1. An earthquake of magnitude 7
An earthquake of magnitude 7.0 or greater has not occurred in either the San Francisco or the Los Angeles area for over 100 years.

2. An earthquake of magnitude 7
An earthquake of magnitude 7.0 or greater has not occurred in either the San Francisco or the Los Angeles area for over 100 years.
But we do know that they do occur and have devastating consequences (as can smaller earthquakes).
San Francisco
1906
M = 7.9 (est.)
Loma Prieta
1989
M = 6.9
Credit: USGS
Image sources:
Accessed December 2013

3. STATEWIDE
For M>=6.7 earthquakes
Indeed, scientists calculate significant earthquake hazards for many parts of California.
Credit: USGS, California Geological Survey, Southern California Earthquake Center
Source:
Accessed December 2013

4. How do scientists calculate the probability of such events occurring?
STATEWIDE
For M>=6.7 earthquakes
How do scientists calculate the probability of such events occurring?
…Especially if they have not happened in the past?
Credit: USGS, California Geological Survey, Southern California Earthquake Center
Source:
Accessed December 2013

5. Learning objectives for this activity:
To use data to determine the probabilities of earthquakes of various magnitudes in the San Francisco and Los Angeles areas.
To compare your results to the regional earthquake probability map for California and assess the regional earthquake hazard along this plate boundary.
Google Earth Imagery with data from SIO, NOAA, U.S. Navy, NGA, GEBCO, LDEO-Columbia, NSF, NOAA.
Accessed December 2013.

6. In this exercise, you will use 30 years of earthquake history ( ) to determine probabilities of large earthquakes over the next year, and over the next 30 years.
The data for come from two searchable databases, based on the parameters below.
Google Earth Imagery with data from SIO, NOAA, U.S. Navy, NGA, GEBCO, LDEO-Columbia, NSF, NOAA.
Accessed December 2013.

7. This presentation helps you work through the data for the San Francisco area. Then you will have the opportunity to do the Los Angeles area on your own.
Google Earth Imagery with data from SIO, NOAA, U.S. Navy, NGA, GEBCO, LDEO-Columbia, NSF, NOAA.
Accessed December 2013.

8. total # of earthquakes 1983-2012 (30 years)
On the worksheet, the number of earthquakes for the San Francisco area has been entered in column B.
San Francisco area A B
magnitude range
total # of earthquakes (30 years)
from database
1716
1326
161 13 3
Recall that earthquakes of magnitude (and greater) have not occurred in this area during the 30-year study period, although we know they have occurred there in the past (e.g. 1906).
Earthquake counts for each magnitude range for the 30-year time period and the area between °N latitude and °W longitude, obtained in December 2013 using the USGS earthquake search engine:

9. total # of earthquakes 1983-2012 (30 years)
On the worksheet, the number of earthquakes for the San Francisco area has been entered in Column B.
San Francisco area A B
magnitude range
total # of earthquakes (30 years)
from database
1716
1326
161 13 3
Recall that earthquakes of magnitude (and greater) have not occurred in this area during the 30-year study period, although we know they have occurred there in the past (e.g. 1906).
What is the likelihood that such earthquakes (and earthquakes of other magnitude sizes) will occur in this area in the future?
…Probability analysis can give an estimate of this likelihood.
Earthquake counts for each magnitude range for the 30-year time period and the area between °N latitude and °W longitude, obtained in December 2013 using the USGS earthquake search engine:

10. Column C: Calculate the average number of earthquakes that occurred in each magnitude range, by dividing Column B by 30.
San Francisco area A B C
magnitude range
total # of earthquakes (30 years)
average # of earthquakes per year
from database
1716
57.20
1326
161 13 3
1716/30 = 57.20
On average, 57.2 earthquakes of magnitude occur in this area every year.
Earthquake counts for each magnitude range for the 30-year time period and the area between °N latitude and °W longitude, obtained in December 2013 using the USGS earthquake search engine:

11. Column C: Calculate the average number of earthquakes that occurred in each magnitude range, by dividing Column B by 30.
San Francisco area A B C
magnitude range
total # of earthquakes (30 years)
average # of earthquakes per year
from database
1716
57.20
1326
161 13 3
1716/30 = 57.20
Earthquake counts for each magnitude range for the 30-year time period and the area between °N latitude and °W longitude, obtained in December 2013 using the USGS earthquake search engine:
Complete Column C.

