section. In the simulations, some modifications were done on the original fault models so as to meet the style required by the EXSIM code. In our analysis, the whole models are considered as a single fault segment with east– west strike and vertical dip. The blue lines in Fig. 2 display the projection of the idealized fault plane on the free surface. As shown in Table 2, the rupture velocity in the original fault models is variable except in the models which do not require rupture velocity. In addition, Bouchon et al. [22] suggested a supershear rupture in the central segment of Izmit rupture located between Izmit and Sakarya. Unfortunately, the EXSIM code uses a constant rupture velocity on fault plane. In our simulations, we tested several rupture velocities ranging from 0.6VS to 1.2VS. The results show that our models do not require a supershear rupture for the whole fault plane of the 1999 Izmit

Table 3 Modeling parameters for the August 17, 1999 Izmit earthquake. Parameter

Parameter value

Fault orientation (strike/dip) Depth of hypocenter (km) Fault dimensions (km) Subfault dimensions (km) Moment magnitude (Mw) Slip distribution

(1) Bouchon et al. [22], (2) C - akir et al. [23], (3) Delouis et al. [24], (4) Reilinger et al. [29], (5) Sekiguchi and Iwata [30], (6) Yagi and Kikuchi [33], (7) our model

Rupture velocity (km/s) Stress parameters (bar) Crustal shear wave velocity (km/s) Crustal density (g/cm3) Attenuation, Q(f) Distance-dependent duration term (s) Geometric spreading

2.8 40 3.5

Kappa operator (k) Windowing function Crustal amplification Local amplification

2.8 180f0.45 0.1nR 1/R (Ro 30 km), 1/R0.75 (30o Ro 100 km) 1/R0.1 (R 4100 km) Station dependent Saragoni–Hart Margaris and Boore [55] Station dependent

earthquake. The supershear rupture velocities that we tried for the BOU model generated high peak accelerations and short durations in the simulations which do not exist in the observations. Assatourians and Atkinson [46] stated that variable rupture velocity has only a slight effect on the predicted response spectra at some stations and negligible effect at others. Consequently, in our analysis we used a standard rupture with 2.8 km/s of rupture velocity. Stress drop is a significant parameter in stochastic simulation that affects the amplitudes at higher frequencies. YAG is the only model from among the rupture models considered in this study that presents a stress drop (120 bars) for the Izmit earthquake [33]. However, Yagi and Kikuchi [33] state that this stress drop is significantly larger than the typical stress drop of 30 bars for inter-plate earthquakes. In addition, Mohammadioun and Serva [47] compute a lower stress drop of 19 bars for Izmit earthquake. We tried stress drop values ranging from 30 to 100 bars in the simulations. As a consequence of the investigations, we decide to use a 40 bar of stress drop that yields minimum error between the synthetic and the observation data. Tibi et al. [31] also estimated a stress drop of 40 bars for the Izmit earthquake. In the simulation, the effects of the propagation path are included in through geometrical spreading, anelastic, and near surface attenuations. As for the geometrical spreading, we compared the results of two studies [48,49], and then we used the function defined by Akinci et al. [48]. As required by the EXSIM code, Akinci’s function was inverted from four segments to three segments by combining the two central segments. For the anelastic attenuation, we examined four models proposed by Akinci et al. [48], Bindi et al. [49], Horosan et al. [50], and Horosan and Boztepe-Guney [51]. We chose the model given by Akinci et al. [48], because it gives the best results when compared with the observations. Kappa (k) is the near surface spectral decay parameter [52]. Kappa values in the region are investigated by Akinci et al. [48], Bindi et al. [53], Durukal and Catalyurekli [54], and Durukal [25]. In this study, kappa values are fixed in trial and error manner improving the fit between simulated and observed spectra at each station. Distance-dependent duration function for the region was also investigated by Akinci et al. [48] which was found to be frequency dependent. Based on our personal communication with the

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Fig. 3. The site amplification functions estimated from H/V spectral ratios for each station. The thick lines indicate the average H/V curves. Thin lines present 7 1 standard deviation curves.

author, we use the duration function as 0.1*R, where R is the distance in km. We tried different duration functions, as well; however, none of them improved the results.

