Examining Earthquake History and Predicting Big Earthquakes.

Examining Earthquake History and Predicting Big Earthquakes
Building a house close to a fault is risky. But how do you estimate the risk? The likelihood of an earthquake of a certain magnitude in any given year is determined using long-term earthquake records. The longer the record, the more reliable are the predictions of the earthquake frequencies. Knowing the earthquake frequencies or recurrence intervals helps us develop communities in earthquake-prone areas. For this exercise, you will act as the geological consultant hired by the town of New Madrid to determine earthquake frequencies and recurrence intervals of large earthquakes. You will collect data from the Center for Earthquake Research and Information (CERI) that has been analyzing earthquake activity in the New Madrid Seismic Zone and created a catalog of earthquakes since 1973. You will use these data to make predictions regarding earthquake frequencies and recurrence intervals of large earthquakes. These are the type of predictions made by geological consultants necessary for city planning and development. This assignment is worth 30 points with point values indicated throughout the assignment.

A) Gathering the Data
1. First go to the Center for Earthquake Research and Information (CERI) website: http://www.ceri.memphis.edu. Click on the Seismic Information and then New Madrid Earthquake Catalog Search on the left side of the webpage. The resulting web form will allow you to search for earthquakes based on their time, magnitude, and location. Time is the first option, and you will examine data over a 30 year time frame by selecting 1980 for the Start Date Year, and 2010 for the End Date Year. Location is the third option, and you should examine all events in the New Madrid region by just choosing the RADIAL SEARCH and leaving the default values as is (Latitude: 35.15, Longitude: -90.05, Radius 500 km). The second option is the magnitude, and this is what you will have to adjust several times to determine how frequent earthquakes of a certain size are.
2. To begin, choose Minimum Magnitude as 1.0 and Maximum magnitude as 1.9. Then click Begin Search. On the Catalog Results Page, you will see the number of events selected at the top of the page. You only need the first number, as it also lists a second number that is over 10,000 and simply indicates the total number of all events in the entire catalog. You should enter the first number in the table below in the first row and of the first column. You will then need to click the back button in your browser to return to the Catalog Search Form. Enter the next magnitude range (2.0-2.9) and click to Begin Search to find the number of events of that size and enter it into the table in the second column of the first row. Repeat this process for each magnitude range in the table and enter the corresponding number of events for each magnitude range in the first row. (5 points)
Magnitude Range 1.0-1.9 2.0-2.9 3.0-3.9 4.0-4.9 5.0-5.9 6.0-6.9 7.0-7.9
Number of Earthquakes from 1980-2010
Number of Earthquakes per Year

Earthquake Recurrence Interval in Years
You should find at least one magnitude range with no earthquakes over that 30 year time period. Does this mean it is not possible for the New Madrid Seismic Zone to have earthquakes of that size? Why or why not? (1 point)

B) Calculating Earthquake Frequency and Recurrence Intervals
1. Next you will need to calculate the number of earthquakes per year. The first row of our table has the number of earthquakes between 1980 and 2010, so you need to convert this to the number of earthquakes over one year. You can do this by dividing each number in the first row by the number of years (end year minus begin year), and then put this newly calculated value in the second row of the table. Do this only for magnitude ranges that do not have 0 earthquakes between 1980 and 2010. We will complete the remainder of the second row in the table later when we figure out how to estimate the number of earthquakes per year for cases with 0 earthquakes from 1980-2010. (5 points)
For which magnitude ranges do we expect to see at least one earthquake each year in the New Madrid Seismic Zone? (1 point)

2. To complete your table, calculate the recurrence interval that is the average time interval between earthquakes of a given magnitude range. This is important for city planners to know, on average, how often earthquakes of a certain size will occur, and hence how likely infrastructure will need to withstand an earthquake of that size. The recurrence interval is calculated by taking 1 divided by the number of earthquakes per year. So for each magnitude range, calculate 1 divided by each number in the second row of the table and place the newly calculated value in the third row of the table. (5 points)
Magnitude 5 earthquakes are considered important because they can be felt across several states in the midcontinent and cause moderate damage to structures near the epicenter. How often does a magnitude 5 earthquake occur in the New Madrid Seismic Zone? (1 point)

C) Using Magnitude-Frequency Relationships to Estimate Large Earthquake Likelihood
1. Now plot the Number of Earthquakes per Year versus the Earthquake Magnitude on the graph below. Note that the Y-axis is logarithmic and that X-axis values indicate the corresponding magnitude range (e.g., 1 = 1.0-1.9, 2 = 2.0-2.9, etc.). You can use Excel to help you plot the points correctly. (4 points)

2. Researchers have determined that earthquakes follow a common phenomenon in nature called universality that the likelihood of an event is proportional to the size of the event. Mathematically, this relationship is called a power-law, which means we can only see the proportional relationship when the values are plotted logarithmically. This why the Y-axis of our plot is logarithmic, and the X-axis is also logarithmic because the magnitude value itself is a logarithmic expression for how big an earthquake is (i.e., a magnitude 7 earthquake is essentially 10 times larger than a magnitude 6 earthquake). So after plotting the data points on this logarithmic graph, you just need to draw a straight line of best fit through the data points to establish the proportional relationship between frequency and magnitude for the New Madrid Seismic Zone. This line is your predictor of the average behavior of the New Madrid faults and how often they will produce earthquakes of different sizes based on the model of universality. When you try to draw the straight line, you will find that the line will not go through the middle of every point, but there will also be one point that is much further away from the trend established by the remaining points. Go ahead a draw your line to ignore this point. (2 points)
Which magnitude range does this outlier point correspond too and why do you think this point does not fit with the overall trend? (1 point)
3. Make sure your best fitting line extends (i.e., extrapolates) as far to the right and left as possible so we can estimate frequency of earthquakes with very large magnitudes that did not occur during 1980-2010. Based on this line, what is the number of earthquakes per year we should expect for magnitude 6.0-6.9? (1 point)

Based on this line, what is the number of earthquakes per year we should expect for magnitude 7.0-7.9? (1 point)

4. As described earlier, the recurrence interval is an important value for city planners to determine how infrastructure such as buildings should be prepared to withstand earthquakes of a given size. What is the recurrence interval for the 6.0-6.9 magnitude range? (1 point)

What is the recurrence interval for the 7.0-7.9 magnitude range? (1 point)

5. The New Madrid Seismic Zone is well known not only for the recent small-to-moderate sized earthquakes, but for a series of large earthquakes in 1811-1812. On the basis of the large area of damage (600,000 square kilometers), the widespread area of perceptibility (5,000,000 square kilometers), and the complex landscape changes that occurred, the New Madrid earthquakes of 1811-1812 rank as some of the largest in the United States since its settlement by Europeans. Because there were no seismographs in North America at that time, and very few people in the New Madrid region, the estimated magnitudes of this series of earthquakes vary considerably and depend on modern researchers’ interpretations of journals, newspaper reports, and other accounts of the ground shaking and damage. The general consensus is that they were at least magnitude 7 and could have been as large as magnitude 8. Based on the recurrence interval you just calculated, are we due for an earthquake in the New Madrid Seismic Zone? Why or why not? (1 point)