GEOS 112L
Introduction to Earth Sciences
Locating Earthquakes
Earthquakes occur along fault lines, where relatively cold rocks move past each other. This
movement does not occur smoothly, but in abrupt jumps as rocks that hold the two sides of a fault
in place break and allow for rapid ground movement along the fault plane. Locating earthquakes
is useful to learn about the spatial orientation and extent of faults, be it for seismic hazard mitigation
or pure scientific interest. In this exercise we will learn a simple technique that allows us to locate
the position of an earthquake and estimate its magnitude.
1. P- and S-waves - a Review
Go back to your textbook and re-read the chapter on P- and S-waves to answer the following
questions.
1.1
1.2
which of the two wave types can propagate through solid and liquid materials, which one is
limited to solids only?
which wave is faster and will arrive at a recording station first?
2. Earthquake Locations: Epicenter and Hypocenter
Fig. 1 shows the location of an earthquake that occurs in a
subduction zone at the fault between the subducted slab and the
overriding plate. Note that the location of the earthquake at
depth is called the hypocenter. The Epicenter of an
earthquake is the projection of the hypocenter onto the surface
of the earth as shown in Figure 1. In this exercise we will
determine the epicenter location of earthquakes from the
Aleutian chain in Alaska.
For shallow earthquakes the position of the epicenter and
hypocenter are approximately the same, for deep earthquakes
the two can differ substantially.
Figure 1: Hypocenter and epicenter of an
earthquake. a) map view, showing the
epicenter, b) crossectional view showing the
relation between hypocenter and epicenter.
(from USGS.)
3.
Determining the Distance between Epicenter and Seismograph
s = D i s ta n c e Tra v e ll e d (m il e s)
Immediately after the occurrence of an earthquake it is important to determine its approximate
location as quickly as possible. Emergency response teams, for example, may need this information,
and mapping the origin of the seismic shock based on ground based observations of seismic damage
can be slow and often contradictory. The following method is a rapid and simple way to determine
the approximate location of an earthquake based on the seismograms recorded at a minimum of three
recording stations.
To determine the distance between the station and the
120
earthquake hypocenter recall the fact that P- and S-waves
travel through the rock at different velocities. If we know
the P- and S-wave velocities (or have a halfway decent
estimate) we can use the time lag between S- and P-waves
80
to determine the distance traveled by both waves.
Imagine two cars starting from the same location (the
hypocenter) and heading to the same destination (the
seismograph) at slightly different speeds. Car 1 obeys the
speed limit of 55 mph, while car 2 goes a bit faster at, say,
40
60 mph. The distance x traveled after the time t by both
cars is given by: s = v t (1) . The position of the two cars
as a function of time is shown in Fig. 2. Fig. 2 can also be
used to determine how long it takes each car to cover a
0
distance x. This procedure is shown in Fig. 3. We can
0
0.4
0.8
1.2
1.6
2
come up with the following table, listing the time it takes
t = Travel Time (hrs)
Figure 2: Position of the two cars as a function of each car to arrive at a distance x from the start and the
time. Since the velocity of the two cars is constant time lag between car 1 and car 2.
the plot of distance vs. time is a straight line with
The time lag between the two cars is plotted in Fig. 4.
slope v. Note that the distance between the two
cars increases steadily with time.
car 2
120
s = Distance Travelled (miles)
car 1
80
40
travel time
for car 2
travel time for
car 1
0
0
0.4
0.8
1.2
t = Travel Time (hrs)
1.6
2
Figure 3: To determine the time necessary for one
of the cars to travel a given distance s, draw a
horizontal line from the y-axis, starting from s until
it intersects the graph, and read the corresponding
travel time from the x-axis.
s (mi) time (car1) time (car 2)
(miles)
(hours)
(hours)
10
0.182
0.167
20
0.364
0.333
30
0.545
0.500
40
0.727
0.667
50
0.909
0.833
60
1.091
1.000
70
1.273
1.167
80
1.455
1.333
time lag
(hours)
0.015
0.030
0.045
0.061
0.076
0.091
0.106
0.121
Table 1: List of travel times for both cars and time lag between the
two cars for given travel distance s.
time lag between the two cars
0.16
0.12
0.08
0.04
0
0
20
40
60
s = distance travelled (mi)
80
Figure 4: time lag for the two cars as a function
of distance s.
repeat these steps for at least two more stations.
the three circles should intersect closely in one area. This is the location of the earthquake
epicenter.
