10 0 50 100 150 200 250 300 350 400 Recurrence Time (yr) Figure 3. 7. Figure 3 i
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10 0 50 100 150 200 250 300 350 400 Recurrence Time (yr) Figure 3. 7. Figure 3 is a histogram showing the number of Mw>6 earthquakes sorted by recurrence interval (the number of years since the last earthquake). Let's use ti to denote the time of last Mw>6 earthquake along this segment of the fault. Predict the probabilities of an Mw>6 earthquake in next 50 yrs (i.e, 2018-2068) for t1 1918, 1818 and 1718. (Hint: if the last earthquake occurred in 1918, what would be the recurrence time if the next one occurred in 2018?)Explanation / Answer
See imagine that the last earthquake(Mw>6) happened in 1918. Then the recurrence time for one to happen in 2018 is 100yrs. Now from the histogram we obtain that for a recurrence time of 100-150 yrs the frequency of earthquake is 4.
Now take t1=1918. Then between 1918 to 2068 the recurence time is 150 yrs, for which the frequency is 8. Therefore in this duration 6 earthquakes could have happened. But as we understood in the above paragraph that 4 earthquakes would have happended in the first 100 years(1918-2018) and hence only two in 2018-68. Therefore, for t1=1918 the probability of an in 2018-68 earthquake is 2/8. Let this be p1=0.25
Generalising: let x= frequency of earthquakes in t1-2018 and y=t1-2068
therefore p=(y-x/)y
Simillarly for t1=1818 the recurrence time till 2018 is 200yrs. Frequency=8
And from 1818to 2068 it is 250 yrs frequency=10
Therefore 2 earthquakes in the 2018-68 with probability=2/10
let p2 =2/10=0.2
Simillary for t1=1718. Till 2018 the recurrence period is 300yrs. Therefore 8 earthquakes. Now for 1718-2068 frequency is 6. Therefore since till 2018 all 6 would have been included in the 8. p3=0
Hence the total probability of Mw>6 Earthquakes in 2018-68 is p1 + p2 + p3=0.25+0.2+0=0.45
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