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Assessing Earthquake Risk: How often does the ‘Big One’ occur?

Predictions using the Gutenberg-Richter relationship are at the heart of earthquake forecasting. How does it work?

Thomas JusterDepartment of Geology, University of South Florida© 2011 University of South Florida Libraries. All rights reserved.

SSAChaz.TCJ.6(trad)

Core Quantitative Literacy TopicsExponents, Logarithms

Supporting Quantitative Literacy TopicsGraphing, extrapolation

Core Geoscience SubjectEarthquakes

The module you are viewing is a PowerPoint slide presentation.

•Navigate from slide to slide using the up/down arrow keys, or the scroll wheel on the mouse if one is available

•Use the mouse to select hyperlinks (underlined, in blue type)

•When done, use the escape key to exit the presentation.

You can and probably should have a spreadsheet open in a separate window, so you can try out things that are explained in the presentation.

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Close this window to proceed with the slide show.

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Getting started

After completing this module you should be able to:

•Calculate the recurrence interval from earthquake frequency data•Estimate the recurrence interval for the expected largest earthquake in an area

Prerequisites:

•You must have completed the module Earthquake Frequency! This modules assumes you have the skills taught in that one, and you won’t get very far without these skills.

Important Note: Just like the Earthquake Frequency module, a key theme of this module is creating and modifying graphs using Excel. The instructions for completing these tasks are very dependent on the version of Excel. Although one can complete this module using any version, the instructions provided are specific to Excel 2007. If you use any other version, you are responsible for figuring out the commands equivalent to the ones described in this module.

Do this first:

Click on the icon to open the embedded spreadsheet file, and immediately save itwith a unique name. You will enter your answers to all the End-of-module questions in this spreadsheet and submit it via Blackboard.

EQ-GR

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Laying out the problem: example from New Madrid, Missouri

The map below, published by the USGS, shows the frequency of earthquake hazards in the USA. The colors correspond to the maximum acceleration as a percentage of g (gravitational acceleration) that can be expected to occur 10% of the time within the next 50 years. In other words, along the western coast there’s a 10% chance that there will be an earthquake within the next 50 years that produces ground accelerations that exceed 64% of gravity. That’s a strong earthquake! For reference, an earthquake producing ground accelerations greater than 100% of g would literally hurl objects into the air.

As you should expect, most of the earthquake hazard in the USA occurs along the west coast, where there’s an active tectonic boundary. However, there are two isolated pockets of hazard in the eastern US. The largest is located near the small town of New Madrid, Missouri.

Q1. What is the maximum expected ground acceleration in Tampa, expected to occur 10% of the time in the next 50 years?

Go direct to End-of-module questions

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Laying out the problem, con’t.

Earthquakes near New Madrid are common, but rarely very large. The red dots on this map represent earthquakes in the New Madrid area from 1974-1995. The largest had M = 5, and struck in March, 1976.

Although no large, damaging earthquakes have ever been recorded by modern instruments, geologists know they have occurred in the past. In particular, historical accounts describe a devastating series of four large earthquakes that occurred in 1811-1812. These earthquakes were felt over an enormous part of the eastern US (over a million square miles; see Endnote 1), and completely leveled the village of New Madrid. The land was tossed about so much that the Mississippi River was said to have flowed backwards for a short time!

Based on the degree of damage, geologists estimate the largest earthquake had a magnitude ≈ 7.5.So here’s the problem:

We know that earthquakes with M = 7.5 can occur along the faults of the New Madrid system, and in order to assess the risk they pose, we need to know how often they occur. However they occur so infrequently that we haven’t recorded one in over 50 years of observing—in fact, the largest earthquake recorded had a magnitude of only 5.0! How can we use the data we do have to estimate the recurrence interval of earthquakes that are so rare we haven’t recorded any?

From the USGS

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Solving the problem using the Gutenberg-Richter relationship

Fortunately, the quantitative relationship between magnitude and frequency—known as the Gutenberg-Richter relationship—allows geologists to infer the recurrence interval of large earthquakes from observations of smaller ones.

There are three steps to using this technique:

1.Estimate the magnitude of the largest earthquake that typically occurs in a given area. The area is usually defined as a segment of a fault, or a series of faults that are related to the same deep forces. The largest earthquake is usually estimated from historical records.

2.Compile all the reliable earthquake data from the area.

3.Create the Gutenberg-Richter plot and extrapolate the relationship between magnitude and frequency to estimate the recurrence interval of earthquakes with the largest typical magnitude.

2. Earthquake data can be obtained from CERI—the Center for Earthquake Research and Information.

1. Based on historical accounts, the largest earthquake in the New Madrid area is M ≈ 7.5

Earthquake scarp from the 1811 New Madrid earthquake; photo from USGS

3. The Gutenberg-Richter plot will allow you to extrapolate the relationship between magnitude and RI to magnitudes larger than the ones observed.

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This is the link. Click on it to open the site in a browser.

Step 2: obtaining the earthquake data

The start and end dates are selected here.

Recall that since magnitude is a continuous variable, we need to specify a range in order so that the frequency or probability of an earthquake of a specific magnitude has meaning. For this activity, the range will extend 0.25 magnitude units above and below the nominal magnitude; i.e., 4.75-5.25 for a magnitude ‘5’ earthquake.

The default area defines a rectangle—all earthquakes in this area will be extracted.

Q2. How many years of data will you have?Go direct to End-of-module questions

Here the magnitude range is specified.

The database starts in 1974, and by specifying a date in the future we will extract data for all years.

