For the following problem set, you will work with the seismicity catalog maintained by the University of Memphis for the New Madrid region in order to make your own frequency-magnitude diagrams and calculate a recurrence interval for a large earthquake at the NMSZ. You will also compare NMSZ data to seismicity catalogs for southern California and the world. The point of this comparison is that you will see that the overall shape of a frequency-magnitude diagram is *scale-independent*. It doesn't matter how big your regional area is, or how many years your catalog covers, the same basic -1 slope coupled to two sections on either end that deviate from -1 will always be there. What changes is the place on the diagram where the deviation occurs? Pay attention to this when you make your different plots.

### Part 1: Get familiar with the NMSZ and its seismicity

Go to the New Madrid Earthquake Catalog Search.

Once you get there, follow my directions to make a 1-year catalog of NMSZ seismicity:

### Video: How to Make a 1-year Catalog of NMSZ Seismicity (2:18)

Here is video above as plain text

Create a word processing document (Microsoft Word, Macintosh Pages, Google Docs, or PDF) to record your work for this problem set.

On the worksheet, paste in your map of the 1-year catalog you made. Then answer the following questions:

**1.1** How many earthquakes are in your catalog?

**1.2** What is the largest magnitude earthquake in your catalog? How many earthquakes are there of this magnitude in your catalog?

**1.3** What's the smallest magnitude earthquake in your catalog? How many earthquakes are there of this magnitude in your catalog?

**1.4** Describe your map in a few sentences. (What part of the country is it? Are the earthquakes sprinkled randomly about or do they cluster in patterns? If the latter, describe what the patterns look like.)

**Double-Check! **Your worksheet should now have a map and answers to the Part 1 questions. If it does, you are ready to take on Part 2.

### Part 2: Making frequency-magnitude plots of NMSZ seismicity

Make three different frequency-magnitude plots using the New Madrid Earthquake Catalog data: The first plot will use the one-year catalog you made in Part 1 of the problem set. In the second plot, you will add curves that correspond to a 10-year, 20-year, and 30-year catalog. The third plot will depict the same data as in the second plot, except that you will normalize all the catalogs to one year. Specific directions follow:

#### Plot 1: Make a frequency-magnitude plot using the one-year-long catalog that you just made in Part 1 of this problem set.

For this plot, all you need are the magnitudes, which are in column 7 of your plain text catalog file. Post to *Questions* if you need help isolating that column. My recommendation is to create a new file in whatever plotting/spreadsheet program you like and then you will type your counting statistics into this new file. In your new file, you want to create the values that will be on the x-axis of your plot. They will be magnitudes from your catalog's lowest to your catalog's highest in 0.1-unit bins. To create the values that will be on the y-axis of your plot, count how many earthquakes in your catalog are *equal to or greater than* each value of magnitude. These are your y-values: cumulative frequency. It's easier to count if you sort your magnitudes first, which is fine to do because we do not care what order they are in for this plot.

Then plot cumulative frequency vs. magnitude.

Use a logarithmic (base 10) scale for the y-axis or take the log of your cumulative frequency data and plot that on a linear axis. You can use a linear x-axis because magnitude is already a power of 10. [Is this confusing? Post to the *Questions* forum if you need help.]

If you are having trouble, see my example plot for a one-year catalog of earthquakes in the New Madrid Seismic Zone (NMSZ). I used the year 1975, so this plot will not be precisely the same as yours, but it should look pretty close.

#### Plot 2: Make a plot that has four different frequency-magnitude curves on it.

Start with the plot you just made.

Go back to the New Madrid Earthquake Catalog and make a catalog for a ten-year time period (you can choose any ten-year period). Overlay the frequency-magnitude curve for this ten-year catalog onto the curve you made in the first plot.

Repeat for a twenty-year period.

Repeat for a thirty-year period.

You should now have one plot with four curves on it.

Make sure each curve is distinguishable (by color or linestyle) and labeled.

#### Plot 3: Make a plot that has four different normalized frequency-magnitude curves on it.

Start with the original one-year catalog plot you made.

Overlay the curve for the ten-year catalog, but normalize the curve to one year. This is accomplished by dividing each of your y-values by 10.

Repeat for the twenty-year catalog (divide y-values by 20)

Repeat for the thirty-year catalog (divide y-values by 30)

You should now have one plot with four curves on it.

Use the same distinguishing color or linestyle for each curve as you did in your second plot.

Dust off your worksheet from Part 1. On the worksheet, first paste your three plots into the worksheet, then answer the following questions:

**2.1** Look at the first frequency-magnitude plot you made of the one-year catalog. Approximately what is the lower magnitude threshold for this catalog? (Follow your data from *right to left* and tell me at about what magnitude the line flattens out to having zero slope?)

**2.2** Now look at the other two plots you made. Do the other curves show a significantly different lower magnitude threshold? From this observation, what do you conclude about the relationship between catalog timespan and lower magnitude sensitivity?

**2.3** Look at the second plot you made. Describe the differences and similarities among the four curves in a few sentences. For example, are the curves of the same shape? Where are the x- and y-intercepts relative to each other? What makes the y-intercepts different? What causes the x-intercepts to be different?

