ORI GIN AL PA PER

Applicability of different ground-motion predictionmodels for northern Iran

H. Zafarani M. Mousavi

Received: 17 June 2013 / Accepted: 16 February 2014 Springer Science+Business Media Dordrecht 2014

Abstract A total of 163 free-field acceleration time histories recorded at epicentraldistances of up to 200 km from 32 earthquakes with moment magnitudes ranging from Mw4.9 to 7.4 have been used to investigate the predictive capabilities of the local, regional,

and next generation attenuation (NGA) ground-motion prediction equations and determine

their applicability for northern Iran. Two different statistical approaches, namely the

likelihood method (LH) of Scherbaum et al. (Bull Seismol Soc Am 94:341348, 2004) and

the average log-likelihood method (LLH) of Scherbaum et al. (Bull Seismol Soc Am

99:32343247, 2009), have been applied for evaluation of these models. The best-fitting

models (considering both the LH and LLH results) over the entire frequency range of

interest are those of Ghasemi et al. (Seismol 13:499515, 2009a) and Soghrat et al.

(Geophys J Int 188:645679, 2012) among the local models, Abrahamson and Silva

(Earthq Spectra 24:6797, 2008) and Chiou and Youngs (Earthq Spectra 24:173215,

2008) among the NGA models, and finally Akkar and Bommer (Seism Res Lett

81:195206, 2010) among the regional models.

Keywords Ground-motion prediction equations Evaluation of fitness Ranking PSHA Northern Iran

1 Introduction

The treatment of uncertainty is the greatest challenge in the current probabilistic seismic

hazard analysis (PSHA) and is an active area of research. It is well known that uncertainty

H. Zafarani (&)International Institute of Earthquake Engineering and Seismology (IIEES), No. 26, Arghavan St.,North Dibajee, Farmanieh, P.O. Box 19395/3913, Tehran, Irane-mail: hamzafarani@yahoo.com; h.zafarani@iiees.ac.ir

M. MousaviDepartment of Civil Engineering, Faculty of Engineering, Arak University, Arak, Iran

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Nat HazardsDOI 10.1007/s11069-014-1151-2

can be divided into two main categories: epistemic (uncertainty in scientific knowledge)

and aleatory (Toro et al. 1997; Budnitz et al. 1997). Currently, in the classical PSHA

approach (McGuire 1978), the aleatory uncertainty is dealt with using the basic assumption

of normal distribution of errors around the mean value of GMPEs and the use of multiple

relations through a logic tree framework (Budnitz et al. 1997) allows for the assessment of

epistemic uncertainty. Therefore, the selection of GMPEs and determination of their

weights in a logic tree analysis is a major part of any seismic hazard analysis (see e.g.,

Bommer and Scherbaum 2008) and is a matter of debate.

The branch weights in a logic tree framework correspond to the degree of belief of

experts in different prediction models. However, due to the lack of domestic experienced

experts in many regions such as Iran, reliability of expert opinion approach is ques-

tionable. Because of this concern, in a recent study (Mousavi et al. 2012) by using a set of

recorded ground-motion data, comparisons are made between a set of candidate ground-

motion models in the Zagros region of Iran. The candidate models were chosen from three

categories: local models that were developed based on the local data, regional models

corresponding to Europe and Middle East datasets, and finally the next generation atten-

uation (NGA) models (Power et al. 2008). The computed residuals with respect to different

ground-motion models were analyzed by using the LH and LLH methods of Scherbaum

et al. (2004, 2009) to rank the different models. One of the most significant results of their

study was that the regional and local ground-motion models show more consistency with

the observed data than do the NGA models.

From the seismotectonic point of view, Iran has been divided into several units (e.g.,

Takin 1972; Nowroozi 1976; Berberian 1976 and Mirzaei et al. 1998). Different seismo-

tectonic and geological characteristics between Zagros and northern Iran [mainly consists

of the Alborz mountain ranges (see Fig. 1)] are the common feature within all these

studies. Thus, the source spectra, path attenuation and site effects attributed to seismo-

tectonic styles, may vary between the mentioned regions. On the other hand, some earlier

studies have claimed that in a broad framework, all parts of Iran can be treated as one unit

(Chandra et al. 1979) and some authors (e.g., Zafarani et al. 2008; Ghasemi et al. 2009a)

derived attenuation relations for the Iranian plateau as a whole. However, more recently,

detailed strong motion studies of Zafarani et al. (2012), Zafarani and Hassani (2013) have

shown different stress drops for the Zagros and northern Iran regions. The estimated values

of stress drops for the northern Iranian earthquakes have a higher mean value of 135 bars

(Zafarani et al. 2012) in comparison with a low value of 66 bars for the Zagros region

(Zafarani and Hassani 2013). This fact was expected since the majority of the northern

Iranian database consists of midplate earthquakes that occur more than 500 km from plate

margins. In contrast, the Zagros region is near the boundary of the Arabian and Eurasian

plates, and the earthquakes in this region should behave more like interplate events (see

Zafarani and Soghrat 2012 for more details).

Cotton et al. (2006) describe how source characteristics, path effects related to geo-

metric spreading and anelastic attenuation and site effects can vary from region to region.

Those underlying physics ideally should be manifest in how a GMPE represents the scaling

of a particular ground-motion intensity measure with respect to magnitude, distance, and

site condition. Taking into account the above discussion, here we try to perform statistical

LH and LLH test on a set of GMPEs to assess their suitability and performance for the

northern Iran region. Following Soghrat et al. (2012), in this study, the whole region of

northern Iran (including Azerbaijan-Alborz and Kopeh Dagh) is taken into account as one

single region (see Fig. 1). This assumption increases the total number of records in the

database, which in return provides more robust results.

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2 Ranking criterion for GMPEs

2.1 Regional dependency of GMPEs

The regional variability of ground motions is currently a matter of debate, mainly due to

the lack of sufficient data. The issue eventually can be solved as newer local models

become available in all tectonic regions (Stafford et al. 2008; Beauval et al. 2012). Some

authors assume that ground motions are not regionally dependent, at least for moderate-to-

large magnitudes (e.g., Stafford et al. 2008). Contrary, other authors have emphasized

significant regional dependency (e.g., Atkinson and Morrison 2009).

Currently, there are a large number of published ground-motion models in the literature

(Douglas 2011). However, the selection and ranking of appropriate models for a particular

target area usually raises serious practical concerns. The main question is that given a set of

data recorded in a specified region, how can one quantitatively judge different candidate

ground-motion models? The approach termed, analysis of variance, was applied by

Douglas (2004a) to compare ground motions for five local regions within Europe; Douglas

(2004b) also compared ground motions from Europe, New Zealand, and California. The

procedure involved calculating and comparing the mean and variance of the log of data

inside particular magnitude and distance bins for two different regions (e.g., Europe and

California) and combined data for those regions. Using this approach, Douglas (2004b)

found more rapid distance attenuation in Europe than California. The visual inspection of

different GMPEs to see whether there is a significant difference between medians is

another simple approach that has been used in order to compare the GMPEs in different

Fig. 1 Major seismotectonic regions of Iran. The northern Iranian earthquakes used in the current study arealso shown (circles)

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regions (see e.g., Stafford et al. 2008; Scasserra et al. 2009). Stafford et al. (2008) based

upon an application of the likelihood approach of Scherbaum et al. (2004) declared that the

NGA models may confidently be applied for most engineering applications within Europe.

They also point out to the potential benefits of merging the NGA and European datasets.

Similar approaches have been used for relatively small numbers of records from parts of

Europe by Hintersberger et al. (2007) and Drouet et al. (2007); the latter study confirmed

the application of global GMPEs to regions outside their zone of origin (i.e., host region),

while the former drew opposite conclusion.

