Assignment4_EarthquakeHazard_50_EMES101.ALL_Fall23
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Dec 6, 2023
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EMES101.ALL Fall23
Assignment Grade: up to 12 points
Group Contribution Grade: up to 3 points
Assignment 4: Determining Earthquake Hazard
Group Number:
Group Members Present (first and last names): Each group member present must WRITE THEIR OWN NAME above to earn credit for contributing to the assignment. Do not write the names of group members who are not present. Scribes’ initials:
Share the scribe duty with everybody present. This means you must rotate who writes the answers to different questions. Once you’ve completed your scribe duty, initial above.
You are part of a team of geologists for the USGS (U.S. Geologic Survey) tasked with determining areas of high seismic risk in the state of California. As a scientist, you know seismic hazard is a factor for determining risk based on:
Risk = Hazard x Vulnerability x Value
Where: Hazard = the chance that the building will experience strong shaking
Vulnerability = the likelihood that the building will collapse due to earthquake hazards
Value = the number of lives potentially affected
The first step in assessing risk is to determine the areas of highest seismic hazard in California (the San Andreas
Fault Zone) with large population centers nearby. Los
Angeles and San Francisco, both are near the San
Andreas Fault Zone, are cities you identify for further
study. Because hazard is dictated by location,
magnitude, and frequency, you will use past earthquake
to calculate mean recurrence interval and estimate
probability.
Learning objectives
•
Use data to determine the probabilities of
earthquakes of various magnitudes in the San
Francisco area and the Los Angeles areas.
•
Compare your results to the regional earthquake
probability map for California and assess the
regional earthquake hazard to determine which
area has a higher seismic hazard.
1
Use the history of earthquakes in the San Francisco and Los Angeles areas to determine the probability of earthquakes of various magnitudes over various time periods. The areas are delineated in the black boxes on the map
The data come from searchable databases. For each search, the investigator enters the area, the period, the magnitude range, and the depth-to-hypocenter range to be searched. The parameters used here are listed:
San Francisco area
Los Angeles area
Latitude range
36.25 - 38.75°N
33.5-35.5°N
Longitude range
120.75 - 123.25°W
116.75-119.75°W
Date range
01/01/1983 – 12/31/2012
01/01/1983 – 12/31/2012
Magnitude ranges
2.0-2.9, 3.0-3.9, up to 9.0-9.9
1.0-1.9, 3.0-3.9, up to 9.0-9.9
Depth range
All
All
Data source
United States Geologic Survey
Southern California Earthquake Center
Searchable database
http://neic.usgs.gov/neis/epic/epic_r
ect.html
http://www.data.scec.org/eq-
catalogs/date_mag_loc.php
Part 1: Calculating Recurrence Interval and Probability
On the data tables for the San Francisco and Los Angeles areas on the following pages, the number of earthquakes in each magnitude range (
Column A
) over 30 years
(1983-2012) has been entered in Column B
.
1.
Fill in the data table for each area by calculating the average number of earthquakes per year (
Column C
) and the mean recurrence interval (MRI) (
Column D
). If you are completing this digitally, use Word’s “Draw”
tool to plot your data points on the graphs. (2 points)
Mean Recurrence Interval for a given magnitude (M) = the number of years the data span
the number of events of a given magnitude (M)
How do you determine MRIs for earthquakes of magnitudes 7.0 and greater when there’s no historic record? Earthquakes of this size have not occurred over the 30-year study period, and thus we do not have enough data to determine the MRI by taking the reciprocal of the average number of earthquakes. However, it is possible to extrapolate MRIs for these large earthquakes by using data for the lower-magnitude earthquakes as
follows: (2 points)
On the graph, plot the MRI (
Column D
) for each magnitude range for which you have data. Plot the earthquake data on the graph in the middle of its corresponding column, in the location for 2.5, 3.5,
and 4.5 earthquakes etc. Note that the vertical scale is logarithmic, and the MRI increases by about
a factor of 10 for each increase in magnitude size.
Draw in a best-fit line with a ruler or the edge of your notebook to the data and extend it to cover the magnitude ranges for which you do not have data. Go here
(
https://serc.carleton.edu/mathyouneed/graphing/bestfit.html
) if you need a refresher on how to construct best fit lines.
Read the extrapolated MRIs for those magnitude ranges and enter them to complete Column D.
2.
In Column E
, determine the probability of earthquakes of each magnitude range occurring in one year. (1 point) Probability can be expressed as either a fractional probability between 0 and 1.0, or as a percentage from 0 - 100% by multiplying the fractional probability by 100. 2
For earthquakes with MRIs of one year or less:
The probability of these earthquakes occurring in any one year is 1/1 = 1.0 or 100%. Record these values for the appropriate magnitude ranges in Column E. The first row has been done for you.
For earthquakes with MRIs greater than one year: Fractional probability = 1/ MRI
and then multiply
by 100 to get % probability: Percent probability = (1/MRI)*100
Note that this is equal to the average # of earthquakes per year. But using the 1/ MRI method allows calculation of probabilities for earthquakes that have not occurred over the study period because we have extrapolated MRIs.
