Stochastic strong ground motion simulations in sparsely-monitored regions: A validation and sensitivity study on the 13 March 1992 Erzincan (Turkey) earthquake

Soil Dynamics and Earthquake Engineering 55 (2013) 170–181

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Soil Dynamics and Earthquake Engineering journal homepage: www.elsevier.com/locate/soildyn

Stochastic strong ground motion simulations in sparsely-monitored regions: A validation and sensitivity study on the 13 March 1992 Erzincan (Turkey) earthquake Aysegul Askan a,n, F. Nurten Sisman b, Beliz Ugurhan c a

Civil Engineering Department, Middle East Technical University, Ankara, Turkey Earthquake Studies Department, Middle East Technical University, Ankara, Turkey c Civil Engineering Department, Stanford University, Stanford, CA, USA b

art ic l e i nf o

a b s t r a c t

Article history: Received 8 February 2012 Received in revised form 20 January 2013 Accepted 22 September 2013 Available online 16 October 2013

Stochastic simulations have recently become quite popular for estimating synthetic ground motion time histories. For seismically active regions that are not well-monitored or studied extensively, input parameters of the simulations should be carefully selected as the reliability of the simulation results directly depends on the accuracy of the input parameters. In the first part of this study, 13 March 1992 Erzincan (eastern Turkey) earthquake (Mw ¼ 6.6), which is recorded at only three strong ground motion stations, is simulated using the stochastic finite-fault method. The source and regional path parameters for this event are adopted from previously validated studies whereas the local site parameters are derived herein. In the second part of the paper, sensitivity of the simulation results with respect to small changes in selected input seismic parameters is investigated. The parameters for which sensitivities are computed include stress drop, crustal shear-wave quality factor and kappa operator. A change of 20% in stress drop value results in 14% change in PGA, whereas a 20% difference in the Q0 value causes 17% change in PGA, and a 20% variation in kappa leads to 15% difference in PGA. Numerical experiments presented in this study prove that the ground motion simulations are prone to trade-off between the source, path and site filters. Hence, input models must be implemented carefully for reliable synthetic ground motions. & 2013 Published by Elsevier Ltd.

Keywords: Stochastic finite-fault model Ground motion simulation Sensitivity Input parameter Erzincan

1. Introduction Studies concerning earthquake ground motions are interdisciplinary by nature and they involve a wide group of research fields ranging from earth sciences to civil engineering; from insurance industry to public policy. In civil engineering, for purposes of seismic design and retrofitting of structures, it is essential to utilize reliable estimates of the seismic loads to which structures will be exposed during their lifetimes. For engineering purposes, empirically-formed Ground Motion Prediction Equations (GMPEs) are frequently used in the estimation of peak ground motion intensity values. However, in some cases, not only the peak ground motion intensity parameters but also the frequency content of any seismic excitation is important for seismic design and analysis. In other words, the full ground motion time series of a past event or an anticipated scenario event might be required. In regions with

n

Corresponding author. Tel.: þ 90 312 210 2423; fax: þ90 312 210 5401. E-mail addresses: [email protected] (A. Askan), [email protected] (F.N. Sisman), [email protected] (B. Ugurhan). 0267-7261/$ - see front matter & 2013 Published by Elsevier Ltd. http://dx.doi.org/10.1016/j.soildyn.2013.09.014

sparse ground motion data, records from other regions with similar seismotectonics are generally employed and averaged for dynamic response analyses of civil engineering structures. For the same purpose, ground motion simulations provide alternative acceleration time series. The fundamental objective of ground motion simulations is to physically model the source mechanisms and regional wave propagation for estimating reliable synthetic records. Since the tectonic features and seismological properties of the Earth vary spatially, regional studies representing the characteristics of the seismic sources, wave propagation properties and site conditions become crucial for reliable ground motion simulations. Alternative simulation methods provide different levels of accuracy for modeling ground motion records. With respect to their modeling assumptions and solution techniques, strong ground motion simulation methods are divided into two major categories: stochastic and deterministic simulations. In stochastic simulations, inherent randomness of the ground motions is taken into account (e.g., [1–3]) whereas deterministic approach relies mostly on numerical solutions of the wave equation (e.g., [4–7]). The deterministic method requires rigorous