2.2 The LH and LLH methods for goodness-of-fit analysis

A practical technique to distinguish between different models and judge their validity is the

simple statistical analysis of residuals. GMPEs are commonly expressed in terms of log-

arithmic quantities; hence, the normalized residual is defined as the difference between the

logarithm of the observations and the logarithm of the model predictions, divided by the

corresponding standard deviations of the logarithmic model.

r logSAobs logSAprerSA

1

where SAobs, SApre, and rSA represent the observed acceleration response spectra in aspecified period, the median model prediction of the response spectra, and the total stan-

dard deviation (i.e., combination of inter- and intraevent standard deviations) of the model,

respectively. Ideally, the so defined residual has a standard normal distribution with zero

mean and unit variance. The compatibility of the applied ground-motion model with the

recorded data is defined as the fitness degree of the residuals to this distribution. Statistical

tests can be utilized to examine the hypothesis that the mean of the residuals is zero and/or

to test the residuals for unit variance (Montgomery and Runger 2003).

The likelihood-based measure (LH) has been recently emerged as another comple-

mentary goodness test which is not only suitable for measuring the model fit, but also for

testing the underlying statistical assumptions (Scherbaum et al. 2004). For instance, if the

original distribution follows a perfect standard normal distribution with the zero mean and

the unit variance, then the corresponding LH transform has a perfectly uniform distribution

with median value equal to 0.5. Any deviation in the mean, the standard deviation, and the

shape of the residual distribution corresponds to a specified distribution, the median, and

the standard deviation of LH values. By using the LH distribution in combination with a

few simple measures, Scherbaum et al. (2004) have proposed a scheme to assess the

performance of different ground-motion models. According to this scheme, the ground-

motion models are categorized into four classes:

In order to rank a ground-motion model in the lowest accepted capability class (C), themodel has to possess a minimum median LH value of 0.2, and an absolute value for the

mean and the median of the normalized residuals, and their standard deviations of less

than 0.75. In addition, the normalized sample standard deviation is required to be less

than 1.5.

The model with rank of intermediate capability class (B) is required to possess amedian LH value of at least 0.3, an absolute value of mean and median of the

normalized residuals and their standard deviations, less than 0.5, and their normalized

sample standard deviation less than 1.25.

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For a model to be ranked in the highest capability class (A), the median LH value mustbe at least 0.4, the absolute value of both measures of the central tendency of the

normalized residual distribution and their standard deviations must not deviate by more

than 0.25 from zero. Besides, the normalized sample standard deviation must be less

than 1.125.

A model that does not meet the criteria for any of these categories is rankedunacceptable or class D.

One of the deficiencies of the above-mentioned LH method is that it still requires a few

subjective decisions, e.g., thresholds for acceptability. The dependency of the results on the

sample size is another drawback of this method. To avoid these shortcomings, Scherbaum

et al. (2009) employed a modern information-theoretic approach that is more general than

the LH method and at least in theory does not depend on ad hoc assumptions such as size of

samples and significant thresholds. Information theory represents an approximate data-

driven approach for model selection and ranking in which model performance can be

expressed by the relative likelihood of a model with respect to the complete candidate set.

The quantitative decision, favoring different candidate models, requires a meaningful

measure to distinguish candidate probabilistic models. Within an information theory

framework, this measure is given by the KullbackLeibler distance (Delavaud et al. 2009).

The distance quantitatively represents the amount of information loss if the first model

(i.e., true model) is substituted by the second model (i.e., approximate model). The key

ingredient, the KullbackLeibler distance, can be estimated from the statistical expectation

of log-likelihoods of observations for the models under consideration. This latter estimator,

LLH, is used here as ranking criterion in an information theory framework. In this study,

the information-theoretic approach in combination with the LH method is used to evaluate

the compatibility of the candidate ground-motion models with the ground-motion data

recorded in the northern Iran region. Finally, it should be noted that other statistical tests

have been proposed/used for selecting and ranking of ground-motion prediction equations.

For example, the NashSutcliffe model efficiency coefficient (E), a commonly used sta-

tistic in hydrology (Nash and Sutcliffe 1970), has been used recently by Kaklamanos and

Baise (2011) to quantitatively compare the predictive capabilities of the NGA models and

their predecessors. According to Kaklamanos and Baise (2011), the value of E may vary

between -? and 100 %; when E is less than zero, the arithmetic mean of the observedvalues has greater prediction accuracy than the model itself. The numerical values of E

may be used to compare alternative models, with higher values indicating better agreement

between observations and predictions. However, though E adequately quantifies the

accuracy of the median predicted values, it does not address the standard deviation rela-

tionships. Also, Kale and Akkar (2013) have introduced an Euclidean distance-based

ranking procedure based on the concept of the Euclidean distance for ranking of GMPEs

under a given set of observed data.

3 The testing dataset and candidate GMPEs

To test the applicability of candidate ground-motion models, we used horizontal compo-

nents of 163 three-component records of 32 earthquakes with magnitude ranging from Mw4.9 to 7.4 in northern Iran. In the database, records with hypocentral distances less than 200

km are chosen and only earthquakes whose moment magnitude estimates are available

have been used.

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In the absence of shear-wave (S-wave) velocities, empirical methods may be employed

to estimate site classifications (see e.g., Zare et al. 1999; Ghasemi et al. 2009b). However,

following Soghrat et al. (2012) for reducing uncertainties in this research, only those

records are considered that their average S-wave velocity to a depth of 30 m (VS30) is

specifically determined in their stations. However, it should be kept in mind that even with

an available measure of VS30, there are still remaining uncertainties, e.g., method used for

estimating VS30, uncertainty on the VS30 estimates and using VS30 that is only a proxy for

site effects (see e.g., Lee and Trifunac 2010).

The dataset has been recorded on the Iranian Strong Motion Network of the Building

and Housing Research Center (http://www.bhrc.ac.ir/ISMN/Index.htm). Table 1 shows the

information about each of the events with the corresponding reference. The name, code

number, epicentral distance, and VS30 of these stations are listed in the Appendix Table 7.

The uncorrected acceleration time series recorded by a given station were corrected for the

instrument response and baseline, following a standard algorithm (Trifunac and Lee 1973).

Multi-resolution wavelet analysis (Ansari et al. 2010) was performed to remove undesir-

able noise from the recorded signals. The characteristics and capabilities of the modified

nonlinear adaptive wavelet de-noising method for correction of highly noisy strong motion

records are described in detail by Ansari et al. (2010). According to Ansari et al. (2010),

displacement response spectra of wavelet de-noised records are more stable than con-

ventional filtered records with respect to different correction functions and a large number

of noisy acceleration records that are usually discarded from sets of records used for

estimating the ground motions can be corrected using this new method.

Figure 2 shows the magnitude-distance distribution of the employed ground-motion

records. The different stations are categorized into two different soil classes (Zare et al.

1999): Rock for VS30 [ 500 m/s and soil for VS30 \ 500 m/s as shown in Fig. 2. The siteclassifications used in the models considered are not identical; nevertheless, the compar-

isons are made for comparable site classes. For example, Soghrat et al. (2012) and Ghasemi

et al. (2009a) use a binary site classification, and therefore, we have grouped the sites into

two classes, i.e., VS30 [ 500 m/s and soil for VS30 \ 500 m/s; while the selected NGAmodels and Kalkan and Gulkan (2004) use site terms that are continues functions of VS30and thus for each station, the corresponding value of V S30 has been used to derive the

related site response term.