12. Column C: Calculate the average number of earthquakes that occurred in each magnitude range, by dividing Column B by 30.
San Francisco area A B C
magnitude range
total # of earthquakes (30 years)
average # of earthquakes per year
from database
1716
57.20
1326
44.2
161
5.37 13
0.43 3
0.10
Earthquake counts for each magnitude range for the 30-year time period and the area between °N latitude and °W longitude, obtained in December 2013 using the USGS earthquake search engine:

13. Column D: Calculate the mean recurrence interval (MRI), or average time between earthquakes, for each magnitude range. One way to get this is to take the reciprocal of the average number of earthquakes per year.
San Francisco area A B C D
magnitude range
total # of earthquakes (30 years)
average # of earthquakes per year
MRI (mean recurrence interval) in years
from database
1716
57.20
0.017
1326
44.2
161
5.37 13
0.43 3
0.10
Earthquake counts for each magnitude range for the 30-year time period and the area between °N latitude and °W longitude, obtained in December 2013 using the USGS earthquake search engine:
On average, an earthquake of this size occurs in this area every years, or every 6.25 days:
0.017 yr x 365 days/yr = 6.25 days.

14. Column D: Calculate the mean recurrence interval (MRI), or average time between earthquakes, for each magnitude range. One way to get this is to take the reciprocal of the average number of earthquakes per year.
San Francisco area A B C D
magnitude range
total # of earthquakes (30 years)
average # of earthquakes per year
MRI (mean recurrence interval) in years
from database
1716
57.20
0.017
1326
44.2
161
5.37 13
0.43 3
0.10
Earthquake counts for each magnitude range for the 30-year time period and the area between °N latitude and °W longitude, obtained in December 2013 using the USGS earthquake search engine:
Complete Column D.

15. Column D: Calculate the mean recurrence interval (MRI), or average time between earthquakes, for each magnitude range. One way to get this is to take the reciprocal of the average number of earthquakes per year.
San Francisco area A B C D
magnitude range
total # of earthquakes (30 years)
average # of earthquakes per year
MRI (mean recurrence interval) in years
from database
1716
57.20
0.017
1326
44.2
0.023
161
5.37
0.186 13
0.43
2.308 3
0.10
10.000
Earthquake counts for each magnitude range for the 30-year time period and the area between °N latitude and °W longitude, obtained in December 2013 using the USGS earthquake search engine:
Straightforward for these magnitude ranges…

16. Column D: Calculate the mean recurrence interval (MRI), or average time between earthquakes, for each magnitude range. One way to get this is to take the reciprocal of the average number of earthquakes per year.
San Francisco area A B C D
magnitude range
total # of earthquakes (30 years)
average # of earthquakes per year
MRI (mean recurrence interval) in years
from database
1716
57.20
0.017
1326
44.2
0.023
161
5.37
0.186 13
0.43
2.308 3
0.10
10.000
But how do we determine MRIs for earthquakes of greater size that have not occurred in the study period – especially when we know they have occurred in the past?
MRI = 1/0 ??

17. Column D: Calculate the mean recurrence interval (MRI), or average time between earthquakes, for each magnitude range. One way to get this is to take the reciprocal of the average number of earthquakes per year.
San Francisco area A B C D
magnitude range
total # of earthquakes (30 years)
average # of earthquakes per year
MRI (mean recurrence interval) in years
from database
1716
57.20
0.017
1326
44.2
0.023
161
5.37
0.186 13
0.43
2.308 3
0.10
10.000
But how do we determine MRIs for earthquakes of greater size that have not occurred in the study period – especially when we know they have occurred in the past?
… we extrapolate from data for those that have occurred.
Earthquake counts for each magnitude range for the 30-year time period and the area between °N latitude and °W longitude, obtained in December 2013 using the USGS earthquake search engine:
MRI = 1/0 ??