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definitions of the sources and wave velocity models of any region of interest. In spite of its accuracy, it is practical only up to certain frequencies due to the computational and physical constraints related to the minimum wavelength used in modeling. Stochastic method, on the other hand, yields an average horizontal component of far field S-waves but it is more practical and computationally not as expensive. Despite the loss of accuracy due to the absence of full wave propagation, it has been employed effectively for various tectonic regions in the world including Turkey (e.g., [8–15]). Recently, hybrid methods are developed for generating broadband ground motions, which combine stochastic and deterministic methods for the simulation of high and low frequency components, respectively. These hybrid methods are employed and validated by several researchers (e.g., [16–19]). Parallel to the growing need for the full acceleration time series for engineering seismology and earthquake engineering purposes, the stochastic simulations have become quite popular recently. Especially, in areas with sparse strong ground motion station networks, the fact that the stochastic simulation methods practically generate frequencies of engineering interest makes their use even more common. In some cases, such as the recent destructive 23 October 2011 Van (Mw ¼7.0, eastern Turkey) earthquake, when records are not sufficient to assess the levels of ground shaking in the near-fault area, practical simulations could be especially useful. However, particularly for those seismically active regions that are not well-monitored or studied, one needs to be more careful as the reliability of the simulation results directly depends on the accuracy of the input parameters. This is because the regional seismic parameters used as the major input to stochastic simulations determine the amplitude and frequency content of the simulated ground motions. Thus, they should be evaluated and employed carefully to yield physical results. In few studies, efficiency of seismic parameters in ground motion simulations is studied by testing alternative models for the simulations (e.g., [20–23]), however systematic approaches and detailed parameter sensitivity studies are required for the assessment of the input parameters in stochastic ground motion modeling. Based on this observation, this paper assesses the efficiency and sensitivity of stochastic ground motion simulations in regions with sparse seismic stations. For this purpose, in this study, we first employ stochastic finite fault method with a dynamic corner frequency approach [24] to simulate the shear wave portion of high frequency near field ground motions of a previous major earthquake in Eastern Turkey. As the case study area, we choose to work in the relatively less studied (when compared to the western parts) and sparsely-monitored Eastern part of the North Anatolian Fault zone (NAFZ). We initially simulate the 13 March 1992 Erzincan earthquake (Mw¼ 6.6) with the few available ground motion records of the event. The input source and path model parameters are carefully selected from previous studies conducted in the region whereas the local site parameters are derived in this study for each station that recorded the mainshock. Then, in the second part of the paper, we investigate the range of simulation results for variations in input model parameters. For this purpose, we perform a local sensitivity analysis for small perturbations in the selected input parameters.

2. Methodology: stochastic finite fault model based on a dynamic corner frequency Finite-fault models aim to predict the ground motion field at near-source observation points while taking into account the finite dimensions of the fault plane. Beresnev and Atkinson [3] proposed the stochastic finite-fault model which discretizes a rectangular fault plane into smaller subfaults and sums the contribution of the

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subfaults where every subfault is treated as a stochastic pointsource with an ω  2 spectrum as introduced in [1]. The hypocenter is placed on one of the subfaults and the rupture is assumed to start propagating radially from the hypocenter with a constant rupture velocity. As the rupture reaches the center of a subfault, that subfault is assumed to be triggered. In this way, the contribution of all subfaults is summed with appropriate time delays in order to obtain the entire fault plane's contribution to the seismic field at any observation point as follows [25]: nl

nw

AðtÞ ¼ ∑ ∑ Aij ðt þ Δt ij Þ i¼1j¼1

ð1Þ

In Eq. (1), AðtÞ is the ground motion acceleration obtained from the entire fault whereas Aij is the ground motion acceleration contribution from the ijth subfault. nl and nw are the number of subfaults along the length and width of main fault, respectively. The time delay for each element Δt ij , is the summation of the time required for the rupture front to reach the element and the time required for the shear-wave to reach the receiver after the element has been triggered [3]. One limitation of the original stochastic finite-fault model as proposed by Beresnev and Atkinson [3] is the constraint on the number of subfaults and the dependence of the total radiated energy on the subfault size. This drawback is overcome by the work of Motazedian and Atkinson [24] with a dynamic corner frequency concept 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 the recent approach as implemented in the computer program EXSIM [24]. The acceleration spectrum Aij ðf Þ of the ijth subfault is defined in terms of source, path and site effects as follows: 2

Aij ðf Þ ¼ CM 0ij H ij 

ð2πf Þ  πf Rij =Q ðf Þβ GðRij ÞDðf Þe  πκf
2 e 1 þ f =f cij

ð2Þ

pffiffiffi where C ¼ ℜθφ 2=4πρβ3 is a scaling factor, ℜθφ is the radiation pattern, ρ is the density, β is the shear-wave velocity, M 0ij ¼ nw M 0 Sij =∑nl k ¼ 1 ∑l ¼ 1 Skl is the seismic moment, Sij is the relative slip weight and f cij ðtÞ is the dynamic corner frequency of ijth subfault  1=3 . Here Δs is the where f cij ðtÞ ¼ N R ðtÞ  1=3 4:9  106 β Δs=M 0ave

stress drop, N R ðtÞ is the cumulative number of ruptured subfaults at time t, and M 0ave ¼ M 0 =N is the average seismic moment of subfaults. Rij is the distance from the observation point, Q ðf Þ is the quality factor, GðRij Þ is the geometric spreading factor, Dðf Þ is the site amplification term, and e  πκf is a high-cut filter to include the spectral decay at high frequencies described with the κ factor of soils [26]. In Eq. (2), H ij is a scaling factor introduced to conserve the high-frequency spectral level of the subfaults [24] where 91=2 8 h
  i > > > > = < ∑ f 2 = 1 þ f =f c 2

 ð3Þ H ij ¼ N 
 2 > > > > ; : ∑ f 2 = 1 þ f =f cij

A significant modification to the original stochastic finite-fault model is the implementation of pulsing subfaults concept by Motazedian and Atkinson [24]. In the pulsing subfault concept, it is assumed that rupture starts and builds up until a specified percentage of the subfaults are ruptured. The subfaults that are actively pulsing contribute to the dynamic corner frequency whereas no contribution comes from the passive ones. This behavior yields a decreasing corner frequency until a constant pulsing area percentage is reached. Afterwards the dynamic corner

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frequency becomes constant. The parameter that controls the percentage of the maximum ruptured area is called pulsing area percentage. In this recent stochastic finite-fault model as described in [24], among all the simulation parameters, pulsing area percentage and the stress drop are the two free parameters that affect the amplitudes of the acceleration spectrum.

