INTRODUCTION
Iran is a country which has high risk of earthquake happening. This country is located on AlpineCaucasianHimalayan belt and many catastrophic earthquakes have destroyed and damaged some parts of it and killed many people. Figure 1 shows recent seismicity of Iran (Tavakoli and GhaforyAshtiany, 1999).
Shiraz; center of Fars province; is the most important city in south of Iran because of its historical places and population. Cultural, economical, social and political importance of Shiraz in addition with the high risk of earthquake happening of this city and its province indicate the necessity of seismic investigation with high accuracy.
This city has been damaged and destroyed several times in previous years (Andalibi and Oveisi, 1999); therefore, in the Iranian Code of Practice for Seismic Resistant Design of Buildings (2005), it has been placed in high seismic risk region and the base acceleration of 0.3 g is recommended for it.
With regard to the importance of this city with more than 2500 years history, existing a lot of historical places and this issue that seismic hazard analysis with high accuracy has not been done for Shiraz so far, therefore in this study it has been emphasized to achieve design acceleration over bedrock, curve of magnitudereturn period and seismic maps in four levels of hazard for this region.
SEISMOTECTONIC STRUCTURE OF SHIRAZ
In order to evaluate the seismic hazard of a region or zone, all the probable seismic sources have to be detected and their potential to produce strong ground motion must be checked. The major faults in Shiraz region and its vicinity are Sabzposhan, Kohenjan, Sarvestan and Karehbas. The list of active faults and their specifications in this region are given in Table 1 and shown in Fig. 2.
SEISMICITY OF SHIRAZ
The happened earthquakes in this area have categorized with respect to information accuracy, into two categories (Kijko, 2000):
• 
Historical earthquakes (earthquakes occurred before the year
1900) 
• 
Instrumentally recorded earthquakes (earthquakes occurred
from the year 1900 up to now). 

Fig. 1: 
Recent seismicity map of Iran. Earthquake magnitude (Richter
scale): ● for M<5; ○ for M= 57; F
for M>7 (Tavakoli and GhaforyAshtiany, 1999) 

Fig. 2: 
Active faults of Shiraz and its vicinity (Andalibi and Oveisi,
1999) 
Table 1: 
The list of main active faults of Shiraz and its vicinity
(Andalibi and Oveisi, 1999) 