Amplification function in stochastic simulation is defined by two functions: crustal amplification function and site amplification function. If station is located on a rock site, using only crustal

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Fig. 4. Comparisons between the simulated and observed data for the seven rupture models (BOU, CAK, DEL, REL, SEK, YAG, RAN) at the six stations (ARC, GBZ, YPT, IZT, SKR, DUZ) are made on the waveforms (time series), duration (Arias intensity) and frequency content (FAS). Black (EW component) and gray (NS component) lines display the observations obtained at each station. The other color lines display the simulation result for each model. The peak ground accelerations (cm/s2) are shown above each waveform. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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Fig. 4. (continued)

amplification function is sufficient. If station is located on soil, then we additionally need a site amplification function. In this study, for crustal amplification, we used generic amplification

function (VS 4760 m/s) given by Margaris and Boore [55]. In order to take into account site amplification at each site, we estimated an average H/V spectral ratios [56] using the available accelerometric

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recordings from the database of ERD. For this, we tried to choose minimum 10 earthquake recordings at each station and used only S wave spectra. In addition, we also acquired ambient noise data at some stations that lack sufficient number of earthquake records. Neither earthquake nor microtremor data were available for MSK station. The H/V curves computed for each station are shown in Fig. 3. No local site amplification function was used at the stations where H/V ratio is close to 1. These stations are generally matched with the site classes A, B,

and in some cases with C (Table 1). This rule was broken at three stations; ARC, GYN and YPT. Although the H/V curves at ARC and GYN stations present a significant amplification peak at 7 Hz and 12 Hz, respectively, we could not use a local site amplification function, because it increased the discrepancy between the simulations and observations. Additionally, we did not use a local site amplification function at YPT station, because its H/V curve is flat although this station is located on site class D.

Fig. 5. The model bias functions representing the difference between the observed acceleration spectra and the simulated acceleration spectra at each station. The thick black lines (AVE) display the average bias function for each model. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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6. Determination of rupture model We first determine the rupture model (i.e. the BOU model, the CAK model, the DEL model, the REL model, the SEK model, the YAG model, and the RAN model) by investigating the fit between the observations and simulations. Six accelerometric stations (ARC, GBZ, YPT, IZT, SKR, and DUZ) located close to the observed surface rupture (Fig. 2) are chosen for the comparisons considering the fact that the slip contributions are better observed at these stations. Fig. 4 shows the comparisons between simulated and observed data for the seven rupture models at these six stations. The comparisons are made on the waveforms (time series), duration (Arias intensity) and frequency content (Fourier spectrum). The Fourier spectrum and PGA value shown on the waveform for each model are the average of 50 trials produced by EXSIM to stabilize the results. The simulated time forms (time series and Arias intensity) shown in Fig. 4 are the result of the trial which is the closest to the average spectrum from the 50 trials which is enough in the comparison of the waveforms. Whereas we only make a visual comparison in the time domain, we defined a model bias function (E(f)), and average error constant (Erms) in the frequency domain in order to compute the misfit between simulations and observations following Assatourians and Atkinson [46] and Ameri et al. [57]:   Oðf Þ Eðf Þ ¼ log Sðf Þ 8 !2 91=2 <1 X k Oðf ij Þ = Ermsj ¼ log :k Sðf ij Þ ; i¼1 where O(f) and S(f) are the Fourier spectra of the observed and simulated signals, respectively, k is the number of the considered frequencies for the jth station. The model bias function for each model is shown in Fig. 5. A negative model bias indicates overprediction of the observation and a positive model bias indicates underprediction of the observation. The average error constants for each model and station are presented in Table 4. The results show that none of the rupture models is sufficient to fully simulate the ground motions observed at all the stations. Considering the waveforms, while the REL model is very successful at the IZT station, it fails at the SKR station. Similarly, while the CAK model is successful at the ARC and GBZ stations, it is not so successful at the YPT and IZT stations. Generally, the BOU and SEK models give the best fit to the observations. The CAK and DEL models produce high peak accelerations, especially at the YPT, IZT, and SKR stations (Fig. 4). The PGAs at these stations produced by the CAK and DEL models are about between two and four times of the recorded values. In these models, the high-slip asperity takes place as a whole below the YPT, IZT, and SKR stations (Fig. 2) and causes the high accelerations in the simulations of these stations. In addition, the DEL model Table 4 The average errors computed at each station for each model. Underline values show the minimum error values. Rupture Models