3. Strong ground motion simulation of the 13 March 1992 Erzincan earthquake The eastern segments of the NAFZ are less investigated and have less dense seismic networks than the western ones. The fundamental objective of this study is to investigate the efficiency and sensitivity of stochastic finite-fault simulations in an area with a sparse seismic network. For this purpose, initially ground motions of 13 March 1992 Erzincan earthquake are simulated. Then, a sensitivity analysis around the selected model parameters is

presented. To quantify the error, misfit functions in terms of observed and synthetic Fourier Amplitude Spectra (FAS), peak ground acceleration (PGA) and the peak ground velocity (PGV) values are defined. 3.1. Background information Erzincan is considered to be one of the most hazardous regions of the world. Historical records evidence 18 large (Mw Z8) earthquakes in the close vicinity of Erzincan within the past 1000 years [27]. It is located in a tectonically very complex regime, in the conjunction of three active faults, namely North Anatolian, North East Anatolian and East Anatolian Fault Zones (EAFZ). These faults characterize the basic seismotectonics of the region. NAFZ displays right-lateral strike-slip faulting whereas EAFZ and North East Anatolian Fault Zones have left-lateral strike-slip faulting. The tectonic map of the region is displayed in Fig. 1, top panel. In the bottom panel of the same figure, red lines indicate the active faults in the region. Erzincan basin is formed as a pull-apart basin

Fig. 1. Top Panel: Map showing the plate tectonics of the Anatolian Block (adapted from http://neic.usgs.gov/neis/eq_depot/2003/eq_030501/). Bottom Panel: Regional map showing the epicenters, rupture zones and the mechanisms of the 1939 and 1992 earthquakes (epicenters are indicated with red and blue stars, respectively) and strong ground motion stations that recorded 1992 Erzincan earthquake (indicated with black triangles). Erzincan basin is also shown within a shaded polygon parallel to the 1992 fault. (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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because of the interactions between NAFZ and Ovacık Faults. It is the largest basin on the NAFZ with dimensions of 50  15 km2 in the close vicinity of Fırat River. The thickness of the alluvial layers goes up to several kilometers at the center of the basin and decreases near the mountain ranges [28]. NAFZ is the most active fault zone in Turkey, yielding several destructive earthquakes in the past 100 years. The destructive earthquake sequence of NAFZ started with 1939 Erzincan earthquake (Ms ¼8.0). This destructive earthquake caused more than 30,000 fatalities and led to the relocation of the city towards North [28]. Following this earthquake, the seismic sequence of this fault zone propagated towards westward. Later, on March 13, 1992 an earthquake of Mw ¼6.6 (Earthquake Research Department of Turkey, ERD) occurred on an eastern segment of NAFZ in Erzincan region, at the intersection of NAFZ and Ovacık faults. The earthquake was reported to have epicentral coordinates of 39.7161N and 39.6291E (ERD). In Fig. 1, bottom panel, the epicenter of the earthquake and the strong ground motion stations that recorded the mainshock are displayed. Although this earthquake is considered to be a moderate magnitude one, it caused severe building damage leading to over 500 fatalities and an economic loss of 5–10 trillion Turkish Liras [29]. The mainshock of 13 March 1992 Erzincan earthquake was recorded only by three strong ground motion stations. The station names, codes, operating institutes, hypocentral coordinates, mean shear-wave velocity at 30 m (Vs30), epicentral distances and the larger of the horizontal peak ground motion acceleration and velocity values are given in Table 1. The ground motions recorded at the stations displayed in Table 1 are obtained from Strong Ground Motion Database of Turkey (via http://daphne.deprem.gov. tr:89 /2K/daphne_v4.php). As the Erzincan region is characterized with high hazard and other potential large earthquakes are anticipated in the future, it is essential to assess the seismicity of this area. This study aims to validate and calibrate the seismological parameters that define the source, path and site effects in Erzincan region using ground motion simulations. Source and path parameters are selected among the previously-validated regional models from the literature whereas the site parameters are derived in this study using the regional past records.

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3.2.1. Source model As the initial step in stochastic finite fault modeling, we model the source mechanism of the 1992 Erzincan earthquake. The stochastic method requires the fault geometry along with dip and strike angles, hypocenter location and depth, rupture velocity, subfault size and the slip distribution on the fault plane. As the source model, among different models [30–32], we test and select the model that minimized the misfit between the observed and simulated spectral amplitudes at the stations. We emphasize that these studies provide mostly consistent source models, indicating that the source mechanism of the event is well-constrained. However, among all, the source model by Bernard et al. [32] minimizes the errors between the observed and computed amplitudes in particular for the low-frequency content of the Fourier acceleration spectra that is governed by the source. In their study, Bernard et al. [32] initially relocated the hypocenter using local and regional records of the earthquake such that the travel time delays between P and S phases are consistent. Then the authors verified their fault model by simulating velocity records of the mainshock using complete Green's functions in a layered medium. We note that this source model by Bernard et al. [32] was also further validated by Berge-Thierry et al. [33]. Thus, in this study, the values of hypocenter location, depth, fault size and orientation, crustal S-wave velocity and rupture velocity are adopted from Bernard et al. [32]. Finally, following the observations of Legrand and Delouis [30] and Bernard et al. [32], uniform slip distribution is used over the fault plane. Table 2 displays the values of the source parameters used in the simulations. 3.2.2. Path model In stochastic strong ground motion simulations, the path effects are modeled via the frequency-dependent attenuation, geometrical spreading, and ground motion duration effects. The whole path attenuation is modeled through frequencydependent quality factor. We tested two alternative models: the first one is the model by Akinci and Eyidogan [34] where the functional form is given as Q¼ 35f0.83. This attenuation model is derived from the frequency-dependent decay of direct S-waves in Erzincan region based on the analyses of 161 earthquakes. The second model is from Grosser et al. [35] where the functional form

3.2. Simulation of the 13 March 1992 Erzincan earthquake For the validation of the ground motion simulation of 1992 Erzincan Earthquake, the three records obtained at the stations listed in Table 1 are utilized. Since the number of stations is very limited, we pay special attention to the selection of the input parameters for validation. For the source and path modeling, we employ well-constrained regional models from past studies. For the site response modeling which should be performed locally for the stations, we derive a regional kappa model along with site amplification models for each station used in this study. The regional kappa model is derived using the previously recorded on strong ground motions at these three stations. Site amplification spectra are computed based on the available geotechnical information at the stations.

