an earthquake of magnitude 7.0 or greater has not occurred in either the san francisco or the los...

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.

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 Francisco1906

M = 7.9 (est.)

Loma Prieta 1989

M = 6.9

STATEWIDE

For M>=6.7 earthquakes

Indeed, scientists calculate significant earthquake hazards

for many parts of California.

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?

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.

In this exercise, you will use 30 years of earthquake history (1983-2012) 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.

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.

On the worksheet, the number of earthquakes for the San Francisco area has been entered in column B.

San Francisco areaA B

magnitude range

total # of earthquakes 1983-2012(30 years)

from database

2.0-2.9 17163.0-3.9 13264.0-4.9 1615.0-5.9 136.0-6.9 37.0-7.9 08.0-8.9 09.0-9.9 0

Recall that earthquakes of magnitude 7.0-7.9 (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).

San Francisco areaA B

magnitude range


from database

2.0-2.9 17163.0-3.9 13264.0-4.9 1615.0-5.9 136.0-6.9 37.0-7.9 08.0-8.9 09.0-9.9 0

Recall that earthquakes of magnitude 7.0-7.9 (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.

On the worksheet, the number of earthquakes for the San Francisco area has been entered in Column B.

San Francisco areaA B C

magnitude range


average # ofearthquakes

per year

from database

2.0-2.9 1716 57.203.0-3.9 13264.0-4.9 1615.0-5.9 136.0-6.9 37.0-7.9 08.0-8.9 09.0-9.9 0

1716/30 = 57.20

On average, 57.2 earthquakes of magnitude 2.0-2.9 occur in this area every year.

Column C: Calculate the average number of earthquakes that occurred in each magnitude range, by dividing Column B by 30.


magnitude range



per year

from database

2.0-2.9 1716 57.203.0-3.9 13264.0-4.9 1615.0-5.9 136.0-6.9 37.0-7.9 08.0-8.9 09.0-9.9 0

1716/30 = 57.20


Complete Column C.



magnitude range



per year

from database

2.0-2.9 1716 57.203.0-3.9 1326 44.24.0-4.9 161 5.375.0-5.9 13 0.436.0-6.9 3 0.107.0-7.9 0 08.0-8.9 0 09.0-9.9 0 0

San Francisco areaA B C D

magnitude range



per year

MRI(mean

recurrence interval) in years

from database

2.0-2.9 1716 57.20 0.0173.0-3.9 1326 44.24.0-4.9 161 5.375.0-5.9 13 0.436.0-6.9 3 0.107.0-7.9 0 08.0-8.9 0 09.0-9.9 0 0

On average, an earthquake of this size occurs in this area every 0.017

years, or every 6.25 days:

0.017 yr x 365 days/yr = 6.25 days.

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.


magnitude range



per year

MRI(mean


from database

2.0-2.9 1716 57.20 0.0173.0-3.9 1326 44.24.0-4.9 161 5.375.0-5.9 13 0.436.0-6.9 3 0.107.0-7.9 0 08.0-8.9 0 09.0-9.9 0 0

Complete Column D.



magnitude range



per year

MRI(mean


from database

2.0-2.9 1716 57.20 0.0173.0-3.9 1326 44.2 0.0234.0-4.9 161 5.37 0.1865.0-5.9 13 0.43 2.3086.0-6.9 3 0.10 10.0007.0-7.9 0 08.0-8.9 0 09.0-9.9 0 0


Straightforward for these magnitude ranges…


magnitude range



per year

MRI(mean


from database

2.0-2.9 1716 57.20 0.0173.0-3.9 1326 44.2 0.0234.0-4.9 161 5.37 0.1865.0-5.9 13 0.43 2.3086.0-6.9 3 0.10 10.0007.0-7.9 0 08.0-8.9 0 09.0-9.9 0 0

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 ??


magnitude range



per year

MRI(mean


from database

2.0-2.9 1716 57.20 0.0173.0-3.9 1326 44.2 0.0234.0-4.9 161 5.37 0.1865.0-5.9 13 0.43 2.3086.0-6.9 3 0.10 10.0007.0-7.9 0 08.0-8.9 0 09.0-9.9 0 0

MRI = 1/0 ??

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.


2.0-2.9 3.0-3.9 4.0-4.9 5.0-5.9 6.0-6.9 7.0-7.9 8.0-8.9 9.0-9.90.010

0.100

1.000

10.000

100.000

1000.000

10000.000

Mean Recurrence Interval (MRI)vs.

Magnitude

MRI

(yea

rs)

Column D: Determining extrapolated MRIs-- On the graph, plot MRIs for earthquakes that have

occurred

San Francisco areaA D

magnitude range

MRI(mean


2.0-2.9 0.0173.0-3.9 0.0234.0-4.9 0.1865.0-5.9 2.3086.0-6.9 10.0007.0-7.98.0-8.99.0-9.9

2.0-2.9 3.0-3.9 4.0-4.9 5.0-5.9 6.0-6.9 7.0-7.9 8.0-8.9 9.0-9.90.010

0.100

1.000

10.000

100.000

1000.000

10000.000


Magnitude

MRI

(yea

rs)

Column D: Determining extrapolated MRIs


magnitude range

MRI(mean


2.0-2.9 0.0173.0-3.9 0.0234.0-4.9 0.1865.0-5.9 2.3086.0-6.9 10.0007.0-7.98.0-8.99.0-9.9

Draw in and extrapolate a best-fit line, then read off extrapolated MRIs for the remaining magnitudes.