BOU CAK DEL REL SEK YAG RAN Average

Stations ARC

GBZ

YPT

IZT

SKR

DUZ

Average

0.176 0.254 0.224 0.169 0.233 0.235 0.213 0.215

0.191 0.243 0.208 0.213 0.200 0.349 0.207 0.230

0.246 0.333 0.323 0.275 0.249 0.284 0.307 0.288

0.232 0.505 0.535 0.278 0.244 0.247 0.180 0.317

0.176 0.299 0.225 0.165 0.184 0.153 0.174 0.197

0.310 0.266 0.435 0.303 0.304 0.279 0.303 0.314

0.222 0.317 0.325 0.239 0.236 0.259 0.231

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has a separate high-slip patch on the eastern tip of the rupture (Fig. 2). This asperity causes high PGA at DUZ station and the simulated waveform presents a phase arrival with high amplitude at the end of the record. This is not in accordance with the recorded data. The YAG model produces low amplitude values at the edgestations (i.e. ARC, GBZ, DUZ), because the fault length in this model is rather short compared to the others and the surface rupture. The ground motion durations obtained from the simulations are generally comparable to those observations. However, while the durations of the simulated waveforms for YPT station are shorter than the observed ground shaking duration, the durations for DUZ station are longer than the observed ground shaking duration. The short duration and high peak acceleration for DUZ station, which is located to the east side of the fault, can be explained by forward directivity effect. Conversely, the long duration and low peak value observed on the records of YPT, which is located near the epicenter, can be explained by backward directivity effect. The differences between the models appearing in time domain are not so obvious in frequency domain. The model bias functions in Fig. 5 show that most of the rupture models underestimate the ground motions at frequencies lower than 0.4 Hz, whereas they overestimate the ground motions at higher frequencies, nearly 7–10 Hz. The underestimation may arise from directivity effect which causes high amplitudes on the observed ground motions in low frequency band. The overestimation observed on high frequencies may arise from the failure of the attenuation function used in this study. While the whole rupture models display similar average bias functions, the minimum average error is obtained with the rupture model of BOU (Table 4). Error constants in Table 4 show that the Fourier spectrum of the SKR station record is modeled the best. The RAN model has the second minimum average error among the models. Actually, one may not expect the RAN model gives better results for the observations recorded especially at the stations located near the high-slip patches on the fault, because the ground motions on specific points are affected significantly from the asperities on the fault plane. Our goal is to see the achievement level of the RAN model taking into account all simulations. Fig. 5 shows that the average success of the RAN model is not so different from the other models. The achievement of the RAN model is satisfactory. The comparisons made in time and frequency domain show that the BOU model gives the best results in simulating the ground motions of Izmit earthquake at near field stations. In the second step, the BOU model is used to simulate the ground motions at the stations located far from the surface ruptures. In the simulation of these stations, we just modified the site amplification function and kappa value depending on station characteristics (see Tables 1 and 3 for the parameters). Fig. 6 compares the simulations with the observations at the remaining 17 stations by using acceleration waveforms and Fourier spectra. Conformity between the simulations and the observations both in waveforms and spectra is very good, except at a few stations. For example at the ATS station, which is located in Avcilar, Istanbul (Fig. 1) where the damage was very high during the Izmit earthquake and high acceleration was recorded at this station despite the distance from the source, the spectral amplitudes and maximum acceleration of the simulation are lower than the observation. Another station at which the simulation has failed to reproduce the recorded ground motions is the MSK. As mentioned earlier, this station is the only station for which we do not have a site effect function. The perfect harmony seen on the high frequencies of the spectra is mainly arisen from the independent usage of the kappa value. However, some stations, for example BTS, CNA, and FAT, require lower kappa values (0.15–0.20 s) than expected for soil sites (Table 1). Kappa values of all stations used in the analysis are