Table 2 Source parameters used in the simulation of the 13 March 1992 Erzincan earthquake. Parameter

Value

Hypocenter location Hypocenter depth Depth to the top of the fault plane Fault orientation Fault dimensions Crustal shear wave velocity Rupture velocity Crustal density Stress drop Pulsing area percentage

39142.3N, 39135.2E 9 km 2 km Strike: 1251, Dip: 901 25 km  9 km 3700 m/s 3000 m/s 2800 kg/m3 80 bar 50

Table 1 Information on the strong motion stations that recorded the 13 March 1992 Erzincan earthquake. Station

Code

Operator name

Latitude (1N)

Longitude (1E)

Mean Vs30 (m/s)

REPI (km)

PGA (cm/s2)

PGV (cm/s)

Erzincan-Merkez Refahiye Tercan

ERC REF TER

ERD ERD ERD

39.752 39.899 39.777

39.487 38.768 40.391

314 433 320

12.83 76.45 65.62

478.77 80.61 40.92

108.43 4.27 4.77

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is obtained as Q ¼122f0.68. That model is derived based on 1045 seismograms recorded at 10 temporarily-installed stations in the Erzincan region to record the aftershocks of the 1992 event. The authors of that study used the coda-Q technique to estimate the attenuation of shear waves as a first approximation [35]. In our simulations, we tested both Q models and concluded that the latter model yields closer spectral amplitudes to the observations particularly for stations REF and TER. We note that this conclusion is valid only for our results as it is well known that there is a tradeoff between the quality factor and the other frequency-dependent parameters employed in the stochastic simulations. For geometric spreading, we use a local model proposed by Akinci et al. [29] given in the following form: R  1:1 ;

Rr 25 km

R  0:5 ;

R 4 25 km

Fig. 2. Amplification spectra at station ERC based on HVSR analyses.

ð4Þ

Finally, the duration of the ground motions is computed using the generic model of Herrmann [36]: T ¼ T 0 þ 0:05R

ð5Þ

where T 0 is the source duration (equal to the reciprocal of the corner frequency) and R is the hypocentral distance.

3.2.3. Site effects Site effects are the combination of local soil amplification and high-frequency decay (kappa) effects at the strong motion stations. In this study, we evaluate both amplification and kappa effects based on accelerograms from past events recorded at ERC, REF and TER stations. Most of the records used for amplification and kappa analyses correspond to weak motions that are recorded during events with 3 oMwo 5. A common methodology used for site response evaluation is the empirical Horizontal to Vertical Spectral Ratio (HVSR) method which was originally introduced by Nogoshi and Igarashi [37] and later improved by Nakamura [38]. This method is based on the assumption that the vertical surface ground motions are less amplified thorough the soft soil layers than are the horizontal components. Initially, in this study the objective was to use HVSR at all stations. However, records with good quality at REF and TER are very limited in number. Station ERC has approximately 30 records that are of good quality. Thus, we initially assess the empirical site amplifications only at ERC with HVSR technique. To calculate the mean HVSR at ERC, we use windows of manuallyselected lengths that correspond to the high amplitude-S-wave portions of the records. We then smooth the computed Fourier amplitude spectra between 0.25 and 25 Hz with a Hann filter of 0.4 Hz-bandwidth. The mean HVSR spectrum is shown in Fig. 2. As the Vs30 values at the stations are close to each other, one option is to use the empirical HVSR of ERC station for the other stations as well. However, as amplification spectrum is very sitespecific, to be precise we perform one-dimensional (1D) site response analyses at each station based on the available geophysical and geotechnical information. We compute the theoretical transfer function for the soil profiles at the three stations in the frequency domain. The soil is modeled as a series of infinite horizontal layers on top of uniform half-space where the input parameters required are the thickness, density, and wave velocity, shear modulus reduction and damping curves of each layer [39]. The geotechnical reports with detailed information for the stations are available on the web page for Turkish National Strong Ground Motion Network (http://daphne.deprem.gov.tr). Tables 3–5 summarize the geotechnical and geophysical properties of soil layers at ERC, REF and TER, respectively.

