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CE 5603 Seismic Hazard Assessment Middle East Technical University, Ankara,Turkey Department of Civil Engineering Prof. Dr. K. Önder Çetin 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. Önder Çetin 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. Önder Çetin 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