Earthquake
Location

An
exercise prepared for EAS 4900 by Tiffany Kit Tam

August
2001

Background Information on Locating an Epicenter

__ __

In an earthquake, stored energy is
suddenly released through a movement along a fault. A fault is a fracture or zone of fractures in rock along which
the two sides have been displaced relative to each other parallel to the
fracture. In the largest earthquakes a
fault length of nearly 100 km can be displaced 10 to 20 meters. The *focus*
of an earthquake is the point on the fault plane where rupture initiates. The *epicenter*
is the point on the surface of the Earth directly above the focus.

Seismic waves emanating from the
focus can travel as body waves or surface waves. *Body waves* travel in
all directions from the focus through the body of the Earth. *Surface
waves *are different from body waves because they don’t travel through the
Earth; instead they are constrained to travel along the surface of the
Earth. The surface waves behave most
like S-waves by causing up and down or side to side movement as they pass, but
they travel slower than the S-waves.

There are two types of body waves;
the compressional or *P waves* and the shear or *S waves*.

*P
waves* (or primary waves) travel with a velocity that depends on the elastic
properties of the rock that they travel through. P-waves are like sound waves.
They are a compression (or expansion) that moves through an elastic (or
fluid) material. A particle in the material moves parallel to the direction of
propagation. These waves can travel through both elastic and fluid materials.
In an elastic material, the velocity of the P wave depends on how easily the
material can be compressed, how easily the material can be bent (sheared), and
the density of the material. P-waves
have the highest velocity of all seismic waves and, therefore, they reach the
seismographs first.

*S
waves* (or secondary waves) are shear waves. They travel with a velocity that depends on how easily the
material can be bent (sheared) and the density of the material. S-waves travel through material as a
rotation, which depends on a shearing motion.
A particle in the material will move in a direction perpendicular to the
direction of travel. Because liquids
can offer no resistance to a shearing motion, the velocity of an S wave is zero
in a liquid. This means that S-waves
don’t travel through liquids. Because S
waves are slower than P waves, they will reach a seismograph after the P-wave.

In order to determine the location of an earthquake, the earthquake needs to be recorded on three different seismographs that are at significantly different locations. The other piece of information needed is the time it takes for P-waves and S-waves to travel through the Earth and arrive at a seismographic station. This information has been collected for many years and is available from travel time curves.

The earth is remarkably symmetric. The symmetry means that wave propagation velocity depends only on depth. Variations with position on the earth are slight compared to variation with depth. Consequently, the distance from an earthquake focus to a second point on the Earth’s surface determines the travel time of a seismic wave (for example a P-wave). The locations of the points do not influence the travel time curve. Seismologists have been able to determine an average travel time of seismic P and S waves for any specified distance. The times have been printed in graphs and tables as a function of distance. These travel times can be compared with those that have been actually measured from any earthquake source to a seismographic station and the approximate distance between the station and focus can be found in the graphs and tables.

If only one station’s arrival time is available, then only the distance to the epicenter can be determined. The epicenter could fall on any point at that distance. If three arrival times are available at three different seismic stations then triangulation can be used to find the location of the focus or epicenter and the time of occurrence of the earthquake.

An exercise to understand the concept of a travel time curve for S and P waves is the walk- run exercise. In this exercise, the teacher divides the class into three groups. The first group will be walkers (the S-waves) and the second will be runners (the P-waves). The third group will be the timers, or the clocks. In a classroom or outside, mark a path to follow with four stations equally spaced along the path. These could be the four corners of a square room. Have the first two groups start at the same time. The individuals in each group should stay together. The timers will record the times each group passes the four stations. Then on a graph, plot the times on the y-axis and the distances on the x-axis. The result is an example of a travel time curve, the time it takes each group to travel the course. (1)

The location exercise given below has levels that are appropriate for different grades. The lowest level of the exercise would be using a flat map to locate the epicenter of a local earthquake. The next level of the activity is using a globe to find the azimuths, latitude, and longitude of an earthquake’s epicenter. The more advanced students could locate current earthquakes from real earthquake data using computer programs.

Some web sites that provide background information and more details on some exercises include the following: (these sites were active 7/26/01)

(1) http://www.eas.purdue.edu/~braile/

For details on the walk-run exercise and many other useful tools.

(2) http://gldss7.cr.usgs.gov/current_seismicity.html

Contains current information or data from recent earthquakes, with P-times, latitudes, longitudes, travel times, origin times, and maps.