Site-response analyses yield the theoretical transfer function as output which is the spectral ratio between the input ground motion at the bedrock level and the surface motion obtained via 1D wave propagation through the soil layers. In this study, as the input accelerogram we use a weak motion record with a PGA of 0.001g measured at ERC during an event of Mw¼ 3.4. Fig. 3a–c show the corresponding amplification spectra at ERC, REF and TER respectively. In several previous studies (e.g., [40–42]), it was shown that the observed and theoretical amplifications are mostly in agreement. Similarly, in this study through Figs. 2 and 3a, we observe that the theoretical transfer function and mean empirical HVSR curve at ERC are consistent in terms of peak frequencies and amplitudes despite some discrepancies. Yet, to be consistent for all stations, for ERC station we do not employ the empirical HVSR but the theoretical amplification spectrum as for stations REF and TER. Next, we assess the kappa effects at the stations. In the original study by Anderson and Hough [26], the linear model for regional distance-dependency of kappa is expressed as κ ¼ κ 0 þpR

ð6Þ

where κ0 is the zero-distance kappa value, ρ is the slope of the linear model and R is epicentral distance. In previous studies, it is discussed that while κ 0 is a station-specific value, ρ is related to the regional path attenuation properties. In stochastic ground motion simulations, it is necessary to use the zero-distance kappa ðκ 0 Þ value since the regional attenuation is already included in the simulations through the frequencydependent quality factor. As discussed earlier, ground motion records with good quality at REF and TER is very limited in number. Thus, majority of the records used in kappa analyses belong to measurements at the ERC station. As the high frequency decay of the records obtained at ERC, TER and REF are observed to be similar; we derive a regional kappa model by combining the records from all stations. For this purpose, the waveforms recorded at those stations during past events are studied individually. To compute the κ values, we follow the procedure introduced by Anderson and Hough [26] where the high-frequency spectral decay is modeled as Aðf Þ ¼ A0 e  πκf ;

f 4f e

ð7Þ

where amplitude A0 depends on source and path properties and f e is the frequency over which the spectrum is approximated with a linear decay on a log(amplitude) versus frequency plot. Before computing kappa values, we initially apply baseline correction and 5% Hann windows tapering on the time series. Then, S-wave windows with length 5 s is picked manually and the corresponding Fourier amplitude spectrum is smoothed between 0.25 and 50 Hz. Finally, the amplitudes are plotted in log-lin space. The frequencies where linear decay of log-amplitudes starts (f e ) and

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Table 3 Geotechnical and geophysical properties of soil layers at ERC. Layer number

Material name

Thickness, H (m)

Vs (m/s)

Modulus curve

Damping curve

1 2 3 4 5 6 7 8 9 10 11 12

Filling Clay Sand Sand Clay Clay Clay Clay Clay Rock Rock Rock

1.4 1.6 2.1 2.7 3.3 4.1 5.1 6.5 5.2 10 10 Infinite

219 170 234 251 300 349 362 402 469 800 1000 2000

Linear Clay–PI¼ 10–20 (Sun et al.) Sand (Seed & Idriss) – average Sand (Seed & Idriss) – average Clay–PI¼ 10–20 (Sun et al.) Clay–PI¼ 10–20 (Sun et al.) Clay–PI¼ 10–20 (Sun et al.) Clay–PI¼ 10–20 (Sun et al.) Clay–PI¼ 10–20 (Sun et al.) Rock(Idriss) Rock(Idriss) Rock(Idriss)

Linear Clay – average (Sun et al.) Sand (Seed & Idriss) – average Sand (Seed & Idriss) – average Clay – lower bound (Sun et al.) Clay – lower bound (Sun et al.) Clay – lower bound (Sun et al.) Clay – lower bound (Sun et al.) Clay – lower bound (Sun et al.) Rock Rock Rock

Table 4 Geotechnical and geophysical properties of soil layers at REF. Layer number

Material Name

Thickness, H (m)

Vs (m/s)

Modulus curve

Damping curve

1 2 3 4 5 6 7 8 9 10 11

Filling Clay Gravel Sand Clay Sand Sand Sand Sand Rock Rock

0.40 0.9 2.8 3.0 6.8 4.7 5.8 7.4 3.0 10 Infinite

305 305 155 339 319 507 619 717 786 1000 2000

Linear Clay–PI¼ 40–80 (Sun et al.) Gravel (Seed et al.) Sand (Seed & Idriss) – Average Clay–PI¼ 40–80 (Sun et al.) Sand (Seed & Idriss) – Average Sand (Seed & Idriss) – Average Sand (Seed & Idriss) – Average Sand (Seed & Idriss) – Average Rock(Idriss) Rock(Idriss)

Linear Clay – upper bound (Sun et al.) Gravel (Seed et al.) Sand (Seed & Idriss) – average Clay – upper bound (Sun et al.) Sand (Seed & Idriss) – average Sand (Seed & Idriss) – average Sand (Seed & Idriss) – average Sand (Seed & Idriss) – average Rock Rock

Table 5 Geotechnical and geophysical properties of soil layers at TER. Layer Number

Material name

Thickness, H (m)

Vs (m/s)

Modulus curve

Damping curve

1 2 3 4 5 6 7 8 9 10 11

Filling Clay Clay Gravel Clay Clay Sand Clay Sand Rock Rock

0.8 1.0 2.3 3.1 3.6 4.5 5.6 7 4.3 10 Infinite

250 250 316 253 230 274 389 431 436 800 2000

Linear Clay–PI¼ 20–40 (Sun et al.) Clay–PI¼ 10–20 (Sun et al.) Gravel (Seed et al.) Clay–PI¼ 20–40 (Sun et al.) Clay–PI¼ 40–80 (Sun et al.) Sand (Seed & Idriss) – Average Clay–PI¼ 20–40 (Sun et al.) Sand (Seed & Idriss) – Average Rock(Idriss) Rock(Idriss)

Linear Clay – average (Sun et al.) Clay – lower bound (Sun et al.) Gravel (Seed et al.) Clay – average bound (Sun et al.) Clay – upper bound (Sun et al.) Sand (Seed & Idriss) – average Clay – average bound (Sun et al.) Sand (Seed & Idriss) – average Rock Rock

ends (f x ) are selected manually for each component to compute the corresponding kappa value. The final dataset used for a regional kappa model consists of 40 records measured at the three stations. We note that the original database had more data than those employed herein however, only the records with clear S-wave arrivals and no signal-to-noise problems are selected for reliable kappa computations. Similarly, records with significant site amplifications are also rejected to reduce possible bias in kappa values. Fig. 4 shows the kappadistance distribution and the linear best fit model. In the simulations, the corresponding zero-distance kappa value (κ0 ¼ 0.066) is used to account for the near surface high frequency attenuation. We note that the kappa estimates for this region are higher than those computed for the western part of NAFZ [10,15] indicating high near surface attenuation in the region.