As it is clear from Fig. 2, the dataset does not include records with Mw [ 6.5 andR \ 90 km, except the one that recorded in the Ab-bar station during the Rudbar M7.4earthquake of June 20,1990 (see Appendix Table 7).

The candidate ground-motion models are firstly introduced in the following section.

Then their fitness to the current dataset is analyzed. Cotton et al. (2006) described in detail

the criteria that should be used primarily as a way of avoiding unintended subjectivity in

the process of selecting the GMPE models before the data testing. Also, we have taken into

account some of the updates of these rejection criteria proposed by Bommer et al. (2010).

We have selected 9 GMPEs derived for different shallow active crustal regions

worldwide, based on the criteria defined by Cotton et al. (2006) that reject candidate

models if: (1) the model is derived for an irrelevant tectonic environment, (2) the model is

not published in a peer-reviewed journal, (3) the dataset used to derive the model is not

clearly presented, (4) the model has been superseded by a more recent publication, (5) the

model does not provide predictions over the entire frequency range of interest to engineers,

(6) the functional form of the model is not appropriate, and (7) the coefficient of the model

was not determined with a suitable regression method.

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http://www.bhrc.ac.ir/ISMN/Index.htm

Taking into account the update of these rejection criteria by Bommer et al. (2010) and to

avoid any inconsistencies caused by magnitude conversion formulas (as different GMPEs

use different magnitude scales), the dataset was restricted only to the events with available

moment magnitude and the GMPEs which are based on the moment magnitude scale were

only selected. Also, the models with limited range of applicability (too small to be useful

for PSHA analysis) have been excluded. We have also taken into account some of the

Table 1 List of earthquakes used in this study

Event no. mm/dd/yyyy hh:mm:ss Latitude () Longitude () M w Focal depth Reference

1 07/22/1980 05:17:06 37.322 50.262 5.6 25 E06

2 10/29/1985 13:13:40 36.68 54.772 6.1 13 P94

3 06/20/1990 21:00:11 36.997 49.222 7.4 12 C94

4 06/24/1990 09:46:01 36.839 49.408 5.3 15 E06

5 07/06/1990 19:34:54 36.864 49.298 5.3 20 E06

6 11/28/1991 17:19:53 36.827 49.589 5.6 8 J02

7 10/15/1995 06:56:34 37.03 49.473 5.2 25 E06

8 02/04/1997 09:53:53 37.681 57.275 5.5 13 J02

9 02/04/1997 10:37:47 37.729 57.312 6.5 6 J02

10 02/05/1997 07:53:45 37.589 57.481 5.2 16 E06

11 02/28/1997 12:57:45 38.109 48.07 6.1 9 J02

12 03/02/1997 18:29:42 37.995 47.892 5.3 10 E06

13 07/09/1998 14:19:18 38.728 48.528 6 ?? J02

14 08/04/1998 11:41:59 37.223 57.338 5.3 19 E06

15 11/08/1999 21:37:23 35.699 61.224 5.5 9 E06

16 11/19/1999 04:40:24 37.321 54.405 5.4 26 E06

17 11/26/1999 04:27:24 36.953 54.896 5.3 10 E06

18 08/16/2000 12:53:02 36.706 54.366 4.9 16 E06

19 06/22/2002 02:58:20 35.597 49.02 6.5 10 W05

20 05/28/2004 12:38:46 36.258 51.566 6.3 22 T07

21 03/27/2004 01:31:22 36.74 54.89 5 14 BHRC

22 05/29/2004 09:23:48 36.489 51.395 5.2 14 E06

23 05/30/2004 01:42:43 36.27 51.48 4.9 10 BHRC

24 05/30/2004 19:27:01 36.518 51.595 4.9 7 E06

25 08/21/2004 03:32:44 37.827 57.647 5.1 15 E06

26 10/07/2004 21:46:18 37.141 54.466 5.6 28 E06

27 10/08/2004 13:45:55 37.214 54.499 4.9 32 E06

28 01/10/2005 18:47:30 37.46 54.53 5.3 29 E06

29 07/11/2007 06:51:12 38.79 48.60 5.3 25 HRVD

30 05/27/2008 06:18:08 36.58 48.75 5 14# BHRC

31 07/03/2008 23:10:06 35.5 58.6 5.1 12 HRVD

32 09/02/2008 20:00:56 38.68 45.82 5 15 HRVD

P94 Priestley et al. (1994), C94 Campos et al. (1994), J02 Jackson et al. (2002), W05 Walker et al. (2005),T07 Tatar et al. (2007), E06 Engdahl et al. (2006), HRVD Harvard Seismology (2011), BHRC Building andHousing Research Centre# This value is based on the IIEES report

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updates of these rejection criteria by Bommer et al. (2010), aiming to identify robust and

well-constrained models based on new quality standards in the formulation and derivation

of models as well as in their applicability range in terms of frequency, magnitude, and

distance. Cotton et al. (2006) and Bommer et al. (2010) also recommend excluding models

which lack either nonlinear magnitude dependence or magnitude-dependent decay with

distance (non-physical models). This issue should be considered just by empirically

developed models, not by finite source stochastic models (e.g., Soghrat et al. 2012). Their

results show that the simple models with a constant magnitude scaling cannot be extrap-

olated to magnitude and distances that are not well represented in the dataset used to derive

them. According to Cotton et al. (2006), empirical ground-motion models with constant

magnitude scaling that are calibrated on a large-magnitude dataset will overestimate the

ground motion from small earthquakes, if extrapolated outside the magnitude range sup-

ported by the model-generating dataset.

The abbreviations of the models are given in the second column of Table 2. From the 9

GMPEs that we have used here, SKZ12, Getal09, and KG04 do not use style-of-faulting as

a predictor variable and have a binary soil/rock classification; therefore, do not satisfy the

criteria number 8 of Bommer et al. (2010). The SKZ12 also uses epicentral distance which

rejects the criteria number 8 of Bommer et al. (2010). The three GMPEs were, however,

retained because a recent study has shown the good performance of local GMPEs in the

Zagros region of Iran (Mousavi et al. 2012). Also, according to Bommer et al. (2010), if the

hazard analysis is to be performed with software that models earthquake occurrences

within area sources as points without simulated fault ruptures for larger earthquakes (as is

the common practice in Iran), then in a sense it would be more appropriate to adopt

GMPEs based on epicentral or hypocentral distance. However, it should be noted that the

hazard analysts in Iran will certainly soon move to other codes able to take into account the

extension of faults (e.g., OpenQuake developed within the Global Earthquake Model

project; http://www.globalquakemodel.org/get-involved/news/openquake/). The Getal09 is

not including response spectra for T = 0.0 (PGA) and therefore does not provide spectral

predictions for an adequate range of response periods, chosen here to be from 0.0 to 2.0 s.

Fig. 2 The magnitudedistance distribution of the employed records used in this study

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http://www.globalquakemodel.org/get-involved/news/openquake/

Therefore, Getal09 satisfy the above stated rejection criteria number 5 of Cotton et al.

(2006). However, we decide to keep it in the candidate GMPEs, considering its good

performance in the Zagros region of Iran (Mousavi et al. 2012).

Candidate ground-motion models were selected from three categories: (1) Ground-

motion models developed specially for the region of Iran, (2) ground-motion models

developed for the Middle East-Europe region, and (3) global ground-motion models

developed by the Next Generation of Ground-Motion Attenuation Models (NGA)

project (Power et al. 2008). The valid range of frequency, magnitude, and distance for

these models, accompanying with the distance type, horizontal component definition, and

host region is indicated in Table 2. All the GMPEs tested using entire database without

considering their distance limitations. However, this is not a crucial issue, because only

two GMPEs (i.e., Getal09 and AB10) have a distance validity range of less than 200 km.