(3) http://www.mysteries-megasite.com/main/bigsearch/earth-4.html

This site has an earthquake database to find information on many earthquakes around the world

(4) http://www.mines.utah.edu/~wmgg/video/Earthquake/Earthquake.html

Worldwide Earthquake Locator, with Up-to-date earthquake information.

(5) http://www.esri.com/data/online/earthquake/index.html

Live Earthquake Maps. Arc-Data Online allows you to browse a wide variety of geographic data to create maps of your areas of interest. Here you can access near real-time seismic data to see maps of the latest earthquake locations. Earthquake maps are provided for both the world and the United States.

(6) http://scec.ess.ucla.edu/earthquake_info.html

Earthquake information FAQ about earthquake from USGS 1906 San Francisco earthquake Fault map of Los Angeles Basin and its vicinities.

(7) http://www.lasip.state.la.us/lesta/earthqua.htm

ABAG Earthquake Maps and Information Big Trouble In Earthquake Country Earthquake Information from USGS Earthquake Information Earthquake Intensity

Earthquake Earthquakes Eye on the...

(8) http://www.eoascientific.com/cus/earth/links/earthquake/index.html

Current Earthquake Information, World Earthquake Information Center Earthquake Bulletin, Near-real-time Earthquake Bulletin provides a description of the earthquake parameters including date, time, latitude/longitude, depth, etc.

(9) http://vcourseware4.calstatela.edu/VirtualEarthquake/RelatedEarthquakeLinks.html

This site contains more Information about Earthquakes and Seismology. Here are a few sites with related information about earthquakes.

(10) http://wwwneic.cr.usgs.gov/neis/current/usa.html

National Earthquake Information Center World Data Center for Seismology.

(11) http://www.cco.caltech.edu/~meltzner/seismolinks.html

Has links to real- time earthquake data, earthquake information by locality/ region, national, world-wide maps and lists of earthquakes, and earthquake catalog searches, and links to strong motion data.

(12) http://www.gps.caltech.edu/seismo/earthquakes/

Contains links to web pages on current earthquake information and other educational links.

(13) http://aamc.geo.lsa.umich.edu

Contains links to recent earthquake recordings, seismograms and graphics for earthquakes and other events, how to find epicentral distance, www resources in earth science education, and other sources of earthquake information.

(14)http://www.geophys.washington.edu/SEIS/PNSN/INFO_GENERAL/learning_resources.html

Contains earthquake learning resources like lesson plans for grades K-12 and links to seismology resource information including references, maps, slides, videos, and databases.

(15)http://www.remc11.k12.mi.us/bcisd/classres/gis.htm

Has links to K-12 lessons and ideas, GPS sites, and to data or information on earthquakes.

(16) http://www.geo.arizona.edu/K-12/earthquake.html

Places to Look for Earthquake Information and Classroom Activities. SASO (Southern Arizona Seismological Observatory) has resources for teaching including Make Your Own Seismogram and Determine the location of an earthquake, Virtual Earthquake allows you to calculate earthquake locations.

(17) http://www.iris.edu/

Good starting point for educational materials and seismic data. Source of travel time curve used in this exercise.

__Focus
Question 1:__

How do seismologists locate the epicenter of a local earthquake using seismograms?

__Materials:__

· At least three seismograms of the same earthquake. (Sample Figure 1)

· Copies of a map of station locations. (Sample Figure 2)

· Metric rulers with millimeter scales.

· Drawing compasses.

· Copies of the Travel Time Curve. (Sample Figure 3)

· Transparencies of sample seismogram, map, and Travel Time Curve. (Can be made from this exercise)

__Objectives:__

**Students will:**

** **

1. Calculate the distance from an earthquake to a seismographic station by using S and P waves from a seismogram of a local earthquake.

2. Use three (or more) calculated distances to locate the epicenter of a local earthquake using triangulation.

**Student’s Procedure for Locating Epicenter:**

1. First, plot the locations of the seismic stations on the map. (For sample, note locations of stations on map)

2. Using an appropriate time scale, determine the time interval between the S and P waves, the time interval for each seismogram is recorded and also record the arrival times of the S and P waves.

3. Using an appropriate time scale for the travel time curve, locate the interval and its corresponding distance from each station’s S and P waves that were obtained from the seismograms.

4. Draw a circle on the map with the center being the seismic station location, which has a radius equal to the distance obtained from the travel time curve.