18. MRI (mean recurrence interval) in years
Column D: Determining extrapolated MRIs
-- On the graph, plot MRIs for earthquakes that have occurred
San Francisco area A D
magnitude range
MRI (mean recurrence interval) in years
0.017
0.023
0.186
2.308
10.000

19. MRI (mean recurrence interval) in years
Column D: Determining extrapolated MRIs
Draw in and extrapolate a best-fit line, then read off extrapolated MRIs for the remaining magnitudes.
San Francisco area A D
magnitude range
MRI (mean recurrence interval) in years
0.017
0.023
0.186
2.308
10.000

20. MRI (mean recurrence interval) in years
Column D: Determining extrapolated MRI’s
San Francisco area A D
magnitude range
MRI (mean recurrence interval) in years
0.017
0.023
0.186
2.308
10.000 50
 300
 1600

21. Column E: Determining the probability of an earthquake occurring in one year.
San Francisco area A C D E F
magnitude range
average # of earthquakes per year
MRI (mean recurrence interval) in years
one year probability
of earthquake occurring
of earthquake not occurring
fractional %
57.20
0.017 0%
44.20
0.023
5.37
0.186
0.43
2.308
0.10
10.000
0.900
90% 50
 300
 1600

22. For earthquakes with MRIs of one year or less
Column E: Determining the probability of an earthquake occurring in one year.
For earthquakes with MRIs of one year or less
San Francisco area A C D E F
magnitude range
average # of earthquakes per year
MRI (mean recurrence interval) in years
one year probability
of earthquake occurring
of earthquake not occurring
fractional %
57.20
0.017
1.000
100% 0%
44.20
0.023
5.37
0.186
0.43
2.308
0.10
10.000
0.900
90% 50
 300
 1600
1/1 = 1.0 or 100%

23. For earthquakes with MRIs greater than one year:
Column E: Determining the probability of an earthquake occurring in one year.
For earthquakes with MRIs greater than one year:
San Francisco area A C D E F
magnitude range
average # of earthquakes per year
MRI (mean recurrence interval) in years
one year probability
of earthquake occurring
of earthquake not occurring
fractional %
57.20
0.017
1.000
100% 0%
44.20
0.023
5.37
0.186
0.43
2.308
 0.43
0.10
10.000
0.900
90% 50
 300
 1600
Fractional probability
= 1 / MRI
1 / = 0.43

24. For earthquakes with MRIs greater than one year:
Column E: Determining the probability of an earthquake occurring in one year.
For earthquakes with MRIs greater than one year:
San Francisco area A C D E F
magnitude range
average # of earthquakes per year
MRI (mean recurrence interval) in years
one year probability
of earthquake occurring
of earthquake not occurring
fractional %
57.20
0.017
1.000
100% 0%
44.20
0.023
5.37
0.186
0.43
2.308
 0.43
0.10
10.000
0.900
90% 50
 300
 1600
Fractional probability
= 1 / MRI
1 / = 0.43
This is also equal to the average # of earthquakes per year. But the 1/ MRI method allows calculation of probabilities for earthquakes that have not occurred - because we have extrapolated MRIs!