2.0-2.9 3.0-3.9 4.0-4.9 5.0-5.9 6.0-6.9 7.0-7.9 8.0-8.9 9.0-9.90.010

0.100

1.000

10.000

100.000

1000.000

10000.000


Magnitude

MRI

(yea

rs)

Column D: Determining extrapolated MRI’s


magnitude range

MRI(mean


2.0-2.9 0.0173.0-3.9 0.0234.0-4.9 0.1865.0-5.9 2.3086.0-6.9 10.0007.0-7.9 508.0-8.9 3009.0-9.9 1600

San Francisco areaA C D E F

magnitude range


per year

MRI(mean


one year probability

of earthquake occurring

of earthquake not occurring

fractional % fractional %2.0-2.9 57.20 0.017 0 0%3.0-3.9 44.20 0.023 4.0-4.9 5.37 0.186 5.0-5.9 0.43 2.308 6.0-6.9 0.10 10.000 0.900 90%7.0-7.9 0 50 8.0-8.9 0 300 9.0-9.9 0 1600

Column E: Determining the probability of an earthquake occurring in one year.


magnitude range


per year

MRI(mean





fractional % fractional %2.0-2.9 57.20 0.017 1.000 100% 0 0%3.0-3.9 44.20 0.023 1.000 100% 4.0-4.9 5.37 0.186 1.000 100% 5.0-5.9 0.43 2.308 6.0-6.9 0.10 10.000 0.900 90%7.0-7.9 0 50 8.0-8.9 0 300 9.0-9.9 0 1600


• For earthquakes with MRIs of one year or less

1/1 = 1.0 or 100%


magnitude range


per year

MRI(mean





fractional % fractional %2.0-2.9 57.20 0.017 1.000 100% 0 0%3.0-3.9 44.20 0.023 1.000 100% 4.0-4.9 5.37 0.186 1.000 100% 5.0-5.9 0.43 2.308 0.43 6.0-6.9 0.10 10.000 0.900 90%7.0-7.9 0 50 8.0-8.9 0 300 9.0-9.9 0 1600


• For earthquakes with MRIs greater than one year:

Fractional probability

= 1 / MRI

1 / 2.308 = 0.43


magnitude range


per year

MRI(mean





fractional % fractional %2.0-2.9 57.20 0.017 1.000 100% 0 0%3.0-3.9 44.20 0.023 1.000 100% 4.0-4.9 5.37 0.186 1.000 100% 5.0-5.9 0.43 2.308 0.43 6.0-6.9 0.10 10.000 0.900 90%7.0-7.9 0 50 8.0-8.9 0 300 9.0-9.9 0 1600



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!


= 1 / MRI

1 / 2.308 = 0.43


magnitude range


per year

MRI(mean





fractional % fractional %2.0-2.9 57.20 0.017 1.000 100% 0 0%3.0-3.9 44.20 0.023 1.000 100% 4.0-4.9 5.37 0.186 1.000 100% 5.0-5.9 0.43 2.308 0.43 43% 6.0-6.9 0.10 10.000 0.900 90%7.0-7.9 0 50 8.0-8.9 0 300 9.0-9.9 0 1600



Multiply by 100 to get %


= 1 / MRI


magnitude range


per year

MRI(mean





fractional % fractional %2.0-2.9 57.20 0.017 1.000 100% 0 0%3.0-3.9 44.20 0.023 1.000 100% 4.0-4.9 5.37 0.186 1.000 100% 5.0-5.9 0.43 2.308 0.43 43% 6.0-6.9 0.10 10.000 0.900 90%7.0-7.9 0 50 8.0-8.9 0 300 9.0-9.9 0 1600



Multiply by 100 to get %


= 1 / MRI

Complete Column E.


magnitude range


per year

MRI(mean





fractional % fractional %2.0-2.9 57.20 0.017 1.000 100% 0 0%3.0-3.9 44.20 0.023 1.000 100% 4.0-4.9 5.37 0.186 1.000 100% 5.0-5.9 0.43 2.308 0.43 43% 6.0-6.9 0.10 10.000 0.10 10% 0.900 90%7.0-7.9 0 50 0.02 2% 8.0-8.9 0 300 0.003 0.3% 9.0-9.9 0 1600 0.0006 0.06%


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, and2) 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!