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Fig. 6. The observed (gray lines; EW: the top trace and NW: the middle trace) and simulated (black line; random horizontal component) accelerograms and Fourier amplitude spectra of the August 17, Izmit earthquake computed by using the BOU rupture model at the remaining 17 stations (see text for explanation). The peak ground acceleration in cm/s2 is shown above each trace.

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Fig. 7. (a) The average model bias function and 71 standard deviation curves computed by using the BOU rupture model for the 23 stations. (b) Comparison of the recorded peak ground accelerations with the simulated peak ground accelerations at 23 stations. (c) Comparison of the recorded peak ground velocities with the simulated peak ground velocities at 23 stations.

below 0.055 s, except YPT station. We have checked the reason of low kappa values which may arise from the low stress drop value used in the simulations, because both parameters affect the amplitudes at high frequencies. We notice that an increase in the stress drop value requires the usage of high kappa values for better conformity especially at high frequencies. However, the high stress drop value impairs irrecoverably the conformity at low frequencies. Therefore, it is not possible to explain the low kappa values with the low stress drop. The high attenuation in the higher frequencies may be the reflection of the fact that the earthquake did not generate high frequency waveforms. The average model bias function for the 23 stations is shown in Fig. 7a. This figure presents the success of the model to generate the spectral amplitudes recorded during the Izmit earthquake. The underestimation of the spectral amplitudes at lower frequencies seen on Fig. 5 emerging due to the directivity effect is not observed in Fig. 7a, because directivity is not effective at the stations away from the fault. The observed peak ground accelerations derived from the geometric mean of the horizontal components are compared with the simulated PGAs in Fig. 7b, in order to see the success of the simulations in amplitudes depending on the distances from the fault. The figure shows that the accelerations reproduced by the simulations are consistent with the observations at various distances. The last comparison is made for the simulated and observed peak ground velocities (PGV) illustrated in Fig. 7c, in order to strengthen the efficiency of the model. The observed PGVs are computed by the integration of the acceleration records and the geometric mean of the peak values of the horizontal components. The high conformity between the observed and simulated PGVs in Fig. 7c lead up to estimate the peak velocities occurred during the Izmit earthquake in the region.

7. Peak accelerations and peak velocities during the Izmit earthquake Having seen the success of the model, we simulate the strong ground motions on a regular grid (0.21  0.21) covering the study area for bedrock conditions. In total, we have obtained simulations

Fig. 8. Distribution of peak ground motions (upper PGA, bottom PGV) simulated at 135 grid points (0.21 X 0.21) for bedrock conditions. The thick black line is the projection of the used fault model on the free surface. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

at 135 points. The PGAs and PGVs are retrieved from the waveforms to get an insight of the distribution and extent of the strong ground shaking. The distributions of PGA and PGV are shown in Fig. 8. As expected, the largest ground shaking is obtained along the ruptured fault plane. The maximum acceleration values reach 785 cm/s2,

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Fig. 9. Comparisons of the attenuation of the simulated PGAs (upper) and PGVs (bottom) with the empirical attenuation relations of Akkar and Bommer [58] (continuous line) and Boore and Atkinson [59] (dashed line) for rock site. The thin lines display the mean 7 1 standard deviation curves.