Different horizontal component definitions have been used in the selected GMPEs; most of

which are simple geometric mean and rotation-independent average horizontal component

(GMRotI50) defined by Boore et al. (2006) (see Table 2). Here, we do not try to convert

estimations of different horizontal component definitions to simple geometric mean of

horizontal components. The geometric mean of horizontal components has been used for

all GMPEs, except one (i.e., KG04) taking into account that some studies have shown that

at all periods the ratio of this measure of horizontal components over the new geometric

mean (GMRotI50) used in the NGA and Ghasemi et al. (2009a) models is near unity (see

Beyer and Bommer 2006). However, since there is a considerable difference (*10 %)between geometric mean and larger horizontal component (Beyer and Bommer 2006),

when testing the KG04 predictive model, the larger spectral value of two horizontal

components is compared with the estimation of the KG04 model.

The NGA project has developed a series of ground-motion models intended for

application to geographically diverse regions; the only constraint is that the region be

tectonically active with earthquakes occurring in the shallow crust (Power et al. 2008).

Five sets of ground-motion models were developed by teams working independently but

interacting with one another throughout the development process. Here, the NGA models

of Boore and Atkinson (2008), Campbell and Bozorgnia (2008), Chiou and Youngs (2008),

and Abrahamson and Silva (2008) are compared with the Iranian strong motion database.

We excluded Idriss (2008) due to its lack of a site term. A significant fraction of the

northern Iranian data has soil site conditions, and hence, the use of a site term is necessary.

According to Kaklamanos et al. (2011), when employing the NGA models, users routinely

face situations in which some of the required input parameters are unknown. They have

presented a framework for estimating the unknown source, path, and site parameters when

implementing the NGA models in engineering practice. Also, they have derived geomet-

rically based equations relating the three distance measures found in the NGA models.

Here, the general strategy was to constrain the input parameters by making the best use

of available local information where this is available and, if not, using reasonable argu-

ments and previous experiences elsewhere to adopt the best plausible set of input

parameters following Kaklamanos et al. (2011). Four different distance measures are used

in the examined ground-motion relations: Rrup, the shortest distance between the station

and the rupture surface (AS08, CB08 and CY08), Rjb, the JoynerBoore distance that is the

closest horizontal distance to the surface projection of the causative fault (AC10, AB10,

KG04 and BA08), Repi, epicentral distance (SKZ12) and Rhypo, hypocentral distance

(Getal09). Horizontal distance from the station to the top edge of the rupture measured

perpendicular to the strike of the fault (Rx) has been also used in the AS08 and CY08

relations as a supplementary distance measure, as part of the hanging-wall scaling.

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For moderate events (i.e., Mw \ 6.0), the epicentral, Repi, and hypocentral distances,Rhypo, are used instead of Rjb and Rrup, respectively, since the causative faults cannot be

well constrained. For the 2004 Baladeh earthquake (Mw 6.2), high-quality, locally recorded

aftershock data (Tatar et al. 2007) have been used to constrain the fault plane geometry.

This was also the case for the 2002 Avaj earthquake (Mw 6.3) which well-recorded af-

tershocks (Tatar et al. 2004) have been used to determine the spatial extent of the fault

plane. For the Rudbar Mw7.4 earthquake of June 20, 1990, which is the largest event in the

database, Berberian et al. (1992) have mapped a pattern of discontinuous surface ruptures

over a length of *85 km. However, the aftershocks distribution does not help in identi-fying the earthquake fault because they were spread over a large area that extends well to

the north of the fault traces identified by Berberian et al. (1992). As reported by Berberian

et al. (1992), the spatial correlation between these aftershock locations and the mainshock

isoseismals was also very poor. Therefore, our fault distances were calculated from the

Berberian et al. (1992) model with an approximate dip angle of *80 (Campos et al. 1994)along the whole length of the fault. For remaining four earthquakes with Mw C 6.0 (i.e.,

Table 2 Candidate ground-motion prediction equations

Model Reference Abbreviations* Main region Component# Frequencyrange (Hz)

Mw:minmax

Distance(km)

Soghrat et al.(2012)

SKZ12 North of Iran PGAGM,PSAGM

0.5020.0 4.67.4 REPI3200

Ghasemi et al.(2009a, b)

Getal09 Iran PSA inGMRotI50

0.3320.0 5.07.4 RHYP0100

Akkar andCagnan (2010)

AC10 Turkey PGAGM,PGVGM,PSAGM

0.5033.3 5.07.6 RJB0200

Akkar andBommer(2010)

AB10 Europe,Middle East

PGAGM,PGVGM,PSAGM

0.3320.0 5.07.6 RJB0100

Kalkan andGulkan (2004)

KG04 Turkey PGAMax,PSAMax

0.5010.0 4.07.4 RJB1.2250

Abrahamson andSilva (2008)

AS08 Western USAandCalifornia

PGA, PGV,PSA inGMRotI50

0.1100.0 5.08.5 RRUP0200

Boore andAtkinson(2008)

BA08 Western USAandCalifornia

PGA, PGV,PSA inGMRotI50

0.1100.0 5.08.0 RJB0200

Campbell andBozorgnia(2008)

CB08 Western USAandCalifornia

PGA, PGV,PSA inGMRotI50

0.1100.0 4.08.5 RRUP0200

Chiou andYoungs (2008)

CY08 Western USAandCalifornia

PGA, PGV,PSA inGMRotI50

0.1100.0 4.08.5 RRUP0200

* Abbreviations of GMPEs used in the current study# GMRotI50, rotation-independent average horizontal component (Boore et al. 2006); subscripts Max andGM, maximum and geometric mean of horizontal components, respectively REPI Epicentral distance, RRUP Rupture distance, RJB JoynerBoore distance, RHYP Hypocentral distance

Nat Hazards

123

event numbers 2, 9, 11, and 13 in Table 1), there was no information on the spatial extent

of the rupture,; therefore, the empirical relations of Wells and Coppersmith (1994) for all

fault types have been used to define the rupture planes assuming that the hypocenters are

located at the middle.

Regarding Rx, which is used in the AS08 and CY08 models for quantifying the

hanging-wall, we also follow the Kaklamanos et al. (2011) formulation that is based on an

important location measure, the source-to-site azimuth, and Rjb (see Fig. 2 in Kaklamanos

et al. 2011). It is worth to say that the hanging-wall effects and details of fault rupture plane

is not crucial in the current study, taking into account the magnitude-distance distribution

of database that is dominated by far-field records from moderate events (see Fig. 2).

Also, the regional values of depth to Vs = 1.0 km/s (Z1.0 for AS08 and CY08) and

depth to Vs = 2.5 km/s (Z2.5 for CB08) have been adopted from crustal velocity studies

in the region (Ashtari et al. 2005; Abbassi et al. 2010; Radjaee et al. 2010; Moradi et al.

2011) in combination with the Chandler et al. (2005) method. Based on a large amount

of velocity data, along with thickness of sedimentary and crystalline layers within

bedrockcollected from all over the worldChandler et al. (2005) has proposed a

methodology, which can be used at the regional level to develop an averaged S-wave

velocity profile for a geological region. In this study, the above approach has been used

to estimate the velocity gradient in the crust (see Fakhimnia et al. 2013 for details).

Alternatively, one can use the empirical relations between Z1.0 and Z2.5 with VS30 that

has been proposed by Chiou and Youngs (2008) and Campbell and Bozorgnia (2008),

respectively. This approach has been adopted by Scasserra et al. (2009) during com-

parison of the NGA GMPEs to Italian database. However, using such empirical relations

developed based on the NGA database (mainly from California), implicitly assumes the

similar velocity gradient in rock for California and studied area sites, which may not be

correct.