60
50
S-P lag time (seconds)
5.
6.
Coming back to our earthquake problem, to find the distance
between the hypocenter and the seismograph we have to do
the following:
1.
obtain an estimate for P- and S-wave velocities. For
this exercise we assume a P-wave velocity VP = 6500
m/s and a S-wave velocity vS = 3700 m/s.
2.
determine the arrival times of P- and S-waves for
three seismograms. Use figure 5 to determine the
hypocenter distance for each station. For help
determining the arrival times of P- and S-waves see
Anatomy of a Seismogram below.
3.
determine the location of your seismic station on the
map.
4.
determine the scale of the map and draw a circle with
radius s (distance between seismograph and
hypocenter) around seismic station. Make sure you
use the appropriate scale! Figure 6 gives the
appropriate travel time graph for the provided
seismograms.
40
30
20
10
0
0
100
200
300
400
Distance from Source (km)
500
600
Figure 5: Plot of S-P lag time vs. distance from hypocenter (also called a travel time graph).
Anatomy of a Seismogram
2000
station: BMR
date: 7-14
Waveform Amplitude
time lag between
P- and S-wave arrivals
0
P-wave
arrival
S-wave
arrival
-2000
0
100
Time (seconds)
200
300
Figure 6 Seismograph trace showing the arrival of p- and s-waves as well as the lag time )t
between the two arrivals.
Figure 6 shows a typical seismogram for an earthquake in Alaska. What is plotted is the movement
of the seismograph needle as a function of time. Time is given at the x-axis in seconds, amplitudes
are given in nanometers/second. Indicated are the arrival of the P- and S-waves. The lag time
between P- and S-waves is also indicated.
Earthquake Magnitudes:
Earthquake magnitude can be determined by measuring the highest waveform of a seismogram and
taking into account the type of seismograph and its distance from the epicenter. the mathematical
details are quite involved and will not be discussed here, but the technique can be simplified for
calibrated seismograms with the help of a nomogram. A nomogram allows the user to determine
the magnitude of an earthquake based on the distance to the epicenter and the maximum wave
amplitude of the seismogram.
The nomogram, shown in Figure 7 consists of three scales. The scale on the left lists the distance
of the seismograph from the epicenter, the scale on the right lists the maximum amplitude of the
seismogram. Note that the scales on both sides are not linear, reflecting the underlying non-linear
mathematical equations. To determine the magnitude of an earthquake connect the seismograph
distance and measured maximum amplitude. the magnitude can then be read directly fromthe center
scale as shown in figure 7.
The seismogram traces provided in lab are unfortunately not calibrated and you won’t be able to use
the nomogram of Fig. 7 to determine the earthquake amplitude. For this reason you will complete
this exercise in a virtual earthquake lab.
Figure 7: Nomogram for magnitude determination. In this example the seismograph was located at a distance of 100 km from
the epicenter and the maximum wave amplitude was 12 mm, leading to a earthquake magnitude of 4.1.
Assignment:
In class:
1.
Using the seismograms and maps provided determine the epicenter location for the July 14th
earthquake.
2.
Where is the epicenter located? Which geological feature caused the earthquake.
At home:
go to http://www.sciencecourseware.com/eec/Earthquake/
and complete the travel time, epicenter location and magnitude exercises.
To turn in:
measurements and interpretations done in class, certificate of completion for virtual earthquake
exercise.