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Creating a table of earthquake data

If you completed the Earthquake Frequency spreadsheet module you should now know what to do—create a Gutenberg-Richter plot, fit a line, extrapolate the line, and make inferences from the extrapolated line. The only thing different is that you will be plotting the recurrence interval (RI) versus magnitude, not the frequency. The RI in years is related to the annual frequency by the formula (see Endnote 2):

Notice I’ve shown you the number of earthquakes with nominal magnitude 3 and lower as of 2010. Your numbers for these magnitudes will obviously be slightly larger!

FreqRI

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extract these data from the CERI database.

To calculate frequency, you will need to know the number of years of data

Your task: create and complete the table shown here, plot the logarithm of RI versus magnitude, fit a straight line to the data, extrapolate the line to magnitude 7.5, and estimate the RI for earthquakes of M=7.5.

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Step 3: using the Gutenberg-Richter plot to estimate RI

This is what your Gutenberg-Richter plot should look like (approximately):

Q3. What is your estimated RI for earthquakes of M=7.5?

Q4. What is your estimated RI for earthquakes of M=6.0 (still a potentially damaging earthquake)?

Q5. You will notice the line does not fit the data very well. A possible explanation is the poor quality of data for low-magnitude earthquakes, which are harder to record. Re-estimate the RI for earthquakes of M=7.5 using just the earthquake data for magnitudes 3.5 and higher (the last four data points).

You will have to create a new plot, and fit a new line to the data.

Go direct to End-of-module questions

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End-of-module assignment

1. Answer questions Q1-Q5 on Slides 3, 6, and 8.

2. In fact, paleoseismic data from buried sand boils suggests that the recurrence interval for great earthquakes (M ≈ 7.5) is only 500 years. If this is true, then the Gutenberg-Richter relationship doesn’t hold in the New Madrid area. What must the relationship look like?

3. Determine the recurrence interval for the largest earthquakes that typically occur in (a) Yellowstone National Park; and (b) Grand Teton National Park. Slide 10 provides an overview of the parks; Slide 11 describes the ANSS web site from which you will extract earthquake data; Slide 12 gives you the boundaries of the rectangular areas for both parks; and Slide 13 shows you some of the data for Yellowstone (but you’ll have to compile the rest yourself.) For both parks determine:

a) The magnitude of the largest earthquake that is expected to occur, which you can estimate with an Internet search of large historic earthquakes; and

b) The recurrence interval, in years, for this earthquake.

In addition,

c) Comment on your confidence in the prediction from the Gutenberg-Richter plot.

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Earthquakes in Wyoming: Grand Teton and Yellowstone National Parks

Now you will apply what you have learned to estimating the recurrence interval for large earthquakes at two famous western parks: Grand Teton and Yellowstone. Both parks are located in Wyoming, but have very different geologic settings.

Yellowstone National Park lies above one of the world’s largest volcanoes. The heat from the features volcano produces the thermal features it’s famous for (like Old Faithful Geyser, which these people waiting for).

Grand Teton National Park is dominated by the Teton Range, a massive block of rock that continues to be uplifted along the Teton Normal Fault. The rapid uplift has produced a spectacular scarp.

Both parks experience earthquakes!

From the USGS

From the National Park Service

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Extracting data from the ANSS catalog

The Advanced National Seismic System website contains various catalogs of earthquake data for the United States. This is where you’ll get the earthquake data needed to produce your Gutenberg-Richter plots.

This is the link. Click on it to open the site in a browser.

You can choose several databases. You should choose the ANSS composite catalog, which is the default.

Choose Catalog in readable format (default)

Here you specify the magnitude range.

You specify the start and end dates here; notice the format. Conduct your search from 1974, when observations started, to 2010.

ANSS looks for earthquake epicenters that fall within a rectangular area. To define the area, you specify the minimum and maximum latitude and longitude.

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Boundaries for earthquake data

These are the boundaries of the rectangles. Notice the negative signs—they are important!

Latitude = 45.1⁰

Latitude = 44.1⁰

Latitude = 43.5⁰L

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Some Yellowstone earthquake data

There are a lot of earthquakes in Yellowstone National Park, and counting all those small ones can be tedious. To relieve you of that burden, I’ve already determined the number of earthquakes with nominal magnitude ≤ 3.5, as shown in this table:

Remember, since magnitude is continuous, we need to create bins. In this case the bin spacing is 0.5 magnitude units wide. So, for example, the ‘Nominal’ magnitude 2 includes all earthquakes with magnitudes between 1.75 and 2.25.

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1. Because the Earth’s crust is older, colder, and more rigid in the east than the west, earthquake waves do not die out as quickly. For example, the figure below shows the effects of the 1895 M=6 New Madrid earthquake, which occurred in 1895, compared to the effects of a larger earthquake in California.

The M=7.5 1811-1812 earthquakes were felt all along the eastern seaboard, including Washington DC (where sidewalks reportedly cracked) and Boston, Massachusetts (where church bells shook until they rung). Return to Slide 4.

(Endnotes continued on next page)

Endnotes

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2. We have previously related recurrence interval to probability, with the formula

where P is the probability of an event occurring in any given time period, and RI has units of the same time period. In most cases the probability can be interpreted as the frequency—for example, if 5 earthquakes were observed in 10 years, then the frequency is 5/10 = 0.50 earthquakes/year, and this is the same as the probability in any given year.

This won’t work, however, when events are so frequent that there are more events than observation periods. For example, what if we observed 15 earthquakes in 10 years? The frequency is 15/10 = 1.5 earthquakes/year, but now we can’t associate this frequency with a probability. Probability is a number between zero and one, so it makes no sense to describe a ‘probability of 1.5’!

We could resolve this problem if we needed to by defining a smaller period of observation; say one month. In that case there would be 15 earthquakes in 10 × 12 = 120 months, so the frequency and probability could be written as 15/120 = 0.125 (12.5%). Return to Slide 7.

Endnotes, con’t.

PRI

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