and the largest PGV values are around 75 cm/s. The strongest ground shaking is associated with the locations of the high slip asperities located to the east and west of the epicenter. These are also correspond to Golcuk and Sakarya settlements which are the worsthit cities during the earthquake. It is important to keep in mind that the simulations are done for bedrock level, and site effects (due to sedimentary layers or topographic effects) are not taken into account. In Fig. 9, the simulated PGAs and PGVs are compared with the ground motion prediction equations developed by Akkar and Bommer [58] and Boore and Atkinson [59] for rock sites. The simulated peak accelerations especially at the distances larger than 10 km from the fault are generally lower than those predicted by empirical attenuation relations. The empirical relations serve as an upper bound for the simulated PGAs. Unlike the PGAs, the majority of the simulated PGV values are in the range of the empirical relations. In the light of our results, the Izmit earthquake can be characterized as a low-PGA earthquake.

8. Results and discussions Finite fault stochastic simulations have previously been proven to be powerful tool for estimating the ground motions during an earthquake. In this study, we have used seven prominent

rupture models of the Izmit earthquake, in order to investigate the success of the rupture models in reproducing near field strong ground motions. The original rupture models have been slightly adjusted in order to suit the EXSIM code. Some parameters, for example the stress drop, the rupture velocity, the attenuation and the duration function have been fixed for the all models taking into account the studies performed for the region. The site effect for each station has been estimated by using H/V spectral ratios. The kappa values have been determined in trial and error manner. The comparisons made in time and frequency domain have shown that the BOU model [22] yields the best matching with the observations at six near field stations. The original fault model and slip distribution of the BOU model was optimized using the records of near field strong motion stations that we also used in our study. Therefore, the success of the BOU model is not a surprise. However, in the original modeling low frequency velocity and displacement waveforms were used, unlike our high frequency acceleration records. In addition, we obtained the best results using a standard rupture velocity (0.8nVS) along the fault plane, whereas the original BOU model utilized supershear rupture (4.8 km/s) on the central segment of the fault. We think that the supershear rupture might have occurred in a part of the fault that only affects the ground motions at stations close to it, but not all the stations. Because the stochastic finite fault approach we used does not account for the overall directivity effect, it causes to some extent differences between the observations and simulations at low frequencies. We tested the success of a simple rupture model (RAN) including random slip distribution along with the detailed models. The results of RAN model are not so different from the other models considering the average model bias functions. Also, at some stations it gives better results than the other models. Why the RAN model is as successful as the models derived by optimization of co-seismic data? A likely source of the success may be coming from the tradeoff between the source models and the site and path parameters. Our results suggest that if the parameters of path and site can be constrained very well, random slip distribution in stochastic simulation can be used to predict ground motions. However, this may also imply that the path and site parameters may be more effective in stochastic modeling than the detailed rupture model taking into account the whole simulation points. Our constrained BOU model reproduces to a large degree the frequency content of the ground motions observed at the 23 stations, and the peak accelerations correlate well with those recorded at these stations. The kappa values constrained in trial and error manner in the simulations are lower in general than the values expected for similar site classes. The low kappa values may be attributed to the lower high frequency content of the earthquake. In the simulations for the whole study area including also the locations where no recording station exist, and considering bedrock condition, the maximum acceleration values reach 785 cm/s2, and the largest PGV values are around 75 cm/s. Although the simulated PGAs increase approximately to the twice of the recorded PGAs, they are still below the ones predicted by the empirical relations. The empirical relations serve as an upper bound for the simulated PGAs. Unlike the PGAs, the majority of the simulated PGV values are in the range of the empirical relations. In the light of our results, the Izmit earthquake can be characterized as a low-PGA earthquake or an earthquake that generated no high frequencies. The low accelerations can be attributed to the low stress drop, due to the large rupture length, because the rupture length derived for Izmit earthquake is approximately twice of the expected length for such an earthquake.

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