3.2.4. Validation of simulations against the records Motazedian and Atkinson [24] state that for a well-constrained input parameter set, the free parameters to be calibrated for the

stochastic finite fault simulations are the stress drop and pulsing percentage area. For the stress drop which governs the overall amplitudes of the ground motion spectra, we tested alternative values and searched for the minimum error between the observed and simulated ground motions. To quantify the misfit, we use a frequency domain error computed as follows: First, by dividing the observed horizontal FAS to the synthetic FAS at every frequency; we obtain a discrete error series as a function of frequencies. The discrete error values are then averaged over the number of stations used in the simulations. This error formulation in frequency domain is given as [15,20] 1 n Ai ðf Þobserved Eðf Þ ¼ ∑ log ni¼1 Ai ðf Þsynthetic

! ð8Þ

where n is the number of stations and Ai ðf Þ is the acceleration spectra at the ith station. Fig. 5 shows the variation of the average error for alternative values of stress drop when all the other simulation parameters are kept constant. As observed from Fig. 5, stress drop value of 80 bar

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Fig. 5. Comparison of misfit versus frequency for alternative values of stress drop.

Table 6 Input parameters used in the simulation of 13 March 1992 Erzincan earthquake.

Fig. 3. Amplification spectra computed from the theoretical transfer functions at the stations: (a) ERC, (b) REF and (c) TER.

Fig. 4. Regional distance dependency of kappa computed at stations ERC, REF and TER.

that minimize the overall misfit is used in the simulations. Finally, the value for the pulsing area percentage is selected to be 50% which gave the closest fit for the lower frequencies. Table 6 summarizes the input source, path and site parameters employed in the simulations. The synthetic accelerograms and the corresponding FAS at ERC, REF and TER are displayed in comparison with the records in Fig. 6.

Parameter

Value

Hypocenter location Hypocenter depth Depth to the top of the fault plane Fault orientation Fault dimensions Crustal shear wave velocity Rupture velocity Crustal density Stress drop Pulsing area percentage Quality Factor

39142.3N, 39135.2E 9 km 2 km Strike: 1251, Dip: 901 25 km  9 km 3700 m/s 3000 m/s 2800 kg/m3 80 bar 50

Geometrical spreading

R  1:1 ; R  0:5 ;

Duration Model Windowing function Kappa factor Site amplification factors

T ¼ T 0 þ 0:05 R Saragoni-Hart Regional kappa model (κ0 ¼ 0.066)) Local model at each station

Q ¼ 122f

0:68

R r 25 km R 4 25 km

At station ERC, although a satisfactory fit is obtained in the high frequencies, there is a clear underestimation of the synthetics in the lower frequencies mostly regarding the source effects. Due to the high amplitude and short duration peaks in the recordings, the acceleration time histories of station ERC imply that the records could be subjected to forward directivity effects. As it does not assign directivity effect to individual subfaults [43], the stochastic finite-fault method is limited in simulating directivity effects. This drawback is the most probable cause of the misfit in the lower frequencies of the ground motions at the station ERC. The East–West (EW) component of station REF is closely matched by the synthetic spectra. On the other hand, the NS component of the observed ground motion exhibits much smaller amplitudes than both the EW component and the synthetic record. Finally, there is a close match between the observed and synthetic spectra at TER station. We attribute this close fit to the fact that the local site response at TER is effectively captured by the theoretical site amplification spectrum employed in the simulations. It is clear in Fig. 6 that the generic duration model [36] does not satisfactorily simulate the duration of the recorded ground motion at TER. As mentioned previously, Erzincan region is located on an alluvial basin. Thus, potential basin effects are expected in these recordings in the form of increased durations as well as large amplitude surface waves as seen in TER record. While a regional duration model could yield better results in terms of ground motion durations, to regenerate the basin effects accurately, rigorous wave propagation modeling is necessary. This would

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Fig. 6. Comparison of FAS and acceleration-time series of the observed and synthetic ground motions of 1992 Erzincan earthquake.

Fig. 7. Comparison of the attenuation of synthetics and observed data with a global (BA08) and a local (AC10) GMPE in terms of: (a) PGA, (b) PGV, 5% damped spectral acceleration at (c) T ¼ 0.3 s, (d) T ¼ 1 s and (e) T ¼ 2 s.

require a high-resolution velocity model of the basin along with complex source and wave propagation models which is out of the scope of this study, but a natural near-future extension of this study and similar studies. Finally, we note that with physics-based models along with heterogeneous wave propagation, one can lead to much better results.

