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International Journal of Earth Sciences and Engineering ISSN 0974-5904, Volume 04, No 06 SPL, October 2011, pp. 200-203

Seismic Hazard Assessment of Metropolitan Tehran by Using Deterministic Attenuation and Epicentral Distribution

G. Ghodrati Amiri

Center of Excellence for Fundamental Studies in Structural Engineering, School of Civil Engineering, Iran University of Science and Technology, Tehran, Iran, Email: [email protected]

H. Razeghi

School of Civil Engineering, Iran University of Science and Technology, Tehran, Iran, Email: [email protected]

A. Kazemi

School of Civil Engineering, Iran University of Science and Technology, Tehran, Iran, Email: [email protected]

ABSTRACT: In this paper, probabilistic seismic hazard analysis (PSHA) is performed for metropolitan Tehran and seismic zoning map is obtained for the area. Suggested method of the PSHA is new from two aspects: first the application of attenuation relationships and second the employed seismic source model. Attenuation models in this study are considered without standard deviation (i.e. they are in deterministic form), while common PSHA method needs probabilistic attenuation models. That is, required uncertainty of the attenuation is originated from the magnitude density function instead of the standard deviation. Seismic source model is also new as it has a statistical stochastic pattern. Convex combinations of Gaussian distributions are used to fit the recorded epicentral coordinates for different magnitude ranges and are integrated into an overall epicentral distribution by using the magnitude density function, so the method is completely fault-free and no geological map is required for the analysis. Moreover, a logic tree is selected to perform a comprehensive hazard analysis. Finally, seismic zoning map is plotted for a specified hazard level in the metropolitan area. Evaluated map is in agreement with a previous seismological study of the city and Iranian code of practice for seismic resistant design of buildings. KEY WORDS: PSHA, deterministic attenuation, epicenter, Gaussian distribution, Tehran. INTRODUCTION Seismic hazard assessment of metropolitan Tehran is of critical importance concerning two aspects: Firstly, as the capital of Iran, Tehran is a highly populated city (with a population of approximately 8 million) where main political and economical centers are located in. Therefore, possible seismic damages are very wide and affect the whole country as well. Secondly, seismological and geological characteristics of the region urge the seismic hazard assessment of it. Active faults (such as North Tehran, Mosha, and South Ray), alluvium deposits of Tehran plain and Rey city, and occurred large earthquakes indicate a high seismicity (Ghodrati et al. 2003). Seismic hazard of Tehran city has been estimated in many studies up to now. By the way, applied methods in those studies are quite traditional. Result of a recent customary probabilistic seismic hazard analysis (PSHA) is available in the present paper for verification (Ghodrati et al. 2003). In these studies, seismic source is modeled by the active fault maps and seismicity parameters. In the case of probabilistic analysis, probabilistic attenuation models are required, in which a standard deviation is offered or assumed for the calculated strong ground motion parameter. Present paper uses a new method to perform probabilistic seismic hazard analysis (PSHA) of the city. Novelty of the method includes both modeling of the seismic source and application of the attenuation relationships. As mentioned above, probabilistic attenuation models are applied inPSHA, so a standard deviation is assumed if an attenuation model is deterministic. The new approach

proposes using attenuation relationships without standard deviations, which means that magnitude uncertainty is employed for probabilistic analysis. Therefore, deterministic attenuation relationships are directly applicable. As already stated, seismic source model is also novel. Statistical data of past earthquakes are processed to model a fault-free seismic source (i.e. epicentral distribution). Though application of fault-free seismic source models is observed in some previous studies (Baratta & Corbi 2004, 2005), source model is used differently in the present study. An overall epicentral distribution is calculated by integrating estimated distributions of different magnitude ranges multiplied by the corresponding magnitude density values. Proposed method in this paper is verified by comparing the obtained seismic zoning map with a map of previous study using a customary PSHA method. Thus, the same logic three analysis, attenuation relationships, and seismicity parameters are used in this paper in order to make a more controlled comparison. Two maps are in agreement with each other, indicating that the present method results in rational values of strong ground motion parameter for a definite hazard level. METHODOLOGY In the present method, seismic source model is a continuous distribution, covering all over the region, not a set of discrete linear or areal zones, which means that each point on the region has the potential of being epicenter.