The minimum depth of seismogenic rupture (ZTOR) is a controversial topic, and little

guidance exists in the literature on its estimation. The method suggested by Kaklamanos

et al. (2011) is used to estimate ZTOR from the hypocentral depth (ZHYP), down-dip rupture

width (W), and dip angle (d), assuming that the hypocenter is located 60 % down the fault

width:

ZTOR maxZHYP 0:6 W sin d; 0 2Also, a minimum depth of 1 km was imposed considering the lack of surface rupture for

the analyzed eventsRudbar earthquake is an exceptionand assuming that depths above

1 km did not radiate significant seismic radiation in the frequency range we are considering

here (see e.g., Campbell 1997).

The detailed comparisons made by Akkar and Cagnan (2010) between a combined

Italian and Turkish accelerometric dataset and different GMPEs have shown that depth can

be of importance for delineating the differences between local and global GMPEs.

Therefore, in the current study, the published focal depths determined by body-waveform

modeling as the most accurate ones have been used if they were available (see Table 1).

For 17 moderate events, the results of Engdahl et al. (2006) which is based on an advanced

technique for 1D earthquake relocation have been used. These depths are more precise than

those available in local and/or international agencies, but less accurate than the body-

waveform inversions. For remaining six moderate events, the depths reported by inter-

national or local agencies have been used.

Nat Hazards

123

4 Ranking results

As a preliminary step toward developing goodness-of-fit analysis, for each of the ground-

motion records described in the Appendix, Table 7 accompanying acceleration response

Fig. 3 Normalized residual histograms for Sa(T = 1.0 s) with respect to different ground-motion models.Solid line shows the expected distribution function for a standard normal distribution

Fig. 4 Distribution of LH values for Sa(T = 1.0 s) with respect to different ground-motion models