3.3. Comparison of synthetics with ground motion prediction equations (GMPEs) To further assess the accuracy of the synthetic ground motions, we compare the attenuation of 500 simulated records at dummy stations around the epicentral area with two GMPEs. We select

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one NGA model by Boore and Atkinson [44] (BA08) and a local model by Akkar and Cagnan [45] (AC10) that is derived using Turkish strong motion data. The comparisons are made in terms of Joyner–Boore (JB) distance as both models employ that particular distance metric. Fig. 7 displays the comparisons between the GMPEs and attenuation of the synthetics for generic rock conditions (Vs30 ¼ 620 m/s) and strike-slip faulting. We observe that for PGA, PGV and 5% damped SA, the attenuation of synthetics is closer to the BA08 model. For all cases, the synthetics are within one standard deviation of AC10, but in general AC10 provides a lower bound for the simulated peaks. It is interesting to note that the global GMPE provides a closer fit to the synthetics. This could be attributed to several reasons one of which might be the regional attenuation differences between the dataset that is used to derive the AC10 model and Erzincan region. In summary, we observe that attenuation of the simulated ground motions follow empirical models closely.

parameter and its value affects the overall spectral amplitudes significantly. When detailed studies for these parameters do not exist, empirical relationships are frequently used to relate stress drop to fault dimensions. Here, to study the sensitivity of ground motion simulations to variations in the stress drop, its value is varied alone by fixing the values of other input parameters to those given in Table 6. Fig. 8 displays the FAS, PGA and PGV sensitivity indices at all stations corresponding to different stress drop values. As observed from Fig. 8, FAS is noticeably sensitive to stress drop. Although the source effects are known to influence the acceleration spectrum at low to intermediate frequencies, it is noted that stress drop affects the simulated amplitudes over a wide frequency range. The variation of SIf corresponding to decreasing stress drop values is greater than that of increasing values of stress drop. This is essentially expected because the seismic moment is a nonlinear function of the stress drop. When

4. A local sensitivity analysis around selected input parameters In order to see the effects of small perturbations in the input parameters on simulation results, a local sensitivity study is performed around a selected group of input parameters. From each group of source, path and site models we pick only one essential parameter (stress drop, quality factor and the kappa factor, respectively) and study its effect on the simulations. For each sensitivity analysis, rest of the parameters remains as they are presented in Table 6. Here, these three parameters are varied with increments of 10% in both positive and negative directions and the sensitivity of simulations in terms of FAS, PGA and PGV is investigated. Further definitions of error, determining the fit in other spectral values such as spectral displacement, velocity or acceleration are also possible but not performed here. The sensitivity index (SI) is defined as the difference of a simulation with a perturbed input parameter with respect to the simulation with the optimum value of the corresponding input parameter as given in Table 6. SI definitions in the frequency and time domain are as follows:  !  Ai ðf Þperturbed  1  SIf ¼ ð9Þ ∑ log  nf req: 0:5 r f r 20 Hz Ai ðf Þoptimum  SIPGA ¼

PGAperturbed  PGAoptimum PGAoptimum

ð10Þ

SIPGV ¼

PGVperturbed PGVoptimum PGVoptimum

ð11Þ

where SIf is the sensitivity index in the frequency domain and SIPGA and SIPGV are the sensitivity indices of PGA and PGV, respectively. nfreq. is the number of discrete frequencies used in the simulation and Ai(f)optimum is the synthetic acceleration spectra of the ith station with the values of the parameters as given in Table 6 whereas Ai ðf Þperturbed is that with the perturbed value of the same parameter. We perform the sensitivity analyses on the three strong ground motion stations studied previously. As the stations have different source-to-site distances and soil conditions, we display the sensitivities at each station separately. 4.1. Sensitivity of simulations with respect to the stress drop The parameters defining the source mechanism in stochastic ground motion simulations are moment magnitude, fault dip and strike, fault length and width, depth of the top of the rupture plane, stress drop, rupture velocity and slip distribution. Among these, stress drop is generally the most ambiguous source

Fig. 8. Sensitivity indices with respect to 10% incremental variations in stress drop values.

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we compare the sensitivities at all stations, peak ground motion intensity parameters are also found to be sensitive to stress drop. From the sensitivity plots of PGA and PGV values with respect to different stress drop values, it is observed that increasing stress drop yields higher peak ground motion intensity values as physically expected. Reducing the stress drop value by 20% causes 14% decrease in both PGA and PGV values; whereas increasing the stress drop values by 20% causes 12% increment in the PGA and PGV values. Given the sensitivities, it is important to estimate this mostly-ambiguous parameter accurately for reliable simulations to be used in engineering applications.

4.2. Sensitivity of simulations with respect to the quality factor The sensitivity of ground motion simulations to path effects is tested through the anelastic attenuation parameter which is defined in terms of the quality factor. As well-known, quality factor is frequency-dependent and has a functional form as n Q ¼ Q 0 f . The sensitivity of synhtetic ground motions to different Q0 and n values is shown in Fig. 9 which suggests that the effect of Q value is significant in intermediate-to-far distances. Station ERC is located at an epicentral distance of 12 km whereas stations REF and TER have epicentral distances of approximately 76 and 65 km, respectively. It is observed from Fig. 9 that as the distance of the station from the fault plane increases, the effect of both Q0 and n values in FAS, PGA and PGV values increase. Since Q effects are found to be less significant in near-field distances due to the governing source effects, the following discussions are based on stations REF and TER. Fig. 9 suggests that decreasing the Q0 values changes the frequency domain sensitivities exponentially whereas increasing it causes a more gradual change. This observation holds true for n values as well, but with less significant effects. By increasing Q0 value, one obtains lower attenuation and thus higher amplitudes. Thus, the increasing trend in SIPGA and SIPGV values is expected. A Q0 value only 10% smaller than the optimum value produces 8%