Our knowledge of earthquakes that occurred before the 20th century is based on data collection from historical and ancient documents; as a result, overestimation might be present in the data. The magnitude of historical earthquakes due to the destructive effects and their social outcomes have been estimated by researchers like Berberian (1976) and Ambraseys and Melville (1982) by consideration of many historical notes.
The investigation of the catalog of earthquakes shows that several earthquakes have occurred with M>6. The historical studies show that Shiraz has been completely destroyed at least twice in the past (Andalibi and Oveisi, 1999).
Seismic data after the year 1900 are important since instruments record them, although they might possess different inaccuracies in the location of epicenter, amount of focal depth and earthquake magnitude. The list of earthquakes occurred in the radius of 200 km from Shiraz is shown in Appendix A.
THE SEISMICITY PARAMETERS OF THIS AREA
The seismic assessment is based on data of the earthquakes occurred in the concerned region and utilization of probabilistic methods. The earthquakes catalog in a radius of 200 km has been gathered and processed, assuming that the earthquakes follow a poisson distribution.
The seismic parameters, such as α and β and M_{max} were calculated using the Kijko (2000) method.
Earthquakes catalogue: The information of the earthquakes in radius
of 200 km of Shiraz, has been gathered from several references like Ambraseys
and Melville (1982), Building and Housing Research Center (BHRC) (http://www.bhrc.ir),
International Institute of Earthquake Engineering and Seismology (IIEES) (http://www.iiees.ac.ir.)
and some websites like USGS (http://www.usgs.gov.).
The reason for the application of probabilistic method and its advantage over
other methods are for the incompleteness of our seismic data regarding magnitude
and focal depth of earthquakes.
The types of magnitude scales were not the same. To change these types to one scale, Equation 1, presented by the Iranian Committee of Large Dams IRCOLD (1994) was employed to transfer m_{b} (body wave magnitude) into M_{S} (surface wave magnitude):
Since foreshocks and aftershocks are events that happen before and after earthquakes (main shock), respectively, therefore the complete list of earthquakes (without the elimination of foreshocks and aftershocks) usually do not follow Poisson distribution, as a result all foreshocks and aftershocks must be excluded. The method, which is used to eliminate the foreshocks and aftershocks, is the variable windowing method in time and space domains by Gardner and Knopoff (1974).
Determination of seismicity parameters based on Kijko method: In order to perform seismic hazard analysis, it is necessary to evaluate the seismicity parameters such as maximum expected magnitude (M_{max}), annual activity rate of earthquake λ and b value of Gutenberg and Richter (1954) relation.
The seismicity parameters are calculated based on the occurrence of earthquakes and the relationship between their magnitudes and frequencies. So far, several methods have presented to evaluate these coefficients based on Gutenberg and Richter (1954) relationship.
With regard to the importance of these parameters to determine seismic hazard; in this paper, the result of Tavakoli (1996) parameters and also Kijko (2000) method are used. In order to combine these results, logic tree method has been used with equal contribution coefficients.
Kijko (2000) method parameters have obtained based on Gutenberg and Richter (1954) relationship and estimation of maximum expected magnitude. In this method, both historical and instrumental earthquakes can be used with suitable classification and also in its program the uncertainty of the earthquake, data are mentioned.
There are three groups of earthquakes data in this method; as follows:
• 
Historical earthquakes (before 1900) with magnitude uncertainty
between 0.3 and 0.5 (Case 1). 
• 
Instrumentally recorded earthquakes from 1900 to 1963 with
uncertainty 0.2 (Case 2). 
• 
Instrumentally recorded earthquakes from 1964 to 2005 with
uncertainty 0.1 (Case 3). 
The results of this method are shown in Table 2 and Fig. 3.
Determining seismicity parameters based on tavakoli’s results: Tavakoli (1996) has divided Iran into 20 seismotectonic provinces, as shown in Fig. 4 and earthquake hazard parameters have been evaluated for each seismotectonic province. In this study, the maximum likelihood method (Kijko and Sellevoll, 1992) has been applied. Suggested values for seismicity parameters for Shiraz (province No. 12) are shown in Table 3. In addition, these parameters were used in this study through logic tree method. Note that to some extent, this method compensates the assumption of seismic homogeneity in the radius of 200 km around Shiraz.
SEISMIC HAZARD ANALYSIS
There are several models for forecasting the occurrence of earthquakes (Kiremidjian and Anagnos, 1983). The most commonly used models are Poisson model (Cornell, 1968; Cornell and Merz, 1975), a timeindependent model and Markov model (Chiang et al., 1984), which is a timedependent model. Poisson distribution assumes that earthquakes are independent events that occur randomly in time. In this study, Poisson model was adopted for its popularity, ease of use and lack of sufficient data for other models.
The Poisson model is given by:
Where:
p_{n} (t) 
= 
Probability of having n events in time period t 
n 
= 
No. of events 
v 
= 
The mean rate of occurrence per unit time 
The magnitude probability density function, f_{M} (M), can be evaluated from GutenbergRichter recurrence relationship proposed:
or:
Where:
α 
= 
axLn 10 
β 
= 
bxLn 10 
λ 
= 
Activity rate 
Considering the magnitude uncertainty proposed by Kijko and Sellevoll (1992), the modified probability density function of magnitude, f (xm, σ) and probability cumulative function of magnitude, F (xm, σ), can be written as:
Table 2: 
Seismicity parameters in different cases for Shiraz 


Fig. 3: 
Annual rates estimated by Kijko (2000) method for Shiraz
and its vicinity 

Fig. 4: 
Seismotectonic provinces of Iran (Tavakoli, 1996) 
Table 3: 
Seismicity parameters for seismotectonic province of Shiraz
(Tavakoli, 1996) 

