GEOL 100
Geology: Principles and Applications
Lab 4: Seismology
Dr. J. G. Anderson, Spring 1995
This lab has three objectives:
- Locate an earthquake.
- Determine the magnitude of an earthquake.
- Find the energy of the earthquake and put it into perspective of the
energy of a more familiar object.
Objective 1. Locate an earthquake
The principles of locating an earthquake are not difficult.
The earthquake sends out different kinds of waves that travel at different
speeds. At a station, they thus arrive at different times.
The difference in travel times is proportional to the distance.
Below we show examples of seismograms.
In this, you should learn to identify two kinds of waves, the P-wave
and the S-wave.
The travel time difference is described algebraically as follows:
- Let R be the distance from an earthquake to a station.
- Let V p be the speed of the P-wave.
- Let V s be the speed of the S-wave.
- The P wave will arrive at the station at time
t p = R/V p
- The S wave will arrive at the station at time
t s = R/V s
- Subtracting, one gets:
(1)
The speeds V p and
V s vary in different depths and locations.
For this lab, we will locate earthquakes that are fairly close to the
stations (within about 100 km).
For this, we will use:
V p = 6 km/sec and
V s = 3.43 km/sec.
Lab Steps:
- Solve Equation (1) for R.
Substitute V p and
V s to find a relationship between R and the
difference in wave arrival times.
- On September 12, 1994 a moderate earthquake occurred someplace in Nevada.
Figure 1 shows a map of the region, and shows the location of some seismic
stations. Digital seismograms from four of those stations are
given on Figures 2a,b,c,d. Using the seismograms in Figure 2 and your solution
in step 1, determine the distance of the earthquake from each station.
- On the map in Figure 1, draw circles with the appropriate radius,
around each station. These circles should all intersect at the same place.
That place is the epicenter of the earthquake.
- Your circles may not all intersect in the same place.
Estimate the uncertainty you have in the location of this earthquake
using these records. List as many possible reasons as you can
for this uncertainty.
Objective 2. Determine the magnitude of an earthquake.
When Charles Richter invented the magnitude of an earthquake, he
wanted a scale that would reduce the huge range of earthquake
sizes into a numbering scheme that would be easier for the
average person to understand. For that reason, he used the
common logarithm of the amplitude of the seismogram. Richter
also wanted a system where in principle, stations at any
distance from the earthquake would come up with the same
answer. The strength of seismic waves decreases as distance
increases, so an adjustment is necessary.
Algebraically, this is expressed as follows:
- Let A be the largest amplitude on a seismogram of an earthquake.
- Let C(R) be the distance correction that depends on R .
- Let M L be the local magnitude,
as defined by Richter.
- Then:
M L = Iog A + C(R) (2)
A table with values of C(R) is given below.
There are a lot of reasons why different stations give slightly
differing estimates for the magnitude. Therefore, when an
earthquake happens, the best magnitude is always announced much
later, after lots of stations have been read and averaged.
The seismograms in Figure 2 are recorded on the digital seismic
stations in the Western Great Basin seismic network. The
original seismograms are given in ``counts'' coming ftom the
digitizer, so they differ from the kind of instrument that
Richter used. Richter used a ``Wood-Anderson seismometer.'' The
seismograms have already been converted to show what
Richter's instruments would have recorded. The vertical
scale is the amplitude this seismogram would have had on the
Wood Anderson seismograph.
Lab Steps:
- For the earthquakes in Exercise 1, go back to each
seismogram. Read the maximum amplitude from each horizontal
component of the record.
- Using the distances you
calculated above, estimate the magnitude from each horizontal
component, and convert that maximum into millimeters.
- Find the
average magnitude, using all the seismograms, and the standard
deviation from the average. Call the average
.
The standard deviation is given by:
(3)
where N is the number of readings you have.
- What is the largest difference between the average
magnitude and one of the individual station magnitudes? List
reasons you can think of why different stations might not give the
same magnitude.
Please note that seismologists have a way to
determine magnitude from many different types of instruments.
The equation you used is only correct for the instrument
Richter used, the Wood-Anderson seismograph.
Table of distance corrections for magnitude,
(in part) from Richter (1958).
R C(R) R C(R) R C(R)
(km) (km) (km)
0 1.4 55 2.7 120 3.1
5 1.4 60 2.8 130 3.2
10 1.5 65 2.8 140 3.2
15 1.6 70 2.8 150 3.3
20 1.7 75 2.85 160 3.3
25 1.9 80 2.9 170 3.4
30 2.1 85 2.9 180 3.4
35 2.3 90 3.0 190 3.5
40 2.4 95 3.0 200 3.5
45 2.5 100 3.0 210 3.6
50 2.6 110 3.1 220 3.65
Objective 3: Put your results into the perspective of something you
are more familiar with.
Richter invented the magnitude thinking it would
be a measure for the amount of energy radiated in an
earthquake. He and Gutenberg developed a formula for the
relationship between energy and magnitude which is still used
today. It is:
logE s = 11.8 + 1.5M
where the energy, E s , is given in ergs.
Lab Steps
- Using the magnitude you just found, estimate the seismic energy.
- To put this energy into perspective, find out how fast a car would
have to be traveling (in miles per hour) to have this much kinetic
energy. If a car traveling at this speed were to crash into a
mountain side, it would cause an earthquake of about the same
magnitude.
From high school science, the kinetic energy of a car is:
where m is the mass of the car, and v is its speed.
Suppose the car weighs 2200 pounds.
You will also need to know these conversion factors:
- At the surface of the Earth, a mass of 1 kilogram weighs 2.2 pounds.
- 1 mile/hour = 44.7 cm/sec
If you need any more conversion factors, you will find them in Appendix A
of the text book (Press and Siever).
Figure l. Seismic stations of the University of
Nevada, Reno Seismological Laboratory (UNRSL). Triangles represent
single component vertical or multiple component seismometers,
squares repesent three-component digital seismometers, and the star
represents the location of the Seismological Laboratory.
North is towards the top of the page.
Figure 2a. Seismograms from digital station WHR.
Figure 2b. Seismograms from digital station WCN.
Figure 2c. Seismograms from digital station KVN.
Figure 2d. Seismograms from digital station WCK.