#020410149 Copyright © 2011 CAFET-INNOVA TECHNICAL SOCIETY. All rights reserved

Seismic Hazard Assessment of Metropolitan Tehran by Using Deterministic Attenuation and Epicentral Distribution Such seismic source model requires a different form of hazard assessment. Hazard density function is calculated by means of a multivariate or joint distribution, variables of which are strong ground motion parameter at the site (as) and coordinates of epicenter (xe,ye). Briefly speaking, p(as) is calculated by p(as,xe,ye) through a double integral:

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do the procedure for a grid of epicentral coordinates per each value of the strong ground motion parameter (as,xe,ye). The logic tree is selected from a previous study of metropolitan Tehran (Ghodrati et al. 2003) to make a more rational comparison between the results of the two studies (Fig. 2). The logic tree analysis includes three attenuation relationships (Ambraseys & Bommer 1991, Sarma & Srbulov 1996, Ramazi 1999) and two seismicity parameter values: first, =1.08, estimated by Kijko 2000 software for historical and 20th century earthquakes data (Ghodrati et al. 2003); second, =1.44, proposed for seismotectonic province of Tehran (Tavakoli 1996). The coefficients of the parameters and relationships are included in parentheses.

p(a s ) =

xe y e

p(a , x , y )dy dx

s e e e

e

(1)

The joint distribution, p(as,xe,ye), is unknown, but it may be obtained by other distributions. Here, the definition for conditional probability density function is helpful:

p ( a s | xe , y e ) =

p ( a s , xe , y e ) p ( xe , y e )

(2)

Conditional distribution of p(as|xe,ye) depends on the attenuation relationship and the magnitude density function. The key point is that for a given epicentral coordinates, the distance from the site to source, R, is fixed and the attenuation relationship, i.e. as=f(R,M), simply relates magnitude (M) to the strong ground motion parameter. Therefore, p(as|xe,ye) is calculated in terms of the magnitude density function, p(M). In the present study, Gutenberg-Richter relationship is selected to represent the magnitude density function (Gutenberg & Richter 1954):

p( M ) = .e - ( M - M

0

Earthquake catalog

Epicentral Dist. p(xe,ye)

Attenuation as=f(R,M)

Magnitude density p(M)

Eq. 2

Conditional Dist. p(as|xe,ye) Hazard density p(as)

)

(3)

Joint Dist. p(as,xe,ye)

Eq. 1

where M and M0 are the magnitude and its lower bound respectively, and is the seismicity parameter. Joint distribution of p(xe,ye) is the stochastic source model or the overall epicentral distribution. It defines the probability of being epicenter for any point of the region. Epicentral distribution is a random spatial model and is evaluated by a fitting process of the events in the catalog. It is better to estimate this distribution for different ranges of magnitude separately, to define sources with distinct period of recurrence, and integrate them as

Fig. 1 Method flowchart

Ramazi 1999 (0.40) Kijko 2000 (0.5) Ambraseys & Bommer 1991 (0.35) Sarma & Srbulov 1996 (0.25) Source Model Seismicity Parameters Attenuation Ramazi 1999 (0.40) Tavakoli 1996 (0.5) Ambraseys & Bommer 1991 (0.35) Sarma & Srbulov 1996 (0.25)

p ( xe , y e ) =

M

p( x , y

e

e

| M ) p( M )dM

(4)

where p(xe,ye|M) is a convex combination of Gaussian distributions, fitted to coordinates of past earthquakes with the magnitude of M. Practically, the integral in Eq. (4) is not functional and must be used as a sum, if so, M would be a magnitude range instead of a point. In the present study, a previously gathered catalog of earthquakes for Tehran region (Ghodrati et al. 2003) is used to estimate the parameters of the seismic source models. Figure 1 shows a flowchart of the presented method. To obtain hazard density function for a site, it is necessary to