**2.4** Look at the second plot you made. Imagine having a catalog that spans 100 years. Using the four curves you made as a guide, extrapolate where the x and y intercepts would each be for a 100-year catalog. What is the largest earthquake you would expect for a 100-year catalog?

**2.5** Look at the third plot you made. Extrapolate your curves and predict how often a magnitude 7 earthquake will occur in this region and how often a magnitude 8 will occur in this region. I want you to make a reasonable eyeball-fit. I am not asking you to *calculate* a best fit line. **If the answer is a fraction less than one, then you can take the reciprocal and predict how many years go by in between magnitude 7's and in between magnitude 8's.

**2.6** You have just used frequency-magnitude relationships to predict a recurrence interval for a large New Madrid earthquake. Cool! What are the sources of uncertainty in the prediction you made in problem 2.5? (One way to realize just how much uncertainty there is in an extrapolation like this one is to try making several slightly different fits to the data that all look "pretty good" to you and see how different your final answers end up being.)

**Double-Check!** Now your worksheet should have the map and answers from Part 1 as well as three plots and answers for Part 2. Hang on to the worksheet and use it for Part 3.

### Part 3: Comparing the NMSZ to Southern Cal and to the world

#### Plot: Southern California

Use the Southern California Earthquake Center Web site to make a seismicity catalog, map, and frequency-magnitude plot.

Go to the Southern California Earthquake Data Center's Earthquake Catalog Search page.

### Video: How to Make a One-Year Catalog of Seismicity (2:10)

Or follow along as a plain text to make a one-year catalog of seismicity.

Take a screenshot of the google map you made and paste it into your problem set.

Make a frequency-magnitude plot for the events in this catalog:

- Start with your frequency-magnitude plot for the one-year NMSZ catalog.
- Overlay the frequency-magnitude curve for your Southern California catalog on the same axes. The magnitudes are in column 5 of the SCEDC catalog file, and they are all you need.
- Make sure each of your curves are distinguishable and labeled.
- Save this plot because you are going to add another curve to it.

#### Add to your plot: The World

Use the United States Geologic Survey catalog to make a one-year global seismicity catalog, and add this data to your frequency-magnitude plot that has Southern Cal and the NMSZ on it.

Go to the USGS Earthquake Search page.

Once you are there, follow my plain text directions for making a one-year global catalog.

Add to your plot!

- Start with the frequency-magnitude plot you made that has a curve for the one-year NMSZ catalog and a curve for the SCEDC catalog.
- Overlay the frequency-magnitude curve for the global catalog on the same axes.
- Make sure each of your curves are distinguishable and labeled.
- Paste this plot into your problem set.

#### A few more questions

**3.1** How many earthquakes are in your one-year catalog for Southern California? What is the largest magnitude earthquake in the catalog? How many earthquakes are there of this magnitude?

**3.2** How many earthquakes are in your one-year catalog for the world? Are you surprised by this number? What is the largest magnitude earthquake in the world catalog? How many earthquakes are there of this magnitude? Remember that we cut off our global catalog at a minimum magnitude of 4.5. Look at your frequency-magnitude curve for the global catalog and estimate how many earthquakes there would be in your catalog if we had gone all the way down to zero for the minimum magnitude. Translate that into an approximate number of earthquakes per day in the world. (wow, huh!)

**3.3** Look at your map of Southern Californian earthquakes. Describe it in a few sentences (i.e., Where are the earthquakes? Do they cluster in space? Beware of artificial clustering that we induced by where we set our search parameters.).

**3.4** Look at the map of one year's worth of earthquakes made by the Advanced National Seismic System and describe it in a few sentences. How do the earthquakes cluster?

**3.5** Compare the frequency-magnitude curves for New Madrid and Southern California. Which one of the two catalogs is has its lower magnitude threshold at a smaller magnitude? Which region is more seismically active in terms of the number of earthquakes? Which region is more seismically active in terms of earthquake magnitude?

**3.6** Compare all three frequency-magnitude curves. How often does a big earthquake (M > 7 or so) happen in the global catalog vs. in the two regional catalogs? Why is this?

#### Submitting your work

Now your worksheet should contain the map and answers from Part 1, the three plots and answers from Part 2, and the map, plot, and answers from Part 3. And the green grass grows all around and the green grass grows all around. Haha, but seriously, save your file in the following format:

L4_catalog_AccessAccountID_LastName.doc (or .yourExtension)

For example, Cardinal pitcher Michael Wacha's file would be named "L4_catalog_mjw52_wacha.doc"

Create one document that contains:

- Part 1 NMSZ map
- Part 1 answers to follow-up questions
- Part 2 three frequency-magnitude diagrams
- Part 2 answers to the follow-up questions
- Part 3 a map for southern Cal
- Part 3 one frequency-magnitude diagram with the NMSZ, SCEC, and USGS catalog data on it
- Part 3 answers to the follow-up questions.

Once you've finished this whole problem set, submit it to the "Earthquake catalog problem set" assignment in Canvas by the due date listed on the table on the first page of this lesson.

#### Grading rubric

I will use my general rubric for grading problem sets to grade this activity.