5. The common intersection of the three or more circles for each of the seismic stations is the earthquakes epicenter.

**Teacher’s Procedure:**

** **

1. To prepare for activity-

Be sure to have at least three different seismograms from different seismic stations of the same earthquake (not too far from the epicenter). Collect the latitude and longitude of the three or more seismic stations. Be sure that the Travel Time Curve has a large enough distance or time difference to be able to conduct the activity. Be sure that the map used has a legend to find the distances of the possible locations of the epicenter, and that the map is big enough to draw the three (or more) circles where the epicenter could be located. Make transparencies to do a sample calculation of the epicenter of an earthquake.

2. For the Introduction-

Ask the students to explain the differences between an epicenter and a focus of an earthquake. Review the distinction if needed.

3. Conduct the activity-

a. Form students into groups to do the activity. Hand out the materials needed to do the activity and tell the students that the seismograms are from the same earthquake, but were taken from different seismic stations.

b. Do a sample calculation with the transparencies of the map, seismogram, and travel time curve.

c. Give directions for finding the epicenter of the earthquake recorded on the seismograms:

1. First plot the locations of the seismic stations on the map.

2. Using an appropriate time scale, determine the time interval between the S and P waves, the time interval for each seismogram is recorded and also record the arrival times of the S and P waves.

3. Using an appropriate time scale for the travel time curve, locate the interval and its corresponding distance from each station’s S and P waves that were obtained from the seismograms.

4. Draw a circle on the map with the center being the seismic station location, which has a radius equal to the distance obtained from the travel time curve.

5. The common intersection of the three or more circles for each of the seismic stations is the earthquakes epicenter.

4. For the conclusion-

Discuss the information that can be obtained from a seismogram, the actual location of the epicenter and focus, why three or more seismograms were used, and how you can tell which seismic station is closet to the epicenter. (Note, in the sample, the epicenter is near the “L” in Lake Sinclair)

Figure 1. Seismograms from a central Georgia Earthquake.

Figure 2. A map of station locations in central Georgia for the earthquake data in Figure 1.

Figure 3. Travel time curve for difference in P and S wave arrival times.

__Focus
Question 2:__

How can seismologists locate the epicenter of an earthquake using three seismograms from teleseisms, a globe and three strings?

__Materials:__

__ __

· At least three P-wave arrival times of the same earthquake recorded at different stations and the origin time of this earthquake. (See Focus Question 3 for sample data, the correct origin time is 21 min, 37 seconds. UT.)

· A globe.

· Metric Rulers with millimeter scales.

· Pieces of String (three for each student)

· Copies of the Travel Time Curve (Sample Figure 4.)

· Transparencies of Travel Time Curve. (Can be made from Figure 4.)

__Objectives:__

__ __

**Students will:**

1. Calculate the distance from an earthquake to three seismograph stations by subtracting the origin time from the P-wave arrival times to get the travel times and use the travel time curve to read the distances.

2. First locate the seismic stations on the globe.

3. Using the equator as a scale for degrees, measure a length of string equal to the distance in degrees from the earthquake to each of the stations.

4. Holding one end of each string at its station, swing arcs to find where all strings intersect.

5. The common intersection of the three or more arcs made by the strings is the earthquake epicenter.

__Teacher’s Procedure:__

** **

Be sure to have at least three different seismograms from different seismic stations of the same earthquake. Collect the latitude and longitude values for the three or more seismic stations. Be sure that the Travel Time Curve has a large enough distance and time difference to be able to conduct the activity. Be sure that the map used has a legend to find the distances of the possible locations of the epicenter, and that the map is big enough to draw the three or more circles where the epicenter could be located. Make transparencies to do a sample calculation of the epicenter of an earthquake.

Ask the students to explain the differences between an epicenter and a focus of an earthquake and what a teleseism is. Review the distinction if needed.

**Activity-**

1. Form students into groups to do the activity. Hand out the materials needed to do the activity and tell the students that the P-wave arrival times are from the same earthquake, but were taken from different seismic stations. See Focus Question 3 for instructions on how to find more data.

2. Do a sample calculation with the travel time curve, globe, and string. Then give directions for finding the epicenter of an earthquake.

a. Calculate the distance from an earthquake to three seismograph stations by subtracting the origin time from the P-wave arrival times to get the travel times and use the travel time curve to read the distances.

b. Locate the seismic stations on the globe.

c. Using the equator as a scale for degrees, measure a length of string equal to the distance in degrees from the earthquake to each of the stations. The string is used to find all possible locations of the epicenter on the globe. The locations are found by placing one end of the string at the station and the length of the string is equal to the distance obtained from the travel time curve from the station to an event.

d. The common intersection of the three or more arcs made by the strings is the earthquake epicenter.