Fig. 2 Applied logic tree RESULTS AND DISCUSSION Epicentral distributions were estimated by fitting convex combinations of bivariate Gaussian distributions to the spatial data of past events. Epicentral distribution was obtained for each magnitude range, and then overall

International Journal of Earth Sciences and Engineering ISSN 0974-5904, Volume 04, No 06 SPL, October 2011, pp. 200-203

202

G. Ghodrati Amiri, H. Razeghi, A. Kazemi applied seismic source models. As Figure 4 shows, epicentral distribution led to expected values of horizontal PGA. Though the PGA variation is abrupt in some part of the map obtained by active fault map, the PGA range is almost the same in both maps. Iranian code of practice for seismic resistant design of buildings suggests a value of 0.35g for horizontal PGA in Tehran, which is near to the obtained values in this method. Relative lack of contour line curvature in the map of fault-free method is due to the vast area of epicentral distribution estimation. While fault map is defined in the metropolitan area, epicentral distribution is estimated for Tehran and nearby provinces due to the lack of statistical data in the city area, which makes the results sound less accurate.

distribution was calculated by Eq. (4) (Fig. 3). The overall distribution in Figure 3 corresponds to =1.08. As expected from Eq. (4), overall distribution is mostly affected by distribution of the events with lower magnitude because of decreasing nature of the magnitude density function. Hazard density functions were calculated for a grid of sites in the metropolitan area. Overall epicentral distributions (for two seismicity parameters) and the logic tree in Figure 2 were applied to the present method to obtain hazard density curves of horizontal peak ground acceleration (PGA). Finally, seismic zoning map was drawn for exceeding probability of 10% in 50 years (0.002). Seismic zoning map calculated by the present method is observed in comparison with a previously obtained one in Figure 4. The main difference between the maps is the

Epicentral Distribution (4<M<5)

38

1e-006

38

06 1e-0

Epicentral Distribution (5<M<6)

1e -00 6

37.5

37.5

37

5e -00 6

37

5e-0 06

36.5

1.3 e-0 05

36.5

36 Latitude (N)

9e-0 06

36 Latitude (N)

05 e-0 1.7

06 5e-0

35.5

1e-0 06

35.5

1.3e-005

06 -0 5e

35

35

9e-006

34.5

34.5

34

34

1e-0 06

33.5 0 33 49 50 100 Km

33.5 0 50 100 Km

49.5

50

50.5

51

51.5 52 Longitude (E)

52.5

53

53.5

54

33 49

49.5

50

50.5

51

51.5 52 Longitude (E)

52.5

53

53.5

54

38

Epicentral Distribution (M>6)

1e-006

38

Overall Epicentral Distribution (M>4)

1e-00 6

37.5

37.5

37

5e -0 06

37

1.3e-005

36.5

36.5

9e-0 06

36 Latitude (N) Latitude (N)

36

6 -00 1e

9e -0 06 5e -0 06

35

9e-0 06

1.7e-005

35

1. 3e -0 0

35.5

1.3 e-0 05

35.5

05 -0 7e 1.

