# Assignment 1 - Middle East Technical University

```CE 5603 Seismic Hazard Assessment
Middle East Technical University, Ankara,Turkey
Department of Civil Engineering
Prof. Dr. K. &Ouml;nder &Ccedil;etin
ASSIGNMENT 4 – Recurrence Rates and Probability Density Functions
1. A sub-zone of the North Anatolian Fault System (Bursa segment) lies within the city
boundaries of Bursa in the nearly pure E-W direction and merging with the North
Anatolian Fault Zone in the NE direction; having a right lateral strike-slip mechanism.
The earthquakes having magnitudes greater or equal to 4.0 ( M  4.0) that were
recorded during the instrumental period of 1900-2003 and the fault geometry are
shown in Figure 1. Table 1 shows the list of earthquakes with respect to their dates
and magnitudes. All of the events plotted in Figure 1 can be considered to have
originated from the Bursa Fault System. Calculate the Gutenberg-Richter Parameters,
a, b,  and  for the given fault based on the available observational data.
Figure 1 : Bursa Fault and nearby events recorded during the last century.
Assignment 4 : Recurrence Rates and Probability Density Functions
CE 5603 Seismic Hazard Assessment
Middle East Technical University, Ankara,Turkey
Department of Civil Engineering
Prof. Dr. K. &Ouml;nder &Ccedil;etin
Table 1 : List of the events shown in Figure 1.
Event No
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
Date
15/04/1905
13/11/1948
03/06/1953
06/10/1964
06/10/1964
20/11/1964
09/11/1968
06/09/1970
21/07/1981
22/07/1981
09/06/1982
01/02/1983
03/11/1983
21/10/1983
27/10/1983
01/01/1988
22/03/1992
21/02/1994
06/09/2003
Magnitude
5.6
5.6
5.3
5.0
7.0
4.1
4.2
4.0
4.1
4.0
4.4
4.8
4.0
4.9
4.3
4.5
4.9
4.0
5.1
2. North Anatolian Fault (NAF) Segment Source Parameters are given below:
Length of Eastern NAF segment = 30 km
Length of Western NAF segment = 50 km
Width of both segments = 10 km
Slip rate = 19 mm/year
Shear Modulus,  = 3.0 1011 dyne/cm2
b value = 0.9
Minimum Magnitude of Interest = 5.0
i)
Assuming the NAF is unsegmented, by balancing the moment-rate, compute
and plot earthquake recurrence relation on the NAF for the two magnitude
density functions listed below:
a. Truncated exponential (truncated at minimum moment magnitude, 5.0 and
maximum magnitude)
b. Youngs and Coppersmith (1985) characteristic model
Assignment 4 : Recurrence Rates and Probability Density Functions
CE 5603 Seismic Hazard Assessment
Middle East Technical University, Ankara,Turkey
ii)
Department of Civil Engineering
Prof. Dr. K. &Ouml;nder &Ccedil;etin
Which model leads to the largest number of earthquakes above magnitude 5.0?
Above magnitude 7?
iii)
Does the difference between earthquake recurrence relations for these two
models represent epistemic uncertainty or aleatory variability?
3. Assuming the NAF is segmented, by balancing the moment-rate, compute and plot
earthquake recurrence relation on the NAF for Youngs and Coppersmith (1985)
characteristic model.
4. For a moment magnitude, Mw= 6.5, plot probability density function for the rupture
length and rupture area and estimate probability of exceedences for rupture length and
rupture area of 30 km and 150 km2 respectively.
Assignment 4 : Recurrence Rates and Probability Density Functions
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