__Conclusion:__

__ __

Discuss the information that can be obtained from a seismogram and why it was not used in this activity, the actual location of the epicenter and focus, and how you can tell which seismic station is closest to the epicenter.

Figure 4, Travel time
curve for teleseisms, from IRIS web site.

__Focus Question 3:__

How do seismologists locate the epicenter of an earthquake using seismograms from teleseisms?

__Objectives:__

__ __

**Students will:**

1. First obtain P- times, longitude, and latitude of the stations. (see USGS web sites for station locations and sources of data)

2. Guess the location of the epicenter and the origin time of the earthquake.

3. Next compute the azimuth and distance of the epicenter with a program such as azidist that is downloadable from the PEPP web page. (http://lasker.princeton.edu/Programs/pc.html)

4. Using the latitude and longitude of the guess and station plug data into program to get the distance in degrees and azimuth from event to station.

5. Then take the guessed origin time minus the arrival P-time, using the difference to find the distance in degrees based on the guess, using the Travel Time Curve (Figure 4)

6. Then take the distance in degrees observed (found in step 5) minus the theoretical distance in degrees to get the difference. If the seismogram has a theoretical distance less than the observed then the epicenter is farther from the station (the distance needs to be increased by that amount calculated).

7. Repeat steps 3 – 6, for the remaining stations.

8. Plot the azimuths from the guessed earthquake location to all the stations.

9. Mark a point on this line for the distance difference found in step 6

10. Draw a line perpendicular to the azimuth line at that point.

11. If all lines cross or intersect at a point, then the origin time is correct and the intersection point is the next guess for the epicenter. If instead they do not intersect at a point, but the perpendicular lines indicate that the distance to all the stations is too far then the chosen origin time was too early, therefore a correction needs to be added to the origin time to make it later. If the lines surround an area and the distance to the stations appear all too short, then the origin time chosen was too late. Use the point closest to all the perpendicular lines as the new guess for the epicenter and estimate the correction to the origin time. The location procedure is then repeated with the new guess until no corrections are needed.

__Data Provided:__

There was an earthquake felt by people on the borders of the Aegean Sea and Greece, with an origin time at about 22:00 (Universal Time, minutes:seconds).

The locations of the seismic stations are:

Location: Arrival P- times: Latitude: Longitude:

Beijing, China 32:34.6 40.0403 116.1750

Lima, Peru 35:50.1 -11.975 -77.0347

Duluth, Minnesota 33:32.7 46.8200 -92.0833

The data above was found at the web site: http://gldss7.cr.usgs.gov/current_seismicity.html, which contains current information or data from recent earthquakes, with P-times, latitudes, longitudes, travel times, origin times, and maps. Links from this page can be followed to find station locations.

An estimated location of the epicenter is: 42.06 20.34

After putting data into PEPP program:

Arc Distance = 72.86º (theoretical)

Back-Azimuth = 45.91º

Calculations:

Guessed T_{O} = 22:00 Arrival P- time = 33:32.7

Guessed T_{O} - Arrival P- time = time traveled on P
curve

Refer to the Travel Time Curve to estimate distance in degrees ≈ 73º

The observed distance in degrees from the station to event was calculated to be approximately 73º.

Observed distance in degrees – Theoretical distance = difference

73º – 72.8 = 0.2º difference.

Because the theoretical distance is less than the observed distance, the epicenter is farther away from the station, therefore, the distance needs to be increased from the station to the event (earthquake). Repeat this process for other stations and until a point of intersection is reached for all lines in order to get the location of the epicenter and the correct origin time.

__References:__

__ __

Bolt, Bruce A. (1993).
__Earthquakes__, W.H.__ __Freeman and Co., Salt Lake City, Utah,
USA

**Relevant web sites
(active July 2001)**

** **

www.geo.mtu.edu/UPSeis/locating.html

www.wpunj.edu/cos/envsci-geo/locating_an_earthquake.htm

http://master.ph.utexas.edu/vicki/ass3.htm

www.indiana.edu/~pepp/curriculum/ridgely.html

http://lasker.princeton.edu/ScienceProjects/curr/waves/seismic_waves.htm

www.tulane.edu/~sanelson/geol111/earthint.htm

http://lasker.princeton.edu/Programs/pc.html