5

06 -0 1e

34.5

1e -0 06

34.5

34

34

33.5 0 50 100 Km

1e-006

33.5 0 50 100 Km

33 49

49.5

50

50.5

51

51.5 52 Longitude (E)

52.5

53

53.5

54

33 49

49.5

50

50.5

51

51.5 52 Longitude (E)

52.5

53

53.5

54

Fig. 3 Epicentral distributions

International Journal of Earth Sciences and Engineering ISSN 0974-5904, Volume 04, No 06 SPL, October 2011, pp. 200-203

Seismic Hazard Assessment of Metropolitan Tehran by Using Deterministic Attenuation and Epicentral Distribution

203

35.85

0.4 1

0.4 15

35.85

5 0.3

7 0.3

9 0.3

0.41

35.8

0.4

0.4 05

0.43

35.8

0.4 5

0.43

0. 3 9

35.75

0.3 85

0.3 95

0.4 1

35.75

0.3 7

5 0.3

0.4 5

0.41

35.7 Latitude (N)

0.4

0.4 05

35.7 Latitude (N)

0. 39

3 0.4

35.65

0. 3 9

0. 3 95

35.65

1 0.4

9 0.3

0.37

35.55

39 0.

35.55

0 5 10 Km

0

95 0.3

0.3 9

0. 39

35.6

0. 37

0. 37 5

0.3 8

0. 3 85

7 0.3

35.6

4 0.

5

10 Km

0.37

35.5 51.25

51.3

51.35

51.4

51.45 Longitude (E)

51.5

51.55

51.6

51.65

35.5 51.25

51.3

0 35 51.35

51.4

51.45 Longitude (E)

51.5

0. 35

33 0 51.55

51.6

51.65

(a)

(b)

Fig. 4 Seismic zoning maps of Tehran for exceeding probability of 10% in 50 years (0.002) by (a) epicentral distribution (present study) (b) active fault maps (Ghodrati et al. 2003) CONCLUSIONS In the present paper, probabilistic seismic hazard analysis was performed for metropolitan Tehran, capital of Iran, and related seismic zoning map was obtained. Applied method in this study is new regarding the seismic source model and employment of the attenuation relationships. Epicentral distribution is used instead of active fault maps, which makes the analysis independent of geological maps. In other words, a catalog of earthquakes suffices to model the seismic source. Moreover, the method does not necessarily require probabilistic attenuation relationships, which means that deterministic relationships are directly applicable, without the need to assume any standard deviation during the estimation of strong ground motion. The mentioned novelties and also verification of the resulted seismic zoning map indicate that the method is easy to use, fast and functional.

[3] [4] Baratta, A. and Corbi, I. (2005). Evaluation of the hazard density function for a site. Computers and Structures, 83(28-30), 2503­2512. Ghodrati Amiri, G., Motamed, R. and Rabet Eshaghi, H. (2003). Seismic hazard assessment of metropolitan Tehran, Iran. Journal of Earthquake Engineering, 7(3), 347-372. Gutenberg, B. and Richter C.F. (1954). Seismicity of the earth and associated phenomena. Princeton, NJ: Princeton University Press. Iranian Code of Practice for Seismic Resistant Design of Buildings (Standard No. 2800) (2005). Building and Housing Research Center, Iran (in Persian), 3rd Edition. Ramazi, H.R. (1999). Attenuation laws of Iranian earthquakes. Proceedings of the 3rd International Conference on Seismology and Earthquake Engineering, Tehran, Iran, 337-344. Sarma, S.K. and Srbulov, M. (1996). A simplified method for prediction of kinematic soil-foundation interaction effects on peak horizontal acceleration of a rigid foundation. Earthquake Engineering and Structural Dynamics. 25(8), 815-836. Tavakoli, B. (1996). Major seismotectonic provinces of Iran. International Institute of Earthquake Engineering and Seismology, Internal Document (in Persian).

[5] [6]

[7]

[8]

REFERENCES

[1]

[2]

Ambraseys, N.N. and Bommer, J.J. (1991). The Attenuation of ground accelerations in Europe. Earthquake Engineering and Structural Dynamics, 20(12), 1179-1202. Baratta, A. and Corbi, I. (2004). Epicentral distribution of seismic sources over the territory. Advances in Engineering Software, 35(10-11), 663­ 667.

[9]

International Journal of Earth Sciences and Engineering ISSN 0974-5904, Volume 04, No 06 SPL, October 2011, pp. 200-203

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