Introduction
An earthquake is a shaking motion of a portion of the earth's crust. this motion results from the passage of elastic waves traveling through the earth away from a place of rupture or faulting. The location of the rupture or faulting, which may be within or below the earth's crust, is called the focus. The point on the earth's surface directly above the focus is called the epicenter. Earthquake foci can occur down to a depth of 435 miles, although 85% of them occur near the surface (less than 40 mile depth). In this exercise you will use the records of an earthquake from several different locations to find the epicenter of the earthquake.
Seismogram
The waves radiating through the earth away from the focus can be recorded by an instrument known as a seismograph which produces a record known as a seismogram. Several types of waves can be detected by a seismograph. Two of these waves can be used to locate earthquake epicenters. These are:
1) "P"- waves or longitudinal wave (also called primary waves because they are the first to appear on a seismogram).
2) "S"- waves or transverse waves (also known as secondary waves because they are the second major wave to appear on the seismogram).
The P waves travel through the crust at a velocity of about 5 miles per second and the S waves at a velocity of about 3 miles per second. Because of this velocity difference, the seismogram will record the arrival of the P-wave first. At a later period of time the seismogram will record the S-wave arrival. The difference in time between the S-wave arrival time and the P-wave arrival time will be a measure of the distance of the seismograph from the epicenter. This time difference can be converted into a distance using a time travel curve (see Figure 6-1).
A third type of wave is also recorded by a seismograph:
3) "LR (or LQ)" - waves are also called surface waves because they travel only near the surface of the earth. They travel slower than either the P or the S waves, and so they arrive later (and are shown after) either the P or the S wave on a seismogram.
Travel - Time Curves
Travel time curves are graphs which show how long it takes for a particular wave to travel a certain distance. Note the curvature of the S and P and the straight line for the surface waves.
If the difference in the arrival times for the P and S at some particular station can be determined, then by using the travel time curves, the distance from that station to the epicenter can be obtained.
For example, in Figure 6-2 (sample seismogram) notice that the P wave arrives ~ 2.1 minutes and the S wave arrives ~ 5.4 minutes. The difference in arrival times (5.4-2.1=3.3) is 3.3 minutes.
To get the distance, you must use the travel time curves given in Figure 6-1:
1) Lay a sheet of blank paper along the S-P (time) axis.
2) Mark two dots on the edge of the paper corresponding to a 3.3 minute time interval.
3) Keeping the edge of the paper parallel to the vertical lines, slide the paper until the two dots lie exactly on the S and P curves.
4) Draw a vertical through the S and P curves at these points until it intersects the horizontal axis.
This gives the epicentral distance between the station and the epicenter (1200 miles for the above example). For a short video click.
Exercises
Sections of seismograms from three stations are given in Figure 6-3.
1) Estimate to the nearest tenth (dime in money terms) of a minute the arrival times of the P and S waves at each station.
Site Name Time of P arrival Time of S arrival Difference (S-P)
Sitka ______________ ______________ ______________
Columbia ______________ ______________ ______________
Honolulu ______________ ______________ ______________
Which station is nearest to the epicenter?______________________________
Which station is farthest from the epicenter?____________________________
2) Using the S minus P times, determine the epicintral distances corresponding these values and enter the results.
Site Name Distance to epicenter
Sitka __________________ miles.
Columbia __________________ miles.
Honolulu __________________ miles.
3) Next you will find the location of the earthquake epicenter distances just obtained.
a) Locate the three sites on the world map (Figure 6-4). The latitude and longitude of each site is as follows:
Site Name -Lat.- -Long.-
Sitka 57 N_ 135 W_
Columbia 35 N_ 81 W__
Honolulu 21 N_ 158 W_
b) Draw a circle about each site with a radius equivalent to the epicentral distance determined for that site. Use a drawing compass and the scale given on the map for this purpose. The three circles should intersect at one point. This point locates the epicenter. The location of the epicenter is at the following:
Lat._________ Long.________.
Short video in preparation.
4) What is the origin time of the earthquake?; that is when did it happen? ___________________________________________________________________
5) State two reasons which could account for the fact that in Figure 6-1, the P and S lines are curved, while the line for the Surface wave is straight.
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NOTE:Electronic "hard copy" in MS Word ver. 6.0 is available for class distribution.
E-Mail ordofmag@mimp.mems.cmu.edu for details.
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