You 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 1
st
year, and
2) The earthquake must not
occur in the 2
nd
year.
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.
3.
In Column F,
determine the probability of each earthquake magnitude not
occurring in a year. This is simply 1.0 (or 100%) minus the probability of that event occurring in a year (Column E). That is, either it occurs, or it does not! Some have been completed for you. (1 point)
Probability of earthquake NOT occurring = 1 – the probability of an earthquake occurring
You have the information to determine earthquake probabilities for any time period. For example:
What is the probability of a 6.0-6.9 earthquake occurring in the San Francisco area in the next thirty
years? To determine this:
Determine the annual probability of such an earthquake not occurring
(0.90 from Column F). Then,
The probability of it not occurring
in two
years is 0.90 x 0.90 = 0.90
2
= 0.81 or 81%
The probability of it not occurring in three
years is 0.90 x 0.90 x 0.90 = 0.90
3
= 0.729 or ~73%
The probability of it not occurring in thirty
years is 0.90
30
= 0.042 or ~4%
The probability of a 6.0-6.9 earthquake occurring
in the San Francisco area in thirty
years is
1 – 0.042 = 0.958 or ~ 96%
3
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You have now calculated earthquake probabilities (see figure 1) and quantified seismic hazard!
Figure 1. CA Earthquake Probability Map Credit: USGS, California Geological Survey, Southern California Earthquake Center. 4
Study area: San Francisco
A
B
C
D
E
F
magnitude range
total # of
earthquakes average # of
earthquakes
per year
MRI
(mean recurrance
interval) in years
one year probability
of earthquake
occurring
of earthquake not
occuring
fractional
%
fractional
%
2.0-2.9
1716
1.0
100%%
0
0%
3.0-3.9
1326
4.0-4.9
161
5.0-5.9
13
6.0-6.9
3
0.900
90%
7.0-7.9
0
8.0-8.9
0
9.0-9.9
0
Study area: Los Angeles
5
A
B
C
D
E
F
magnitude range
total # of
earthquakes average # of
earthquakes
per year
MRI
(mean recurrance
interval) in years
one year probability
of earthquake
occurring
of earthquake not
occuring
fractional
%
fractional
%
2.0-2.9
21471
1.0
100%%
0
0%
3.0-3.9
1830
4.0-4.9
209
5.0-5.9
26
6.0-6.9
2
7.0-7.9
0
8.0-8.9
0
9.0-9.9
0
Part 2: Analysis 4.
The statewide probability map suggests that overall, there is a 99% chance of a damaging M6.7 or greater earthquake occurring somewhere in the state in the next 30 years. Should resources for earthquake 6
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preparedness be spread evenly across the state or concentrated in specific areas (consult figure 1)? Support your answer by explaining your team’s reasoning. (1 point)
5.
No earthquake with magnitude 7.0-7.9 has occurred in the San Francisco area over the 30-year study period. What is the probability of an earthquake of magnitude 7.0-7.9 occurring in the San Francisco in the
next 30 years? Use the probability data rounded to the second decimal place and show all your work. (1 point)
6.
Do you think the probability from the previous question is high enough to warrant concern? Why or why not? (1 point)
7.
What is the probability of a magnitude 7.0-7.9 earthquake in the Los Angeles area in the next 30 years? Use the probability data rounded to the second decimal place and show all your work. (1 point)
7
8.
Do you recommend San Francisco or Los Angeles be California’s priority for a future seismic risk assessment (see page 1 of this assignment for the overall purpose of your study)? Why? (1 point)
9.
Why are you concerned with estimating the seismic hazard for only M7.0-7.9 earthquakes for these two cities? Conversely stated, why are you and you team not
concentrating on M8.0 and M9.0+ earthquakes, which release more energy and have a greater potential for damage holding all other factors constant? Explain your reasoning. (1 point)
Please complete your peer assessment now.
8
In recognition that the functionality, satisfaction, and academic benefits of group work largely depend on equal participation and the perceived value of each group members’ contributions, up to 3 points of the Group Contributions portion of your course grade will be based on peer assessment according to the rubric in Qual.
Complete the peer assessment here
(or access using the QR Code with the photo app on your phone)
for all group members EXCEPT yourself
, including members from other groups you may have worked with temporarily. You can access the survey ONCE
so be sure to evaluate ALL
your group members by selecting ALL
their names when asked who you are assessing (consult the names written the front page or take a picture of the names if you’ll be completing the peer assessment later). There is no requirement for how many group members receive certain points;
evaluate them fairly, honestly and based on their effort and quality of their contributions. Because assignments are formative assessments, judging peers on the accuracy of their contributions is secondary. Your feedback will always remain confidential. Your peer assessment score will be the average of
those submitted by your group members. If you do not complete a peer assessment for each of your group members, you will not receive your peer assessment points.
Download a .pdf of your responses after submission as proof of completion.
The survey closes at the end of the late-submission window for this assignment.
9
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