25. For earthquakes with MRIs greater than one year:
Column E: Determining the probability of an earthquake occurring in one year.
For earthquakes with MRIs greater than one year:
San Francisco area A C D E F
magnitude range
average # of earthquakes per year
MRI (mean recurrence interval) in years
one year probability
of earthquake occurring
of earthquake not occurring
fractional %
57.20
0.017
1.000
100% 0%
44.20
0.023
5.37
0.186
0.43
2.308
 0.43
 43%
0.10
10.000
0.900
90% 50
 300
 1600
Fractional probability
= 1 / MRI
Multiply by 100 to get %

26. For earthquakes with MRIs greater than one year:
Column E: Determining the probability of an earthquake occurring in one year.
For earthquakes with MRIs greater than one year:
San Francisco area A C D E F
magnitude range
average # of earthquakes per year
MRI (mean recurrence interval) in years
one year probability
of earthquake occurring
of earthquake not occurring
fractional %
57.20
0.017
1.000
100% 0%
44.20
0.023
5.37
0.186
0.43
2.308
 0.43
 43%
0.10
10.000
0.900
90% 50
 300
 1600
Fractional probability
= 1 / MRI
Multiply by 100 to get %
Complete Column E.

27. Column E: Determining the probability of an earthquake occurring in one year.
San Francisco area A C D E F
magnitude range
average # of earthquakes per year
MRI (mean recurrence interval) in years
one year probability
of earthquake occurring
of earthquake not occurring
fractional %
57.20
0.017
1.000
100% 0%
44.20
0.023
5.37
0.186
0.43
2.308
 0.43
 43%
0.10
10.000
10%
0.900
90% 50
0.02 
 2%
 300
0.003 
 0.3%
 1600
0.0006 
 0.06%

28. We have just calculated annual probabilities of earthquakes.
But what about longer time periods?
The probability of an earthquake occurring over any time period is 1 (or 100%) minus the probability of the earthquake not occurring over that time period (either it happens or it does not).
So, consider a two-year time period. For an earthquake to not occur over two years, two conditions must be met:
1) The earthquake must not occur in the 1st year, and
2) The earthquake must not occur in the 2nd year.
And to get the combined probability, we multiply the individual probabilities of the two events.
Thus we need to determine the probability of an earthquake not occurring in one year…and that is easy!

29. = 1.0 or 100% minus the probability of it occurring
Column F: Determining the probability of an earthquake not occurring in one year.
= 1.0 or 100% minus the probability of it occurring
(i.e. either it happens or it does not)
San Francisco area A C D E F
magnitude range
average # of earthquakes per year
MRI (mean recurrence interval) in years
one year probability
of earthquake occurring
of earthquake not occurring
fractional %
57.20
0.017
1.000
100%
0.00 0%
44.20
0.023
5.37
0.186
0.43
2.308
 0.43
 43%
0.57 
 57%
0.10
10.000
10% 50
0.02 
 2%
 300
0.003 
 0.3%
 1600
0.0006 
 0.06%
1.0 – 1.0 = 0.0
or 0%
= 0.57
or 57%

30. = 1.0 or 100% minus the probability of it occurring
Column F: Determining the probability of an earthquake not occurring in one year.
= 1.0 or 100% minus the probability of it occurring
(i.e. either it happens or it does not)
San Francisco area A C D E F
magnitude range
average # of earthquakes per year
MRI (mean recurrence interval) in years
one year probability
of earthquake occurring
of earthquake not occurring
fractional %
57.20
0.017
1.000
100%
0.00 0%
44.20
0.023
5.37
0.186
0.43
2.308
 0.43
 43%
0.57 
 57%
0.10
10.000
10% 50
0.02 
 2%
 300
0.003 
 0.3%
 1600
0.0006 
 0.06%
1.0 – 1.0 = 0.0
or 0%
= 0.57
or 57%
Complete Column F.

31. Column F: Determining the probability of an earthquake not occurring in one year.
San Francisco area A C D E F
magnitude range
average # of earthquakes per year
MRI (mean recurrence interval) in years
one year probability
of earthquake occurring
of earthquake not occurring
fractional %
57.20
0.017
1.000
100%
0.00 0%
44.20
0.023
5.37
0.186
0.43
2.308
 0.43
 43%
0.57 
 57%
0.10
10.000
10%
0.90
90% 50
0.02 
 2%
 0.98
 98%
 300
0.003 
 0.3%
 0.997
 99.7%
 1600
0.0006 
 0.06%
 0.9994
 99.94%

32. Now we have the information we need in order to determine earthquake probabilities for time periods longer than one year. For example:
What is the probability of a earthquake occurring in the San Francisco area in the next 30 years?