magnitude range


per year

MRI(mean





fractional % fractional %2.0-2.9 57.20 0.017 1.000 100% 0.00 0%3.0-3.9 44.20 0.023 1.000 100%4.0-4.9 5.37 0.186 1.000 100%5.0-5.9 0.43 2.308 0.43 43% 0.57 57%6.0-6.9 0.10 10.000 0.10 10%7.0-7.9 0 50 0.02 2% 8.0-8.9 0 300 0.003 0.3% 9.0-9.9 0 1600 0.0006 0.06%

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)

1.0 - 0.43 = 0.57or 57%

1.0 – 1.0 = 0.0or 0%


magnitude range


per year

MRI(mean





fractional % fractional %2.0-2.9 57.20 0.017 1.000 100% 0.00 0%3.0-3.9 44.20 0.023 1.000 100%4.0-4.9 5.37 0.186 1.000 100%5.0-5.9 0.43 2.308 0.43 43% 0.57 57%6.0-6.9 0.10 10.000 0.10 10%7.0-7.9 0 50 0.02 2% 8.0-8.9 0 300 0.003 0.3% 9.0-9.9 0 1600 0.0006 0.06%


= 1.0 or 100% minus the probability of it occurring(i.e. either it happens or it does not)

1.0 - 0.43 = 0.57or 57%

1.0 – 1.0 = 0.0or 0%

Complete Column F.


magnitude range


per year

MRI(mean





fractional % fractional %2.0-2.9 57.20 0.017 1.000 100% 0.00 0%3.0-3.9 44.20 0.023 1.000 100% 0.00 0%4.0-4.9 5.37 0.186 1.000 100% 0.00 0%5.0-5.9 0.43 2.308 0.43 43% 0.57 57%6.0-6.9 0.10 10.000 0.10 10% 0.90 90%7.0-7.9 0 50 0.02 2% 0.98 98%8.0-8.9 0 300 0.003 0.3% 0.997 99.7%9.0-9.9 0 1600 0.0006 0.06% 0.9994 99.94%


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 6.0-6.9 earthquake occurring in the San Francisco area in the next 30 years?


magnitude range


per year

MRI(mean





fractional % fractional %2.0-2.9 57.20 0.017 1.000 100% 0.00 0%3.0-3.9 44.20 0.023 1.000 100% 0.00 0%4.0-4.9 5.37 0.186 1.000 100% 0.00 0%5.0-5.9 0.43 2.308 0.43 43% 0.57 57%6.0-6.9 0.10 10.000 0.10 10% 0.90 90%7.0-7.9 0 50 0.02 2% 0.98 98%8.0-8.9 0 300 0.003 0.3% 0.997 99.7%9.0-9.9 0 1600 0.0006 0.06% 0.9994 99.94%

First, find the probability of a 6.0-6.9 earthquake not occurring in one year.

Then…

If the probability of a 6.0-6.9 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= 0.902 = 0.81 or 81%,

- the probability of it not occurring in three years is0.90 x 0.90 x 0.90 = 0.903 = 0.729 or 73%,

- the probability of it not occurring in 30 years is 0.9030

0.9030 = 0.042 = 4%

If the probability of a 6.0-6.9 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= 0.902 = 0.81 or 81%,

- the probability of it not occurring in three years is0.90 x 0.90 x 0.90 = 0.903 = 0.729 or 73%,

- the probability of it not occurring in 30 years is 0.9030

0.9030 = 0.042 = 4%

And so the probability of it occurring in 30 years is

1 – 0.042 = 0.958 = 96%

This is how scientists calculate earthquake

probabilities – and thus quantify the

hazard.

No earthquake with magnitude 7.0-7.9 has occurred in the San Francisco area over the 30-year study period.

1a. Calculate the probability of a M = 7.0-7.9 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?

Probability of a M = 7.0 - 7.9 earthquake not occurring in the San Francisco area in one year (from worksheet).

0.98 = 98%

Probability of a M = 7.0 - 7.9 earthquake not occurring in the San Francisco area in 30 years:

0.9830 = 54.4%

Probability of a M = 7.0 - 7.9 earthquake occurring in the San Francisco area in 30 years:

1 – 54.4 = 45.6% or close to a 50:50 chance

Probability of a M = 7.0 - 7.9 earthquake not occurring in the San Francisco area in one year (from worksheet).

0.98 = 98%

Probability of a M = 7.0 - 7.9 earthquake not occurring in the San Francisco area in 30 years:

0.9830 = 54.4%

Probability of a M = 7.0 - 7.9 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.

2. Suppose that a particular area has a MRI of 30 years for earthquakes of M = 6.0-6.9. 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?

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.

Further applications (optional)

4. Use the provided spreadsheet and graph to repeat the analysis for the Los Angeles area.

5. What is the probability of a magnitude 7.0-7.9

earthquake in the Los Angeles area in the next 30 years? How does this compare to what you calculated for a magnitude 7.0-7.9 earthquake in the San Francisco area?

an earthquake of magnitude 7.0 or greater has not occurred in either the san francisco or the los...

Documents

earthquake of magnitude

earthquakes of magnitude

years of earthquake

number of earthquakes

probabilities of earthquakes

regional earthquake

smaller earthquakes

san francisco1906