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lower PGA whereas a 10% larger Q0 yields 6% higher PGA. The decay is smoother for PGV values. A Q0 value 10% smaller than the initial value produces 5% lower PGV whereas 10% larger Q0 leads to 4% higher PGV in the simulations. By varying n value, one generates a frequency-dependent sensitivity of FAS. For frequencies higher than 1 Hz, an increment in n value has the effect of decreasing the level of attenuation and thus increasing the amplitudes. However, for frequencies lower than 1 Hz, the opposite holds true. The dependence on the frequency range leads to variable behaviors of PGA and PGV sensitivities. Since PGV is mostly affected by low-to-intermediate frequencies, in this frequency range, an increment in n value causes amplitudes to decrease. On the other hand, increasing n values causes an increase in the amplitudes of higher frequencies that affect PGA values. This explains the increase of PGA and the decrease of PGV with increasing n. We note that 10% increment in n value causes 5% increase in PGA and 1% decrease in PGV.

4.3. Sensitivity of simulations with respect to the Kappa factor The parameters defining the site model in stochastic ground motion simulations are frequency-dependent site amplification factors and diminution factor. In this study kappa operator is used as the diminution factor and a regional model for distancedependency of kappa is derived. It is meaningful here to study the sensitivity of simulations to kappa factor which is one of the most ambiguous simulation parameter and is not investigated for Turkey in detail so far other than a few studies [10,15]. The sensitivity analyses for the kappa operator are shown in Fig. 10. It is clear that changing the kappa value increases the FAS sensitivities linearly. Since the kappa values acts as diminution filters, increasing kappa decreases the amplitudes. The variation in PGA and PGV is exponential with a slowing rate since the spectrum is dependent on kappa values by e  πκf . Considering the average sensitivities at the three stations, changing kappa by 20% yields a 15% difference in PGA values and a 7% difference in

Fig. 9. Sensitivity indices with respect to 10% incremental variations in Q0 (top panel) and n (bottom panel) values.

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parameters can produce significant changes in the simulations. Thus, it is very important to utilize a well-constrained stress drop value, a crustal quality factor that represents the regional anelastic losses in the study area as well as local models for site effects such as amplification and kappa factor. It is essential to clarify here that these findings are specific to the particular method used for simulations. Additional numerical experiments are required for other simulation methods and for further conclusions. Considering the overall sensitivities, we conclude that in regions without well-studied or established input parameters one needs to be careful while performing the simulations. When the sensitivity is high for a certain parameter, the most physical regional value has to be investigated or derived in some cases. This is because the interaction between the high sensitivity source, path and site parameters could lead to trade-offs which have to be avoided for reliable synthetic ground motions.

5. Conclusions

Fig. 10. Sensitivity indices with respect to 10% incremental variations in kappa factor.

PGV values. The sensitivity of PGA with respect to kappa is much higher since kappa filter affects mostly the higher frequencies. Thus, since they directly influence the frequency content as well as high-frequency amplitudes, kappa factors should be studied in detail and regional models such as the model derived in this study should be used in ground motion simulations. 4.4. Discussion on the sensitivity of simulations In the preceding subsections, we presented the sensitivity of the ground motion simulations with respect to small changes in the stress drop, anelastic attenuation (quality factor) and kappa factor. These fundamental parameters are selected among many source, path and site parameters and investigated here as they often can be ambiguously employed in the simulations. From the numerical experiments, stochastic simulations are found to be most sensitive to crustal quality factor. Stress drop and kappa values are confirmed to be other critical parameters in ground motion simulations. Since majority of the input parameters are frequency-dependent, the trade-off between the path and site

Stochastic simulations have recently become quite popular for estimating synthetic ground motion time histories. It has become clear once again after the recent 23 October 2011 Van (eastern Turkey) earthquake (Mw¼7.1), that it is essential to use practical simulation techniques in sparsely-monitored regions for estimating the ground motion levels in the vicinity of the fault as well as for studying the earthquake mechanism itself. This by default brings the need for validation and sensitivity studies concerning ground motion simulations. With this objectives, in this study we initially employed the stochastic finite-fault method with a dynamic corner frequency approach for simulating the strong ground motions of the 13 March 1992 Erzincan, eastern Turkey earthquake (Mw¼ 6.6) with the few available ground motion records of the event. The source and path parameters of Erzincan region are determined from well-constrained previous studies. The site parameters such as the amplification factors and kappa operators are derived herein to account for the local site effects. We note that the site models presented in this study could be potentially used and verified in future similar studies related to the Erzincan region. In the second part of the study, a parametric sensitivity analysis is performed around the optimum input parameters. Among the parameters tested which includes stress drop, quality factor and kappa operator, and the crustal shear-wave quality factor is determined as the most sensitive parameter. Stress drop and kappa values are confirmed to be other critical parameters in ground motion simulations. Numerical experiments demonstrated that for regions without well-studied or established input parameters one needs to be careful while performing the simulations to avoid any trade-off between the high sensitivity source, path and site parameters. We note that the effects of other source parameters (such as variable rupture velocity and slip distribution) that are not studied in this paper could be quite significant in the resulting ground motions as discussed by other authors (e.g., [46,47]). However, a more physical and complex source model is required for such source-related parametric studies. Finally, it is crucial to use regional parameters with high accuracy in the simulations. In cases where regional parameters are not studied or verified in advance, simulation results are only reliable when validated against observed ground motions.

Acknowledgments This study is partially funded by Turkish National Geodesy and Geophysics Union through the project with grant number: TUJJB-

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