33. First, find the probability of a 6.0-6.9 earthquake
not occurring in one year.
San Francisco area A C D E F
magnitude range
average # of earthquakes per year
MRI (mean recurrence interval) in years
one year probability
of earthquake occurring
of earthquake not occurring
fractional %
57.20
0.017
1.000
100%
0.00 0%
44.20
0.023
5.37
0.186
0.43
2.308
 0.43
 43%
0.57 
 57%
0.10
10.000
10%
0.90
90% 50
0.02 
 2%
 0.98
 98%
 300
0.003 
 0.3%
 0.997
 99.7%
 1600
0.0006 
 0.06%
 0.9994
 99.94%
Then…

34. If the probability of a 6. 0-6
If the probability of a earthquake not occurring in the San Francisco area in one year is 0.90,
- the probability of it not occurring in two years is
0.90 x 0.90= = 0.81 or 81%,
- the probability of it not occurring in three years is
0.90 x 0.90 x 0.90 = = or 73%,
- the probability of it not occurring in 30 years is
= = 4%

35. If the probability of a 6. 0-6
If the probability of a earthquake not occurring in the San Francisco area in one year is 0.90,
- the probability of it not occurring in two years is
0.90 x 0.90= = 0.81 or 81%,
- the probability of it not occurring in three years is
0.90 x 0.90 x 0.90 = = or 73%,
- the probability of it not occurring in 30 years is
= = 4%
And so the probability of it occurring in 30 years is
1 – = = 96%

36. This is how scientists calculate earthquake probabilities – and thus quantify the hazard.
Credit: USGS, California Geological Survey, Southern California Earthquake Center
Source:
Accessed December 2013

37. No earthquake with magnitude 7. 0-7
No earthquake with magnitude has occurred in the San Francisco area over the 30-year study period.
1a. Calculate the probability of a M = earthquake occurring in the San Francisco area in the next 30 years.
1b. Do you think this is high enough to warrant concern? Why or why not?

38. 1 – 54.4 = 45.6% or close to a 50:50 chance
Probability of a M = earthquake not occurring in the San Francisco area in one year (from worksheet).
0.98 = 98%
Probability of a M = earthquake not occurring in the San Francisco area in 30 years:
= 54.4%
Probability of a M = earthquake occurring in the San Francisco area in 30 years:
1 – 54.4 = 45.6% or close to a 50:50 chance

39. 1 – 54.4 = 45.6% or close to a 50:50 chance!
Probability of a M = earthquake not occurring in the San Francisco area in one year (from worksheet).
0.98 = 98%
Probability of a M = earthquake not occurring in the San Francisco area in 30 years:
= 54.4%
Probability of a M = earthquake occurring in the San Francisco area in 30 years:
1 – 54.4 = 45.6% or close to a 50:50 chance!
So even though an earthquake of magnitude 7.0 or greater has not occurred in the San Francisco area in over 100 years, there is a 50:50 chance that it will occur in the next 30 years.

40. 2. Suppose that a particular area has a MRI of 30 years for earthquakes of M = Suppose a M=6.7 earthquake occurs in that area this year. How does this affect the probability of such an earthquake occurring next year?

41. 3. This map shows a 99% chance of a damaging earthquake occurring somewhere in the state in the next 30 years.
Should resources for earthquake preparedness be spread evenly across the state? Support your position.
Credit: USGS, California Geological Survey, Southern California Earthquake Center
Source:
Accessed December 2013

42. Further applications (optional)
4. Use the provided spreadsheet and graph to repeat the analysis for the Los Angeles area.
What is the probability of a magnitude earthquake in the Los Angeles area in the next 30 years? How does this compare to what you calculated for a magnitude earthquake in the San Francisco area?