Nat Hazards

123

Ta

ble

3R

ank

ing

of

mod

els

bas

edo

nth

eL

Hm

eth

od

for

dif

fere

nt

per

iods

Model

nam

eR

ank

ME

DL

Hr

ME

DN

Rr

ME

AN

NR

rS

TD

NR

r

LH

ranki

ng,

PG

A

CY

08

A0.4

50.0

5-

0.0

60.1

5-

0.0

40.0

91.1

20.0

7

AS

08

B0.4

60.0

3-

0.4

90.1

1-

0.4

40.1

01.0

50.0

7

KG

04

B0.4

60.0

4-

0.0

90.1

20.0

40.1

01.1

30.0

7

AB

10

C0.3

20.0

50.7

40.1

60.7

50.1

01.1

10.0

7

BA

08

C0.4

30.0

60.1

20.1

20.1

80.1

11.2

60.0

8

SK

Z12

C0.4

80.0

50.5

10.0

90.5

80.0

90.9

50.0

6

AC

10

D0.2

20.0

31.2

30.1

11.2

50.0

80.8

90.0

5

CB

08

D0.2

70.0

4-

0.8

90.1

1-

0.7

70.1

11.3

20.0

9

LH

ranki

ng,

T=

0.1

s

AS

08

A0.4

50.0

6-

0.1

00.1

0-

0.0

90.0

91.0

70.0

7

CY

08

B0.4

20.0

50.3

20.0

80.2

60.1

01.1

50.0

7

Get

al09

B0.4

10.0

40.4

90.1

70.3

70.0

91.0

10.0

6

KG

04

B0.4

10.0

4-

0.0

80.1

7-

0.0

70.1

11.2

10.0

7

BA

08

C0.3

50.0

50.1

60.1

10.3

40.1

21.2

90.0

8

CB

08

C0.3

40.0

4-

0.3

50.1

7-

0.4

10.1

21.2

80.0

8

SK

Z12

C0.4

20.0

40.6

30.1

20.6

60.0

91.0

40.0

6

AB

10

D0.2

40.0

51.0

40.1

80.9

20.1

01.1

30.0

7

AC

10

D0.1

80.0

21.3

50.0

81.3

50.0

80.9

30.0

6

LH

ranki

ng,

T=

0.2

s

KG

04

A0.5

20.0

70.0

30.0

90.1

30.0

91.0

80.0

8

AS

08

B0.5

10.0

7-

0.2

80.0

9-

0.3

00.0

91.0

10.0

7

BA

08

B0.4

40.0

50.2

10.1

20.2

50.1

11.1

90.0

8

CY

08

B0.5

10.0

50.3

00.1

10.2

70.1

01.0

90.0

8

Get

al09

B0.5

20.0

60.4

80.0

90.4

90.0

90.9

80.0

7

AB

10

C0.4

30.0

60.6

10.1

00.6

50.1

01.0

70.0

7

CB

08

C0.3

30.0

6-

0.5

80.1

2-

0.5

40.1

11.2

50.0

9

SK

Z12

C0.4

30.0

60.5

00.1

50.5

10.1

01.0

80.0

7

Nat Hazards

123

Ta

ble

3co

nti

nued

Model

nam

eR

ank

ME

DL

Hr

ME

DN

Rr

ME

AN

NR

rS

TD

NR

r

AC

10

D0.2

30.0

41.1

50.1

01.1

30.0

80.8

50.0

6

LH

ranki

ng,

T=

0.5

s

CY

08

A0.4

90.0

30.0

10.1

3-

0.0

20.1

01.0

80.0

8

AB

10

B0.5

00.0

40.3

00.1

10.2

20.0

80.9

90.0

7

AS

08

B0.4

20.0

6-

0.2

20.1

4-

0.3

30.0

91.0

50.0

7

BA

08

B0.4

50.0

6-

0.1

50.1

5-

0.1

40.1

11.1

90.0

8

Get

al09

B0.5

20.0

40.3

80.1

10.3

90.0

80.9

40.0

7

SK

Z12

B0.5

30.0

40.2

90.0

90.2

10.0

80.8

70.0

6

KG

04

B0.5

30.0

5-

0.4

30.1

1-

0.2

80.0

80.9

40.0

7

AC

10

D0.3

90.0

60.8

10.1

40.8

00.0

80.8

70.0

6

CB

08

D0.2

30.0

4-

1.0

60.1

7-

1.0

30.1

11.2

20.1

0

LH

ranki

ng,

T=

0.7

5s

AB

10

A0.5

70.0

50.1

30.0

90.0

90.0

80.8

30.0

6

AS

08

A0.4

80.0

30.0

40.1

1-

0.0

10.0

91.0

00.0

7

BA

08

A0.4

40.0

6-

0.2

00.1

0-

0.2

10.1

01.0

90.0

7

CY

08

B0.5

30.0

4-

0.0

40.1

0-

0.1

20.0

91.0

10.0

8

Get

al09

B0.5

40.0

30.3

30.1

00.3

10.0

70.8

10.0

6

SK

Z12

B0.5

50.0

50.3

80.0

70.3

30.0

70.7

80.0

5

KG

04

B0.5

20.0

3-

0.6

40.0

8-

0.6

50.0

70.8

00.0

5

AC

10

C0.5

00.0

50.6

00.1

10.6

50.0

70.8

00.0

5

CB

08

D0.2

70.0

4-

1.1

00.1

1-

1.1

60.1

01.1

00.0

8

LH

ranki

ng,

T=

1.0

s

AB

10

A0.5

60.0

40.1

00.1

10.0

20.0

80.8

30.0

5

AS

08

A0.5

10.0

50.1

50.1

10.1

00.0

90.9

90.0

7

CY

08

A0.5

10.0

4-

0.1

90.1

1-

0.2

50.0

91.0

20.0

6

BA

08

B0.4

90.0

5-

0.2

90.1

2-

0.3

20.1

01.1

10.0

7

Get

al09

B0.5

80.0

40.2

20.1

10.2

60.0

70.8

10.0

5

SK

Z12

B0.5

40.0

50.3

30.1

00.3

20.0

70.7

90.0

5

Nat Hazards

123

Ta

ble

3co

nti

nued

Model

nam

eR

ank

ME

DL

Hr

ME

DN

Rr

ME

AN

NR

rS

TD

NR

r

KG

04

C0.5

40.0

3-

0.5

10.0

7-

0.5

70.0

70.7

70.0

5

AC

10

C0.5

30.0

50.5

10.0

80.5

10.0

70.8

10.0

5

CB

08

D0.2

40.0

4-

1.1

80.1

1-

1.2

30.1

01.1

00.0

7

LH

ranki

ng,

T=

1.5

s

AB

10

A0.5

10.0

3-

0.0

70.1

2-

0.1

00.0

80.9

20.0

6

AS

08

A0.4

90.0

60.1

80.1

20.1

80.0

91.0

50.0

7

Get

al09

A0.6

00.0

5-

0.0

50.1

0-

0.1

00.0

80.8

40.0

6

SK

Z12

A0.5

30.0

40.1

20.1

20.1

10.0

80.8

90.0

6

AC

10

B0.5

30.0

40.3

80.0

90.4

30.0

80.8

70.0

5

CY

08

B0.4

50.0

6-

0.2

20.1

3-

0.3

00.1

01.1

30.0

7

KG

04

C0.4

80.0

5-

0.6

20.1

0-

0.6

40.0

80.9

10.0

6

BA

08

C0.4

10.0

5-

0.4

50.1

4-

0.4

90.1

01.1

40.0

8

CB

08

D0.2

50.0

5-

1.0

90.1

4-

1.2

50.1

01.2

10.0

8

LH

ranki

ng,

T=

2.0

s

AB

10

A0.5

40.0

4-

0.1

00.1

2-

0.1

40.0

80.9

10.0

6

Get

al09

A0.5

40.0

30.1

80.1

10.1

30.0

70.8

10.0

6

SK

Z12

A0.5

20.0

5-

0.0

70.1

4-

0.1

00.0

80.9

10.0

6

AC

10

B0.5

00.0

50.4

10.0

80.4

40.0

80.8

80.0

5

AS

08

B0.4

20.0

60.3

30.1

00.3

10.1

11.1

20.0

8

CY

08

B0.4

20.0

6-

0.1

70.1

3-

0.2

30.1

01.1

60.0

7

KG

04

C0.4

40.0

5-

0.6

50.0

9-

0.6

90.0

90.9

60.0

6

BA

08

C0.4

50.0

5-

0.4

40.1

4-

0.5

20.1

01.1

40.0

7

CB

08

D0.2

80.0

7-

1.0

60.1

7-

1.1

80.1

11.2

40.0

8

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123

spectra, Sa(T), have been calculated at a series of periods (0.0 s (i.e., PGA), 0.1, 0.2, 0.5,

0.75, 1.0, 1.5, and 2 s) using the selected ground-motion models. The clearest and simplest

way to identify the presence of potential biases in the model predictions is the visual

inspection of residual histograms. Using the residuals plots, one is able to identify the

group of GMPEs which are best-fitting the data and to identify the GMPEs which are

providing the worse fit to the data. The residual set associated with each model has been

determined using Eq. (1) for desired periods. For example, the histograms of the residuals

of the models for period of 1.0 s are shown in Fig. 3. The procedure may be repeated for

the predetermined periods. The standard normal distribution functions which are expected

for each set are also plotted for each case in Fig. 3. From inspection of this figure, it is

apparent that SKZ12, Getal09, AS08, and AB10 have done a better job of predicting

desired values.

As a second step, the LH method has been applied to rank ground-motion models into

four classes A, B, C, and D. Figure 4 shows the distribution of LH values for

Sa(T = 1.0 s). It is difficult to judge qualitatively which one is more similar to a uniform

distribution. The quantitative goodness of fit of models to data in this method is evaluated

by using the median LH values (MEDLH) and the median, mean, and the standard

deviation of the normalized residuals (MEDNR, MEANNR, and STDNR, respectively).

The corresponding standard deviations of these measures (r) are calculated using thecomputer-aided statistical technique of bootstrap resampling (Efron and Tibshirani 1993).

By using these measures and based on the scheme presented in the former sections, the

ground-motion models are ranked in the categories A, B, C, or D (Table 3). The relative

similarity of ranking results for different periods may be interpreted as a sign of method

stability, though some studies have shown that the adequacy between a model and

observations is depending on the period considered (see e.g., Beauval et al. 2012; Delavaud

et al. 2012). This hypothesis is examined in Table 3, which shows the LH-based rankings

of models in different periods. Inspection of the results shows that three models: AS08,

CY08, and Getal09 are ranked A or B for all considered periods. Another finding is that

two models CB08 and AC10 are assigned rank D, or unacceptable, six and four times,

respectively.

Table 4 Final ranking of models based on the LH method for united residuals

All periods

Model name Rank MEDLH r MEDNR r MEANNR r STDNR r

AS08 A 0.47 0.02 -0.04 0.04 -0.07 0.03 1.07 0.03

CY08 A 0.47 0.02 -0.01 0.05 -0.05 0.03 1.11 0.03

Getal09 A 0.52 0.01 0.25 0.04 0.23 0.03 0.92 0.02

SKZ12 B 0.51 0.02 0.35 0.03 0.33 0.03 0.95 0.02

KG04 B 0.49 0.02 -0.32 0.04 -0.28 0.03 1.04 0.03

AB10 B 0.49 0.01 0.32 0.04 0.30 0.03 1.05 0.02

BA08 B 0.43 0.02 -0.13 0.05 -0.11 0.04 1.22 0.03

AC10 D 0.36 0.02 0.81 0.05 0.82 0.03 0.93 0.02

CB08 D 0.27 0.01 -0.92 0.06 -0.95 0.04 1.25 0.03

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123

Table 5 Ranking of models based on the information-theoretic (LLH) method for different periods

Rank LLH Model Rank LLH Model

PGA (T = 0.0 s) T = 0.1 s

1 1.54 KG04 1 1.68 AS08

2 1.55 CY08 2 1.76 Getal09

3 1.59 BA08 3 1.77 KG04

4 1.65 AS08 4 1.78 CY08

5 1.67 SKZ12 5 1.85 CB08

6 1.68 AB10 6 1.88 BA08

7 1.97 CB08 7 1.98 SKZ12

8 2.74 AC10 8 2.31 AB10

Getal09 9 3.06 AC10

T = 0.2 s T = 0.5 s

1 1.63 KG04 1 1.58 CY08

2 1.64 BA08 2 1.62 KG04

3 1.65 AS08 3 1.64 BA08

4 1.66 CY08 4 1.65 SKZ12

5 1.73 Getal09 5 1.66 AB10

6 1.74 SKZ12 6 1.68 Getal09

7 1.85 CB08 7 1.68 AS08

8 1.95 AB10 8 2.12 AC10

9 2.61 AC10 9 2.38 CB08

T = 0.75 s T = 1.0 s

1 1.46 AB10 1 1.41 AB10

2 1.50 AS08 2 1.47 AS08

3 1.52 Getal09 3 1.50 Getal09

4 1.53 CY08 4 1.56 SKZ12

5 1.55 SKZ12 5 1.56 CY08

6 1.58 BA08 6 1.67 BA08

7 1.68 KG04 7 1.80 KG04

8 1.92 AC10 8 1.85 AC10

9 2.44 CB08 9 2.60 CB08

T = 1.5 s T = 2.0 s

1 1.49 AB10 1 1.53 AB10

2 1.52 Getal09 2 1.53 SKZ12

3 1.53 SKZ12 3 1.55 Getal09

4 1.59 AS08 4 1.75 AS08

6 1.76 CY08 6 1.80 CY08

7 1.89 AC10 7 1.88 AC10

8 1.89 BA08 8 1.95 BA08

9 1.96 KG04 9 2.13 KG04

10 2.84 CB08 10 2.79 CB08

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In the current PSHA calculations, it is not possible for now to take into account different

GMPEs depending on their period-dependent efficiency, so there are arguments for

merging the dataset. Also, since the ranking results are more or less stable for the different

periods, it has been decided to merge all residuals into a unit set and then repeat the

ranking procedure. Table 4 shows the ranking of models based on this united residuals set.