Where:
C_{σ} (xm, σ) and D_{σ}
(xm, σ) 
= 
Correction functions 
A_{1} 
= 
Exp (βm) 
A_{2} 
= 
Exp (βm_{max}) 
σ 
= 
The error of reported magnitude and magnitude x belongs to the domain
⟨m, m_{max}⟩ 
m 
= 
The threshold magnitude 
m_{max} 
= 
The maximum expected magnitude 
In this part, probabilistic seismic hazard analysis is used for determining peak ground acceleration for four hazard levels. This procedure is divided into five steps:
• 
Collecting of earthquakes catalogue. 
• 
Recognition of seismic sources and modeling of them. 
• 
Calculating of seismicity parameters by Kijko (2000) method
and using Tavakoli’s seismicity parameters. 
• 
Selection of suitable attenuation relationships. 
• 
Deriving the amount of PGA at this area by dividing it into
subzones with software SEISRISK III (Bender and Perkins, 1987). 
Around first three steps, it has been discussed enough before, but about steps 4 and 5 some information will be mentioned in the following.
Attenuation relationships: Attenuation relationship is one of the most
important parameters in seismic hazard analysis that displays the amount of
PGA in different distance and magnitude of earthquakes.
In this study after assessment of available relationships, finally four relations have been selected by Ambraseys and Bommer (1991), Sarma and Srbulov (1996), Ramazi (1999) and Ghodrati Amiri et al. (2007). Their logic tree coefficients for these relations are 0.1, 0.1, 0.3 and 0.5, respectively.
Relationship between maximum expected magnitude and fault rupture length: The relationship between maximum expected magnitude and fault length depends on the understanding of the seismotectonic and geotectonic behavior of the concerned area. In general, Eq. 6 for any given region can be written:
Where:
L 
= 
Rupture length 
M 
= 
Maximum expected magnitude 
a and b 
= 
Constant coefficients. 
The rupture length is a percentage of fault length, which causes the earthquake and varies for different fault lengths. Nowroozi (1985) has offered Eq. 7 after studying over ten severe earthquakes in Iran and observing active faults ruptures. The faults under study include Zagros fault, North Alborz fault, North Tabriz fault, Zafareh fault in north of Isfahan, Dehshir fault in southeast of Isfahan, the fault of Babak city in Kerman and the faults of Doroone and DashteBayaz in Makran region.
In Eq. 7, M_{S} is surface wave magnitude and L is
rupture length in meters.
Probabilistic seismic hazard analysis: In order to analysis, at first based on the faults map in Fig. 2, the seismic sources are modeled into linear and area forms and the seismicity parameters calculated, then results are introduced by SEISRISK III (Bender and Perkins, 1987) software. Then the whole area of interest was subdivided into a grid of 8*7, total of 56 sites and probabilistic seismic hazard analysis was carried out for each site. The output of program was the anticipated Peak Ground Acceleration in g with 2, 10, 20 and 50% probabilities of being exceeded during life cycles of 50 years or for the ground motion return periods of 75, 225, 475 and 2475 years. As shown in Fig. 5, logic tree analysis has been utilized for the output of SEISRISK III.

Fig. 5: 
Applied logic tree for seismic hazard analysis 

Fig. 6: 
Final zoning map (PGA over bedrock) of Shiraz and its vicinity
using logic tree for 75year return period map and the border of Shiraz
(thick line) 

Fig. 7: 
Final zoning map (PGA over bedrock) of Shiraz and its vicinity
using logic tree for 225year return period map and the border of Shiraz
(thick line) 

Fig. 8: 
Final zoning map (PGA over bedrock) of Shiraz and its vicinity
using logic tree for 475year return period map and the border of Shiraz
(thick line) 

Fig. 9: 
Final zoning map (PGA over bedrock) of Shiraz and its vicinity
using logic tree for 2475year return period map and the border of Shiraz
(thick line) 
These return periods used in this study are according to the hazard levels
in Seismic Rehabilitation Code for Existing Buildings in Iran (IIEES, 2002).
Isoacceleration maps for four hazard levels have been shown in Fig.
69. With regard to these maps, it is obvious that southwest
of Shiraz has the most probable seismic acceleration.
CONCLUSIONS
This research studied seismic hazard and seismic zoning of Shiraz and its vicinity
based on probabilistic approach. The significant results of this study can be
summarized as: (1) generation of a preliminary seismic zoning map (PGA over
bedrock) that can be used, with caution, as a guide for determining the design
earthquake, (2) production of an updated and complete earthquake catalogue considering
both historical and instrumental events (Appendix A) and (3) utilization of
different worldwide attenuation relationships using logic tree method. The seismic
hazard analysis carried out in this study was based on the assumption of an
ideal bedrock case and therefore no influence of local soil condition is taken
into consideration.
This research presents the maps of maximum probable acceleration over bedrock for four levels of hazard as what Seismic Rehabilitation Code for Existing Buildings in Iran (IIEES, 2002) needs. The PGA in the interested area, ranges from 0.1 to 0.17 g for a return period of 75 years, 0.15 to 0.29 g for a return period of 225 years, 0.18 to 0.39 g for a return period of 475 years and from 0.26 to 0.66 g for a return period of 2475 years.
The comparison of the results with the recommended PGA in Iranian Code of Practice
for Seismic Resistant Design of Buildings (http:www.bhrc.ir)
(0.3 g) shows that the recommended PGA is lower than what it has been achieved
in this study in some parts of the region. The southwest of Shiraz has the
most probable seismic acceleration. This PGA can cause major structural damage
in important structures and lifeline systems.
APPENDIX A
Earthquake catalogue in the radius of 200 km for Shiraz 