Each period corresponds to a residual vector that the LH and LLH analysis can be per-

formed on it. Putting all residual vectors together leads to greater residual vector which

represents the overall behavior of a considered attenuation model. Tables 4 and 6 show the

results of application of LH and LLH analysis on this residual vector, respectively. Table 4

can be considered as the final ranking of models based on the LH method. According to

this ranking, two models CB08 and AC10 should be excluded from the acceptable models.

Also, two models developed specially for Iran region, Getal09 and SKZ12, are ranked A

and B, respectively. On the other hand, regarding the regional models that are models

developed for the Europe and Middle East, only one model, i.e., AB10 show an acceptable

performance (rank B).

As the final step of performance analysis, the average sample log-likelihood (LLH) has

been calculated for each of the seven considered periods, using the Eq. (1). Table 5

compares the mean LLH values for the candidate ground-motion models in different

periods. As it is clear, some of the GMPEs are more compatible with the testing database

for nearly all periods. A final period-independent ranking can be defined based on the

average LLH values of all periods, as is shown in Table 6. As it is clear, the ranking for the

top four models is based on very close LLH values (Table 6, 1.61 for Getal09, 1.63 for

AS08, 1.64 for CY08 and 1.65 for SKZ12) and more robust discrimination among them

may require more data.

By comparing the Table 4 with Table 6, the agreement of the LH and the information

theory method (LLH) in ranking of the models is confirmed. The two models that were

ranked as D with the LH method are also placed at the bottom of Table 6.

5 Discussions and conclusions

The difference between local, regional, and global ground-motion prediction models has

been investigated in order to determine their applicability for northern Iran. Two different

Table 6 Final ranking of modelsbased on the information-theo-retic (LLH) method for allperiods

All periods

Rank LLH Model

1 1.61 Getal09

2 1.63 AS08

3 1.64 CY08

4 1.65 SKZ12

5 1.72 AB10

6 1.74 BA08

8 1.77 KG04

9 2.26 AC10

10 2.35 CB08

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123

approaches have been used here to evaluate candidate ground-motion models. First, by

using a set of recorded ground-motion data, the computed residuals with respect to

different ground-motion models were analyzed by using the LH method. Based on this

method, two models (AC10 and CB08) were unacceptable and the remaining models

were ranked as A or B. However, it should be noted that there are reliable differences in

ranking results from one period to the other (i.e., period-dependent ranking), taking into

account that the number of records for each period is significant. In other words, the

residuals can be merged, but it gives another result which should not erase the period-

dependent ranking.

Second, information theory (LLH) was employed to rank the models, again. The good

agreement of these two methods confirms the reliability of the final ranking. One of the

main results of the current study is that some non-indigenous GMPEs show a high degree

of consistency with the data from northern Iran region (i.e., Abrahamson and Silva 2008;

Chiou and Youngs 2008). A similar conclusion was made by Delavaud et al. (2012) who

tested the global applicability of GMPEs for active shallow crustal regions. According to

Delavaud et al. (2012), some models in particular demonstrated a strong power of geo-

graphically wide applicability in different geographic regions with respect to the testing

dataset. Due to a paucity of data, the testing of the method developed here does not include

data from earthquakes with Mw [ 6.5 and R \ 90 km, except one. Taking into account thelimited number of observations, the issue is open till more strong motion records (par-

ticularly near-field ones) became available. The conclusions/results are restricted/limited

(are not rigorous) and should be used with caution. In such situations, the use of physics-

based models such as Soghrat et al. (2012) should be preferred taking into account their

more consistency with the physics of earthquakes; though even in such models, there also

may be significant uncertainties associated with the input parameters required for the

simulations. Based on the results of the current study, five GMPEs have been proposed for

PSHA analysis in the region. The best-fitting models (considering both the LH and LLH

results) over the entire frequency range of interest are those of Ghasemi et al. (2009a) and

Soghrat et al. (2012) among the local models, Abrahamson and Silva (2008) and Chiou and

Youngs (2008) among the NGA models, and finally Akkar and Bommer (2010) among the

regional models.

Although Turkey and Iran have similar tectonic regimes (shallow active crustal), the

predictive models derived for Turkey generally are not applicable for Iran (Northern Iran)

according to the findings of this study. After careful inspection, it is clear that the

Turkish data of KG04 and AC10 are primarily from western Turkey. Using the coda

normalization method for the direct S-waves, Horasan and Boztepe-Guney (2004) has

reported S-wave attenuation in the Sea of Marmara, western Turkey as Qs(f) = 40f1.03,

while Zafarani et al. (2012) have obtained an average value of Qs(f) = 101f0.8 for

northern Iran region based on the generalized inversion of the S-wave amplitude spectra.

This implies that the northern Iranian strong motion data attenuate slower than those of

western Turkey at low frequencies (i.e., T [ 1 s). This is confirmed by the period-dependent ranking results from the LLH method. As it is clear, the Turkish-based

attenuation model KG04 has a suitable performance at the T = 0, 0.1, 0.2, 0.5, and

0.75 s (see Table 3 and 5). However, the model fails to predict northern Iranian data at

T = 1.0, 1.5, and 2.0 s.

Regarding the NGA models, recordings from California cover almost 60 % of the BA08

and CB08 models, while it consist only 40 % of the AS08 and CY08 models (Power et al.

2008). Also, it is important to recognize the large number of Taiwanese records in the

AS08 and CY08 models, taking into account the similarity of shear-wave quality factor in

Nat Hazards

123

the Taiwan (Qs(f) = 125f0.8; Sokolov et al. 2000) and northern Iran regions

(Qs(f) = 101f0.8; Zafarani et al. 2012). This may be the reason of the better performance of

the two latter models, i.e., AS08 and CY08 models.

The similar performance of Ghasemi et al. (2009a), developed based on the whole

Iranian plateau database, and Soghrat et al. (2012), established specifically for northern

Iran, may be questionable and surprising. However, it should be taken into account that

the Scherbaum et al. (2004, 2009) approaches used here assess overall goodness of fit of

data to a model, i.e., all aspects of the model performance and accuracy are evaluated in

a lumped manner. If one of the model components was in error, that effect could be

obscured through compensating errors in the comparison process of normalized residuals

to the standard normal variate (Scasserra et al. 2009). Accordingly, while the results of

the current study are promising with respect to the similar performance of Ghasemi

et al. (2009a) and Soghrat et al. (2012) relations in northern Iran, a formal analysis of

the adequacy of the models with respect to magnitude scaling, distance scaling, and site

effects is also needed. The details of this procedure will be published in a separate paper

(Mousavi et al. 2013). Also, careful inspection shows that the Ghasemi et al. (2009a)

and the Soghrat et al. (2012) equations are very close in the range of 10100 km (see

Fig. 15 in Soghrat et al. 2012), which is the dominant distance range of the current

dataset.

Regarding our conclusions, it should be taken into account that according to Musson

(2009), if an empirical GMPE is to be used in probabilistic seismic hazard assessment,

the model would probably be subject to extrapolate beyond the parameter space within

which it was constructed, especially for hazard at low annual probabilities, even with the

proviso that the dataset is reasonably extensive and well selected. In this case, the

features of the model, especially its functional form, may turn out to have unexpected and

undesirable implications. Although a ground-motion model may be a correct represen-

tation of its dataset, the effects of the functional form applied can be such that it becomes

doubtful whether the model should be used for probabilistic hazard purposes. Therefore,

although the local model of Ghasemi et al. (2009a) did a good job of prediction for the

limited database of northern Iran, but care must be taken when using it in a real seismic

hazard project, especially for low hazard levels; taking into account its simple functional

form.

Finally, if we would like to find corresponding weights of different GMPEs to be used in

PSHA, we may do so by using the procedure suggested by Mousavi et al. (2012). The

method combines the results of the LH and information theory methods, in two steps.

These weights provide a quantitative alternative to expert opinions in seismic hazard

projects and can be used to complement expert opinions, where these may be available or

replace expert opinions when these are unavailable.

Acknowledgments The authors acknowledge the Building and Housing Research Centre of Iran forproviding them with the accelerograms and shear-wave velocities used in the current study. This study wassupported by the International Institute of Earthquake Engineering and Seismology (IIEES) funds, ProjectG-05-92: Seismicity and Seismic Hazard Studies for an International Hotel in Tehran, Iran This financialsupport is gratefully acknowledged. Finally, we are very grateful to two anonymous reviewers for theirinsightful and constructive comments, which significantly improved the manuscript.

Appendix

See Table 7.

Nat Hazards

123

Ta

ble

7T

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reco

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Nat Hazards

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Nat Hazards

123

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54

.46

69

15

S3

41

12

3B

and

ar-e

-Gaz

35

57

/02

36

.76

53

.95

67

71

S3

47

12

4E

stal

kh

Po

sht

35

59

36

.46

53

.48

50

13

3R

57

2

12

5D

ibaj

35

90

36

.43

54

.23

27

83

R5

26

12

6M

oje

n3

62

2/0

13

6.4

85

4.6

51

67

6R

87

6

12

7Q

apan

-e-O

lya

36

36

/01

37

.62

55

.68

15

14

5S

41

0

12

8M

ino

odas

ht

36

39

/01

37

.23

55

.37

36

10

1S

44

9

12

9G

hal

eS

hok

at3

86

23

6.3

55

4.9

12

11

01

R6

58

13

0A

gh

Gh

ala

35

56

/02

37

.01

54

.46

18

23

S3

41

13

1G

om

ish

an3

56

83

7.0

75

4.0

81

44

9S

32

2

13

2G

om

ish

an3

60

73

7.0

75

4.0

89

46

7S

32

2

13

3B

and

ar-e

-Gaz

36

09

36

.76

53

.95

47

10

1S

34

7

13

4N

oza

rA

bad

36

11

36

.80

53

.25

27

16

0S

43

8

13

5A

liA

bad

36

12

36

.90

54

.85

34

71

R5

62

136

Gonbad

-e-K

avoos

3614

37.2

455.1

61

97

5S

402

13

7In

cheh

Boru

n3

61

83

7.4

65

4.7

21

63

22

S2

83

138

Kal

aleh

3619/0

237.3

855.5

01

8108

S375

13

9R

amy

an3

62

1/0

23

7.0

25

5.1

44

08

4R

82

7

14

0M

oje

n3

62

2/0

23

6.4

85

4.6

51

71

10

R8

76

14

1G

org

an3

62

33

6.8

45

4.3

86

17

1S

29

1

14

2D

ibaj

36

24

36

.43

54

.23

24

11

9R

52

6

14

3A

gh

ban

d3

63

53

7.6

65

5.1

82

07

6S

40

2

14

4B

ile-

Sav

ar4

41

73

9.3

64

8.3

23

17

1R

53

3

Nat Hazards

123

Ta

ble

7co

nti

nued

Nu

mb

er.

Sta

tio

nn

ame

Cod

eC

oo

rdin

ate

C.P

GA

a(c

m/s

/s)

Hy

po

centr

ald

ista

nce

Sit

ebV

S30

ne

14

5H

elab

ad4

41

93

7.9

44

8.4

22

59

7S

38

7

14

6O

dlo

o4

42

23

9.3

04

8.1

62

47

5S

44

5

147

Tal

eb-e

-Qes

hla

qi

4424

38.4

048.2

12

36

1R

978

14

8R

azi

44

23

38

.63

48

.10

21

59

R7

20

149

Esl

am-A

bad

4426

38.1

347.9

41

8104

R1,3

26

15

0L

ahro

od

44

25

38

.51

47

.83

14

92

R9

81

15

1N

amin

44

21

38

.42

48

.48

15

43

R1

,236

15

2S

aeen

gh

ale

46

01

36

.31

49

.07

19

47

R6

42

15

3S

olt

aniy

eh4

60

23

6.4

44

8.8

05

71

7S

46

6

15

4D

arse

jin

46

06

36

.02

49

.24

16

82

R6

36

15

5S

ird

an4

60

73

6.6

54

9.1

98

35

0S

35

2

15

6K

ash

mar

46

14

35

.24

58

.47

15

32

S3

25

15

7R

ivas

h4

61

53

5.4

85

8.4

64

21

5R

52

0

15

8C

hen

ar4

71

03

5.2

85

8.9

11

54

2R

94

0

15

9Y

ekan

kah

riz

46

61

38

.67

45

.40

29

46

R7

38

16

0M

aran

d4

66

33

8.4

44

5.7

73

72

7R

54

6

16

1S

hab

esta

r4

66

43

8.1

84

5.7

11

35

7R

92

2

16

2T

aso

oj

46

65

38

.31

45

.36

14

65

R7

09

16

3Z

anji

reh

46

66

38

.46

45

.37

14

56

R9

19

aC

.PG

Aco

rrec

ted

pea

kg

rou

nd

acce

lera

tio

nb

SS

oil

,R

Ro

ck

*B

ased

on

Zar

eet

al.

(19

99)

and

Gh

asem

iet

al.

(20

09b);

atth

ese

site

s,g

ener

icv

alues

of

27

5,

50

0,

and

1,0

00

m/s

hav

eb

een

assi

gn

edfo

rV

S30

of

clas

ses

III,

II,

and

I,re

spec

tiv

ely

Nat Hazards

123

References

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Abrahamson N, Silva W (2008) Summary of the Abrahamson & Silva NGA ground motion relations. EarthqSpectra 24:6797

Akkar S, Bommer JJ (2010) Empirical equations for the prediction of PGA, PGV and spectral accelerationsin Europe, the Mediterranean Region and the Middle East. Seism Res Lett 81:195206

Akkar S, Cagnan Z (2010) A local ground-motion predictive model for Turkey, and its comparison withother regional and global ground-motion models. Bull Seismol Soc Am 100:29782995

Ansari A, Noorzad A, Zafarani H, Vahidifard H (2010) Correction of highly noisy strong motion recordsusing a modified wavelet de-noising method. Soil Dyn Earthq Eng 30:11681181

Ashtari M, Hatzfeld D, Kamalian N (2005) Microseismicity in the region of Tehran. Tectonophysics395:193208